Handbook of Microwave Technology. Volume 2, Applications

Handbook of Microwave Technology VOLUME

2

This Page Intentionally Left Blank

Handbook of M icrowave Technology VOLUME

2

Applications

Edited by

T. Koryu Ishii Department of Electrical and Computer Engineering Marquette University Milwaukee, Wisconsin

ACADEMIC PRESS San Diego

New York

Boston

London

Sydney

Tokyo

Toronto

This book is printed on acid-free paper.

Copyright © 1995 by ACADEMIC PRESS, INC. All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Academic Press, Inc. A Division of Harcourt Brace & Company 525 B Street, Suite 1900, San Diego, California 92101-4495

United Kingdom Edition published by Academic Press Limited 24-28 Oval Road, London NW1 7DX Library of Congress Cataloging-in-Publication Data Handbook of microwave technology / edited by T. Koryu Ishii. p. cm. Includes index. Contents: v. 1. Components and devices -- v. 2 Applications. ISBN 0-12-374696-5 (v. 1). -- ISBN 0-12-374697-3 (v. 2) 1. Microwave devices--Handbooks, manuals, etc. I. Ishii, T. Koryu (thomas Koryu), date. TK7876.H345 1995 621.381'3--dc20 CIP PRINTED IN THE UNITED STATES OF AMERICA 95 96 97 98 99 00 MM 9 8 7 6

5

4

3

2

1

94-48777

Contents of Volume 2

Contributors Preface

xxi

xxiii

CHAPTER

Klystrons Brian Roach

I. Klystron Characteristics Introduction RF Circuit

I I

Electron Beam System 2. Klystron Applications Linear Accelerator Applications Communication Applications

9

Industrial Heating Applications Radar Applications

12

3. Klystron Specification

12

Electronic Performance Parameters Operating Parameters Environmental Parameters

17 19

14

vi

Contents of Volume 2 Life and Reliability Physical Parameters Miscellaneous Items

20 21 21

4. Design and Fabrication of Klystrons Typical Design Methodology 22 Construction 24

22

5. Noise and Stability Characteristics Noise 25 Stability

27

6. Klystron Protection References

CHAPTER

25

28

30

2

Magnetrons Wayne Love I. Introduction

33

2. Microwaves

35

3. Components of the Magnetron Cathode Anode Output

37 41 43

4. Space Charge

43

5. Magnetic Field

46

6. Power Adjustment Pulsing

36

46

46

Reduction of Anode Current

47

Adjustment of Magnetic Field

48

Attenuation of Microwave Energy 7. Rieke Diagram

50

8. Power Supplies

51

9. Magnetron-System Interface General 53

50

53

Contents of Volume 2

vii

Common Problems and Causes Additional Reading

CHAPTER

55

55

3

Traveling-Wave Thermionic Devices Jeffrey D. Wilson I. Introduction

57

2. Cathodes

57

Thermionic Emission

57

Secondary Emission

60

3. Electron Guns Perveance

60

60

Convergence Ratio

60

Electron Gun Types

61

Grids

62

4. Electron Beam Focusing Brillouin Flow

62

62

Confined Flow

63

Periodic Permanent Magnet Focusing Thermal Beams

64

5. Linear-Beam Traveling-Wave Tubes Applications Helical Circuit

65 65

Coupled-Cavity Circuit High-Frequency Circuits Attenuators and Severs

67 70 71

Transitions and Windows

72

Electron Beam Collectors

72

74

6. Linear-Beam Backward-Wave Devices Backward-Wave Amplifiers

77

Backward-Wave Oscillators

78

7. Magnetrons

64

64

General Operation

Simulation

63

79

77

eee

VIII

Contents of Volume 2

Applications 79 General Operation 80 Anode Slow-Wave Circuit Strapping 82 Coaxial Magnetrons 83 Simulation 84

80

8. Crossed-Field Amplifiers Applications 84 General Operation 85 Power and Efficiency 85 High-Frequency CFA 86 Low-Noise High-Gain CFA Amplitron 87

84

87

9. Crossed-Field Backward-Wave Oscillators Applications 87 General Operation 88 Frequency Tuning 89 References CHAPTER

87

90 4

Gyrotrons, Magnicons, and Ubitrons Paul Tallerico

I. Introduction

97

2. Gyrotron Principles of Operation 3. Gyrotron Design 4. Gyrotron Structure 5. Gyrotron Fabrication

98

103 104 108 II0

6. Gyrotron Performance

7. Prebunched Gyrotrons and the Magnicon 8. Gyrotron Applications

112

9. Gyrotron Mode Purity

114

10. Ubitron Principles

114

II. Ubitron Structure

115

III

Contents of Volume 2

ix

12. Ubitron Performance References

CHAPTER

116

116

5

The Peniotron David Gallagher and Gtinter D6hler

I. Introduction

121

2. The Traditional Peniotron Principle of Operation

123

123

Small-Signal Calculations

124

Large-Signal Calculations

126

Performance of Traditional Peniotrons Traditional Peniotron Design

126

127

3. Nontraditional Peniotrons

130

Square and Rectangular Waveguides The "True" Gyropeniotron Circular Waveguides

130

130

131

The Magnetron-Type Peniotron

132

Other Peniotron and Peniotron-like Devices References

CHAPTER

133

133

6

Thermodynamics of Microwave Devices K. Fricke, V. Krozer, and H. L. Hartnagel

Nomenclature I. Introduction

137 138

2. Conductive Heat Transfer Steady-State Heat Conduction Unsteady-State Heat Conduction

139 139 142

Electrical Equivalent of Thermal Conduction 3. Convective Heat Transfer

145

Single-Phase Convective Heat Transfer Boiling Heat Transfer

149

145

145

x

Contents of Volume 2 4. Heat Transfer by Radiation

151

5. Measurement of the Thermal Resistance IR Measurement

155

155

Liquid-Crystal Measurement Electrical Measurement

155

156

6. Thermal Enhancement Techniques

156

7. Thermal Properties of Electronic Materials References CHAPTER

163

164 7

Microwave Antennas John Hill and Mary Lynn Smith I. Antenna Defined

168

Antenna Requirements and Specifications

168

2. Microwave Integrated Circuit (MIC) and Monolithic Microwave Integrated Circuit (MMIC) Antennas 187 3. Radiation Pattern Synthesis

193

Antenna Patterns with Nulls in Particular Directions Antenna Patterns with Specific Distributions

194

194

Antenna Patterns with Low Sidelobes and Narrow Beams 4. Antennas for Missiles

UHF Antennas

195

196

S-Band Antennas

197

C-Band Beacon Antennas

198

5. Measuring RF Leakage of Test Couplers 6. Materials

201

Conductors

201

Dielectrics References CHAPTER

203 204

8

Propagation at Microwave Frequencies Ernest K. Smith

I. Introduction General Relations

207 207

199

194

Contents of Volume 2

xi

Atmospheric Refractive Index Propagation in Free Space

212 213

Carrier-to-Noise Ratio (C/N)

214

2. Attenuation Mechanisms

215

Attenuation Due to the Gaseous Atmosphere Attenuation Due to Rain

215

220

Attenuation Due to Fog and Cloud

227

Attenuation Due to Snow and Ice Crystals Attenuation Due to Sand and Dust

227

228

3. Terrestrial Line-of-Sight Propagation

228

Diffraction Fading Due to Partial Obstruction of the Path Fading Due to a Multipath and Scintillation

230

Fading Due to Variation in the Angle-of-Arrival 4. Propagation beyond the Horizon Diffraction

230

231

Tropospheric Scatter

231

Atmospheric Ducting

232

5. Earth-Space Propagation

232

Geometry for the Geostationary Orbit Ionospheric Effects

234

Tropospheric Effect

237

Mobile Satellite Propagation Effects 6. Mobile Propagation Effects 7. Short-Path Propagation 8. Noise

241

References

242

CHAPTER

230

233

239 240

240

9

Consumer Applications of Microwaves: Microwave Ovens and Accessories Koji Iwabuchi, Ichiro Fukai, and Tatsuya Kashiwa I. Microwave Oven Design Fundamentals [I] Moding Region

249

249

229

oo

Xll

Contents of Volume 2 Arcing Region

251

Overheating Region

251

Low'Efficiency Region

251

Recommended Region

252

2. Microwave Field Visualization Background

252

Formulation

253

Example [I I]

252

254

3. Microwave Leakage Minimization Design Door Structures

256

Radial Line Filters [20, 21]

260

Perforated Plates and Wire Gauzes 4. Operation and Maintenance [24] Operation Procedure Maintenance

256

260 271

271

271

5. Microwave Oven Accessories and Containers Accessories and Their Use

272

Containers and Their Use References

CHAPTER

272

274

10

Industrial Applications of Microwaves T. Koryu Ishii

I. Microwave Heating Temperature Rise

277 277

Approximate Equations for Temperature Rise 2. Microwave Curing Rubber Curing

281

281

Tire and Asphalt Curing

284

3. Microwave Material Processing Microwave Thawing Microwave Drying Microwave Heating

284 285 289

284

280

271

xiii

Contents of Volume 2

4. Microwave Applications in Agricultural Industries 5. Microwave Applications on Forest Products 6. Microwave Application on Sensing

293 296

297

7. Microwave Object Identification

300

Microwave Radiometer Technique

300

Microwave Monostatic or Bistatic Radar Technique

300 300

Microwave Reflection or Radiation Pattern Recognition Technique 8. Microwave Data Communications General Configurations Data

301

Modulator

301

Microwave Transmitter Microwave Launcher

301 302

Microwave Transmission System Microwave Catcher

303

Microwave Receiver

303

Data Display References

CHAPTER

300

300

302

303 303

II

Biomedical Applications of Microwave Engineering Joseph H. Battocletti

I. Electrical Properties of Biological Materials

309

2. Heat Deposition in Biological Material, Particularly Man 3. Exposure Guides and Standards

323

4. Microwave Hyperthermia for Cancer Treatment The Bioheat Equation Applicators

327

328

330

5. Microwave Monitoring, Imaging, and Sensing One-Antenna, Active Sensing, Remote Life Detection

332 332

One-Antenna, Passive Scanning, Thermography or Radiometry Two-Antenna, Microwave Imaging References

315

340

337

333

xiv

Contents of Volume 2

CHAPTER

12

Chemical Applications of Microwaves Thomas C. Ehlert

I. Microwave Absorption Spectroscopy 347 Introduction 347 Classifications of Molecules 347 Conditions 347 Rotational Energies 348 Resonant Frequencies 349 Probability of Absorption--Attenuation of Microwaves Transition Cross Section 350 Population of the Lower Quantum State 351 Nuclear Statistical Weight 352 Limitations 352 Widths and Shapes of Spectral Lines 352 2. Nuclear Magnetic Resonance Spectroscopy 353 Introduction 353 Nuclear Magnetic Dipole Moment 353 Magnetic Dipole Moment Components 354 Magnetic Dipole Energy States 355 Allowed Transitions between Energy States 355 Details of Spectra 355 Relaxation Processes 357 Power Saturation 357 High-Field NMR 357 NMR Spectra of Solids 358 Fourier Transform NMR 358 3. Electron Spin Resonance Spectroscopy 359 Introduction 359 Electron's Magnetic Dipole Moment 359 Magnetic Dipole Moment Components 359 Magnetic Dipole Energy States 359 Allowed Transitions between Energy States 359 Spectra 360 Relaxation Processes 360 4. Chemical Synthesis and Analysis Using Microwave-Produced Plasmas 360

350

Contents of Volume 2

xv

Apparatus 360 Theory 361 Synthesis 361 Analysis 362 5. Thermal Effects Introduction Heating

362 362

362

Reaction Rate Enhancement References CHAPTER

363

363 13

Electron Paramagnetic Resonance James S. Hyde

I. Introduction

365

2. Continuous Wave Bridges: 0.5-35 GHz 368 One-Arm Bridges 369 Reference-Arm Bridges 375 Detection of Dispersion 378 Reference-Arm Bridge with a Low-Noise MicrowaveAmplifier Notes on Advanced Microwave Bridges 383 3. Resonators for EPR Spectroscopy 384 Multipurpose TE~0zCavity 384 EPR Cavity Problems 386 Multipurpose Cavity Accessories 387 Conversion to Other Rectangular TE Modes 391 Other EPR Microwave Cavity Designs 395 Other Types of EPR Sample-Containing Structures 398 References

CHAPTER

399

14

Microwave Navigational Aides G. Stephen Hatcher and Goson Gu

PartA:

THE GLOBAL POSITIONING SYSTEM

I. General Description Space Segment

404

404

381

xvi

Contents of Volume2 Control Segment User Segment

405 405

2. Position Fixing

405

Concept of Position Fixing

405

Satellite-Position Acquisition and Radio Ranging Clocks

407

407

Pseudorangesand Navigation Equations 3. Time Measurement

408

408

4. Velocity Measurement 5. Signal Structure

409

410

6. Navigation Message

410

7. Navigation Solution and Dilution of Precision The Navigation Solution Dilution of Precision (DOP) 8. Error Sources

413

414

Space Segment

414

User Segment

414

Propagation Link

415

9. Differential GPS

415

Concept of Differential GPS

415

Implementation of Differential GPS 10. Summary Part B:

411

411

415

416

DOPPLERNAVIGATION SYSTEM

I. General Description

417

2. Fundamental Principles of Doppler Radar

418

3. Functional Description of Doppler Radar

421

Antenna

421

Transmitter and Receiver Frequency Tracker

422

422

4. Doppler-Radar Performance and Errors Doppler-Radar Performance Doppler-Radar Errors

424

423

423

xvii

Contents of Volume 2

425

5. The Navigation Computer Additional Reading CHAPTER

425

15

Microwave Applications for Law Enforcement John Tomerlin and John Fuhrman

I. Introduction 2. Historical

429 431 432

3. Moving Radar 4. Mechanical Errors

433

5. Mechanical Interference 6. Photo Radar

434

435 436

7. Testing for Accuracy Tuning Fork Calibration Tuning Fork Tests

437

438

Microwave Transmission Low-Voltage Supply

438

439

Doppler Audio 439 Electromagnetic Interference Speed Accuracy 440 8. Does Radar Increase Safety? Additional Reading CHAPTER

439 448

448

16

Microwave Radio Communication George Kizer

I. Introduction

449

2. Equipment-Dependent Radio Performance Analog Systems

451

Digital Systems

454

Estimating End-to-End Digital Radio Performance

451

457

3. Transmission-Path-Dependent Radio Performance Transmission Path Loss

466

465

xviii

Contents of Volume 2 Received Signal Variation ("Fading")

472

Atmospheric (Nonrain) Absorption

473

Rain Loss

474

Reflection ("Fresnel Zone") Fading

477

Obstruction ("Diffraction") Fading

478

Power Fading Duct Fading

485 486

Atmospheric Multipath Fading

487

4. Path Availability Calculations 5. Conclusion References

CHAPTER

492

501 502

17

Microwave Instrumentation and Measurements Aksel Kiiss

I. Scattering Parameters

505

S-Parameter Measurements

505

Uncertainties Caused by Adaptor VSWR 512 Uncertainties Caused by the Harmonic Content of the Test Signal Inaccuracies in Transmission Measurements ($2~and S~2) 2. Transmission Measurements

514

Transmission Measurement Magnitude Transmission Measurement Phase 3. Reflection Measurements 4. Electrical Delay 5. Group Delay

514 516

520

525 525

6. Noise Figure/Noise Temperature Measurements Definitions of the Noise Figure/Noise Temperature Noise Figure

512

527 527

528

Absolute Accuracy of Noise Figure Measurements 7. Microwave Power Measurements Thermal-Based Power Detectors Diode-Based Power Detectors Diode-Based Power Meters

538 538

540 540

534

512

Contents of Volume 2

xix

Frequency Calibration Factor Peak Power Meters

541

542

Accuracy: How to Calculate Your Measurement Uncertainty RSS and Worst-Case Calculations

542

544

Measurement Techniques for Improved Measurement Accuracy

544

8. Microwave Frequency Measurements (CW and Pulsed) Single-Shot, Precision VCO Characterization HP 5372A Specification Summary Specifications

545

546

550

9. Measurement of Phase Noise Power Spectral Density Short-Term Frequency Stability

558

560

Long-Term Frequency Stability (Figure 21)

CHAPTER

545

568

18

Microwave Mathematics James Richie

I. Preliminary Definitions

569

Phasor Notation and Fourier Transform

569

2. Mathematical Functions for Microwave Engineering Complex Functions

571

Generalized Functions

573

3. Vectors and Matrices Definition

576

Properties

577

Hermitian Adjoint

576

578

Commutator and Anticommutator Tensors and Dyadics Group Theory 4. Vector Spaces Definition

578

579 579

579

Linear Independence Inner Product

580

580

Orthonormality

580

Gram-Schmitt Process Inequalities

581

581

578

571

XX

Contents of Volume 2

5. Linear Operator Theory 581 Definition 581 Properties 582 Inverse 582 Similarity Transformation 582 Projection Operators 583 Adjoint Operators 584 Unitary Operators 584 Eigenvalue Problem 584 6. Function Spaces

585

7. Vector Fields 586 Operations 587 Theorems 589 Vector Identities 589 589

8. Differential Equations and Their Solutions Analytic Techniques 590 Numerical Solutions 595 9. Integral Equations and Their Solution Tabulated Solutions 599 Asymptotic Methods 599 Numerical Solutions 600 References CHAPTER

599

602 19

Microwave Materials Hamid H. S. Javadi

I. Introduction

605

2. Dielectric Properties of Compounds

608

3. Properties of Manufactured Special-Purpose Compounds 4. Thin Films

635

5. Electromagnetic Properties of Metals

635

6. Physical and Electromagnetic Properties of Bulk and Thin-Film Superconductors 638 References Index

642 645

626

Contributors

Numbers in parentheses indicate the pages on which the authors' contributions begin. Joseph H. Battocletti (309) Department of Neurosurgery, Medical College of Wisconsin, MCW Clinic at Froedtert, Milwaukee, Wisconsin 53226 Giinter D6hler (121), Tube Research and Development, Northrop Grumman Corporation, Rolling Meadows, Illinois 60008 Thomas C. Ehlert (347), Department of Chemistry, Marquette University, Milwaukee, Wisconsin 53233 K. Fricke (137), Technische Hochschule Darmstadt, Institut ftir Hochfrequenztechnik, D-64283 Darmstadt, Germany John Fuhrman (429), AUTO SCENE, Laguna Beach, California 92615 Ichiro Fukai (249), Department of Electrical Engineering, Hokkaido University, Hokkaido, Japan David Gallagher (121), Tube Research and Development, Northrop Grumman Corporation, Rolling Meadows, Illinois 60008 Goson Gu (403), Summit Design, Inc., Renton, Washington 98055 H. L. Hartnagel (137), Technische Hochschule Darmstadt, Institut fur Hochfrequenztechnik, D-64283 Darmstadt, Germany G. Stephen Hatcher (403), Summit Design, Inc., Renton, Washington 98055 John E. Hill (167), Watkins-Johnson Company, San Jose, California 95131 James S. Hyde (365), Biophysics Research Institute, Medical College of Wisconsin, Milwaukee, Wisconsin 53226 T. Koryu Ishii (277), Department of Electrical and Computer Engineering, Marquette University, Milwaukee, Wisconsin 53233

xxi

xxii

Contributors

Koji Iwabuchi (249), Kashiwa Works, Hitachi Hometech, Ltd., Chiba-ken 277, Japan Hamid H. S. Javadi (605), Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109 Tatsuya Kashiwa (249), Department of Electrical Engineering, Hokkaido University, Hokkaido, Japan Aksel Kiiss (505), MITEQ, Inc., Hauppauge, New York 11788 George Kizer (449), Alcatel Network Systems, Richardson, Texas 75081 V. Krozer (137), Technische Hochschule Darmstadt, Institut ftir Hochfrequenztechnik, D-64283 Darmstadt, Germany Wayne Love (33), Richardson Electronics, Ltd., LaFox, Illinois 60147 James Richie (569), Department of Electrical and Computer Engineering, College of Engineering, Marquette University, Milwaukee, Wisconsin 53233 Brian Roach (1), Varian Associates, Inc., Palo Alto, California 94303 Mary Lynn Smith (167), Watkins-Johnson Company, San Jose, California 95131 Ernest K. Smith (207), Department of Electrical and Computer Engineering, University of Colorado, Boulder, Colorado 80309 Paul Tallerico (97), Los Alamos National Laboratories, Los Alamos, New Mexico 87545 John Tomerlin (429), AUTO SCENE, Laguna Beach, California 92615 Jeffrey D. Wilson (57), Lewis Research Center, NASA, Cleveland, Ohio 44135

Preface

The

purpose of this book is to provide a compact, ready reference tool on practical microwave technology to practicing technicians, scientists, and engineers. Readers may be trained in the field of microwave technology or may be trained in their own field but not necessarily in the field of microwave technology. This book is written with care for the latter category of audience as well as for the former. Consequently, this book is also useful to people in business and industry as well as to science and engineering students who are involved in microwave technology. Not only is this book a ready reference tool at present but it is also a good investment for use in the future. The emphasis of this book is to answer the question of "how to" rather than that of "why so." Chapters are full of useful formulas, charts, graphs, tables, examples, and diagrams for analysis and are designed for daily use. These reference resources are clearly explained and easily applicable to specific practical cases that the readers may encounter in their professional activities. Naturally the field of microwave technology is so vast that, no matter how well covered, it is impossible to include everything in one volume of limited size. For this reason, the Handbook of Microwave Technology is split into two volumes. Volume 1 covers "Components and Devices" used in microwave circuits, and Volume 2 covers "Applications" of microwave technology. This enormously wide area of microwave technology, which spans both fundamentals and applications, is condensed into two, compact, conveniently portable volumes for easy reference. Since both volumes are written independently of each other, the audience may choose one or both volumes depending on their needs. For those who wish to acquire information beyond the materials presented in this book, complete lists of references are provided at the end of every chap. . .

XXIII

xxiv

Preface

ter. The quest for "why so" and further information is realized by making full use of these references. The editor thanks chapter contributors, suppliers of industrial resources, providers of permissions for copyrighted materials, and those who provided clerical assistance. He also acknowledges assistance from the publisher's staff. Without their assistance, perseverance, and patience, this book may never have been completed.

T. Koryu Ishii Editor

Milwaukee, Wisconsin 1995

CHAPTER

Klystrons Brian Roach

I. Klystron Characteristics Introduction 17"

l~xlystrons are linear beam tubes. Although they are available as both oscillators and amplifiers, only amplifiers will be discussed in this chapter. This is because most oscillator applications have been supplanted by solid-state alternatives. Klystrons are inherently narrow-band devices, although some klystrons have some degree of tunability. They have high gain and are capable of operation at high peak and average power. They are capable of either pulsed or CW operation. Table 1 delineates some broad performance capabilities of klystrons. Note that most desirable characteristics of these tubes are enhanced at higher peak power or lower frequency. (This is explored in greater depth under Electronic Performance Parameters.) Figure 1 shows the essential elements of a klystron in a simplified form. As can be seen from the figure, klystrons are divided into two portions; the RF circuit and the electron beam system [1, 2]. (References [1] and [2] are recommended for a more complete description of klystron operating principles.)

RF Circuit Klystron RF circuits are fairly simple, at least when compared with traveling wave tube circuits. The circuit comprises a number (typically

Handbook of Microwave Technology, Volume 2

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

Brian Roach

TABLE I Klystron Overview

Characteristic

Typical values

Center frequency Peak power output Average power output Bandwidth Gain Efficiency

Focus Electrode

Anode

300 MHz-40 GHz 100 W-150 MW 1 0 0 W - 1 MW 0.1-10% 20-60 dB 20-70%

Input

Electron

Cavity

Beam

Output Cavity

Magnet

\

Collector Cathode

.. ~ t~ I~1~~..r''////'//I~L Electron

I--

Gun

// RF Input

Input Window

Output Window

;~1 RF Output

Figure I. Simplified klystron layout.

between three and six) of resonant cavities. These cavities are disposed around the electron beam and operate in the TM010 mode. The electric fields associated with this mode are depicted for a typical cavity in Figure 2. This figure also shows an electron beam traversing the cavity. As depicted in Figure 1, the RF signal is coupled through a ceramic window into the input cavity. The electron beam is slightly modulated in the input cavity and is remodulated by the intermediate cavities. By the time the electron beam reaches the output cavity, it is highly modulated (strongly bunched). The output cavity couples the amplified signal back into the transmission line to the outside world. This interaction with resonant cavities is the klystron's greatest strength and greatest weakness. The fact that there are no beam-circuit synchronism requirements (as in TWTs and crossed-field devices) means that klystrons are comparatively less demanding to design and manufacture. The lack of backward traveling waves means that klystrons are, for most

I. Klystrons

/ / . . . . _ _ _ _ _Electron __ beam

~

Electric field lines (peek of RF cycle)

i

I

Figure 2. Klystroncavity:TM010 mode.

practical purposes, unconditionally stable. However, the principle of resonant interaction inherently restricts the bandwidth capability of klystrons. From a systems point of view, klystrons are sometimes regarded as narrow-band elliptic filters with gain. Figure 3 shows a gain model for a four-cavity klystron amplifier. An n-cavity tube can be modeled as an ( n - 1)-pole filter. Figure 4 shows a calculated response for a typical five-cavity (four-pole) klystron. Various types of hybrid devices have been built to circumvent the limitations of the resonant circuit [3]. Examples of these devices are the Twystron and the extended interaction klystron (EIK). It is worthwhile to note that some of the same stability considerations that apply to wave tubes also apply to these hybrid tubes.

Figure 3. Klystron small signal gain model.

Brian Roach

.E

50

,

40

'1

3o

"~

Gain poles

20 lO

~

o

~

-10

~

-20

Gain zero

I

+2O0 -200 fo Freq. (MHz dev. from fo) Figure 4. Calculated klystron small signal gain.

The Twystron [4, 5] was invented to address an aggravating fault of klystrons, viz, that it is possible to bunch the electron beam internally over a wide frequency range, but impossible to couple it efficiently to the outside world with a simple resonant output cavity. The Twystron substitutes a wave tube circuit for the output cavity. Electronic bandwidths in excess of 15% have been demonstrated with Twystrons at the 6-MW peak power level. The ElK [6] substitutes sections of shorted wave tube circuits for one or more of the resonant cavities normally present. In one class of applications, the output cavity is treated in this manner. This confers advantages similar to those of the Twystron. It also allows the possibility of higher peak and average power compared with klystrons with simple resonant output cavities [7-9]. In another class of applications, all of the cavities are treated in this manner. This is particularly advantageous in higher frequency ( > 30 GHz) tubes [10]. The RF circuit of most klystrons is entirely within the vacuum envelope. Tubes of this type are called internal cavity tubes. In external cavity tubes, the RF cavities are distinct from the vacuum envelope. They are clamped onto the tube by the user. External cavity tubes can be cheaper to replace, because the RF cavities are reusable. Problems with multipactor on the ceramic and RF arcing, along with the need to tune the tubes in the field, have tended to inhibit the broad application of external cavity tubes. Figure 5 shows a detail of a typical external cavity.

I. Klystrons

/

E~etyna'

Ceramic window

External cavity Figure 5. Klystroncavity:externalcavitytype.

Electron Beam System The electron beam system can be divided into three parts; the electron gun, the magnetic circuit, and the collector. Electron Gun

The electron gun is the source of a klystron's electron beam. It is probably the most critical subassembly of a klystron. Most of the significant properties of linear beam devices are acutely sensitive to the properties of the electron beam. And the properties of the electron beam are highly sensitive to small gun dimensional changes, cathode surface chemistry, etc. References [1, 2, 11-13] discuss the subject of electron guns and cathodes in far greater detail than this chapter. The cathode is the portion of the electron gun which actually emits the electrons. The cathodes of all practical klystrons are thermionic; they must be heated to emit electrons. During operation, the surface of the cathode is maintained at temperatures ranging between 800 and 1100°C by a heater (or filament). Over the years, great effort has been devoted to the enhancement of desirable cathode properties. These properties are high current emission per unit area, long life, operation at lower temperatures, and resistance to poisoning. Table 2 enumerates the more significant types of klystron cathodes along with some miscellaneous comments. References [14-16] explore the subject of cathode materials in greater depth. The heater (or filament) of an electron gun is aptly named. It is the portion of the gun which heats the cathode to its required operating temperature. Differences in cathode size and warm-up-time requirements

Brian Roach TABLE 2 Cathode Types

Comments

Type Oxide Impregnated tungsten Coated tungsten

Pulse width/emission restrictions, easily poisoned Most commonly used Susceptible to damage, high-emission capability

have produced a variety of heater types. Most heaters, though, comprise a coiled tungsten wire which heats the back of the cathode button by conduction or radiation. The remainder of the electron gun provides the electrodes required to initially accelerate, form, and modulate the electron beam. The guns of all practical klystrons are of the Pierce type and are ceramic metal assemblies. The fact that klystrons use Pierce-type cathodes establishes the current-voltage relationship of klystrons, k = i/V3/2,

where i is the beam current, V is the beam voltage, and k is a constant called perveance. The microperveance of a tube is the perveance times 10 6. Note that microperveance is often loosely referred to simply as perveance. The microperveance of most klystrons ranges between 0.5 and 2. Pulsed klystrons normally utilize pulsed electron beams. Although it is possible to simply pulse the high voltage applied to the electron gun, frequently a control electrode is introduced into the gun. This permits the beam to be pulsed with the application of a voltage less than the full beam voltage. The figure of merit/x is the ratio of the beam voltage divided by the control electrode voltage swing. Table 3 describes the common types of control electrodes used in klystrons for pulsing the electron beam.

TABLE 3 Types of Control Electrodes

Type None (cathode pulsed) Mod anode Focus electrode Intercepting grid Nonintercepting grid

Control/x

Comments

1 2 8 50 30

Most suitable for high beam voltage Usable for perveance variation Older type Low duty cycle Mechanical complexity and difficulty of design

I. Klystrons

7

Beam Focusing Once formed by the electron gun, the electron beam must be maintained at a small diameter for a considerable distance while it passes through the RF circuit. Both the space charge of the beam itself and the RF interaction tend to cause the beam to spread. Maintenance of the beam diameter is critical; lost electrons are not able to interact with the RF circuit, contributing to losses of efficiency. More significantly, the power in the electron beam is usually more than that required to damage or destroy the RF circuit. In principle, beam confinement may be achieved with either magnetic fields or electrostatic fields [17]. In practice, however, almost all klystrons utilize magnetic focusing. References [1, 2, 11-13, 18] discuss magnetic focusing methods in greater detail. The minimum amount of magnetic field required to maintain a "pencil" electron beam at a constant diameter is the Brillouin field. The Brillouin field (B b) in gauss is B b = 8.3 × 10-411/2/(V1/4r), where V is the beam voltage, I is the beam current, and r is the beam radius in inches. Because the electron beam becomes highly bunched in a klystron, the actual magnetic field is typically maintained at a multiple of two to three times the Brillouin field. Klystrons can use permanent magnets (PM), periodic permanent magnets (PPM), or solenoids to supply magnetic focusing fields. Permanent magnets are frequently used for the focusing of klystrons below a peak output power level of about 10 kW. This peak power restriction is dictated by the long magnetic gaps which are typical of klystrons of higher peak power levels. (Permanent magnet weight is approximately proportional to the cube of the magnetic gap length.) Note that the SLAC klystrons are a conspicuous exception to this rule. The use of the term "permanent magnet focusing" is somewhat deceptive, in that it refers to klystrons that have a single uniform focusing field in the RF interaction area. Arrays of smaller magnets (PPM focusing) [19, 20] can be used to create a chain of alternating magnetic fields around the electron beam. PPM focusing is used infrequently on klystrons. It is not usable on designs of low peak power (less than about 10 kW) because of the space requirements of the multiple pole pieces and magnets along the beam path. The comparatively poor beam transmission characteristics ( ~ 90%) of PPM focusing tend to restrict the average power output to less than 1 kW. Newer techniques, however, may extend the average power capability of PPM focused klystrons [21]. Progress in higher energy prod-

8

Brian Roach

uct magnets has aided appreciably in the development of lightweight permanent magnet and PPM klystrons. Solenoids are used for focusing klystrons of all power outputs and frequencies. As alluded above, solenoids are usually the focusing method of choice for high peak and average power klystrons. Collector

After the electron beam traverses the RF interaction area, it passes into the collector. Most collectors are rather massive copper cups which serve to dissipate the unused power of the electron beam into heat. A collector must be capable of dissipating the full power of the beam (i.e., no RF modulation plus a safety factor). Almost every imaginable type of heat transfer has been utilized for the dissipation of this heat, including liquid cooling, boiling heat transfer, air cooling, conduction cooling, and radiative cooling [22]. Liquid and air cooling are, however, the most common types of cooling. Collectors are frequently electrically isolated from the RF circuit (which is usually at ground potential). This permits the measurement of body current, that being beam interception on the RF circuit. The application of a negative bias to an isolated collector is called "depressing" the collector. This permits the recovery of some of the beam power that would otherwise be converted into heat. The use of depressed collectors on klystrons is possible, although somewhat uncommon. The high electronic efficiency of klystrons not only reduces the incentive to use depressed collectors, but also makes the design of such collectors difficult. This is because the efficient extraction of energy from the electron beam tends to result in a wide mixture of electron velocities as electrons leave the output gap. This wide spread of electron velocities complicates the design of depressed collectors for klystrons. A depressed collector klystron is described under Communication Applications.

2. Klystron Applications Klystrons are found in linear accelerators, communications, industrial heating, radar systems, and other miscellaneous applications. These applications have typically resulted from good operating characteristics at high power, low noise characteristics, and the comparative low cost of klystrons.

Linear Accelerator Applications The Varian VKS 8252 klystron, used in a medical linear accelerator, not only is a good example of an accelerator application, but also is similar to

I. Klystrons

9 TABLE 4 Klystron Example: VKS-8252 Characteristic Center frequency Bandwidth Peak power output Average power output Drive power Beam voltage Beam current Modulation type Cooling Focusing type Size Weight

Value 2.856 GHz 5 MHz 5.5 MW 5.5 kW 100 W 120 kV 83 A Cathode pulsed Water Solenoid 37 in. long 111 lb (without solenoid)

many tubes that are used in narrow-band radar applications. The operating characteristics are shown in Table 4. It is a five-cavity tube. The input and second cavities are nominally tuned to the center frequency, whereas cavities three and four are tuned above the band. This tuning of cavities above the pass band (inductive tuning) is done to enhance the efficiency of the tube. The output cavity is tuned to the band center. The klystrons used at SLAC have been described many times [23-25]; their detailed performance will not be enumerated here. The performance of the basic S-band tube has been extended to 150 MW. SLAC and Mitsubishi have also made noteworthy progress at the X band, with reports of 30 MW at narrow pulse widths from SLAC and of 4 MW from the Mitsubishi tube at 5 /zS pulse width. The development of useful X-band klystrons for accelerator applications, if not in hand, can be said to be nearly in hand [26, 27].

Communication Applications Tunable CW medium-power klystrons have found extensive use in satellite up-link applications. These applications often require the ability to tune the instantaneous bandwidth across some frequency range. The Varian VKX-7799 (Figure 6) is able to position a 2% instantaneous bandpass across a 6% tuning range. The instantaneous bandwidth is achieved by stagger tuning the driver cavities and by using a double-tuned output circuit. Table 5 shows the characteristics of this tube. The 7799 is somewhat atypical, in that the majority of satellite communication klystrons are actually PM focused. Reference [28] describes a permanent magnet fo-

I0

Brian Roach

Figure 6. VKX-7799 klystron (solenoid not shown).

cused tube for a similar application. Reference [29] describes another PM focused tube and provides detailed performance information. Lower frequency klystrons are used in many UHF TV transmitters. The Varian VKP-7990 is an interesting klystron developed for that application. It is a solenoid focused tube that is fitted with a five-stage depressed collector. Without collector depression, its efficiency in saturated operation is 55%. With collector depression the tubes overall effiTABLE 5 Klystron Example: VKX-7799 Characteristic Center frequency Bandwidth CW power output Drive power Beam voltage Beam current Cooling Focusing type Size Weight

Value 7.9-8.4 GHz (tunable) 175 MHz 10 kW 3W 14.3 kV 2.3 A Water/glycol Solenoid 16 in. long 20 lb (without solenoid)

II

I. Klystrons TABLE 6 Klystron Example: VKP-7990 Characteristic

Value

Center frequency Bandwidth Peak power output Drive power Beam voltage Beam current Cooling Focusing type Size Weight

470-810 MHz (tunable) 6 MHz (8 MHz with lower gain) 64 kW 20 W 26 kV 4.5 A Water Solenoid 62 in. long 300 lb (solenoid weight, 500 lb)

ciency improves to 70% [30, 31]. The 7990 has another feature worthy of note; like most UHF TV tubes, it is an external cavity tube. Table 6 describes the characteristics of the 7990.

Industrial Heating Applications Industrial heating applications take advantage of the high efficiency and high average power capabilities of klystrons [32]. This application has essentially no bandwidth requirement, so that tube performance can be optimized for efficiency. Lein has reported an electronic efficiency (i.e., no collector depression) of 75% [33], although the limit for practical tubes is probably 70%. The Varian VKP-8275 is an example of a tube used in industrial heating. It is used to cure epoxy-wood laminates. Its characteristics are summarized in Table 7. TABLE 7 Klystron Example: VKP-8275 Characteristic Center frequency Bandwidth Average power output Drive power Beam voltage Beam current Cooling Focusing type Size Weight

Value 910-920 MHz (tunable) 4 MHz 100 kW 2W 32 kV 6.5 A Glycol/water Solenoid 70 in. long 325 lb (solenoid weight, 700 lb)

12

Brian Roach TABLE 8 Klystron Example: VKX-7809 Value

Characteristic Center frequency Bandwidth Average power output Drive power Beam voltage Beam current Cooling Focusing type Size Weight

10.0-10.25 GHz (tunable) 50 MHz 2.5 kW 0.3 W 9.5 kV 1.0A Air Permanent magnet 15 in. long 55 lb (includes magnet)

Radar Applications Radar might be called the classic application of klystrons. The low-noise characteristics of klystrons make them attractive for illuminators. The availability of very high peak power makes klystrons ideal for use in search radar transmitters. They also are potential candidates for active seeker transmitters. The VKX-7809 is a good example of an radar illuminator tube. Table 8 delineates its characteristics, whereas its noise performance is shown in Figure 18. Note that gridded tubes of this class are appropriate for use in pulse doppler radars. The Varian VKS-8345 (Figure 7) is a good example of a larger pulse radar tube. It has six cavities plus a two-cavity EIK output. The first four cavities are tuned across the bandpass of the tube for gain. The remaining two are tuned above the upper band edge to promote efficiency. EIKs, as mentioned previously, typically have limits on the allowable range of beam voltage and load mismatch. These limits are imposed by the stability requirements of the output circuit. The beam voltage of this tube must be maintained between 108 and 120 kV, and the load mismatch must be 2 : 1 or better between 2.9 and 3.5 GHz. The 8345 is a cathode pulsed tube. The characteristics of this tube are summarized in Table 9.

3. Klystron Specification Specification of klystrons (as with most devices) is complicated by the fact that most of the desirable performance factors are interdependent. A1-

I. Klystrons

I

~

iii!~

.....C~ii!:ili~dlii

Figure 7. VKS-8345 klystron (solenoid not shown).

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

14

Brian Roach TABLE 9 Klystron Example: VKS-8345

Characteristic Center frequency Bandwidth Peak output power Average output power Drive power Beam voltage Beam current Cooling Size Weight

Value 3.0 GHz 200 MHz 4.0 MW 6.7 kW 400 W 117 kV 80 A Water 43 in. long 140 lb (without solenoid)

though some of the more obvious interactions will be discussed, the reader should be cautioned that all of the most desirable performance parameters are not achievable in a single device. The electronic performance, operating parameters, environmental performance, reliability, mechanical envelope, and other miscellaneous items must be addressed when specifying klystrons. Electronic Performance Parameters

One of the more significant klystron performance interactions is between peak power and most other electronic parameters. In general, klystrons with high peak output power tend to display more favorable gain, bandwidth, and efficiency compared with lower peak power designs. Another tradeoff involves the relationship among perveance, efficiency, and bandwidth. High perveance tends to favor broad bandwidth, whereas low perveance tends to favor better efficiency [34]. Figure 8 shows the relationship between bandwidth and peak power for three types of tubes. Tubes with simple resonant output cavities have a lower bandwidth capability compared with those with double-tuned outputs, whereas Twystrons and ElKs are capable of the greatest bandwidth. Although klystrons can operate at arbitrarily low peak power, the poor performance of low peak power tubes, coupled with the availability of viable technical alternatives, tends to limit practical designs to peak power levels higher than a few hundred watts. The upper limit to peak power is not yet entirely clear; the performance of the accelerator tubes under Linear Accelerator Applications is representative of the state of the art. At frequencies below the high X or Ku band, the practical limits seem to

15

I. Klystrons 10,000

1,000

o / o/4,~/

/

1oo

I_O I

/

, ,,I,,,~

I

,,,,,,,I

, ,

10

I

Bendwidth (%) Figure8. KIystronbandwidthcapability,

be RF breakdown in the interaction gaps and electron gun voltage hold-off [35]. At higher frequencies, the limiting factors appear to be available electron beam power and tube efficiency [36]. Klystrons that operate at short pulse widths (less than 1 /~S) will have a higher peak power capability than those that operate at longer pulse widths. The practical available average power output of klystrons is shown in Figure 9. This figure neglects tubes at frequencies below 8 GHz, for which the ultimate performance limits have not yet been established [37, 38]. This is not too surprising when one considers the power supply require,~

250

""

100

Liquid Cooled Q.

0

10

k-

o £3_

Air I

13 ID >

<

' ''''I

10 Frequency

100

(GHz)

Figure 9. Klystron average power capability,

|6

Brian Roach

ments for tubes that feature extremely high average output power. For example, a 50% efficient 1-MW tube would require a 2-MW power supply. References [39, 40], however, speculate that a simple-minded extrapolation of Figure 9 to lower frequencies is very likely appropriate. Figure 9 is limited to tubes with simple resonant output circuits and shows the effect of coolant choice on maximum output power. Note that the choice of liquid coolants other than water will result in an average power capability somewhere between the lines for liquid-cooled and air-cooled cases. Other design factors, such as requirements for tunability or lightweight focusing schemes, can further reduce the average power capability of practical tubes. Klystrons in the frequency range depicted in this graph have been operated at higher average power levels (e.g., 1 MW at the X band [9]). However, the robustness of such designs is questionable. Figure 10 shows a normalized curve of power output as a function of RF drive. This curve clearly shows a characteristic of klystrons, which is a rapid dropoff of output power when RF drive is increased past the saturation level. In some klystrons, RF overdrive past the point of saturation can cause damage to the RF circuit. This is due to the spreading of the electron beam which usually accompanies RF overdrive. Figure 11 shows an accompanying phenomenon: an increase in electrical length as saturation is approached. The derivative of this curve is referred to as AM to I'M conversion. AM to PM conversion is spurious phase modulation that accompanies amplitude modulation when klystrons are run near saturation.

1.0 ~o

.8

5 g

.6

\

.4

.2 ¢Y I

I

I

I

I

.2 .4 .6 .8 1.0

I

I

I

1.4

Relative RF drive power Figure I0. Typical normalized klystron input-output curve.

17

I. Klystrons

20@ -O

cO_

15 -

Ma

105 -

~~--~~l,

Typ.

-15 -10 -5 0 RF drive power (dB below sat) Figure II. Change of electrical length with F~Fdrive.

I O9 E v

Response at saturated power output

.

>

"-

Band I - " " ~ edge

°~ "~ 2

I

I

6160

I

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6180 6200 6220 Frequency (MHz)

6240

Figure 12. Typical group delay characteristics.

Figure 12 shows the group delay characteristics of a typical klystron. Group delay varies most rapidly at the band edges of most klystrons.

Operating Parameters Figure 13 and Table 10 show a klystron in schematic form, along with some significant operating parameters. Each of these parameters should be specified at its normal operating level and at some absolute maximum level. An absolute maximum level should be used as a guide for the limitation of peak transients. Note that in many (or most) cases, continuous operation at an absolute maximum level will result in tube failure.

18

Brian Roach

I by

+

Pd

Eb(

Ff

,k

Im

,fTiy

Figure 13. Klystron schematic diagram.

The operating parameters of tubes will affect RF performance. The changes in operating parameters, along with their accompanying effects, are referred to as "pushing figures." These pushing figures are important, because they will dictate the degree of regulation required from the power supply or modulator. Ripple of the beam voltage creates both phase and amplitude modulation of the amplified signal. There are simple relationships which describe this pushing. (These are valid for small excursions--ones that are not large enough to appreciably affect the efficiency or saturation characteristics of the device.) The amount of amplitude modulation is determined by the variation of power into the tube times the tube efficiency. The change of output power is

(AV)(5/2)(P/V), where P is the power output of the klystron and V is the beam voltage. TABLE 10 Klystron Operating Parameters Symbol

Eb /k Ef If /by egk eco Im Pd Po

Description Beam voltage Cathode current Heater current (WRT cathode voltage) Heater voltage (WRT cathode voltage) Body current Grid turn-on voltage (WRT cathode voltage) Grid cutoff voltage (WRT cathode voltage) Solenoid current RF drive power RF output power

I. Klystrons

19

Beam phase pushing is caused by the change in the electrical length of the tube. To calculate this number, the electrical length of the tube must be known. This parameter is typically between 2000 to 5000 °. The change in a klystron's phase length with changing beam voltage is

(AV)~/(2V), where 4~ is the phase length of the tube and V is the beam voltage. Ripple on the heater voltage can induce sidebands on the signal due to magnetic modulation of the electron beam. This effect can be minimized through careful design of the heater windings. Where even a small amount of this modulation is objectionable, the use of DC heater supplies is sometimes required. In extreme cases, a synchronous heater power supply may be used. The source and load impedance presented to a klystron will have an effect on its performance. The situation is somewhat different between narrow-band and broadband tubes. In a narrow-band tube, the effects of source and load impedanc,e variation are small changes in tube gain and bandwidth. It is usually possible to design tubes that will maintain specification across a 1.3:1 variation of impedance. In a broadband tube, variation of the source and load impedance can result in excessive amplitude ripple in the tube's power output vs frequency response. Source and load variations as small as 1.1:1 can be quite significant in this regard. Isolators and circulators are frequently required in demanding applications. Note that in the case of EIKs and Twystrons, an excessive load mismatch (even out of band) can cause oscillations. Environmental Parameters

The environmental performance of klystrons should be regarded from two viewpoints; survival of the device and operation with fidelity while under stress. Generally, within rather gross bounds, temperature does not affect the survival of klystrons. However, temperature, and specifically the temperature of the RF circuit, can have a noticeable effect on electronic performance. This is because of dimensional changes in the resonant cavities, which causes detuning of their resonant frequencies. This effect can be considerably mitigated with cavity and mechanical tuner thermal compensation. In cases in which extreme stability is required under a wide range of ambient conditions, the temperature of the body must be controlled via a small temperature-controlled coolant loop. Klystrons are very susceptible to damage from mechanical stress. Spurious modulations of the amplified signal are also quite possible during periods of mechanical stress. These spurious modulations are commonly referred to as "microphonics."

20

Brian Roach

There is little useful general advice on shock and vibration specification that can be given. Klystrons are capable of operating to demanding specifications under the harshest mechanical conditions. However, the effort required to design a tube for such an application can be very great. The effort to verify tube performance during mechanical stress can also be very great. Pains should be taken to carefully specify the environmental stress that will actually be placed on the klystron. Unrealistic mechanical excitations should not be specified (e.g., sinusoidal sweeps). The difficulty of verifying electronic noise parameters while mechanical stress is applied should not be underestimated. Because klystrons operate at high voltages, voltage standoff and corona are concerns when operation at high altitude is required. As vacuum tubes, klystrons are not affected by radiation exposure (except for degradation of the mechanical properties of the assembly under conditions of extreme long-term exposure).

Life and Reliability The life and reliability of klystrons are highly dependent on system design and maturity. Klystrons are frequently the first component to fail in the event of system malfunction. Poorly designed or new systems can induce large numbers of tube failures. Particular tube sockets will frequently induce disproportionate numbers of failures compared with similar sockets in other locations. Tube failures should always be the occasion for system, as well as klystron, failure analysis [41, 42]. The main end of life mechanism for klystrons is cathode depletion. This mechanism is related to the temperature that the cathode is run at, which, in turn, is a function of gun design and selection of cathode material type. Generally, tube designs at higher frequency and higher peak power tubes will have a shorter life than other tubes. Numerous studies on cathode life have been conducted using various test vehicles [43]. However, these test results are not always strictly applicable to actual klystrons. This is partly due to the fact that operating tubes are not as favorable an environment for cathode materials as the test vehicles typically used in the studies. Fixed station klystrons have recorded lives in excess of 70,000 hr, although klystron lives of 15,000 to 40,000 hr are more the norm. A mechanical wearout mechanism is present in tunable klystrons. These tubes have mechanisms that require a portion of the vacuum envelope to be a deformable wall or bellows. Vacuum leaks can develop after some number of tuner cycles. Depending on the tube design, the average number of permissible tuner cycles is highly variable~from nearly infinite to less than 100 cycles in some designs.

21

I. Klystrons TABLE II Typical Klystron MTBFs

Application

Typical MTBF (hr)

Reliability factors

Airborne

1,000-5,000

Shipboard

5,000-10,000

Ground mobile (operating) Ground transportable

5,000-10,000 10,000-20,000

Ground fixed

20,000 +

Cycling, size, cooling, shock/vibration, temperature extremes Cycling, salt air/humidity, shock/vibration, power surges Cycling, power surges, shock/vibration, dust/dirt Cycling, power surges, shock/vibration, dust/dirt 24 hr/day operation, easy access, controlled/sheltered environment

Another wearout mechanism is present in fast-start guns. Quick-start guns will typically have a finite number of quick-start cycles. Table 11 gives typical MTBF figures for tubes in mature systems. Although this table was developed from data derived from a variety of linear beam tubes, it is quite relevant to klystrons in particular. This table clearly shows the link between environmental stress and tube MTBF. Airborne applications show the poorest reliability for two reasons; the environmental stress of the application and the fact that airborne tube protection schemes are sometimes less elaborate than those used in ground-based applications.

Physical Parameters Klystron size and weight are, to great degree, dictated by the operating requirements of the system. Klystrons of higher frequency, lower peak and average power, and smaller gain/bandwidth tend to be smaller and lighter. The main degrees of klystron design freedom involve the selection of cooling type and magnetic focusing circuits. The tubes described in Section 2 will give the reader some notion of typical klystron sizes and weights. Note that tubes intended for airborne applications can be considerably lighter. This is due to the typical specification of fairly high frequency ( > 8 GHz) and the use of rare earth permanent magnets.

Miscellaneous Items Klystrons require an excellent vacuum (between 10 .7 and 10 .9 T) for proper operation. Unfortunately, gas will evolve from the walls of the

22

Brian Roach

tube, especially during operation. Even a klystron with no leaks will suffer degradation of vacuum while on the shelf due to gas diffusion through the walls of the tube. Fortunately, klystrons will pump themselves to some degree during operation. However, in some cases, ion pumps or getters are specified. They are particularly recommended for large tubes, applications for which a fast turn-on after storage is required, or designs in which internal walls reach unusually high temperatures during operation. The modulation requirements of the system will have a profound effect on the specification and design of the electron gun. The higher the required /z for a gridded tube, the greater the difficulty of gun design. There are similar tradeoffs involved in heater turn-on time. Generally, the shorter the time is, the greater the complexity of the gun. For example, extremely short turn-on times (less than 1-2 s) require elaborate bombarder-type heaters, which, in turn, require a programmed heater turn-on profile and an additional HV supply. It is easier to design fast turn-on guns for physically small tubes without extreme RF performance or long-life requirements [44].

4. Design and Fabrication of Klystrons Klystrons, although more simple than wave tubes, are still complex devices. The RF, electron beam, thermal, and mechanical properties of tubes all tend to be highly interactive. This means that the task of designing klystrons is a complex and iterative one. There is no single design code or methodology that begins with the desired properties of a tube and yields a workable design. Fortunately, the requirement to design a tube from the ground up is infrequent; usually, there is an existent design that needs only to be modified to meet some new requirements.

Typical Design Methodology A scenario for a bottom-up design of a klystron is shown below. Although it is laid out in a linear process, in reality it is highly iterative. As in any design process, the experience of the designer can sharply reduce the number of required iterations. The design of modern klystrons relies heavily on the use of computer modeling [45, 46]. The first task is small signal modeling of the tube. Based on the assumed properties of the electron beam and cavities, this process establishes the required cavity tunings and cavity spacings required to obtain a required gain-bandwidth product. These small signal programs are typi-

I. Klystrons

23

cally proprietary; all of them follow the gain model of Figure 3 rather closely. The next task is large signal modeling of the device [46-48]. Small signal design best models the first portion (buncher section) of the tube; the large signal design addresses itself to the tunings and cavity spacings of the last two or three cavities. The design of the output circuit (simple resonant, double tuned, EIK, traveling wave) is also done at this stage. The next task is realization of the cavity or circuit properties assumed in the previous two steps. This can be done with physical cold test models [49] or with the use of appropriate computer codes (LALA, Superfish, SOS, etc.). The next step is design of the electron beam system. This includes the determination of the electrode geometries of the electron gun and the magnetic field requirements for proper beam formation. Usually, specialized proprietary codes are used for this purpose. In many cases, gun prototyping is done in beam analyzers [50]. These are test stands in which prototype guns can be exercised. Inside the beam analyzer, a small aperture is scanned across the gun's electron beam at various axial positions to measure the beam profile. The design of the magnetic focusing circuit is the next task. There are an increasingly large number of magnetostatic codes available for this purpose. Properly done, the results of this modeling can be extremely accurate. The amount of experimental cut and try should be minimal. Next comes thermomechanical design. There are a variety of inputs to this stage of design: The probable thermal fluxes derived from the electron beam and RF properties of the klystron. The physical requirements of the RF electron beam portions of the tube. The mechanical and environmental requirements of the application. The thermal and cooling design must be done with great care, as collector average power densities of hundreds of W/cm 2 are fairly common, and densities higher than 1 kW/cm 2 are not unheard of. Finite element thermomechanical modeling programs are frequently used in this stage of design. Last comes the layout and design of assemblies and piece parts. Standard mechanical CAD packages are normally used. This is an especially important stage, because the necessary design craftsmanship translates rather directly into high operating reliability and good manufacturing yield. Particular attention must be paid to proper braze joint'or weld joint design.

24

Brian Roach

Construction

Klystrons, like other high-power microwave tubes, are of ceramic metal construction. Most of the materials are chosen with an eye toward high. purity and low vapor pressure. Outside of the electron gun, the metals used are primarily OFHC copper and 300 series stainless steel. Where magnetically soft parts are required, low carbon steel and pure iron are used. High-purity ceramic (mainly alumina, but occasionally berylia) is utilized for voltage standoff purposes and microwave windows. The predominant construction method for smaller tubes is furnace brazing, usually with silver-copper and gold-copper braze alloys. The brazing is generally done in hydrogen. Larger tubes tend to use a greater proportion of welding in their construction. Great pains are taken in tube construction to minimize contamination. This is due to two reasons. First, contamination can inhibit the flow of alloy during brazing, causing leaks. Second, seemingly trivial amounts of contamination inside the vacuum envelope can result in endless amounts of gas during tube processing and operation. Therefore, manufacturers exercise stringent control on materials used in tubes. Most piece parts are subjected to a series of chemical cleaning baths. Assembly operations are often carried out in clean rooms to minimize contamination by dust, finger grease, etc.

Figure 14. Major subassemblies of a K~-band klystron.

25

I. Klystrons

Typically, there will be several levels of assembly before the tube is evacuated in a bake-out furnace. Figure 14 shows a Ka-band tube at the subassembly stage. Several steps of tube dress and RF processing will follow before construction is complete. References [51] and [52] describe the materials and technology of tube construction in great detail.

5. Noise and Stability Characteristics Noise Klystrons are amplifiers that can be represented by the gain and noise blocks that are normally used in system design. Typical noise figures for klystrons range from 30 to 40 dB. The total noise power output (or output per unit frequency) is readily calculable given the noise figure, gain, and bandwidth of the klystron. All calculations of this type start with the assumption of thermal noise at the input of the amplifier. These calculations are appropriate only for in-band noise. Klystrons usually attenuate out-of-band signals, so out-of-band noise is determined by the beam noise figure and the out-of-band response of the output circuit. Reference [2] has examples of typical noise calculations. Figure 15 illustrates typical levels of random noise. Figure 4 shows the out-of-band response of a typical five-cavity tube. Typical klystron intermodulation properties are depicted in Figures 16 and 17. Figure 16 shows the relative power output for a typical klystron. It shows the total output power of a klystron driven into saturation with two equal carriers. This total output power includes all intermodulation prod-

I Typical signal output power level

40 t

N

m 13

0 -40 -80

-120 -160 -200

.f-~- f .

f

/lyplcal

f

f

f

f

f

f

f

f

f

noise power level

f / ~

V l l l l l l l J J J J /

f

,

100kHz

1M~Hz 10MHz A f from fo

100MHz

Figure 15. Typical klystron noise power output,

26

Brian Roach 0

Single carri

o

o •

-5

0 0 O_

o 3

-10

°N

~

0

0

~

m "o

-15

,/

I

I

I

I

-20 -15 -10 -5 RF drive (dB below saturation)

J

0

Figure 16. Typical input- output curves - - one-carrier and two-carrier cases.

ucts and is somewhat lower than the single-carrier saturated power output. Figure 17 shows the relative amplitude of the largest intermodulation product under these conditions. Typical klystron harmonic output levels are - 3 0 dB down from the fundamental for the second harmonic and - 5 0 dB down for higher harmonics. This can be rather difficult to verify, however. This is because harmonic frequencies are in the overmoded frequency range of the waveguide outputs used by most klystrons. Klystrons generally exhibit low AM and PM noise; typical curves are shown in Figure 18 for the VKX-7809. These levels of AM and PM noise can be severely compromised, however, by ion oscillations. Ion oscillations

~

-10

"E -15

E~~

-20

.E

-25

~g ~ -3o

~' ~ -35

_J

m

-40

-o v

"2 "4 "6 "8-10-12-14-16 RF drive (dB down from 2 carrier sat)

Figure 17. Largest intermodulation product (with reference to either carrier).

27

I. Klystrons -6O "-

-80

•

-100

k_ O 0

m

0

_~

-120

m

'~

-140

•0-~

- 160

_

AM noise h

Z

I

10 DeviGtion

from

I

I

100 f o (KHz)

Figure 18. Typical klystron AM and PM noise (VKX-7809, 40-dB gain).

are described in References [12, 53, 54]. Careful attention to magnetic design and meticulous tube processing are required to eliminate these troublesome instabilities. Other sources of noise are actually caused by variation of the power supply voltages. These pushing factors are addressed under Operating Parameters.

Stability Although the basic klystron is usually regarded as unconditionally stable, there are, in reality, some possible instabilities that can occur [55]. RF leakage from the output flange to the input flange can cause oscillations in extreme cases and gain anomalies in less extreme cases. Internal feedback is possible in the form of electrons that have become turned around and propagate toward the gun. This is more likely to occur in tubes with depressed collectors, permanent magnets, or ultra-high-efficiency tubes. Note that these possible gain anomalies are especially significant to applications that have critical intermodulation requirements. Multipactor is a secondary electron discharge that is possible in the presence of strong RF and magnetic fields. It can occur on output drift tube tips, output windows, or the cavity ceramics of external cavity klystrons. Multipactor on drift tubes can manifest itself in the form of gain "clamping" or other anomalies. Multipactor on ceramics can easily cause the thermal shattering of the ceramic. Several stratagems are available to prevent multipactor [56-58]. An excessive mismatch at the output of an EIK or a Twystron can cause oscillations. This is the case both in and out of band. The allowable

28

Brian Roach

mismatch at different frequencies is a function of the particular design. EIKs and Twystrons can also oscillate if an inappropriate beam voltage is applied. The performance of a typical tube is outlined under Radar Applications. Low-frequency gun oscillations and monotron oscillations result from the interaction of a high-power electron beam and structures with RF resonances. They are possible in some extremely high-power designs [59-61]. Grid oscillations can result from the interaction of the low-frequency L and C characteristics of the grid with the power supply. They manifest themselves as an unexpected LF or HF modulation of the amplified signal. In an analysis of this phenomenon, the gun control electrodes should be regarded as the elements of a triode or tetrode.

6. Klystron Protection Tube protection is an area which cannot get enough attention. It presents a very real dilemma to the power supply designer. On the one hand, good tube protection can greatly enhance the reliability of a system. But, on the other hand, the complexity of the schemes required can, of themselves, contribute appreciably to the overall complexity of the supply and the difficulty of its design. However, there is an adage that should be borne in m i n d m t h e tube is the most expensive fuse in the entire system. Reference [62] contains useful information and references for power supply designers. The first level of protection that must be afforded klystrons is physical. Handling damage is a major failure mechanism in most fielded klystron systems. It can be greatly reduced by thoughtful design of the transmitter and the logistic system for supplying replacement tubes. Proper shipping containers, convenient tube lift points or handles, easy socket accessibility, and proper personnel training are keys to the elimination of this mode of failure. High-voltage arcs can occur either inside or outside the vacuum envelope. Wherever the location, a sustained arc can easily damage the tube. Depending on the location of the arc and the size of the tube, as little as a few joules of energy can be enough to cause damage. The power supply design should be such that stored energy is quickly dumped in response to internal tube arcing. Usually a fast acting switch (or crowbar) is required. A possible exception to this rule is a switching power supply. In switching systems with low-energy storage, simply shutting down the inverter can sometimes be sufficient to prevent klystron damage.

I. Klystrons

29

Waveguide RF arcs are not uncommon in high-power microwave systems. Arcs will propagate toward the klystron and will break the output window if no action is taken to extinguish the arc. Arc detection is best done with a photodetector aimed at the output window. The output power must be reduced within 10 ~S to prevent damaging the window. This can be achieved in any number of ways; reduction of RF drive, modulator shutdown, crowbarring, etc. The grid and RF circuit (body) of the tube are susceptible to damage by the electron beam. Peak and average overcurrent sensing must be provided for these elements. The supply should react to overcurrent conditions by shutting down pulsing, crowbarring, etc. The specific trip level and speed of response will be peculiar to the klystron type in question. The supply should be designed so that inappropriate voltages cannot be applied to the tube or applied in the wrong order. The manufacturer's limits on operating voltages and currents should be embodied in a system of interlocks. In gridded tubes, the interlocking of operating voltages is especially important. Operating voltages must be applied in a particular order. First, the specified cutoff (eco)voltage must be applied to the grid. Then, the beam voltage may be applied to the cathode. Grid pulsing should not be enabled until the beam voltage clears a preset level. Supply shutdown, especially in the presence of fault conditions, must be carefully considered. Never apply a positive voltage to a grid when the beam voltage is off [63]. In most klystrons, interruption of coolant flow is speedily followed by tube destruction. Therefore, interlocks are highly recommended for coolant flow. In liquid cooled tubes, coolant quality can be of crucial importance. In tubes with high collector wetted wall temperatures, pH, ion content, oxygen content, sulfur content, and bulk resistivity must be maintained within specified limits [64-66]. The situation is somewhat less critical for air-cooled tubes, for which the dust or salt content of the cooling air can be of concern. Other interlocks are typically used for miscellaneous purposes such as operator safety or ion pump current (tube vacuum level). The temperature of the cathode must be carefully controlled to obtain long life. Practically speaking, this means that the heater power must be appropriately set. Miram curves are the best way to determine the appropriate level of heater power that is required for any given tube. They are also a tool for exploration of other electron gun problems [67]. Heaters usually require protection against excessive current upon turn-on. Heater wire will typically run at a temperature of 1500°C. Therefore, the hot (or operating) resistance will be considerably higher than the

30

Brian Roach

cold resistance. If the operating heater voltage is applied to a cold heater, the resulting surge of current can be enough to damage the heater. The use of a current-limited supply or a ramped application of heater voltage is recommended.

Acknowledgments I thank my colleagues at Varian for their contributions of material used in this chapter. I also express my gratitude to my wife and family for their forbearance and support.

References [1] Chodrow, Fundamentals of Microwave Electronics. New York: McGraw-Hill, (1964). [2] Staprans et al., High power linear beam tubes, Proc. IEEE, Vol. 61, pp. 299-330, Mar. 1973. [3] Faillon et al., Wide band klystrons and TWT's, ITG Vacuum-Electron Displays Meet., Garmisch-Partenkirchen, May 1989; see also Vortrage der ITGnFachtagung 1989. Berlin: VDE-Verlag, 1989. [4] Anon, "Twystron Hybrid TWT's," Varian Assoc., Palo Alto, CA, Mar. 1973. [5] LaRue et al. Multi-megawatt hybrid TWT's at S-band and C-band, IEEE Electron Devices Meet., 1964. [6] Chodrow et al., A high efficiency klystron with distributed interaction, IRE Trans. Electron Devices, Vol. ED-8, pp. 44-55, Jan. 1963. [7] Zhao, Impedance measurement technique for double gap klystron cavity, SLAC-PUB2751; see also IEEE Trans. Electron Devices, Vol. ED-29, pp. 316-320, Feb. 1982. [8] Lee et al., Design and performance of a 150 MW klystron at S band, IEEE Trans. Plasma Sci., Spec. Issue High Power Electron Gener., Vol. PS-14, Dec. 1985. [9] Mann et al., "X Band CW Generator Final Report," USAF Rep., Final Tech. Rep. RADC-TR-69-338, Mar. 1970. [10] Viant, "95 GHz EIA for Airborne High Power Transmitters," U.S. Army Laboratory Command Rep., R & D Tech. Rep. SLCET-TR-83-0399, 1983. [11] Pierce, Theory and Design of Electron Beams, 2nd Ed. New York, Van Nostrand, 1954. [12] Gilmour, Microwave Tubes. Dedham, MA: Artech House, 1986. [13] Gittins, Power Traveling Wave Tubes. New York: American Elsevier, 1965. [14] Cronin, Practical aspects of modern dispenser cathodes, Microwave J., Vol. 22, pp. 57-62, Sept. 1979. [15] Falce, Dispenser cathodes: The current state of technology, IEEE Electron Devices Meet., pp. 448-451, 1983. [16] Green, Modern thermionic cathodes, IEEE Int. Electron Devices Meet., pp. 925-928, 1987. [17] Day, New developments in electrostatically focused klystrons, Microwave J., Vol. 13, pp. 59-63, Apr. 1970. [18] Harrold et al., Permanent magnets for microwave devices, IEEE Trans. Magn., Vol. MAG-4, pp. 229-239, Sept. 1968. [19] Sterrett et al., The design of periodic magnetic focusing structures, IRE Trans. Electron Devices, Vol. ED-5, pp. 35-42, Jan. 1958. [20] Schindler, An improved procedure for the design of PPM assemblies, IEEE Trans. Electron Devices, Vol. ED-13, pp. 942-949, Dec. 1966.

I. Klystrons

31

[21] Legerra et al., A convergent confined flow focusing system for millimeter wave tubes, IEEE Int. Electron Devices Meet., 1983. [22] Scott, Cooling of Electronic Equipment. New York: John Wiley & Sons, 1974. [231 Merdinian et al., High power permanent magnet focused, S-band klystron for linear accelerator use, Proc. 5th Int. Congr. Microwave Tubes, Paris, p. 242, Sept. 1964. [24] Merdinian et al., Klystron for SLAC, IRE Trans. Electron Devices, Vol. ED-14, pp. 700-705, Oct. 1967. [25] Lee et al., 50 MW klystron for the Stanford Linear Collider, IEEE Electron Devices Meet., pp. 144-147, 1983. [26] Hayashi et al., High power X-band klystron, IEEE Electron Devices Meet., pp. 371-374, 1989. [27] Allen, "RF Power Sources," SLAC Rep. SLAC-PUB-4646, May 1988. [28] Faillon, Six GHz earth station klystron, Microwave J., Vol. 23, pp. 57-60, July 1980. [29] Anon, "The VA-936 Klystron Series," Publ. No. 3724A. Varian Assoc., Palo Alto, CA, Sept. 1978. [30] McCune, "UHF TV Klystron Multistage Depressed Collector Development Program," NASA Contractor Rep. CR182190, Sept. 1988. [31] McCune, Klystron performance using multistage depressed collector, IEEE Electron Devices Meet., 1987. [32] Kanavets et al., High efficiency multi-cavity klystrons (optimization of bunching and energy exchange), Elektron. Tekh., Ser. I, Elektron. Svch., No. 11, pp. 33-45, 1976. [33] Lien, High efficiency klystron amplifiers, 8th Int. Conf. Microwaves Opt. Gener. Amplification, Proc., Amsterdam, Conv. Rec. MOGA-70, Sept. 1970. [34] Mihran, The effect of drift length, beam radius, and perveance on klystron efficiency, IEEE Trans. Electron Devices, Vol. ED-14, pp. 201-206, Apr. 1967. [35] Symons, Scaling laws and power limits for klystrons, IEEE Int. Electron Device Meet., pp. 156-159, 1986. [36] Nordquist et al., Performance capability of Ka-band klystrons, IEEE Int. Electron Device Meet., pp. 370-374, 1988. [37] Kojima et al., Super high power klystron for JT-60, IEEE Conf. Plasma Sci., Pittsburg, June 1985. [38] McCune, A 250 KW CW X-band klystron, IEEE Int. Electron Devices Meet., 1967. [39] McCune, Klystrons for present and future lower hybrid resonance applications, Fourth Int. Symp. Heating Toroidal Plasmas, Rome, Mar. 1984. [40] McCune, New developments in high power klystrons for lower hybrid resonance heating applications, 13th Eur. Conf. Controlled Plasma Fusion Heat., Schliersee, Ger., Apr. 1986. [41] Allen et al., Performance of the SLAC Linear Collider klystrons, Part. Accel. Conf., Washington, DC, Mar. 1987. [42] Houts et al., "Microwave Tube Reliability--Actual vs. Predicted--A Realistic Appraisal," E I A / R A D C Rep., Jan. 1991. [43] Shroff et al., Life test results of various dispenser cathode types, IEEE Int. Electron Devices Meet., pp. 643-647, 1987. [44] Treseder et al., Design of quick start, high current density cathodes, IEEE Int. Electron Devices Meet., pp. 453-455, 1983. [45] True, Computers and tubes--Today and tomorrow, IEEE Int. Electron Devices Meet., pp. 436-439, 1983. [46] Kageyama, Large signal analysis of broad-band klystron with design applications, IEEE Trans. Electron Devices, Vol. ED-24, pp. 3-11, Jan. 1977.

32

Brian Roach

[47] Kosmahl et al., Two dimensional evaluation of energy extraction in output cavities of klystron amplifiers, IEEE Trans. Electron Devices, Vol. ED-20, pp. 883-890, Oct. 1973. [48] Drobot, Large scale simulation of electron devices, IEEE Int. Electron Devices Meet., pp. 668-671, 1984. [49] Ginzton, Microwave Measurements. New York: McGraw-Hill, 1957. [50] Miram, Diagnostic techniques with a computer controlled beam analyzer, IEEE Int. Electron Devices Meet., pp. 708-711, 1986. [51] Kohl, Handbook of Materials and Techniques for Vacuum Devices. New York: Reinhold, 1967. [52] Rosebury, Electron Tube and Vacuum Techniques. Reading, MA: Addison-Wesley, 1965. [53] Mihran, Positive ion oscillations in long electron beams, IRE Trans. Electron Devices, Vol. ED-3, pp. 117-121, July 1956. [54] McCune, Ion oscillations in pulsed klystron amplifiers, IEEE Int. Electron Device Meet., pp. 148-150, 1983. [55] Tomiyasu, Spurious output from high power pulsed microwave tubes and their control, IRE Trans. Microwave Theory Tech., Vol. MTT-9, pp. 480-484, Nov. 1961. [56] Preist et al., On the heating of output windows of microwave tubes by electron bombardment, IRE Trans. Electron Devices, Vol. ED-8, pp. 243-251, July 1961. [57] Talcott, The effects of titanium films on secondary electron emission phenomena in resonant cavities and at dielectric surfaces, IRE Trans. Electron Devices, Vol. ED-9, pp. 405-410, Sept. 1962. [58] Vaughan, Multipactor, IEEE Trans. Electron Devices, Vol. ED-35, pp. 1172-1180, July 1988. [59] Tomiyasu, Diode oscillations in high voltage klystrons, IRE Trans. Electron Devices, Vol. ED-8, pp. 243-251, July 1961. [60] Tomiyasu, Method for suppressing diode oscillations in high voltage klystrons, IRE Trans. Electron Devices, Vol. ED-8, pp. 381-386, Sept. 1961. [61] Blotekjar et al. "Optimum RF Field Distribution of Monotron Cavities," USAF RADC Contract AF 61 (052)-264 (RADC TN 61-14), Sept. 1960. [62] Skolnik, Radar Handbook. New York: McGraw-Hill, 1970. [63] Ewell, Protection of medium power pulse klystrons, Power Modulator Symp., San Diego, June 1990. [64] Anon, "Recommendations for Cooling High Power Klystrons," Publ. No. 2071 (AEB17A). Varian Assoc., Palo Alto, CA. [65] Anon, "General Procedure for Flushing and Back-Washing Liquid Cooled Klystrons," Publ. No. 2070 (AEB-17B). Varian Assoc., Palo Alto, CA. [66] Anon, "Cleaning and Flushing Klystron Water and Vapor Cooling Systems," Publ. No. 3364 (AEB-32). Varian Assoc., Palo Alto, CA. [67] Grant, A powerful quality assurance technique for dispenser cathodes and electron guns, IEEE Int. Electron Devices Meet., pp. 334-339, 1984.

CHAPTER

2 Magnetrons Wayne Love

I. Introduction IVlagnetrons are devices which are efficient generators of microwave energy. They were the first device capable of generating high-power microwaves and were instrumental in the development of the first radar systems used in World War II. They are vacuum diodes that are made up of circular resonant cavities around a cathode immersed in a perpendicular magnetic field. This magnetic field results in a force that changes the motion of electrons from a straight path to one that is curved. It is this curved motion that allows for a simple and efficient means of electron bunching that abstracts pC energy from the electrons to the RF field to produce the high-power microwave output. There are two types of magnetrons. Pulsed magnetrons have very high peak output power (kilowatts to several megawatts) of a very short duration. The anode voltage is turned on and off hundreds of to ten thousand times a second, allowing high peak power but maintaining low average or total power over time. Current frequency ranges for pulsed magnetrons are less than 1 GHz to over 5 GHz. Pulsed magnetrons are still used in radar applications, but they will not be specifically discussed in this chapter as this book is on microwave power. Much of what can be said about continuous wave magnetrons are also true about pulsed-type magnetrons. Continuous wave (CW) magnetrons have continuous output power from a few watts to up to 10 kW. The most common application of the CW

Handbook of Microwave Technology, Volume 2

33

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

34

Wayne Love

magnetron is in the home microwave oven. Millions of these magnetrons are made on highly automated production lines every year. Most CW magnetrons oscillate at a frequency of 2450 or 915 MHz, but CW magnetrons have been developed at other frequencies. The field of microwave energy has more applications now than just a few years ago. The reasons to use microwave energy over other methods of heating include lower cost, ease of operation, process cleanliness, environmentally cleanliness, limited space, and it may be the only method of heating the material or process. Applications include the following: Cooking food Removal of moisture Generation of plasma Extruding rubber Destruction of waste

Pasteurizing waste Sintering ceramic Heating of chemical reactions Medical applications Mineral processing.

The consumer oven magnetrons have output power of under 1 kW and typically cost under $150 mainly because of demand and manufacturing techniques. Because of this demand, there is intense competition among the manufacturers that make these magnetrons. These manufacturers also have relatively large expenditures for research and development of new magnetron types and processing. Most of the assembly lines that make consumer-type magnetrons are completely automated. Home cooker magnetrons are generally air cooled and have very short warm-up times before they start to operate. They also have a relatively short life expectancy of under 100 hr, but they are typically used only a few minutes a day. Microwave ovens have different power settings which are achieved by turning the magnetron on and off every few seconds, giving different average output powers. Commercial oven magnetrons are much like their consumer magnetron counterparts but only with higher output power (1 to 2 kW). They are used in catering, cafeteria, and institutional settings, where there is a need for warming or cooking a larger quantity of food. Some of these magnetrons are water cooled because of the higher output power, and some of these higher power magnetrons are manufactured by the cookertype manufacturers. Plasma generation is a field that is growing rapidly. The microwaves are used to excite gas at partial pressure to generate a plasma glow discharge. This glow discharge can be used for deposition or removal of materials at relatively low temperatures. Plasmas can be generated at RF frequencies, but as the frequency increases ion bombardment is less intense. This lower level of ion bombardment causes less damage to the substrate materials that it is being used on. The requirements that are

35

2. Magnetrons

placed on these magnetrons are output power stability and, in some cases, frequency stability. The generation of the plasma glow discharge will cause the output power of the magnetron to change. This change in output power can be a problem if it is too great. Special cooling is required in some cases because these magnetrons are often operated in ultra-clean clean rooms. Industrial magnetrons have output power from over 2 to 10 kW. They almost always operate at frequencies of 2450 and 915 MHz and are almost all water cooled. Some of these magnetrons also have air cooling because of the heat that is generated during operation. Most of the industrial magnetrons are made on labor-intensive production lines because of the relatively small quantity made every year. Their construction is more rugged than the cooker magnetrons, and they typically have a longer life. Because of a wide variation of applications, the equipment manufacturer must ensure that the proper conditions for the operation of the magnetron are in place.

2. Microwaves Microwaves are part of the electromagnetic spectrum with wavelengths much shorter than the wavelengths of the radio broadcast spectrum. They are given by the relationship A = C/f,

where A is the wavelength in meters, f is the frequency in cycles per second (Hz), and C is the speed of light (3 x 108 m/s). Microwaves can be directed, much like water in a pipe, through coaxial lines or waveguides. Coaxial lines are two concentric metallic conductors separated by a nonconductor. They are often flexible but generally cannot transmit large amounts of power. Using common-size coaxial lines and connectors, only a few hundred watts can be transmitted. For many applications, waveguides are the better choice, as they are able to transmit high power. Waveguides are metallic tubes of a circular or rectangular cross section of specific dimensions. It is these dimensions which determine what frequency of microwave radiation a waveguide can propagate. The magnetron can be attached to and inject microwaves down the waveguide. The microwaves propagate down the waveguide as a sinusoidal wave. If the work or load absorbs all of the wave, then there is no reflection. This occurs when the resistive load and the source load have equal impedance. This condition is called matched load.

Wayne Love

36 VS~

f

~METER

/

VOLTAGE- ~ STANDING

<~

MICROWAVE REFLECTED

WAVE

Figure I. Method for measuring the voltage standing wave ratio.

If the load impedance is not the same as the source impedance, then all of the power is not absorbed by the load and some of it is reflected. The reflected wave then combines with the transmitted wave, resulting in a wave for which only the amplitude varies and the position stands still. The maximum and minimum amplitudes have not changed and can be measured as a ratio. This ratio is called the voltage standing wave ratio, or VSWR. It is important that the VSWR of the load is known, because, if a VSWR is too high, an appreciable amount of energy will be reflected back to the magnetron which could cause severe damage. If the load changes, the VSWR also changes. The VSWR can be written as VSWR = Vmax/Vmi n -=- ( V i --1-V r ) / ( V i - Vr), where Vi and Vr are the voltage due to the incident and reflective wave, respectively. The VSWR can be measured with a network analyzer or using a piece of waveguide with a slot cut into the side into which a probe that measures voltage is inserted. This is called a slotted line. The voltage can then be measured at the maximum and minimum (Figure 1). This is done with a small microwave signal injected into the waveguide with the load in place. Figure 2 shows the percentage of energy that is reflected as the VSWR changes.

3. Components of the Magnetron The magnetron is a crossed-field vacuum tube. This means that the flow of electrons, the electric field, and the magnetic field are mutually perpendicular to each other. Figure 3 shows the essential components of the magnetron.

37

2. Magnetrons

VSWR 1.00

Power Trans. (%) 100

Power Refl. (%) 0

VSWR 1.25

Power Trans. (%) 98.8

Power Refl. (%) 1.2

1.01

100

0

1.26

98.7

1.33

1.02

100

0

1.27

98.6

1.4

1.03

100

0

1.28

98.5

1.5

1.04

100

0

1.29

98.4

1.6

1.05

99.9

O. 1

1.30

98.3

1.7

1.06

99.9

0.1

1.32

98.1

1.9

1.07

99.9

0.1

1.34

97.9

2.1

1.08

99.9

0.1

1.36

97.7

2.3

1.09

99.8

0.2

1.38

97.5

2.5

1.10

99.8

0.2

1.40

97.2

2.8

1.11

99.7

0.3

1.42

97.0

3.0

1.12

99.7

0.3

1.44

96.7

3.3

1.13

99.6

0.4

1.46

96.5

3.5

1.14

99.6

0.4

1.48

96.3

3.7

1.15

99.5

0.5

1.50

96.0

4.0

1.16

99.5

0.5

1.52

95.7

4.3

1.17

99.4

0.6

1.54

95.5

4.5

1.18

99.3

0.7

1.56

95.2

4.8

1.19

99.2

0.8

1.58

94.9

5.1

1.20

99.2

0.8

1.60

94.7

5.3

1.21

99.1

0.9

1.62

94.4

5.6

1.22

99.0

1.0

1.64

94.1

5.9

1.23

98.9

1.1

1.66

93.8

6.2

1.24

98.9

1.1

1.68

93.6

6.4

F i g u r e 2.

Voltage standing wave ratio, percentage

of

transmitted power, and reflected power,

Cathode

The cathode is the source of electrons and has a negative potential with respect to the anode. It is usually tungsten wound in the shape of a helix

38

Wayne Love

VSWR 1.70

Power Trans. (%) 93.3

Power Refl. (%) 6.7

VSWR 7.00

Power Trans. (%) 43.7

Power Refl. (%) 56.3

1.72

93.0

7.0

7.50

41.5

58.5

1.74

92.7

7.3

8.00

39.5

60.5

1.76

92.4

7.6

8.50

37.7

62.3

1.78

92.1

7.9

9.00

36.0

64.0

1.80

91.8

8.2

9.50

34.5

65.5

1.82

91.5

8.5

10.00

33.1

66.9

1.84

91.3

8.7

11.00

30.6

69.4

1.86

91.0

9.0

12.00

28.4

71.6

1.88

90.7

9.3

13.00

26.5

73.5

1.90

90.4

9.6

14.00

24.9

75.1

1.92

90.1

9.9

15.00

23.4

76.6

1.94

89.8

10.2

16.00

22.1

77.9

1.96

89.5

10.5

17.00

21.0

79.0

1.98

89.2

10.8

18.00

19.9

80.1

2.00

88.9

11.1

19.00

19.0

81.0

2.50

81.6

18.4

20.00

18.1

81.9

3.00

75.0

25.0

25.00

14.8

85.2

3.50

69.1

30.9

30.00

12.5

87.5

4.00

64.0

36.0

4.50

59.5

40.5

5.00

55.6

44.4

5.50

52.1

47.9

6.00

49.0

51.0

6.50

46.2

52.8

Figure 2. (Continued)

with a layer of carbide on the outer diameter. The cathode must be heated to emit electrons. This is accomplished in the CW magnetrons in two ways: (1) direct heating of the cathode (filament) by passing electric current

39

2. Magnetrons

INDIVIDUAL RESONANT CAVITY STRAPS

VANE TIP END SHIELDS- - ~ CATHODE

Figure 3. Partial sections of a cathode and an anode. The interaction section is the area between the cathode and the vane tips.

through it and (2) electrons in an oscillating magnetron returning to the cathode, causing heat. This is called back-bombardment and can generate substantial heat. Back-bombardment will be explained in more detail below, but also can cause damage to the cathode if it becomes excessive. This back-bombardment increases as the output power in a magnetron increases. In order for the cathode temperature to remain constant, the filament current applied to the cathode must be decreased as the output power, and back-bombardment, is increased. This is given as a curve called the filament reduction curve (Figure 4). It is important to know that this curve must be followed, as too small a cathode temperature will cause insufficient electron emission and too high a cathode temperature will cause overheating of the cathode. Both conditions will cause permanent failure of the cathode (Figure 5).

40

Wayne Love

>v LU

m

c-

E .

m

In

Anode Current (mA) Figure 4. Filament voltage reduction with an increase in anode current. The filament voltage with zero anode current is called the standby voltage.

The cathode has a layer of tungsten carbide on the outside diameter and is said to be carburized. The purpose of this coating is to reduce the temperature that is needed to emit electrons and increase life by retarding the migration of thorium. Thorium is a metal that is added to the tungsten to aid in emission. A by-product of this chemical reaction is the formation

OVER TEMPERATURE ~

\,,

/NOMINALTEMPERATURE

I TIME

Figure 5. Graph showing cathode life with cathode temperature.

41

2. Magnetrons

of CO and C02, both of which are gasses. This gas must be absorbed by getters that are placed inside the vacuum tube. The end shields of the cathode prevent the escape of electrons from the vane tip area, which is called the interaction region. The cathode is in the interaction region and is part of the resonant system. Energy can couple into the cathode and be transmitted by the cathode through the input. Many magnetrons have a filter system at its input to reduce this unwanted microwave radiation. Anode

The anode is usually made of copper to minimize microwave losses and is a set of resonant cavities placed around the cathode. It has an equivalent LC circuit in parallel, as shown in Figure 6. The inductor is representative of the individual cavity that is between two vanes. The capacitance is representative of the area at the vane tips. This LC circuit has a resonant frequency of oscillation that is called the PI mode. The PI mode is the most efficient mode of operation, but there are other modes of oscillation that are unwanted. If the magnetron is oscillating in these other unwanted modes, it is said to be moding. These unwanted modes of oscillation are close to the PI mode, but there are methods to separate the PI mode from the others: the strapping of vanes with a conductor, the use of a rising-sun anode, and the use of the coaxial

Figure 6. LC circuit equivalent for a I O-cavity unstrapped magnetron,

42

Wayne Love

magnetrons. The strapping of the anode is the most common method for continuous wave magnetrons. In the strapping method, conducting straps are attached to alternate vanes. In the PI mode, alternate vanes are at the same potential; thus no additional inductance is introduced by the straps. The straps will change the capacitance, and the PI mode frequency will be separated from the unwanted modes. Moving the position of these straps can shift the operating frequency of the magnetron by changing the capacitance of the circuit. This is one method to set the resonant frequency of the magnetron during assembly. When modes other than the PI mode are present, the alternate vanes are at different potentials from each other and the straps will introduce both inductance and capacitance. Because of the different potentials on the alternating vanes, there are currents that flow through the straps. If the current becomes too great, the straps can burn out. For this reason, it is essential that the magnetron not be allowed to operate while it is moding. The anode must also be able to dissipate large amounts of heat caused by the electrons that strike the vane tips. Some of the industrial magnetrons have to dissipate over 3000 W of power while operating. Most of

Manufacture I

Parts

e°c° Incoming

Parts

Cold Test

Chemical Process

Final Vacuum

eoCo Vacuum

Leak

Check

Carburize

Post Exhaust Process

eoCo Sub Assy.

(inc. welding I and brazing) I

Seal

Catho~

I Sub Assy. I

Assemble

Basing

Magnet Charge

Exhaust and Exhaust Processing

Age & Test

Ship

Figure 7. Flow chart showing the essential processing of CW magnetrons,

43

2. Magnetrons

this energy is at the tips of the vanes, so the design and heat transfer away from the tips must be maximized. Most of the high-power magnetrons are water cooled or cooled by a combination of water and air.

Output The output is the means of coupling the microwave energy from the cavities to the waveguide. It is usually a loop in one of the cavities to extract energy or a coaxial type which is a conductor that is connected to a vane. It is important that the output be hardy enough that it may transmit the energy from the cavity to the waveguide. It must also not change shape or position during handling or processing. All of the CW magnetrons must have the above parts, and most are assembled and processed similarly. Figure 7 shows a flow chart that is typical for industrial types but could also be used for other types of CW magnetrons.

4. Space Charge Without a magnetic field, the magnetron would act as a diode (Figure 8). Electrons emitted from the cathode would travel radially outward in a straight path to the anode. There is a force on the electron due to the electric field of - e E . In the presence of a magnetic field that is perpendicular to the electric field, there is a force of (e/c)v on the electron in addition to the electric field force. This magnetic field impedes the path of

Figure 8. Cathode and anode with an electron path (a) in a diode, (b) in the presence of a high magnetic field, and (c) in a magnetic field at the Hull cutoff voltage.

44

Wayne Love

Region of / Current ] t~ 1===4

o

o

Magnetic Field Figure 9. The Hull cutoff voltage for a magnetron of specific dimensions.

the electron. The path of the electrons is now circular, which provides an efficient means of bunching of the electrons which is the method increasing the power output. There is an anode voltage that in the presence of the magnetic field and electric field of the electrons just reaches the anode and current flow. Below this voltage there is no current flow. This voltage is called the Hull cutoff voltage and is dependent on the magnetic field, the electric potential, the radius of the anode, and the radius of the cathode (Figure 9). In the presence of a PI-mode electromagnetic field, there are alternating positive and negative voltages on the vanes. If an electron leaves the cathode into an accelerating field, the electron will speed up and extract energy from the electromagnetic field. These higher energy electrons will be greatly affected by the magnetic field and will be returned to the cathode. This causes heating of the cathode and is the back-bombardment talked about earlier. As the anode voltage is increased, so this backbombardment and the filament voltage must be reduced to keep the cathode temperature constant. Electrons that enter the electromagnetic field from a decelerating field give up some of their DC energy to the electromagnetic field. If the angular velocity of the electron is such that it is always in a decelerating field, then almost all of the energy is given up to the electromagnetic field and strikes the anode (Figure 10). Because there are regions of electrons that are a decelerating field and not in an accelerating field and because these regions move with an angular frequency proportional to the resonant cavity frequency, there is a

45

2. Magnetrons

___3 Figure 10. Electron a enters the electromagnetic field at time TI into an accelerating field and gains energy, It interacts with the magnetic field and spins back to the cathode. Electron b enters the electromagnetic field at T~ and is decelerated, losing energy to the electromagnetic field. At T2 the electron again is in a decelerating field and the electron loses more energy,

cloud of electrons with spokes like that of a wheel (Figure 11). The number of spokes is ~1 the number of cavities. As the spokes move in a decelerating RF field, the electrons that are toward the negative potential vane are decelerated while the electrons close to the vane with positive potential are accelerated. This causes the electrons in the spoke to bunch even further. The bunching of the electrons in each spoke tends to keep the spokes equally spaced. Electrons that do hit the anode have nearly given up their energy.

Figure II. Electron cloud showing "spokes" of anode current,

46

Wayne Love

5. Magnetic Field The magnetic field causes the circular path of the electrons in the electron cloud. It must be as close to parallel in relation to the axis of the cathode as possible in the interaction region. It is also important that the field not change with time in order to keep the output power constant. The magnetic field can be formed from permanent magnets or electromagnets. Permanent magnets can lose their flux by moving or removing any part of the magnetic circuit or by removal of magnetic charge. The magnetic charge can be removed by bringing the magnetron close to iron, including setting it on a metal shelf for storage. These conditions will change the magnetic field and the magnetron must be returned to the manufacturer to be recharged. The permanent magnet magnetrons are sold with the magnets in the magnetic circuit. This adds to the price of the magnetron but is a small percent of the total cost. No additional cost or equipment is required. The electromagnet version requires a separate power supply for the electromagnet. The electromagnet is not temperature stable as the resistance of the coil will change with temperature. Feedback circuits can be used to adjust the input power to the electromagnet. The electromagnet and most of the magnetic circuit is purchased only once. It is only the vacuum tube that needs to be replaced. Replacement may be a little more difficult as the magnetic field may need to be fine tuned to match each magnetron's characteristics.

6. Power Adjustment There is a need for the output power of the magnetron to be varied. Several methods are used to change the power that is applied to the work or load. They include the following: Pulsing the output power of the magnetron. Changing the anode current. Changing the magnetic field. Adjusting the microwave energy that goes to the load.

Pulsing Pulsing the output power of a magnetron to vary the power to the load is a common method that is used in most home cooker ovens. This is not the same as that employed for pulsed magnetrons that are used in radar

47

2. Magnetrons

systems. These cooker oven magnetrons are pulsed very slowly, sometimes on for 2 to 5 s and then off for 2 to 5 s. In this manner, the average power to the load can be controlled. There must be a timing circuit in the power supply which adds complexity and cost. The power to the load is not continuous, which is not compatible with industrial applications. Highpower industrial magnetrons must follow a filament reduction curve. This means that for most industrial magnetrons there is a typical filament warm-up time of 5 to 20 s at the filament stand by voltage, and then the filament voltage is to be reduced after the anode current is increased. This filament warm-up time is greater than the entire o n / o f f cycle above and virtually rules out the use of this type of power adjustment. The home cooker magnetron has no filament reduction, and the power is not continuous and is not a problem for this application. Reduction of Anode Current The reduction of anode current is another method of adjusting the output power. A change in input power will result in a change in output power. The output power of a magnetron is directly proportional to the anode current. Figure 12 shows the relationship between anode voltage and anode current. Note that as the anode voltage increases initially there is little anode current. This small "leakage" current has not been adequately explained. At a voltage that is determined partially by the magnetic field, current will start to flow and the magnetron will start to oscillate. This voltage is called the Hartree voltage and is dependent on the magnetic

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~,, ~ i ' ~ J ~

~ml m

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C~

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Hartree Voltage

I I

0t--

Anode Current (mA) Figure 12. Anode voltage vs anode current, At the Hartree voltage, the magnetron starts to oscillate.

Wayne Love

48

/ Anode Voltage

t~ 0

/

>

0 c-

<

jy

/"

/

"-1 m

o=._ O 13..

Anode Current Figure 13. Performancecurve adjustingthe power by anode current.

field, the anode radius, the cathode radius, and the wavelength. In the oscillating region, a large change in anode current will give a small change in anode voltage. Most power supplies are current stabilized to maintain output power. Figure 13 shows the output power versus the anode current. The anode voltage is also presented on the same graph. This is called a performance curve and is usually in the data sheet of the magnetron. It is noted that the filament voltage must be increased as the anode current is reduced. This method of adjusting the output power requires that the power supply be able to adjust the anode current. This results in a more costly supply, but it is a method that does allow the magnetron to operate continuously, which is required in most industrial applications.

Adjustment of Magnetic Field Another method of power adjustment that is possible is to change the magnetic field. Figure 14 shows anode voltage versus anode current curves with changing magnetic fields. Note that the curves are identical except that they are offset with the higher anode voltage needed as the magnetic field increase. It also shows that the power is reduced as the magnetic field increases.

49

2. Magnetrons

ANODE Figure 14. Graph showing the performance of a magnetron with changing magnetic field,

Figure 15 shows the output power versus the magnetic field for a specific magnetron. A change of 10% in magnetic field will change the output power by 60%. Changing the magnetic field requires a separate power supply to power an electromagnet, but it can be a low power supply. This low power supply is isolated from the high voltage supply and can easily be adjusted to give the desired output power. Many of the indus7000

. . . . . . . 8000

.

,,i

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.

.

.

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.

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Figure 15. Output power vs magnetic field for a 6-kW magnetron, A small change in magnetic field results in a large power output change,

50

Wayne Love

I1 I 1 I 1 Magnetron

Power Splitter

Power

Splitter

Power Splitter

J LJ I ]

Figure 16. Method of splitting/reducing power to loads.

trial-type magnetrons have both a permanent and an electromagnet magnet in one package, whereas others use just an electromagnet. Again, this method allows for continuous operation and easy power adjustment.

Attenuation of Microwave Energy There is another method of power adjustment to the load that does not have any affect on the magnetron. It involves attenuating the microwave energy between the magnetron and the load, but it is a mechanical method and is complex and very costly. Along the same lines are splitting the microwave energy and coupling it into multiple loads (Figure 16). This allows the use of just one magnetron and power supply, which could be a large cost savings over multiple magnetrons and power supplies. It does utilize power splitters or directional couplers in waveguide systems if the power is high or coaxial systems if the power is low. A major disadvantage is, if the system has a fault power to a load or group of loads that cannot be shut down, the entire system must be turned off for repair. This could lead to expensive equipment down time.

7. Rieke Diagram The Rieke diagram (Figure 17) is a circular diagram which, for fixed input conditions, shows the output power and in which the frequency change of the magnetron is plotted against the phase and the magnitude of the VSWR. This is the load as seen by the magnetron and is measured from a

51

2. Magnetrons 0,40X

0,35),

\

/

o,3oX.\

/0,45X /

0,25),--

---0 reference plane

/° o,2ox/ ~ ' , ~ ~ " ' y , ~ , , ~

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Figure 17. Rieke or load diagram. The "sink" phase is also the phase of maximum output power.

reference point that is specified by the magnetron manufacturer. The phase angle is the distance from the reference point measured in relation to the wavelength, and the magnitude is minim~am at the center and maximum at the outer diameter. There is a region in which, with a mismatched load, the power is high and the frequency contours converge. This is known as the "sink phase" and is the region in which the magnetron must be operated. The magnetron should be not operated "out of sink." There are other regions that the magnetron is allowed to operate in and will be shown on the Rieke diagram supplied in each data sheet.

8. Power Supplies The term continuous wave magnetron implies that the output power is continuous and consistent. This is not correct in reality, as the smoothness

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Wayne Love

FREQUENCY Figure 18. The output spectrum using a three-phase full-wave rectified, smoothed power supply.

or ripple on the anode voltage tend to change the output spectrum. Figures 18-20 show the output spectrum of the same magnetron under the same operating conditions except for the type of power supplies, as shown.

FREQUENCY Figure 19. The output spectrum using an LC stabilized power supply.

53

2. Magnetrons

FREQUENCY Figure 20. The output spectrum using a single-phase full-wave rectified power supply. This is the power supply recommended for this magnetron.

9. M a g n e t r o n - System Interface General

Cooling Cooling must be performed in an environment free of oils and dust and at the pressure specified by the manufacturer. The temperature must not be too much over room temperature. The temperature and air pressure should be measured at the magnetron, and the air should be filtered. The filters should be checked and cleaned often. Water-cooled magnetrons must have the correct water flow and temperature. The water jacket and water carrying system should be checked for blockage and leaks every time the magnetron is operated.

Protection Monitoring for microwave leakage for the protection of the operators should be present. The system should be interlocked in such a way as to turn off the high voltage and stop the oscillation should the leakage become too high.

54

Wayne Love

All magnetrons should be operated using a thermoswitch which shuts off the high voltage in the event of improper cooling. The system should also be monitored for overcurrent and overvoltage. Overcurrent can occur when there is an internal arc that can cause damage to the magnetron. There should also be an arc detector in the waveguide that should shut off the high voltage and the oscillation. This can prevent damage to the waveguide components and the magnetron. Ideally, the reflection of power back toward the magnetron should be monitored and the high voltage turned off if it becomes too high. An alternative is the use of a circulator which isolates the magnetron from the reflected power. The magnetron must be connected to the correct launching section. This sets the correct VSWR and the height of the antenna into the waveguide. This is important because, if the antenna is too close to the waveguide, the electromagnetic field becomes very intense, causing arcing from the waveguide to the antenna. This could damage the magnetron or the waveguide. The magnetron must also be tightly connected to the launching section with the output gasket fully compressed. Failure to do so will allow microwave leakage and can burn the gasket, output, and launcher due to the high energy that is present at this loose connection. The input contact must also make good contact as the filament current should not be lost at the input as resistive losses. The filter box, if supplied, should never be tampered with. The inside of the filter box and the components in the filter box form a filter, and tampering with the components or filter box may change the filtering.

General Handling Magnetrons have brittle cathodes and are fragile. They should be handled with care. Even tapping on the same table that the magnetron is on could break the filament. The output ceramic should be kept clean. As the ceramic becomes dirty, less microwave energy is transmitted. This could cause the temperature to become too high and crack the ceramic output. If the magnetron has been stored for a long period of time, it may be 1 beneficial to operate the filament standby voltage for ~ to 1 hr with the proper cooling on. Magnetrons that are stored will generate a small amount of residual gas. Operating the filaments will activate the getters to reduce the amount of gas in the magnetron. Magnets and magnetic material should be kept away from the magnetron as this will affect the magnetron's magnetic field during both operation and storage.

55

2. Magnetrons

Common Problems and Causes Problem

Possible cause

Low power output

Incorrect anode current Incorrect V S W R Incorrect filament voltage Incorrect magnetic field Incorrect power supply Incorrect V S W R Dirty output Incorrect launching section Dirty waveguide Too high output power Incorrect filament voltage End of life Gas in magnetron Incorrect filament voltage Incorrect V S W R End of life Short filament warm-up time Gas in magnetron Incorrect power supply Mechanical stress D a m a g e from arcing Incorrect cooling Dirty i n p u t / o u t p u t

O u t p u t arcing

Emission drops

Moding

Broken i n p u t / o u t p u t

Additional Reading Colins, G. B. Microwaue Magnetrons, MIT Radiation Laboratory. Series. New York: McGraw-Hill, 1948. Gilmour, A. S., Jr. Microwaue Tubes Dedham, MA: Artech House, 1986. Metaxes, A. C., and Meredith, R. J. Industrial Microwave Heating. London: Peter Peregrinus, 1983. Montgomery, C. G. Technique of Microwaue Measurements, MIT Radiation Laboratory Series. New York: McGraw-Hill, 1947. Philips Data Book, Magnetrons for Microwaue Heating. 1989. Sander, K. F. Microwaue Components and Systems Wokingham, Engl: Addison-Wesley, 1987. Slater, J. C., Microwave Electronics. Princeton, NJ: Van Nostrand, 1950. Terman, F. E., Electronic and Radio Engineering, 4th Ed. New York: McGraw-Hill, 1955.

This Page Intentionally Left Blank

CHAPTER

3 Traveling-Wave Thermionic Devices Jeffrey D. Wilson

I. Introduction rT~

l r a v e l i n g - w a v e thermionic devices are vacuum tubes that generate or amplify microwaves. This chapter will cover slow-wave devices in which energy is delivered to the microwave field through interaction with electrons produced by a cathode and traveling with a velocity approximately equal to the phase velocity of the microwave. The two main categories of slow-wave devices are linear beam (O-type) and crossed-field (M-type). Their general characteristics are compared in Table 1. The applications, operation, and performance of cathodes, electron guns, electron beam focusing, linear-beam traveling-wave tubes, linear-beam backward-wave devices, magnetrons, crossed-field amplifiers, and crossed-field backward-wave oscillators will be summarized in this chapter.

2. Cathodes Thermionic Emission Thermionic emission results when a heat source supplies the electrons near the surface of a cathode with enough energy to overcome the

Handbook of Microwave Technology, Volume 2

57

58

Jeffrey D. Wilson TABLE I Linear-Beams vs Crossed-Field Devices

Linear-beam devices

Crossed-field devices

Beam parallel to DCelectric and DCmagnetic fields

General electron direction, pc electric field, and PC magnetic field orthogonal Difficult to analyze Moderate gain Very high efficiency and power Light weight Usually high noise

Analyzable High gain Moderately high efficiencyand power Heavy weight Relatively low noise

potential barrier at the surface. It is used as the electron beam source in all linear-beam and most crossed-field devices. Saturated Emission

The saturated or temperature-limited emission current density is given approximately by the R i c h a r d s o n - D u s h m a n equation, J = Ao T2 exp (-4~/kT),

(1)

where T is the absolute temperature, e is the electronic charge, k is Boltzmann's constant, A 0 = 1.20 × 106 (A/mZdeg2), and 4~ is the work function, which is the difference in energy between the top of the conduction band of the solid and the vacuum. Experimentally it is found that the work function is dependent on temperature and to a good approximation, 4~ = 60 + a T ,

(2)

where a is the temperature coefficient of change in work function [44]. Space-Charge Limited Emission

Under most operating conditions, negative space charge accumulates just outside the cathode and repels some of the emitted electrons to the cathode. The current is then less than the saturated value and is said to be space charge limited. The relationship between the cathode-to-anode voltage V and the cathode current I in a space-charge-limited diode is given by the Child-Langmuir law: I = P V 3/2,

(3)

where P is the perveance, which depends only on the geometry of the diode [44].

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Jeffrey D. Wilson

Emission Enhancement With the advent of modern surface analysis equipment, dramatic improvements in thermionic cathode emission capabilities have been achieved since 1970 [103]. An active research effort is currently being directed to an improved theoretical understanding of the thermionic emission mechanism, and it is expected that this will further advance cathode capabilities [54, 86].

Thermionic Cathode Types Some of the more common thermionic cathode types along with their compositions and characteristics are listed in Table 2.

Secondary Emission Electrons bombarding a surface cause other electrons, known as secondary electrons, to be emitted. This secondary emission is very important in crossed-field devices and can provide the major and sometimes entire source of current. Thermionic cathode materials with significant secondary emission that are commonly used in crossed-field devices are platinum, thoriated tungsten, beryllium oxide, and aluminum oxide [44, 78, 99].

3. Electron Guns An electron gun consists of a cathode electron source with focusing electrodes that produces an electron beam for interaction with the microwave field propagating in the slow-wave circuit. The two principal parameters of electron gun design are perveance and convergence ratio.

Perveance The perveance, defined by Equation (3), is a measure of the current obtainable with a given voltage and is a function of only the gun geometry. Typical values of gun perveance range from 0.01 x 10 -6 to 1.5 x 10 -6 A / ( V ) 3/2 (pervs) [49]. Relative advantages of high versus low perveance guns are given in Table 3.

Convergence Ratio The convergence or compression ratio is the ratio of the cathode area to the minimum beam area. The higher the convergence ratio, the higher is

61

3. Traveling-Wave Thermionic Devices TABLE 3 Factors Considered in Selecting Gun Perveance for a "I'WT (Hansen [49]) Factors that favor high perveance

Factors that favor low perveance

Low voltage usually avoids breakdown RF performance is better, especially for broadband operation Gain per unit length is higher

Lower magnetic focusing field Electron gun easier to design Slow-wave circuit has larger dimensions Higher collector efficiency

the beam current density that can be produced. However, higher convergence ratios give rise to greater beam spreading due to transverse electron velocities and geometrical misalignments. Typically convergence ratios are in the range of 10:1 to 50:1 [49]. Electron

Gun Types

Pierce Gun

The most common type of gun design is the spherical-cathode solidbeam gun, also known as the Pierce gun [31, 90, 101, 108], shown in Figure 1. It is based on a conical segment of a spherical diode and has focusing electrodes positioned to maintain spherical equipotentials between the cathode and the anode.

Focus electrode -7 / Cathode7 / /.- / / ~- ~

/ - Shadow grid RF // input Control I " ~°il I / / - grid /

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62

Jeffrey D. Wilson

Hollow-Beam Pierce Gun A variation of this design is the hollow-beam Pierce gun [50, 109, 110], in which the cathode is ring shaped and a center focusing electrode is added. This gun can be used when a very high perveance is needed [101]. However, high convergence is much more difficult to obtain than in a solid-beam gun [50].

Magnetron Injection Gun Both a large convergence ratio and a large perveance can be achieved with a magnetron injection gun [20, 67, 101, 115]. This gun produces a hollow beam with a design that utilizes a cylindrical cathode and a concentric anode. Magnetron injection guns are not often used in slowwave thermionic traveling-wave devices because they are difficult to design and produce chaotic beams [111].

Grids A single intercepting grid located close to the cathode can be used to control the beam current in a low-power TWT, that is, one with no more than a few hundred watts of beam power. Typically 10 to 20% of the beam current is intercepted by the grid. This becomes a problem in high-power TWTs but can be virtually eliminated by introducing a second grid known as the shadow grid, located next to the cathode, as shown in Figure 1. The shadow grid is at the cathode voltage and is aligned so that it suppresses electron emission from those portions of the cathode which would otherwise give rise to interception at the positively biased control grid [51, 101, 105, 106].

4. Electron Beam Focusing After its formation by the electron gun, the electron beam passes through the slow-wave circuit of the TWT. To prevent the circuit from intercepting electrons, the beam is contained at an approximately constant radius by an axial magnetic field.

Brillouin Flow The standard method of containing the electron beam is by providing a uniform axial magnetic field with a solenoid. In Brillouin flow [13, 43] the outward force resulting from the radial space-charge electric field of the

63

3. Traveling-Wave Thermionic Devices

beam is exactly balanced by the inward force of the axial magnetic field. The magnetic flux density required for Brillouin flow is given by 8.307

Bz =

× 10-41~/2 gl/4 a ,

(4)

where all quantities are in MKS units and B z is the axial magnetic flux density, I 0 is the beam current, V0 is the beam voltage, and a is the beam radius.

Confined Flow In practice, the interaction of the beam with the microwave (often referred to as RF, for radio frequency) signal produces significant changes in the beam density. Because of the sensitivity of Brillouin flow to perturbations, a large oscillating or scalloping beam edge radius can occur, resulting in unacceptable levels of beam interception. The amplitude of this beam ripple can be significantly reduced by linking magnetic flux to the cathode and increasing the axial magnetic field in the TWT body from 1.5 to 3 times the Brillouin value [45]. Confined or immersed flow results when practically all the magnetic flux in the TWT body threads the cathode. If the axial magnetic field is m times the Brillouin value, minimum scalloping is obtained if the cathode is in an axial magnetic field, B c, given by Bc=

B~r2o ~ r2 1

1 m2'

(5)

where r 0 is the beam radius and r c is the cathode radius [45].

Periodic Permanent Magnet Focusing Although a uniform magnetic field provides for the least beam ripple, a solenoid focusing magnet is large, is heavy, dissipates a large amount of power, and usually must be cooled by forced air or liquid. Because of these disadvantages, a solenoid is typically used only on very high power TWTs with very high current density beams. To reduce the weight of the focusing system, the vast majority of TWTs make use of periodic permanent magnet (PPM) focusing [43, 85, 97, 102]. In a PPM stack, the beam is surrounded by a series of typically 10 to 40 Alnico or samarium cobalt permanent magnet rings with alternately reversing magnetic fields, separated by iron pole pieces as shown in Figure 2. The weight of a PPM stack of n magnets needed to focus a given

64

Jeffrey D. Wilson Magnet -~

F Iron polepiece

\ S

Sectional view, showing two magnets

End view

tO

o O~ c

Figure 2. Periodic permanent magnet (PPM) focusing structure (Hansen [49]).

beam is between 1/n 2 and 1/n that of an equivalent single permanent magnet [43].

Thermal Beams Real electron beams do not possess true laminar flow due to the transverse velocity components of the electrons emitted from the cathode. These thermal velocities make it more difficult to contain the beam than if the flow were laminar, and thus a somewhat stronger focusing magnetic field is required [2, 52, 56, 90].

5. Linear-Beam Traveling-Wave Tubes Applications The most common traveling-wave thermionic device is the linear-beam traveling-wave tube [43-45, 49, 69, 82, 89]. Because of their very wide bandwidth and high power gain, traveling-wave tubes (TWTs) are extensively used in radar, space communications, and electronic countermeasure (ECM) systems.

65

3. Traveling-Wave Thermionic Devices

General Operation A simplified schematic of a T W T is shown in Figure 1. The electron gun produces an electron beam which is injected into a slow-wave circuit, which is usually a helix or coupled-cavity structure. An R F signal passes into the vacuum interior of the T W T through a ceramic window at the R F input and then propagates through the slow-wave circuit with a phase velocity approximately equal to the beam velocity. The beam and propagating R F signal interact such that energy is transferred to the R F signal. The amplified R F signal then passes out of the vacuum interior at the RF output, and the spent electron beam is absorbed by the collector.

Helical Circuit The most common slow-wave circuit for TWTs is the helix, as represented in Figure 1. The helix has a virtually constant phase velocity over a wide range of frequencies and has by far the largest bandwidth of any T W T slow-wave structure. It possesses a high-interaction impedance and is thus able to produce a high gain in a short length. State-of-the-art output power versus frequency for CW helix and helix-derived TWTs (to be discussed later) is shown in Figure 3.

100

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6 10 20 Frequency, GHz

40 60 100

Figure 3. State-of-the-art peak and average output power for helix and helix-derived traveling-wave tubes (Hansen [49]).

Jeffrey D. Wilson

66

Dispersion Relationship By approximating the helix with a helically conducting sheet [45, 89], one obtains the following relationship,

( ya)2io( ya)Ko( ya)

(to =

II(Ta)KI(Ta )

--acotqJ

c

)2 ,

(6)

where I0, I1, K0, and K 1 are modified Bessel functions, a is the helix radius, 0 is the helix pitch angle, to is the angular frequency, c is the speed of light, and 7 is the radial propagation constant,

3' = to

2

Up

C

2 ,

(7)

with v o being the phase velocity. A graphical solution of Equations (7) and (8) gives a practically constant value for the phase velocity over a wide bandwidth. A good approximation is v o = c tan qJ.

(8)

Dispersion Shaping The naturally large bandwidth of a helix TWT can be extended into ultra-broadband operation over several octaves by modifying the boundary conditions around the helix. This dispersion shaping has been achieved by using dielectric supports, conducting shields, and longitudinally conducting wires and vanes [6, 63, 75, 80, 88, 92].

Interaction Impedance The interaction impedance for the fundamental mode of a helix is approximately 15c K 0 = M e~, toa

(9)

with M2 being the impedance reduction factor obtained by integrating the radial variation of the electric field over the cross section of the beam of area S [43]: 1

M 2=

SI2o( ya)

flJ( /r) dS.

(10)

3. Traveling-Wave Thermionic Devices

67

Figure 4. Contrawound helix slow-wave circuit (Cain and Grow [I 9], © 1990 IEEE),

Efficiency Enhancement In order to increase the efficiency of power conversion from the electron beam to the microwave signal, the helix pitch can be gradually decreased in the output section. This slows the axial propagation of the microwave signal in approximate synchronism with the decelerating electron beam. Such a circuit modification is known as a velocity taper and can strongly increase efficiency without degrading phase linearity [28, 73, 104]. Helix Derivative Circuits

Figure 4 shows the contrawound helix circuit [19, 23], consisting of two concentric helices wound with reversed pitches. Figure 5 shows the more common ring-bar circuit [8, 76]. Both of these circuits are capable of significantly higher power and efficiency than the single helix circuit. Their frequency bandwidths are significantly less, however, with a maximum capability of about 30%. Coupled-Cavity Circuit

The coupled-cavity circuit consists of a chain of inductively or capacitively coupled copper or copper-coated resonant cavities, with a common version represented in Figure 6. The axial phase velocity of the RF signal passing through the cavities is approximately equal to the velocity of the electron beam passing through the beam apertures (shown in Figure 6). Because this circuit can handle higher beam voltages and greater heat dissipation than the helix circuit, considerably higher peak and average

Figure 5. Ring-bar slow-wave circuit, (Cain and Grow [I 9], © 1990 IEEE),

68

Jeffrey D. Wilson /-- Ferrule

/-Coupling slot

/

/

. .

.

.

.

.

.

. .

.

.

.

.

.

.

.

L Beam aperture Figure 6. Coupled-cavity slow-wave circuit.

powers can be obtained from it. Another advantage is that the structure is ideally suited for PPM focusing. However, the frequency bandwidth capability is typically less than 10%, significantly less than that of the helical circuit. Peak- and average-power capabilities of PPM-focused and solenoid-focused coupled-cavity TWTs are shown in Figure 7.

Equivalent Circuit Analysis The dispersion and impedance properties of a coupled-cavity circuit can be estimated by an equivalent circuit analysis [21, 26, 45] or can be 1000 ==-

B.,,,,

u

~ ,

~ , ~ /

/ - Peak solenoid

100 _ - - . - ~

&

10 _--

0

I 2

J I = l llll I 4 6 10 2O Frequency, GHz

J I J l llll 40 60 100

Figure 7. State-of-the-art peak and average output power for solenoid and periodic permanent magnet (PPM) focused coupled-cavity traveling-wave tubes (Hansen [49]).

69

3. Traveling-Wave Thermionic Devices

obtained numerically by some of the computer programs listed later in this section. Usually the coupling slots (Figure 6) are small and the dispersion equation solution is of the form shown in Figure 8a with the "slot" pass band in a higher frequency range than the "cavity" pass band. This creates what is known as a fundamental backward-wave circuit because the fundamental harmonic in the cavity pass band has a negative phase velocity. Also shown in Figure 8a is the beam characteristic line, the slope of which is proportional to the electron beam velocity. The TWT operation takes place in the second harmonic of the cavity pass band at the intersection with the beam characteristic line. When the coupling slots are sufficiently large, the dispersion equation solution is of the form shown in Figure 8b. In this fundamental forwardwave circuit, the TWT operation takes place in the first harmonic of the cavity pass band. In order to suppress undesirable oscillations, resonant losses must be employed at the frequency corresponding to the intersection of the beam characteristic with the slot pass band curve [45]. Other fundamental forward-wave circuits are the centipede structure [45] and the cloverleaf structure [24, 45]. These types of circuits are used in high-voltage, high-power pulse applications [101]. Distortion Reduction

Coupled-cavity circuits produce significantly more amplitude and phase distortion with respect to frequency than do helical circuits. This distortion Slot pass band

Cavity pass

T ¢: o" =,. 14.

/ / /

/

/

/

/

I

/

I

Cavity pass band

I I I I I I Beam I characteristic

/

i I Beam characteristic

Slot pass band

i

/

I

I

9O

180

I

I

1

I

270 360 90 180 Phase change/cavity, deg

I

I

270 360

Figure 8. Dispersion curves and beam characteristic line for a fundamental backward-wave coupled-cavity traveling-wave tube slow-wave circuit.

70

Jeffrey D. Wilson Circuit

coupling

l~::i::i::i.-l~Jli;i;i;i~'~::i::ilili~il;i;iii~iiiiiiiii~iiiiil;i~r~i::iiiiii|

.o,o-oU=

=

Electron

beam

ii:.iiii, N

Web

N

N

N

Spacer

Figure 9. Ferrulelesscoupled-cavitycircuit (Wilson et al. [ 121], © 1990IEEE).

can be reduced an order of magnitude by eliminating the ferrules shown in Figure 6 and constructing the circuit with alternating copper "webs" and "spacers," as shown in Figure 9 [77]. A ferruleless coupled-cavity circuit has less interaction impedance per cavity than a ferruled circuit, resulting in a weaker feedback- and distortion-producing backward wave.

Efficiency Enhancement As in the helix circuit, the efficiency of a coupled-cavity TWT can be greatly increased by slowing the phase velocity of the microwave in approximate synchronism with the decelerating electron beam [119]. This technique has been shown to more than double the efficiency of a coupled-cavity circuit [121].

High-Frequency Circuits The upper frequency limit for useful helical and conventional coupled-cavity circuits is about 60 GHz. However, a type of low-efficiency coupled-cavity circuit known as the ladder circuit [60] has been successfully used to produce TWTs at frequencies up to 100 GHz. The ladder is produced by machining two copper "combs," or circuit halves, and joining them at the teeth. The ladder is then sandwiched between two cover plates as shown in Figure 10. The power and bandwidth characteristics of the ladder circuit are largely determined by the geometry of the coupling slots. A ladder circuit

71

3. Traveling-Wave Thermionic Devices

Flat cover plate-~

Coupling slot ~

• ~ - Slab

ladder

Beam

~/

~nnel-/: J " ~------ Alternate slots on back side

Flat cover / plate - J

Figure I0. Single-slot staggered ladder slow-wave circuit (Acker [I ]).

with an "in-line" coupling geometry has achieved 800 W average power and a 1000-MHz bandwidth at 95 GHz, whereas a circuit with a "doublestaggered" coupling geometry has achieved 100 W average power and a 20-GHz bandwidth at 90 GHz [60]. A t t e n u a t o r s and Severs

If the power reflection coefficients at the output and input terminals are, respectively, P0 and Pi dB below unity, the gain of the T W T is G dB, and the cold loss is L dB, undesired oscillations may occur when

G-L-po-Pi

> 0.

(11)

Typical values of these parameters limit small signal gain to about 26 dB and large signal gain to about 20 dB [45]. Thus to produce a higher gain it is necessary to use a two- or three-section circuit. In a relatively low power helix circuit, the sections can be separated by an attenuator, consisting of a lossy resistive coating applied to the dielectric rods supporting the helix. In high-power circuits, a sever is used to physically separate the sections. At the sever, each circuit section is terminated in a matched load [45].

72

Jeffrey D. Wilson

The attenuator or sever prevents oscillations by preventing reflections at the output terminal from reaching the input terminal. Although the attenuator or sever kills the forward-growing wave, current and velocity modulation remain on the electron beam to restart the microwave signal for further amplification in the next section. To minimize the gain degradation effect of an attenuator or sever, its length should be kept to a minimum and gain in the output section should be as high as possible [98]. Transitions and Windows

At the RF input and output of a traveling-wave tube, transitions must be made between the circuit and the feed waveguides. A transition with low reflection over a broad bandwidth can be designed by gradually altering the geometry of the circuit into that of the waveguide. However, such a transition has the disadvantage of being long and increasing the weight of the traveling-wave tube package. Thus usually shorter, more abrupt transitions are generally used, with a shunt susceptance placed in the waveguide to help minimize the impedance mismatch [45]. The input and output signals pass into and out of the vacuum interior of a traveling-wave tube through dielectric windows. The window design must provide high-power transmission and low reflection over the required frequency range. In general, good window dielectric materials should have a high value of the factor

• tan 6 '

(12)

where k is the thermal conductivity, e is the dielectric constant, and 6 is the "dielectric loss angle," the angle between the total current flowing in the dielectric and the displacement current that would flow in a similar, but loss-free, dielectric [45]. Electron Beam Collectors

Single-Stage Collectors The RF amplification process extracts only a small percentage of the kinetic energy from the electron beam, typically 5 to 30%. The remaining energy of the electrons in the spent beam can be absorbed with a simple cylindrical pot collector [45]. By depressing the voltage of the collector electrode to a value less than that of the circuit, the total power supplied to the TWT is reduced,

3. Traveling-Wave Thermionic Devices

73

resulting in an increase in overall efficiency as defined by n

=

[ Prfout ] / [

P0 + Ph + Pso, - Prec ],

where Prfout is the RF output power, P0 is the input beam power, Ph is the power supplied to the cathode heater, Psol is the power supplied to the solenoid if the TWT is solenoid focused, and Prec is the power recovered in the collector by decelerating electrons [defined in Equation (15)]. In a depressed collector circuit, the cathode-to-collector voltage Vc is typically 30 to 70% that of the cathode-to-anode voltage V0. The total power supplied is reduced from that for a TWT with a nondepressed collector, and the overall efficiency is improved by the factor

Zc

-~0 (1 -- ?~int) -+- Tlint

]-l

,

(14)

where Tlint is the fraction of the beam current that is intercepted on the anode and slow-wave circuit. Typical values for this factor range from 1.4 to 3.0 [45].

Multistage-Depressed Collectors A multistage depressed collector (MDC), which collects spent beam electrons on several electrodes at different depressed voltages, can increase the overall efficiency of a TWT to a much greater extent than is possible with a single-stage depressed collector [72]. MDCs can very significantly reduce power consumption by increasing overall efficiency in helical TWTs [32, 71], coupled-cavity TWTs [120], and klystrons [79]. In an MDC, the electrodes are designed to prevent primary and secondary electrons from backstreaming out of the MDC and to optimize the recovered power given by

Prec-

N E I V 0 - V, lln, n--1

(15)

where V0 is the beam voltage, Vn is the voltage on electrode n, and I, is the current collected on electrode n. The recovered power can be increased by treating the copper MDC electrodes to suppress secondary emission. The treatment involves either the application of various forms of highly textured carbon to the electrodes [27, 93, 94] or a direct texturing of the copper surface by ion bombardment [29]. Secondary emission suppression of the MDC electrodes can result in an increase in the TWT overall efficiency by an amount on the order of five percentage points [93].

74

Jeffrey D. Wilson

Simulation

Small-Signal Analysis In the TWT small-signal theory of Pierce [43, 89], it is assumed that the RF quantities are small compared with their D¢ counterparts so that nonlinear terms can be neglected in the equations of motion. Only the space harmonic of the circuit field in synchronism with the beam is considered, and it is assumed that RF motion of the electrons occurs only in the axial direction and that the DC forces are balanced by the focusing scheme. An equation for the current induced from the beam onto the circuit is combined with an equation for the signal on the circuit to determine the propagation characteristics of the circuit waves. The solution consists of four waves: a growing forward wave which contributes to the circuit gain, a decaying forward wave, a constant amplitude forward wave, and a backward constant amplitude wave. The following parameters are used in calculating the small-signal gain of a TWT.

Gain Parameter Kni

C =

]1/3

4Vo

,

(16)

with I 0 being the beam current, V0 being the beam voltage, and K n being the beam interaction impedance for the nth space harmonic (the electromagnetic field harmonic in synchronism with the beam).

Impedance f lEznl2 dS K n --

2[~2ps

,

(17)

where Ezn is the amplitude of the axial electric field of the nth space harmonic, ~n is the phase constant of the nth space harmonic, P is the average circuit power flow, and S is the cross-sectional area of the beam.

Electronic Wavelengths col N -

2,n-u o

,

with u 0 being the beam velocity and l being the circuit length.

(lS)

75

3. Traveling-Wave Thermionic Devices

Synchronization Parameter 0 ~ Upn b

(19)

~.

Upn

with yon being the phase velocity of the nth space harmonic.

Attenuation Parameter 0l¢.0

d = ~,

(20)

/Z0C

with a being the attenuation constant, where the electromagnetic wave amplitude decays along the circuit as exp -~z.

Space-Charge Parameter 2 OJq

QC

=

4C2¢o2 ,

(21)

with ¢Oq being the reduced plasma frequency.

Reduced Plasma Frequency (22)

OOq = Rcop,

where the reduction factor R is a function of both the beam diameter and its proximity to the tunnel wall [11, 43] and Wp is the plasma frequency.

Plasma Frequency wv =

~ epo mE 0

,

(23)

where e is the electron charge, P0 is the charge density, m is the electron mass, and e 0 is the permeability of free space.

Initial Loss Factor A1 ~-- 20 log

(24) -

-

76

Jeffrey D. Wilson

with the 3s given by the complex roots of the cubic equation 62 =

1

( - b + ja + j6)

- 4QC,

(25)

where 61 is the root with positive real part, 62 is the root with negative real part, and 63 is the root with zero real part. Space-Charge Loss Factor 62 + 4QC A2 = 20 log

(26)

Growing Wave Parameter B = 54.6[Re( 61) ].

(27)

G(dB) = A 1 + A 2 + BCN.

(28)

Small-Signal Gain

Charts giving A = A 1 + A 2 and B in terms of b, d, and QC are available [12]. For the simplest case with b = 0, d = 0, and QC = 0, the value of A is - 9 . 5 4 dB and the value of B is 47.3.

Large-Signal Analysis In the first section of a TWT circuit, the signal grows exponentially with distance as predicted by small-signal theory. However, as the signal becomes larger, it increases less rapidly and reaches a peak at saturation. In this region of nonexponential growth, the assumptions of small-signal theory are no longer valid, and a nonlinear large-signal analysis [96] must be performed via computer to obtain accurate solutions. Computer Software This section lists samples of electromagnetic field, thermal-mechanical, and electron b e a m - R F large-signal interaction computer software codes that have been used in TWT analyses. A R G U S [38, 62]. This software calculates resonant frequencies and fields, transient fields, and RF electromagnetic field-electron beam interaction in 3D. DDM H E L I X TWT [33]. Deformable-disk model simulates RF electromagnetic field-electron beam interaction in 2D for helical TWT.

3. Traveling-Wave Thermionic Devices

77

E G U N [57]. This software calculates trajectories of electrons in electrostatic and magnetostatic focusing systems with 2D fields and 3D particle trajectories. Used extensively in gun and collector design.

MAF/A [116, 117]. This software calculates resonant frequencies and fields, transient fields, and RF electromagnetic field-electron beam interaction in 3D. MA GNUS-3D [81, 91]. This software calculates 3D magnetostatic fields. MARC [5]. This software analyzes thermal/mechanical properties of slow-wave circuits in 3D. NASA CC TWT [118]. This software analyzes interaction between a 3D electron beam and 2D RF electromagnetic fields in coupled-cavity TWTs. SOS [40, 70, 114]. This software calculates resonant frequencies and fields, transient fields, and charged particle trajectories in 3D. SUPERFISH [48]. This software calculates resonant frequencies and fields in 3D axially symmetric cavities in cylindrical coordinates.

6. Linear-Beam Backward-Wave Devices Backward-Wave Amplifiers Applications

The linear-beam backward-wave amplifier (BWA) is an electronically tunable amplifier with a very narrow instantaneous bandwidth and very wide tunable bandwidth. The frequency of operation is presented by the intersection of the beam line and the first backward (n = - 1 ) space harmonic in Figure 11 and can be easily and rapidly changed by altering the beam voltage and thus the slope of the beam line. General Operation

In the conventional single-stage BWA, the RF input signal enters the slow-wave circuit (usually helix) at the collector end, and the RF output

78

Jeffrey D. Wilson

n--

I

am

li

_

0

~r

2~r

0= 139 Figure II. Approximate dispersion curves for a helix slow-wave circuit. Backward-wave amplification takes place at the frequency given by the intersection of the beam characteristic line with the first backward (n = - I) space harmonic. Forward wave amplification takes place when the beam characteristic line is nearly coincident with the fundamental (n = 0) space harmonic, to is the angular frequency, u0 is the beam velocity, p is the helix pitch, a is the helix radius, and c is the speed of light (Gewartowski and Watson [43 ]).

signal exits at the gun end. The helix voltage is adjusted so that the beam interacts with the n = - 1 space harmonic as represented by its intersection with the beam line OA in the dispersion (also known as Brillouin or to-#) diagram of Figure 11. This space harmonic is termed a backward wave because the group velocity and energy propagation are in the backward direction, whereas the phase velocity is forward. The theory of backward-wave interaction is available [43, 53, 68].

Cascade Backward-Wave Amplifier A cascade BWA [30, 43] has higher power gain and much higher gain stability than the single-stage BWA. It is a practical narrow bandwidth amplifier that is voltage tunable over a wide frequency range. This device, as represented in Figure 12, includes two helices, one terminated at the gun end and the other terminated at the collector end. The input signal is amplified by the first helix, and the modulation produced on the beam is carried by space-charge waves to the second helix, where further amplification occurs.

Backward-Wave Oscillators

Linear helical backward-wave oscillators (BWOs) [43, 53, 59, 61, 68, 69] are widely used in voltage-tuned signal generators because of the following characteristics.

3. Traveling-Wave Thermionic Devices

79

i- Electron i gun J Termination i v~/V ~ [ .

Input signal.

Output . signal

v ho

Termination ~A/V ~ "I "

Collector -J

Figure 12. Cascade backward-wave amplifier (Gewar~owski and Watson [43]).

1. By changing voltage, the BWO can be tuned rapidly over a very wide range of frequencies. 2. The BWO produces an extremely clean signal, with the desired output signal being at least 60 dB larger than the total power at all spurious frequencies. 3. The frequency of oscillation is extremely stable. 4. BWOs can be designed to operate in a very high frequency range up to the > 1000-GHz level [3, 4, 39, 42, 64, 65, 83]. The BWO circuit is the same as that of the BWA except that the RF input is replaced with a passive termination. The beam current is increased from zero by increasing the anode voltage. When the beam current reaches a point termed the starting current, IsT , the tube breaks into oscillation [43, 46, 61]. The state-of-the-art maximum power output for BWOs decreases exponentially from about 10 MW at 30 GHz to about 2 mW at 1000 GHz [7].

7. Magnetrons Applications The multicavity traveling-wave magnetron [10, 17, 25, 41, 43, 44, 66, 87] is a crossed-field microwave oscillator capable of producing megawatts of pulsed power at frequencies up to 30 GHz. Efficiencies typically range from 40 to 70%. Because of their low cost, small size and weight, and low voltage requirements, magnetrons are extensively used in radar systems, microwave ovens, and diathermy equipment.

80

Jeffrey D. Wilson

General Operation A schematic diagram of a conventional magnetron is shown in Figure 13. A cylindrical cathode is surrounded by an anode consisting of a reentrant slow-wave circuit. The region between the cathode and the anode is filled with a uniform magnetic field parallel to the cylindrical axis, which causes the electrons emitted from the cathode to rotate around the cathode in a dense turbulent hub, known as the Brillouin cloud. The slow wave structure of the anode propagates an RF wave around its circumference with a phase velocity equal to that of the outer edge of the Brillouin cloud. In the electron-wave interaction, electrons flow to the anode in "spokes" which rotate in synchronism with the RF field, producing oscillation at a resonant frequency. One of the resonators of the slow-wave circuit is coupled inductively to a loop formed from the center conductor of a coaxial cable. The coaxial cable in turn delivers the RF output signal to the load.

Anode Slow-Wave Circuit The multicavity anode is a slow-wave structure, propagating an RF wave at approximately the same velocity as that of the electrons at the outer edge of the Brillouin cloud. The dispersion curve is shown in Figure 14, with the curve repeating every 2rr radians. For an anode with N cavities and with pitch p between cavities, only those values of the phase constant /3 = w/Up for which ~Np = 2rrm

form=0,1,2,...N/2

(29)

are allowable. These values o f / 3 are represented by the vertical lines in

I

L End hat Figure 13. Magnetron (Gewartowski and Watson, [43]).

81

3. Traveling-Wave Thermionic Devices

o~ N/2

f

¢0 N/2-1

e) N/2-2

e) N/2-3 E

I

I~

I "

o e = ~p

Figure 14. Dispersion curve for a magnetron slow-wave circuit with N cavities with pitch p between cavities. Allowable values of the phase constant are represented by the vertical lines.

Figure 14. It is always desired that the magnetron operate in the m = N/2 or rr mode for which the phase shift per cavity is rr radians. The resulting electric field pattern for an eight-cavity circuit is shown in Figure 15.

Figure 15. Electric field pattern for the ~- mode in an eight-cavity magnetron with pitch p.

82

Jeffrey D. Wilson

Strapping The frequency of the desired m = N/2 or 7r mode is much different from the frequency corresponding to the undesired mode m = ( N / 2 ) - 1, as represented in Figure 14. It can be shown [41] that typically the ( N / 2 ) - 1 mode frequency is only 1 to 3% different from the rr mode frequency. To prevent oscillation in the undesired mode, the frequency separation between the two modes is increased by a procedure known as strapping [41, 1121. In a strapped magnetron, two parallel wires or fiat ribbons are mounted on the anode structure ends, making electrical contacts to alternate vanes. This causes the frequency separation between the rr mode and the ( N / 2 ) - 1 mode to be about 25 to 35% in low-power magnetrons and about 10 to 14% in high-power magnetrons [44]. Thus oscillation in the undesired modes can be prevented. At frequencies on the order of 10 GHz and higher, straps become very difficult to fabricate because of the small dimensions of the anode. At these high frequencies, rising-sun anode structures of the form shown in Figure 16 can be used to separate mode frequencies [74].

/-

Anode vane

Cathode slot

Figure 16. Rising-sun magnetron.

83

3. Traveling-Wave Thermionic Devices

Coaxial Magnetrons General Operation The coaxial magnetron [44, 66], as shown in Figure 17, contains a multicavity anode similar to that of a conventional magnetron. However, the anode is surrounded by a high-Q coaxial cavity operating in the TE011 mode. Slots in the back walls of alternate anode cavities couple the fields in these resonators to the surrounding coaxial cavity. In the 7r mode, the fields in every other cavity are in phase and couple in the same direction into the coaxial cavity. The coupling with the surrounding cavity stabilizes the magnetron in the desired ~ mode of operation, eliminating the need for strapping.

Characteristics The coaxial magnetron has several important advantages over a conventional strapped magnetron [66]. 1. Because the mode spectrum is controlled by the coaxial cavity, the number of cavities can be larger. This permits a larger cathode to be used, resulting in lower cathode loading and higher possible power. Also the interelectrode spaces are larger, reducing the voltage gradients. These factors provide enhanced reliability and lifetime.

Cathode-~

/-- Anode lot

Electric ./ field line - /

\ ~--

Coaxial cavity

Figure 17. Electric field pattern in a coaxial magnetron,

84

Jeffrey D. Wilson

2. The unstrapped resonator system has a higher impedance and a higher Q than its strapped equivalent. Combined with the high Q of the cavity, this results in a higher circuit efficiency. 3. The coaxial cavity greatly increases frequency stability. 4. Tuning the frequency of a coaxial megnetron is more easily accomplished by changing the volume of the cavity with a movable end plate. Tuning can also be accomplished by using rotating dielectric paddles in the high-electric-field region of the coaxial cavity. 5. Spectrum quality is generally improved with reduced spurious output.

Inverted Coaxial Magnetron A version of the coaxial magnetron in which the cathode surrounds the anode is known as an inverted coaxial magnetron [9, 58]. Because of the much larger cathode in the inverted design, much higher power densities, lower cathode current densities, or both can be obtained. A disadvantage is that it is more difficult to suppress spurious modes in an inverted design.

Simulation The accurate numerical simulation of crossed-field devices is considerably more difficult than that of linear beam devices. Computer simulation models for magnetrons and other crossed-field devices are described in References [22, 36, 37, 95, 122].

8. Crossed-Field Amplifiers There are two main categories of crossed-field amplifiers (CFAs): injected beam and distributed emission. Injected-beam CFAs [34, 113] were the first crossed-field amplifiers to be developed and used an electron gun to inject electrons into the interaction region. Although they demonstrated high gain and bandwidth, injected-beam CFAs have since been replaced by other devices and are no longer produced. The rest of this section will be devoted to the distributed-emission CFA [17, 43, 44, 78, 100].

Applications The CFA is a compact, low-weight, high-power, highly efficient amplifier with bandwidths up to 25%. Because of these advantages along with its relatively low-voltage operation, the CFA has found wide application in

3. Traveling-Wave Thermionic Devices

85

powerful mobile radar systems. It is commonly used as a final stage in an efficient amplifier chain with a linear TWT or klystron as the driver. Its high phase stability makes it useful in phased array applications. Another advantage is that cold cathode operation is possible, with the current supplied entirely by secondary emission. Peak power can reach a megawatt at a frequency of 10 GHz. Efficiencies are typically 40-70%.

General Operation Both forward-wave and backward-wave circuits are used in distributedemission CFAs. The electrons move in the same direction as the power growth in a forward-wave device and in the opposite direction of power growth in a backward-wave device. The main characteristic difference between a forward-wave and a backward-wave CFA is the bandwidth. In a forward-wave CFA, the bandwidth at a fixed c a t h o d e - a n o d e voltage value is usually about 10-20% for radar applications and can be as large as an octave in ECM applications. In a backward-wave CFA, the instantaneous bandwidth is narrow, but the frequency of operation can vary over about 10% by adjusting the anode-cathode voltage. The CFA geometry is very similar to that of the magnetron oscillator. The major difference is that the anode slow-wave circuit of the CFA is nonreentrant (does not close on itself). Instead, the input and output ends of the circuit are each connected to separate external transmission lines. When the RF input power is above a threshold value, electron bunches in the form of current spokes of nearly constant amplitude rotate around the circuit. Each current spoke induces two circuit waves, one traveling toward the input and the other, toward the input. In a CFA, only the waves traveling toward the output add in phase. Since each spoke induces equal power into circuit, the circuit wave grows, with power increasing linearly with distance. Thus the power gain of a CFA is much less than that of a linear beam TWT in which the power increases exponentially with distance.

Power and Efficiency Provided that the input power exceeds the threshold value for spoke stability, the power generated in a CFA is independent of the RF power input. The power generated can be increased only by increasing the anode voltage and current. Neglecting circuit attenuation, the output power is the sum of the input power, Pin, and the generated power, Pgen" Thus the

86

Jeffrey D. Wilson

amplifier gain is a function of the power input:

(30)

G = Pin "+"egen.

Because the CFA is a saturated amplifier, it cannot be used in amplitude modulation and is limited to frequency and phase modulation applications. The overall power efficiency in a CFA is typically 40-70% and is defined as the product of the electronic efficiency and the circuit efficiency, Pout - Pin

97 "-" 97cTle ~--- Va0 Ia0

'

(31)

where Tie is the electronic efficiency, ~7c is the circuit efficiency, Pout is the RF power output, Pin is the RF power input, Va0 is the DC anode voltage, and Ia0 is the DC anode current. The circuit efficiency, neglecting loss due to back-bombardment of the cathode, is given by

'r/c-

Pout-Pin Pgen

__[ -

1

Pin] egen

2al

(1 -

exp-2~l),

(32)

where Pgen is the power generated, a is the circuit attenuation constant, and l is the circuit length in the azimuthal direction. The electronic efficiency, neglecting loss due to back-bombardment of the cathode, is given by

m(.o 2 m

2eVa0/32

T~e = 1+

Iaomfl2K [ G + 1 2/32e

1 G-

,

(33)

1

where m is the mass of an electron, e is the electric charge of an electron, 13 is the RF phase constant, co is the angular frequency, B is the magnetic flux density, G is the power gain, and K is the beam-coupling impedance at the circuit given by

2

Emax K = 2/32P ,

(34)

where Emax is the peak electric field and P is the power flow [43].

High-Frequency CFA Since the rotational velocity of the current spokes is about an order of magnitude less than the velocity equivalent of the DC voltage, the periodic pitch distance of the slow-wave circuit is much less than that of a

3. Traveling-Wave Thermionic Devices

87

corresponding linear beam TWT. This allows the CFA to be compact, but limits the power and also makes fabrication of conventional circuits for frequencies higher than about 10 GHz impractical. However, CFA operation has been extended into millimeter-wave frequencies with an axial-gain CFA [78]. This device has an inverted cathode surrounding a staggered-slot structure. A prototype has demonstrated 50 kW of peak output power between 35 and 36.25 GHz with 10 dB of gain.

Low-Noise High-Gain CFA The primary disadvantages of the CFA have been high noise and low power gain. However, dramatic improvements in both of these characteristics have been achieved by incorporating a slow-wave structure into the cathode that is matched to that of the anode. The gain has been increased from a typical value of 10-15 dB to 20-30 dB and the noise, reduced by approximately 30 d B / M H z from a typical value of 45-50 d B / M H z [78]. This development promises even wider applications for CFAs in the future.

Amplitron The Amplitron (Raytheon trademark name) is a distributed-emission backward-wave crossed-field amplifier with no drift region between the RF output and the RF input [14, 35]. The absence of a drift region allows electron spokes to recirculate through the circuit, and this regenerative electronic feedback permits extremely high efficiencies on the order of 60-80%. The most common use for Amplitrons has been in powerful radar systems [17, 99]. Because of their very high efficiency and extremely long lifetime when incorporating pure platinum secondary emitting cathodes, it has been proposed that a large array of Amplitrons could be used to beam microwave energy to Earth from space [15]. Another device that could be used for this purpose is the magnetron directional amplifier, which consists of a magnetron in combination with a passive directional device [16,181.

9. Crossed-Field Backward-Wave Oscillators Applications The crossed-field or M-type backward-wave oscillator (MBWO), also known as the carcinotron, is a voltage tunable oscillator with a broad

88

Jeffrey D. Wilson

bandwidth on the order of 20%, efficiency up to 50%, and CW output power of typically 100-200 W [41, 44]. MBWOs have the advantage over magnetrons of being nearly instantaneously tunable over a wide frequency range. In this respect the MBWO is similar to the linear-beam BWO, but with the advantages of high efficiency, linear tuning, and high frequency stability. However, the MBWO produces considerably more noise [43]. Because of their high frequency agility and high noise, the primary use for MBWOs is as noise-jamming signal sources in ECM equipment.

General Operation Figure 18 shows the typical configuration of an MBWO. A ribbon-shaped electron beam is injected into the region between the sole and the slow-wave circuit. Oscillation occurs as energy is coupled from the electron beam to the RF wave on the circular slow-wave circuit. Because this is a backward-wave circuit, the RF signal grows as it travels from the collector end to the electron gun end, where the RF output connector is located. The cathode is a cylinder with a fiat side from which the electrons are emitted. The electrons move toward the accelerating anode and are

Collector RF attenuator

\

/ r

/- Grid / - Accelerating / anode / / - - Cathode

ou u,

Slow-wave structure

X._ Sole .................. Electron beam RF wave

Figure 18. M-type backward-wave oscillator (Gewartowski and Watson [43]).

89

3. Traveling-Wave Thermionic Devices

formed into a beam by the grid. The magnetic field parallel to the axis and the pC electric field between the negative sole and the positive anode (slow-wave circuit) force the ribbon beam to travel in a circle in close proximity to the circuit. The circular slow-wave circuit is of the form of a folded waveguide. This circuit is known as an interdigital delay line and is designed so that the phase velocity of the first backward-wave space harmonic is in synchronism with the beam velocity [84]. Noise in the electron beam initiates the propagation of space harmonic waves in the slow-wave circuit. The electrons congregate in bunches which work their way toward the circuit, giving up energy to the first harmonic backward wave. The operating frequency depends on the beam velocity which in turn depends on the applied anode and sole voltages.

Frequency Tuning MBWOs can be turned over frequency ranges between 25 and 40% by varying the sole voltage, anode voltage, or both. Tuning curves for a typical MBWO in which the cathode voltage is varied with constant sole voltage are shown in Figure 19. The frequency tuning is nearly linear with voltage

350 300 =,.

o~ 250 Q. U. rr 200

150

I m

~4

m

o 2 ,,_

4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 Frequency, GHz

6.4 6.6

Figure 19. Tuning curves for a representative M-type backward-wave oscillator (Litton Industries L-3726). These data correspond to fixed values for the sole voltage and cathode current of 2450 V and 300 mA, respectively (Gewartowski and Watson [43]).

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Jeffrey D. Wilson

b e c a u s e t h e e l e c t r o n drift v e l o c i t y is l i n e a r l y r e l a t e d to t h e I~C e l e c t r i c field in t h e i n t e r a c t i o n s p a c e . I n c o n t r a s t , t h e e l e c t r o n v e l o c i t y in t h e l i n e a r - b e a m B W O is p r o p o r t i o n a l to t h e s q u a r e r o o t of t h e t u n i n g v o l t a g e [43].

References [1] A. E. Acker, New techniques vitalize mm-wave CCTWT development and producibility, Microwave Systems News and Comm. Tech., Vol. 16, No. 13, pp. 68-79, 1986. [2] K. Amboss, Verification and use of Herrmann's optical theory of thermal velocity effects in electron beams in the low perveance regime, IEEE Trans. Electron Devices, Vol. ED-11, No. 10, pp. 479-485, 1964. [3] E. A. Ash and J. Froom, Slow-wave structures for millimetre-wavelength backward-wave oscillators, Electron Commun., Vol. 38, No. 2, pp. 264-275, 1963. [4] L. R. Barnett, R. W. Grow, and J. M. Baird, Backward-wave oscillators for the frequency range from 600 GHz to 1800 GHz, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 858-861, 1988. [5] K. F. Bartos, E. B. Fite, K. A. Shalkhauser, and G. R. Sharp, "A Three-Dimensional Finite-Element Thermal/Mechanical Analytical Technique for High-Performance Traveling Wave Tubes," NASA TP-3081, 1991. [6] B. N. Basu, B. B. Pal, V. N. Singh, and N. C. Vaidya, Optimum design of a potentially dispersion-free helical slow-wave circuit of a broad-band TWT, IEEE Trans. Microwave Theory Tech. Vol. MTT-32, No. 4, pp. 461-463, 1984. [7] P. Bhartia and I. J. Bahl, Millimeter Wave Engineering and Applications. New York: John Wiley and Sons, 1984. [8] C. K. Birdsall and T. E. Everhart, Modified contra-wound helix circuits for high-power traveling-wave tubes, IRE Trans. Electron Devices, Vol. ED-3, No. 10, pp. 190-204, 1956. [9] W. M. Black, R. K. Parker, R. Tobin, G. Farney, M. Herndon, and V. L. Granatstein, A hybrid inverted coaxial magnetron to generate gigawatt levels of pulsed microwave power, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 175-178, 1979. [10] H. A. H. Boot and J. T. Randall, Historical notes on the cavity magnetron, IEEE Trans. Electron Devices, Vol. ED-23, No. 7, pp. 724-729, 1976. [11] G. M. Branch and T. G. Mihran, Plasma frequency reduction factors in electron beams, IRE Trans. Electron Devices, Vol. ED-2, No. 4, pp. 3-11, 1955. [12] G. R. Brewer and C. K. Birdsall, Traveling-wave tube propagation constants, IRE Trans. Electron Devices, Vol. ED-4, No. 2, pp. 140-144, 1957. [13] L. Brillouin, A theorem of Larmor and its importance for electrons in magnetic fields, Phys. Rev., Vol. 67, No. 8, pp. 260-266, 1945. [14] W. C. Brown, Description and operating characteristics of the platinotronmA new microwave tube device, Proc. IRE, Vol. 45, No. 9, pp. 1209-1222, 1957. [15] W. C. Brown, Adapting microwave techniques to help solve future energy problems, IEEE Trans. Microwave Theory Tech., Vol. MTT-21, No. 12, pp. 753-763, 1973. [16] W. C. Brown, Status of the microwave power transmission components for the solar power satellite, IEEE Trans. Microwave Theory Tech., Vol. MTT-29, No. 12, pp. 1319-1327, 1981. [17] W. C. Brown, The microwave magnetron and its derivatives, IEEE Trans. Electron Devices, Vol. ED-31, No. 11, pp. 1595-1605, 1984. [18] W. C. Brown, The SPS transmitter designed around the magnetron directional amplifier, Space Power, Vol. 7, No. 1, pp. 37-49, 1988.

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[19] W. N. Cain and R. W. Grow, The effects of dielectric and metal loading on the dispersion characteristics for contrawound helix circuits used in high-power travelingwave tubes, IEEE Trans. Electron Devices, Vol. ED-37, No. 6, pp. 1566-1578, 1990. [20] M. Caplan and C. B. Thorington, Improved computer modelling of magnetron injection guns for gyrotrons, Int. J. Electron., Vol. 51, No. 4, pp. 415-426, 1981. [21] R. G. Carter and L. Shunkang, Method for calculating the properties of coupled-cavity slow-wave structures from their dimensions, lEE Proc., Part H, Vol. 133, No. 5, pp. 330-334, 1986. [22] D. Chernin and A. Drobot, Computer simulations of re-entrant crossed-field amplifiers, IEEE Electron Devices Meet. Tech. Dig., pp. 521-524, 1990. [23] M. Chodorow and E. L. Chu, Cross-wound twin helices for traveling-wave tubes, J. Appl. Phys., Vol. 26, No. 1, pp. 33-43, 1955. [24] M. Chodorow and R. A. Craig, Some new circuits for high-power traveling-wave tubes, Proc. IRE, Vol. 45, No. 8, pp. 1106-1118, 1957. [25] G. B. Collins, ed., Microwave Magnetrons. New York: McGraw-Hill, 1948. [26] H. J. Curnow, A general equivalent circuit for coupled-cavity slow-wave structures, IEEE Trans. Microwave Theory Tech., Vol. MTT-13, No. 9, pp. 671-675, 1965. [27] A. N. Curren, Carbon and carbon-coated electrodes for multistage depressed collectors for electron-beam devicesuA technology review, IEEE Trans. Electron Devices, Vol. ED-33, No. 11, pp. 1902-1914, 1986. [28] A. N. Curren, R. W. Palmer, D. A. Force, L. Dombro, and J. A. Long, High-efficiency helical traveling-wave tube with dynamic velocity taper and advanced multistage depressed collector, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 473-476, 1987. [29] A. N. Curren, K. J. Long, K. A. Jensen, and R. F. Roman, An effective secondary electron suppression treatment for copper MDC electrodes. IEEE Int. Electron Devices Meet. Tech. Dig., pp. 777-780, 1993. [30] M. R. Currie and J. R. Whinnery, The cascade backward-wave amplifier: A high-gain voltage-tuned filter for microwaves, Proc. IRE, Vol. 43, No. 11, pp. 1617-1631, 1955. [31] W. E. Danielson, J. L. Rosenfeld, and J. A. Saloom, A detailed analysis of beam formation with electron guns of the Pierce type, Bell Syst. Tech. J., Vol. 35, pp. 375-420, 1956. [32] J. A. Dayton, H. G. Kosmahl, P. Ramins, and N. Stankiewicz, Analytical prediction and experimental verification of TWT and depressed collector performance using multidimensional computer programs, IEEE Trans. Electron Devices, Vol. ED-26, No. 10, pp. 1589-1598, 1979. [33] H. K. Detweiler, "Characteristics of Magnetically Focused Large-Signal Traveling Wave Ampliferes," Rome Air Development Center Tech. Rep. RADC-TR-68-433, Griffiss Air Force Base, NY, 1968. [34] O. Doehler, Injection Type Tubes, in Crossed-Field Microwave Devices (E. Okress, ed.), Vol. 2, pp. 3-10, 155-164. New York: Academic Press, 1961. [35] G. E. Dombrowski, Theory of the amplitron, IRE Trans. Electron Devices, Vol. ED-6, No. 10, pp. 419-428, 1959. [36] G. E. Dombrowski, Simulation of magnetrons and cross-field amplifiers, IEEE Trans. Electron Devices, Vol. ED-35, No. 11, pp. 2060-2067, 1988. [37] G. E. Dombrowski, Computer simulation study of primary and secondary loading in megnetrons, IEEE Trans. Electron Devices, Vol. ED-38, No. 10, pp. 2234-2238, 1991. [38] A. T. Drobot, C. L. Chang, K. Ko, A. Mankofsky, A. Mondelli, L. Seftor, and P. Vitello, Numerical simulation of high power microwave sources, IEEE Trans. Nucl. Sci., Vol. NS-32, pp. 2733-2737, 1985.

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[39] D. C. Forster, High power sources at millimeter wavelengths, Proc. IEEE, Vol. 54, No. 4, pp. 532-539, 1966. [40] F. Friedlander, A. Karp, B. D. Gaiser, J. S. Gaiser, and B. Goplen, Transient analysis of beam interaction with the antisymmetric mode in a truncated periodic structure using the three-dimensional computer code "SOS," IEEE Trans. Electron Devices, Vol. ED-33, No. 11, pp. 1896-1901, 1986. [41] O. P. Gandhi, Microwave Engineering and Applications. New York: Pergamon Press, 1981. [42] P. Garcin, D. Grauleau, R. Gerber, and L. Teyssier, New technologies used for the 1 THz backward-wave oscillator, IEEE Int. Electron Devices Meet. Tech. Dig., pp 850-853, 1988. [43] J. W. Gewartowski and H. A. Watson, Principles of Electron Tubes. Princeton, NJ: Van Nostrand, 1965. [44] A. S. Gilmour, Microwave Tubes. Norwood, MA: Artech House, 1986. [45] J. F. Gittins, Power Travelling-Wave Tubes. New York: American Elsevier, 1965. [46] R. W. Grow and D. R. Gunderson, Starting conditions for backward-wave oscillators with large loss and large space charge, IEEE Trans. Electron Devices, Vol. ED-17, No. 12, pp. 1032-1039, 1970. [47] G. A. Haas, in Methods of Experimental Physics (V. W. Hughes and H. L. Schultz, eds.), Vol. 4, Part A, pp. 1-38. New York: Academic Press, 1967. [48] K. Halbach and R. F. Holsinger, Superfish--A computer program for evaluation of RF cavities with cylindrical symmetry, Part. Accel., Vol. 7, pp. 213-222, 1976. [49] J. W. Hansen, US TWTs from 1 to 100 GHz, Microwave J., Vol. 32, No. 6, pp. 179-193, 1989. [50] L. A. Harris, Toroidal electron guns for hollow beams, J. Appl. Phys., Vol. 30, No. 6, pp. 826-836, 1959. [51] L. A. Harris, Closely-spaced, aligned grids in vacuum tubes, IRE Trans. Electron Devices, Vol. ED-8, No. 11, pp. 481-488, 1961. [52] J. R. Hechtel, Magnetic focusing of electron beams in the presence of transverse velocity components, IEEE Trans. Electron Devices, Vol. ED-28, No. 5, pp. 473-482, 1981. [53] H. Heffner, Analysis of the backward-wave traveling-wave tube, Proc. IRE, Vol. 42, No. 6, pp. 930-937, 1954. [54] L. A. Hemstreet, S. R. Chubb, and W. E. Pickett, Electronic properties of stoichiometric Ba and O overlayers adsorbed on W(001), Phys. Rev. B, Vol. 40, No. 6, pp. 3592-3599, 1989. [55] G. Herrmann and S. Wagener, The Oxide-Coated Cathode, Vols. 1 and 2. London: Chapman & Hall, 1951. [56] G. Herrmann, Optical theory of thermal velocity effects in cylindrical electron beams, J. Appl. Phys., Vol. 29, No. 2, pp. 127-36, 1958. [57] W. B. Herrmannsfeldt, "Electron Trajectory Program," Stanford Linear Accelerator Center Rep. 331, Stanford Univ., Stanford, CA, 1988. [58] J. F. Hull, The Inverted Magnetron, in Crossed-Field Microwave Devices (E. Okress, ed.), Vol. 2, pp. 291-300. New York: Academic Press, 1961. [59] A. T. Isaacs and S. T. Dangzalan, Broadband BWO's to 50 GHz, Microwave J., Vol. 17, No. 3, pp. 39-51, 1974. [60] B. G. James and P. Kolda, A ladder circuit coupled-cavity TWT at 80-100 GHz, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 494-497, 1986. [61] H. R. Johnson, Backward-wave oscillators, Proc. IRE, Vol. 43, No. 6, pp. 684-697, 1955.

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[62] F. Kantrowitz and I. Tammaru, Three-dimensional simulations of frequency-phase measurements of arbitrary coupled-cavity RF circuits, IEEE Trans. Electron Devices, Vol. ED-35, No. 11, pp. 2018-2026, 1988. [63] S. Kapoor, R. S. Raju, R. K. Gupta, S. N. Joshi, and B. N. Basu, Analysis of an inhomogeneously loaded helical slow-wave structure for broad-band TWT's, IEEE Trans. Electron Devices, Vol. ED-36, No. 9, pp. 2000-2004, 1989. [64] A. Karp, Traveling-wave tube experiments at millimeter wavelengths with a new, easily built, space-harmonic circuit, Proc. IRE, Vol. 43, No. 1, pp. 41-46, 1955. [65] A. Karp, Backward-wave oscillator experiments at 100 to 200 kilomegacycles, Proc. IRE, Vol. 45, No. 4, pp. 496-503, 1957. [66] E. Kettlewell, The Magnetron Oscillator. London: Mills & Boon, 1971. [67] G. S. Kino and N. J. Taylor, The design and performance of a magnetron-injection gun, IRE Trans. Electron Devices, Vol. ED-9, No. 1, pp. 1-11, 1962. [68] R. Kompfner and N. T. Williams, Backward-wave tubes, Proc. IRE, Vol. 41, No. 11, pp. 1602-1611, 1953. [69] R. Kompfner, The invention of traveling wave tubes, IEEE Trans. Electron Devices, Vol. ED-23, No. 7, pp. 730-738, 1976. [70] C. L. Kory, J. D. Wilson, J. W. Maruschek, and D. L. Schroeder, Simulation of cold-test dispersion and interaction impedances for coupled-cavity tube slow-wave circuits, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 763-766, 1992. [71] H. G. Kosmahl and P. Ramins, Small-size 81- to 83.5-percent efficient 2- and 4-stage depressed collectors for octave-bandwidth high-performance TWT's, IEEE Trans. Electron Devices, Vol. ED-24, No. 1, pp. 36-44, 1977. [72] H. G. Kosmahl, Modern multistage depressed collectors--A review, Proc. IEEE, Vol. 70, No. 11, pp. 1325-1334, 1982. [73] H. G. Kosmahl and J. C. Peterson, "A TWT Amplifier with a Linear Power Transfer Characteristic and Improved Efficiency," NASA TM-83590, 1984. [74] N. Kroll, The Rising Sun System in Microwave Magnetrons (G. B. Collins, ed.), pp. 83-117. New York: McGraw-Hill, 1948. [75] L. Kumar, R. S. Raju, S. N. Joshi, and B. N. Basu, Modeling of a vane-loaded helical slow-wave structure for broad-band traveling-wave tubes, IEEE Trans. Electron Devices, Vol. ED-36, No. 9, pp. 1991-1999, 1989. [76] R. H. LeBorgne, C. Goodman, R. R. Hull, O. Sauseng, and G. M. Lee, Development of an 800 watt KA-band ring-bar TWT, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 881-884, 1990. [77] H. C. Limburg, J. A. Davis, I. Tammaru, J. P. Vaszari, and J. D. Wilson, Reducing the gain and phase variation in high power MMW TWTs, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 381-384, 1988. [78] G. H. MacMaster, Current status of crossed-field devices, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 358-361, 1988. [79] E. W. McCune, "UHF-TV Klystron Multistage Depressed Collector Development Program," NASA CR- 182190, 1988. [80] B. J. McMurtry, Fundamental interaction impedance of a helix surrounded by a dielectric and a metal shield, IRE Trans. Electron Devices, Vol. ED-9, No. 3, pp. 210-216, 1962. [81] N. Mahale and S. Pissanetzky, Recent advances in MAGNUS computational technology for three-dimensional nonlinear magnetostatics, IEEE Trans. Electron Devices, Vol. ED-35, No. 11, pp. 2034-2038, 1988. [82] J. T. Mendel, Helix and coupled-cavity traveling-wave tubes, Proc. IEEE, Vol. 61, No. 3, pp. 280-298, 1973.

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CHAPTER

4 Gyrotrons, Magnicons, and Ubitrons Paul Tallerico

I. Introduction

As the

operating frequency increases above 10 or 20 GHz, the fundamental mode cavities and circuits for classical electron devices become smaller and more expensive. The cross-sectional area of a microwave cavity is proportional to the square of the operating wavelength, and the skin depth decreases as the square root of frequency. These two effects combine and tend to make the power versus frequency curve for any given type of RF generator decrease a s f-2.5. In addition, as frequency increases, the small size of the circuits makes heat removal difficult and limits both the peak and the average power that are achievable by conventional microwave electron devices. Cavity tolerances are properly expressed as a fraction of the wavelength, so, as the frequency increases, it becomes more difficult and expensive to produce a resonant cavity. As early as 40 years ago, several researchers realized that rather than modulating the cavity or circuit walls, one could modulate the beam in a simple cylindrical circuit and still have a good microwave interaction. Generators based on the periodic modulation of the electron beam within a very simple circuit or waveguide are discussed in this chapter. The devices in the gyrotron are fast-wave devices, since the phase velocities of the simple circuits (such as ordinary waveguide) are faster than the velocity of light, rather than slow wave devices, such as the classical microwave devices.

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The gyrotron or electron cyclotron maser employs electron cyclotron resonance and an interaction with azimuthal electric fields to convert the rotational energy from an electron beam to microwaves. The device was first proposed by Twiss [1] in 1958 with a classical analysis and by Schneider [2] in 1959 with a quantum mechanical analysis. The classical theory was also independently published by Gapanov [3] in 1959. Flyagin and Gapanov wrote an excellent historical review [4] of this subject in 1977. The gyrotron is a very important millimeter-wave generator because it can operate with a higher-order mode interaction cavity that is several times larger both in length and diameter than the fundamental mode cavity used in most competing generators, such as klystrons or travelingwave tubes. The output cavity is typically many wavelengths long since the output interaction is distributed rather than concentrated. Thus the power density on the output cavity walls and the peak fields in the output cavity are significantly lower than those in the classical electron devices. The gyrotron finds uses in electron cyclotron resonance heating and current drive in fusion plasma research, and the devices are actively under development in the United States, Japan, Europe, and the former Soviet Union. The gyrotron family of electron devices includes the gyrotron monotron oscillator that is the usual meaning of the word gyrotron, as well as the gyroklystron, the gyro-backward-wave tube, and the gyro-travelingwave tube. The original gyrotron oscillator is the device that is used in most applications, and it is the simplest and most advanced member of the family. The amplifier version of the gyrotron, the gyroklystron, is under development, and the experimental results are described below. The magnicon is a deflection-modulated amplifier whose output cavity can look similar to that of a gyroklystron, but the interaction between the electron beam and the RF fields utilizes TM, rather than TE, modes. Only a single magnicon has yet been built, but the efficiency is so high, 73%, that it is included in this chapter. Several new projects to produce better magnicons at different frequencies are also under way. The ubitron was the first electron device that utilized a circuit that was several times larger that the wavelength. The ubitron's circuit, like that of the gyrotron, could be a factor of 10 to 100 larger in area than that of a conventional klystron or traveling-wave amplifier; hence its power generation possibilities are also one or two orders of magnitude higher than those of conventional microwave tubes. Ubitrons are not yet commercially developed, and their operation is discussed in Section 10.

2. Gyrotron Principles of Operation The gyrotron oscillator is shown schematically in Figure 1. An electron beam is produced in a hollow-beam electron gun (usually a magnetron-

4. Gyrotrons, Magnicons, and Ubitrons

99

GUNSOLENOID

MAINSOLENOID

-

~

MODULATINGANODE CATHODE

OUTPUT WINDOW

Figure I. Sketch of a gyrotron oscillator.

injection gun [5]) and then transported in an adiabatic compression system that is designed to produce a very small, intense, hollow, spiraling beam in the interaction cavity with a high ratio of transverse-to-longitudinal energy. This is the principle of the magnetic mirror, and the beam can be reflected if the compression process is too strong for the imperfections of the beam. Upon emerging from the gun region, the hollow beam drifts in a gradually increasing magnetic field to increase the transverse energy at the expense of the longitudinal energy. The beam is then bunched in a TEnm field. The interaction proceeds as follows. The beam is initially unbunched at the entrance to the cavity, and the beam is uniformly distributed azimuthally. Let the axial magnetic field be B0: then the rotational frequency of the beam is given by

fl c = eBo/( moT),

(1)

where 3' is the relativistic factor for the beam and is given by 3' = (1

+

U21/C2)-1/2,

(2)

where v is the electron velocity and c is the velocity of light in vacuum. The basic bunching process is shown in Figure 2: the hollow beam is performing the cyclotron rotation in accordance with Equation (1), and each individual beamlet makes a small circular motion in the plane perpendicular to the beam axis. Assume that there is a TE01 field also acting on the beam and that the cyclotron frequency matches the frequency of the cavity field. The electrons that are accelerated by the azimuthal electric field gain energy (electrons labeled 1 in Figure 2) and, by Equation (1), rotate at a lower frequency and lose phase as they drift,

I00

Paul Tallerico

) E

2

E ~

3 3

4

4 3 ~

3 2 ~ E<

1 2

E

4 1

Figure2. Azimuthalbunchingprocessintheg,/rotron.

whereas electrons that are decelerated (labeled 3 in the figure) by this field rotate faster and gain phase as they drift. The electrons at positions 2 and 4 are only slightly perturbed by this electric field. Now consider the situation 180 ° of phase later, as shown in the lower quadrant of Figure 2. The azimuthal electric field has reversed, and the electrons have completed approximately half a cyclotron revolution. The electrons numbered 1 are still gaining energy, and they will continue to lose phase, whereas the set numbered 3 still lose energy and gain phase. After a longer drift space, there is a net bunching of electrons around the electrons with the 4 label, and a rarefaction near the 2 label. The RF frequency is tuned to several percent away from the cyclotron frequency, so the azimuthally bunched beam can give up a substantial fraction of its perpendicular energy to the RF fields. This is the basis for gyrotron interaction, and the bunching mechanism is called the negative mass instability. Because of the mass variation with energy, the gyrotron can operate only with this relativistic effect, so it becomes difficult to design a member of the gyrotron family that operates below about 30 kV, and around 100 kV is a practical upper limit of operation for CW gyrotron oscillators, but pulsed amplifiers and

4. Gyrotrons, Magnicons, and Ubitrons

I01

oscillators can be designed to operate above 500 kV. Both the linear and the nonlinear theory of the gyrotron are reviewed in Reference [6]. The TE01 fields must also have a radial and axial magnetic field, and the radial magnetic field interacts with the beam's azimuthal motion to bunch the beam in the axial direction. This axial bunching is called the Weibel instability and is not a relativistic effect. These two mechanisms both operate in all cyclotron resonant devices, but it can be shown that the gyrotron interaction predominates when the circuit support waves with a phase velocity Vph > c, whereas the Weibel instability predominates for Uph < C. Thus devices that use the negative mass instability have cavities that are sections of cylindrical waveguide operated fairly close to cutoff, whereas Weibel devices require a slow-wave circuit to keep the wave phase velocity below c. The basic gyrotron instability is easier to access experimentally, because the guide wavelength in the almost cutoff circuit is so long that small axial position variations make little difference to the RF fields that the particles experience. Devices using the Weibel instability are similar in operation to traveling-wave tubes, and they have the potential for very wide bandwidth. The interactions are not required to utilize the TE0a cavity mode: the only real requirement is that the circuit support a TE mode, and this field must have a relatively strong azimuthal electric field at the beam's radius. Thus TE modes with very high indices are used to generate the highest powers and frequencies. These modes are called whispering gallery modes for historical purposes, and they have most of their RF energy concentrated near the cavity walls. The magnetic field must be supplied by a superconducting solenoid for frequencies above about 30 GHz, since the field required is proportional to the cyclotron frequency, which is almost the same as the RF frequency. However, operation is also possible at a harmonic of the cyclotron frequency, in which the solenoidal fields are reduced. In addition, many modes of operation are possible at harmonics of the cyclotron frequency. One of the most straightforward modes of operation is to use the nth harmonic of the cyclotron frequency with an nth azimuthal harmonic for the RF field. In this case, the beam should encircle the axis, n bunches are formed, and this usually reduces the possible efficiency of the device. When the beam encircles the axis, the gyrotron is called a large-orbit gyrotron, and the beam is usually generated by a hollow cathode in a region of magnetic field of one polarity followed by an acceleration space and then followed by a magnetic cusp into a region in which the magnetic field is reversed to spin the beam. This procedure results in a high ratio of rotational to longitudinal energy in the beam, and the rotational energy is then converted to RF energy in the output section of the device. The subject of large-orbit gyrotrons is

Paul Tallerico

102

reviewed in Destler et al. [7], and Destler's group has produced 500-MW pulses at 15.5 GHz at 10% efficiency with a multivane resonator large-orbit gyrotron. Another type of cyclotron interaction is the peniotron, which is the interaction of an azimuthal E field, with angular node number n, with the s harmonic of the cyclotron frequency, subject to the constraint that

A INPUT

CAVITY

~

[ RF INPUT

RF OUTPUT

WINDOW GUN COILS

COLLECTOR MAIN FIELD COILS

B WINDOW il

~1 I

I RF OUTPUT

J l RF INPUT COLLECTOR

GUN COILS POLE PIECE

MAIN FIELD COILS

,i

NM

] RF INPUT

\ RF OUTPUT

D<M

>\

GUN COILS

WINDOW COLLECTOR

MAIN FIELD COILS C. T H E G Y R O T R A V E L I N G - W A V E A M P L I F I E R

Figure 3. Some members of the gyrotron family of electron devices. (A) The two-cavity gyroklystron; (B) the two-cavity large-orbit gyrotron" (C)the gyro-traveling-wave amplifier.

103

4. Gyrotrons, Magnicons, and Ubitrons

s = n - 1. This interaction was first described by Yamanouchi et al. [8] in 1964. In this interaction, phase bunching is not involved, and the beam experiences all phases of the RF wave. In principle, very high efficiencies may be achieved, but this goal has been difficult to realize in practice, primarily because much smaller values of velocity spread are allowed for this type of distributed interaction. Another important advantage of the peniotron is that the spent beam, after the output cavity, is almost monenergetic, so the excess energy may be recovered with depressed collector techniques [9]. The gyroklystron, a klystron made on the gyrotron principle, has also been proposed, and a schematic of a two-cavity gyroklystron is shown in Figure 3A. The beam is excited by the fields in an input cavity, then it drifts in a cutoff region with no applied RF fields, the beam next loses its rotational energy in an output cavity, and finally the spent beam is collected on a collector, which may be depressed for highest system efficiency. The similarity with a conventional klystron is very high, but the RF fields are TE modes in the gyrotron case, and the bunching is azimuthal, rather than longitudinal. The gyroklystron may also be made from either a large-orbit or a quasi-optical gyrotron, as long as at least two cavities separated by drift spaces are used. An example of a two-cavity, large-orbit gyroklystron is shown in Figure 3B. The gyro-traveling-wave amplifier, shown in Figure 3C, is also a direct analog of its O-type counterpart. Once again, both gyro devices are less tolerant of longitudinal velocity spread than the conventional gyrotron, so the experimental work has been limited. Some experimental results will be discussed in Section 6.

3. Gyrotron Design Given a frequency and output power, the gyrotron oscillator may be approximately designed simply from the dispersion relation for the cavity and from the dispersion relation for the fast cyclotron wave on the electron beam. The cavity dispersion relation is O) 2 - - 1 2 , w 2 c 2 / L 2

2 , -+- OJco

(3)

where w is the operating frequency, l is the axial eigennumber of the cavity, L is the cavity length, and COcois the cutoff frequency of the cavity. Equation (3) determines the cavity frequency. The first term on the right of Equation (3) is the proportional to the square of the axial propagation constant, the coefficient depends on the axial shape of the field, and the form given here is for the sinusoidal variation that results in a cavity with parallel walls or for a very weak taper. In the usual gyrotron, operation is near the cutoff frequency, so the second term predominates. For a YEmp l

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Paul Tallerico

mode in a cylindrical waveguide, co = Vmp/R o, where R 0 is the cavity radius and Vmp is the p t h root of J ' ( x ) = O. The fast cyclotron wave dispersion relation is = lrcvll/L + sl2 c,

(4)

where Vii is the axial component of the electron velocity, s is the harmonic number of the magnetic field, and l-Ic is the relativistic cyclotron frequency, given in Equation (1). The nearby modes of the cavity must also be found, and the starting currents for each mode are calculated by considering a linear coupling term between Equations (3) and Equation (4), as shown by Danly and Temkin [19].

4. Gyrotron Structure The gyrotron oscillator is shown in Figure 1 in its most common implementation. A magnetron-injection gun (MIG) immersed in an axial magnetic field is used to form a dense, hollow electron beam. The MIG gun also has a modulating anode, and this anode voltage must be carefully controlled to control the mode purity of the oscillator. Regulation of 100 or 200 V in a 60-kV modulating anode supply is often required for stable operation. Modern gyrotrons often have a second anode to further control the beam. Unlike conventional electron tubes, the cathodes are normally operated as temperature limited, because the beam itself would oscillate under space-charge-limited conditions. Temperature-limited operation also allows one to have an independent control of the beam's current by varying the heater power. The beam follows a magnetic flux line, and the magnetic field increases by several times (up to 25 times) the strength at the cathode. This increase in the magnetic field converts, by Busch's theorem (conservation of canonical angular momentum), most of the beam's axial energy into rotational energy. The figure of merit for this energy conversion is called a, and a is the ratio of the beam's perpendicular velocity to its axial velocity. Most gyrotrons require an a > 1, and a's of about 2 or 2.5 are common for good gyrotrons. It is desired to have very little radial motion on the beam in the oscillator cavity, so the compression and drift operation is performed gradually and adiabatically, resulting in many centimeters of compression space, often 30 to 50 cm. Microwave oscillations are also possible in this drift space, so the space is often loaded with high-power microwave absorbers to eliminate these inadvertent oscillations. Lossy ceramics are used to load the drift spaces, and, in high-power CW gyrotrons, the cooling of these loads is a difficult technical problem.

105

4. Gyrotrons, Magnicons, and Ubitrons

The oscillator cavity need only be a wide place in the drift tube to support an oscillation, but provisions must be made to extract the microwave power. The output cavity is typically a complex open resonator, as shown in Figure 4, rather than a simple cylindrical resonator. The complex cavity is used to produce a variation in the azimuthal electric field in the axial direction, to optimize the interaction. The azimuthal field profile is also shown in Figure 4. Another advantage of the complex cavity is that the narrow part can prebunch the beam and force the main part to oscillate in the desired mode, rather than in competing modes. The cavity starts as an abrupt increase in the drift tube diameter, and this usually is made to resonate with a TE01 mode. The beam is designed to travel along the radius of the maximum electric fields in the cavity. The output end of the cavity often has a larger diameter, corresponding to a TE04 mode, for example, to allow more area for cooling in the CW case. By careful design (in the complex cavity case) one can obtain an inner maximum of an electric field of the TE04 mode to be at the same radius as the TE01 E-field maximum, and, of course, both sections must resonate at the

OUTPUT TAPER TEo3 REGION

TEol REGION

DRIFT TUNNEL

AXIS OF ROTATION

E FIELD AT BEAM RADIUS

J AXIAL DISTANCE

Figure 4. A complex-cavity output resonator and the resulting profile of the azimuthal electric field.

106

Paul Tallerico

desired frequency. An outward tapered section on the output end of the complex cavity is used to couple a portion of the RF energy to the collector. This tapered section must be carefully designed to preserve the mode purity of the oscillation: if it is too abrupt, many modes will be excited, and the desired mode purity will be lost. Thus the beam and the RF radiation leave the output cavity coaxially, but the beam is separated from the output radiation by an abrupt decrease along the axial direction of the magnetic focus field. This loss of the focus field forces the beam to expand abruptly in the radial direction under the influence of its own space charge, and it is intercepted over the collector surface. The output power is often transmitted in a 2.5-in. diameter overmoded waveguide, and a down-taper is also incorporated in the collector area, since the collector diameter is often over 2.5 in. in diameter. The overmoded cylindrical waveguide is used because the fundamental mode guide has too much loss at high frequencies. Once again, this taper must be gradual enough to preserve the output mode purity. Finally, when there is no danger of the electrons hitting the output window, a single- or double-disk window is employed to isolate the gyrotron's vacuum system from the external environment. The double-disk window is required for high average power, and it consists of two ceramic windows, separated by a space through which a coolant flows to carry away the heat produced by the dielectric losses in the ceramics. Thus the entire gyrotron (in the highpower case)will often have a length of about 3 m, although the electron gun and the output cavity are each only a few centimeters long. Several other types of gyrotron oscillators are possible. One such variant, the quasi-optical gyrotron, is shown in Figure 5. Here the gun and collector system are similar to those described above, but the resonator is essentially optical and consists of two confocal mirrors, spaced the correct distance apart to support a resonance at the desired frequency. Output coupling is via a hole in one of the mirrors or a partially transmitting mirror, as in an optical cavity. The resonator and output system are very well decoupled from the electron beam system, except in the region in which they overlap and provide the gyrotron interaction. Gyrotrons with the quasi-optical resonator perpendicular and at other angles to the beam have been built. Unlike conventional cavities, the quasi-optical cavity can be made with high Q well into the submillimeter band. Side-coupling apertures [10, 30] to the gyrotron cavity are practical at the lower microwave frequencies to provide the same decoupling of the RF fields and the collector region. At high CW powers, such as the 1-MW gyrotron at 110 GHz, the power density in the collector region would be above the practical limit of 1.5 k W / c m 2 if the collector had the same diameter as the output waveguide. The novel solution of placing an axial aperture in the output waveguide has been used [11] to separate the spent electron beam

4. Gyrotrons, Magnicons, and Ubitrons

107

CERAMIC INSULATOR COLLECTOR&[ SOLENOI~ \~ IC INSULATOR

s~~o~

MYLAR OUTPUT DOW

(

l

RESONATOR MIRROR

Lossg crPaMlCS GATE VALVF..-~-~ _E

OD L

G ANODE

~ ELECTRONGUN SOLENOID

CATHODE J

Figure 5. The quasi-optical gyrotron oscillator.

from the output radiation. The collector can then have a larger diameter than the output waveguide. The large-orbit gyrotron, shown in Figure 6, has been one of the most successful harmonic gyrotrons. Here the beam encircles the axis, and it is spun up by a cusp magnetic field. A cavity with a structure similar to that of a magnetron is employed to generate the fields with the proper azimuthal harmonic. GUN COILS

MULTIVANE OUTPUT RESONATOR PLASTIC OUTPUT WINDOW

/

ii F,~,~o-~,ss,o~~ CATHODE

~

~ =SO,~NO,O

STEEL POLE PIECE

Figure 6. The large-orbit gyrotron.

108

Paul Tallerico

Although not part of the gyrotron, the focus solenoids and their power supplies are important pieces of auxiliary equipment. For fundamental cyclotron-mode devices, superconducting solenoids are required at about 35 HGz, and these also require some form of helium supply or a helium refrigeration system. Only a few percent of transverse magnetic field are allowed from the solenoid, and the magnetic field tolerances increase with the output frequency of the gyrotron.

5. Gyrotron Fabrication Commercial gyrotrons are fabricated in the same manner as other commercial vacuum tubes: the cavities and collector are made from high-quality, oxygen-free, high-conductivity copper, the insulators are generally alumina, and the output windows are made of alumina or berillyia ceramics. Most of the remaining components are stainless steel, and the components are assembled with high-temperature vacuum brazing techniques, so the completed gyrotron may be baked out at 400 to 500 ° C to result in a vacuum that is lower than 1 x 10 - 7 T after bake out. For high-duty factor, high-average-power gyrotrons, the best construction methods must be used to achieve a decent life. The power densities on the cavity walls and in some areas of the collector are high in high-power gyrotrons, so careful attention to cooling must be paid. Most high-power gyrotrons are water cooled. The temperature-limited MIG generally has an impregnated metal cathode, and the cathode current density is generally below 5 or 10 A / c m 2, even for frequencies above 100 GHz. The geometry of the MIG electron gun is favorable to a modest current density (see Figure 5) as the beam thickness depends on the cathode thickness times the tangent of a small angle, the cathode tilt angle which is typically 10 to 30 °. The MIG is inherently unstable, like its parent, the magnetron, and the shallowest angles make the thinnest beams with the highest current density, but they are generally the most unstable. Therefore, hollow-beam Pierce guns have been proposed as an alternative. Small differences in the beam size or location at the cavity change the operating characteristics, so each gyrotron tends to require more time for factory tests than do conventional tubes. Many gyrotrons are experimental models, and these exhibit a very large variation of fabrication methods. The experimental gyrotrons are typically short-pulse, low-duty-factor devices, and they can tolerate poorer vacuum and a shorter life. The electron gun must be high quality, most U.S. experimenters purchase these guns from commercial suppliers, and gate valves are sometimes used to separate the gun from the main interaction

109

4. Gyrotrons, Magnicons, and Ubitrons

A 104

lO3 x

8

A

o

a.

Q.

o Pershing et al. [32] KJnkunaga et al. [33] v Kreischer et al. [34] [] Mitsunaka et al. [35] A Kreischer et al. [36] o Alberti et al. [42] × Grimm et al. [43]

lO2

101

i

i

i

i

i

50

i

100

i

i

[

150

i

i

i

i

]

i

i

250 I

200

I

i

]

i

300

i

L

i

i

350

Frequency, GHz 103

102

O O. Q.

O

101

o Felch et al. [30] Ives et al. [38] [] Myasiniko et al. [39] A Thumm [40] v Flyagin et al. [41]

I

10 0

20

40

60

80

100

120

140

160

180

Frequency, GHz Figure 7. (A) Short-pulse and (B)long-pulse (over 0.3 s) achievements in gyrotron development.

I I0

Paul Tallerico

region. Little cooling is required on either the cavity or the collector, and thin output windows of ceramic or even mica suffice for experiments. The focus solenoids are very important for proper gyrotron operation, and these systems must be carefully fabricated for stable operation. When superconducting solenoids are required for their high fields, the expense and complications of the solenoid system increase due to helium requirements and thermal insulation requirements. For short-pulse gyrotrons, Bitter magnets and even pulsed solenoids have been used or proposed.

6. Gyrotron Performance Many commercial gyrotrons have been developed by leading vacuum tube manufacturers. Figure 7 is a performance map showing power versus frequency for the CW and pulsed gyrotrons now commercially available. The 1-MW CW power limit has been in existence for almost a decade, and it is related to the difficulty in cooling the collector area. These commercial gyrotrons all operate at 80 to 100 kV. The frequency and output power depend on several variables, including cathode current, modulating anode voltage, beam voltage, and magnetic field in the oscillator cavity. The gyrotron's output power or frequency is often mapped out in terms of one of these variables, as is shown in Figure 8. Peak powers up to almost 3

HIGH INTERCEPTION REGION 2+

~ "

2.6

+

o

~+E,,,,,,I

"-o

x

x

_

P/

I

5 ~

2.4

i

x

x

o2. ___L./

x ARCING REGION

I

2 5.6

5.7

5.8

5.9

6.0

CAVITY MAGNETIC FIELD, T

Figure 8. Mode map for a ~rotron.

6.1

6.2

63

4. Gyrotrons, Magnicons, and Ubitrons

I I I

1 GW have been achieved at several frequencies. A few experimental gyrotrons have been optimized for operation at many frequencies, with step tuning when the mode in the cavity changes. For example, in Reference [13] output powers of up to 22 kW were obtained over the frequency range of 301 to 503 GHz with a single gyrotron. In the CW regime, another gyrotron [25, 31] operated from below 100 GHz to over 300 GHz with 20 W of power and up above 500 GHz at the second harmonic. In these wide-range gyrotrons, the device operates in many modes, one at a time, and the output frequency will follow the magnetic field for a while and then jump to a new mode and a new set of realizable frequencies. Thus, not all the frequencies in the range are accessible, but, nonetheless, the gyrotron is a powerful and flexible millimeter-wave generator.

7. Prebunched Gyrotrons and the Magnicon Most gyrotrons produced to date have been oscillators, and the major application is plasma heating, so the question of phase synchronization of many sources has not been important in most applications. For some applications, such as phased-array transmitters and particle accelerators, many separate but phase-controlled sources are required. Many researchers have studied a gyrotron oscillator that is stabilized by injecting an external RF signal into the cavity before the beam enters. With this method, phase locking becomes possible, but the locking bandwidth and gain are both better if the external signal is injected into a separate cavity, which may even be a region of the output cavity. Manheimer et al. [16] have given an excellent review of the methods and limitations of both injection locking and prebunching in gyrotrons. The injection cavity may be much more than a prebuncher. Luhmann et al. [17] use an injected RF signal to both prebunch and accelerate an electron beam, which then excites a higher-frequency output cavity. The acceleration cavity operates as a cyclotron resonance accelerator, and it can transfer a reasonable fraction of the input microwave power into bunched cyclotron motion [26]. The experimental results so far have produced about 6.7 kW at 10% efficiency at 27.7 GHz, and the soundness of the principle has been demonstrated. The magnicon is a deflection modulated amplifier (shown schematically in Figure 9) that transports a solid electron beam in a T M l I 0 mode deflection cavity into an expanding spiral by means of a two-phase excitation of the deflection cavity to achieve a rotating wave and therefore a rotating angle of deflection. The beam is also in a static, but varying with

I 12

Paul Tallerico

I.

DEFLECTION SYSTEM

ELECTRON ' GUN GUN FOCUS COIL

~

1'

OUTPUT

I i / ,, WINVOW

Ii

~

~

>

~

]

OUTPUT CAVITY

COLLECTOR COLLECTOR COIL

Figure 9. Schematic of the magnicon.

distance, magnetic field. After a suitable drift distance that maximizes the radial excursion of the beam, there is a sudden change in the magnetic field, and the radial beam motion is converted to cyclotron resonance motion. This transverse motion then interacts with a TE mode output cavity as in a conventional gyrotron, but of course the output is phase locked to the deflection cavity fields. The theory of the magnicon is reviewed in Reference [27]. The most exciting aspect of the gyrotron is that the first experiments by Nezhevenko [18], the inventor of the device, have yielded overall efficiency of 73% with a very high electronic efficiency of 85%, but at the low frequency of 0.915 GHz. Multiple deflection cavities are required for higher gain, just as in the klystron, and it appears possible to produce higher output frequencies by operating the output cavity at harmonics of the input frequency. Projects on magnicon development have been started at the Navy Research Laboratory [28] and at Los Alamos [29], and the Russian work is also continuing.

8. Gyrotron Applications The major application for the gyrotron is electron cyclotron resonance heating and plasma formation for fusion experiments. Although the fusion budget has been sharply reduced by the U.S. government, fusion research is quite aCtive in other parts of the world. The magnetic fields in tokamaks are in the 4 to 10-T regime, so the appropriate electron cyclotron resonant frequencies are from 110 to 280 GHz. The hybrid ion-electron resonance frequency is also utilized for plasma heating and control, and this frequency is usually between 5 and 10 GHz, well within the range of conventional devices, but gyrotrons are sometimes used because of their higher average power capabilities. Gyrotrons for fusion heating in plasmas

4. Gyrotrons, Magnicons, and Ubitrons

I 13

have been under development for over 10 years, with the power or frequency goals gradually increasing. For example, the U.S. Department of Energy funded research whose goal was 1 MW CW at 28 GHz in 1980 and then 1 MW CW at 60 GHz; the present goal remains at 1 MW CW, but now it is at 110 GHz. As an example of plasma heating, the International Thermonuclear Experimental Reactor (ITER) electron cyclotron wave system will require 28 MW installed at 120 GHz, for gas breakdown, plasma formation and preheating, and plasma current profile control. Also proposed, but not yet approved, is 28 more 1-MW systems at 140 GHz for plasma heating at the center and burn control. Although the ITER fusion reactor [12] has not yet been built, it is a major cooperative effort among Euratom, Japan, the former Soviet Union, and the United States, and it is most probable that it will be built. The ITER reactor is representative of the optimism for the gyrotron in the fusion community today. High-power microwaves simply are excellent for performing a large variety of required functions in fusion experiments. Two gyrotrons have also been developed for the Tokamak Upgrade experiment at Frascati, Italy. These gyrotron oscillators deliver up to 1 MW for 1-s pulses at a frequency of 8 GHz. This requirement would have been a very advanced project for a klystron, but the goals were met rather easily for the gyrotrons. One of the gyrotrons for this project has a rather complicated, 12-way divider to take the output power into 12 WR-137 waveguides and feed a grill antenna, which couples into the plasma. With this method, powers up to 700 kW, and a 1-s pulse length are delivered into a 4:1 mismatch [23]. Gyrotron instability has been proposed as a method of accelerating particles [26], and it has been experimentally utilized, but the particle energy goes into cyclotron motion, which is not very desirable in many accelerators. Another possible application of the gyrotron that takes advantage of the high average power available is RF heating of various high-value products. In particular, the sintering of ceramics at gigahertz frequencies has been proposed, with the expectation being that the heating and cooling cycles can be reduced from hours to minutes, allowing higher throughput. A second advantage of RF processing is that nonequilibrium ceramics may be possible, for components that would react in an ordinary oven may not have time to complete their reaction when rapidly heated by microwaves. Another proposed application of the gyrotron family of generators is their use as drivers for very high power particle accelerators. The next-generation electron-positron linear collider may well require GW total peak powers at frequencies in the 10- to 20-GHz range, and research on gyroklystrons is being pursued for this goal. The initial results have been encouraging, and already over 23 MW of peak power has been produced at 10 GHz [24].

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Paul Tallerico

Pulsed gyrotrons along with pulsed solenoids, have been proposed for millimeter and submillimeter radars [12] that may be able to provide near photographic quality images, but so far such radars have not been built with vacuum electronic devices. Lightweight, compact, harmonic gyrotrons have been proposed as radar drivers, and some work in this area is being done [11]. A gyroklystron amplifier has been designed for the N A S A / J P L Deep Space Radar System [15] at the Goldstone Antenna Facility that would provide 400 kW of CW power at 34.5 GHz. This power level would be very difficult to provide with a klystron, and the intent is to provide better mapping of deep space objects with such an amplifier.

9. Gyrotron Mode Purity In a typical fusion experiment, high average RF power is produced in a gyrotron and transmitted over some tens of meters of overmoded waveguide. Then, near the fusion reactor, the RF energy is sent to an antenna that is designed to radiate a single mode efficiently into the plasma. RF power that was either generated in the gyrotron or converted by the transmission system into other waveguide modes is generally lost in the waveguide walls or reflected by windows or the antenna system. Thus, mode purity is an important issue for most plasma heating experiments. Mode purities of 98% have been achieved at 8 GHz, but the typical mode purity at 50 GHz is more like 90%. In the more recent plasma applications, the mode content at the end of a transmission system is specified to the gyrotron vendor, and the vendor must design the transmission system so as to not degrade the gyrotron mode purity. Gyrotron oscillators can change their operating modes in response to the modulating anode voltage or axial focus field. Thus these parameters must be stabilized rather more carefully than with lower frequency devices to preserve mode purity.

10. Ubitron Principles The ubitron was invented by Phillips in 1957, when he realized that, rather than utilizing a periodic circuit through which a linear electron beam propagates, one could also make an amplifier by utilizing a linear circuit, like a rectangular waveguide, and a periodic electron trajectory. The ubitron is related to the undulator work of Motz [20], which was also the foundation of the free electron laser. The ubitron is like a gyrotron in that the interaction area can be 100 times larger than that in a traveling-wave tube at the same frequency, so much greater output powers are possible

4. Gyrotrons,

115

Magnicons, and Ubitrons

with the gyrotron or ubitron. An excellent historical review of the device is provided by the original inventor, Phillips [11]. A periodic beam at a high voltage, usually over 100 kV, can interact with a fast waveguide mode to make an amplifier or oscillator. The bunching and energy extraction are axial, and the potential efficiency is high, even though the interacting fields and particle motion are transverse. The ubitron is the prototype of the free electron laser, although this fact was not noticed until the free electron laser had been independently developed.

I I . Ubitron Structure A sketch of the first ubitrons is shown in Figure 10. A thin, solid beam travels through an ordinary rectangular waveguide operated in the TE01 mode to a collector. The beam is deflected by a system of permanent magnets that make an alternating magnetic field perpendicular to the beam axis. The beam then describes a sinusoidal motion in the direction perpendicular to both the magnetic field and the unperturbed beam axis. The basic schematic is much like a modern free electron laser operating in an amplifying mode. The electromagnetic radiation enters and exits the waveguide aided by 45 ° reflectors at each end of the interaction region, which have holes in them at the center for the beam. The cavity loading is selected by the output coupling.

,//SOLENOID

i"}

iiii~i[~

-

~

" iiiii -ii " " O ii'::ii

[7 WAVEGUIDF

....P:".,,50, 5,,',:"0,,5,,i:'0,,,5,15.',',:",,, :i'",,ix,b,,:5.:::",,, ::?,

~',~

MAGNETRON INJECTION i GUN

,:,::,:

:

:

J

....t POLEPIECE

~

~'::ii'i:

i

~ -,, LAMINATEDSTEEL AND COPPER INTERACTION CIRCUIT Figure I0. Sketches of early ubitrons.

COOLING OwIUTPUT

I 16

Paul Tallerico

12. Ubitron Performance The original ubitrons were at the S band, and interference between the desired TE01 mode and the TM 11 mode was quickly seen, and overcome, by preferential loss mechanisms to reduce the Q of the undesired mode. Maximum power at the S band was 1.2 MW, corresponding to a 10% efficiency [19]. The highest frequency results obtained by Phillips were 150 kW at 54 GHz and a maximum efficiency of 6%, with only 70 kV of beam voltage [19]. At this frequency, a hollow beam and a slotted slow-wave circuit were used. The magnetic bumps were produced by building the circuit from alternating sheets of copper and iron, so the iron disturbed the focusing field. This device was certainly a parent of the gyrotron, with its magnetron injection gun for the hollow beam, the RF power going through the collector, and its use of an output window located coaxially with the beam, but positioned after the collector. These early ubitrons were designed fro high peak power at 50 to 60 GHz, and, indeed, the ubitron power record lasted for over two decades, until the 1-MW gyrotron was developed. Interest in the ubitron has been renewed because of the bandwidth possibilities of the device. Gains of up to 20 dB over a 25% bandwidth in the 12- to 16-GHz range [20-22] have been achieved with an ubitron.

References [1] [2} [3] [4] [5] [6]

[7]

[8]

R. Q. Twiss, Radiation transfer and the possibility of negative absorption in radio astronomy, Aust. J. Phys., Vol. 11, pp. 564-579, 1958. J. Schneider, Simulated emission of radiation by relativistic electrons in a magnetic field, Phys. Rev. Lett., Vol. 2, pp. 504-505, 1959. A. V. Gapanov, Interaction between electron fluxes and electromagnetic waves in waveguides, Izv. Vyssh. Vchebn. Zaved., Vol. 2, pp. 450-462, 1959. V.A. Flyagin, A. V. Gapanov, M. I. Petelin, and V. K. Yulpatov, The gyrotron, IEEE Trans. Microwave Theory Tech., Vol. MTT-25, pp. 514-521, June 1977. W. Lawson, Magnetron injection gun scaling, IEEE Trans. Plasma Sci., Vol. PS-16, pp. 290-295, Apr, 1988. P. Sprangle and A. T. Drobot, The linear and self-consistent nonlinear theory of the electron cyclotron maser instability, IEEE Trans. Microwave Theory Tech. Vol. MTT-25, pp. 528-544, June 1977. W. W. Destler, E. Chojnacki, R. F. Hoeberling, W. Lawson, A. Singh, and C. D. Striffler, High power microwave generation from large-orbit devices, IEEE Trans. Plasma Sci., Vol. PS-16, pp. 71-89, Apr. 1988. K. Yamanouchi, S. Ono, and Y. Shibata, Cyclotron fast wave tubemThe doubled ridged traveling wave peniotron, Proc. 5th Int. Conf. Microwave Tubes, (Paris), pp. 96-102, 1964.

4. Gyrotrons, Magnicons, and Ubitrons

117

[91 M. E. Read, W. G. Lawson, A. J. Dudas, and A. Singh, Depressed collectors for high-power gyrotrons, IEEE Trans. Electron Devices, Vol. ED-37, pp. 1579-1599, 1990. [lO] L. Ives, K. Felch, C. Hess, H. Jory, R. Pendleton, A. LaRue, M. Chodorow, J. Feinstein, L Zitelli, and R. Martorana, Design and test of an 8 GHz, 500 kW, side coupled gyrotron, Int. Electron Devices Meet. San Francisco, Dec., pp. 152-154, 1988. [lOa] J. Neilson, K. Felch, J. Fienstein, H. Huey, H. Jory, R. Schumacher, and M. Tsirulnikov, Design of a 1 MW gyrotron with b e a m / R F separation, Proc. 16th Int. Conf. Infrared Millimeter Waves, Lausanne, Aug., pp. 120-121, 1991. [11]

R. M. Philips, History of the ubitron, Proc. 9th Int. Free Electron Laser Conf.,

Williamsburg, VA, Sept. pp. 1-9, 1987. [12]

[13]

[14] [15]

[16]

[17] [18] [191 [20] [21] [22]

[23]

[24]

[25]

L. Rebuffi, V. Parail, N. Fujiisawa, H. Hopman, W. Lindquist, H. Kimura, W. Nevins, M. Sironi, D. Swain, and J.-G. Wegrowe, Issues for the development and the design of an electron cyclotron wave system for ITER, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 568-571, pp. 1990. H. Guo, Y. Carmel, and V. L. Granatstein, A compact phase-locked harmonic gyrotron for modern millimeter wave radars, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 4-9, 1990. E. F. Eison, A 35 GHz seeker testbed RADAR, Millimeter Wave Technol. IV Radio Freq. Power Sources, Orlando, FL, May, pp. 109-113, 1987. D. J. Hoppe and A. M. Bhanji, High Power K6 Band Transmitter for Planetary Radar and Space Craft Uplink, Proc. l Oth Int. Conf. IR and MM Waves, Lake Buena Vista, FL, pp. 89-91, 1989. W. M. Manheimer, B. Levush, and T. A. Antonsen, Jr., Equilibrium and stability of free-running, phase-locked, and mode-locked quasi-optical gyrotrons, IEEE Trans. Plasma Sci., Vol. PS-18, pp. 350-367, June 1990. C. S. Kou, D. B. McDermott, N. C. Luhmann, Jr., and K. R. Chu, Prebunched high-harmonic gyrotron, IEEE Trans. Plasma Sci., Vol. PS-18, pp. 343-349, June 1990. O. A. Nezhevenko, The magnicon: A new RF power source for accelerators, IEEE Part. Accel. Conf. Rec., San Francisco, May, pp. 2933-2942, 1991. B. G. Danly and R. J. Temkin, Generalized nonlinear harmonic gyrotron theory, Phys. Fluids, Vol. 29, pp. 561-567, 1986. H. Motz, W. Thon, and R. M. Whithurst, Experiments on radiation by fast electron beams, J. Appl. Phys., vol. 24, pp. 826-833, 1953. C. E. Enderby, and R. M. Phillips, The ubitron amplifier--A millimeter-wave TWT, Proc. IEEE, Vol. 53, p. 1648, Oct. 1965. D. E. Pershing, R. H. Jackson, H. Bluem, and H. P. Freund, Improved amplifier performance of the NRL ubitron, Proc. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 137-139, 1990. P. Garin, G. Mourier, J. M. Krieg, and A. Dubrovin, Extensive experimental results on a 1 MW, 8 GHz gyrotron and the transmission system, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 768-770, 1990. S. Tantawi, W. Main, P. E. Latham, B. Hogan, H. Matthews, M. Rimlinger, W. Lawson, C. D. Striffler, and V. L. Granatstien, Studies of high-power X-band amplification from an over-moded three cavity gyroklystron with a tunable buncher cavity, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 195-196, 1990. G. F. Brand, P. W. Fekete, K. Hong, K. J. Moore, and T. Idehara, Gyrotron IVA, Conf. Dig., 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 496-498, 1990.

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[26] W. H. Miner, Jr., P. Vitello, and A. T. Drobot, Theory and numerical simulation of a TEal 1 gyroresonant accelerator, IEEE Trans. Microwave Theory Tech., Vol. MTT-32, pp. 1293-1301, Oct. 1984. [27] M. M. Karliner, E. V. Kozyrev, I. G. Makarov, O. A. Nezhevenko, G. N. Ostreiko, B. E. Persov, and G. V. Serdobintsev, The magniconmAn advanced version of the gyrocon, Nucl. Instrum. Methods Phys. Res., Vol. A269, pp. 459-473, 1988. [28] W. M. Manheimer, Theory and conceptual design of a high-power highly efficient magnicon at 10 and 20 GHz, IEEE Trans. Plasma Sci., Vol. 18, pp. 632-645. June 1990. [29] P. Tallerico and D. Rees, Fields and trajectories in the magnicon, Proc. IEEE Part. Accel. Conf., San Francisco, May, pp. 640-642, 1991. [30] K. Felch, T. S. Chu, H. Huey, H. Jory, J. Neilson, and R. Schumaker, Design considerations for a 1 MW CW gyrotron with an internal converter, Conf. 18th Int. Conf. Infrared Millimeter Waves, Colchester, Engl., Sept., pp. 517-518, 1993. [311 K. D. Hong, G. G. Brand, and T. Idehara, Second harmonic operation on GYROTRON V, Conf. Dig., 17th Int. Conf. Infrared Millimeter Waves, Pasedena, CA,

Dec., pp. 390-391, 1992. D. E. Pershing, R. D. Seeley, R. H. Jackson, and H. P. Freund, NRL ubitron performance, Conf. Dig., 17, Int. Conf. on Infrared Millimeter Waves, Pasedena, CA, Dec., pp. 50-51, 1992. [33] T. Kikunaga, T. Shimozuma, H. Asano, Y. Yasojima, and K. Nakashima, Experimental Studies of a 120 GHz megawatt gyrotron, Conf. Dig. 16th Int. Conf. Infrared Millimeter Waves, Lausanne, Aug. pp. 118-119, 1991. [34] K. E. Kreischer, M. A. Bastien, T. L. Grimm, W. C. Guss, and R. J. Temkin, Megawatt power level gyrotrons, Conf. Dig. 16th Int. Conf. Infrared Millimeter Waves, Lausanne, Aug. pp. 116-117, 1991. [32]

[35] Y. Mitsunaka, K. Hayashi, Y. Hirata, Y. Itoh, T. Kariya, M. Komuro, T. Okamoto,

[36]

[37]

[38]

[39]

[401 [41]

Y. Okazaki, T. Sugawara, A. Yano, T. Nagashima, and K. Sakamoto, A high-power 120 GHz whispering-gallery-mode gyrotron with a built-in quasi-optical mode converter, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec. pp. 318-320, 1990. K. E. Kreischer, T. L. Grimm, W. C. Guss, R. J. Temkin, and K. Y. Xu, "Research at MIT on High Frequency Gyrotrons for ECRH," MIT Plasma Fusion Center Rep. PFC/JA-90-37, Oct. 1990. K. E. Kreischer, M. Blank, W. C. Guss, S. K. Lee, and R. J. Temkin, High frequency, megawatt gyrotron experiments at MIT, Conf. Dig. 18th Int. Conf. Infrared Millimeter Waves, Colchester, Engl., Sept. pp. 515-516, 1993. L. Ives K. Felch, C. Hess, H. Jory, J. Neilson, R. Pendleton, J. Shively, M. Chodorow, J. Feinstien, A. LaRue, and L. Zitelli, Design and test of an 8 GHz, 500 kW, side-coupled gyrotron, Conf. Dig., 14th Int. Conf. Millimeter Waves, Wurtzburg, F.R.G., Oct. pp. 71-72, 1989. V. E. Myasnikov, A. P. Cayer, S. D. Bogdanov, and V. I. Kurbatov, Soviet industrial gyrotrons, Conf. Dig., 16th Int. Conf. Infrared Millimeter Waves, Lausanne, Aug. pp. 127-128, 1991. M. Thumm, Progress in development of high power gyrotrons, Conf. Dig. 18th Int. Conf. Infrared Millimeter Waves, Colchester, Sept., pp. 6-7, 1993. V. A. Flyagin, A. L.. Goldenberg, and V. E. Zapevalov, State of the art gyrotron investigation in Russia, Conf. Dig., 18th Int. Conf. Infrared Millimeter Waves, Colchester, Engl., Sept., pp. 581-584, 1993.

4. Gyrotrons, Magnicons, and Ubitrons

119

S. Alberti, B. G. Danly, G. Gulotta, E. Giguet, T. Kimura, W. L. Menninger, J. L. Rullier, and R. J. Temkin, High-power cyclotron Autorresonance maser (CARM) experiments, Conf. Dig., 17th Int. Conf. Infrared Millimeter Waves, Pasedena, CA, Dec., pp. 128-129, 1992. [43] T. L. Grimm, P. M. Borchard, K. E. Kreischer, and R. J. Temkin, High power operation of a 200-300 GHz gyrotron oscillator, Conf. Dig. 17th Int. Conf. Infrared Millimeter Waues, Pasadena, CA Dec., pp. 190-191, 1992.

[42]

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CHAPTER

5 The Peniotron David Gallagher and Gfinter D6hler*

I. Introduction

The peniotron

is similar to a gyrotron in several ways: (a) it is a fast-wave device, there is no slow-wave structure, and the interacting RF wave propagates with a phase velocity greater than the speed of light through a waveguide circuit; (b) the circuit is immersed in a uniform, axial, DC magnetic field; (c) the electrons in the electronic beam orbit around the lines of the magnetic field at the cyclotron frequency; (d) the RF interaction between the RF wave and beam acts primarily to convert the beam's orbiting (or transverse) energy into RF energy; and (e) as in all known fast-wave devices, the bandwidth is narrow. Peniotrons are, however, different from gyrotrons in the mechanism for which this energy conversion takes place. Whereas in the gyrotron the interaction involves a bunching of electrons resulting from relativistic mass effects, the peniotron involves neither and therefore can be a low-voltage device. Also the efficiency is potentially very high. In the peniotron, the electron beam can be a large envelope of orbiting electrons as in the gyrotron. Such a device is called a gyropeniotron and is capable of power levels comparable to those of gyrotrons and has applications similar to those of gyrotrons. However, in many cases the electron beam is simply a hollow, axis-encircling (rotating) beam (i.e., one beamlet of the gyrotron beam). The major peniotron types are

tDeceased November

5, 1993.

Handbook of Microwave Technology, Volume 2

121

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

GallagherandD6hler

m22

illustrated in Figure 1. The circuit for a peniotron can be a ridged or cross-shaped rectangular waveguide operating in the TEl0 mode traditional peniotron or can be one of many other waveguide shapes: rectangular, square, round, slotted (magnetron), coaxial, etc. These single-beamlet devices have the potential to generate or amplify hundreds to thousands of watts of RF power at frequencies up to hundreds of gigahertz and therefore have applications for communications and radar at millimeterwave frequencies at which high efficiency and moderate power levels are desired or required and at which broad instantaneous bandwidths are not needed.

B Hollow ,~.,..., ~ .

. . .

Rotating

~

~

Beam

~// "

i

RF Wave ~ _

_

TEIO

-

C

~ E

F Electron Beam

TE31 Figure I. Peniotron types. (A) Traditional four-ridge peniotron; (B) traditional peniotron with a cross-shaped waveguide; (c) square waveguide peniotron; (D) rectangular waveguide peniotron; (E) "true" gyropeniotron; (F) magnetron-type peniotron.

123

5. The Peniotron

2. The Traditional Peniotron The traditional peniotron, invented in the mid 1960s by the Japanese [1] and revived in the late 1970s in the United States [2], is illustrated schematically in Figure 1A, which shows a four-ridged (double-pair-ridged) rectangular waveguide immersed in a constant axial (longitudinal) magnetic field, B 0, and a thin, hollow electron beam rotating symmetrically between the ridges at the cyclotron frequency toc and drifting with constant axial velocity vz. A transverse electric (TEl0) mode with frequency to is assumed to propagate axially (z-direction)with propagation constant k. The main advantage of the traditional peniotron over nontraditional designs is that the waveguide can be designed so that only the TEa0 mode (the fundamental propagating mode) can propagate at the operating frequency, and so there are no moding problems.

Principle of Operation The principle of operation of the basic peniotron interaction can be seen in Figure 1A. Depending on the phase of the RF wave, the electrons near the ridges are accelerated (decelerated) by the strong electric field between ridges, causing the electron orbit to increase (decrease) in size. Assume now that the RF field of the wave changes by one complete period (or integral multiple thereof) during the time it takes the electron to perform half a revolution to reach the other ridge pair. The electron is now accelerated (decelerated) by a force which is smaller (larger) than previously, because the electron is farther from (closer to) the ridges. Thus, during each complete revolution, the electron loses some energy to the wave regardless of the initial RF phase. As long as the alternating acceleration and deceleration of the electrons remain "in phase," the electrons will continue to lose transverse energy until all energy is converted to RF energy and the orbit size becomes vanishingly small, thus leading potentially to a device with very high efficiency, but narrow bandwidth. Expressed mathematically, the above condition for resonance is to o = t o - k v

z=Sto c

S=2P

P=

1,2,3,...,

(1)

where too is the Doppler-shifted frequency, P is the spatial harmonic number of operation, and the cyclotron frequency is given by to c = ( e / y m ) Bo ,

where e l m is the charge-to-mass ratio of the electron and 7 is the factor

124

Gallagher and DBhler

at which v is the total electron velocity and c is the speed of light. The factor of 2 reduces the magnetic field requirement by a factor of 2, and higher values of P reduce it further. Note that no relativistic effects are involved in the interaction. (1 -- U2/C2) - 1/2

Small-Signal Calculations Small-signal calculations were made by decomposing the TEl0 mode of the four-ridged waveguide (approximated by line charges) in a Fourier series, solving for the small signal displacements, and applying Arnaud's equation to obtain a dispersion equation [3]. In a plane perpendicular to the axis, the functional dependence of the transverse electric field component along the circumference of the DC electron orbit is an expansion of terms of the form exp (-jnq~), so that the field as seen by the moving electron is given by exp j(tOt - kz - nq~) = exp jtOnt, where tOn = tO - - k v z ntOc, n is any integer, and z and q~ are the electron's axial and angular positions, respectively. The peniotron resonance occurs when ton "" -I'- toc :=~ to 0 "-

( n - 1) tOc,

peniotron,

(2a)

(tOn = +tOc leads only to net absorption for RF power), which is when the electrons are alternately accelerated and decelerated at a rate equal to the cyclotron frequency. The peniotron is therefore called a "resonant" device, in contrast to "synchronous" devices such as gyrotrons for which tOn =

0 ~

tOO = F/tOc,

gyrotron (cyclotron maser)

(2b)

and the electrons remain in a relatively constant phase of the RF wave [4]. In the traditional peniotron, only odd values of n yield nonzero coefficients. Thus Equation (1) is retrieved, where P = 1,2,3 (S = 2,4, 6) corresponds to n = 3, 5, 7, respectively. If one introduces the normalized parameters 13 =/3e(1 + jD6)~ o =/3e(1 + Db)

f i e - (tOo- 2PtOc)/Vz, where /3, /30, and /3e are the hot, cold, and at-resonance propagation constants, respectively, the dispersion equation, in the absence of spacecharge effects, becomes

6 ( 6 + j b ) = 1,

115

5. The Peniotron

whose solution, ~ = x + j y , is shown in Figure 2 as a function of b. The gain parameter D is given by D 2 = 1/2(I/V)(v2/vz

2)a2p ,

where I and V are the beam current and beam voltage, respectively, v is the electron velocity, and z2p is the coupling impedance given by Z2 P

2 2 ) - 1 R - Z ( r 0 / R ) 4p F sina((zP + 1)0) , = Z0(1 - COcut/~o

where z 0 is the characteristic impedance of the waveguide at infinite frequency (typically near 200 f~ [3]), ¢.Ocut is the cutoff frequency of the waveguide, r 0 is the beam radius, R is the minimum distance from the waveguide center to the ridges, 0 is the angle made by two rays starting at the center, one extending toward the end of the ridge and the other horizontally, and F is a fudge factor equal to 0.13 to fit large-signal calculations. The cosine factor is an important design consideration for the ridges. The gain per unit length at center frequency is given by G = 8.7/3eD. When space-charge effects are considered, they are found to be negligible under most conditions, particularly for thin beams [5]. The bandwidth is determined by the range of b from - 1 to 1, but is unimportant because the actual bandwidth, as determined by large-signal calculations, is much narrower.

3

N

b

F

x

-1 -2

-3 -3

Figure 2. Normalized velocity parameter b.

-2

-1

1

2

gain and phase velocity parameters

3 x and y versus cold phase

126

Gallagher and D6hler

TABLE I Simulated Sample Results for Vo = 10 kV; I 0 = 0.5 A; v t / v z = 2; and an Ideal Beam of Zero Thickness, Ripple, and Velocity Spread [2]

P

1

2

3

4

r 0 (cm) (at 90 GHz) B (gauss) (at 90 GHz) Gain/orbit (dB) Length (orbits, NO) 3-dB bandwidth (A~o/w) 2 PNo (A~o/¢o) Transverse efficiency

0.019 16,000 1.41 25 0.019 0.95 95%

0.038 8000 1.47 21 0.0104 0.87 77%

0.057 5300 1.18 27 0.0052 0.84 65%

0.076 4000 0.83 34 0.0030 0.82 50%

Large-Signal Calculations Large-signal calculations of efficiency were performed by the Soviets [6, 7]. Also, Northrop has developed a computer code which calculates large-signal gain and efficiency in all peniotron- and gyrotron-type devices. The code employees single-electron ballistics and takes into account beam thickness, velocity spread, beam scalloping, circuit losses, the true RF fields in the waveguide, the growth of the RF wave along the circuit, and any attenuators that might be employed. It can calculate bandwidth by injecting signals of different frequencies. Table 1 shows sample results for four optimized designs (ideal beam) for P = 1, 2, 3, and 4, where V = 10 kV, I = 500 mA, and U t / / U z = 2. Note that the instantaneous bandwidth is a little less than 1 / ( 2 P N ) , where N is the required circuit length in orbits.

Performance of Traditional Peniotrons In the mid 1960s, the Japanese obtained 6% efficiency from a 10-GHz peniotron operating in the P = 1 fundamental and with a 10-kV, 5-mA beam injected off center into the magnetic field by a CRT-type gun. Then in the 1980s, Northrop developed experimental peniotrons at 8 GHz ( P = 1 fundamental) and 16 GHz ( P = 2 harmonic), first as oscillators and then as amplifiers, and finally at 45 GHz (amplifier, P = 1) and 90 GHz (oscillator, P = 2) the later of which is presently in development. Progress is summarized in Table 2 [8].

127

5. The Peniotron TABLE 2 Northrop Peniotron Development

8-GHz oscillator 16-GHz harmonic oscillator 8-GHz amplifier 16-GHz harmonic amplifier 45-GHz amplifier 45-GHz oscillator 90-GHz oscillator (cross-shaped WG) 90-GHz oscillator (rising sun WG) aTransverse efficiency is twice as much

Output power

Efficiency a

2 kW 200 kW 3 kW 156 W 300 W 750 W Nominal 5W

30% 3.7% 36% 1.3% 8-12% 11%

Instantaneous bandwidth

2% 6% 1%

year 1981 1982 1982 1983 1986 1987 1992 1994

( U t ; / U z -- 1).

Traditional Peniotron Design

Basic Design of the 45-GHz Peniotron Amplifier A drawing of the 45-GHz peniotron amplifier is shown in Figure 3. On the left is the electron gun whose purpose, together with the magnetics, is Electron gun Gun pole piece Gun solenoid Field reversal \,

and adiabatic compression pole piece RF input 90° bend and transition Attentuator Circuit Main solenoid Collector

Figure 3. Design of a 45-GHz peniotron amplifier.

128

Gallagher and D6hler TABLE 3 45-GHz Peniotron Design Parameters

Center frequency Beam voltage (V0) Beam velocity ratio (Ut//Uz) Beam current Mean cathode radius (r c) Magnetic field at the cathode

45 GHz 9 kV 1 400 mA 0.162 40 g

Cathode thickness (Ar/r c) Cathode loading Magnetic field in circuit Mean beam radius in circuit Circuit length Circuit cutoff frequency

15% 2.5 A/cm 2 8000 g 0.0114 in. 6 in. 42 GHz

to generate the required thin, hollow, rotating beam, which passes through the circuit. On each end of the circuit are the input and output ports. The output consists of a tapered waveguide transition from the double-pair ridge waveguide to the standard rectangular waveguide, followed by a 90 ° bend in the standard waveguide, which contains a three-quarter wavelength impedance transformer (RF window). Inside the circuit is a short attenuator to suppress rereflection oscillations. A short section of the copper waveguide is replaced by inserts made from lossy material, which provide about 40 dB of attenuation. The electron beam exits the circuit through a hole in the 90 ° bend and is collected by the isolated collector shown on the left. Key design parameters are included in Table 3. Beam Formation

Gun designs to generate a thin, annular axis-encircling electron beam (with low ripple) fall into two categories: nonaxially symmetric (i.e., corkscrew) gun designs and axially symmetric gun designs (which require a field reversal). The convergent (spherical) hollow Pierce gun (with total magnetic confinement) is the gun type used in all the Northrop peniotrons. The gun consists of three stages: (1) a hollow, nonrotating, nonconverging beam is generated from a spherical Pierce-type electron gun with total magnetic confinement; (2) a magnetic field reversal causes the beam to rotate at the cyclotron frequency; and (3) an adiabatic compression of the magnetic field reduces the beam radius as required for entering into the circuit. The physical limitation of this approach is that the area convergence of the Pierce gun can be only about 2, thus placing the burden of beam compression primarily on the third stage. The way around this limitation is the "novel" gun approach [8], in which the beam is still

5. The Peniotron

129

compressing when the field reversal is approached. This approach also reduces beam ripple to a few percent. Electron guns have been developed by Litton [6] and Varian Associates [10], which, in addition to the principles described above, makes use of an iron, flux-concentrating center post so that all emitted electrons enclose the same magnetic flux, thus resulting in reduced velocity spreads. Circuit Fabrication

The problem with achieving a good I/0 match to the circuit depends on achieving good tolerances in circuit waveguide dimensions, particularly at millimeter wave frequencies. This problem was solved at 45 GHz by machining the ridges separately as ribbons and then fixturing and brazing them into a blank waveguide half. However, at 90 GHz, the ribbons could not be fabricated and so a cross-shaped waveguide was developed (see Figure 1B). The simulated interaction strength actually increased slightly over that of the comparable four-ridge design. However, at 90 GHz and higher, the brazing of two waveguide halves becomes a problem because of RF losses at the braze seam. Therefore the latest technique is to braze up a stack of predrilled copper pellets, one of them being graphite to provide for an attenuator, and then wire EDM the stack to any shape waveguide desired [11]. Figure 4 shows such a circuit with a slotted magnetron shape.

Figure 4. Ten-vane magnetron-type waveguide with a graphite section for the attenuator.

130

Gallagher and D6hler

3. Nontraditional Peniotrons The purpose of this section is to discuss briefly the many nontraditional peniotrons (often called gyropeniotrons) that have been proposed, theoretically analyzed, and developed. Experimental work has been reported for square waveguides and magnetron-type waveguides. In any of these devices, the principle of peniotron amplification resides with the alternating acceleration-deceleration of the electrons during any cyclotron period and with increasing electric field strength with increasing radius of the orbiting electrons. In opposite directions, the field strength is either symmetric (i.e., traditional peniotron) or antisymmetric, the interaction frequency being even or odd multiples (S) of the cyclotron frequency, respectively, only odd or even values of n yielding nonzero coefficients (Small-Signal Calculations).

Square and Rectangular Waveguides The Japanese [12] have resumed experimental peniotron development using a square waveguide with the TEl1 RF mode, as shown in Figure 1C. In this configuration, the RF field strength increases antisymmetrically about the center of the waveguide (or beam), and so the resonant frequency is at odd multiples of the cyclotron frequency. An experimental oscillator operating in the fundamental mode (to = coc) was constructed and tested at 10 GHz with a 30-kV, 0.92A beam with v t / v z = 3 and cavity dimensions 2.1 x 2.1 x 15 cm. The output power was 10 kW. Alignment of the beam, circuit, and magnetic field is extremely critical and was accomplished to within 0.002 in. by the use of a laser beam. Another proposed configuration for the peniotron is a rectangular waveguide propagating in the TE20 mode with the beam in the center, as shown in Figure 1D. As in the square waveguide the RF field strength increases antisymmetrically from the center toward the left or right. This device was studied theoretically by the Chinese [13, 14]. Efficiencies of 51 and 11% were simulated for operation near co = coc and to = 3w c, respectively.

The "True" Gyropeniotron Another nontraditional peniotron is what might be called the "true" gyropeniotron, because, instead of an axis-encircling beam, the typical polyhelical gyrotron beam is employed. Ono et al. [15] proposed a device (Figure 1 E ) w h i c h exploits exclusively the peniotron interaction in a

5. The Peniotron

131

gyrotron beam. In the device illustrated here, the beamlet centers are placed on the electric field null of the TE02 mode, so that, as the electrons turn in their orbits, they are alternately accelerated and decelerated by the azimuthal electric fields. The principle of operation is the same as that for the traditional peniotron, except that the electric fields are in opposite directions on each side of each beamlet orbit (antisymmetric). This device was simulated with encouraging results, but for very high beam power. Beam voltage and current ranged from 40 to 80 kV and 20 to 140 A, respectively, whereas beam efficiency was around 50%, for operation at o~0 = 3<0c. Z. G. Chen in Germany developed a ballistic large-signal theory of such devices operating in any TE mode and at any harmonic and obtained an efficiency of 45% for the TE03 mode operating in the S = 3 harmonic. For an electron velocity spread of 10%, the efficiency dropped to 30% [16]. Many theoretical papers have been published on the existence of peniotron interactions in the traditional gyrotron beam [17-20].

Circular Waveguides The gyrotron-peniotron interactions exist quite naturally in an axis-encircling hollow beam in a circular waveguide propagating in the TEmn mode because the transverse electric field component is of the form 2 cos(nq~) = e j~+ + e -j~+, the second term of which is the nth term in the Fourier expansion of the electric field which leads to Equations (2) discussed under Principle of Operation. Thus a high harmonic device is made possible by operating in a TEmn mode with a high value of n. A number of theoretical papers from all over the world have been published about the peniotron interaction in such a device. Two Russians authors [21, 22] made calculations of efficiency. Brand [23] from Australia studied both interactions from the linearized Vlasov equation of motion and calculated the ratio of the energy transfer rate (or starting current) of the peniotron to the gyrotron interaction to be ~ o / ( k v ~ ( n - 1)). He solved a more general set of slow equations of motion for calculating all gyro-type devices [24] Yokoo et al. [25] (Japan), Dohler and Gallagher [26] and Lashmore-Davies [27] (England) presented self-consistent small-signal theories and calculated small-signal gain. The later works also consider TM modes. In Vitello's work, peniotron and cyclotron maser (gyrotron) efficiencies are compared for equivalent TEmn 1 modes, and 80-90% (70-80%) efficiencies in the TE211 (TE311) mode, s = 1 (2), with the guiding center shifted by up to 40% (20%) of the beam radius and with velocity spreads, A v ~ / v ~ o , up to 30% were simulated [28]. Lau and Chernin provided a

132

Gallagher and D/Shier

critical examination of traditional theoretical treatments of AC spacecharge effects for many devices including the peniotron [29]. As a special case, the harmonic autoresonant peniotron ( H A R P ) w a s proposed by the University of Utah [30, 31] and is also being studied by the Japanese (see the following section). In the HARP, the phase velocity is assumed to be equal to the speed of light. Under such conditions, 7 ( 1 - v z / c ) = Co (Co being a constant). The decelerating effect of the electric fields acts not only on the transverse electron velocity but also on the longitudinal velocity, so the efficiency is larger. Also, the resonance frequency remains constant as 7 and v z decrease, so that no magnetic field tapering is necessary. Such a device holds promise at very high voltages. For example, if V = 250 kV (7 = 1.489) and v t / v z = 2.022, then C o = 1, and it is theoretically possible to achieve a total beam efficiency of 100%.

The Magnetron-Type Peniotron Closely related to the round waveguide peniotron is the magnetron-type peniotron, in which the round waveguide is slotted (or vaned) in order to enhance the coupling impedance of the higher harmonics. A six-vaned circuit is illustrated in Figure 1F. Such a structure will couple more strongly to the higher harmonic modes of the peniotron interaction than either the ridged or the cross-shaped waveguide. For an N-vaned structure the azimuthal dependence of the R F field is of the form exp (-jncp), where n = N / 2 for the rr mode (RF fields 180 ° out of phase in alternating gaps between vanes) and n = N for the 2rr mode (all gaps in the same phase). Equations (2) still apply, and, therefore, the six-vaned structure illustrated above can operate in the rr mode as a third harmonic gyrotron or an equivalent to a fundamental mode ridged peniotron (co o = 2Pco c, where P = 1). Higher harmonics are possible by increasing N, by operating in the 27r mode, or by operating in a spatial harmonic of the magnetron waveguide: n ~ (2P - 1)n, where P = 1, 2, 3, etc. The magnetron-peniotron was studied and simulated by the University of Utah [32-34] and analyzed by Vitello [35]. Theoretical analysis by Ganguly et al. [36] has simulated extremely high efficiency (75%) for the interaction between the rr mode and the n - 1 = 2 ( P = 1) peniotron 2. Also, a basic beam efficiency mode of a 70-kV, 3.5-A beam with V t / U z of 22% was simulated for n - 1 as high as 8 ( P = 4). He has also analyzed backward wave oscillations (BWOs) [37} and absolute instabilities [38] for similar devices. BWOs were also analyzed by the Russians [39]. Currently, experimental work to develop peniotrons using such slotted circuits is underway at a number of laboratories. Northrop [11] has fabricated a peniotron oscillator designed to generate 20 kW in the S = 4 harmonic at 95 GHz. The circuit consists of 10 slots of alternating depths -

"

5. The Peniotron

133

(rising-sun structure, which avoids the competition with the fourth harmonic gyrotron). NRL is developing an S = 2 harmonic peniotron using a rising-sun 6-slot structure to generate 100 kW [40]. The Japanese have measured 1.9 kW output power at 10 GHz in the S = 2 harmonic in a 6-slot circuit [41] and observed some power at 100 GHz in the S = 10 harmonic in a 22-slot circuit [42], both circuits being of the simple magnetron type. They have also published experimental results showing more than 70% electronic efficiency obtained from an autoresonant peniotron oscillator using a magnetron-type cavity [43]. Experimental work is also being done at UCLA and Polytech University [44].

Other Peniotron and Peniotron-Like Devices

The Chinese have proposed several novel peniotrons. Zhang [45] proposed a peniotron to operate in a coaxial waveguide, with the axis-encircling hollow beam orbiting around the inner electrode. In another work by Zhang [46], a radial electrostatic field is applied between the inner and the outer electrodes to help hold the beam in its rotational trajectory and allow for reduced (or no) required magnetostatic focusing field. Zhou et al. [47] and Huang and Guo [48] proposed a quasioptical peniotron and calculated an efficiency in the third harmonic (~o0 = 3coc) of 31.4%. Finally, a peniotron-like interaction was found in the free electron laser. [49].

References [1] K. Yamanouchi, S. Ono, and Y. Shibata, Cyclotron fast wave tube--the double ridges travelling wave peniotron, Proc. 5th Int. Conf. Microwave Tubes, Paris, pp. 96-102, 1964. [2] G. Dohler, D. Gallagher, and R. Moats, The peniotron: A fast wave device of efficient high power MM-wave generation, Int. Electron Devices Meet., pp. 400-403, 1978. [3] G. Dohler, and D. Gallagher, The peniotron: An efficient high power MM-wave amplifier, Published in AD C019 920 Proceedings of the DARPA /Tri-Service Millimeter Wave Conference (8th) April 3-5, 1979, pp. 355-361. [4] G. Dohler, and W. Friz, Physics and classification of fast-wave devices, Int. J. Electron., vol. 55, pp. 505-521, 1983. [5] G. Dohler, and B. Wilson, A small signal theory of the peniotron, Int. Electron Devices Meet., pp. 810-813, 1980. [6] S. P. Kuznetsov, D. I. Trubetskov, and A. P. Chetverikov, Nonlinear analytic theory of the peniotron, Soy. Tech. Phys. Lett., Vol. 6, pp. 498-499, 1980. [7] S. P. Kuznetsov, and A. V. Osin, Some problems in the theory of the peniotron, Radio Eng. Electron Phys., Vol. 29, pp. 91-98, 1984. [8] G. Dohler, D. Gallagher, R. Moats, and F. Scafuri, Recent peniotron results at 45 GHz, Int. Electron Devices Meet., pp. 311-314, 1987; see also Int. Electron Devices Meet., pp. 328-331, 1981; pp. 845-848, 1984.

134

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[9] T. A. Hargreaves, G. P. Scheitrum, T. Bemis, and L. Higgins, Design and construction of a 95 GHz, 4th harmonic oscillator experiment, Int. Electron Devices Meet., pp. 347-350, 1993. [ 10] W. DeHope, et al., Initial tests of a high power, broadband, harmonic GyroTWT, Int. Electron Devices Meet., pp. 355-358, 1993. [11] G. Dohler, D. Gallagher, J. Richards, and F. Scafuri, Harmonic high power 95 GHz peniotron, Int. Electron Devices Meet., pp. 363-366, 1993. [12] K. Yokoo, M. Razeghi, N. Sato, and S. Ono, Experiments on the high efficiency operation of the modified peniotron oscillator, Int. J. Electron., Vol. 67, pp. 485-490, 1989. [13] G. Jianming, and L. Shenggang, Linear and nonlinear analyses on gyropeniotron in a rectangular waveguide, Int. J. Electron., Vol. 65, pp. 637-644. [14] L. Zhou, Kinetic theory of travelling wave gyropeniotron in a rectangular waveguide, Int. J. Electron., Vol. 65, pp. 631-636, 1988. [15] S. Ono, K. Tsutaki, and T. Kageyama, Proposal of a high efficiency tube for high power millimeter or submillimeter wave generationmThe gyro-peniotron, Int. J. Electron., Vol. 56, pp. 507-519, 1984. [16] Z. G. Chen, Analysis and simulation on the performance of a gyro-peniotron amplifier, Int. J. Infrared Millimeter Waves, Vol. 14, pp. 197-211, 1993; see also Vol. 13, pp. 1535-1555, 1992; Vol. 14, pp. 23-33, 777-781, 1993. [17] G. Dohler, Peniotron interactions in gyrotrons, Int. J. Electron., Vol. 56, pp. 617-640, 1984. [18] P. Vitello, and K. Ko, Mode competition in the gyropeniotron oscillator, IEEE Trans. Plasma Sci., Vol. PS-13, pp. 454-462, 1985. [19] A. P. Chetverikov, Intensification of electromagnetic oscillations in a gyropeniotron, Radiophys. Quantum Electron., Vol. 33, pp. 553-558, 1990. [20] S. C. Zhang, Unified single-particle theory of free-electron maser amplifiers, Phys. Rev. A, Vol. 46, pp. 5154-5160, 1992. [21] V. A. Zhurakhovskii, Theory of a relativistic peniotron, Radio Phys. Quantum Electron., Vol. 29, pp. 550-556, 1986. [22] A. A. Kurayev, Peniotron with Hnm operating modes of a circular waveguide, Soy. J. Commun. Technol. Electron., Vol. 35, pp. 61-65, 1990. [23] G. F. Brand, Energy transfer equation for high-harmonic cyclotron maser and peniotron interactions, Int. J. Infrared Millimeter Waves, Vol. 5, pp. 853-858, 1984. [24] G. F. Brand, Slow equations of motion for gyrotron and peniotron interactions, Phys. Fluids B, Vol. 4, pp. 2983-2991, 1992. [25] K. Yokoo, H. Shimawaki, X. J. Wang, N. Sato, and S. Ono, Correct self-consistent small signal analysis of peniotron mode in rotating electron-beam devices, Int. J. Electron., Vol. 65, pp. 619-630, 1988. [26] G. Dohler, and D. Gallagher, The small-signal theory of the cyclotron maser and other gyrotron-type devices, IEEE Trans. Electron Devices, Vol. 35, pp. 1730-1745, 1988. [27] C. N. Lashmore-Davies, A unified theory of gyrotron and peniotron interactions, Phys. Fluids B, Vol. 4, pp. 1047-1057, 1992. [28] P. Vitello, Design considerations for gyro-peniotron oscillator, Int. J. Infrared Millimeter Waves, Vol. 8, pp. 487-515, 1987. [29] Y. Y. Lau, and D. Chernin, A review of the AC space-charge effect in electron-circuit interactions, Phys. Fluids B, Vol. 4, pp. 3473-3497, 1992. [30] J. M. Baird, L. R. Barnett, R. W. Grow, and R. C. Freudenberger, Harmonic AutoResonant Peniotron (HARP) interactions, Int. Electron Devices Meet., pp. 913-916, 1987.

5. The Peniotron

135

[31] J. M. Baird, R. C. Freudenberger, R. W. Grow, and L. R. Barnett, Ring-resonant cavity [32]

[33]

[341

[35] [36] [37]

[38] [39] [40]

[41] [42]

[43] [44]

[45] [46] [47] [48] [49]

for the harmonic auto-resonant peniotron (HARP), Int. Electron Devices Meet., pp. 854-857, 1988. P. S. Rha, L. R. Barnett, J. M. Baird, and R. W. Grow, Self-consistent large signal theory and simulation of high harmonic gyrotron and peniotron oscillators operating in a magnetron-type cavity, Int. Electron Devices Meet., pp. 535-538, 1985. P. S. Rha, L. R. Barnett, J. M. Baird, and R. W. Grow, Self-consistent simulation of harmonic gyrotron and peniotron oscillators operating in a magnetron-type cavity, IEEE Trans. Electron Devices, Vol. ED-36, pp. 789-801, 1989. M. C. Pate, R. W. Grow, and J. M. Baird, Comparative TE model analysis and extended parameter calculations of magnetron-wall waveguide for gyro-peniotron applications, IEEE Trans. Electron Devices, Vol. ED-36, pp. 1976-1982, 1989. P. Vitello, Non-linear analysis of a gyro-peniotron oscillator, Proc. 13th Int. Conf. Infrared MM Waves, Honolulu, pp. 431-432, 1988. A. K. Ganguly, S. Ahn, and S. Y. Park, Three dimensional nonlinear theory of the gyropeniotron amplifier, Int. J. Electron., Vol. 65, pp. 597-618, 1988. A. K. Ganguly, G. S. Par, and C. M. Armstrong, Linear analysis of backward wave oscillations in azimuthally varying transverse electric TE modes, Phys. Fluids B, Vol. 5, pp. 1639-1646, 1993. A. K. Ganguly, Y. Y. Lau, and S. Ahn, Absolute instabilities in gyropeniotron amplifiers, Phys. Fluids B, Vol. 4, pp. 3800-3805. A. P. Chetverikov, Nonstationary theory and simulation of the backward wave peniotron oscillator, Int. J. Infrared Millimeter Waves, Vol. 14, pp. 213-238, 1993. G. S. Park, C. M. Armstrong, A. K. Ganguly, R. H. Dyser, and J. L. Hirshfield, High efficiency 35 GHz gyro-peniotron, Vacuum Electron. Annu. Ree. Proc., Crystal City, VA, IV-l-IV-4, 1993. H. Shimawaki, K. Sagae, N. Sato, K. Yokoo, and S. Ono, 2nd cyclotron harmonic peniotron experiments, Int. Electron. Devices Meet., pp. 787-90, 1991. T. Ishihara, K. Sagae, H. Shimawaki, N. Sato, K. Yokoo, and S. Ono, Experiments of 10th cyclotron harmonic peniotron, Int. Electron Devices Meet., pp. 367-370, 1993. S. Musyoki, K. Sagae, K. Yokoo, N. Sato, and S. Ono, Experiments on highly efficient operation of the auto-resonant peniotron oscillator, Int. J. Electron., Vol. 72, pp. 1067-1077, 1992; see also Vol. 69, pp. 827-834, 1990; Vol. 71, pp. 715-722, 1991. K. K. Tiong, and S. P. Kuo, Operation of a high harmonic cusptron oscillator, Int. J. Electron, Vol. 70, pp. 815-825, 1991. S. Zhang, Coaxial waveguide gyro-peniotron, Int. J. Infrared Millimeter Waves, Vol. 7, pp. 869-880, 1986. S. Zhang, Gyro-peniotron focused by radial electrostatic field and axial magnetostatic field, Int. J. Electron. Vol. 61, pp. 1081-1089, 1986. L. Zhou, M. Jiang, H. Guo, and Y. He, Quasi-optical gyro-peniotron at high cyclotron harmonics, Int. J. Electron. Vol. 57, pp. 1065-1075, 1984. H. Huang, and H. Guo, Complex quasi-optical cavity gyropeniotron and gyrotron interaction, Int. J. Electron. Vol. 65, pp. 337-350, 1988. G. Dohler, and D. Gallagher, Beam wave interactions in free electron lasers, Int. J. Electron., Vol. 65, pp. 483-496, 1988.

This Page Intentionally Left Blank

CHAPTER

6 Thermodynamics of Microwave Devices K. Fricke, V. Krozer, and H. L. Hartnagel

Nomenclature AS

Ai Cf Csf Cp D E Eb Eba

f0 F~s Gr hc

hfg K(x) k Nu Pdiss Pin, Pout

m2 m2

Area of the surface Area of surface i Friction coefficient Experimentally determined constant Specific heat at constant pressure Characteristic length and diameter Emitted power per unit area Emitted power per unit area of a black body Emitted power per unit area and unit wavelength of a black body Correction factor Radiation shape factor Grashof number convective heat transfer coefficient Enthalpy of vaporization Elliptic integral of the first kind Thermal conductivity Nusselt number Dissipated power Input i)c power Input and output microwave power

Handbook of Microwave Technology, Volume 2

137

W s/kg K m W/m 2 W/m 2 W/m 3

W/m 2 K Ws/kg W/Km W W W

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

138 Pe Pr q qc R th Re S St T TO Ts v vm vs Z a a • A /x /x s v p p z ~w

Fricke, Krozer, and Hartnagel P&let number Prantl number Conductive heat transfer rate Convective heat transfer rate Thermal resistance Reynolds number Conduction shape factor Stanton number Temperature Heat sink temperature and fuid temperature Surface temperature Velocity Mean velocity Free stream velocity Width of a structure Absorptivity Coefficient of volumetric expansion Emissivity Wavelength Dynamic viscosity Dynamic viscosity at the walls Kinematic viscosity Density Reflectivity Transmissivity Mean shear stress

W W K/ W

K K K m/ s m/ s m/s m 1/ K m kg/m s kg / m s m2/s kg / m 3

N/m 2

I. Introduction

In

microwave semiconductor packages heat is generated due to losses in conductors or resistances and due to active devices with efficiencies lower than 100%. If the input oc power is Po~ and if Pout and Pin are the output and input microwave powers, respectively, the dissipated power, Paiss, is given by

Pdiss = PDC + Pout- Pin.

(1)

The basic consideration of the microwave device thermal design is to minimize the device temperature T by optimizing the thermal resistance, Rth,

T-To Rth=

Pdiss

where TO is the heat sink temperature.

(2)

139

6. Thermodynamics of Microwave Devices

Basically heat can be transferred by conduction, convection, and radiation. In this chapter the fundamental principles of heat transfer are reviewed. Another important issue of thermal design is to match the mechanical expansion parameters of the package with those of the semiconductor. Thermal enhancement methods for microwave devices and circuits are discussed in Section 6.

2. Conductive Heat Transfer Conduction is the mode of heat transfer along a temperature gradient within a solid, liquid, or gaseous medium or between solid media in direct intimate physical contact. The process of conductive heat transfer within the solid can be viewed as the transfer of internal energy by direct molecular communication. Detailed analysis of heat transfer by conduction can be reviewed in numerous books on heat transfer, for example, Kreith [42], Simonson [72], Holman [33], and Cheremisinoff [13]. The determination of the conductive thermal properties of microwave devices and packages, for example, thermal conductivity, thermal resistance, and maximum intrinsic temperature, is a major task in thermal design due to the ultimate limits on performance imposed by heat removal. Conductive heat transfer can be considered either under steadystate or transient (unsteady-state) conditions. Steady-state conduction prevails when the devices or circuits are operated at continuous pc or RF power levels, which is the case for CW operation. Unsteady-state conduction is observed during pulsed operation. Both steady-state and transient heat conduction can be modeled by an electrical equivalent of the thermal problem, utilizing the analogy between conductive heat transfer and electrical conduction. This analogy is extensively used for the determination of the thermal resistance of packages, circuits, and individual devices, which has been, for example, described by Minot [54], Min [53], Le Jannou [47] and Pence [64].

Steady-State Heat Conduction According to the theory of heat conduction, the rate of heat flow, q, per area, A, is proportional to the temperature gradient. The positive proportionality constant is called thermal conductivity, k, and is determined by Fourier's law, q A

OT -

Ox

(3)

The thermal conductivity is a material property and can be determined

140

Fricke, Krozer, and Hartnagel

from measurements of heat transfer according to Equation (3). The different measurement approaches are outlined in Section 5. Values for the thermal conductivity of metals, semiconductors, substrates, and isolators are tabulated in Section 6 in Tables 8 through 11. The thermal conductivity of most materials is a function of temperature. The temperature dependence of the thermal conductivity of metals, semiconductors, ceramics, and gases is indicated in Figure 1. From Table 1 the thermal conductivity of several compound semiconductors can be evaluated. Steady-state conduction in higher dimensions including internal sources is given by the nonlinear Poisson equation, V(kVT) + 4 = 0 ,

(4)

or, assuming homogeneous thermal conductivity, v2r

a

+ ~- = o •

(5)

1000

>,, .

Cu

m

> u :D

0

u

Au

"-'-"

~AI-Si

Mg _ Brass

100

~

Mo

E eI---

10

lO0

1000

Temperature [K] 1000 >,

Ag

> u

W E 0

u ~

Zn 100 N, Pb

L

v2 A 10

o

,

2;0

,

J

,oo

,

6;0

,

8;0

,

ooo

Temperature [KI Figure I. Thermal conductivity as a function of temperature. (d) isolators, and (e) gases.

(a and b) metals, (c) semiconductors,

6. T h e r m o d y n a m i c s

of M i c r o w a v e

141

Devices

10000

C

.4..o

1000

•~

GaP

~ -o

100

c - y' E

°) O

GoAs ~

InP

.._o

O

E

...-.

10

InAs

L-.

r"

I(]0

' 200

' 31]0 ' /-,00 ' 500

' 61]0 ' 7(]0

1000

' B00 ' 9(]0

Temperature [K] d

10000

>

1000

.-

Diamond BeO

S-145

E L..

1o

D-Mot

D-450

cl--

,

,

~

Sapphme

~

corning , .,

,

J

,

~

,

quartz

,

I

100

200

300

400

500

600

?00 ' 800 ' 91]0

1000

Temperature [ K]

H2

>

"ID c-

01

u O

.-.

E L_

QJ

c-

0.01 100

,

,

1000

Temperature [K] Figure I.

(Continued)

Equation (5)can be solved analytically for a limited number of geometries, and therefore finite-difference or finite-element methods are commonly applied to solve this equation [6, 10, 16, 26-28, 30, 42, 44, 46, 48, 53, 58, 75, 82, 83, 86], especially utilizing commercial packages such as ANSYS

142

Fricke, Krozer, and Hartnagel TABLE I Approximation of the Thermal Resistivity of Ternary and Quaternary Compound Semiconductors as a Function of Composition [I - 3] 1

Ga l_xlnxAs InASl_xPx

GaASl_xPx Gal_xAlxAs Inx_xGaxP Inl_xGaxAsyPl_ r

K cm

~--V-

Compound

2.27 + 7 3 . 4 3 x - 72x 2 3.7 + 2 7 . 7 7 x - 30x 2 2.27 + 1 9 . 0 3 x - 20x 2 2.27 + 2 8 . 8 3 x - 30x 2 1.47 + 7 1 . 8 3 x - 72x 2 1.47 + 7 1 . 8 3 x - 72.23y - 1.26xy - 72x 2 -

25y 2

[67], PHOENICS, and CAEDS [4]. In the case of temperature-dependent thermal conductivity the exact solution of equation (5) can be obtained by using the Kirchhoff transform technique described by Joyce [36]. Many practical problems of heat transfer can be considered in only two dimensions, for which the heat transfer rate per unit depth is dependent only on the temperature difference on each surface. In this case, the thermal resistance can be evaluated by the simple relation R th = 1/(k S), where S is the so-called conduction shape factor. Table 2 together with Figure 2 indicates various examples of systems for which analytical solutions exist. Further examples can be readily found in Kreith [42] and Holman [33].

Unsteady-State Heat Conduction Transient heat conduction problems commonly occur in pulse-driven microwave systems during thermal cycling, etc. The Fourier equation in three dimensions for this case reads OT

V(kVT) = Cpp Ot

(6)

and for homogeneous thermal conductivity of the material reads

V 2 T = Cpp OT k

at

1

OT

a

at'

= --g--

(7)

TABLE 2 Conduction Shape Factors

Figure

Conduction shape factor (S)

2a

S = 4a]--Jl(X)coth(wx/a) x Jo

2b

$1 =

,.oo

Reference

sin x

4aI 1

1-

fo~ sin x X1 I1 = Jo - - J l ( X ) - - xX2 dx

4aI 1 .

4kl

"

[91

dx

$2 -

I2

[43]

I2 7rk 2

Jo'~ sin x J l ( X ) e x p ( - w l x / a )

I2 =

~

t a n h ( w 2 x / a ) dx;

X2

x~ = 1 + A 1 e x p ( - 2 w l x / a ) ; k2 Y1 = 1 - - - t a n h ( w 2 x / a ) ;

Z 1

-

-

Y2

Y1 Y2

1 - A 1exp(-2WlX/a)

X 2 -

k2 Y2 = 1 + - - t a n h ( w 2 x / a )

k 1

kl

,.~ sinx 2c

S = 2aJo - - ~ J l ( X ) c o t h ( w x / a ) dx

2d

S = 2 Z ~

2e

S = 2 Z - -

2e

4w) S---(rrZ)ln - - • t > 0 rrr

K(p2)

r=a

2f

Pl = sinh ~

K(Pl)

K(P2) K(pl )

1+

" P2

=

_

°

Pl-

2a w- t --

¢ =

Pl

P2

cosh(~'a/w)

2g

-

S _

1

K(Pl) K(P2)"

+0.236 ---

1 1+ r

~/ =

[32a]

[32a]

= ~/1 "

p2

P2

--

7r(2a + s)

Pl

t = 0

<0.35

X 1 = sinh ~w sinh

Xl

2Z

tanh(rr a / w)

=

(sinh( )) 2 r

[83]

tanh

1 .

1 +ln

K(p2) S = 2Z -K -( P"l )

[9]

~w

1 + r1 + r2

.

(1 + rl)(1 + r2)

)

[32a] p2

= V/1

P2

-

[32a1

(sinh( )) 2 r 1 ----

r 2 --

X1 sinh ~

"

sinh

X 1 = sinh ~w sinh

2w

2a_,_2s,)

2w

X

tanh( ) 'wS

z K(R2) 2h

S-

2 K(pl)

Pl-

P2

tanh (-~w) ~d

=

V/1 - p2

[32a]

144

Fricke, Krozer, and Hartnagel

TO

TO

'O

"u

TO

LTo g

~

TO,.,

c

b

~

s

w

d

I-

2%s

-I

IO v

_

"T0 Figure 2. Schematic drawing of the geometries for the calculation of the conduction shape factor.

where a is the thermal diffusivity, cp is the specific heat of the material at a constant pressure, and p is the density of the material. If the system contains internal heat sources, then Eq. (7) changes to the form

VZT + -k

=

-a7

'

(s)

6. Thermodynamics of Microwave Devices

145

In practical transient heat flow problems acceptable accuracy can be achieved by assuming that the internal thermal conductive resistance of the system is small compared with the external thermal resistance between the surface of the system and the surroundings. The ratio of the internal to external thermal resistance is called the Biot number, of the form hL/k, where h is the average unit surface conductance, and L is the significant length determined by dividing the volume of the system by its surface area. The Biot number should be less than 0.1 in order to obtain reasonable approximations of the temperature distribution. A further important transient heat conduction problem is the introduction of convective boundary conditions at the surface of the system. Solutions for several geometries have been presented in graphical form with the aid of Heisler charts [33, 42].

m

Electrical Equivalent of Thermal Conduction Steady-state and transient conductive heat flow can be effectively characterized by means of its electrical equivalent. In particular, for packaged devices and circuits, electrical equivalent circuits greatly facilitate the evaluation of the overall thermal resistance, including the effect of geometry and the various thermal properties of the solders, heat sinks, and packages. If the electric current I and the electric potential V are set equivalent to the heat flow rate q and the temperature T, respectively, then the thermal resistance is equivalent to the ohmic resistance. For transient analysis it is required that the thermal capacitance of the entire system under consideration, Cth = ¢ppXIZ, where ~F determines the volume, is a lumped parameter. Only in this case the thermal capacitance can be set equivalent to the electrical capacitance.

3. Convective H e a t Transfer Single-Phase Convective Heat Transfer Heat transfer by convection takes place at the interface between a solid and a fluid (liquid or gas) provided a temperature gradient exists between the surface of the solid and that of the fluid. A detailed analysis of this phenomenon may be found, for instance, in the books of Kreith [42], Kaka~ [37], and Simonson [72]. The formulas given in this section refer only to one-phase convective heat transfer.

146

Fricke, Krozer, and Hartnagel

One can distinguish between free convection and forced convection heat transfer. In the first case the fluid moves only because of its density changes arising from the hot solid surface. In the second case the medium is forced to pass across the surface of the solid with a certain speed. The convection heat transfer is strongly dependent on the condition of the boundary layer. At low velocity, v, and high viscosity of the fluid, v, laminar flow is observed, whereas at higher velocity and lower viscosity the flow becomes turbulent. A measure of this effect is the dimensionless Reynolds number, Rel, vD Re D = ~ , l,'

(9)

with a characteristic length of the solid surface, D. The heat transfer rate by convection, _qc may be described by an average convection heat transfer coefficient, h c, qc = A s h c( Ts - T0),

(10)

where Ts and A s are the surface temperature and the area of the solid surface and To is the temperature of the fluid. For a more detailed description a local convective heat transfer coefficient has to be defined [37, 42]. This is especially important if the surface of the solid is not homogeneously heated. In the literature convection heat transfer problems are commonly expressed in terms of dimensionless groups which are listed in Table 3. The Nusselt number Nu is given as a product of dimensionless groups with certain exponents, nl, n2, and n3: Nu = C R e nl P r n2 G r n3,

(11)

The exponents of this equation and the constant C may be fitted experimentally. Knowing the Nusselt number it is easy to compute the convective heat transfer coefficient h c. In Tables 4 and 5 approximate formulas are given for the average Nusselt number for special arrangements which are shown in Figure 3. The heat transfer rate qc is obtained using Equation (10). The power P needed to ensure a certain forced convection can be computed using the mean shear stress at the wall, ~w, the free stream mean velocity, v s, and the area, A s" AszwVs Pf = ~ .

fo

(12)

147

6. Thermodynamics of Microwave Devices TABLE 3 Dimensionless Groups Symbol

Name

Group

vD Re o

Reynolds number

Remarks

vDp -

v

Ix

vDpcp Pet)

P6clet number

Pr

Prandtl number

Nuo

Nusselt number

k

Re D Pr

CoN

Material constant

k

hcD k

gD3ol A Tp 2 Gr D

Grashof number

St

Stanton number

tz2 hc

NUD

VCpp

Re D Pr

The factor f0 counts for the additional friction due to the geometrical form of the arrangement. It also may include the effect of fins, having a lower temperature than the walls which have to be cooled [81]. The mean shear stress at the wall, ~w may be obtained directly by _ pv 2 Tw=ff

2

'

(13)

where Cf is the mean friction coefficient. Generally Cf can be computed using the Reynolds analogy: ogt Pr e/3 =

Cf 2

.

(14)

Especially for tubes with the diameter, d , the friction factor in laminar flow, f, can be expressed by the experimentally obtained approximation [72] 4%pv

f = 4Cf =

2

2

64 - Red

(15)

and, for turbulent flow up to Reynolds numbers of 2 × 10 5, by Holman [33]: f = 4Cf =

2 4"rwP Vm

0.308

2

- ReO.25 .

(16)

148

Fricke, Krozer, and Hartnagel TABLE 4 Average Nusselt Numbers for Forced Convection Cooling Average Nusselt Number

Figure 3a

Nu

Nui. = 0.664 Reds 5 Pr °'33

Remarks

Reference

Laminar flow

[42, 72]

Re L < 5 . 105;pr > 0.1 3a

Nui. = 0.13(ReL Pr) °5

Laminar flow

[42]

ReL < 5 . 105;Pr < 0.1 ( 3b

d )1/3( ~ )0.14

Nu a = 1.86 Re d P r ~

~ss

Laminar flow

[71]

Re d _< 2100; Pr > 0.7 3b

3c

Nu d = 3.65

(

)o.14 /x /Xs

NuDH = 1.86 ReDh P r - - ~

Laminar flow

[80]

Re a < 3000 Laminar flow

[42, 71]

ReDH < 2100; Pr > 0.7 2ab D H -

3a

Nu L = 0.036 Pr°33(Re~ 8 - 23,200)

a+b

Turbulent flow

[5, 42]

Re L > 5- 105;pr > 0.5 3b

Nu d = 0.024 Re °8 Pr 1/3

Turbulent Flow

[40]

0.7 < P r < 5 104 < Re d < 105 3c

NUDH = 0.024 Re °'8 Pr °'37

Turbulent flow

[80]

ReDH > 3000 2ab D H -

3g

See reference

a+b

[19]

In both cases a smooth surface of the tube is assumed, U m is the mean velocity of the fluid. The pressure drop in a tube with length L and diameter D can be expressed by 4L AP = ~w-~--.

(17)

149

6. Thermodynamics of Microwave Devices TABLE 5 Average Nusselt Numbers for Free Convection Cooling Average Nusselt n u m b e r Figure

(Nu)

Remarks

Reference

3d

Nu L = 0.59(Gr L Pr) °25

L a m i n a r flow 10 4 _< G r L Pr _< 109

[51, 72]

3d

Nu L = 0.129(Gr L Pr) °33

Turbulent flow 109 _< Gr L Pr < 1012

[51, 72]

3e

Nu L = 0.54(Gr L Pr) °-25

L a m i n a r flow 10 5 < G r L P r < 1 0

[51, 72]

3e

Nu L = 0.14(Gr L Pr) °33

3f

Nu d = 0.47 G r 027 Pr °'25

8

Turbulent flow Gr L Pr > 10 s

[51, 72]

L a m i n a r flow

[13]

Re d < 2100; Pr > 0.7 3g

See Reference

[79]

Boiling Heat Transfer In this section cooling by vaporization is discussed. The arrangement which is considered consists of the hot plate at the temperature Ts which has to be cooled and which is covered by a liquid. Without any agitation of the liquid, this process is called pool boiling. The cooling properties of this arrangement are strongly dependent on the excess temperature ATx = T s - T s a t above the boiling point. At low ATx pure convection heat transfer is observed. If the temperature is increased individual bubbles due to beginning evaporation are formed. Simultaneously the boiling heat transfer coefficient h b increases because the bubbles have an increasing stirring effect. Additionally the heat transfer by evaporation becomes relevant. This regime is called nucleate boiling. At the critical excess temperature the maximum heat transfer coefficient h b is reached. A further increase of ATx results in coalescing bubbles. A vapor film is formed which covers the plate surface. The thermal resistance of this film causes a decrease of h b. This regime is called the film boiling region. Further information of the pool boiling behavior of liquids is found in the books of Holman [33] and Kreith [42]. For the heat flux per unit area, q b / A , in the nucleate boiling regime Rohsenow [68] proposed an experimentally fitted equation,

hfg

= Csf

~lhf~

g ( p l - pv)

P r ~ "7

(18)

150

Fricke, Krozer, and Hartnagel

b

! e

d

O

,

)

g

H

Figure 3. Schematic drawing of the geometries for the calculation of the convective heat transfer.

where ¢1

h~ /Zl or

g Pl' Pv

Pr~

specific heat of the saturated liquid enthalpy of vaporization viscosity of the liquid surface tension of the liquid-to-vapor interface gravitational acceleration densities of the saturated liquid and vapor Prantl number of the saturated liquid

Ws/kg K W s/kg kg/m s N/m m/s 2 kg/m 3

151

6. Thermodynamics of Microwave Devices

Values of the experimental determined constant, Csf , may be found in the books of Holman [33] and Kreith [42].

4. Heat Transfer by Radiation In contrast to heat transfer by convection and conduction heat transfer by radiation does not require a special medium for propagation. Therefore radiative heat transfer has to be considered especially under vacuum conditions. Radiation is essentially an electromagnetic wave emitted from a surface with a certain temperature. The emitted power per unit wavelength and per area of an ideal black body at a temperature, T, is given by Planck's law,

C1A -5 Eb'x-- e c2/;~7"- 1 '

(19)

c 1 = 3.74 x 1 0 - 1 6 W m 2 and c 2 = 1.44 X 1 0 - 2 K m .

(20)

with

Planck's law results in a spectral distribution of the emitted power with its maximum at the wavelength ~'max,

¢3 '~max- T ' m

(2a)

with c 3 = 2.8978 x 1 0 - 3 K m . Integrating Planck's law over wavelengths from 0 to ~ yields the total emitted power per unit area (Stefan-Boltzmann Law),

E b -- trT 4,

(22)

with tr = 5.67 x 1 0 - 8 W / K 4 m 2. Real surfaces emit less power than the ideal black body. The emitted power per unit area of such a gray body is described using the emissivity e: E

(23)

= e E b.

The emissivity e of various surfaces is listed in Table 6. It depends strongly on surface conditions such as smoothness and chemical content. If radiation strikes a surface, a part of the power is reflected by a factor (reflectivity, p), another part (transmissivity, ~-) is transmitted, and the rest is absorbed (absorptivity, a). Therefore one obtains the balance: ~'+p+a=

1.

For most cases the approximation a = e is valid.

(24)

152

Fricke, Krozer, and Hartnagel TABLE 6 Emissivities of Metals and Nonmetals Material

Temperature

Emissivity

(K) Metals Copper Steel Lead Steel Magnesium Tungsten Aluminum Stee 1 Lead Molybdenum Platinum Aluminum Steel Nickel Molybdenum Aluminum Nickel Copper Gold Gold Silver

Oxidized Rolled Oxidized Oxidized Oxidized Filament Casted P o lish ed Oxidized Filament Polished Rolled Polished Polished Polished Polish ed Polished Polished

430 300 472 300 550-1100 3589 300 300 300 1000-2867 300-900 300 385 385 385 300-450 300 300 530 700 500-900

Polished

0.76 0.67 0.63 0.61 0.55-0.2 0.39 0.3 0.24-0.29 0.23 0.096-0.202 0.05-0.104 0.08 0.074 0.072 0.071 0.04-0.06 0.045 0.03-0.04 0.018 0.022 0.02-0.032

Nonmetals Glass Water

300 273-385

0.94 0.95-0.963 0.3-0.18

A1203, 99.5%

For the exchange of radiation between two surfaces, one enclosing the other, i and j on temperatures Ti and T:, a shape factor F/,: is introduced for complete enclosures. The heat transfer rate between the surface A i and the surface Aj is given by

r;) q(i,j)

1

-

E i

1

1 -

e:

+ ~ - ~ - ~ eiA i Fi,jA i EjAj

"

(25)

In this equation ideal diffuse surfaces are assumed. This means that the

6. Thermodynamics of Microwave Devices

153

TABLE 7 Radiation Shape Factors for Diffuse Surfaces

1)_ 2

cos A 4a

Reference

Radiation shape factor

Figure

F12 =

(l+ t h

2 A + arcsin

[41]

1+~

[11, 20, 66]

3g

See references

4b

El2-- ~ 1 ( 1 + R 2 + R 2 - ¢ ( 1

2 22) + R 2 + R 2 2 ) 2 - 4R1R

[81]

ri

Ri=

x2) 2 E1

A = X 2Y1 arctani -~1

4c

F12 -

Ti'X1X2 ai

~ In

YI=¢I+X

X i = - if"

2"

)

+

1

4 X 2 In

ai

+A

X1Y 2 arctan

Y2=¢I+X

[21,41]

2 1

Xlarctan X---7 + X2arctan X2

Xl = ~ "

4e

1 + X21 + X 2

X~ - X 2 arctan X 2

1

1

F12 = ~ 1

+-

-- X1 arctan

o

~ 1 2 arctan ]/FY12

(1+Y12)X 2 (l+Y12)X 2 1+Y12]) YIY12 + X 2 In YzY12 - In YIY2) [81]

Y12 = X2 + X2;

II1

= 1 +

X 2"

Y2

=

1 +

X2

2 X 3 )2 F12 =2-~1

-

ai

Xi-

b

1+

1+

+

2

2

-

1+

1+

2

2

[21]

radiation is constant in all directions. Especially the radiation of nonconductors is concentrated in the direction normal to the surface, whereas conductors exhibit broader directivity.

154

Fricke, Krozer, and Hartnagel

Because of the geometrical symmetry one obtains the equivalence (26)

Z i f i,j = Z j F j , i.

The shape factor Fi, j is defined by 1

Fi'j=

cos ~i COS ~j- d A i d A y

Aifi[j"A"A

"n'r 2

"

(27)

In this equation ~i is the angle between the normal to the surface of A i and the connecting line between A i and Aj. In Table 7 the shape factors Fi, j for different arrangements (Figure 4) are presented. In all cases ideal diffuse surfaces are assumed. The procedure for the computation of the radiative heat transfer among more than two surfaces is discussed in detail by Holman [33]. A more rigorous treatment of radiative heat transfer can be found for instance in the books of Gray [29], Cheremisinoff [13], Holman [33], Simonson [72], and Kreith [42].

F2

e

°_1_ 2

o2 ~ ~ ~ - ~

a_L 2

Figure 4. Schematic drawing of the geometries for the calculation of the radiation shape factor.

6. Thermodynamics of Microwave Devices

155

5. M e a s u r e m e n t of the T h e r m a l Resistance IR Measurement For the IR measurement [49, 70] the infrared radiation from the surface of a semiconductor chip is detected using an IR microscope. Usually the detector in the microscope is liquid-nitrogen cooled. Since the IR emission of the chip depends on the emissivity of the different materials on the chip surface a calibration has to be performed prior to the measurement. The advantage of this method is that a profile of the chip surface temperature can be measured by scanning the measured spot over the chip surface. The spot is approximately 25 /zm in diameter. The measurement takes place as follows: • The chip is heated uniformly to certain temperatures. The corresponding calibration profiles of the detected IR radiation are measured and stored in a computer. These profiles are a measure of the emissivity of the chip surface at a certain point. • In the measurement step the heat sink is kept at a fixed temperature (generally the ambient temperature). The active device is biased and the IR-radiation profile is measured. Comparison with the data of the calibration step yields the temperature profile.

Liquid-Crystal Measurement The technique of measuring the temperature distribution of a hot surface by liquid crystals [49, 54, 83] uses the fact that the molecules of liquid crystals are aligned if the temperature is less than the isotropic temperature. At higher temperatures the molecules are disordered. For the measurement a thin film of liquid crystals is spun onto the surface to be measured. The film has to be as thin as possible since it improves the thermal conductance. The surface of the sample is illuminated with polarized light. A second polarizer is placed in the path of the light reflected from the device under test. Before the measurement the second polarizer is rotated such that an uncovered surface appears black. A part of the light is passing through the system, if the coated sample is colder than the isotropic temperature. This is accomplished by the liquid crystals which work as an additional polarizer. Spots on the surface above the isotropic temperature appear dark because no additional polarization is produced by the liquid crystals. This technique is useful to detect hot spots on the surface and to determine the thermal resistance of a device. For this purpose the device

156

Fricke, Krozer, and Hartnagel

is biased until the isotropic temperature of the device is reached. The temperature difference between isotropic and heat sink temperatures divided by the dissipated DC power yields the thermal resistance.

Electrical Measurement The temperature of a device can also be determined by an electrical method in which a temperature-dependent characteristic of the device is used as a temperature sensor. This may be the temperature-dependent current-voltage characteristic of a Schottky diode [83] or the resistance of the gate metallization [22a, 23], in the case of a MESFET. For bipolar devices the temperature dependent base-emitter voltage needed to maintain a certain collector current is proposed [3a]. The measurement is performed as follows: • For the calibration the device under test is heated uniformly in an oven to a certain temperature. The temperature-dependent electrical characteristic of the device is measured with short pulses. The data of this measurement are stored. • In the measurement step the heat sink temperature is kept constant and the device is biased for normal operation. This bias condition is interrupted for short periods in which the temperature-dependent electrical characteristic is evaluated. Comparison with the calibration data yields the temperature of the device under operation conditions provided the interruptions for the measurement are short enough. This method can be used to determine the thermal resistance of a device.

6. Thermal Enhancement Techniques A schematic drawing of a microwave device inserted into a package with a conductive, convective, and radiative cooling possibilities is illustrated in Figure 5. Also indicated are the respective conductive thermal resistances of device, solder chip carrier, package, finned heat sink, etc. The total thermal resistance can be obtained by means of the equivalent circuit. For a detailed analysis the interfacial effects among the different materials have to be included: 1. gap between two materials increases Rth and 2. mismatch of energy bands in the momentum space yields an increased R th due to reflection of phonons at the interface even in singlecrystal transitions.

6. Thermodynamics of Microwave Devices

I S7

q Rc chip

Rc solder

Rc pack.

Rcl

Rc2

U U Ta= Temperature of Air

Ta

Ta

To

Figure 5. Schematic drawing of a packaged device with a heat sink and the equivalent thermal circuit for steady-state heat transfer. chip

flip- chip

embedded

A

ftatpack

0

X

1000 ~_

..-

100 8 C 2

10-

~

1

E

0.1

"

,, cooting

-

~ w o t e r ~

"

~,_

= -

'=

~

=

microchonne[ cooting

±

forced air cooting- air s t r e a m vetocity [ m / s ] forced water, cooting, water, vetocity [0.1m/s] micr'ochannet cooting, water" pressure drop[psi] Figure 6. Comparison of calculated thermal resistances of chip devices, flip-chip mounting, embedded mounting, and a flat-pack package for different cooling methods.

The thermal resistances can be calculated according to the following formulas due to conduction, Rcona, convection, Rconv, and radiation, Rrad"

Rc°nd =

1 kS

1 Rc°nv = -

hcA s

T 1 -- T~

Rrad=

o'AF12(T 4 _ T4)

.

(28)

158

Fricke, Krozer, and Hartnagel

The expression for R r a d gives the thermal resistance of a radiating body at temperature T 1 surrounded by a black surface on temperature T2 [42]. T~ is a reference temperature [Equation (10)] which is needed in the equation of the transferred heat:

qrad--

1 W---( T -

1-

T~).

(29)

r'rad

TABLE 8 Thermal and Electrical Properties of Metals at Room Temperature k Material

a

w ) ( 10.6

Ag 430 A1 204-240 Au 315-345 40%Au-60%Pt 26 10%Au-90%Pt 76.3 97%Au-3%Si 27 80%Au-20%Sn 57 Brass, 7 0 % C u - 3 0 % Z n 81-116 Constantan, 60%Cu-40%Ni 22.7 Cr 68.8 Cu 380-398 In 82 Mg 171.3 Mo 130-146 Ni 90 NiFe 15 Pb 30-35 Pb-5%Sn 63 50%Pb-50%Ti 46 Pd 71.2 Pt 73 Sn 30 Steel = 50 Ta 54.4 Ti 22.6 W 150 Zn 113

p

co

pd kg

x g-

( × 10-6~ cm)

18 25 14.3

1.6 2.6 2.4

234 900 130

10.5 2.7 19.3

5.2

385 410

8.5 8.9

385

12.3 15.9 17.5 14 4 17 33 4 13 4.14 29 29 29 11 9 23 12 4.5 9 4 29

13 1.7 8.2

( Ws

4.8 1.75

1013 250 450

8.95 7.3 1.74 10.2 8.9

25

130

11.34

10.66 10.66 13 15.65 47.6 5.5 11.5

180 243 134 230 460 151 489 133 385

12 14-19

16.6 4.5 19.3 7.3

159

6. Thermodynamics of Microwave Devices

In the example of Figure 5 T2 is the temperature of the plane opposite to the finned heat sink. T~ may be chosen as the temperature of the surrounding air (T~ = Ta). Each of these resistances can be individually minimized in order to facilitate the heat flow from the device active region to the surrounding area. An example of the determination of the overall thermal resistance of a similar structure has been developed by Donzelli [18]. Improvement of

TABLE 9 Thermal Properties of Insulators at Room Temperature k

Material

AIN 90% A1203 99% A1203 BeO BN Diamond D- MAT 6 D-450 b Epoxy 70% SiO 2 Epoxy glass Glass Glass/ceramics Polimide P T F E 6002 c Quartz Sapphire SiC (poly) Si3N 4 SiO 2 S-145 b TiO 2 Triazine

(w) 70-320 16.7-20 25-37 150-370 500-1300 2200 8.8 4.18 0.2 2 = 0.76 0.3-5 0.07 0.44 1.4 42 40-270 25-30 1.4 34 7 0.2

a

Cp

pd

10-6) (Ws) (

× ~

k-~

2.56-4.5 6.7 6.3-8 5.4-8.5 4.8 1.0 8.2 2.9 20 15 0.4-0.6 3.0 50 24

736 770 770 1020 498 6200 837 821

3.3 3.9 3.9 2.9 5.4 3.5

837 728

2.71

6 3.4 0.8-30 0.5 12.8 7.5 50

930 780 620 170 1400 967

× 103m-5-

TDLQ a

w) 0.087-0.82 0.067-008 0.29-0.49 0.4-1.55 1.59-4.14 0.036-0.056 0.026

0.004-0.145 0.0014 3.98 3.2

0.41-0.5 0.0002-0.0016

4.24

0.19 0.00017

Note. For details, see Kurokawa [45], Werdecker [84], McGillivray [52], Koba [39], and Miyashiro [55]. aTDLQ is the thermal dielectric loss quotient: T D L Q = [ k ( W / m • K)]/[8.854 ( p F / m ) •r tan ~ • 104]. bRegistered trademark of TRANS-TECH, Inc. CRegistered Trademark of Rogers Corp.

160

Fricke, Krozer, and Hartnagel

the thermal resistance of the semiconductor chip can be obtained by the following: • applications of a substrate material with higher thermal conductivity for example, InP instead of GaAs, or GaAs grown on Si; • thinning of the chip, via holes [15, 25], flip-chip mounting [83], or plated heat sinks [74]; and • appropriate thermal device design [17, 18, 26, 28, 36, 75]. The thermal resistance of the solder can be optimized by increasing the effective contact area and solder thickness. Further discussion is included in the review paper of Fletcher [24] and in the contributions of

TABLE 10 Electrical Properties of Insulators at Room Temperature er Material

AIN 90% m 1 2 0 3 99% A120 3 BeO BN Diamond D - M A T (a) D-450 (a) Epoxy 70% SiO 2 Epoxy glass Glass Glass/ceramics Polimide P T F E 6002 (b) Quartz Sapphire SiC (poly) Si3N 4 SiO 2 S-145 (a) TiO 2 Triazine

8.8-9.1 9.4 8.5-9.8 6.7 7.1 5.5 8.9-14 4.5 3.8 4-5 3.8-7 3.9-7.8 3.5-5 2.94 3.8 9.4-11.6 40 6 ~ 10 10 85 3.1

Emax

p

~ cm

(f~ cm)

( × 10 -4)

0.14-0.17 0.2 0.2 0.1

5.0- 1013-1.0 • 1014 > 1.0. 10 TM > 1.0. 10 TM > 1.0. 10 TM ~ 1.0" 1013 1.0-1020 > 1.10 TM = 1.0- 10 TM 4 • 1016 1.0 • 1011

5-10 3 1 5 5

(Mv)

10 0.08 0.08

tan

< 2 < 4

1 1.0.1016 = 1.0. 101° 10 4 0.0007

0.08

> 1.0 • 10 TM 1.0" 1016 1.0" 1014 > 1.. 10 TM

12 1 500

< 2 40

>__ 1.0. 1013

Note. For details see Kurokawa [45], Werdecker [84], McGillivray [52], and Koba [39]. aRegistered trademark of T R A N S - T E C H , Inc. bRegistered trademark of Rogers Corp.

161

6. Thermodynamics of Microwave Devices

Pavio [63] and Prior [65]. The package thermal resistance has a large influence on the overall thermal resistance as has been indicated by Pence [64], Le Jannou [47], Ohsaki [60], Tummala [78], Wesseley [85], Ortega [61], Ozmat [62], Harkins [32], Estes [22], and Handa [31]. The convective heat transfer can be improved by the following: • • • plate •

forced convection instead of natural convection [32]; optimization of the dimension of the fins [19, 79]; utilizing two-phase convective heat transfer by using heat pipes or pipes [14, 38, 76, 87]; and optimization of the cooling agent (water, liquid nitrogen, etc.)

The heat transfer by radiation can be improved mainly by the proper choice of the surface of the radiator in order to achieve a high emissivity, e. Also the allowance of a higher surface temperature (higher active device temperature) yields a lower thermal resistance.

TABLE II Electrical and Thermal Properties of Semiconductors at Room Temperature

k Material

Bi2Te 3 GaAs GaN GaP GaSb Ge InAs InP InSb PbTe Si a-SiC /3-SIC

W

a

10-6)

•

× ---U0.2 46 150 77-110 33 60 26 70 12 0.4 148 500 500

Emax

c--~

4.5-6.63 5.6 5.3 6.7 5.7 5.19 4.56 5.04

13.1 9.5 11.1

0.6

16 12.55 12.35 17.7

1.0

2.6 5.5 5.5

11.9 9.7 9.7

0.5 4.0 4.0

5.0

Cp

p

ws t 325 487 436 255 310 252 310 207

5.32

710

2.33

5.32

Note. For further details, see Brice [7] (GaAs), Brice [8] (InP), Sze [73], Miiller [56], ( I I I / V compounds), Neuberger [57] ( I I I / V compounds), Johnson [34] (thermal expansion), and Matus [50] (SIC, GaAs, and Si, diamond).

162

Fricke, Krozer, and Hartnagel

10 ,---., oO

E •¢

,--._,

1 ~

>,, th cE]

-

0

2

0.1

0.01 100

1000

Temperoture[K] Figure 7. Density of gases as a function of temperature. TABLE 12 Thermal Properties of Solders T

Solders

Composition

(°C)

Ag Cu Au Ge Au In Au Si Au Si Au Sn Au Sn Au Ti Pb Ag Pb In Pb In Pb Sn Pb Ti Ag Pb Ti Ag Pb Ti Ag Ti Ag

72-28% 88-12% 82-18% 96.4-3.6% 94-6% 80-20% 71-29% 80-20% 97.5-2.5% 95-15% 81-19% 90-10% 92.5-5-2.5% 97-1-1.5% 93-5-2% 96-4%

780 E (a) 356 E (a) 415-485 370 370 280 E (a) 278 280 303 E (a) 292-314 270-280 275-302 300 309 280 221

k W

( 1°-6 t

27

12.3

57

15.9

25.53

(a) E, eutectic temperature.

The simulated results for the thermal resistance for a number of packages are illustrated in Figure 6. It can be inferred from this figure that flatpack packages are efficient for forced air and water cooling, whereas

163

6. Thermodynamics of Microwave Devices

the bare chip exhibits the lowest thermal resistance in the case of microchannel cooling. Pence [64] also gives closed form expressions for the thermal resistance for each cooling method.

7. Thermal Properties of Electronic Materials The thermal and electrical properties of metals, semiconductors, insulators, and substrate materials are summarized in Tables 8-11 for room temperature. The quantity TDLQ in Table 9 determines the measure of suitability of isolating materials for applications in microwave circuits. Insulating materials with high thermal conductivity, low loss, and low capacity yield high values of the TDLQ. From the parameters given in Tables 8-11 and Figure 7 the thermal diffusivity can be determined directly. The thermal properties of solders are given in Table 12 The consideration of the different expansivities (see figure 8) of the various materials is of paramount importance for device design [65, 69], device and circuit attachment [63, 65], material fabrication [35, 69], and package design [12, 55], because of the stress introduced if materials with different expansivities are attached together.

.--.

20 18

~"

16

b

~-x

........-

-"

Cu

.........-

.....-

12 10

BeO

o tO 13. X

i,i

/.,

~ / A l t o y / , " |

100

I

200

i

I

3o0

i

I

~00

2

i

"~ SiC I

,

500

1

600

i

I

|

700

Temperature [K] Figure 8. Expansivity of different materials as a function of temperature.

800

164

Fricke, Krozer, and Hartnagel

References S. Adachi, J. Appl. Phys., Vol. 53, pp. 8775-8779, 1982. S. Adachi, J. Appl. Phys., Vol. 54, pp. 1844-1848, 1983. S. Adachi J. Appl. Phys., Vol. 58, pp. R1-R29, 1985. M. G. Alderstein, and M. P. Zaitlin, IEEE Trans. Electron Dev., vol. ED-38 No. 6, pp. 1553-1554, 1991. [4] D. Agonafer, and S. Furkay, 6th Annu. IEEE Semicond. Therm. Temp. Meas. Symp., SEMI-THERM, Phoenix, AZ, p. 103, 1990. [5] R.A. Baker, and A. Sesonske, Nucl. Sci. Eng., Vol. 13, 282, 1962. [6] J. P. A. Bastos, N. Sadowski, and R. Carlson, IEEE Trans. Magn., Vol. MAG-26, pp. 536-539, 1990. [7] J.C. Brice, in Properties of GaAs, 2nd Ed., pp. 1-25. London: INSPEC, 1990. [8] J. C. Brice, A. D. Prins, S. Adachi, K. Haruna, D. J. Dunstan, and H. Maeta, in Properties of InP, pp. 3-23, London: INSPEC, 1991. [9] R.B. Brooks, and H. P. Mattes, Bell Syst. Tech. J., Vol. 50, pp. 775-784, 1971. [10] R. A Brow, T. A. Kinney, P. A. Sachinger, and D. E. Bornside, J. Cryst. Growth, Vol. 97, pp. 99-115, 1989. [11] L. Buller, and B. McNellis, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-4, pp. 538-544, 1978. [12] R. Chanchani, and P. M. Hall, IEEE Trans. Components Hybrids Manuf. Technol. Vol. CHMT-13, pp. 743-750, 1990. [13] N. P. Cheremisinoff, Heat Transfer Pocket Handbook. Houston, TX: Gulf Publishing Co., 1984. [14] P.V. Ciekurs, and W. D. Brokaw, Microwaves RF, Vol. 27, pp. 83-88, 1988. [15] O. P. Daga, K. Fricke, and H. L. Hartnagel, J. Electrochem. Soc., Vol. 133, pp. 2660-2661, 1987. [16] R. Darveaux, I. Turlik, L.-T. Husang, and A. Reisman, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-12, pp. 663-672, 1989. [17] J. Dell, T. S. Kalkur, Z. Meglicki, A. G. Nassibian, and H. L. Hartnagel, (1984). Int. J. Electron., Vol. 57, pp. 155-160, 1984. [18] P. Donzelli, G. Ghione, and C. U. Naldi GaAs '90, Gallium Arsenide Appl. Symp., Rome, pp. 120-125, 1990. [19] G.N. Ellison, IEEE Trans. Parts Hybrids Packag., Vol. PHP-4, 371-378, 1976. [20] G.N. Ellison, IEEE Trans. Parts Hybrids Packag. Vol. PHP-4, 517-522, 1979. [21] ESA, Spacecraft Thermal Control Design Data, Vol. 1. Nordwijk, Netherlands: ESTEC, ESA Publications Div., 1989. [22] R. C. Estes, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 843-859, 1992. [22a] D. B. Estereich, 5th Annual IEEE Semicond. Therm. Temp. Meas. Symp. San Diego, CA, Feb. 7th-9th, 1989. [23] W. Fallmann, H. L. Hartangel, and P. C. Mathur, Electronl Lett., Vol. 7, pp. 512-513, 1971. [24] L. S. Fletcher, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-13, pp. 1012-1021, 1990. [25] K. Fricke, Die Optimierung des GaAs-Leistungs-MESFET unter Beeriick-sichtigung seiner verteilten Eigenschaften. Diisseldorf: VDI Verlag, 1989. [26] G.-B. Gao, M.-Z. Wang, X. Gui, and H. Morko~, IEEE Trans. Electron Devices, Vol. ED-36, p. 854-863, 1989. [27] G.A. Garfinkel, Circuit Des., Vol. 7, pp. 54-57, 1990. [1] [2] [3] [3a]

6. Thermodynamics of Microwave Devices

165

[28] G. Ghione, P. Golzio, and C. U. Naldi, Alta Freq., Vol. 57, pp. 311-320, 1988. [29] W. A. Gray, and ~r. Miiller, Engineering Calculations in Radiatiue Heat Transfer. Oxford: Pergamon Press, 1974. [30] A. Hadim, A. T. Chang, A. Chu, and A. Yskamp, Trans. ASME, J. Electron. Packag., Vol. 111. pp. 54-60, 1989. [31] T. Handa, S. Iida, and Y. Utsunomiya, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-16, pp. 384-387, 1993. [32] L . E . Harkins, and D. J. Nelson, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 761-770, 1992. [32a] R. K. Hoffman, Integrierte Mikrowellenschaltungen. Springer Verlag, 1983. [33] J.H. Holman, Heat Transfer, 3rd Ed. New York: McGraw-Hill, 1968. [34] R. W. Johnson, Final Rep. Workshop High Temp. Electron., Albuquerque, NM, pp. C3-C18, 1989. [35] A.S. Jordan, and R. Caruso, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-11, pp. 464, 1988. [36] W.B. Joyce, Solid-State Electron., Vol. 18. pp. 321-322, 1975. [37] S. Kaka~, R. K. Shah, and W. Aung, eds., Handbook of Single-Phase Conuectiue Heat Transfer. New York: John Wiley & Sons, 1987. [39] R. Koba, and W. A. Russell, Final Rep. Workshop High Temp. Electron., Albuquerque, NM, pp. C185-C210, 1989. [40] H. Kraussold, Forsch. Ingenieures., Vol. 4, pp. 39-44, 1933. [41] F. Kreith, Radiation Heat Transfer for Spacecraft and Solar Power Plant Design, pp. 204-229. Scranton, PA: Int. Textbook Co., 1962. [42] F. Kreith, Principles of Heat Transfer. New York: Intext Educational Publishers, 1973. [43] V. Krozer, "Verfahren der Kleinsignal- und Grossignalanalyse und Charak-terisierung von Mikrowellenschaltungen und Bauelementen mit Hilfe der Volterra Reihe," Ph.D. Thesis, Darmstadt, Germany, 1991. [44] H. Kuhn, Wiss. Z. Tech. Uniu. Dresden, Vol. 39, pp. 18-23, 1990. [45] Y. Kurokawa, K. Utsumi, H. Takmizawa, T. Kamata, and S. Noguchi, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-2, pp. 247-252, 1985. [46] J.H. Lau, Trans. ASME, J. Electron. Packag., Vol. 111, pp. 312-320, 1989. [47] J. P. Le Jannou, and Y. Yuon, IEEE Trans. Components. Hybrids Manuf. Technol., Vol. CHMT-14, pp. 366-373, 1991. [48] W. Liu, and B. Bayraktaroglu, Solid-State Electron., Vol. 36, pp. 125-132, 1993. [49] H.M. Macksey, in GaAs FET Principles and Technology (J. V. DiLorenzo, and D. D. Khandelwal, eds.), pp. 257-278, Dedham, MA: Artech, House, 1982. [50] L.G. Matus, J. A. Powell, and J. B Petit, Trans. 1st Int. High Temp. Electron. Conf., Albuquerque, NM, pp. 222-228, 1991. [51] W.H. McAdams, Heat Transmission, 3rd Ed. New York: McGraw-Hill, 1954. [52] K. McGillivray, Final Rep. Workshop High Temp. Electron. Albuquerque, NM, pp. C163-184, 1989. [53] Y. J. Min, A. L. Palisoc, and C. C. Lee, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-13, p. 980, 1990. [54] M. Minot, "Auantek Application Note," ATP-1072/7-86, 1986. [55] F. Miyashiro, N. Iwase, A. Tsuge, F. Ueno, M. Nakahashi, and T. Takahashi, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-13, pp. 313-319, 1990. [56] G. Miiller, H. Jacob, in Landolt-B6rnstein, New Series (K.-H. Hellwedge and O. Madelung, eds.), Vol. 17d, pp. 12-17. Berlin: Springer-Verlag, 1984. [57] M. Neuberger, III-V Semiconduction Compounds. New York: IFI/Plenum Data Corp., 1971.

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Fricke, Krozer, and Hartnagel

[58] C.K. Ng, IEPS Proc. Tech. Conf., 9th Annu. Int. Electron. Packag. Conf., San Diego, pp. 530-534, 1989. [59] P . Y . C . , Normington, M. Makalingam, and T. Y. Tom Lee, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 806-814, 1992. [60] T. Ohsaki, IEEE Trans. Components Hybrids Manuf. Technol. Vol. CHMT-14, pp. 254-261, 1991. [61] A. Ortega, and H. Kabir, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 771-777, 1992. [62] B. Ozmat, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, 860-869, 1992. [63] J.S. Pavio, IEEE Trans. Microwave Theory Tech., Vol. MTT-35, pp. 1507-1511, 1987. [64] W. E. Pence, and J. P. Krusius, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-13, pp. 245-251, 1990. [65] C.J. Prior, and E. J. Crescenzi, Jr., Microwave J., Vol. 31, pp. 157-164, 1988. [66] S.N. Rea, and S. E. West, IEEE Trans. Parts Hybrids Packag., Vol. PHP-2, 115-117, 1976. [67] C.J. Ritter, Proc. Tech. Program, NEPCON East '89, Boston, 1989. [68] W.M. Rohsenow, Trans. ASME, Vol. 74, pp. 969-975, 1952. [69] B. S. H. Royce, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-11, p. 454, 1988. [70] F. N Seschi, B. S. Perlman, and J. M. Cusack, IEEE MTT-S, Int. Microwave Symp. Dig., p. 143, 1977. [71] E.N. Sieder, and G. E. Tate, Ind. Eng. Chem., Vol. 28, p. 1429, 1936. [72] J. R. Simonson, An Introduction to Engineering Heat Transfer, 3rd Ed. New York: McGraw-Hill, 1967. [73] S.M. Sze, Physics of Semiconductor Devices, 2nd Ed. New Delhi: Wiley Eastern, 1981. [74] G.C. Taylor, D. Bechtle, S. G. Lin, P. Jozwiak, and R. Camisa, Microwaves RF, Vol. 30, pp. 00-00, 1991. [75] G.C. Titinet, P. M. Scalafiotti, CSELT Tech. Rep., Vol. 18, pp. 37-41, 1990. [76] T. Y. Tom Lee, and M. Makalingam, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 778-785, 1992. [77] T.Y. Tom Lee, and J. A. Andrews, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 786-793, 1992. [78] R. R. Tummala, IEEE Trans. Components Manuf. Technol., Vol. CHMT-14, pp. 262-271, 1991. [79] D . W . Van de Pol and K. Tierney, IEEE Trans. Parts Hybrids Packag., Vol. PHP-10, pp. 267-271, 1974. [80] D. van Leyen, Wiirmeiibertragung. Berlin: Siemens AG, 1971. [81] VDI, VDI-Wiirmeatlas. Diissseldorf: VDI-Verlag, 1963. [82] A. Virzi, J. Cryst. Growth, Vol. 97, pp. 152-161, 1989. [83] S. H. Wemple, and H. C. Huang, in GaAs FET Principles and Technology (J. V. DiLorenzo, and D. D. Khandelwal, eds.), pp. 309-349. Dedham, MA: Artech House, 1982. [84] W. Werdecker and F. Aldinger IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-4, pp. 399-404, 1984. [85] H. Wessely, O. Fritz, M. Horn, P. Klimke, W. Koschnick, and K. H. Schmidt, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-14, pp. 272-284, 1991. [86] I. Witte, Wiss. Z. Tech. Univ. Dresden, Vol. 39, pp. 23-26, 1990. [87] S.M. You, T. W. Simon, and A. Barcohen, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 823-831, 1992.

CHAPTER

7 Microwave Antennas John Hill and Mary Lynn Smith

The

necessary length of this chapter precludes extensive treatment of any one antenna subject. The objective is primarily to direct the reader to sources of detailed theory and design information. Thus this chapter provides a very broad view of microwave antennas. The material is organized to follow the outline of a generic antenna specification. A microwave antenna has been arbitrarily chosen to be an antenna with an operating frequency higher than 1 GHz or with a wavelength of 30 cm (11.8 in.) or less. An upper frequency has not been reached, although the FIRST (far infrared and submillimeter telescope) antenna is being designed for the 300- to 3000-GHz frequency band. The first microwave antenna may have been a cylindrical parabola with a spark-gap-driven dipole at the focal point, built by Heinrich Hertz in the 1880s. Following this, little work was done at microwave frequencies until the 1930s, when the beginnings of World War II created the conditions which fostered the development of radar. By 1947, when Microwave Antenna Theory and Design [1] was published, the principles of most antennas in use today had been established. The 45 ensuing years have seen the refinement of those early designs and the development of the wide-band frequency-independent antennas (spirals and log periodic dipole arrays) and the narrow-band transmission-line antennas (microstrip patch) and the phased array. An antenna engineer given a sleeping potion in 1947 and awakened in 1995 would have little trouble understanding current antennas. He would,

Handbook of Microwave Technology, Volume 2

167

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

168

Hill and Smith

however, be amazed by the test equipment and the amount of antenna literature available. See the bibliography for a list of publications found to be valuable in the daily work of antenna design.

I. A n t e n n a Defined An antenna is a transducer which converts electromagnetic fields in space into current on a transmission line, converts current on a line to an electromagnetic field, or both. The purpose of an antenna is to transmit RF energy in a defined direction or to receive RF energy from a defined direction. Often the same antenna is required to do both.

Antenna Requirements and Specifications For the purpose of this discussion, an antenna requirement is the performance desired by the buyer. An antenna specification is the description of an antenna and its performance for the purpose of selling. Antennas are unique when compared with most other microwave devices. They are one-port reciprocal devices from the point of view of bench testing, for their second port is accessible only with a very special measuring tool, the pattern range. Impedance characteristics and power capability are tested in the transmit mode. Pattern characteristics are usually measured in the receive mode even when the antenna is to be used to transmit. An antenna's performance is determined by its physical structure and by its location. The step-by-step definition of an antenna requirement/specification is a convenient method of introducing antenna principles. An antenna requirement/specification will contain most of the following parameters. Following sections will treat the definitions in more detail. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Frequency Beamwidth Directivity Gain Polarization (of an Antenna) Sidelobes Squint Voltage Standing Wave Ratio (VSWR) Power Handling G/T Site Environment Special Terms

7. Microwave Antennas

169

Each subject will include some or all of the following: a. b. c. d. e. f. g.

Definition Units Related terms Measurement accuracy Significance Comments References

A requirement or specification implies that the parameters defined can be verified by testing and that the test results are accurate enough for the purpose intended. Because the measurements of an antenna's characteristics are often complex, a test procedure is an important adjunct to the specification, and it is the test procedure, rather than the specification, which usually determines an antenna's acceptance. Acceptance criteria are very significant when an antenna is required to perform in a complex environment such as a ship, aircraft, missile, or spacecraft. An antenna requirement should have some basis in reality. It is recognized that advances come about through attempts to meet difficult requirements, but unrealistic expectations lead to frustration on both sides. "A man's reach should exceed his grasp," but not beyond nature's limits. Thus many of the following approximations serve to define the possible and help the system engineer avoid the unobtainable. Frequency

The frequency range over which all of the other parameters apply. Units: Gigahertz Related terms: F h = highest frequency and F 1 = lowest frequency Bandwidth = F h / F 1 = 2 / 1 = octave Percentage bandwidth = ( F h / F 1 - 1)100 Center frequency = C F h X F 1 To divide a frequency range, F~ to F h into rl subbands of equal ratio, 1 . In swept frequency measurements the points within the sweep are usually not critical. Beginning and ending frequencies should be set with care. The number of points in the sweep (when using a synthesized source) should be sufficient to reveal all the peak values. Significance: Frequency is the first antenna requirement to be established and may result from factors external to system design. The performance of broadband antennas, for which bandwidth is 50% or greater, is not particularly sensitive to frequency. Microstrip patch antennas and waveguide slot arrays, however, with a bandwidth of 5% and less, must be tested at exact frequencies.

x" x = '~/F h / F

170

Hill and Smith

Comments: The majority of microwave antennas operate at frequencies of 1 to 18 GHz, with diminishing usage from 18 to 40 GHz. Above 40 GHz the horn is the most practical device, as other types become difficult to fabricate. Any type requiring coaxial lines above 18 GHz becomes impractical, although coaxial connectors to 65 GHz are available. Beamwidth

Usually taken to be the half-power beamwidth, the angle between the two directions in which the amplitude of the major lobe is one half the maximum value. Usually two orthogonal beamwidths (such as vertical/ horizontal and E p l a n e / H plane) are defined, with maximum and minimum values. Figure 1 illustrates beamwidth and other pattern characteristics. Figure 2 is the standard spherical coordinate system used in antenna measurements. Units: Degrees and decibels from peak Related terms" Principal half-power beamwidths, E plane, H plane, radiation pattern, and free space Measurement accuracy: Beamwidth is measured at the two intersections of the pattern trace and the reference level. Two factors are to be considered: the accuracy of the positioning and recording equipment and the accuracy of reading the data. If beamwidth is manually read from a

3 dB BEAMWIDTH

I1|! llll III1! I|1| IIII 1

'~II Ii,,i I

]

'°III11!oJAL,oL ,ll ",olllIII ,R,i~[l:J ii

t

.... ................ .[... I .... I I.... I .... I .... I I.... I .... I ................. ,I"

L

G, UN

t

t 1

ISOTROPIC LEVEL

°i~

~l~!

I~

ill r r!,t.... I/t

_,~,"~ ....=........,,,,~,,~"......[ 11I..l,.v,............ I ..................L.. II~ ................L............!t i -180

-150

-:120

-90

-60

o -30 AZIMUTH

~o

do

CI e g r e e s

Figure I. Pattern characteristics,

90

/...........,t/,,,I t ....

~o

150

|

180

171

7. Microwave Antennas O:O e

Z

0

=

90" 27'0"

" ' ~ ~.

v 0=90" 11, - 90"

0:90" ÷:o"

~

/

o : 180"

Figure 2. Standard spherical coordinate system.

pattern plot, accuracy is about 10% of the beamwidth. If determined with automatic equipment, accuracy may be about 5% of beamwidth. Significance: Beamwidth defines the capability of the antenna in directing transmitted energy in a desired direction or its ability to receive or reject waves from different directions. An antenna of narrow beamwidth and low side lobes may be considered a spatial filter. An antenna with very narrow beamwidth must be pointed accurately in order to derive benefit from the higher gain. Comments: Common beam shapes are pencil beam; fan beam; cosecant squared beam; monopulse beam; conical scan beam; cardiod beam; dipole pattern; isotropic pattern (omnidirectional).

Directivity The ratio of the maximum radiation intensity in a given direction to the radiation intensity averaged over all directions. (In the following discussion it is assumed that an antenna is a reciprocal device; therefore transmitting and receiving cases are interchangeable and equivalent. For further reading on reciprocity, see Reference [2].) Directivity is a measure of an antenna's radiation intensity in a particular direction and is the ratio of that radiation intensity to the average intensity over a sphere. Directivity is usually expressed in decibels

172

Hill and Smith

Figure 3. Directivity defined by power flow. (A) Power flow through a convenient spherical boundary, (B) power flow through a square area of I square degree, and (C) power flow through a circular area of 4 square degrees.

above isotropic and does not include efficiency factors such as ohmic and mismatch losses. Directivity is related to beamwidth. Assuming that a significant amount of radiated power is not diverted into minor lobes, directivity is inversely proportional to beamwidth. A simplified approximation of directivity may be found by considering a spherical boundary at which the power radiated by a directional antenna may be measured. All power may be imagined to flow outward and through the surface shown in Figure 3A. This surface may be divided into areas each occupying 1° in the vertical plane and 1° in the horizontal plane. The total surface of a sphere contains 41,253 square degrees, 360 2 4rr square radians (steradians) = 4rr - ~ = 41,253 square degrees. If all the power radiated flows through 1 square degree, as shown in Figure 3B, the directivity in that direction would be 41,253 times greater than if the power flowed equally through the surface of the sphere, which is the case with an isotropic, or point source radiator. The directivity, D, is then D=41,253/1

and

DaB= 101og10D=46dB.

A somewhat more accurate approximation of directivity from the pattern assumes that all power flows through an area which is circular in cross section, as in Figure 3. The area of a circle inscribed in the square is 4~r of the square area; therefore the resulting directivity is D = (41,253/®1®2)'47r = 52,525/191192,

7. Microwave Antennas

173

where 1~102 are the measured orthogonal beamwidths of the pattern DaB = 10 log10 52,525 = 47.2 dB.

In practical antennas, the beam is usually circular in cross section with many minor lobes and with the beamwidth measured at the - 3 - d B points. To account for this the assumption is made that 55% of the power radiated flows through the half-power beamwidth of the main lobe. The directivity is now approximated by DdB -- 10 log10 2 9 , 0 0 0 / O 1 0

2.

This is an approximation, but useful for estimation. Table 1 lists other useful approximations relating beamwidth, gain, and directivity for parabolas, horns, and arrays. TABLE I Formulas for Beamwidth and Directivity of Representative Aperture-Type Antennas Aperture

Aperture type

illumination

Beamwidth

efficiency (%)

(from aperture)

Directivity (from aperture)

100

O -

Uniformly i l l u m i n a t e d linear array

100

O1=

a

beamwidth)

10a 2

58A Uniformly i l l u m i n a t e d circular aperture (hypothetical)

Directivity (from

D -

~2

Sidelobes (dB)

52,525 D-

02

-18

,O

51A -13

a

16ab D -

?b,t

A.2

41,253 D-

O10 2

51A 02-

b 56A

Rectangular horn

60

-13

01 aE

E plane

8aEa H

D

/~2

D=

31,000 O102

67A H plane ~-ah--~

60

- 26

0 1 -aH

5a 2

72A Nonuniformly illuminated

55

0 -

a

D -

h2

29,000 D-

circular aperture a>>A Source. Courtesy of Watkins-Johnson Co. [6].

DdB = 10 log10 D

02

- 26

174

Hill and Smith

Directivity, D O

0 = 0°

0 = 90 °

0 - 900

001

~ 0o

0 = 180 ° Figure 4. Broad beamwidth antenna pattern.

For broad-beamwidth antennas, such as satellite terminal antennas, with beamwidths on the order of 100 ° to 280 °, the simple pencil-beam approximations yield pessimistic values of gain. For these antennas, with patterns similar to those of Figure 4, the graph of Figure 5 is useful. The graph was prepared from the equation [3]: {~ -{- COS - 1

[(1

+ k

-

2~Do)~(1

-

k)].

Gain

Gain is simply directivity reduced by antenna dissipation losses. Gain and effective area: Gain, G, to be precise, is defined for the transmitting case and effective area, Ae, for the receiving case. The properties are related by G = 4~'Ae/A 2 or

A e = GAZ/41r.

In practice, the distinction is generally ignored. Units: Isotropic decibels (dBi) for gain with respect to the theoretical isotropic source of like polarization. Frequently, the letter 1 or c is added to dBi to indicate the polarization (i.e., dBic for gain with respect to the

175

7. Microwave Antennas

Beam SemiAngle 8o

Imllm/limlmml

140° ~1~ 13°°

120°

11o°

.o

Backlobe

• 1O0°

90 °

-20 dB -15d

/

•

-

8o °

70° -10 dB

~ ,

-,,,,

6o °

50°

o

I 1 1

1 I J 1

2

I I 1

3

1 I I

4

1 1 ! I 5

Gain (dB) Figure 5. Directivity versus beam semiangle for broad beamwidth antennas,

isotropic source of circular polarization and dBil for gain with respect to the isotropic source of linear polarization). Related terms" Partial gain, realized gain, directivity, and effective area Measurement accuracy: The measurement of gain is probably the most difficult of all antenna measurements. It is an indirect measurement with a number of variables. With extreme care and attention to detail, + 0.25 dB is achievable. The standard gain antenna substitution method is usually used. The three-antenna method is also used. Refer to References [2] and [4], Microwaue Antenna Measurements, for a more detailed discussion of gain measurement methods. Measuring the gain of circularly polarized antennas adds another dimension of difficulty, for there is no circularly polarized standard gain reference. A method often used is to measure the gain of the antenna with reference to two orthogonal linear

176

Hill and Smith

polarizations, O1 and

~2" Gain

is then

G = (Gol + G o 2 ) / 2 .

Significance: Gain defines the capability of an antenna in a communications link. Directivity defines the antenna's ability to reject waves from other than the desired direction. Comments: "Gain" in a specification usually refers to the gain of the antenna in the direction of maximum radiation for matched polarization, yet the performance of interest is partial realized gain, for a stated polarization, in a stated direction. This is the parameter of interest to the systems engineer. To obtain this value, it is important to specify the point in the system at which the gain is to be defined. This point is usually at the connector nearest the antenna, whereas the gain from the system point of view is at the input to the receiver or output of the transmitter. References: Gain is discussed in most antenna books. Kraus [5] is recommended. For a simplified explanation, with minimum mathematics, see Reference Hill [6].

Polarization (of an Antenna) In a given direction, the polarization of a wave radiated by an antenna or the polarization of a wave which produces maximum power at a receiving antenna's terminals. Units: Decibels for polarization ratios and ' ellipticity; degrees for orientation of polarization ellipse; and right or left hand for sense Related terms: Elliptical, circular, right-hand circular, left-hand circular, linear, vertical, horizontal, slant linear, copolarization, cross polarization, axial ratio, and dual polarization Measurement accuracy: (a) Right-hand/left-hand circular: A right or wrong measurement and easily gotten wrong. The surest method is to test against a circularly polarized antenna of unmistakable polarization such as a spiral or helix. (b) Axial ratio: Easily tested with a rotating linear source antenna. Make sure that the antenna does not spin too fast for the recording system. The source must be truly linear and not elliptically polarized. (c) Tilt of ellipse: A factor of the mechanical accuracy of the positioning system and of the precision with which the plot can be read Significance: Varies with application, but in general the antenna's polarization requirement stems from a system requirement. Comments" Polarization can be the most complex of an antenna's characteristics. In the coupling of energy between antennas the polarizat i o n / g a i n factor is the essence of the link, yet the polarization aspect is often inadequately considered in the procurement requirement. All polarization is elliptical, with major and minor axes. The ellipticity is defined in

7. Microwave Antennas

177 TABLE 2 Polarization Mismatch Loss Equations

{5

{

Ellipse Ellipse

-101oglo{1/2 + 1/2

4TTTR+ ( 1 - - y 2 ) ( 1 - - T 2 ) ( C O S 2 / 3 ) ] t , (1 + 7 2 ) ( 1 + 7 2 )

]/

0 Ellipse (

)

Linear

+7 2) - 1 0 1 O g l o { 1 / 2 - 1 / 2 [ ( 1-72)(c°s2/3)])(1

(1)

(2)

/

{5

Ellipse {

Circular

-10log10 1 / 2 + 1/2

(1 + y 2 )

(3)

®

\ Linear Linear

-10log m 1 / 2 + 1/2

[ (co~,

(4)

/

\ Linear Circular

{

-10log10 1 / 2 - 1 / 2

O.

® Circular Circular

[°1) ~

= +3dB

= 0 d B when 7T¢ = 7R¢ --1010810{1/2 + 1/2(YTCYRC)} = + ~ dBwhen Yvc = --7RC

(5)

(6)

®

Note: Equations (1) through (6) are from Air Force Test Range Technical Report AF WTR-TR-65-1, by Benhring W. Pike, P. E. 7 = ellipticity ratio, the signed voltage ratio of the major axis of the polarization ellipse to its minor axis, where (1 > 171 > ~); /3 = polarization mismatch angle (0°>/3 > 90°); T, transmitting; R, receiving; E, elliptically polarized; C, circularly polarized. Source. Courtesy of Watkins-Johnson Co. [8].

terms of the voltage axial ratio: ar - Ema x / E m i n

or, in decibels,

AR = 20 lOgl0 (ar).

Table 2, from Reference [5], lists equations for computing polarization mismatch loss.

Circularly Polarized Antennas Circularly polarized (CP) antennas are generally more complex than those designed for linear polarization. CP antennas may be divided into two categories.

178

Hill and Smith

a /

,~

eix

~

Horn with

Dielectric Phasor

Diploe ossed 8lot In Wavegulde

Y

al Spiral

••Horn

with

~ ~

/

M(~:rnidee~ line r Spiral Cavity Back

~"

b

o

~ybpd r Crossed Log-Periodic Dipole Array

I I RH LH Circular Polarization

I Dual-Polarized Quad-Ridged Horns

d ler I

LH RH Circular Polarization

Figure 6. Category I antennas (a). Category II antennas (b),

Category I antennas are those which are circularly polarized by virtue of the structure of their radiating aperture, exemplified by such types as spirals and helices. Their polarization cannot be changed except by changing the structure. A variety of category I antennas are illustrated in Figure 6a. Some of the antennas shown in Figure 6 show a sense of polarization that is obvious from the structure. It is not always obvious from the external appearance of a CP antenna that it is circularly polarized and

7. Microwave Antennas

179

what is the sense of polarization. However, those antenna illustrations not showing a defined sense of circular polarization indicate that the polarization sense is determined by factors not easily depicted in the diagrams. Category II antennas, illustrated in Figure 6b, usually consist of orthogonal elements, the outputs (inputs) of which are combined in phase quadrature. An example is the dual-polarized horn with an external 90 ° hybrid coupler. This type is capable of producing both right-hand and left-hand circular polarization simultaneously. With additional circuitry, six polarizations can be produced, as illustrated in Figure 7.

90 °

Hybrid Coupler

Ii

II 180 o Hybrid Coupler

o

.-

O3O ~ f-

I

Transmitter or Receiver

Transmitter or Receiver

E V =Vertical

Slant ~ ~ Left ~ , ~ R i g h t

E

R~

Left Circular

Slant

PEH=Horizontal I

Figure 7. Dual-polarized antenna with external circuitry to produce six polarizations,

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Hill and Smith

Polarization and Space Diversity With complex propagation paths, for which the characteristics of the field at a given point are difficult to assess, a diversity receiving antenna system may be useful for reliable communication. Diversity may be of different types: space diversity, in which two antennas are separated by several wavelengths, and polarization diversity, in which a multimode antenna or two antennas of orthogonal polarization are used. References: For further reading on polarization, see References [7-101. Sidelobes Radiation pattern lobes other than the primary lobe, or the main lobe Special definition: Where the main beam shows slope reversals, a side lobe is presumed to exist if the reversal is 2 or 3 dB deep. Refer to Figure 1. Units: Decibels, usually with respect to the peak of the main lobe Related terms" Minor lobes, shoulder lobes, coma lobes, and back lobe Measurement accuracy: Depends upon the linearity/dynamic range of the measurement system and the test environment. For high-level sidelobes near the main beam, expect _+0.5 to 1 dB of accuracy. For far-out and low-level sidelobes more than 30 dB below the main beam, assume that the levels are essentially undefined unless special care has been taken with the measurement. Significance: In collimating antennas, such as reflectors and arrays, the location and magnitude of the sidelobes reveal phase and amplitude discrepancies. Basically, energy in sidelobes is wasted. In ground-based satellite communication antennas, sidelobes are a source of noise and impacts G~ T. Comments: In directional antennas, sidelobes serve as a figure of merit, because the design and construction are revealed by the sidelobe levels. Sidelobes can be very difficult, and thus costly, to reduce and should not be overly specified if the application does not require low sidelobe levels.

Squint The deviation of the center of a beam from a reference point as a function of the frequency, polarization, or orientation. Usually defined as the variation of the bisector of the half-power beamwidth angle with respect to a mechanical reference. Refer to Figure 1.

7. Microwave Antennas

I 81

Related terms: Boresight Measurement Accuracy: Same as that for beamwidth Significance: Squint is an important parameter when beam direction must serve a function such as direction finding or when the maximum gain direction must be pointed in a given direction. Comments: Once the antenna has been removed from the pattern range, the mechanical reference provided by the mount or a boresight telescope is the only indication of beam direction.

Voltage Standing Wave Ratio (VSWR) The ratio of incident to reflected voltage at the antenna input. A measure of how well the antenna, as a transducer, matches the impedance of the transmission line to the impedance of space Units: VSWR, a ratio, as n:l Return loss: Decibels Reflection coefficient: A number between 0 and 1 Related terms: Mismatched and matched Measurement accuracy: Variable, depending on the method of measurement. Required accuracy should be to a level which ensures compliance with the requirement. Significance: Depends on the application. A VSWR of 3:1 in a receiving system will cost 1.25 dB in gain loss. The same VSWR in a transmitting system could destroy the transmitter. Loss from VSWR is calculated as follows, mismatch loss = Pm/P -- 1 / ( 1 --Ip] 2) = (S + 1 ) 2 / 4 S , where Pm is the power delivered if matched, P is the power delivered, p is the return loss, and S is the VSWR. Comments: Note that the definition of gain does not include VSWR losses. From the system point of view, such loss must be considered. In coaxial systems, VSWR with respect to an impedance of 50 1) is usually required. In waveguide systems the type of waveguide and VSWR are specified.

Power Handling The power the antenna is capable of accepting at its input terminal and subsequently radiating; for a receiving antenna, the power incident from another source, such as an adjacent radar. (The frequency of the source may be outside the nominal frequency band of the receiving antenna.)

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Hill and Smith

Units: Watts Related terms: Average power, peak power, duty cycle, pressurization, altitude, critical altitude, ionization, and multipaction Measurement accuracy: The capability of the testing facility to measure power. Usually an indirect measurement by means of a sampling directional coupler Significance: Determines the ability of the antenna to continue to function in the system. Power breakdown is usually not self-healing, except for ionization at altitude. Comments: The power stated in the requirement is generally greater than the power available in the system for which the antenna is intended. Measurement difficulties include obtaining a reliable power source, location of the test, interference problems, altitude, and temperature chambers.

Design of Antennas for High Power Antennas capable of handling high power are not necessarily different, but they must be designed with low conductor and dielectric losses and must avoid high voltage and high current densities. In high-power application, two situations are encountered: high average power and high peak power. For high average power, the common failure mode is excessive heating of the antenna parts. To avoid this, ohmic losses must be kept low and cooling of critical areas may be provided. At high peak powers, failures result from voltage breakdown and arcing. To handle high peak power, voltage gradients within the antenna must be kept below the ionization level. Usually, the power-limiting element in the antenna is the transmission line, because this is where the energy is most concentrated. The limiting factors are voltage breakdown and excessive heating. Waveguides have higher power handling capabilities than coaxial lines. The usual problem with waveguide is voltage breakdown, rather than heating. This is due in part to the fact that an average power exceeding the capability of the waveguide is simply not available. However, peak power that exceeds the capability of the waveguide is available, resulting in voltage breakdown. In a coaxial line, however, for which the diameter must be kept small to avoid moding problems, it is easy to exceed both the peak and the average power capability of the line. Additionally, coaxial lines have an inherent average power limitation, for the center conductor must carry the same current as the outer conductor, and virtually all the current is carried near the conductor surface. Thus the current density and I ZR losses are many times higher in the center conductor, which is thermally isolated from any possible heat

7. Microwave Antennas

1I]3

sink. Specific techniques in high-power design include the following: Choose metals of high conductivity (copper, aluminum, or silver) and dielectrics of low loss. Minimize abrupt discontinuities and sharp corners. Use low-Q matching structures. Avoid designs of an inherently narrow frequency band. Make circuit elements with generous cross sections and large spacings. Above 8 GHz, try to use a waveguide.

G/T "G over T" is a figure of merit, applied to satellite communications antennas. G is gain as previously defined. T is system noise temperature and includes noise received by the antenna, noise resulting from losses in the transmission line, and the noise figure of the preamplifier. It is measured at the output of the preamplifier or some other specified point. System noise temperature includes antenna noise temperature. Antenna noise temperature is defined in Reference [11]. The antenna noise temperature expressed in kelvins at a specific frequency is equal to the effective temperature of a passive matched load having an equal available noise power output per unit bandwidth. It is defined in the following relationship,

N=kT, where N is the available noise power output per unit bandwidth in watts/hertz, k is the Boltzmann's constant in watts/kelvin hertz, and T is the noise temperature in kelvins. Standard: From Reference [11], "It shall be standard to specify the antenna noise temperature at the feed output flange, including all feed contributions. Any active circuit elements (e.g., amplifiers, detectors) shall not be included. It shall be standard to specify the noise temperature for specific frequencies and polarization at the same point in the antenna as the antenna gain is specified. It shall be standard to specify noise temperature versus elevation angle above the horizon." Comments: To compute G/T, perform the following: [ antenna gain (power ratio relative to isotropic) ]

G~ T = 10 log ~0

(system noise temperature in kelvins)

or

( G / T ) dBK

(antenna gain) dB~ -- 10 log(system noise temperature in kelvins).

184

Hill and Smith

S/te The location of the antenna with respect to structure which can affect the antenna's performance Related terms: Ground plane and radome Measurement accuracy: The characterization of an antenna's performance in its location can be a difficult task. Highly directive antennas such as parabolic reflectors and arrays larger than 20A are little affected by objects to the sides and rear of the aperture, with one important exception: antennas used in satellite communications, in which noise temperature is significant and in which this noise is introduced into the system via the antenna's reception of noise from the Earth or sky. Patterns of broad-beam antennas are more affected by environment and can be rendered nearly useless if the antennas are incorrectly sited. Antennas on aircraft, missiles, and ships should be tested in the location at which they are to function, but this is difficult and can be very expensive. All antennas should be tested in their radomes. Comments: Most antenna requirements define "free-space" performance, yet most antennas are situated in far from free-space conditions. Frequently, a circular ground plane several wavelengths in extent is specified for test purposes. In this case, the edge of the ground plane becomes a significant part of the measured pattern. Ground planes often have rolled edges or attached absorber to mitigate the problem. Scale models are often used to simulate the antenna site. This is especially useful when the antenna location is on an aircraft or a ship. The frequency must also be scaled so that the features of the environment (i.e., the aircraft or ship), measured in wavelengths, are representative. There are two major limitations to this technique: the pattern range's upper frequency capability and its capacity to handle large models. As an example, an S-band antenna operating at 2.2 GHz whose environment is scaled by ~0 would have to operate at 22 GHz. Because of the expense of characterizing the performance of an antenna in its working location either at full scale or with scale models, methods have been developed for calculation of this performance. The following discussion was provided by Plane Avionic Enterprises, Inc. [12].

General Theory of Diffraction (GTD) GTD models calculate reflections and diffractions from canonical structures (cylinders, plates, cones, spheres, and ellipsoids), summing resultant energy from the many paths (phase relative) to provide point-to-point gain. By calculation, vehicles may be assessed if redefined from their real structures into appropriate canonical shapes. Computer models using GTD techniques permit a main

7. Microwave Antennas

| 85

structure in cylindrical or ellipsoid (single or dual) form, supported by numerous plates, to make up a representative structure, thereby defining the platform. Data are input through mathematical (three-dimensional) coordinates in terms of X, Y, and Z relative to a fixed point (nose or other data). Such a definition is complex and time consuming, being a manual ( m a n / m a c h i n e ) f u n c t i o n . The GTD methodology is reliable in calculating rays via reflective and diffraction paths although somewhat suspect in the transition or border regions existing between the two.

Unified Theory of Diffraction (UTD) The UTD is a method which supplements GTD by providing reliable assessment of energy transfer in those transition regions. Platform Geometry Definition The ALDAS platform geometrical definition consists of cylindrical, rectangular, and ellipsoidal construction, permitting different axis sizes with and without nose cones (truncated or not) together with up to 30 cylinders for other structures, up to 30 plates (each permitting up to 15 corners), and up to 30 four-cornered obstacles. Error checking is included to avoid frequency/geometry inconsistencies, nonplane coordinate definition, etc. Plates and blockages are computer assessed for attachment or edge radiation (wedge or rolled), and surface-mounted antennas are automatically dimensioned and positioned for appropriate phase centering. References: For the complete theory of scale modeling and for the theory of GTD and UTD, see References [13, Chaps. 4 and 32, respectively]. For a brief discussion, see Reference [5]. Environment

The conditions which affect the antenna's survival or reliability Related terms: Temperature, wind, altitude (vacuum), vibration, pyrotechnic shock, acoustic level, sand and dust, humidity, and salt fog Measurement accuracy: The characterization of an antenna's performance in its environment is often difficult, and some combinations may be nearly impossible to measure, such as the recording of patterns at temperature extremes. Frequently only the antenna VSWR is monitored during temperature or vibration testing, and even here the test fixture affects the measurement. Thus a reference in situ VSWR is recorded, and deviations from that reference are evaluated. After testing, normal measurements may be made to test for permanent change or damage. Significance: Designing an antenna to function and survive in extreme conditions can be a difficult problem, in which the electrical design

1116

Hill and Smith

problems are relatively insignificant when compared with the mechanical design problems.

Special Terms Deviation from Omni This specification is used in defining the pattern performance of omnidirectional antennas. Such antennas are actually semidirectional and usually receive or transmit over a hemisphere (such as the pattern of a conical spiral) or omnidirectionally in the azimuth plane (such as the pattern of a biconical antenna). A true omniantenna, which is omnidirectional over a sphere, is not possible for any given polarization. "Any continuous vector field on a Euclidean sphere must have a singularity." (See References [14] and [15]. The ideal omniantenna should receive equally well over the required sector of a sphere. This performance is difficult to achieve and so the performance must be given a tolerance; thus "deviation from omni" refers to this tolerance in terms of gain variations which occur as a function of azimuth angle, elevation angle, polarization, or frequency. The requirement may state "Deviation from omni shall not exceed + 2 dB over 360 ° in azimuth, 0 ° to +45 ° in elevation, for any linear polarization." After the antenna is designed and built, it will probably not meet the specification in its entirety. After negotiation the specification will be modified to add " T h e gain (or axial ratio or deviation from omni) will be met over 90% of the area (or frequency)." Such compromises are necessary because of the difficulty of building a true omnidirectional antenna. To test pattern performance, the antenna would be rotated 360 ° in azimuth, stepped in elevation 5 °, rotated in azimuth 360 °, and so on, whereas the linear polarized source antenna is rotated continuously. The specification is met when amplitude extremes lie within the + 2-dB sector as illustrated in Figure 8. Caution should be used in defining gain for omnidirectional antennas. For some, gain is the mean amplitude, whereas others choose to define it as the peak amplitude. Axial ratio is the variation between the adjacent maximum and minimum amplitudes resulting from the rotating source polarization. Nominal "Nominal" is a favorite word and is used instead of the more appropriate "approximate" when the specification writer (the seller) does not wish to be pinned down to a definite specification. Typical "Typical" in a specification means that the parameter defined is not unconditional. Frequently it means that the performance

7.

Microwave

187

Antennas

MAXIMUM GAIN IIII

.................................................................................................. 1' ........ i' ............. I........

, ,,,! ~ , w ~vv~ ~,~v~v,~w~w~ ~,^ ~gjv ~ WW~Vv~v'!Iv~,v,.~,.. ,~ -v~,;w~ " t

T,O

.....

. . . . . . . . . . . . . . . . . .

1

I. . . .

MINIMUM GAIN DEVIATION FROM OMNI

SPINNING POLARIZATION TRANSMITFER

PATTERN CUT

.uLu~

-180

/

~

.... I .... 1.... 1.... I .... 1.... 1.... I .... 1.... 1.... 1.... 1.... 1.... I .... 1.... I .... 1.... 1.... 1.... I .... 1.... 1.... 1.... 1.... 1.... 1.... 1.... t .... I .... 1.... 1.... 1.... l .......

-150

- t;:)0

-90

-60

-30

Azimuth Figure

8.

Pattern

of an

0

30

60

90

t20

150

t80

degrees elliptically

polarized

antenna.

described is better than the specified value, but that performance will vary from unit to unit.

2. Microwave Integrated Circuit (MIC) and Monolithic Microwave Integrated Circuit (MMIC) Antennas MIC and MMIC antennas are a natural evolution of integrated circuit components in the microwave and millimeter-wave frequency range. Some of the integrated circuit antennas that have been developed are bow ties, cat whiskers, circular slots, dielectric rods, dipole arrays, slots, slot arrays, vees, and Vivaldi antennas [16]. There is an ever-increasing need for monolithic integrated circuits combining amplifiers, antennas, diodes, and transistors on the same substrate. The fastest growing field using MIC and MMIC antennas is the imaging system for military and scientific applications, such as astronomy, atmospheric studies, interferometers, military radar and radiometry, plasma diagnostics, and spectroscopic applications. References [17] and [18] provide a more detailed description of these applications. These imaging systems map the radiation intensity of a distributed source. This radiation intensity is then correlated to the

188

Hill and Smith

various applications. In the past, a single detector has been used in a mechanically or electrically scanned imaging system. This technique has proven to be too slow and inadequate for many applications. A millimeter-wave imaging array consisting of a large number of antennas each with its own detector, placed at the focal plane of an imaging system, would correct these deficiencies. The outputs from the detectors make up the image. Examples of some the detectors that might be used are Schottky diodes, SIS junctions, and microbolometers. This results in a faster imaging system. A monolithic focal-plane imaging array is an even more attractive solution. See Reference [19] for more detail. In these systems, the antennas and detectors are integrated on dielectric substrates. A benefit of using monolithic integrated circuits is that, as the frequency is increased, the advantages of using them tend to increase. The fabrication of the structures becomes easier as more integrated circuit technology can be used. Since more devices can be put on each wafer, the unit cost decreases. Also, as frequency increases, the dielectric losses become less of a problem. Dielectric losses are related to the conductivity of the semiconductor. The relation = o-v//x/e, where o-, /z, and e are the conductivity, magnetic permeability, and electric permittivity, respectively, gives the upper limit of the power loss coefficient. Thus, since the loss per guide wavelength decreases as 1 / f and since a is nearly independent of frequency, the dielectric losses will decrease with increasing frequency. For a thorough discussion of this refer to Reference [20]. However, these advantages are counterbalanced by limited power, low gain, and a very narrow bandwidth. The thermal capacity of the substrate materials limits the power. By arraying the antennas, the gain can be improved. Bandwidth, input impedance, mutual impedance, radiation efficiency, and radiation patterns are effected by the substrate thickness and relative permittivity [21]. The antennas are usually thin-film metal geometries on a substrate. The dielectric substrates commonly used are gallium arsenide, quartz, and silicon. Dielectric substrates are excellent surface waveguides. This is to say that the energy radiated into a substrate at angles larger than the critical angle is completely reflected and becomes a surface wave in the dielectric. This is discussed in detail in Reference [17]. When surface waves come in contact with the integrated circuit, they become shock waves. The electrical charge associated with the surface wave shocks the circuit, causing intermittant disruptions and possible permanent damage. These surface waves have a fundamental mode with no cutoff and can cause cross-talk between adjacent antennas. When placing the antenna on

7. Microwave Antennas

189

a dielectric substrate, surface waves can be avoided by ensuring that the phase velocity of the guided wave is less than that of the surface waves. If this is not done, the energy will escape from the waveguide and disperse as shock waves in the substrate. Metal antennas cannot be deposited on thick dielectric substrates because the waves in the guide will be faster than the surface waves in the substrate, thus causing shock waves in the substrate. However, metal antennas can be deposited on sufficiently thin dielectric membranes without detrimental shock waves. An example of this is the microstrip antenna. Another alternative would be to sandwich or encase the metal antenna in a uniform dielectric as discussed in References [18] and [22]. Providing that transparent materials are available for the substrate and superstrate, this solution can be used over the millimeter-wave frequency range. Some of the more transparent materials and their absorption coefficients, as discussed in Reference [18], are optosil fused quartz (1.3 d B / c m ) , polyethylene (0.2 d B / c m ) , polypropylene (0.2 dB/cm), silicon (2.~, d B / c m , when the resistivity > 10 o h m / c m ) , and TPX (0.26 dB/cm). By using semiconductor material for the substrate and superstrate, a Schottky diode could be integrated with the antenna. Substrate mode powers can also be reduced by using twin-slot and twin-dipole designs. These designs also improve the patterns. The substrate mode is used by tapered-slot antennas to control the shape of the beam. To eliminate substrate modes, a lens is often mounted on the back of the substrate. Unfortunately, the lens degrades the patterns and increases dielectric absorption losses. However, improvements have been made with a twoelement Yagi antenna with a TPX lens and spiral and log-periodic antennas with quartz substrate lenses. These improvements are discussed in Reference [19]. By integrating the antennas on silicon oxynitride membranes less than a micrometer thick, both the substrate modes and the substrate lens problems can be reduced. Since the membrane is small compared with a wavelength, allowing the antenna to effectively radiate in free space, the free-space antenna design techniques can be used. Figure 9 shows an integrated circuit combining an all-dielectric antenna and waveguide with Schottky diodes. The antenna consists of a tapered dielectric rod etched from a silicon wafer. The guided radiation is fed into the Schottky diode by a V-shaped metallic coupler. The diode is located at the apex of the coupler. In the plane of the V, an electric field is created. Thus, without the use of conventional metal waveguides, efficient in-coupling of radiation is provided by the coupler. This design is discussed in detail in Reference [20]. An example of a two-dimensional monolithic millimeter-wave imaging array is shown in Figure 10. It consists of a two-dimensional array of

190

Hill and Smith

Sil

Membl

E-Fi

Tapered Trapezoidal Dielectric

~un Back)

Antenna

"•..r-.--

Tapered

Dielectric-Rod Antenna

Silicon Membrane

~

V Coupler

~ .... Diode (at Vertex) ~'X~x~'~ - ' - Bonding Pads Figure 9. All-dielectric integrated circuit antenna and waveguide with Schottky diodes.

pyramidal horns etched in silicon. A probe antenna is suspended inside each horn on a 1-~m-thick silicon oxynitride membrane. The energy incident on a resolution cell is collected by the horn which then focuses it on the probe antenna. The interconnections, detectors, and dipoles for the probe are all integrated on the same silicon wafer. The advantage of this approach is that the probe antennas are much smaller than a unit cell. This leaves as much as 75% of the wafer surface for connections and electronics. Reference [19] discusses this design in more detail. A notch radiator (Figure 11) consists of a strip-line input with tapered slot lines forming notches on the ground planes on either side. The perpendicular intersection of the strip line and slot lines couples the energy to the notches. The slot lines are terminated by short circuits, whereas the strip line is terminated by an open circuit. The notch radiation is explained in greater detail in Reference [23].

191

7. Microwave Antennas Contact Pads Front Wafer Back Wafer Nitride Lne

Reflecting Cavity Space for Detection Circuits

Radiated Pattern

Figure I0. Two-dimensional monolithic millimeter-wave imagingarray,

Slot Line

Top Metalization

. . . .

Short Circuit

. /

/

l

Strip Line

Top Dielectric

/

i

-

-

Center Metalization

f

-

/ ' ~ , ~ _ ~ ~

/,/

/

,,~,/~

Circuit Short Circuit

. ~

,

,

~

/ / /

/'~

Slot Line Figure II. Explodedview of a notch radiator.

Bottom Dielectric Bottom Metalization

192

Hill and Smith Air

Slot Antenna \\

Ground Plane

~\\\\\\\\\\\\\\\\\\\~\

Y.

~v'

Air

~v'

o

/

Air Microstrip Dipole I

~

/

/

/

--,

h

v'

\kS <-- Oc

@d f "

~,\

\\\\\ Ground Plane

Figure 12. Printed-circuit dipole and slot antennas on a substrate.

Figure 12 shows printed circuit dipole and slot antennas on a substrate. The microstrip dipole tends to perform better than the slot for various reasons. It radiates in only one direction. The dipole does not excite the TM 0 mode as much as the slot does. Its lowest order TE mode on an ungrounded substrate is cut off. When the substrate thickness is the cutoff thickness of the TE 0 mode, radiation efficiency is optimized. If a radiation efficiency of better than 50% is desired, the substrate relative permittivity, er, must be less than or equal to 4.5. Bandwidth increases monotonically with increasing e~ and is maximum beyond the TE 0 substrate thickness cutoff. However, a maximum bandwidth of approximately 27% at e~ = 9.4 can be obtained for a substrate thickness which corresponds to the optimum radiation efficiency substrate thickness. For further comparison between the printed circuit dipole and the slot antenna, refer to Reference [21]. Reference [24] discusses a monolithic microwave integrated circuit dipole antenna, which is shown in Figure 13. The antenna consists of a semiconductor layer having the proper doping concentration profile. The

193

7. Microwave Antennas Control Electrode (Doped Poly Si) Gate Insulator

Feed/Receive Region

(SiO2) Doped

Semiconductor (Si)

2h

t

Sapphire or Suitable Semiconductor Substrate

Figure 13. Monolithic microwave integrated circuit dipole antenna.

semiconductor layer may be n-silicon, n-gallium arsenide, or another semiconductor material that is compatible with the substrate. A brief sampling of MIC and MMIC antennas and of their advantages, problems, and possible applications has been presented. It is hoped that some understanding of what MIC and MMIC antennas are and how they can be used was gained. For more in-depth discussion, please refer to the various referenced papers.

3. Radiation Pattern Synthesis As defined in Reference [5], radiation pattern synthesis is the process of finding the source or array of sources that produces a desired pattern. Given the desired radiation characteristics and system constraints, the antenna's configuration, its excitation distribution, and its geometrical dimensions can be derived. The desired pattern must first be represented by an analytical model. This model is then translated into an antenna model using radiation pattern synthesis. Reference [25] defines three main categories of radiation pattern synthesis: 1. Antenna patterns with nulls in particular directions 2. Antenna patterns with specific distributions 3. Antenna patterns with low side lobes and narrow beams.

194

Hill and Smith

Radiation pattern synthesis is used to design linear arrays and line sources whose array and space factors produce the desired radiation pattern. By multiplying the element factor and the space or array factor, the pattern is formed. An in-depth description of each method is beyond the present scope; however, the differences and similarities among, as well as the advantages and disadvantages of, the various methods will be addressed. It is hoped that this information will help the reader decide which method of synthesis will best suit his or her needs. One can then refer to the annotated bibliography to find a detailed description of the desired method. Antenna Patterns with Nulls in Particular Directions

The Schelkunoff method will synthesize arrays with patterns having nulls in specified directions. The location and number of nulls are required to perform the pattern synthesis. Given this information, the number of elements in the array and their excitation coefficients can be derived. Antenna Patterns with Specific Distributions

Both the Fourier transform method and the Woodward method will synthesize arrays with patterns having specific distributions. These methods of pattern synthesis are sometimes called pattern shaping. The Fourier transform method requires a complete description of the pattern. From that description, a discrete or continuous source antenna system's excitation distribution can be derived. The Woodward method samples the pattern at various discrete locations. Each sample is associated with a harmonic current. The field of this current is called a composing function. A summation of the composing functions corresponds to the synthesized pattern. The Fourier transform method is well suited for patterns which are analytically simple, allowing integration in closed form. It also yields the least-mean-square deviation from the desired to the reconstructed pattern. The Woodward method is more flexible. It can be used with patterns that cannot be expressed analytically. Although the method's sample points are identical to those of the desired pattern, points in between the sample points vary uncontrollably. This means that a least-mean-square deviation cannot be obtained. Antenna Patterns with Low Sidelobes and Narrow Beams

There are three methods under this category: the Dolph-Tschebyscheff method; the Taylor line-source (Tschebyscheff error) method; and the

195

7. M i c r o w a v e Antennas

Taylor line-source (one parameter) method. The Dolph-Tschebyscheff method yields the smallest possible sidelobe level for a given first null beamwidth and vice versa. The Taylor line-source (Tschebyscheff error) method yields an optimum compromise between sidelobe level and beamwidth. The first minor lobes are equal and at the desired level. The remaining lobes decay monotonically. The Taylor line-source (one parameter) method yields a pattern in which all minor lobes decay monotonically. By using one of the six pattern synthesis methods described above, the antenna configuration for almost any type of radiation pattern can be derived. Once the type of radiation pattern required has been defined, the synthesis method is chosen. The antenna configuration and excitation distribution are then determined using this method.

4. Antennas for Missiles Missile antennas have special requirements stemming from the severe environmental conditions encountered during launch and reentry and

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Figure 14. Coordinate system for missile antennas,

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from test range criteria. Missiles fired from U.S. test ranges carry the antennas for three frequency bands: UHF (408-425 MHz), for the flight termination system; S-band (2.2-2.29 GHz) for telemetry; and C-band (5.4-5.9 GHz) for the radar beacon. It is probable that future missiles will be required to also carry GPS antennas in the L-band (1.575 GHz). The coordinate system for missile antenna patterns is shown in Figure 14.

UHF Antennas

Although not within the microwave frequency range, the UHF antennas for missiles share the pattern and environmental requirements of the other bands.

Figure 15. Flush-mounted slot antenna.

197

7. Microwave Antennas

S-Band Antennas

The test range requirements for the S-band are to be found in Reference [26]. The S-band antennas should provide, ideally, spherical pattern coverage so that telemetry signals will be received at the ground station regardless of missile orientation. Because placement of enough antennas to accomplish this is generally impractical, the requirement is usually satisfied with pattern levels above some minimum level over 80 to 90% of the sphere. The antennas are usually two or three flush-mounted rectangular slots disposed around the missile body and oriented with the plane of polarization along the z axis. A typical slot antenna is shown in Figure 15. An alternative to the set of individual slots is the "wrap-around" antenna, which can be an array of microstrip antennas on a common substrate, although rectangular slots with a strip-line feed network have been produced. The microstrip antenna is shown in Figure 16. (The

Figure 16. Wrap-around antenna.

198

Hill and Smith

missile test engineer's desire for an antenna that could be wrapped around the missile and mounted without cutting large holes in the structure led to the development of microstrip radiators and thence to the patch antenna. Tactical missiles carry only S-band telemetry antennas during test firings, so these antennas are not usually a part of the design.) The individual slot antennas are used when the missile diameter is large and when temperatures above 350°F are expected. In high-temperature applications, in which temperatures can reach 1500°F, the antenna slot is filled with quartz (silicone dioxide) which protrudes to the surface of the missile skin so as to preserve a smooth outer surface. On large-diameter missiles, for which a wrap-around antenna or a large number of antennas would be impractical, three or four antennas are installed. During flight, the antenna in the appropriate location is automatically selected. This method is especially useful when the missile communicates via a relay satellite, when adequate link margins are difficult to achieve. C-Band Beacon Antennas

The C-band beacon is usually a circularly polarized flush-mounted helix in a quartz-filled cavity, as illustrated in Figure 17. The beacon is to aid the

Figure 17. Flush-mounted helix in a quartz-filled cavity.

199

7. Microwave Antennas

skin-tracking radar. The largest missiles carry no more than three or four beacon antennas. The usual complement is two. For further reading on missile antennas, see Reference [27].

5. Measuring RF Leakage of Test Couplers Test couplers are used to isolate an antenna from its surrounding environment. The test coupler is designed to mount over the antenna. Each coupler consists of an antenna surrounded by an outer casing. The outer casing is used to contain the RF from both the antenna and the test coupler's antenna. R F signals are transmitted and received by both antennas. It is this capability that simulates the radio communication link. This simulation is used to thoroughly test and verify the communication system. In addition to making this type of testing possible, test couplers also alleviate problems of interference and personnel safety during testing. This makes the RF leakage of test couplers mounted on antennas very important. Verifying the amount of RF that leaks from a test coupler mounted on an antenna is somewhat involved. The following discussion will go through the calculations involved in measuring the RF leakage. Most of the equations refer to the test setup shown in Figure 18. The calculations required for measuring RF leakage are as follows: 1. Calculate the wavelength of the frequency at which the leakage measurement is to be made. a = c/f,

where a is the wavelength (m), c is the speed of light in free space (3 × 10 s m / s ) , and f is the frequency (Hz). 2. Calculate the path loss between the a n t e n n a / t e s t coupler and the measuring antenna. L = [a/(4rrr)] 2 LdB = 10 1Ogl0( L ) , where L is the path loss (unitless ratio), L dB is the path loss (dB), and r is the distance between the a n t e n n a / t e s t coupler and the measuring antenna (m). If the distance for the test facility and the distance specified for the measurement do not agree, the path loss will need to be calculated for both distances, Ltest and Lspec (in decibels). 3. Calculate the total attenuation used to set the reference level and the input power level at the antenna. R E F = REF1 + REF2,

Hill and Smith

200

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Power

Sensor

Power

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where R E F is the total attenuation used on the output power meter, PO (dB); REF1 is the loss of the cable used to connect the antenna to the attenuators, REF2 (dB); and REF2 is the amount of attenuation used to ensure that the output power meter is not overdriven (dB). 4. Calculate the total attenuation on the input power meter. AI = A l l + AI2, where AI is the total attenuation used on the input power meter, PI (dB); A l l is the attenuation of the directional coupler (dB); and AI2 is the amount of attenuation used to ensure that the input power meter is not overdriven (dB). 5. Calculate the value to set the input power level at the antenna. PO = D P -

REF,

where PO is the power level to be read on the output power meter (dB) and DP is the power level at which the antenna is to operate (dB). 6. Calculate the value to be read on the P h a s e / M a g display when establishing a reference level. VRD = P O -

LS,

201

7. Microwave Antennas

where V R D is the value to be read on the P h a s e / M a g display (dB) and LS is the loss of the cable among the measuring antenna, SGH, and the harmonic converter (dB). 7. Calculate the gain of the leakage from the a n t e n n a / t e s t coupler. GT = MVD

-

Ltest

-

GR + LS - DP,

where GT is the gain of the leakage (dB), MVD is the measured value on the P h a s e / M a g display (dB), and G R is the gain of the measuring antenna, SGH (dB). 8. Calculate the power transmitted by the leakage. PT=GT

+ DP,

where PT is the power transmitted (dB). 9. Calculate the power density of the leakage at the distance specified. PD=PT+L spec where PD is the power density (dB). 10. Calculate the electric field intensity of the leakage at the distance specified.

where E is the electric field intensity ( ~ V / m ) . The RF leakage of a test coupler is usually field intensity at some distance. A common value Since it is not practical to have a test range 300 setup and calculations allow the leakage to be reasonable test range.

specified as an electric is 194 ~ V / m at 300 ft. ft long, the above test measured on a more

6. Materials This section includes materials suitable for use in microwave antennas. The listing is not exhaustive. Materials are divided into two categories: conductors and dielectrics.

Conductors Aluminum

Nearly the universal building material for antennas. Used in the form of sheet metal, castings, and machined parts

202

Hill and Smith

Virtues ductor

Inexpensive, light (good strength-to-weight ratio), good con-

Faults When used with connectors which are of brass or are gold or silver plated, a dissimilar metal condition exists. Stainless steel connectors are better, but are not without problems. Center conductors, usually of beryllium or copper, are also dissimilar to aluminum. Conductive joints in aluminum cannot be made with normal solder techniques. Finish Unfinished aluminum alloys form their own protective coating (aluminum oxide)which is, unfortunately, a dielectric. Alodine (iridite) is the preferred finish, after which paint can be applied. A special low-resistance treatment is available. Anodize is excellent for corrosion or abrasion protection, but is a dielectric and thermal barrier. Joining Welding and dip brazing are preferred for conductive joints. Conductive silver epoxy can be used for conductive joints if environmental concerns can be satisfied. Stainless Steel Useful for structure when corrosion resistance, high-temperature capability, or both are required.

Virtues

Corrosion resistance

Faults Heavy, poor electrical conductor and poor thermal conductor. Difficult to machine Finish Passivate. If a solder joint is required, tin plating can be first applied. Painting of stainless steel can reduce its corrosion resistance. Brass An alloy of copper and zinc, useful for prototype work (hence "brassboard")

Virtues Faults Joining

Can be soldered and is easily machined Heavy, poor electrical conductor. Poor corrosion resistance Soldering and brazing

Finish "Bright dip" for temporary appearance. Gold plate for conductivity and tarnish resistance

7. Microwave Antennas

203

Bronze

An alloy of copper and tin. One of the most enduring of all alloys. Other characteristics similar to those of brass.

Copper The universal conductor, but not generally used as a construction material

Virtues Useful for prototype work. Can be easily soldered. By the plating process, on a mandrel, very intricate and close-tolerance parts can be made. Faults Heavy (low strength-to-weight ratio) and soft (malleable). Surface tarnishes quickly. Does not adhere well with adhesives Joining Finish

Brazing (when in oxygen-free form) and soldering Gold plate and tin plate

Dielectrics

Dielectric materials are used in antenna construction in two basic ways: 1. As a structure to support conductive parts which must be electrically isolated and as covers, similar to radomes, for horns and slots to contain or exclude pressure. In this application characteristics of rigidity and workability are paramount. Composites are in this group. 2. As electrical elements such as in a lens or as a phasing plate in waveguide sections of antennas. In these applications the index of refraction is of prime importance, along with loss characteristics. Dielectrics may further be divided into plastic and ceramic categories. 1. Plastic dielectrics include epoxies, flourides, polyesters, and polyimides. 2. Ceramics include quartz (silicon dioxide), alumina (aluminum oxide), and beryllia (berillium oxide). For listings of properties of materials, see References [5, p. 851; 26, Chap. 46].

204

Hill and Smith

References* [1] S. Silver, ed., Microwave Antenna Theory and Design, 2nd Ed. Boston: Boston Technical Publishers, 1964. (Orig. publ. 1947.) (Volume 12 of the Rad Lab Series.) An excellent exposition of the state of the antenna art in 1964. Most of it is applicable today. A significant milestone in antenna history. [2] IEEE Standard Test Procedures for Antennas, IEEE 149-1979, Appendix B. New York: Institute of Electrical and Electronics Engineers, 1979. The standard includes the following (partial listing): pattern measurement; characterization of amplitude, phase, and polarization; errors in gain measurement; boresight measurement; radome effects; power handling; radiation hazards; mechanical properties. [3] K. M. Keen, Method permits gain estimation for very wide-beam, satellite-terminal antennas, Microwave Syst. News, pp. 83-87, Oct. 1985. [4] J. S. Hollis, T. J. Lyon, and L. Clayton, Jr. eds., Microwave Antenna Measurements. Atlanta: Scientific-Atlanta, 1970. A complete text for a course in antenna measurement with primary emphasis on pattern measurement, which includes directivity, gain, and polarization. Includes the theoretical basis of the parameters. Also discusses the measurement equipment required. [5] J. D. Kraus, Antennas, 2nd Ed. New York: McGraw-Hill, 1988. (Orig. publ. 1950.) This is the second edition of the antenna "bible" first published in 1950. Includes antenna history, theory and many applications. The best source for discussion of the helical antenna (invented by Kraus). Good for discussion of gain and directivity. Includes a good definition of pattern synthesis and a basic form of synthesis, pattern multiplication. [6] J. E. Hill, Gain of directional antennas, TechNotes, Watkins-Johnson Co., Vol. 3, No. 4, July/Aug. 1976. [7] IEEE Standard Definitions of Terms for Antennas, IEEE Std 145-1983. New York: Institute of Electrical and Electronic Engineers, 1983. This standard presents a consistent and comprehensive vocabulary suited for the effective communication and understanding of antenna theory. [8] J. E. Hill, Antenna polarization, TechNotes, Watkins-Johnson Co., Vol. 6, No. 4, July/Aug. 1979. [9] B. W. Pike, "Power Transfer Between Two Antennas with Special Reference to Polarization," Air Force Systems Command, AD637134, Tech. Rep. AFWTR-TR-65-1, Vandenberg Air Force Base, CA, Dec. 1965. Any engineer concerned with polarization should have this report, as should anyone interested in the imaginative presentation of technical material. [10] H. R. Reed and C. M. Russell, Ultra High Frequency Propagation. Boston: Boston Technical Publishers, 1966. Contains much more than a discussion of propagation. Excellent presentation on polarization, gain, and effective area. [11] "Electrical and Mechanical Characteristics of Earth Station Antennas for Satellite Communications," EIA Standard EIA-411-A, Electronic Industries Association Engineering Dep., Washington, DC, 1986. This document provides standard terms, definitions and concepts for the mechanical and RF design of earth station antennas and offers a standard methodology for verification of RF performance. [12] J. Gibbs, Plane Avionic Enterprises, Inc., Gloucester, Ontario, private communication.

*This bibliography is in addition to referenced works, a listing of publications the authors have found to be valuable in the daily work of antenna design. It is not comprehensive, but a library of these works would suffice for most design work.

7. Microwave Antennas

205

[13] Lo and Lee, eds., Antenna Handbook. Princeton, NJ: Van Nostrand-Reinhold, 1988. The most comprehensive handbook at this time, 1991. It includes fundamentals and mathematical techniques. Most types of antennas and arrays are discussed, with much information on applications. [14] D. W. Beckett, Elementary Topology. New York: Academic Press, 1967. [15] W. G. Scott and K. M. Soo Hoo, A theorem on the polarization of null-free antennas, IEEE Trans. Antennas Propag., Vol. AP-14, Sept. 1966. [16] C. Zah, R. C. Compton, and D. B. Rutledge, Efficiencies of elementary integrated-circuit feed antennas, Electromagnetics, Spec. Issue Printed-Circuit Antennas Devices, pp. 239-254, Mar. 1983. [17] D. B. Rutledge and M. S. Muha, Imaging antenna arrays, IEEE Trans. Antennas Propag., Vol. AP-30, pp. 535-540, July 1982. [18] S. E. Schwarz and D. B. Rutledge, Moving toward near ram-wave integrated circuits, Microwave J., Vol. 23, pp. 47-67, June 1980. [19] G. M. Rebeiz, D. P. Kasilingam, Y. Guo, P. A. Stimson, and D. B. Rutledge, Monolithic millimeter-wave two-dimensional horn imaging arrays, IEEE Trans. Antennas Propag., Vol. AP-38, pp. 1473-1482, Sept. 1990. [20] C. Yao, S. E. Schwarz, and B. J. Blumenstock, Monolithic integration of a dielectric millimeter-wave antenna and a mixer diode: An embryonic millimeter-wave IC, IEEE Trans. Microwave Theory Tech., Vol. MTT-30, pp. 1241-1247, Aug. 1982. [21] N. G. Alexopoulos, P. B. Katehi, and D. B. Rutledge, Substrate optimization for integrated-circuit antennas, IEEE Trans. Microwave Theory Tech., Vol. MTT-31, pp. 550-557, July 1983. [22] D. B. Rutledge et al., Antennas and waveguides for far-infrared integrated circuits, IEEE J. Quantum Electron., Vol. QE-16, pp. 508-516, May 1980. [23] K. Simon, J. Wendler, R. Pozgay, and M. Schindler, "MMIC Compensation Network for Phased Array Element Mismatch," Raytheon Co. Research Div. Final Rep. for Naval Research Laboratory, 73 pp., Sept. 1990. [24] F. C. Jain, R. Bansal, and C. V. Valerio, Jr., Semiconductor antenna: A new device in millimeter- and submillimeter-wave integrated circuits, IEEE Trans. Microwave Theory Tech., Vol. MTT-32, pp. 204-207, Feb. 1984. [25] C. A. Balanis, Antenna Theory Analysis and Design, pp. 243-257, 658-699. New York: Harper & Row, 1982. This reference explains each of the six methods of radiation pattern synthesis. It should be sufficiently detailed for most designer's needs. It discusses each method in a step by step manner and then demonstrates each with examples. If more detailed descriptions are required, a detailed bibliography will lead to the original papers that presented each method. [26] "IRIG Standard Coordinate System and Data Format for Antenna Patterns" (IRIG Document 253-65), Secretariat, Range Commanders Council, White Sands Missile Range, New Mexico. This document defines a standard coordinate system for representation of antenna patterns. Polarization with respect to RF links is treated in tutorial fashion. [27] J. E. Hill, S-band antenna systems for missiles, Proc. Int. Telemetering Conf., Washington, DC., Sept. 1969. [28] R. C. Johnson and H. Jasik, eds., Antenna Engineering Handbook, 2nd Ed. New York: McGraw-Hill, 1984. (Orig. publ. 1961.) From the preface to the first edition: "The 'Antenna Engineering Handbook' is intended to serve as a compendium of antenna design data and principles.., it will prove most useful to the engineer who is actively engaged in designing antennas, it will also be of considerable use to the electronic systems engineer who desires to understand the capabilities and limitations of the a n t e n n a . . . "

206

Hill and Smith

[29] R. G. Corzine and J. A. Mosko, Four Arm Spiral Antennas. Norwood, MA: Artech House, 1990. Explains in great detail the principles of four-arm spiral direction-finding systems. A combination of theory and practical applications. [30] J. A. Kuecken, Exploring Antennas and Transmission Lines by Personal Computer. New York: Van Nostrand-Reinhold, 1986. This book is more than promised by its title. It simply explains many basic antenna principles. It will not show you how to design an antenna, but how to predict performance and understand what is going on. It includes many "basic" programs for computation of patterns of parabolas, arrays, shaped beam antennas. [31] D. M. Pozar, Antenna Design Using Personal Computers. Dedham, MA: Artech House, 1985. [32] A. W. Rudge, K. Milne, A. D. Olver, and P. Knight, eds., The Handbook of Antenna Design, 2 vols. London: Peter Peregrinus, 1983. A uery comprehensiue treatment of all aspects of antennas. Extensiue theory.

CHAPTER

8 Propagation at Microwave Frequencies Ernest K. Smith

I. I n t r o d u c t i o n M i c r o w a v e is taken here to mean frequencies above 1 GHz. However, when relevant data are available in the low U H F range (0.3-1 GHz), they will occasionally be included. In order to conform with current international practice every attempt has been made to be compatible with the latest readily available texts of the International Radio Consultative Committee (CCIR) [20] of the International Telecommunications Union (ITU). The designation CCIR formally disappeared in 1994. The designation is now ITU-R.

General Relations

Homogeneous Media Three parameters are needed to specify a homogeneous medium: The permeability/x, the permittivity e (or dielectric constant e/e0), and the conductivity ~r. From these the refractive index, n, defined as v velocity of propagation in the medium n = - = , c velocity of propagation in free space

Handbook of Microwave Technology, Volume 2

207

(1)

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

208

Ernest K. Smith

can be derived, G J£ ) 1/2

~/ G

(2)

n =

G0 /-~o

e0

as ~ = / z 0 (the permeability of free space) for most circumstances. We define complex dielectric permittivity ec, or Ec = E - - j ~ , ¢.0

(3)

and complex dielectric constant e', Gc E' =

O" = Er--j~

G0

,

(4)

¢-OE0

where Er = G/E 0 is the relative permittivity or dielectric constant, and or is the conductivity ( S / m ) . Shown in Figure 1 are the relative permittivity Er and conductivity o- as a function of frequency for a series of situations encountered in practice. Plane Waves

The electric field intensity, E, of a plane wave traveling in the x direction is given by

(5)

E = E 0 exp j(oot - k x ) V / m ,

where E o is a known value of field intensity in V / m at x = 0; w is the angular frequency equal to 27r f, where f is the frequency in hertz; t is the time in seconds; x is the distance in meters; 2T/"

k=

A =j~O~c

=a

+ j / 3 m -1

(6)

(k is the propagation constant); _ 1] 1/2 o/ "-

Np/m

(7)

209

8. Propagation at Microwave Frequencies

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.... 5 102 2 5 1032 Frequency

5 1042

5 105 2

5 106

(MHz)

Figure I. Relative permittivity, er, and conductivity, ~, as a function of frequency (CCIR Rec. 527-2 [21]). (A) seawater (average salinity, 20°C); (B) w e t ground' (C) freshwater, 20°C; (D) medium dry ground' (E) very dry ground; (F) pure water, 20°C; (G) ice (freshwater).

(a is called the attenuation constant, and as shown here is in nepers per meter but will later be represented decibels per kilometer, where 1 Np = 8.686 dB, if the voltage or current is represented); 1 Np = 4.343 dB, if the power is represented, as in certain fields such as remote sensing

210

Ernest K. Smith

radio astronomy [4a], [73]

2/lj2 ]

1/2

13-

~

1 +

~toe

+ 1

rad/m

(8)

(/3 is termed the phase constant). Both a a n d / 3 are positive and real [67].

Reflection and Refraction Reflection and refraction occur at an interface at the Earth's Surface.

Vertical Polarization

The voltage reflection coefficient Pv is e' sin 0 - V/e' - c o s 2 0 "

-

-

Pv

Horizontal Polarization

°

e' sin 0 + V/e' - cos 2 0

(9)

The voltage reflection coefficient Ph is sin 0 - V/e' - COS 2 0

Ph -- sin 0 + V/e' - c o s 2 0 "

(10)

Shown in Figure 2 are the magnitude and phase of the reflection coefficient for horizontal and vertical polarization for seawater and medium-dry ground. If the subsurface m e d i u m is nonconducting ( o - = 0), then a Brewster angle, 0 B, where the signal is totally transmitted and the reflection coefficient Pr = 0, may be defined as in optics by 1)1/2

0 B = tan -1 - -

.

(11)

Er

EXAMPLE" Let ~?r = 81 at 1 GHz and tr = 0. Then 0 B = t a n - l ( 1 / 81) 1/2= 6.3 °. This is the case for (fresh- or salt-)water but due to its conductivity Pv experiences a null but does not decrease to zero. For " m e d i u m - d r y ground," as seen in Figure 2, 0 a = t a n - l ( 1 / 1 5 ) 1/2 = 14.5 °. On the other hand, for very dry ground, E r = 3 and 0 a = t a n - l ( 1 / 3 ) 1/2 = 30 °. In practice these are the two extremes encountered. As can be seen in Figure 2 these estimates are useful approximations. The real part of Pv is negative for 0 < 0 B and positive for 0 > 0 B. The real part of Ph is negative for all 0. In consequence a circularly

211

8. Propagation at Microwave Frequencies

a

b

1.0

E

~

0.8

II II II II II II II II

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0

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20

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~

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90

0 0.1

0.2

0,5

1

2

5

,~

g2LX 10

20

50

90

Grazing angle, ~o (degrees)

Figure 2. Magnitude and phase of the reflection coefficient of a plane surface as a function of grazing angle, ~ for vertical, V, and horizontal, H, polarizations (CCIR Report 1008-1 [27]). (a) seawater, (b) medium dry ground.

polarized wave will be reflected with the same sense of rotation for 0 < 0 B and a reversed sense for 0 > 0~. Note. The effects of ground constants on electromagnetic wave propagation are a classical problem, and the reader is referred to standard texts, for example, References [9, 10, 68, 72].

Penetration Depth The transmitted wave (magnitude, V/1 - p 2 ) is attenuated as it travels in the conducting subsurface medium. The electric field intensity E is given by E ~ e - ~ z , where Z is distance and a is the attenuation coefficient. Penetration depth, 3, is defined [67] as the distance in which E / E o = e-1 or a decrease of 8.686 dB. This decrease is illustrated for a series of media in Figure 3.

212

Ernest K. Smith 103 5 2 102 5

~" 2 .E 0

5

•-~ ~

a.

2 6

g 2

10-1 5 2

10-2 10 -22

510 "1 2

5

1

2

5 10 2

5 1022

5 1032

5 104 2

5 105

Frequency (MHz)

Figure 3. Penetration depth, ~i, as a function of frequency (CCIR Rec. 527-2 [21]): For characteristics of A - G , see Figure I.

Atmospheric Refractive Index

The most widely used expressions good to three significant figures [2, 21, 47-49, 100] are total,

N=(n_

1 ) x 106= -77.6( ~ p + - -4810e --~ ) ,

(12)

dry air, N

= 77.6Pd/T

,

(13)

and water vapor, N-

72e e T + 3.75 × 105 T2 ,

(14)

where n is the index of refraction, N = (n - 1) × 106 is refractivity, T is the temperature in kelvins, p is the total atmospheric pressure in millibars, Pd is the partial pressure of dry air in millibars, and e is the partial pressure of water vapor in millibars.

213

8. Propagation at Microwave Frequencies

Note. For greater precision and broader scope, the reader is referred to Thayer [108], Hill et al. [63], Liebe [76], and Bevis et al. [8a]. Water vapor density p in g / m 3 is related to e in millibars and T in kelvins, e

p = 216.5--. T

(15)

Substituting Equation (15) into Equation (12)yields a practical form of the S & W relation, namely, U = (n

-

77.6 ~(p T

1)10 6=

+ 22.22p).

(16)

Propagation in Free Space The range equation (also known as the Friis equation [63a]) relates received power Pr to transmitted power Pt as

e r --

PtGrGt A2 (47rR)2 W,

(17)

where G r is the receiving antenna gain above an isotropic antenna in the direction of the transmitter, G t is the transmitting antenna gain similarly defined, A is the wavelength in free space in meters, R is distance between antennas in meters, and Pt is the transmitter power in watts. Path Loss

47rR ) Lfs =

a

Pt =

er

(18)

is the loss if G r and G t are isotropic antennas. Lfs is also called the "free space loss." Another expression of Equation (17) in terms of carrier power C and receiving antenna aperture is C =

PtGtAr (EIRP) A r 47rR 2 = 4,rrR2 ,

(19)

where E I R P = PtGt stands for Effective Isotropic Radiated Power, A r is the effective area of the receiving antenna and is related to gain above an isotropic radiator by GA 2 = Ar 47r = GAi,

(20)

214

Ernest K. Smith

where /~2 Ai--

4rr

(21)

is the effective aperture for an isotropic radiator.

Carrier-to-Noise Ratio ( C / N )

C/N is basic to microwave transmission. If the noise can be expressed in terms of thermal noise, then C

etatGr

(EIRP)G r

-~ ~-- ZfskTsysn = t f s k L y s n

,

(22)

where Tsys is the system noise temperature in kelvins, k = 1.38062 × 10 -23 J / K is Boltzmann's constant, and B is the bandwidth in hertz. It is common practice to express Equations (17)-(22) in terms of decibels. Given in order these expressions are (log, logarithm to base 10)

(Pr)dBw = (Pt)dBw -k- (Gr)dB i q- (Gt)dB i -+- 20log

~

-

20 log

R

-

21.98

(23) (24)

( L f s ) d B = 20 log R - 20 log ,~ + 21.98.

EXAMPLE: Assume R = 38,000 km and ,~ = 3 cm. Lfs = 201og(38 × 106) - 201og0.03 + 21.98 = 151.60 + 30.46 + 21.98 = 204.04 dB ( C ) d B w = (Pt)dBw -+- ( G t ) d B i -+- 10 log A r - 20 log R - 10.99

(25)

10 log A r = (G)dBi + 20 log ,~ -- 10.99 dB above 1 m 2

(26)

10 log A i = 20 log h - 10.99 dB above i m 2

(27)

( C / N ) d B - (EIRP)oBw + ( a r ) d B i -

(Zfs)d B

+ 2 2 8 . 6 0 - 10 log Ts - 10 log B.

(28)

215

8. Propagation at Microwave Frequencies

EXAMPLE: Assume f = 1 GHz, R = 39,000 km, Pt = 100 W, G t = 25 dB, and G r = 45 dB. Evaluate C/N if Ts = 100 K and B = 100 kHz. c

2.99792458 x 108

f

109

EIRP =

PtGt =

- 0.299792 m

20 + 25 = 45 dBw

Lrs = 20 log39 x 1 0 6 - 20 log(0.299792) + 21.98 = 151.82 + 10.46 + 2 1 . 9 8 - 184.26 dB

C/N

= 45 + 45 - 184.26 + 228.60 - 20 - 50 = 64.34 dB.

2. A t t e n u a t i o n Mechanisms Attenuation at frequencies above 1 GHz occurs almost exclusively in the troposphere for either terrestrial or E a r t h - s p a c e line-of-sight (LOS) paths. Scintillation, ionospheric and tropospheric, can produce serious signal degradation, but as energy is not subtracted from the signal, it is not considered here to be attenuation. Attenuation mechanisms for LOS paths are due to absorption of energy from the wave, or scattering of energy out of the wave, due to atmospheric gases hydrometers (rain, cloud, fog, or hail), dust, or aerosols.

Attenuation Due to the Gaseous Atmosphere Two atmospheric gases produce significant absorption at frequencies between 1 and 300 GHz. These are molecular oxygen and water vapor.

Oxygen Oxygen has modest U H F / E H F absorption and has over 30 absorption lines between 50 and 70 GHz (which merge into a single broad line at sea level pressures) and an isolated line at 118.74 GHz [21, 76]. The specific attenuation, 70 ( d B / k m at NTP: 15°C and 1013.25 mbar pressure), of dry air (due mainly to oxygen) is shown in Figure 4. Analytically, it is represented by [55]

Y0 =

6.09 7.19 x 10 -3 + f2 + 0.227 + ( f -

4.81 57) 2 + 1.50 f2 X 10 -3 d B / k m (29)

9_ 16

Ernest K. Smith 102

!

.

1 1 H20

/

/

02 [/

2

/

r

!

/

5

I

u._.

,(

e~ r.~ --

H20

I!/' I

A

/\

10-1 !

5

I

/

2

/

10"2

/

..

02

I 2

o,/ j

5

1

I I

1

I

/

I

\i I L

'J l

/

/

..,I"

/ ~.''f

I 1

/'

/

/

\~'I

!

1 10 2 Frequency,[ (GHz)

i

o/

i

t ]

!

!J 5

102

2

3,5

Figure 4. Specific attenuation of molecular oxygen and water vapor (Report 719-3 [21]). Pressure, 1013 mbar; temperature, 15°C; water vapor, 7.5 g / m 3.

for f < 57 GHz and by 7o = [3.79 x lO-Tf +

0.265 ( f - 6 3 ) 2+ 159

x ( f + 198)2 X 10 -3 d B / k m

0.028 (f-

118)2 + 1.47

] (30)

8. Propagation at Microwave Frequencies 300 200

217

h

1 I

LI

1

.

I j.~ jdL/ \ Jk J~ J[

100 r \ j k . , i LI ~" L J i ~/1 iii l - I , /! Ik./ IJ~ I v:t\¢ V% l

50 ~" 20

/,Vl~l:V

,./

lO

~

Ik,, 1

IL /Ill IV~I t

\

)"IL ;t ~l ilill ,llJ ;I;I.1 I11

iv

'-

5

/,

.,,..,

~3 F/,

/

E: 2 (b N

1

/

0.1

~

/

|/

50

....

15

ilill

llll,'ll

~l/I

~I /

~

iv~

~

!

1

\

l,v

,Ill II

v I/~I o v l, ~ x v I '~'-'""--" " I i\/~ //l ~ " - . . "-~ " [ ' I "U . . . . "~ [ L

I

I

I

k~

-

.

\ 1

ivi I 11 IV

'-: /]

/ ]

52

J

,/ ~i !i I~i~i I/

j

,y. "

0.2

~

I ~

/

0.5

v

Jl

I

"-~0

20

54

58

56

64

60 62 Frequency, f (GHz)

/

66

M

68

70

Figure 5. Total zenith oxygen absorption, 50 to 70 GHz, for selected initial heights (Report 719-3 [21 ]; [761).

for f > 63 GHz, where f is the frequency (GHz). In the oxygen absorption band (50-70 km) the specific attenuation has a complicated height (pressure) dependence, and the specific attenuation can be estimated from Figure 5 [76]. The total zenith attenuation at ground level is given in Figure 6. Water Vapor For water vapor the specific attenuation, Y~o, reflects the absorption lines at 22.2, 183.3, and 325.4 GHz. An expression, including the quadratic dependence on water vapor density, is given by [21, 55] %, = {0.050 + 0.0021p +

3.6 (f-

22.2) 2 + 8.5

89 (f-

10.6

+ (f-

183.3) 2 + 9.0

}

325.4) 2 + 26.3 fZp10-4 d B / k m

(31)

for f < 350 GHz, where f is the frequency in gigahertz and p is the water vapor density in g / m 3. Conversion of water vapor partial pressure e in millibars into density p is given by Equation (15).

218

Ernest K. Smith

~n

5

..=

o

10 "1

1

2

5

lo

2 Frequency (GHz)

5

10=

2

4

Figure 6. Total zenith attenuation at ground level (Report 719-3 [21]). Pressure, I atm; temperature., 20°C; water vapor, 7.5 g/m 3

Conversion of relative humidity H,o into water vapor density p can be obtained from e

H,o = 1 0 0 - - , e s

(32)

219

8. Propagation at Microwave Frequencies

where e s is the saturation water pressure over liquid water in millibars [16]. 17.502t e s = 6.1121 exp

t + 240.97

} ,

(33)

where t is T - 263.15 in degrees centigrade. Note. 1.8t(°C) = t(°F) - 32, where t is in degrees F a h r e n h e i t . Hence, p =

2.167Ho~e s T

.

(34)

EXAMPLE: W h a t is the specific a t t e n u a t i o n at 30 G H z of water vapor at sea level if the relative humidity is 50% and the t e m p e r a t u r e is 75°F?

Solution. t(°C) =

75 - 32 1.8 = 23"9°"

F r o m E q u a t i o n (33), 17.502( 23.9) es = 6.1121 exp{

= 6.1121 exp(1.5786) = 29.63 mbar.

23.9 + 240.97

F r o m E q u a t i o n (34), 2.167(50)(29.63) p

292.78

= 10.97 g / m 3.

F r o m E q u a t i o n (31), 3.6 Y~o = {0.050 + 0.0021(10.97) +

(30-

(30 - 22.2)2 + 8.5

10.6 (30-

8.9 ~ (30)2(10.97) 10_4 d B / k m 325.4) 2 + 26.3 )

= {0.050 + 0.023 + 0.052 + 4.5 × 10 -4 + 10-4}(0.9873) = 0.123 d B / k m .

183.3) 2 + 9.0

220

Ernest K. Smith

Note. Figure 4 shows 0.08 d B / k m for p = 7.5 g / m 3 and t = 15°C. Because 7o~ is roughly linear with p to 12 g / m 3 extrapolating the value in Figure 4 would yield a 7,0 of 0.117 d B / k m .

A t t e n u a t i o n D u e to Rain

Rain consists of water droplets with diameters ranging from about 0.2 mm (drizzle) to 7 mm. Small raindrops ( < 2 mm diameter [85a] are largely spherical, but large drops become flattened and acquire a dimple in the bottom side. The best known studies of drop-size distribution as a function of rain rate are Laws and Parsons [74], Marshall and Palmer [78], Joss et al. [69], and Prupacher and Pitter [91]. Below 30 GHz attenuation is due almost solely to absorption. Above 30 GHz scattering becomes increasingly important. A distinction is then made between the absorbed (coherent) signal and the scattered (incoherent) component [86]. Predicting attenuation due to rain is an important but complex problem, and a variety of models have been developed [36, 65]. The principal ones are the Rice-Holmberg model [94] for the percentage of the year in which rainfall exceeds a given rate, the Dutton-Dougherty model [42-44], the global model [34], the two-component model [35], the Lin model [64, 77], the simple attenuation model (SAM) [103, 104], and the CCIR model [22]. The CCIR method will be outlined here. Specific attenuation due to rain is equally applicable to terrestrial and Earth-space (slant) paths.

Rainfall Statistics Specific attenuation due to rain is a function of frequency, rainfall rate, drop-size distribution, fall velocity, and path orientation. Good reviews of the various aspects may be found in Allnutt [2], Boithias [9], CCIR [22], Flock [48], Ippolito [64, 65], and Crane [37]. The CCIR proposes two methods for regions for which local rainfall statistics are not readily available [22]. One method divides the world into 15 rain climate zones and specifies the rainfall intensity exceeded for 0.001 to 1.0% of the year for each zone. The disadvantage of the zonal method is that boundary discontinuities of a factor of 2 may exist. The second so-called contour method is reproduced here. The land areas of the world are contoured for rain rate exceeded 0.01% of the year (52.56 min). The rainfall rates at other percentages of the year are then derived from this single value. This method has the advantage of continuity but does not allow for the variation of rainfall distribution with climate. For example, in

221

8. Propagation at Microwave Frequencies 165 ° 75 ~

150 °

135 o

120 o

105 °

90 o

75 o

60 °

45 °

30 ° 75 °

x.

60 ° ~

v,.._

-"~---_. ~ ,

1...~..5~ _ - - - - - "

15 °

'

.

~

0°

o

15 °

•

60

40

60o

'I ~ K . . ~ . ~ O 0

0°

~,

15 °

10 1 30 °

30 °

80 45 °

'60

30 60 ° 165 °

150 °

135 °

120 °

105 °

90 °

75 °

450

20

60 °

45 °

60 ° 30 °

Figure 7a. Rainfall contours for 0.01% of the time for the Americas (Report 563-4 [22]).

the Midwest of the United States the rainfall is largely convective (thunderstorm related), whereas on the West Coast of the United States the rain is largely stratiform and the cumulative distributions are very differ-

222

Ernest K. Smith

b 30°

15 °

0°

15 °

30 °

45 °

60 °

-

600

4~

4oi"

~

4,))

"--~j

30°

/

"

i

30°

1 30 °

15~'

O'

15°

30°

45"

60°

Figure 7b. Rainfall contours for 0 . 0 1 % of the time for Europe and Africa (Report 563-4 [22]).

ent, although the 0.01% rain rate may be the same. The CCIR rainfall contours for 0.01% of the time are given in Figures 7a, 7b, and 7c. The curve parameter is the rain rate in millimeters of rain per hour with an integration time of i min. The contour maps come from Report 563-4 [22].

8. P r o p a g a t i o n at M i c r o w a v e

C

60 °

75 ~

223

Frequencies

90 ° •

105 °

120 °

135 ° 'xY-.,-'

150 ° "-J

165 °

180 °

,

60 °

165° 75°

y ,e eo

20

45 °

/

,

4 0 ~

.

45 °

,~

J

0°

,o0

~-, " ~

0o

,oo

15 °

30 °

~

30 °

60

~?

40 4o 45 °

60°60°

~j/

75 °

90 °

105 °

120 °

135 °

150 °

165°

450

180 °

I

Figure 7c. Rainfall contours for 0 . 0 1 % o f the t i m e f o r Asia and Australia ( R e p o r t 5 6 3 - 4 [22]),

Step 1. Obtain the rain rate Ro.ol exceeded for 0.01% of the time from Figure 7. Step 2. Compute the specific attenuation "YR ( d B / k m ) from the nomogram given in Figure 8.

224

Ernest K. Smith

Step 3. Determine the specific attenuation A p for the rainfall rate exceeded for the percentage of time P desired by the following relation: YP

= 0.12P-(O.546+0.043 log P).

(35)

")/0.01

This formula gives factors of 0.12, 0.39, 1, and 2.14 for 1, 0.1, 0.01, and 0.001% of the time. For use between 0.001 and 0.1% of the time, this relationship is not bad. EXAMPLE: What is the specific attenuation for rain exceeded 1% of the time for Boulder, Colorado, for horizontal polarization at 30 GHz? METHOD:

Step 1. Obtain the rain rate from Figure 7a for 40°N, 105°W longitude. This is found to be 32 m m / h . Step 2. From the nomogram in Figure 8 we obtain a value of 6.4 d B / k m for 0.01% of the time. Step 3. From Equation (35) we deduce that for 1% of the time the factor is 0.12 of the attenuation for 0.01% of the time. Hence, ")/1.0

:

0.12(6.4) = 0.77 d B / k m .

Path Attenuation

Heavy rain usually occurs in ceils of a few kilometers in extent. Thus, the attenuation applicable for 0.01% of the time at a location should not be multiplied directly by the path length but by a shorter length to account for lighter rain over some parts. The effective path length Le~ is obtained by multiplying the actual path length L by a path reduction factor, r.

r=

I + L /L o

(36)

where L 0 = 35 exp(-0.015R0.01). For example, in the problem above, if a terrestrial path length of 10 km were specified and R0.01 = 32 m m / h , Equation (36)would give L 0 = 21.66, r = 0.684, and Leff = 6.84 km.

225

8. Propagation at Microwave Frequencies

Terrestrial Paths The rain attenuation for 0.01% of the time is given simply by

(/0.01)path -- "Y0.01Leff"

(37) .

Equation (35) can then be invoked to obtain the percentage of the time desired by

Ap

Tp -

Ao.01

.

(38)

Yo.oa

Earth-Space (Slant) Paths The procedure for Earth-space paths for elevation angle 0 > 5 ° is given in Report 564-4 [22]. A nomogram for computing specific attenuation for vertical and horizontal polarization as a function of rainfall rate and frequency is given in Figure 8.

Step 1. Calculate the effective rain height h R for the station latitude from 3.0 + 0.0284~ hR(km) = 4 . 0 - 0 . 0 7 5 ( 4 ) - 3 6 )

0 < 4) < 36° ~ <36°.

(39)

Step 2. Calculate the slant path length L~ in the rain, L -

(hR-- hs ) sin 0

km

'

(40)

where h s is the station altitude above sea level.

Step 3. Calculate the horizontal projection L G of L s, L G = L s cos 0.

(41)

Step 4. Calculate the path reduction factor r as in Equation (36) but substituting L G for L, r°°l = 1 + L G / L o

(42)

where L o = 35 exp(-0.015Ro.o1).

Step 5. Calculate the path attenuation Ao.ol for 0.01% of the time,

Ao.ol = YRLsro.ol.

(43)

226

Ernest K. S m i t h

.-- 6O

-

50

-

40

-

30

0

3( h :-- 20 25 - 15

L

9O

GHz (V)

10

20-

GHz (H)

SO

mm/h

10

dB/km 6O 5O

-

5

-

4

-

3

.

2

-

1

1514.

A0 ~0

0.8 -

2O

0.6 -

0.5

-

0.4

0.3 -

0.2

-

0.1

:-- 0.05 - 0.04 0.03 - 0.02

8.

0.01 0.005

6'

- 0.002 -- 0.001 f,

Figure 8. N o m o g r a m

S ,?

f o r c o m p u t i n g specific attenuation f o r vertical, V, and horizontal, H, polarization as

a function o f rainfall rate and f r e q u e n c y (Report 7 2 1 - 3 [22]).

227

8. Propagation at Microwave Frequencies

EXAMeLE: What is the attenuation due to rain exceeded 0.01% of the time for an Earth station in Boulder receiving a satellite transmission at a 30 ° elevation angle (slant path) and a frequency of 30 GHz? METHOD: From the previous example the specific attenuation due to R0.0~ at 30 GHz = 6.4 d B / k m .

Step 1. h n = 4.0 - 0.075(40 - 36) = 3.7 km. Step 2. Station altitude hs = 5400 ft = 1.658 km, ( 3 . 7 - 1.66) sin 30 ° = 4.08 km.

Ls =

Step 3. L c = 4.08 cos 30 ° = 3.53 km. Step 4. L o = 35 exp(0.015 × 32) = 21.66 km,

ro.ol

=

1 + 3.53/21.66

= 0.86.

Step 5. A0.01 = (6.4)(4.08)(0.86) = 22.46 dB. Attenuation Due to Fog and Cloud Both fog and cloud involve water (or ice) particles too small to precipitate (smaller than 0.17 mm). A relation proposed by Altshuler [3] appropriate from about 30 to 100 GHz is 18 A = -1.347+0.0372A

+

0.022 t,

(44)

where A is attenuation in d B / k m / g / m 3, A is the wavelength in millimeters, and t is t e m p e r a t u r e in degrees centigrade. Gerace and Smith [53] have compared several cloud models.

Attenuation Due to Snow and Ice Crystals Snow, as a consequence of its different complex refractive index, produces much less effect on attenuation than does rain. An exception is at the melting layer (close to the 0°C isotherm), where snow (and ice crystals) becomes covered with a layer of water. Ice crystals (in ice clouds) can have a significant effect on depolarization of the signal, however [2, 13].

228

Ernest K. Smith

Attenuation Due to Sand and Dust Sand and dust particles in the air, particularly in the case of sand and dust storms in desert areas, are generally not significant at frequencies below 30 GHz. Theoretical work by Chu [32], who related radio attenuation to optical visibility, measurements by Ghobrial [54] in the Sahara, and a review by Goldhirsh [56] should be accessed by the interested reader.

3. Terrestrial Line-of-Sight Propagation Propagation loss on terrestrial line-of-sight paths relative to the free-space loss is the sum of different contributions as follows [23], [60], [61], [62] 1. 2. path; 3. 4. 5. 6.

attenuation due to atmospheric gases; diffraction fading due to obstruction or partial obstruction of the fading due to multipath, beam spreading and scintillation; attenuation due to variation of the angle of arrival/launch; attenuation due to precipitation; and attenuation due to sand and dust storms.

Of these six items, numbers 1, 5, and 6 are treated in Section 2. The curvature C of a ray traveling in the spherically stratified atmosphere is given by ldn

C -

ndh

cos 0

(45)

where n is the index of refraction, h is the height of refraction, and 0 is the angle of elevation. In the troposphere n is approximately unity, as is cos 0 for a near-horizontal path. Under these conditions Equation (18) becomes simply dn C = - ~--h-.

(46)

A convenient transformation for a ray traveling nearly horizontally over a spherical Earth makes the ray path straight but changes the apparent radius of curvature of the Earth to maintain the same separation between the surface and the ray. 1 --

ro

dn +

1 =

dh

,

Kr o

(47)

229

8. Propagation at Microwave Frequencies

where r 0 is the true radius of the Earth, say, 6371 km, and Kr o is the effective radius of the Earth. Replace d n / d h with ( d N / d h ) × 10 -6, where N = ( n - 1) 106 is refractivity. On the average, over the Earth, d N / d h = - 4 0 ( N / k m ) . Under these conditions K ~- 4 (the so-called Earth radius condition). If dN/dh = - 1 5 7 , then K = ~ and the ray is trapped or ducted near the surface of the Earth. On the other hand, if d N / d h = 0, then the ray behaves as if there is no atmosphere. If dN/dh becomes positive, then the ray is curved away from the Earth's surface. Common practice in siting a terrestrial circuit is to design the terminals so that 0.6 Fresnel zone clearance exists. The first Fresnel zone is the ellipsoid with the transmitting and receiving antennas as focii, in which the distance from the transmitting antenna to the surface and then to the receiving antenna is just a half wavelength greater than the straight line between the two antennas. The 0.6 Fresnel zone criterion says that any obstruction of the path will be no closer to the straight line path than 0.6 of the perpendicular distance from that path to the first Fresnel zone ellipsoid.

4

Diffraction Fading Due to Partial Obstruction of the Path

Diffraction loss over average terrain for losses A c greater than 15 dB can be approximated by the formula [23]

A c = - 2 0 h / F 1 + 10 dB,

(48)

where h is the height (in meters) of the most significant blockage from the path trajectory (h is negative if the top of the obstruction of interest is above the line of sight), and F 1 is the radius of the first Fresnel ellipsoid and is given by

F 1 = 17.3

did2 fd

]1/2 m,

(49)

where d 1 and d 2 are the distances from the terminals to the path obstruction in kilometers, d is the distance between terminals in kilometers, and f is the frequency in gigahertz. EXAMPLE: What is the diffraction loss for a transmission system operating over a 10-km path at 30 GHz if an obstruction at the midpoint rises 2.5 m above the path trajectory.

230

Ernest K. Smith

METHOD:

F 1 = 17.3

A c = -20

(5)(5) (30)(10)

1/2

= 5.0m

-2.5) + 10= +10+ 10=20dB. 5

Fading Due to a Multipath and Scintillation Multipath propagation occurs when more than one propagation path exists between the transmitter and the receiver. This can be due to reflections from the ground and terrain obstacles or from one or more tropospheric layers with steep vertical variations in the refractive index. A good up-todate discussion is found in CCIR Report 338-6 [23]. Descriptions of this subject may be found in the papers by Bullington [18, 19], Morita [83], Barnett [5], Olsen et al. [87], and Olsen and Segal [86a]. The phenomenon of scintillation occurs over all paths but is particularly marked above 10 GHz. Amplitude scintillation has been discussed by Boithias [9] and is treated in Section 5 of CCIR Report 718-3 [25]. Amplitude scintillations are due to turbulent irregularities in the refractive index of the propagating medium, which also give rise to phase scintillations and angle-of-arrival scintillations.

Fading Due to Variation in the Angle-of-Arrival Variation in the angle-of-arrival is closely related to beam spreading or dcfocusing and constitutes a slow nonselective type of fading that is particularly prevalent over water [112].

4. Propagation beyond the Horizon At microwave frequencies signals are propagated beyond the horizon by diffraction, tropospheric scatter, ducting, and rain scatter. Of these four mechanisms only diffraction and tropospheric scatter are useful for providing communications service. Ducting and rain scatter are important interference mechanisms but are not sufficiently dependable for service use. Most computational methods are based on NBS Technical Note 101 [84].

8. Propagation at Microwave Frequencies

231

Diffraction Diffraction can be divided into two categories: diffraction around the smooth Earth and that over obstacles. Diffraction over a smooth Earth is a classical area investigated by Norton [85], Bremmer [14], and others. Current reviews with nomograms and charts may be found in Boithias [9], Maclean and Wu [77a], and CCIR Report 715 [24]. Attenuation, A, in the terrestrial diffraction zone is given approximately by David and Voge [39, Eq. 4.20a]. A = 0 . 6 2 / [ A ( m ) ] 1/2 d B / k m .

(50)

Diffraction over obstacles is also treated in CCIR Report 715 and by Boithias [9]. In practical applications a terrain profile between the trans4 mitter and the receiver is commonly prepared on ~ Earth paper. In one technique the elevation angles to the nearest obstacles are then drawn from the transmitting and receiving locations. Calculations are then made in terms of the angle between these two lines and the separation distance. Multiple knife edges have been treated by Vogler [111].

Tropospheric Scatter Tropospheric scatter propagation was first predicted by Booker and Gordon [11] and expanded on by Gordon in 1955, and Wheelon in 1959, as a faint signal scattered from the common volume of two antennas. An alternate theory, based on partial reflections from horizontal gradients in the refractive index in the common volume of the antennas, is given in Feinstein [45, 46], and Friis et al. [51]. The mechanism has been employed in circuits with high-gain antennas at each terminal to cover distances of 40 to 500 km with capacity up to 10 Mbps, at frequencies of 100 MHz to 5 GHz [93]. Troposcatter, as it is known, is now primarily used on military intermediate distance circuits for which a dependable low-datarate service is required. A general relation for basic transmission loss, Lb, and a series of curves is given by Boithias [9]. L b = 30 log F + 30 log d + 1.5G + 102 dB,

(51)

where F is the frequency in megahertz, d is the distance in kilometers, and G is the refractive index gradient in the common volume, in N / k m (G is usually negative). More complete treatments are found in Roda [95], and Reynolds [93].

232

Ernest K. Smith

Atmospheric Ducting Ducting occurs when the vertical gradient in the refractive index, d N / d h , equals or exceeds - 1 5 7 N units per kilometer (the value at which the downward curvature of the ray becomes equal to the curvature of the surface of the Earth). One of the earliest comprehensive reports is that of Booker and Walkinshaw [12], who treat the duct as a waveguide. Transmission loss in duct propagation is less than normal because the wave is constrained to spread in two dimensions rather than three. A relation between the basic transmission loss, L b, for two stations, both located in a duct, is given [25] by L b = Lbf -- 10 log d + A dB,

(52)

where L is the basic transmission loss for free-space conditions, d is the separation distance in kilometers, and A is an attenuation term to account for leakage and reflection losses. A duct is similar to a waveguide in that a cutoff frequency exists below which the duct is ineffective. Ducts are also effective only for waves launched at very low elevation angles. Duct propagation commonly occurs over water and is a significant source of interference. In the CCIR [21] it is treated in Reports 238-6 (transhorizon propagation), 563-4 (radio meteorology), and 718-3 (effects of refraction). Other treatments are found in Bean and Dutton [7], Dougherty and Hart [41], and Hall [62].

5. Earth - Space Propagation This section deals primarily with satellite communications. An overview is found in a special section of the IEEE Proceedings for June, 1993, edited by Stutzman [102]. Readers interested in deep-space propagation problems are referred to Yuen [114]. Earth-space propagation is treated under three headings: ionospheric effects, tropospheric effects, and mobile satellite propagation (ocean surface, terrain, foliage, and building effects). In the case of propagation from fixed Earth stations only the first two effects need to be considered. The third category becomes important for the mobile-satellite and broadcast-satellite services. Texts on satellite communications which also treat propagation are Gagliardi [52], Miya [81], Morgan and Gordon [82], Pratt and Bostian [90], and Roddy [96]. Texts which specialize in the propagation aspects of satellite communications are Allnutt [2], Flock [48], and Ippolito [64, 65]. The CCIR [20] treats satellite communications in several of its Green Books (e.g., Volumes II, IV, VIII, X, and XI) but most notably in Volume IV. Propagation aspects

233

8. Propagation at Microwave Frequencies

are treated under Section F in Volume V (nonionized media), most notably in Report 564-4, and in Report 263-7 of Section F in Volume VI (ionized media). Effective in 1994, Study Groups V and VI of the former CCIR are combined as Study Group III of the ITU Radio Bureau, now abbreviated ITU-R.

Geometry for the Geostationary Orbit Most satellite communication problems involve satellites in the geostationary orbit (GEO) located 35,768 km above the Earth's geographic equator, although low earth-orbitting (LEO) satellites have become of interest. For most propagation problems it is necessary to know the elevation angle, 0, the distance, d, from the Earth station to the satellite, and, in some cases, the azimuth angle, ~b. Miya [81] includes very convenient transparent overlays which can be used to provide first-order answers. It is necessary to know the longitude of the satellite and the latitude and longitude of the Earth station. SS, Space Station; ES, Earth Station; h, 35,768 km; r0, 6371 km. Note. Equatorial r 0 = 6378.16 km and polar r 0 = 6356.78 km.

ES

SS

SS 4"

h

/

/

ro

234

Ernest K. Smith

Step 1. Solve for c = cos-I(COS b cos a), C "-- C O S - I ( c o s { A

longitude} cos{A latitude}).

Step 2. Solve for d using the law of cosines,

d 2 = r 2 + (h + ro ) 2 - 2ro(h + ro)COS c'. Step 3. Solve for • to get (9 = • -

A Long

90 °

(h + ro )2--- d 2 -t- r 2 - 2 r o d cos ~ . a

Step 4. Obtain azimuth 180 ° + a,

cos a = tan b cot c.

A Latitude

Ionospheric Effects Ionospheric effects at microwave frequencies can be divided (roughly) into those due to the total number of electrons between the transmitter and the receiver and those due to electron density irregularities in the path (ionospheric scintillation). Both types of effects are highly influenced by the temporal variations of the ionosphere; diurnal, seasonal, and solar cycle. Good modern references on ionospheric behavior are Davies [40], Goodman [59], McNamara [79] and Rawer [91a]. Another source for ionosphere temporal effects is CCIR [20], Volume VI.

Earth's Magnetic Field [40, Section 2.4] The Earth's magnetic field is quite complex near the surface. However, with increasing altitude the field tends to approach that of an Earth-centered magnetic dipole inclined about 11 ° from the axis of rotation and penetrating the Earth's surface at 79.1°N and 289.1°E of Greenwich in the northern hemisphere. The radial or vertical component Z of this dipole field, considered to be positive if directed inward, is given by Z = - 2 H 0 ( a / r ) 3 sin ~b.

(53)

The horizontal component H of the field is given by H = Ho(a/r)

3 cos 6,

(54)

and the total field F is given by F = Ho(a/r)3(1

+ 3sin 2 q~)1/2,

(55)

where H 0 = 0.31 g a u s s ( G ) = 0.31 × 10 -4 tesla (T, the SI unit), a =

235

8. Propagation at Microwave Frequencies

6371 km and is the mean radius of the Earth, r is the distance to the center of the Earth, and ~b is the geomagnetic latitude (i.e., that oriented on the magnetic dipole axis instead of on the rotational axis). The geomagnetic dip I is given by tan I = Z / H

= 2 tan(~),

(56)

where • is the geomagnetic latitude in degrees. EXAMPLE: What is the total field F at 6.6 Earth radii from the center of the Earth (geostationary orbit) at a longitude at which the geographic and geomagnetic equators cross? Solution.

We take the value of H 0 as 0.31 G or 0.31 × 10 -4 T. Then

F = {0.31/(6.6)3}{1 + 3sin2(0)} 1 / 2 = 1.08 × 1 0 - 3 G = 1.08 × 10 -7 T. (57)

Faraday Rotation [17, 40] Faraday rotation refers to the twisting of the polarization axis of the radio wave as it passes through the ionosphere. At frequencies in the vicinity of or below the peak plasma frequency (usually between 1 and 10 MHz) of the ionosphere encountered by the radio wave, the full Appleton-Hartree expression [40] for the refractive index in a magnetoionic medium must be used. At microwave frequencies, for all considerations except Faraday rotation, the refractive index simplifies to that of a nonmagnetic medium. In the case of Faraday rotation the quasilongitudinal, or QL, approximation to the Appleton-Hartree equation is used (good over 99% of the Earth's surface at frequencies above 1 GHz). The QL approximation for the refractive index, n, is n 2 = ] - X/(1

_+ YL)

R = +_1,

(58)

where X = ( f c / f ) 2 , YL = Y c ° s 0 = ( e / m ) F cos 0 / (27rf), fc = 9(Ne )1/2 = plasma frequency, in hertz, f is the operating frequency, R is the polarization ( + 1, right-hand circular; - 1 , left-hand circular), e l m is the charge-to-mass ratio of electrons, and N e is the electron density in e l e c t r o n s / m 3. Note. The plus and minus signs in the denominator of Equation (58) indicate that the signal divides into two counter-rotating circularly polarized components traveling at slightly different velocities upon entering the ionosphere and recombines on exiting. The different velocities cause the changed polarization. One might expect that a signal rotated in one

236

Ernest K. Smith

direction while going from space to Earth would unwind on the return trip. In fact the rotation is additive [17, Section 13.7]. The equation for Faraday rotation is O = (2.36 × 1 0 4 / f z ) f N B L dl radians.

(59)

EXAMPLE" Assume that the ionosphere can be represented by a uniform slab of electrons 400 km thick centered at a height of 400 km and having a density of 1012 e l e c t r o n s / m -3. Assume that B L is given as 0.3 G and that the operating frequency is 1 GHz. , = (2.36 104/1018)(4 X 105)(3 X 10-5)(1012) = 0.283 rad = 16.2 °.

Excess Group Delay, zl R [2, 40] The group range delay, or excess group delay, refers to the excess delay over that in free space and is actually made up of two parts, one due to the ionosphere and the other due to the troposphere [50]. The ionosphere part of the range delay is given by AR -

40.3 f2 z

fNdl

=

40.3 ~n2z (TEC) m,

(60)

where

f

dl = TEC

is the total electron content of the column between the Space Station and Earth Station (or vice versa). EXAMPLE: Let f = 1 GHz and TEC = 1018 e l e c t r o n / m 2. The excess range delay is AR=

40.3 (109)2 (1018) = 40.3 m.

Thus the equivalent free space path is 40.3 m longer than the actual path due to the ionosphere. TEC may vary by an order of magnitude diurnally. The troposphere delay is significant but is much less variable. The variable part is due largely to water vapor and may vary diurnally by only 10-20 cm. However, the two-frequency technique used to assess the ionospheric term cannot be used for tropospheric excess range delay because the tropospheric refractive index is essentially nondispersive.

237

8. Propagation at Microwave Frequencies

Excess Phase Delay, A gp Phase change due to the ionosphere is negative, whereas that due to the troposphere is positive. This is a consequence of the ionospheric refractive index being less than 1, whereas that in the troposphere is greater than 1. The ionospheric reduction in the phase path is given by 8.44 × 10 - 7 A~b =

× TEC rad.

(61)

fHz

Ionospheric Scintillation Ionospheric scintillations are caused by irregularities in electron density of a few meters to a few kilometers. Scintillations affect the amplitude, phase, and angle-of-arrival of radio waves [40, 59]. A useful index to compare scintillation data is the scintillation index, $4, which is defined as the "standard deviation of received power, _P, divided by the average value of received power, P," [15]. Thus m

[~(p - p)2] 1/2 S4 =

_ P

.

(62)

For simplicity of scaling, a scintillation index, SI, has been defined [113]. SI = A f -n,

(63)

where A is a proportionality constant and n varies between about 1.6 for low values of S 4 to 0.8 for high values.

Phase Scintillations Phase scintillations [40] are measured by the rms fluctuation of phase 4). The frequency dependence is given approximately by ¢~rms --

Bf -1,

(64)

where B is a proportionality factor. The dependence on the sunspot cycle for S 4 and (I)rm s is 1 + 0.04R12 [40], where R12 is the 12-month runningaverage sunspot number. The geographic dependence is portrayed in Figure 9. As can be seen scintillation is most virulent in an equatorial belt during the peak of the sunspot cycle, nextmost virulent in the auroral zones, and least virulent at midlatitudes [6].

Tropospheric Effects Tropospheric attenuation effects have been treated fairly comprehensively in Section 2. Here we add the cross-polarization and scintillation effects due to propagation, now very important due to frequency reuse of the same channel on two orthogonal polarizations.

238

Ernest K. Smith SOLAR MAXIMUM

L- BAND 1 20(1 15c

SOLAR MINIMUM

Io=

5d 2d F11d

o.lil

•~"

o

z z

Figure 9. Global incidence of ionospheric scintillation fades at the L band during the solar maximum and minimum [6].

Depolarization in Satellite Communications

Depolarization due to the ionosphere is treated under Geometry for the Geostationary Orbit. Tropospheric depolarization can occur due to rain, ice crystals, or multipath. Good treatments may be found in Allnutt [2], Ippolito [64, 65], Pratt and Bostian [90], and others. The two terms most commonly used to express depolarization consequences are crosspolarization isolation, XPI, and cross-polarization discrimination, XPD. Consider orthogonal transmitted fields "a" and "b." At a receiving antenna copolarized components a c and bc are received, but if there is depolarization in the propagation medium some energy from a will show up on the b polarization as b x. We define [90] XPI and XPD as follows: XPI = 20 log]o I~ac dB

XPD = 20 lOgl0 -a-

riB.

(65)

(66)

In most instances the two terms XPI and XPD will be the same. Rain depolarization is caused by nonspherical raindrops which induce differential attenuation and phase shift in the orthogonal components of radio waves passing through them [4]. Tropospheric Scintillation

Tropospheric scintillation tends to be a significant problem only for low-elevation angles at the Earth Station [105]. Thus, because most satel-

239

8. Propagation at Microwave Frequencies

lite circuits operate at higher elevation angles, tropospheric scintillation is rarely a problem. Measurements have been made by Crane [2] and Karasawa and Matsudo [70], and theory has been developed by Tatarski [107]. Calculation methods for elevation angles above and below 4° are given in CCIR Report 564-4 [22].

Mobile Satellite Propagation Effects There are special problems in the mobile satellite services that are unique. For the land mobile satellite service these have to do with the effects of foliage, terrain, and man-made structures. For the maritime mobile satellite service reflection and scattering from the ocean surface are the problems. In the aeronautical mobile satellite service the problem is long delayed echoes from the Earth's surface. Land Mobile Satellite Service

Empirical results taken over a variety of terrain and foliage conditions for elevation angles from 10° to 50 °, most notably by Vogel and Goldhirsh [57, 58, 109, 110], at UHF and L-band frequencies are the most significant data in this area. The CCIR treatment is found in Report 1009-1 [27]. Theoretical treatment is primarily based on Beckmann and Spizzichino [8]. At frequencies around 1.5 GHz single-tree attenuation is 10-20 dB, and 99% service typically requires a 10-dB attenuation margin. Ionospheric and tropospheric effects are as described under Geometry for the Geostationary Orbit and Ionospheric Effects.

Maritime Mobile Satellite Service The maritime situation is more amenable to analysis than the land situation in that the direct signal is not obstructed and the ocean surface is easier to model. A two-step process is required [28]. The amplitude of the coherently reflected component, Er, relative to the direct signal is given in Reference [80].

Er = I R I G r

f --u2 2 I° mu2 ) 2

4rrh o sin u =

A

(67)

0i

(68)

where R is the specular reflection coefficient of the sea, G r is the antenna gain toward the specular point relative to boresight gain, I 0 is the modified Bessel function of the first kind and of zero order, h 0 is rms height of the sea waves measured from the mean level, A is the wavelength of the radio

240

Ernest K. Smith

signal, and 0 i is the grazing angle (taken as equal to the elevation angle). The maximum fade depth, Amax, of the coherent component occurs when E r is in antiphase with the direct component E 0. A max --

-

20 l o g ( 1

-

E r).

(69)

The values of E r and Ama x decrease with increasing wave height, elevation angle, and frequency. At the same time an incoherent component, E s, builds up [8, 71]. The resultant signal has a Ricean distribution [8]. Aeronautical Mobile Satellite Service

For the aeronautical service [2], the altitude of the aircraft may be above most tropospheric attenuation. Ionosphere effects will be the same as those for other services. Important factors are high doppler shifts due to high aircraft speeds, small antennas, and problems of visibility while banking. The analysis of sea-surface reflection for maritime satellite systems is appropriate for aeronautical satellite systems for over-water flights. Measurements have been made by Sutton et al. [106], Zaks and Anderson [115], and others; simulations have been made by Davarian [38]. The subject is treated in CCIR Report 1148 [29].

6. Mobile Propagation Effects Land mobile services are now being discussed under the headings of vehicular mobile (a relatively high-power service) [98] and portable (a digital low-power hand-held service) [88]. Both are primarily urban services for which the Rayleigh distributed multipath components commonly constitute the received signal. Overviews of the vehicular propagation problems are available in Jakes [66], Lee [75, 75a], Parsons [89], and CCIR Report 567-4 [30]. Most current systems operate just below 1 GHz, the lower limit under consideration here. The portable communication service [33] is in its formative stage, and frequencies in the 0.5 to 5-GHz range are being considered for terrestrial applications and up to 45 GHz is being considered for satellite systems.

7. Short-Path Propagation Included under this title are indoor propagation, indoor-to-outdoor, and short-path outdoor propagation. While current interest is perhaps most active in the new allocations in the 1- to 3-GHz band [96a], there is also

241

8. Propagation at Microwave Frequencies

interest extending up into millimeter wavelengths. Personal communications networks (PCNs) are a driving force. A review of this topic is found in Bach Anderson, Rappaport, and Yoshida [4a]. Penetration into buildings at 800-900 MHz is described by Bultitude [19a] and Walker [llla]. Ground floor penetration losses averaged 18.0 dB with a standard deviation of 7.7 dB for urban samples. CCIR treatments are found in Report 567-4, Sections 6 and 10 [30] which deals with buildings, and Report 880-2 which concentrates on propagation in tunnels and mines [31].

8. Noise Noise at microwave frequencies is primarily of natural origin. Extraterrestrial noise of galactic and solar origin dominates the UHF part of the spectrum, whereas noise of atmospheric origin dominates above 10 GHz [99]. For a medium in local thermodynamic equilibrium Kirchoff's Law states that emission is equal to absorption at all frequencies [79]. The maximum and minimum values of natural noise are illustrated in Figure 10. Report 720-2 [26] treats natural noise at microwave frequencies.

80

60

2.9x 10 8

A O I,-IJJ

>

40

J '

O n,l

2.9x10 s

,< 20 "10 UL

,, ..~IGALACTIC

o

~?//~

I

RAINy..

QUANTUM\

-

290.

-20

\

"<" e O S M IC \ ~ - - - t - x % ' 7 " IJall

100

I

I f4~lr"-'l

1 GHz

i l i]l~

COSMIC J~J

10

100

i

i J~J~J

0.29

1 THz

FREQUENCY

Figure 10. Maximum and minimum levels of natural noise [I 01].

242

Ernest K. Smith

References

[1] S. E. Alexander, Radio propagation within buildings at 900 MHz, Electron. Lett., Vol. 18, pp. 913-914, 1982. [2] J. E. Allnutt, Satellite-to-Ground Radiowave Propagation--Theory, Practice, and System Impact of Frequencies Aboue 1 GHz, IEE London: Peter Peregrinus, 1989. [3] E. E. Altshuler, A simple expression for estimating attenuation by fog at millimeter wavelengths, IEEE Trans. Antennas Propag., Vol. AP-32, pp. 757-758, 1984. [4] A. Aresu, A. Marellucci, and A. Paraboni, Experimental assessment of rain anisotropy and canting angle in a horizontal path at 30 GHz, IEEE Trans. Antennas Propag., Vol. AP-41, pp. 1331-1335, 1993. [4a] J. Bach Anderson, T. S. Rappaport, and S. Yoshida, Propagation measurements and models for wireless communications channels, IEEE Commun. Mag., Vol. 33, pp. 42-49, 1995. [5] W. T. Barnett, Multipath propagation at 4, 6 and 11 GHz, Bell Syst. Tech. J., Vol. 51, pp. 321-361, 1972. [6] S. Basu, E. MacKenzie, and S. Basu, Ionospheric constraints on V H F / U H F communication links during solar maximum and minimum periods, Radio Sci., Vol. 23, pp. 363-378, 1988. [7] B. R. Bean and E. J. Dutton, Radio Meteorology. New York: Dover, 1968. [8] P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces. New York: Pergamon Press, 1963. [8a] M. Bevis, S. Businger, S. R. Chiswell, T. A. Herring, R. A. Anthes, C. Rocken, and R. H. Ware, GPS meteorology: Mapping zenith wet-delays onto precipitable water, J. Appl. Meteor., Vol. 33, pp. 379-386, 1994. [9] L. Boithias, Radiowave Propagation. New York: McGraw-Hill, 1987. [10] H. G. Booker, Energy in Electromagnetism. London: Peter Peregrinus, 1982. [11] H. G. Booker and W. E. Gordon, A theory of radio scattering in the troposphere, Proc. IRE, Vol. 38, pp. 401-412, 1950. [12] H. G. Booker and W. Walkinshaw, The mode theory of tropospheric refraction and its relation to wave-guides and diffraction, Meteorol. Factors Radio-Wave Propag., Rep. Conf. Phys. Soc. R. Meteorol. Soc., London, Taylor & Francis, London, 1946. [13] C. W. Bostian and J. E. Allnutt, Ice-crystal depolarization on satellite-earth radio paths, Proc. IEE, Vol. 126, pp. 951-960, 1979. [14] H. Bremmer, Terrestrial Radio Waves~Theory of Propagation. Amsterdam: Elsevier, 1949. [15] B. H. Briggs and J. A. Parkin, On the variation of radio star and satellite scintillation with zenith angle, J. Atmos. Terr. Phys., Vol. 25, p. 339, 1963. [16] A. L. Buck, New equations for computing vapor pressure and enhancement factor, J. Appl. Meteorol., Vol. 20, pp. 1527-1532, 1981. [17] K. G. Budden, The Propagation of Radio Waves. Cambridge, Engl.: Cambridge Univ. Press, 1985. [18] K. Bullington, Radio propagation fundamentals, Bell Syst. Tech. J., Vol. 36, pp. 593-626, 1957. [19] K. Bullington, Phase and amplitude variation in multipath fading of microwave signals, Bell Syst. Tech. J., Vol. 50, pp. 2039-2053, 1971. [19a] R. J. C. Bultitude, Measurement, characterization and modelling of indoor 800/900 MHz channels for digital communications, IEEE Commun. Mag., Vol. 25, 1987.

8. Propagation at Microwave Frequencies

243

[20] CCIR, The International Radio Consultative Committee (CCIR) of the International Telecommunication Union (ITU) meets every four years in Plenary Session. Its conclusion in the form of Recommendations and Reports are issued about one year later. The XVIIth Plenary Assembly of the CCIR met in Dusseldorf in May 1990. (Avail. from ITU, Geneva or National Technical Information Service, Springfield, VA.) [21] CCIR, Reports of the CCIR, Annex to Vol. V, "Propagation in Non-Ionized Media," XVII Plenary Assem. CCIR (Int. Consultatiue Comm., Dusseldorf May~June 1990). (Avail. from NTIS.) [22] CCIR, "Rain Attenuation is Drawn from Reports 563-4, 721-3, 338-6, and 564-4," Reports of the CCIR, Annex to Vol. V, ITU, Geneva, 1990. [23] CCIR, "Propagation Data and Prediction Levels Required for Terrestrial Line-of-Sight Paths," Reports of the CCIR, Annex to Vol. V, Rep. 338-6, pp. 355-420, 1990. [24] CCIR, "Propagation by Diffraction," Reports of the CCIR, Annex to Vol. V, Rep. 715-3, pp. 44-59, 1990. [25] CCIR, "Effects of Tropospheric Refraction on Radio-Wave Propagation," Reports of the CCIR, Annex to Vol. V, Rep. 718-3, pp. 149-188, 1990. [26] CCIR, "Radio Emission from Natural Sources in the Radio Frequency Range Above About 50 MHz," Reports of the CCIR, Annex to Vol. V, Rep. 720-2, pp. 205-225, 1990. [27] CCIR, "Propagation Data for Land-Mobile Satellite Systems for Frequencies Above 100 MHz," Reports of the CCIR, Annex to Vol. V, Rep. 1009-1, pp. 536-549, 1990. [28] CCIR, "Propagation Data for Maritime Mobile-Satellite Systems for Frequencies Above 100 MHz," Reports of the CCIR, Annex to Vol. V, Rep. 884-2, pp. 515-535, 1990. [29] CCIR, "Propagation Data for Aeronautical Mobile-Satellite Systems for Frequencies Above 100 MHz," Reports of the CCIR, Annex to Vol. V, Rep. 1148, pp. 550-564, 1990. [30] CCIR, "Propagation Data and Prediction Methods for the Terrestrial Land-Mobile Service Using the Frequency Range 30 MHz to 3 GHz," Reports of the CCIR, Annex to Vol. V, Rep. 567-4, pp. 310-341, 1990. [31] CCIR, "Short Distance Radio Wave Propagation in Special Environments--Buildings, Tunnels and Mines, etc.," Reports of the CCIR, Annex to Vol. V, Rep. 880-2, pp. 350-351, 1990. [32] T. S. Chu, The effect of sand storms on microwave propagation, Bell Syst. Tech. J., Vol. 58, pp. 549-555, 1979. [33] D. C. Cox, H. W. Arnold, and P. T. Porter, Universal digital portable communications: A system perspective, IEEE J. Sel. Areas Commun., Vol. SAC-5, pp. 764-773, 1987. [34] R. K. Crane, Prediction of attenuation by rain, IEEE Trans. Commun., Vol. COM-28, pp. 1717-1733, 1980. [35] R. K. Crane, A two-component rain model for the prediction of attenuation statistics, Radio Sci., Vol. 17, pp. 1371-1387, 1982. [36] R. K. Crane, Comparative evaluation of several rain attenuation prediction models, Radio Sci., Vol. 20, pp. 843-863, 1985. [37] R. K. Crane, Estimating the risk for Earth-satellite attenuation prediction, Proc. IEEE, Vol. 81, pp. 905-913, 1993. [38] F. Davarian, Irreducible error rate in aeronautical satellite channels, Electron. Lett., Vol. 24, pp. 1332-1333, 1988. [39] P. David and J. Voge, Propagation of Waues. New York: Pergamon Press, 1968. [40] K. Davies, Ionospheric Radio. London: Peter Peregrinus, 1989. [41] H. T. Dougherty and B. A. Hart, Recent progress in duct propagation predictions, IEEE Trans. Antennas Propag., Vol. AP-27, pp. 542-548, 1979.

244

Ernest K. Smith

[42] E. J. Dutton, "Earth-Space Attenuation Prediction Procedures at 4 and 16 GHz," Off. Telecommun. Rep., pp. 77-123, 1977. [43] E. J. Dutton and H. T. Dougherty, "Modeling the Effects of Clouds and Rain upon Satellite-to-Ground System Performance," NTIS No. COM-75-10950, Springfield, VA, 1973. [44] E. J. Dutton, H. K. Kobayashi, and H. T. Dougherty, An improved model for Earth-space microwave attenuation distribution prediction, Radio Sci., Vol. 17, pp. 1360-1370, 1983. [45] J. Feinstein, Tropospheric propagation beyond the horizon, J. Appl. Phys., Vol. 22, 1292-1293, 1951. [46] J. Feinstein, Partial reflections in tropospheric propagation, Trans. IRE Prof. Group Antennas Propag., Vol. PGAP-3, pp. 101-111, 1952. [47] W. L. Flock, Remote Sensing and the Environment--Remote Sensing and Telecommunication. Englewood Cliffs, NJ: Prentice-Hall, 1979. [48] W. L. Flock, "Propagation Effects on Satellite Systems at Frequencies Below 10 GHz-A Handbook for Satellite System Design," 2nd Ed., NASA Reference Publication 1108 (02), 1987. (Avail. from NASA Propagation Information Center, Univ. of Colorado, Boulder.) [49] W. L. Flock, Froehlich/Kent Encyclopedia of Telecommunications, Vol. 7: Electromagnetic Signal Transmission, pp. 147-196. New York: Marcel Dekker, 1994. [50] W. L. Flock, S. D. Slobin, and E. K. Smith, Propagation effects on radio range and noise in Earth-space telecommunications, Radio Sci., Vol. 17, pp. 1411-1424, 1982. [51] H. T. Friis, A. B. Crawford, and D. C. Hogg, A reflection theory for propagation beyond the horizon, Bell Syst. Tech. J., Vol. 36, pp. 627-644, 1957. [52] R. M. Gagliardi, Satellite Communications. Princeton, NJ: Van Nostrand-Reinhold, 1991. [53] G. Gerace and E. K. Smith, A comparison of cloud models, IEEE Antennas Propag. Mag., Vol. 32, No. 5, pp. 32-38, 1990. [54] S. F. Ghobrial, Effects of sandstorms on microwave propagation, Proc. Natl. Telecommun. Conf., Houston, TX, Vol. 2, pp. 43.5.1-43.5.4, 1980. [55] C. J. Gibbons, Improved algorithms for the determination of specific attenuation at sea level by dry air and water vapor, in the frequency range 1-350 GHz, Radio Sci., Vol. 21, pp. 945-954, 1986. [56] J. Goldhirsh, A parametric review and assessment of attenuation and backscatter properties associated with dust storms over desert regions in the frequency range 1-10 GHz, IEEE Trans. Antennas Propag., Vol. AP-30, pp. 1121-1127, 1982. [57] J. Goldhirsh and W. J. Vogel, Roadside tree attenuation measurements at UHF for land-mobile satellite systems, IEEE Trans. Antennas Propag., Vol. AP-35, pp. 589-596, 1987. [58] J. Goldhirsh and W. J. Vogel, "Propagation Effects for Land Mobile Satellite Systems: Overview of Experimental and Modelling Results," NASA Reference Publication 1274, NASA Scientific and Technical Information Program, Washington, DC, 1992. [59] J. M. Goodman, H. F. CommunicationsmScience and Technology. Princeton, NJ: Van Nostrand-Reinhold, 1992. [60] GTE Lenkurt, "Engineering Considerations for Microwave Communications Systems." San Carlos, CA, 1970. [61] M. P. M. Hall, Effects of the Troposphere on Radio Communications. London: Peter Peregrinus, 1979. [62] M. P. M. Hall and L. W. Barclay, Editors, Radio Wave Propagation. London: Peter Peregrinus, 1989.

8. Propagation at Microwave Frequencies

245

[63] R. J. Hill, R. S. Lawrence, and J. T. Priestly, Theoretical and calculational aspects of the radio refractive index of water vapor, Radio Sci., Vol. 17, pp. 1251-1257, 1982. [63a] D. C. Hogg, Fun with the Friis free-space transmission formula, Antennas Prop. Mag., Vol. 35, pp. 33-35, 1993. [64] L. J. Ippolito, Radio Wave Propagation in Satellite Communications. Princeton, NJ: Van Nostrand-Reinhold, 1986. [65] L. J. Ippolito, "Propagation Effects Handbook for Satellite Systems D e s i g n ~ A Summary of Propagation Impairments on 10 to 100 GHz Satellite Links with Techniques for System Design," 4th Ed., NASA Reference Publication 1082 (04), 1989. (Avail. from NASA Propagation Information Center, Univ. of Colorado, Boulder.) [66] W. C. Jakes, Mobile Communications Design Fundamentals. H. W. Sams and Co., 1974. [67] C. T. A. Johnk, Engineering Electromagnetic Fields and Waves. New York: John Wiley & Sons, 1988. [68] E. C. Jordan and K. G. Balmain, Electromagnetic Waves and Radiating Systems, 2nd Ed., Englewood Cliffs, NJ: Prentice-Hall, 1968. [69] J. Joss, J. C. Thams, and A. Waldvogel, The variation of rain drop size distribution at Locarno, Proc. Int. Conf. Cloud Phys., Toronto, pp. 369-373, 1968. [70] Y. Karasawa and T. Matsudo, Characteristics of fading on low-elevation angle Earth-space paths with concurrent rain attenuation and scintillation, IEEE Trans. Antennas Propag., Vol. AP-39, pp. 657-661, 1991. [71] Y. Karasawa and T. Shiokawa, Characteristics of L-band multipath fading due to sea surface reflection, IEEE Trans. Antennas Propag., Vol. AP-35, pp. 956-966, 1984. [72] D. E. Kerr, ed., Propagation of Short Radio Waves, MIT Radiation Laboratory Series, Vol. 13. New York: McGraw-Hill, 1951. [73] V. Kourganoff, Basic Methods in Transfer Problems~Radiative Equilibrium and Neutron Diffusion. New York: Dover, 1963. [73a] J. D. Kraus, Radio Astronomy (2nd Ed.), Cygnus Quasar Books, 1986. [74] J. O. Laws and D. A. Parsons, The relation of rain drop size to intensity, Trans. Am. Geophys. Union, Vol. 24, pp. 43-460, 1943. [75] W. C. Y. Lee, Mobile Cellular Telecommunications Systems. New York: McGraw-Hill, 1988. [75a] W. C. Y. Lee, Mobile Communications Design Fundamentals (2nd Ed.). New York: John Wiley and Sons, 1993. [76] H. J. Liebe, M P M - - A n atmospheric millimeter-wave propagation model, Int. J. Infrared Mm Waves, Vol. 10, pp. 631-650, 1989. [77] S. H. Lin, H. J. Bergmann, and M. V. Pursley, Rain attenuation on Earth-space paths ~Summary of 10-year experiments and studies, Bell Syst. Tech. J., Vol. 59, pp. 183-228, 1980. [7:7a] T. S. M. Maclean and Z. Wu, Radiowave Propagation over Ground. London: Chapman and Hall, 1993. [78] J. S. Marshall and W. M. Palmer, The distribution of raindrops with size, J. Meteorol., Vol. 5, pp. 165-166, 1948. [79] L. F. McNamara, The Ionosphere: Communications, Surveillance and Direction Finding. Huntington, New York: Krieger Publishing Co., 1991. [80] A. R. Miller, R. M. Brown, and E. Vegh, New derivation for the rough surface reflection coefficient and for the distribution of sea-wave elevations, lEE Proc., Part H, Vol. 131, No. 2, pp. 114-116, 1984. [81] K. Miya, ed., Satellite Communications Engineering. Tokyo: Lattice Co., 1975.

246

Ernest K. Smith

[82] W. A. Morgan and G. O. Gordon, Communications Satellite Handbook. New York: Wiley (Interscience), 1989. [83] K. Morita, Prediction of Rayleigh fading occurrence probability of line-of-sight microwave links, Rev. Electr. Commun. Lab., Vol. 18, pp. 11-12, 1970. [84] NBS, "National Bureau of Standards Technical Note 101, Revised I and II," AD 687820 and AD 687821, 1967. (Avail. from NTIS, Springfield, VA.) [85] K. A. Norton, The calculations of ground-wave field intensities over a finitely conducting spherical Earth, Proc. IRE, Vol. 29, p. 623, 1941. [85a] T. Oguchi, Electromagnetic wave propagation and scattering in rain and other hydrometeors, Proc. IEEE, Vol. 71, pp. 1029-1078, 1983. [86] T. Oguchi, Effects of incoherent scattering on attenuation and depolarization of millimeter and optical waves due to hydrometeors, Radio Sci., Vol. 21, p. 717, 1986. [86a] R. L. Olsen and B. Segal, New techniques of predicting multipath fading distribution on V H F / U H F / S H F line-of-sight paths in Canada, Can. J. Elect. Comp. Eng., Vol. 17, pp. 11-23, 1992. [87] R. L. Olsen, T. Tjelta, L. Martin, and J. E. Doble, Towards a more accurate method of predicting the distribution of multipath fading on terrestrial microwave links, Electron Lett., Vol. 22, pp. 902-903, 1986. [88] F. C. Owen and C. D. Pudney, Radio propagation for digital cordless telephones, Electron. Lett., Vol. 25, No. 1, 1989. [89] J. D. Parsons, IEE Electromagnetic Wave Series 30, Chap. 30, pp. 262-278. London: Peter Peregrinus, 1989. [90] T. Pratt and C. W. Bostian, Satellite Communications. New York: John Wiley and Sons, 1986. [91] H. R. Prupacher and R. L. Pitter, A semi-empirical determination of the shape of drops, J. Atmos. Sci., Vol. 28, pp. 86-94, 1971. [91a] K. Rawer, Wave Propagation in the Ionosphere. Kluwer Academic Publishers, Dordrecht, Boston, London, 486 pages ($175.00!). [92] T. S. Rappaport, Statistical channel impulse response models for factory and open plan building radio communications system design, IEEE Trans. Commun., Vol. 39, pp. 794-807, 1991. [93] J. N. Reynolds, "Understanding Troposcatter Propagation," M.S. Thesis in Telecommunications, Univ. of Colorado, Boulder, 1990. [94] P. L. Rice and N. R. Holmberg, Cumulative time statistics of surface point rainfall rates, IEEE Trans. Commun., Vol. COM-21, pp. 1131-1136, 1973. [95] G. Roda, Troposcatter Radio Links. Norwood, MA: Artech House, 1988. [96] D. Roddy, Satellite Communications. Englewood Cliffs, NJ: Prentice-Hall, 1989. [96a] C. M. Rush, Summary of conclusions of the 1992 World Administrative Radio Conference, IEEE Antennas Prop. Mag., Vol. 34, pp. 7-14, 1992. [97] G. B. Rybicky and A. P. Lightman, Radiative Processes in Astrophysics. New York: Wiley (Interscience), 1979. [98] J. Shapira, Channel characteristics for land cellular radio, and their system implications, IEEE Antennas Propag. Mag., Vol. 34, No. 4, pp. 7-16, 1992. [99] E. K. Smith, Centimeter and millimeter wave attenuation and brightness temperature due to atmospheric oxygen and water vapor, Radio Sci., Vol. 17, pp. 1455-1464, 1982. [100] E. K. Smith and S. Weintraub, The constants in the equation for atmospheric refractive index at radio frequencies, Proc. IRE, Vol. 41, pp. 1035-1037, 1953. [101] A. D. Spaulding, G. H. Hagn, and J. M. Goodwin, eds. Worldwide minimum environmental radio noise levels (0.1 Hz to 100 GHz), Proc. Symp. Eft. Ionosphere Space Terres. Syst., O N R / N R L , pp. 177-182, Jan. 1978.

8. Propagation at Microwave Frequencies

247

[102] W. F. Stutzman, Prolog to the special section on propagation effects on satellite communication links, Proc. IEEE, Vol. 81, pp. 850-855, 1993. [103] W. L. Stutzman and Dishman, A simple model for the estimation of rain-induced attenuation along Earth-space paths at millimeter wavelengths, Radio Sci., Vol. 17, pp. 1465-1476, 1982. [104] W. L. Stutzman and Dishman, Correction to "A simple model . . . . Radio Sci., Vol. 19, p. 946, 1984. [105] W. F. Stutzman et al., Results from the Virginia Tech propagation experiment using the OLYMPUS satellite 12, 20, and 30 GHz beacons, IEEE Trans. Antennas Propag., Vol. AP-42, in press, 1994. [106] R. W. Sutton, E. H. Schroeder, A. D. Thompson, and S. G. Wilson, Satellite aircraft multipath and ranging experiment results at L-band, IEEE Trans. Commun., Vol. COM-21, pp. 639-647, 1973. [107] V. I. Tatarski, Wave Propagation in a Turbulent Medium. New York: Dover, 1967. (Transl. from Russ. by R. A. Silverman.) [108] G. D. Thayer, An improved equation for the radio refractive index of air, Radio Sci., Vol. 8, pp. 803-809, 1974. [109] W. J. Vogel and J. Goldhirsch, Fade measurements at L-band and UHF in mountainous terrain for land-mobile satellite systems, IEEE Trans. Antennas Propag., Vol. AP-36, pp. 104-113, 1988. [110] W. J. Vogel and U. S. Hong, Measurement and modelling of land-mobile satellite propagation at UHF and L-band, IEEE Trans. Antennas Propag., Vol. AP-36, pp. 707-719, 1988. [111] L. E. Vogler, An attenuation function for multiple knife edge diffraction, Radio Sci., Vol. 17, pp. 1541-1546, 1982. [llla] Walker [112] A. R. Webster, Angle of arrival and delay times on terrestrial line-of-sight microwave links, IEEE Trans. Antennas Propag., Vol. AP-31, pp. 12-17, 1983. [113] H. E. Whitney, J. Aarons, and C. Malik, A proposed index for measuring ionospheric scintillations, Planet Space Sci., Vol. 17, p. 1069, 1969. [114] J. H. Yuen, ed., "Deep Space Telecommunications Engineering." JPL, NASA, 1982. [115] C. Zaks and S. Anderson, Aeronautical satellite data link measurements over the North Atlantic: Test results, Proc. 7th Int. Conf. Digital Satellite Commun., Munich, pp. 557-563, May 1986.

This Page Intentionally Left Blank

CHAPTER

9 Consumer Applications of Microwaves Microwave Ovens and Accessories Koji Iwabuchi, Ichiro Fukai, and Tatsuya Kashiwa

I. Microwave Oven Design Fundamentals [I ]

It

is most important to design a cavity of an oven to optimize a load impedance to a magnetron. The performance and longevity of the magnetron greatly depend on its operating points on the Rieke diagram. The Rieke diagram reveals both output power and frequency characteristics on the Smith chart. Test probes have been developed to measure the impedance of the cavity. The probes have the same antenna structure as that of the magnetron. Figure 1 shows a typical magnetron structure. Figure 2 shows a test probe structure. Figure 3 shows the block diagram of the impedance measurement system. Figure 4 shows the Rieke diagram with a recommended region as well as several restricted regions. Each region is explained as follows.

Moding Region The moding region is the place where moding easily may occur if the load impedance loci are in the region and if the length of a waveguide for connecting the magnetron to the cavity is short.

Handbook of Microwave Technology, Volume 2

249

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

250

Iwabuchi, Fukai, and Kashiwa

Antenna

Magnet (ferrite)

de core

(ferrite) Fi Iter case containin~ choke coils

Feed through capacitor

Figure I. Magnetron structure.

Antenna

r--n

Mounting plate

Stub

Adaptable to N-type connector Figure 2. Test probe structure.

251

9. Consumer Applications of Microwaves

Matching post

Oven

(Cavity)

//

\

F

/Test

probe

L°ad"---...~.l ~

TurntableS'

_ - ;I.... ~Lb

L

Network analyzer --

I

Sweep generator Figure 3. Impedancemeasurementsystem.

Arcing Region Microwave arc may occur around the antenna of the magnetron if the load impedance loci are in the region. Sometimes, the arc may occur between the antenna and an inside wall of the waveguide.

Overheating Region The antenna and choke coil parts may be overheated if the impedance loci are in the region. Even if the loci are only near the region, the above parts may be considerably overheated.

Low-Efficiency Region This region is a little different from the other restricted regions. Magnetron operation for a very short time in the region may be acceptable. However, if the magnetron is operated for a considerably long time in the region, since its efficiency is very low, the output power obtained will be very low and the magnetron will become very hot. Therefore, a better cooling system is required to keep the temperature of the magnetron lower.

252

Iwabuchi, Fukai, and Kashiwa Reference plane (Antenna axis) O ~ o a VSWR50

d

f

f,

18.0 c41~.~fJ 60"

270"~-t-

90" (5) Recomended region

240"

t20"

210'

150"

t80" Operating condition : Power supply :Single phase, full-wave rectifier without f i l t e r Average anode current • 300mA Filament voltage : 3.3V Navegulde : EIAJ standard launcher Nagnetron : 214214

~Output power . . . . . . . . . . F.requency (fo=2.45fiNHz) VSNR" Voltage standing wave ratio

Figure 4. Rieke diagram.

Recommended Region It is recommended for oven design that the impedance loci under the load conditions of typical usage are in t h e region. The highest efficiency and stable oscillation will be obtained.

2. Microwave Field Visualization Background The advent of computers enables us to estimate the microwave field easily by visualizing computed values. At the current stage, visualization is no

253

9. Consumer Applications of Microwaves

longer indispensable for optimum oven design. There are four versatile computational approaches appropriate to microwave oven analysis [2], namely, the finite-difference time-domain (FD-TD) method, transmission line matrix (TLM) method, finite element method (FEM) [3], and the method of moments (MoM). The FD-TD method is the simplest and does not use matrix computation, since Maxwell's equations are discretized directly. In this section, visualization of the microwave fields in an oven using the FD-TD method [4, 5] is carried out. Formulation

Basic Formulation Maxwell's equations are shown as follows,

OH /x~=

-V×E

(1)

OE e~ +~rE=V ×H, Ot

(2)

Ot

where E, H, e, /x, and o- are the electric field, magnetic field, dielectric constant, permeability, and conductivity, respectively. In the FD-TD method, the above equations are discretized directly as the central difference. For example, H x and Ey are formulated as follows, Hn+l/2(i,j,k)

= Hn-1/2(i,j,k) 1 + ( E yn( i , j , k + 7)

-(En(i,j

-

E;(i,j,k

-

½))At/Az/tx

1 1 + 7, k) - E ~ ( i , j - -~,k))At/Ay/ix

(3)

Eyn + l ( i , j , k ) = C a E y ( i , j , k ) n

+ C b ( H xn + l / 2 ( i , j , k

c

(H2+

72(i +

1 + -~) - H xn + l / 2 ( i , j , k 1

j,

_ H2+

1/2(i

½))At/Az/e

1 j, k ) ) A t / A x / E , __ g, (4)

where

Ca

--

(l

-

R ) / ( 1 + R); C b = 1/(1 + R); R = ~rAt/2/e; At is the

254

Iwabuchi, Fukai, and Kashiwa

time increment; Ax, A y, and Az are the spatial increments; the superscript n signifies that the fields are to be computed at n At; and i, j, and k represent the points (i Ax, j A y, and k Az) in the FD-TD mesh.

Boundary Conditions On conductive boundaries, such as cavity surfaces, the electric field component tangential to the conductive plane or the magnetic field component normal to it is assumed to be zero. Input conditions and absorbing boundary conditions are described in References [4, 6, 7].

Treatment of Foods Since the electromagnetic wavesare shortened in dielectric materials such as foods, in this region, the meshes should be generated more finely than those in free space. Consequently, in the computation of cavity fields, local refinement or nonuniform mesh techniques are important to the reduction of the computation memory. These techniques are described in detail in References [8-10].

Example [I I ] Figure 5 shows the computed cavity model. The feed is carried out using the horizontally connected waveguide. The input frequency is 2.45 GHz. The spatial increment for each direction, Ax = A y = Az (Ad), is 5 mm. The time increment At is chosen as Ad

at _< v c'

Magnetron

Cavity\ \

~

(5)

[Unit:mm]

300

/

Waveg

l"-,Jsot

z

I II

~---

if'--,._

C.0mputed position (e.g., y=3Omm)

Figure 5. Structure of an analyzed microwave oven.

9. Consumer Applications of Microwaves

255

x (mm) 300 Waveguide

Ratio (%)of each E2 to max. E2

(".... "'i

250

', \../I l

2oo

',-

"-\-.,

\,

Microwave L - v A 5 0

~

/"\

J:

............

,i i

18

~

I

J:

31

';

44

100

," ,' , I\

.

~

56

~

", ]; . . . . . . . . . . . . i

5o

:

'

~

= 50

0 0

t.

= 100

/

6g 82 g5

I

150

200

250

300

z(mm)

Figure 6. Contour distribution for visualizing the square of electric fields, E 2 (y = 75 mm).

where c is the speed of light, considering the stability of the method. Figures 6 and 7 show the calculated distributions of the square of electric fields E 2 (i.e., E 2 = E x 2 + Ey 2 + E z 2) in the horizontal planes. Similarly, Figures 8 and 9 show those in the vertical planes. From these visualized figures of the fields, the performance of the oven can be easily understood by taking into account which part is strong or weak.

x (mm)

Waveguide

-.?'-.

250

, ~ /-\ ', ' I \ !', ', , ~', ',~(-~ ~ Ratio{%)of each

l~?.3..~.,/y

, ,,. ) ,

I---.-~/..,

~,,',',~

~:,I.'~',

Microwave [Z~>I50

~',:'/, . . . . .

:.r~,

~',,

,, j

_'~_-~_ -.-/

-.."----~

,', ,,, L_J ,

/,, ,,~\ . . . . . ~

,.

~

......

-

/

~

) , i :',

50 2._~_--_:...; ~ - "

"

I

0

50

/

" "

"

I

100

150

............

,

/,' .' /,, .' .... / ,,' ,,,'/~q ~j

,'"

5

18

,-',,

/ ,"

~..~-'i-l-',, x,.~ \ ,,'-),

............

\~',.: ~, "

"~I',-,"-,

/ ~ ,' ~ -

E=tomax. E'

.' '," "-'-'

-

44

56 6g

i ', (~ ' ............

82

" "-'

95

'

I

200

250

300 z(mm)

Figure 7. Contour distribution for visualizing the square of electric fields, E 2 (y = 30 mm).

Iwabuchi, Fukai, and Kashiwa

256

y (mm) Waveguide

150

:---,,,

~. ,I00 Microwave~_~ ( "1 50

i i,,

~ ', Ji

:

/I/Ii

:

,'

,

,,

,i I

t

: :i

0

0 Fig.B

,,

,"

50

100

.,

" .... .'

.."

............

" --. ...... is •

," ....... "-.

-

~

: I ,"i". 150

Ratio {%)of each E= to max. E=

200

18 31 44

.. I': 250

300 z (mm)

Contour distribution for visualizing square of electric

fields E2 (x:150mm)

Figure 8. Contour distribution for visualizing the square of electric fields, E 2 (X

y (ram)

--

150 mm).

Ratio (%)of each

150

Waveguide

, 100

It', :,(!!

Microwave [E~

(

............ 44

~ 50 "" \ ""' ,

, I~', '.

0 0

50

100

150

200

250

- . . . . . . . . . . . 82 .g5 300 z(mm)

Figure 9. Contour distribution for visualizing the square of electric fields, E 2 (X

=

75 mm).

3. Microwave Leakage Minimization Design This section is about microwave leakage suppression in the ISM band of 2.4-2.5 GHz. The reason for suppression is that it is much better economically to reduce spurious microwaves from magnetrons themselves. The suppression of harmonic radiation from microwave ovens, for example, is described in References [12-16].

Door

Structures

Particularly, it is important and difficult to suppress microwave leakage from the periphery of a door of a microwave oven. All the door structures here have been adopted to microwave ovens. Figures 10-14 indicate only peripheral metal portions for attenuating microwave energy from the door periphery. In these figures, h is the free-space wavelength (i.e., 122 mm) at the center frequency in the above ISM band.

9. ConsumerApplicationsof Microwaves

257

Flange around oven access opening

Choke

cavity~ :ontact surface Open Close FigureI0. Chokestructurewithoutslits.

Choke Structure without Slits or Cutouts

Figure 10 indicates a general choke structure without slits or cutouts for promoting its effect on microwave attenuation characteristics. This structure can reduce microwave leakage to a very low level because of the following reasons: (1) With a narrow path (e.g., its gap < 1 mm) behind a choke entrance, the reflection between a high impedance at the choke entrance and a low impedance at the narrow path is very large,

Trapezoidal Flangearoundovenaccessopening

~ C o ~ : d c ~ r n n m ~ ~ ~~

met/iecealp

~/~/~

i~~Y/~~ ~><~Choke ~ r ~ ~ ~ _ entrance ; ~ ; ~ m e c ~ t a : ~ ~ ~ ~~ ~ ~ . / Contactsurface Open Close FigureI I. Chokestructureforfundamentalandsecondharmonicwaveswithtrapezoidalmetalpieces.

258

Iwabuchi, Fukai, and Kashiwa

Flange around oven access opening

avl y r e s o n a t ~ ~ . ~ / ~ . C o n t a c

Open

U-shaped conductive piece

t surface

Close

Figure 12. Choke structure with a wall surface comprising U-shaped conductive pieces.

(2) With a larger choke cavity than those of the following four choke structures with slits or cutouts, the choke structure in Figure 10 has a broad attenuation frequency bandwidth.

Choke Structure for Fundamental and Second Harmonic Waves [15] The choke structure in Figure 11 is equipped with a microwave attenuating cavity consisting of a fundamental wave choke channel and a second harmonic choke channel in opposition to each other, back to back.

P S]iL structure

Flange around oven access opening

Choke groove__[..~ Open

Close

Figure 13. Choke structure with grooves having different cha~cteristic impedances in the depth dire~ion.

259

9. Consumer Applications of Microwaves

Flange around oven access o p ~ ~

Capacitive slot

Oven wall ~

Finger-like

conductive member

Choke path ()~/2) Open

Close

Figure 14. Choke structure with capacitive slots along the choke path,

A wall surface defining the second harmonic choke channel has a periodic structure provided with a plurality of trapezoidal metal pieces, a tip of each of which is bent inward. The periodic structure efficiently guides leaking microwave energy into the microwave attenuating cavity and promotes a microwave energy leakage preventive effect. The choke structure is suitable for reduction in size and thickness and permits a microwave oven with an improved space factor to be provided.

Compact Choke Structure by the Resonance Principle [17] In Figure 12, the cavity resonator with a wall surface comprising U-shaped conductive pieces can be assumed to be a parallel resonance element constituting an equivalent inductance, L, and an equivalent capacitance, C. The L may be made smaller as the C is made larger, with the resonance frequency (i.e., 2.45 GHz) kept constant. The C becomes larger as the gap G of the choke entrance is made smaller. The L is relative to the area A × B of the rectangular cross section of the cavity resonator. Consequently, the cavity area A × B may be made smaller as the gap G is made smaller. As a result, both dimension A and dimension B can be made smaller than A/4.

Compact Choke Structure by the Impedance Conversion Principle [18] The choke structure in Figure 13 has a groove wall corresponding to a grounded conductor, a number of strip conductors arranged with line width A and pitch P, and a groove bottom, so as to minimize leakage propagation in the longitudinal direction of the groove. Further, the choke

260

Iwabuchi, Fukai, and Kashiwa

groove has different characteristic impedances in the depth direction so that the impedance Z s from the choke entrance becomes infinite in a region shorter than A/4. As a result, the depth l T and widths B 1 and B 2 of the groove can also be made less than A/4.

Choke Structure with Capacitive Slots [19] As shown in Figure 14, the capacitive slot along a A / 2 choke path prevents higher-order modes from passing across the path and permits leakage microwave energy having a free-space wavelength to propagate only in parallel with the path. That is, since the propagation direction and wavelength (e.g., 122 mm) in the microwave energy are kept constant, the choke structure with a plurality of capacitive slots can easily reduce the leakage microwave energy to a lower level. Radial Line Filters [20, 21] The radial line filter in Figure 15 is provided to prevent microwave energy from entering the coaxial line of a turntable metal shaft or detachable sheathed heater mounting. The radial line is a line along which an electric field and a magnetic field advance outward or inward between two parallel conductor disks. The advantage of the radial line filter is that the axialdirection size can be reduced. Figure 15 indicates attenuation frequency characteristics of the filters having different sizes. The characteristics are calculated with the method in Reference [20]. Perforated Plates and Wire Gauzes Some illustrations useful for predicting microwave leakage through reflective surfaces having circular apertures, square apertures, or wire gauzes in metallic fiat plates are presented in this section. Those reflective surfaces have been adopted to reduce microwave leakage from a viewing screen in a door, paths of light or forced-circulation air in oven walls, intakes or outlets for cooling air in a cabinet, and the like. Attenuation levels necessary for the above viewing screen, paths, and both the intakes and the outlets are approximately 50, 30-35, and 20 dB, respectively.

Circular Apertures in a Metallic Flat Plate [22] The attenuation equation here is applicable to arrangements having either a 60 ° (staggered) or 90 ° (square) aperture pattern, as shown in Figures 16 and 17. Accounting for reflection on the surface of the arrangements and the attenuation constant inside the small aperture as a circular waveguide beyond the cutoff of a TEll mode, the equation for

9. Consumer Applications of Microwaves

~61

Variable height HH(mm) at gap G=2 (ram)

HH=20 H:5,

HH=25H=7

I

]

n ~72.2 ~10

Variable gap G(mm) at height HH=20 (mm) 10 G=2H=5.2

Ill

G=1.5 N=4.8 if G=I H=4.4

I Ill

2.3 2.4 2.5 2.6 2.7 Frequency (GHz)

-.

HH:i5 H~.7

\

"~

10

._

G=2iH~5.4

i

30

,,.~-

~5o HH=20 H=514V HH=25H=7.2 .2 2.3 2.4 2.5 2.6 2.7 Frequency (GHz) .~I0

•2 2.3 2.4 2.5 2.6 2.7 Frequency (GHz)

~ 5o

6=i.5 H=5.i 'if'G=1 H=4.75

i ili

I

~ 70 2. 2 2.3 2.4 2.5 2.6 2.7 Frequency (GHz)

10

HH=15 H=3.7

G:2H:5.4

~3o / - ~'~ ,,YY(X t H=5.4 1"~..,' 17\ ~5o HH=20 VHt{=25 H=7.2 i

i|I

I

2 2.3 2.4 2.5 2.6 2.7 Frequency (GHz)

.2 2.3 2.4 2.5 2.6 2.7 Frequency {GHz)

0.8

==l

Figure 15. Attenuation characteristics of radial line filters.

In c ide n t plane

H

Incident TEM wave E

E :Electric field H :Magnetic field 8" Incident angle T : P l a t e thickness

Perforated metal plate T Figure 16. Relation between a perforated metal plate and an electromagnetic field.

Iwabuchi, Fukai, and Kashiwa

262

© ~=6

I

I -

IO.= ,/-fp 2

Figure 17. Circular aperture arrangements. (a) Staggered aperture arrangement. (b) Square aperture arrangement.

attenuation (i.e., transmission loss) is

t

S = 201og10 2rrD 3 cos 0

t

+ 8.686T

¢I

1.706D

-

t -t -~

(dB), (6)

where P and Q are pitches between apertures in the directions of x and y, respectively, D is the aperture diameter, h is the free-space wavelength, 0 is the incident angle, and T is the plate thickness. In Equation (6), the attenuation S is minimum at the incident angle 0 = 0 °. To comply with the regulations concerning microwave leakage from microwave ovens, the attenuation should be kept large enough to reduce the microwave leakage below the regulations at 0 = 0 °. In the case of 0 = 0 °, D < P and Q << A, Equation (6) is approximately expressed with Equation (7). 3PQA) 32.0T S = 20 lOgl0 2,n-D3 -F ~

(dB)

(7)

By the way, the opening ratio A for the aperture arrangements in Figure 17 is expressed as follows: 7rD 2

A =

4PQ

× 100

(%)

x/~-rrD 2 6p 2

xl00

(%)

(to the 60 ° aperture pattern).

(8)

263

9. Consumer Applications of Microwaves

Attenuation 50dB T: Plate thickness (mm)

1.4 1.3

/

1.2

//,," ,'/"

50 55 ~Openin.g.

o* io°

1.1

/"

# J

#

"

""

/

~ratio(%}

,0j~B

~,

oooe'

1.0 ...-... i==

T=.05 0.I 0.15 0.2 0.25 0.3

ooSoS" / ,s* 3r

Cc /

0.9

~0.8 o_

/

.,=0.7 t,j .,-i

o-0.6

L-PJ

0.5 0.4 0.3 0.2 0.3

0.4

0.5

0.6 0.7 Diameter D(mm)

0.8

O.g

I

Figure 18. Recommended sizes of circular apertures for an attenuation of 50 dB with a high opening ratio.

Attenuation 50dB 3.6 T: Plate thickness T=O.4

//

0.6

O.B

11.Omm

I I ~I/' / ,,./I / ~/~. i I I I l,f///'~ I I//~Y~;/.~. ///~ ~ ~ .I / ~Cf~~/~

3.4 3.2 3.0 ~ ' 2 B• ~.m ,', 2.6

45 50

Opening

'°1

ratio (%)

//.-~../-/./~.~-"~

"=2.4

u .,1,-1

"-' 2.2 CI.

1.8

/S/~F~ZJ-I~//

~'~~~/

1.6 1.4 ~"-~. ~f~-)/7 1.2 ~ ' I " 1.0

1.2

1.4

1.6 i.B 2.0 Diameter O(ram)

2.2

2.4

Figure 19. Recommended sizes of circular apertures for an attenuation of 50 dB.

264

Iwabuchi, Fukai, and Kashiwa

14 13 12 11 ._. 10 9

T: Plate thickness ,

,

,

cT=°"4ram~ / ~ l Y / Attenuation / ,=,, 00:00

[ /~//"/

===

///

°

/ . ~ ~

50 45 ~Opening .

B (_1

7 6

.,-4

o_

~~°__

5

. ~ . ~~. ~ ~ "~ < j ~ , ~- _vI 0

4

u,,,,,, } Attenuation 6

3

I

2

3

4

5

...

6

Diameter D(ram)

7

Figure 20. Recommended sizes of circular apertures for an attenuation of 30- 35 dB.

Additionally, in the case of the 60 ° aperture pattern, the more practical Equations (9) and (10) are derived from Equations (7) and (8), respectively.

,n-D 10 (S-32"OT/D)/20

P-

2

P=

10D

3 v/_3_h

6A

"

T: Plate thickness

22 21 20 Ig IB _.17

I

I

1

I

,-T=O. 4mm ~ Attenuation

25dB

<

0.6 0 8

~

--

(10)

//// ////

Opening. ratio I l l . . . . . . . . . . . . . 45 50 -55 60 65

I/// ///>" ...////_ ..-'~

|16

(9)

,-14

o-12 II I0 g B

.J~~~.~T=O.

~mm - ~ A t t e n u a t i 0 n

-

--

7 6

6

7

8

g I0 11 Diameter D (ram)

12

13

Figure 21. Recommended sizes of circular apertures for an attenuation of 20- 25 dB.

265

9. Consumer Applications of Microwaves

33 32 31 30 29 2B 27 26 25 24 " 23 '-' 22

T:P1ate thickness

Attenuat)on 20dB ( T=0.4 0._6 0.8

\

15~B T=0.4 0.6 0.8 I.~0

~v~7/... ~" ', / 7 , / / //6"

\ 9'> - 7 / - \ /'7,~ ~//'I //,5, ~ / 5o z 7"ll. ~..~ s5 /.,~.~//i 6o opening.

Z/l~ //>2" .////

I

///J

/bJ~U /

70

t..-

2o

x w//

//. ~

~

~

~-~ ~

- o. B

IO

------ -0.6

16 / / ' ~ ~ ~ - ~ - ' ~

i2

13

14

.10dB

-o.4

15

16 17 IB Diameter D(mm)

Ig

20

21

p]

22

-

Figure 22. Recommended sizes of circular apertures for an attenuation of 10-20 dB with a high opening ratio.

Assuming A to be 122 mm, Equations (9) and (10) are illustrated as Figures 18-22.

Square Apertures in a Metallic Flat Plate Arrangements of square apertures corresponding to those of the circular apertures in Figure 17 are illustrated in Figure 23. Assuming that the opening area of a square aperture is equal to that of a circular aperture, an equation relative to both apertures is obtained as follows, 2W D =

a

•

¢~,

(11)

b

o: '/~-P2 w

~:go" IZ] !--1 Fl~yO [-I

w

Y

L_x

L_x

Figure 23. Square aperture arrangements. (a) Staggered aperture arrangement. (b) Square aperture arrangement.

266

Iwabuchi, Fukai, and Kashiwa

Attenuation 50dB ^

T:P1ate thickness (ram)

1.5

~-0.05 0.1 0.15 0.2 0.25 0.5

1.4 1.3

/ ///,/

1.2 1.1 1.0 ...-.

~o.9 CL

i

=O.B

~J¢~

/ //,~~~ / / / ~ ~ ~ / ~ ~ ~ ~

~o ~

~ . ~ ~,o ~~

/.

~.0.7 0.6 0.5 0.4 0.3 0.2

0.2

0.3

0.4

0.5 0.6 0.7 Aperture width W(ram)

O.B

O.g

I

Figure 24. Recommended sizes of square apertures for an attenuation of 50 dB with a high opening ratio.

T: Plate thickness 22

,-T=O. 4mm~ Attenuation < 0.8 20dB ,.- 1.0

20 1B

/~,,~ 0R=45% 50 [Opening 55 60 / r a t i o

~

.~16

B5

"r - 14 •13. ,-, 12 10 B 6

6

7

8 g I0 II Aperture width W(mm)

12

13

Figure 25. Recommended sizes of square apertures for an attenuation of 20 dB.

9. Consumer Applications of Microwaves

267

where W is the square aperture width and D is the circular aperture diameter. The attenuation equation [Equation (12)] for the square apertures is obtained by substituting the right side of Equation (11) for D in the first term of Equation (6) and also by changing the last term of Equation (6) to the attenuation constant inside the small aperture as a rectangular waveguide beyond the cutoff of a TE m mode.

S = 20 logl0

16W3

+ 8.686T

2rr)

-

~

~-

,

(12)

where P and Q are pitches between square apertures in Figure 23. In the case of W < P and Q << A, Equation (13) may be substituted for Equation (12).

S = 20 loglo

27.3T

( 3V@-~PQA 16W3

+ T

(dB).

(13)

The opening ratio A for the square apertures in Figure 23 is expressed

Attenuation20dB (

33 32 31 30 29 28 27 26 _.25 ~24 Q- 23

"

~

•

T: Plate thickness (ram) T=0.4 0.6 03 //h ,~/// //,z/

/I///

2o X l l

/.i'~.

19

i / ~ "/ ,~////./~

/~ ~"

//////"

/

~

f ~

13

14

60

~//'~

"~

65

70

Opening.

ratio (%}

~..~ 75

~...':..--"~ ~

- / ~ ~ ~ / ~ ~ ~ T=I.0 16 ~ ~ ~J~~~~O.8 15 ~ ~ ' - , ~ ~ ~ ~ 0 . 6 •I~B 14 ~ / ~---~q.4 ~ 1312

15dB A

/ / ~/ ~" / ~ / - - 50 zY// ..~./~..--

~

///2"

zY// /,6 ~

g

=0.4 0.6 0.81.0

15

16 17 18 19 Aperture width W(mm)

.

20

21

22

Figure 26. Recommended sizes of square apertures for an attenuation of 10-20 dB with a high opening ratio.

Iwabuchi, Fukai, and Kashiwa

268

with Equation (14). 2

W

A=

-F

× 100

(%).

(14)

In the case of the P = Q aperture pattern, the more practical Equations (15) and (16) are derived from Equations (13) and (14), respectively. W3 P = 4

(15)

10(S-27"3T/W)/20

3V'-~h

10W v/A .

P=

(16)

Assuming h to be 152 mm, Equations (15) and (16) are illustrated as Figures 24-26.

/

/

/ II

/

/

,,,s

"" •

/ / //....; /

n r-r.) .,-.4 r'~

2

,," /

/

'"

t

-~ I

I

/

00""

I

¢

"f. ,", ";'"

,#

.," "

.. ,,"

-',

/

" "

~,.-" , "

~'

~,40 - - 45 50

"/"

z",.-

,

/

~3

~25dB30

/

/ /

4

Attenuation

/

,"

Opening

ratio

..

"'"

............

,,>.. / . ~ .~"

~,,.

40% 50

70

~-'/

BO

-

,.'2 / ' , s i ,~,j I ,,,., ;..~//5/ I.,, I.,7 , , ' . . : ; - ~ " /!i" "1f !,~J," " 11

.,,., , ~ 1

~Y 0

0

0.2

0.4

0.6

O.B

I

1-

-1- -I

Wire diameter D(mm)

Figure 27. Recommended sizes of wire gauzes for an attenuation of 25- 50 dB.

269

9. C o n s u m e r Applications of Microwaves

Wire Gauzes [23]

The attenuation S and opening ratio A equations for wire gauzes in Figure 27 are, respectively,

(dB)

S = 20 log10

(17)

0.83 exp - ~ 2P In exp - ~

-

1

TABLE I Operation Procedure for Microwave Cooking 1. Open the door a n d p u t the food in the oven. • The food must be placed on the turntable or on the rack placed on the turntable. If the food sticks out of the turntable, the turntable cannot rotate smoothly. • When closing the door, push it against the oven till it clicks. If the door is not closed securely, the microwave oven may not operate.

4. Set the cooking time by turning the T I M E / W E I G H T dial. • For accurate timing let the pointer pass the required time, and then bring it back to that time. • The cooking time can be changed during cooking. The cooking time scale is graduated in the unit of 15 seconds up to 10 minutes and in the unit of 5 minutes for the period from 10 minutes to 60 minutes.

I

TIME

2. Press the M I C R O button. • The word "MICRO" appears in the cooking function indicator window.

~

MICRO

5. Press the START button. • The oven lamp is turned on, and cooking is started.

START

3. Select the cooking power by turning the P O W E R S E L E C T dial. • Set the pointer in the power indicator window to the desired power level. POWER SELECT

0 6. When the sound "ding" is heard, take out the food. • The cooking time pointer is set to 0, and the power is turned off. • If the user sets the pointer to a selected time again without opening the door, the cooking is restarted. • To stop cooking before the sound "ding" is heard, bring the pointer to 0.

270

I w a b u c h i , Fukai, and K a s h i w a TABLE 2 C l e a n i n g and C a r e

The points of cleaningare "Immediately" and "often". Clean the microwave oven after turning off the power and pulling out the plug. • Clean the microwave oven after it has cooled. Oven Each time food has been cooked, wipe off the dirt or food splashes as soon as •

(Ceiling, walls, bottom, and inside of door)

Cover

~ M ~ . ~ ~l '+

possible. Greasy spots should be wiped off with a cloth soaked in mild detergent. • If the dirt is left in the oven for a long time, it cannot be wiped off easily, it will hold the smell of the food, and it may cause corrosion or rusting. Also, arcing may occur and the side cover may be scorched because the

microwaveis concentrated on the food splashes. • If the side cover becomes too dirty to be cleaned, replace it. /~ • Check the microwave oven for any visible damage, such as a misaligned etergent door, damaged door seals around the door or dents in side the oven cavity or on the door. Ensure that the door and door sealing areas are clean before use, clean with a mild detergent, water and a soft cloth. Do not use scouring pads, powder or other abrasive materials.

Rotary table

Always keep the rotary table clean. When it is soiled with food splashes or grease, remove the food splashes or grease by a sponge or cloth soaked with mild detergent and wash it in water. • If food splashes are left on the rotary table, arcing may occur because the microwave is concentrated on the food splashes. • Keep the rotary table at its position in the oven except when it is to be cleaned.

Halogen glass cover Halogenglasscover

Always keep the halogen glass cover clean. When it is soiled with food splashes or grease, wipe them off by a cloth or sponge soaked with mild detergent. • If food splashes are left on the halogen glass cover, arcing may occur because the microwave is concentrated on the food splashes. NOTE: Clean the halogen glass cover after it is cooled sufficiently.

Turntable, low-rack, and high-rack

When the turntable, low-rack, or high-rack is soiled with grease or food splashes, remove the soil by a sponge soaked in mild detergent, wash it in water, and dry it. • If the grease or food splashes are left on the turntable or rack, the turntable or rack may be damaged or corroded because it is heated partially.

Cabinet

Wipe the cabinet with a soft cloth. • When the cabinet is soiled heavily, wipe it with a cloth soaked in mild detergent and then wipe off the mild detergent thoroughly by a wet towel wrung hard. • Do not splash water on the air outlets.

Oven

lamp replacement

To replace the oven lamp, pull out the power supply cord and remove the screw from the oven lamp cover on the top surface of the cabinet. Remove the oven lamp cover and replace the old 20-watt bulb with a new one.

CAUTIONS

Do not rub the oven and accessories with a wire brush or sharp-edged tool.

Do not apply oven cleaner, benzene, or thinner to the sudace of the panel or door.

The surface will be scratched,

The letters on the panel may fade, and the surface may lose gloss or it may be corroded.

..,J-

271

9. Consumer Applications of Microwaves

and P

a

D P

/ 2 x 100 /

(%)

(18)

where P is the pitch between wires and D is the wire diameter. It is practically convenient to rewrite Equations (17) and (18) as

0.83 /

-p D =

lnll exp

AlO-S/2°2p )

(19)

10D P =

(20) a0-TA

"

Assuming A to be 122 mm, Equations (19) and (20) are illustrated as Figure 27.

4. Operation and Maintenance [24] This section is excerpted from an instruction manual for a microwave oven equipped with a turntable for even heating and two halogen heaters for grill cooking.

Operation Procedure Table 1 shows an example of the operation procedure for microwave cooking.

Maintenance Table 2 shows a way of cleaning and care for the microwave oven.

5. Microwave Oven Accessories and Containers This section also is excerpted from the same instruction manual described in Section 4.

272

Iwabuchi, Fukai, and Kashiwa TABLE 3 Turntable for Even Heating

How to set rotary table and turntable Locate the rotary table onto the mechanism in the middle of the bottom of the oven, and place the turntable on top. Make sure it is located properly to prevent any damage when turntable operates.

J/

4

~

table

TABLE 4 Racks for Grill Cooking

.

LOW-RACK 1 ~

MICROWAVE GRILL I MICROWAVEAND COOKING COOKINGj GRILLCOOKING

EXPLANATION

ACCESSORY .

.

.

Use the low-rackfor browning poultry or meat. It must be used with the turntable and may be combined with the high-rack and used for griiling.

YES

YES

YES

.,

HIGH-RACK

Use the high-rack for browning or grilling food. It must be set on the turntable.

YES

YES

YES

TURNTABLE

The turntable is an enameled plate specially made for the microwave oven. It must be set on the rotary table and used at all times.

YES

YES

YES

,,

How to combineaccessories MICROWAVE/GRILL COOKING

GRILL COOKING

NOTE: Only the combinations illustrated above are allowed; do not run the oven with the accessories combined in other ways.

Accessories and Their Use

Table 3 illustrates a setting method for the turntable. Table 4 shows a method of treating racks for grill cooking. Containers and Their Use

Table 5 shows containers and their use for the microwave oven.

l/l I-..{:

~nlLU

nn

C t~ cO

U

o~.

~o

•~

>-

0 Z

0 Z

>-

~ iii >.

>-

0

~o LU

~

~ ~.

7O

~o W

, ,4__

m

•~ (D

0~,~

~ ~ "~ 0

~e~..

C~

E

o eJe~SSelE)

.tO

E ._c o

°

"~

,¢~

.

~)

_

.o_

~ o

~

0

0

0

0

Z

0

co LU >.

Z

0 Z

Z

0 Z

Z

Z

>.

~n LU >.

Z

UJ >_

0

~ >.

Z

1.11 >.

8

o

~

•~ o

C

a.)

" ~" ~ '~

0 o

0

Z

0 Z

Z

Z

c~

~

W >.

~o

111 >.

.oo

0~)'~

,-o Q) o ::) ~-o~ o'~ ",- ,-

. oxUo

~

=8

.~ ,-~

E~

:~.,,,-~o

,_ _ ~."= "7-."[:

~rO ._:_-. t ~- r -

"a~

~ ~ "~'~ t~

~o :m

o

~o~

._o®~,E ,-

=_~>~

~

l--~z~

,~ E.

I--

"~

.100

0

~

0

"-'

oo

13 0

o (I) 0 ¢) =.. =_

E q) (D

.O r0~ 0 (I) (I)

8d

o~ ~ 8x Q'U)

o~ r~_o

8

(-

t-

e

>, n

r-

6 eJeM 0!~Seld

.---"

oo

r-

0

c~

E

to

oc~

>

b r-

c o o ~) rh-

._~

E

a

O~

oo

-a~=

eJe~ 0!w'eJ80

(].)

O

o

c~

cO

j:: o .,,_,

"o c~

,,--,

cD

.,-q

5=

. ,...q

~o

cO c~

O

cO j : :

,.c:

~o

cO

~: "o o ©

,,.9,o = E

©

"O

cO

cO

274

Iwabuchi, Fukai, and Kashiwa

References [1] Hitachi, Ltd., "Hitachi Magnetrons," CE-E622 0291, Feb. 1991. [2] C. Lorenson, The why's and how's of mathematical modelling for microwave heating, Microwave World, Vol. 11, No. 1, Spring 1990. [3] X. Jia, Experimental and numerical study of microwave power distributions in a microwave heating applicator, Microwave Power Electromagn. Energy, Vol. 28, No. 1, pp. 25-31, 1993. [4] M. De Pourcq, Field and power-density calculation in closed microwave systems by three-dimensional finite differences, lEE Proc., Patt H, Vol. 132, pp. 360-368, Oct. 1985. [5] K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics. Boca Raton, FL: CRC Press, 1993. [6] K. K. Mei and J. Fang, Superabsorption--A method to improve absorbing boundary conditions, IEEE Trans. Antennas Propag., Vol. AP-40, pp. 1001-1010, Sept. 1992. [7] K. McInturff and P. S. Simon, Closed-form expressions for coefficients used in FD-TD high-order boundary conditions, IEEE Microwave Guided Wave Lett., Vol. 3, pp. 222-223, July 1993. [8] I. S. Kim and W. J. R. Hoefer, A local mesh refinement algorithm for the time domain-finite difference method using Maxwell's curl equations, IEEE Trans. Microwave Theory Tech., Vol. MTT-38, pp. 812-815, June 1990. [9] S. S. Zivanovic, K. S. Yee, and K. K. Mei, A subgridding method for the time-domain finite-difference method to solve Maxwell's equations, IEEE Trans. Microwave Theory Tech., Vol. MTT-39, pp. 471-479, Mar. 1991. [10] D. T. Prescott and N. V. Shuley, A method for incorporating different sized cells into the finite-difference time-domain analysis technique, IEEE Microwave Guided Wave Lett., Vol. 2, pp. 434-436, Nov. 1992. [11] T. Kashiwa, H. Naya, and I. Fukai, A new transducer for thermography to observe the electric field distributions in a microwave oven, Microwave Opt. Technol. Lett., Vol. 4, No. 2, pp. 81-83, Jan. 1991. [12] A. Harada, S. Kitakaze, and T. Oguro, Reduction of 5th harmonic electromagnetic interference from magnetrons and microwave ovens, J. Microwave Power, Vol. 22, No. 1, pp. 3-11, 1987. [13] H. Saito and M. Mino, Improved magnetron with very low level harmonic radiation, Proc. 20th Ann. Microwave Symp. IMPI, pp. 133-136, Aug. 1985. [14] K. Kaneko, K. Iwabuchi, and A. Harada, "Waveguide Filter Used in a Microwave Oven," U.S. Pat, 4,749,973, June 1988. [15] K. Iwabuchi, T. Funamizu, and T. Kubota, "Microwave Heating Apparatus with Fundamental and Second Higher Harmonic Chokes," U.S. Pat. 4,475,023, Oct. 1984. [16] K. Iwabuchi, T. Kubota, Y. Sugaya, T. Kashiwa, and I. Fukai, Effect of conductor losses in new-structure filters for suppressing microwave leakage, in Electronics and Communications in Japan, Part II: Electronics, pp. 80-90, 1993. [17] K. Iwabuchi, T. Kubota, Y. Tanaka, and M. Tawada, "Radiation Sealed Door in a Microwave Heating Apparatus," U.S. Pat. 4,868,359, Sept. 1989. [18] S. Kusunoki, T. Nobue, and T. Kashimoto, "Electromagnetic Wave Energy Seal Arrangement," U.S. Pat. 4,584,447, Apr. 1986. [19] J. M. Osepchuk and J. E. Simpson, "Energy Seal for High Frequency Energy Apparatus," U.S. Pat. 3,767,884, Oct. 1973.

9. Consumer Applications of Microwaves

275

[20] K. Iwabuchi, K. Kaneko, and M. Aoyama, New generation of combination microwave oven and automatic bread making function, Proc. 40th Int. Appliance Tech. Conf., pp. 465-484, May 1989. [21] K. Iwabuchi, M. Tawada, N. Kanagawa, M. Aoyama, and K. Yamazaki, "Microwave Oven Having Automatic Bread Making Function," U.S. Pat. 4,845,327, July 1989. [22] T. Y. Otoshi, A study of microwave leakage through perforated flat plates, IEEE Trans. Microwaue Theory Tech., Vol. MTT-20, pp. 235-236, Mar. 1972. [23] X. X. Peyton, Biological Effect of MicrowaL~e Radiation, Vol. 1, p. 32. New York: Plenum Press, 1961. [24] Hitachi Sales (U.K.), Ltd., "Microwave Oven MR-7970 Instruction Manual."

This Page Intentionally Left Blank

CHAPTER

10 Industrial Applications of Microwaves T. Koryu Ishii

I. Microwave Heating Temperature Rise

The

temperature rise of a sample due to microwave irradiation when there is no melting, no evaporation, no thermal conduction loss, and no thermal radiation loss is given by

T - To = f0 ~--~SP(1 -p2)dt,

(1)

where To is the initial temperature of the sample (°C), T is the temperature of the sample after microwave irradiation for ~- (s), ~- is the microwave irradiation time in seconds at power P (W), P is the irradiating microwave power (W), C is the average specific heat of the sample (cal/°C kg), M is the mass of the sample (kg), p is the microwave voltage reflection coefficient, and ~ is the thermal equivalent of energy, 0.239 cal,/J. The temperature rise of a sample when only melting is involved is given below. In the part of the sample left unmelted, T' -

T o=

f0• C ,1M , ~ P ( 1 -

p

2) ( 1 - ' r / ) d t ,

(2)

where C' is the average specific heat of the unmelted sample (cal/°C kg),

Handbook of Microwave Technology, Volume 2

277

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

278

T. Koryu Ishii

M' is the mass of the unmelted sample (kg), and r# is the ratio of the mass of the melted sample to that of the unmelted sample. In the part of the sample that melted, T" - T' -~ f~, C"M" ~:P(1 - p2)~/dt,

(3)

where T' is the melting point of the sample (°C), T" is the temperature of the melted sample (°C), C" is the average specific heat of the sample ( c a l / C ° kg), M" is the mass of the melted sample (kg), and z' is the time at which the sample started to melt. The temperature rise of a sample when only thermal conduction loss is involved is T-

TO --

f0"

(P(1 - p2) _ G A T ~ ) - ~

dt,

(4)

where G is the thermal conductance between the sample and a heat sink (W/°C) and ATs is the temperature difference between the sample and the heat sink (°C). The temperature rise of a sample when only thermal radiation loss is involved is T-

To - - f o

•(P ( 1 - p 2 ) - SsE A T Ads )'- ~ d t ,

(5)

where E is the emissivity of the sample (W/°C), ATA is the temperature difference between the surface of the sample and the surrounding atmosphere (°C), and S is the surface area of the sample (m2). The temperature rise of a sample when only the thermal conduction loss and the thermal radiation loss are involved is

T-

TO=

So{

CM

-

The temperature rise of a sample when only the thermal evaporation of the sample is involved is • ~:P(1 _ p 2 ) - m h

r-r°=fo

CM

dt,

(7)

where rn is the mass of the sample evaporated in 1 s ( k g / s ) and h is the latent heat of the evaporated sample (cal/kg). The temperature rise of a sample when thermal conduction loss, thermal radiation loss, and sample

279

I0. Industrial Applications of Microwaves

evaporation are involved is r-

To =

P(1 - o 2) - m A - ~ G AT~ + "o

Latent Heat of Vaporization The amount of heat (cal) required to vaporize 1 kg of the sample without a change in temperature ( c a l / k g ) is the latent heat of vaporization.

Emissivity The amount of energy radiated from 1 m 2 of a surface in 1 s for a I°C temperature difference between the surface and the surrounding atmosphere ( J / m 2 °C s and W / m 2 °C) is the emissivity.

Thermal Conductivity The amount of thermal energy flowing across a square meter of a sample cross section in 1 s for 1 m of thickness with a temperature difference of 1°C ( J / ° C s m and W / ° C m) is the thermal conductivity.

Thermal Conductance The amount of thermal energy flowing in 1 s across cross section S (m 2) and distance 1 (m) is the thermal conductance, S

c

=g7'

(9)

where G is the thermal conductance ( J / ° C s and W/°C), g is the thermal conductivity ( J / ° C s m and W / ° C m), S is the cross-sectional area (m2), and l is the thickness of the sample (m).

Specific Heat The amount of thermal energy required to raise 1 kg of sample by 1°C ( J / ° C kg) is the specific heat.

Thermal Equivalent of Energy ] J -

0.239 cal

1 cal = 4 . 1 8 4 J

Induction Heating (Conduction Heating)

/o t

1-p

2) d t = ~

Jo"

Ri 2 dt = M C ( T -

To) ,

(10)

where R is the electrical resistance of the sample ( ~ ) and i is the induced

280

T. Koryu Ishii

microwave current in the sample (A). The temperature rise in induction heating is

T - TO= f ~ P ( 1 - p2) dt MC "o

(11)

M = m c SS,

(12)

where m c is the specific weight of the sample heated (kg/m3), S is the surface area of microwave irradiation (m2), and 6 is the skin depth of microwave penetration through sample surface S (m), 1 8 - - V/,.n.f~o. ,

(13)

where f is the operating microwave frequency (Hz), /~ is the magnetic permeability of the sample to be heated ( H / m ) , and tr is the electrical conductivity of the sample to be heated (S/m). Dielectric Heating ,r to e. " e 2

fo, P ( 1 - p 2 ) d t = L f o , - - - - f - - d t d u = M C ( T - T o ) ,

(14)

where e is the microwave electric field strength in the sample (V/m), u is the volume of the sample (m3), e = e ' - j e " is the permittivity (F/m), jtoee =jwe'e + toe"e is the displacement current density (A/m2), and we"e is the microwave heating current density (A/m2). ~.~ EVVe

tan S -

weVe

E vv

e'

(loss tangent).

Hybrid Heating (Combination of Conduction and Dielectric Heating)

~P(1

So

-

p 2) dt

=

~ (o" + toe")e 2

SSo

2

dt du

= M C ( T - To)

O" -[- t O E "

tan S -

O.}E r

(loss tangent).

(15)

Approximate Equations for Temperature Rise

Solid Heating T-To<_

e(a CM

p): T

(16)

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I0. Industrial Applications of Microwaves

Liquid Heating TO <

T-

(17)

r.

-

CM

Gas Heating

_,2), T-

TO < -

.

(18)

CM

2. Microwave Curing Rubber Curing When uncured rubber is heated to a temperature range of 150-180°C and the temperature is maintained for a sufficient time, depending on the quality and composition of the rubber sample, the rubber product will be cured [1]. A general block diagram of a microwave rubber curing system is shown in Figure 1. In this figure, the microwave power generator must be equipped with the output microwave power meter and reflected power meter. The impedance matching device must be adjustable using a screw tuner [2] or an E - H tuner [2]. The screw tuner should be limited to relatively low-power application. It will produce arcing at high-power operation. The applicator of microwaves to the rubber sample to be cured can be a standing wave type, a nonresonant type, or a traveling wave type. Standing-wave-type applicators usually produce the hot spots and cold spots. Therefore, they are not convenient except when the sample is small enough to be placed on the hot spot. If this is the case, the advantage is good heating efficiency. A cross-sectional view of a standing wave microwave applicator for rubber curing is shown in Figure 2. Uncured rubber is placed in a ceramic mold and pressed. The ceramic mold is placed at

I

Microwave Power Generator

Impedence Matching Device

I I I t

'

I

IApplicatorl

II

I with I ' i Rubb , i I, I

Microwave Shield Figure I. A general block diagram of a microwave rubber curing system.

282

T. Koryu Ishii

~.

d

Pressure

,,~

tiii;!iiii:ililili;i!i:i i ceMroauTjC

Wave°ie

l Cavity _ Resonator

!il

I

Figure 2. Cross-sectional view of a standing wave rubber curing applicator,

the hot spot of the microwave cavity resonator. The ceramic mold provides for low microwave loss, and it is almost transparent against microwaves. When the sample size is large, the ceramic mold grows larger. Therefore, the ceramic mold has to be placed in a large well field stirred microwave oven. Most microwave oven cavities are nonresonant. The field stirring, turntable, or both are needed to heat the sample uniformly, avoiding both the hot and the cold spot effects. An example of a traveling wave rubber curing applicator is illustrated in Figure 3(A). Microwaves are fed from a microwave power generator to a meander line which is reflectionlessly terminated at its end [2]. The traveling microwaves propagate along the meander line. Traveling microwave fields develop between the meander line and the grounded conducting conveyor belt. In this microwave field, pressed and molded uncured rubber is exposed and microwave heated. In traveling wave heating, there is always a tendency to get more heat at the input side of microwaves than the output side. Therefore, the sample and the circuit must have a relative motion. The direction of sample motion must be opposite the direction of microwave power flow for uniform heating. In the case of Figure 3B the traveling wave structure is a helix. The sample is a round rubber rod. The whole traveling wave structure must be placed inside a shielding tunnel for the safety of operators and prevention of radio interference [3]. In Figure 1, the impedance matching device must be adjusted to minimize reflection from the applicator by monitoring the reflection meter. An automatic impedance matching machine which keeps the reflection from the applicator at a minimum all the time is available from

283

I0. Industrial Applications of Microwaves

A

Input Microwave Power ,,

~o,,o~n

/

-,,-,

=

Microwave Power Termination

Meander Line

,-,

' Motlon

=

Ceramic Mould Containing Pressed Uncured Rubber

V/]-

Grounded Conveyor Belt

B Uncured

Rubber Microwave Power Input Figure 3. Microwave traveling wave rubber curing system.

TABLE I Microwave Rubber Curing Parameters

Rubber NBR and PVC NBR OE-SBR BBP

Optimum cure temperature (°C)

Optimum cure time (min)

Microwave power needed (W/cm 3)

165 165 165 165

9.4 4.3 6.0 13.0

55.6 55.6 55.6 55.6

Note. Microwave frequency, 2450 MHz.

T. Koryu Ishii

284 TABLE 2 Microwave Tire Curing Data [3]

Tire

Weight (kg)

Number of tires

5.2 19 --

15 ---

Wheelbarrow solid tire [3] Forklift solid tire [3] Giant off-road tire tread [4]

Microwave Heating power (kW) time (min) 1.5 3 100

20 10

Microwave frequency 2.45 GH 2.45 GHz 915 MHz

TABLE 3 Microwave Asphalt Curing Data [5] :

Asphalt curing temperature Depth of penetration of heat Operating frequency Microwave power density Application time duration

150°C 6 in. 2450 MHz 8 W/cm 2 1 ~h

microwave p o w e r e q u i p m e n t vendors. T h e reflection changes all the time as the r u b b e r is cured. In Table 1, the curing t e m p e r a t u r e , curing time, and curing p o w e r of various types of r u b b e r are tabulated.

Tire and Asphalt Curing Tire curing data and asphalt curing data for road r e p a i r [5] are t a b u l a t e d in Tables 2 and 3, respectively.

3. Microwave Material Processing [78, 80] Microwave Thawing Frozen Meat T h e t e m p e r a t u r e rise e q u a t i o n is given as E q u a t i o n (15). T h e p e r m i t tivity is shown in Table 4 [6].

10. IndustrialApplications of Microwaves

285

Frozen Vegetables [7] Initial temperature Thawing temperature Microwave heating time Microwave frequency Microwave power feed a

20OF + 28°F 0.4 min / lb 915 MHz 3 kW -

aNot absorbed power.

Frozen Biological Samples: [8, 9, 87] Thawing oven, 10-in. cube Organs and tissues, a 17-in. cube Initial temperature Final temperature Heating rate Microwave power reflection coefficient Thawing oven Frozen blood and plasma Heating time Initial temperature Final temperature

1 kW, 2.45 GHz 2 kW, 2.45 GHz - 176°C - - 79°C + 10°C 200°C/min Up to 0.9 220 W, 2.45 GHz 500 W, 2.45 GHz 0.03 min / ml sample 30oc + 37°C _

8

0

o

C

_

_

a Both organs and tissues must have a turntable.

M i c r o w a v e Drying

Microwave Milk Drying (Microwave Freeze-Dry under Vacuum) [10] Frozen whipped milk in vacuum (4.3 cm in diameter and 5.0 cm high) Initial density Final temperature High pressure Low pressure Microwave frequency Initial microwave power Final microwave power Initial sample mass Final sample mass Drying time

268 K 340-430 kg / m 3 293 K 8000 Pa 132 Pa 2450 MHz 100 W 85 W 28.84 mg 4.04 mg 38 min

286

T. Koryu Ishii TABLE 4 Relative Permittivity of Frozen Meat [6]

Frequency (MHz)

Temperature (°C)

e 'r

- 20°C -40°C - 20°C -40°C

4.1 3.5 4.6 3.6

2450 MHz 915 MHz

0.55 0.14 0.66 0.14

20 s 9s 40 s 100% 5%

High-pressure cycle Microwave on cycle (with high pressure) Low-pressure cycle (with microwave power off) Initial moisture Final moisture

Microwave Frozen Thin Plate Drying [11] The drying time, t d, is given by

Pws A H s td

=

Pf

Kd In m Kf • ~ ~ - ,

Kd

1

(19)

Kf where Pws is the density of free water in the frozen region (kg/m3), AH s is the enthalpy of sublimation of ice (2.834 × 106 J/kg), Pf is the microwave power absorbed by the frozen plate (W), Kf is the microwave dissipation coefficient of the frozen plate (W/mV 2) [11], and K d is the microwave dissipation coefficient of holder plates of the frozen plate ( W / m V 2) [11].

Microwave Paper Drying [12] mf = m 0 exp - ~ - ~-E g r, where mf is the final value of moisture, m 0 is the initial value of moisture, is the time parameter, r/ is the conductance parameter, E 0 is the peak microwave electric field parallel to the sheet of paper, and r is the microwave irradiation time.

287

I0. Industrial Applications of Microwaves

Microwave Coated Film Drying [13, 81, 82] Film speed Microwave dryer length Film Coating Coating thickness Drying rate Microwave generator output Hot air temperature Film temperature Microwave frequency

1000 fpm 8ft Synthetic polyethylene Polyvinylidene chloride 3-4 lb per 3000 ft 2 3.5 lb of water per kilowatt of microwave 60 kW 160-200°F 212°F minimum 2450 MHz

Microwave Carpet Backing Drying [14] Microwave frequency Initial moisture Final moisture Microwave power Drying time

2450 MHz 45% 5% 4.2 kW/yd 2 7 min

Microwave Leather Drying [15] Microwave frequency Microwave applicator Leather thickness Initial moisture Final moisture Microwave power density Drying time

2450 MHz Microwave oven 4 mm thick 6O% 0.0% 0.06, 0.09, 0.12, 0.15, 0.18, and 0.21 W/cm 2 90, 58, 37, 27, 20, and 18 min

Microwave Clothes Drying [16] Microwave frequency Microwave power Initial moisture Final moisture Drying time

2450 MHz 1850 W / k g of dry clothes 30% 0% 15 min

288

T. KorTu Ishii Sharpened Ridge

Ridge Waveguide

"-.,

/

I I / I

Choke

Choke

Printed Paper

~, I + ~ ~ " m i n ' [

////////////////// 1/2 in.

Metallic Base

I I

I__yq_

^ / 0.02 in.

Figure 4. Cross-sectional view of an applicator from a microwave ink-line dryer [ 17].

Microwave Ink-line Drying [17] Microwave frequency Microwave power Applicator Drying time Microwave power leakage

2450 MHz 200 W Knife-edge applicator with choke slots (see Figure 4.) 0.5 s, 24 in. long 2-6 mW/cm 2

Microwave Vacuum-Assisted Biomass Drying [18] Microwave frequency Microwave oven power Sample Initial moisture Final moisture Drying time Vacuum pressure

2450 MHz (estimation) 750 W (estimation) Acid-impregnated corn stover (60 gm) 25% 7% 4 min 508 mm Hg

Microwave Coal Drying [19, 86] Sample Microwave frequency Microwave oven power Initial moisture Final moisture Drying time

Loy Yang Brown Coal, 30-mm sphere 2450 MHz 650 W 80% 1% 400 s

10. Industrial Applications of Microwaves

2119

Microwave Dye Drying [20] Microwave frequency Microwave oven power Sample

Initial moisture Final moisture Drying time

2450 MHz 2.5 kW maximum, low ventilation. Dye on cotton cloth 0.2152 m wide and 16.5 m long, rolled on a core of 2.54 cm. Cloth dry weight, 240 g. Roll diameter, 7.62 cm 85% 10% 10 min (1000 W), 22 min (500 W), and 44 min (250 W)

Microwave Pencil Slats Drying [21] Microwave frequency Microwave oven power Microwave application time Sample

2450 MHz 4.5 kW 45 s 40 pairs of slats, 9 pencils per slat

Microwave Heating Microwave Heating of Ar and He [22] Interaction chamber Operating microwave power Gas pressure Efficiency Gas flow Maximum gas temperature Pulse duty cycle

TE01 circular waveguide 1 MW (pulse), 250 kW (pulse), and 23 kW (CW) 1-3 atm 20-90% (pulse) and 25-60% (CW) 200-400 L / min 135°C [870 kW (pulse)] 0.6%

Microwave Heating of Methane [23] Interaction chamber Operating microwave power Operating microwave frequency Gas pressure Operating temperature

TEl0 rectangular waveguide 3 kW maximum, 120 pps 2.45 GHz 100 kPa 1400°C / min N i catalyst

290

T. Koryu Ishii

Application mode

240-ms pulse packet followed by 5.76-s pause Up to 2 rain Up to 31%

Total machine time Pulse duty cycle

Microwave Heating of Aqueous Sulfur [24] Operating frequency Sample carrier Heating cavity VSWR

8.9 GHz Glass tube along cavity axis TM0a 1 cylindrical cavity. Length 6 cm; radius, 1.2 cm 1.2

Microwave Heating of Gravy and Milk [25] Operating frequency Heating cavity Sample loading tube VSWR Operating microwave power Rate of temperature rise

896 MHz TMol o cylindrical cavity. Diameter, 20 cm; length, 16.5 cm Diameter, 7 mm; dielectric tube 2 (gravy) and 12 (milk) 5 kW 120°C/s

Microwave Heating of Nylon Monofilament [26] Operating frequency Microwave power Heating cavity Filament speed Temperature in Temperature out

2.45 GHz 99-138 W TMol o cavity. Filament on axis. Length, 14 in. 144- 280 ft / min 40-100°C 190 + 4°C

Microwave Heating of Coal and Pyrite [27] Operating frequency Operating power Heating waveguide

2.45 GHz 2 kW WR-340, terminated by a water load

10. Industrial Applications of Microwaves

Samples Reflected power Final temperature Initial temperature Heating rate

291

Dahm, Childers, Pittsburgh No. 8, and Illinois No. 6. 1 x 2 x 30 cm 100 W 150-320°C 15°C 1.3-3.97 K / s

Microwave Heating of Alumina and Silica [28] Operating frequency Operating microwave power Initial temperature Final temperature Microwave application time Heating cavity Sample rod

2.45 GHz 400 W 15°C 1700°C 10-15 min TMo~0 rectangular cavity Mounted along the central E-axis

Microwave Heating of Oil Shale [29] Operating frequency Operating microwave power Heating waveguide Sample holder Samples Microwave application time Net energy ratio

2.45 GHz 100 W WR 284 with a reflectionless termination 20-ram-diameter quartz tube Oil shale, 10 x 10 x 23-mm rectangular block 16 min 3

Microwave Heating of Iron Ore-Carbon [30] Operating frequency Operating microwave oven power Sample Initial temperature Final temperature Microwave application time

2.45 GHz 750 W Fe203, A1203, and brown coal, 20-mm-diameter pellet 100°C 300°C 15 min

292

T. Koryu Ishii

Microwave Heating of Radioactive Ash [31, 88-90] Operating frequency Microwave power Ash vitrification rate Vitrification temperature Volume reduction rate

915 MHz 25 kW 25.3 kg / h 1400°C 90% rain

Microwave Heating of PVC [32] Sample Microwave frequency Microwave oven power Initial moisture Final moisture Drying time

PVC beads, g1- ~ 1 in. in diameter. 2.5-cm-thick bed on a 100-g drying tray 2.45 GHz 750 W/200 g 31% 2% 24 min (1 of conventional method)

Microwave Heating of Seal Spots on Cartons [33] Operating frequency Operating power Seal spot area Application time Input VSWR Leakage power Applicators

2.45 GHz 1 kW per spot maximum 6 cm 2 1 s maximum Less than 2 5 mW/cm 2 Slotted ridge waveguide strip-line applicators

Microwave Heating of PVC and EO for Diffusion [34] Operating frequency Microwave oven power Sample Diffusion time Diffusion temperature Initial EO concentration Final EO concentration

2.45 GHz 750 W PVC tubes in EO gas, 1200 m g / L 3 h (~1 of conventional method) 55°C 10,900 ppm 100 ppm

293

10. Industrial Applications of Microwaves

Microwave Heating of Cigarettes [35] Operating frequency Microwave power Microwave heater cavity Conveyor belt speed Number of cigarette layers Air blower capacity Cigarette processing capacity

2.45 GHz 4.5 kW maximum 55 cm wide, 40 cm high, and 45 cm long 0.3 to 3 m / m i n 5 to 10 16 m3/min 3000 cigarettes/min

Microwave Heating of Bitumen/Asphalt [36] Operating frequency Microwave power Microwave tank Sample weight Mode stirring Sample temperature Conversion efficiency Heating time

896 MHz 30 kW Diameter, 1.5 m; length, 3 m 12,080 kg Variable polarizer 200°C minimum 48% NA

4. Microwave Applications in Agricultural Industries Microwave Vacuum Drying of Sliced Parsley Root [37, 83] Operating frequency Microwave oven power Sample Initial moisture Final moisture Microwave irradiation time Air pressure Air temperature Sample temperature

2.45 GHz 2 kW 500 g sliced parsley roots 100% maximum 20% 32 rain (-~ of conventional method) 5-9 Tort 26-27°C 57-58°C

Microwave Drying of Cottonseed [38] Operating frequency Microwave oven power Germination

2.45 GHz 200 W 56% (normal)

294

T. Koryu Ishii

Initial moisture Final moisture Microwave application time Seed mass temperature Air blower Seed container Sample seed quantity

22% 20.5% 6 min 130°F 25 CFM ventilation Plexiglas 8- x 12- x 3-in. mesh tray 700 g

Microwave Treatment of Tree Seeds [39] Microwave frequency Microwave oven power Sample Germination rate Microwave application time

2450 MHz 500 W with water load 100 white spruce seeds 32% 35s

Microwave Treatment of Douglas Fir Tree Seeds [40] Microwave frequency Microwave power Sample seeds Microwave application time Germination rate

2450 MHz 100 W 120 seeds, 3 g, single layered 2 min 77% (46% if not treated)

Microwave Drying of Field Corns [41, 84] Microwave frequency Microwave oven power Sample Initial moisture Final moisture Microwave application time Air temperature Air ventilation

2450 MHz 1.5 kW 625 g of field corns, shelled 22.2% 11.8% 8 min 15-30°C 26-52 ft3/min

Microwave Heating of Corn Fields [42] Microwave frequency Microwave radiation power

2.45 GHz 2.4 kW

10. Industrial Applications of Microwaves

295

E-plane sectoral horn antenna (15 × 3.4 in.) mounted at the top of a 6-ft tower 25- × 25-ft corn field 60 h 5-19 mph - 6 ° C minimum and - I ° C maximum 1 Snowstorm, 5 in. accumulation 90% Less than 10 m W / c m 2 at 25 ft

Antenna Sample Test time duration Wind Air temperature Weather Survival rate Power density

Microwave Warming of Plants [43] Microwave frequency Microwave radiation intensity Test chamber temperature Sample leave temperature Sample plant Test period Survival rate

915 and 2450 MHz 15 m W / c m 2 -5oc + 20°C Wax bean plants 4h 100%

Microwave Application of Insecticides on Grain [44] Microwave frequency Microwave power Samples Wheat temperature Insect mortality Wheat flow rate

2.45 GHz 1.2 kW Tribulium confusum in wheat grain 65 °C 100% 2.25 l b / m i n

Microwave Application of Insecticides on Tobacco [45] Microwave frequency Microwave power Samples Sample temperature Insect mortality Conveyor belt speed Conveyor belt width Shredded tobacco thickness Tobacco weight in oven

2.45 GHz 1.7 k W / k g Tobacco moths and cigarette beetles 55°C 100% 1 m / min 30 cm 12 cm 7 kg

296

T. Koryu Ishii

Microwave Application of Insecticides for the Pecan Weevil [46] Microwave frequency Microwave oven power Sample size Motal temperature Motality rate Exposure time

2.45 GHz 800 W 4.8- × 4.8- × 2.1-cm polystyrene box with pecan pieces with weevils 80°C 100% 16s

Microwave Repasteurization of Pasteurized Milk [47] Microwave frequency Microwave oven power Samples Initial bacterial count Microwave irradiation time Final temperature of milk Final bacterial count Untreated shelf life Treated shelf life

1450 MHz 750 W 200 ml of l 1-day-old pasteurized homogenized milk 108-2/ml 2 min 60°C 102.5/ml 10.7 days 19.7 days

5. Microwave Applications on Forest Products Microwave Drying of Veneer [48-50] Microwave frequency Microwave power Sample Initial moisture Final moisture Air flow speed Dryer temperature Drying time

NA 600 W 42- x 23- X 0.06-cm oak veneer, multilayer sample 90% 10% 4m/s 150°C 132 s (conventional drying time, 363 s)

Microwave Bending of Wood [51] Microwave frequency Microwave oven power

2.45 GHz 0.6-2.4 kW

I0. Industrial Applications of Microwaves

Microwave irradiation time Wood bending temperature Sample

297 1-3 min 90-110°C 100% wet, 409 x 1 x 2 cm, for example

6. Microwave Application on Sensing [52, 53, 57, 79, 91] Moisture of Wheat [54] Microwave frequency Sample container Test setup

9.4904 GHz 100 x 150 x 200 mm, Plexiglas Transmitter horn and receiver horn. Apertures, 79 x 54 mm each and 150 mm apart A = (2.309 % moisture) - 16.234 dB A~b = (28.995 % moisture) + 307.422 ° 25°C

Sensing by attenuation Sensing by phaseshift Test temperature

Moisture of Rice [55] Microwave frequency Sample holder Sensor plate

10.5 GHz, 10 mW, solid-state oscillator Any holder or duct larger than the sensor plate which must make contact with the grain U-shaped microstrip line. The microstrip line side makes contact with grain.

Moisture of Grain [56] Microwave frequency Sample holder Sensor Sensing principle Sensitivity

500 and 600 MHz, HP 8654B signal generator Cylindrical metallic container or rectangular metallic container A short monopole antenna at an end of a coaxial line inserted into the grain container Phase angle of voltage reflection change due to moisture. HP8405A vector voltmeter. 0-100 ° phase angle change for a 0-80% moisture change for the peanut. 0-17 ° phase angle change for a 12-25% moisture change for rice. 0-20 ° phase change for a 0-20% moisture change in soil

298

T. Koryu Ishii

Moisture of Coal [58, 86] Microwave frequency Sample holder Sensing principle Sensitivity Sensing equipment

3 GHz S-band waveguide Phase shift 30-90% phase change for 0-30% moisture HP8410 Network Analyzer

Moisture of Coal [59, 86] Microwave frequency Sample Sensing principle Sensitivity Sensing equipment

2.8-3.8 GHz Coal belt 40 to 250 mm thick, 0 to 15% moisture Phase shift 25 ° to 78 ° phase shift Impedance bridge

Target Range [60, 67, 68] Microwave frequency Sample Sensing principle Sensing range Accuracy

10.3 GHz Sensing of iron ore in a blast furnace Frequency modulation radar 0-10m _+75 mm

Length [60] Microwave frequency Sample Sensing principle

Accuracy

10.3 GHz Length of steel slab Doppler radar frequency counter is triggered by a photocell sensing both ends of the moving slab [67, 68]. 2 mm

Thickness of Thin Metal Plate [60, 61] Microwave frequency Sample Sensing principle Accuracy

Swept frequency in the X-band Hot steel plate less than 2 mm thick Differential resonator technique Better than 2.5 ~m

Thickness of Thick Metal Plate [60] Microwave frequency Sample

X-band frequency modulation Hot steel plate greater than 3 mm thick

I0. Industrial Applications of Microwaves

Sensing principle Accuracy

299

Differential frequency modulation radar technique _+75 ~ m

Fiber Orientation in Paper [62] Microwave frequency Sample Sensing principle Dual mode Cavity size Sample position

3.4 GHz A sheet of paper Dual mode cavity resonator technique. Anisotropy of paper makes different resonance frequencies. TEl01 and TE011 A cubic cavity, 6.3 × 6.3 x 6.3 cm Sample paper is sandwiched in the center gap of the cubic cavity resonator.

Alcohol Vapors [63] Microwave frequency Sample holder Sensing principle Sensitivity

9.481 GHz Tunable cylindrical cavity resonator Perturbation of resonance frequency due to e' of alcohol vapor - 46.8 kHz / T for ethanol; - 40.4 kHz / T for methanol

Permittivity of Dielectric Plate [64, 85] Microwave frequency Sensor Sensitivity

2.360 GHz, unloaded Slot-line resonator, 5 cm long 160 MHz / unit of e r

Flaw/Defect of Tires [651 Microwave frequency Sensing principles Configuration

Hairline Cracks on Microwave frequency Sensing principle Sensing range

X-band Microwave transmission through the sample Microwave radiators mounted along the tire axis. A receiver diode array mounted on a holder surrounding the tire outside. The tire rotates between the transmitter and the switchable receiver-diode array. Metal

[66-68]

10.525 and 73 GHz Microwave reflections and the Doppler effect From close range to up to 1.5 miles

300

T. Kor,/u Ishii

7. Microwave O b j e c t Identification Microwave Radiometer Technique The microwave radiometer is a sensitive microwave receiver with a highresolution receiver antenna which scans the object to be identified. The scan of the antenna is synchronized with an electron beam scan of a displaying cathode ray tube. Thus the image of the object is displayed on the CRT scope and identified. All objects at finite temperature emit microwaves.

Microwave Monostatic or Bistatic Radar

Technique [69]

Monostatic radar uses only one antenna for transmission and reception. Using microwaves of millimeter wavelengths and short pulse duration periods, a high-resolution radar can be built to display an image of a target for identification. A bistatic radar has two antennas. One for the transmitter and the other for the receiver. The transmitter may not be of high resolution. The transmitter and the receiver may be located in separate locations. The receiver has a high-resolution scanning antenna for microwave image production on a display CRT for imaging.

Microwave Reflection or Radiation Pattern Recognition Technique Instead of the CRT display on radiometers or radars, the receiver output can be fed into a pattern recognition integrated circuit chip which contains neuronetworks so that the chip can be programmed to recognize the particular pattern of the receiver output signals.

8. Microwave D a t a Communications General Configurations General configurations of a microwave data communication system are shown in Figure 5. This is a one-way communication system for broadcasting. If a two-way communication system is desired, another system which is identical to Figure 5 in reverse sequence will be set up for reverse communication. In such cases, the carrier microwave frequencies for the forward communication and the reverse communication are chosen to be different to avoid interference.

I0. IndustrialApplicationsof Microwaves Data !'~

Modulator

301

f

Microwave H Microwave Launcher Transmitter

1~

MicrowaveTransmissionSystem

L•

MicrowaveReceiver H

H Microwave Catcher Data Display

Figure5. Generalconfigurationof aone-waymicrowavedatacommunicationsystem. Data

Temperature, pressure, distance, location, computer data, and so on which are information to be transmitted are termed the data. The data usually require a transducer to translate the data to electrical signals [70]. The electrical signals are most of the time digital electrical voltages [71]. If the data are analog, an analog-to-digital converter may be necessary if the communication system chosen is a digital communication system. Modulator

The modulator produces modulation signals for the transmitter [72]. If the communication system is an analog communication system, the type of modulation employed is generally AM (amplitude modulation), ~M (frequency modulation), or PM (phase modulation). If the communication system is digital, then the type of modulation employed is generally ASK (amplitude shift keying), FSK (frequency shift keying), or PSK (phase shift keying) modulation [70]. Depending on the selection of the type of modulation, the modulator IC (integrated circuit) chips are commercially available [73]. Such chips accept electrically converted data input and produce modulation signal output to the transmitter. Microwave Transmitter

The microwave transmitter can be AM, FM, PM, ASK, FSK, or PSK depending on the selection of the type of communication system. It can be a low-power transmitter or a high-power transmitter depending on the distance for signal transmission. The transmitter contains the input impedance matching network, the microwave oscillator, the microwave power amplifier, and the output impedance matching network. The trans-

302

T. Koryu Ishii

mitter accepts the modulation signals. The transmitter generates the microwave carrier signals, and it will be intensified sufficiently strong enough for transmission. The microwave oscillator can be a tunnel diode oscillator, Gunn diode oscillator, impatt diode oscillator, transistor oscillator [74], or Klystron oscillator [74] depending on the power and tuning characteristics desired. The microwave amplifiers can be transistors [74], Klystrons, traveling wave amplifiers, or power Klystron amplifiers [74] depending on the power and tuning characteristic requirements.

Microwave Launcher

The type of microwave launcher depends on the microwave transmission system. If the microwave transmission system is a transmission line such as the two-wire line, coaxial cable, or waveguide [75], then the microwave launcher is an impedance matching transformer between the transmitter and the transmission line [75]. If the microwave transmission system is a space such as the outdoor open air, the indoor open air, space, the urban atmosphere, or the forest atmosphere, the microwave launcher consists of an appropriate microwave antenna and an impedance matching transformer between the transmitter and the antenna [75].

Microwave Transmission System

A microwave transmission system connects the transmitter and the receiver. It can be an open space or a transmission line. If the transmission system is an open atmosphere, a change in microwave attenuation due to weather conditions must be taken into consideration. A fade margin as high as 40 dB should be considered for the worst weather. If the microwave transmission will go through a window glass pane, a pane fade margin as high as 25 dB per glass pane should be considered for secure data transmission. There will be signal fading due to moving objects between the transmitter launcher and the receiver catcher. The moving object fade margin could be as high as 5 dB. If the transmission system is a waveguide, there will be dispersion. This does not affect transmission quality if the data bit rate is low. For high-bit-rate and high-speed communication, the effect of dispersion will appear. The signal wave form will be deteriorated at the receiving end. In a digital communication system, even the received data signals deteriorate due to dispersion of the transmission system at the receiving end; through the use of the signal regeneration technique, as long as the presence of the signal is recognized, the original data signal can be recovered [70].

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303

Microwave Catcher

If the microwave transmission system is a transmission line, then the microwave catcher is an impedance matching transformer between the transmission line and the receiver. If the microwave transmission system is an open atmosphere, the microwave catcher consists of a microwave receiving antenna and an impedance matching transformer between the antenna and the receiver. Microwave Receiver

A microwave receiver can be AM, FM, PM, ASK, FSK, or PSK depending on the type of modulation employed. Sometimes, monolithic integrated circuit chips for entire microwave receivers are commercially available. If not, subsystem integrated circuit chips such as the low-noise amplifier chip, the heterodyne mixer chip, the IF amplifier chip, the down-converter chip, the video and audio amplifier chips, and the demodulator chip are commercially available [67, 73, 76, 77]. The sensitivity of the receivers [75] varies between - 1 0 and - 1 2 0 dBm depending on the sophistication of the receiver circuit and the type of modulation of the communication system. Data Display

The data display can be an audio or a video display or a printout. In most cases, an impedance matching circuit is required between the receiver output and the data display unit for the best results. References [1] H. F. Schwarz, R. G. Bosisio, M. R. Wertheimer, and D. Conderc, Microwave curing of synthetic rubbers, J. Microwave Power, Vol. 8, Nos. 3/4, pp. 303-322, Nov. 1973. [2] T. K. Ishii, Microwave Engineering. Washington, DC: Harcourt Brace, 1989. [3] R. A. Shute, Industrial microwave systems for rubber industry, J. Microwave Power, Vol. 6, No. 3, pp. 193-205, Oct. 1971. [4] R. Edgar, Robotics in large scale curing processes, J. Microwave Power, Vol. 21, No. 3, pp. 194-195, 1986. [5] R. G. Bosisio, J. Spooner, and J. Granger, Asphalt road maintenance with a mobile microwave power unit, J. Microwave Power, Vol. 9, No. 4, pp. 381-386, Dec. 1974. [6] R. E. Mudgett, D. R. Mudgett, S. A. Goldblith, D. I. C. Wang, and W. B. Westphal, Dielectric properties of frozen meats, J. Microwave Power, Vol. 14, No. 3, pp. 209-216, Sept. 1979. [7] K. O. Weil, T. W. Moeller, C. L. Bedford, and W. M. Urbain, Microwave thawing of individually quick frozen red tart cherries prior to pitting, J. Microwave Power, Vol. 5, No. 3, pp. 188-191, Nov. 1970.

3t:)4

T. Koryu Ishii

[8] W. A. G. Voss, R. V. Rajotte, and J. B. Dossetor, Applications of microwave thawing to the recovery of deep frozen cells and organs: A review, J. Microwave Power, Vol. 9, No. 3, pp. 181-194, Sept. 1974. [9] A. Checcucci, G. Benelli, M. Duminuco, M. L. Gaetani, P. Paoletti, S. Vannini, and M. Morfini, Reliability of microwave heating for hemoderivative thawing, J. Microwave Power, Vol. 18, No. 2, pp. 163-168, June 1983. [10] K. Ben Sonda, C. Akyel, and E. Bilgen, Freeze dehydration of milk using microwave energy, J. Microwave Power, Vol. 24, No. 4, pp. 195-209, 1989. [11] J. Sochanski, J. Goyette, T. Bose, and C. Akyel, Freeze-drying of thin plates by microwave, J. Microwave Power, Vol. 26, No. 2, pp. 90-99, 1991. [12] G. Roussy, J.-M. Thiebant, A. Bennani, and N. Mouhab, A kinetic model for microwave drying of paper, J. Microwave Power, Vol. 23, No. 1, pp. 29-38, 1988. [13] E. W. Stephansen, Microwave drying of coated films, J. Microwave Power, Vol. 7, No. 3, pp. 241-243, Sept. 1972. [14] H. Small, J. D. Hatcher, and D. W. Lyons, Microwave drying of latex carpet backing, J. Microwave Power, Vol. 7, No. 1, pp. 29-34, Mar. 1972. [15] M. A. K. Hamid, S. S. Stuckly, P. Bhartia, and N. Mostowy, Microwave drying of leather, J. Microwave Power, Vol. 7, No. 1, pp. 43-48, Mar. 1972. [16] M. Hamid, Microwave drying of clothes, J. Microwave Power, Vol. 26, No. 2, pp. 107-113, 1991. [17] A. L. Van Koughnett and W. Wyslouzil, A microwave dryer for ink lines, J. Microwave Power, Vol. 7, No. 4, pp. 347-351, Dec. 1972. [18] G. Lightsey, C. George, W. Wehr, and G. Bharat, Evaluation of microwave and radio-frequency drying in the acid hydrolysis of biomass, J. Microwave Power, Vol. 23, No. 1, pp. 11-15, 1988. [19] N. Standish, H. Worner, and H. Kaul, Microwave drying of brown coal agglomerates, J. Microwave Power, Vol. 23, No. 3, pp. 171-175, 1988. [20] J. E. Pendergrass, J. D. Hatcher, and D. W. Lyons, Deposition of finishes and dyes in materials dried using microwave heating, J. Microwave Power, Vol. 7, No. 3, pp. 207-213, Sept. 1972. [21] K. Oshima, T. Toishi, T. Muranaka, T. Serikawa, and T. Hiratsuka, Microwave presssetting equipment for pencil manufacture, J. Microwave Power, Vol. 10, No. 1, pp. 19-26, Mar. 1975. [22] J. J. Moriarity and W. C. Brown, Toroidal microwave discharge heating of gas, J. Microwave Power, Vol. 3, No. 4, pp. 180-186, Dec. 1968. [23] J. Wan, M. Tse, H. Husby, and M. Depew, High power pulsed microwave catalytic processes: Decomposition of methane, J. Microwave Power, Vol. 25, No. 1, pp. 32-38, 1990. [24] P. A. Vuorinen and P. N. Bruce, X-band model of microwave applicator for liquid heating applications, J. Microwave Power, Vol. 11, No. 2, pp. 99-104, June 1976. [25] A. C. Metaxas, Rapid heating of liquid foodstuffs at 896 MHz, J. Microwave Power, Vol. 11, No. 2, pp. 105-116, June 1976. [26] H.-F. Huang, Temperature control in a microwave resonant cavity system for rapid heating of nylon monofilament, J. Microwave Power, Vol. 11, No. 4, pp. 305-313, Dec. 1976. [27] G. E. Fanslow, D. D. Bluhm, and S. O. Nelson, Dielectric heating of mixtures containing coal and pyrite, J. Microwave Power, Vol. 15, No. 3, pp. 187-191, Sept. 1980. [28] A. J. Berteand and J. C. Badot, High temperature microwave heating in refractory materials, J. Microwave Power, Vol. 11, No. 4, pp. 315-320, Dec. 1976.

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[29] J. R. Butts, J. E. Lewis, and F. R. Steward, Microwave heating of New Brunswick oil shale, J. Microwave Power, Vol. 18, No. 1, pp. 37-41, Mar. 1983. [30] N. Standish, H. Worner, and G. Gupta, Temperature distribution in microwave-heated iron ore-carbon composites, J. Microwave Power, Vol. 25, No. 2, pp. 75-80, 1990. [31] C. Shibata and H. Tamai, An improved microwave melting furnace for radioactive wastes, J. Microwave Power, Vol. 25, No. 2, pp. 81-87, 1990. [32] A. Wehr, C. George, and G. Lightsey, Solvent recovery by microwave radio-frequency processing, J. Microwave Power, Vol. 25, No. 2, pp. 100-103, 1990. [33] W. Wyslouzil and S. Kashyap, Single sided microwave applicators for sealing cartons, J. Microwave Power, Vol. 20, No. 4, pp. 267-273, 1985. [34] C. Gibson, I. Matthews, and A. Samuel, Microwave enhanced diffusion in polymeric materials, J. Microwave Power, Vol. 23, No. 1, pp. 17-28, 1988. [35] T. Hirose, I. Abe, M. Iwahashi, T. Suzuki, K. Oshima, and T. Okamura, Microwave heating of multi-layered cigarettes, J. Microwave Power, Vol. 13, No. 2, pp. 126-129, June 1978. [36] N. A. Heard, Microwave heating of bitumen in road delivery tanks, J. Microwave Power, Vol. 21, No. 2, pp. 76-78, 1986. [37] W. Sobiech, Microwave-vacuum drying of sliced parsley root, J. Microwave Power, Vol. 15, No. 3, pp. 143-154, Sept. 1980. [38] R. A. Wesley, D. W. Lyons, T. H. Garner, and W. E. Garner, Some effects of microwave drying on cottonseed, J. Microwave Power, Vol. 9, No. 4, pp. 329-340, Dec. 1974. [39] S. C. Kashyap and J. E. Lewis, Microwave processing of tree seeds, J. Microwave Power, Vol. 9, No. 2, pp. 97-107, June 1974. [40] J. A. Jolly and R. L. Tate, Douglas-fir tree seed germination enhancement using microwave energy, J. Microwave Power, Vol. 6, No. 2, pp. 125-130, July 1971. [41] G. E. Fanslow and R. A. Saul, Drying field corn with microwave power and unheated air, J. Microwave Power, Vol. 6, No. 3, pp. 229-235, Oct. 1971. [42] R. G. Bosisio, N. Barthakur, and J. Spooner, Microwave protection of a field crop against cold, J. Microwave Power, Vol. 5, No. 1, pp. 47-52, Mar. 1970. [43] R. G. Bosisio and N. Barthakur, Microwave protection of plants from cold, J. Microwave Power, Vol. 4, No. 3, pp. 190-193, Oct. 1969. [44] M. A. K. Hamid and R. J. Boulanger, A new method for the control of moisture and insect infestations of grain by microwave power, J. Microwave Power, Vol. 4, No. 1, pp. 11-18, Mar. 1969. [45] T. Hirose, I. Abe, M. Kohno, T. Suzuki, K. Oshima, and T. Okakura, The use of microwave heating to control insects in cigarette manufacture, J. Microwave Power, Vol. 10, No. 2, pp. 181-190, July 1975. [46] S. O. Nelson and J. A. Payne, Pecan weevil control by dielectric heating, J. Microwave Power, Vol. 17, No. 1, pp. 51-55, Mar. 1982. [47] C. P. Chiu, K. Tateishi, F. V. Kosikowski, and G. Armbruster, Microwave treatment of pasteurized milk, J. Microwave Power, Vol. 19, No. 4, pp. 279-282, Dec. 1984. [48] P. Chen, P. Schmidt, and M. Sanio, An exploratory study of microwave heating in drying of hardwood veneer, J. Microwave Power, Vol. 25, No. 1, pp. 53-59, 1990. [49] R. C. Vasishth and W. A. Cote, Microwave redry veneer, J. Microwave Power, Vol. 4, No. 3, pp. 158-161, Oct. 1969. [50] J. Wilson, Radio-frequency drying of wood veneer-commercial use, J. Microwave Power, Vol. 24, No. 2, pp. 67-73, 1989. [51] M. Norimoto and J. Bril, Wood bending using microwave heating, J. Microwave Power, Vol. 24, No. 4, pp. 203-212, 1989.

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[52] W. A. G. Voss, Microwave instruments for material control, J. Microwave Power, Vol. 4, No. 3, pp. 210-216, Oct. 1969. [53] A. Kraszewski, Microwave aquametrymA review, J. Microwave Power, Vol. 15, No. 4, pp. 209-220, Dec. 1980. [54] A. Kraszewski, S. Kulinski, and Z. Stosio, A preliminary study on microwave monitoring of moisture content in wheat, J. Microwave Power, Vol. 12, No. 3, pp. 241-251, Sept. 1977. [55] Y. Miyai, A new microwave moisture meter for grains, J. Microwave Power, Vol. 13, No. 2, pp. 163-166, June 1978. [56] A. Thansandote and J. Ponukkha, Shielded-open-coaxial-line and short-monopole reflection techniques for measuring moisture content of grain and peanuts, J. Microwave Power, Vol. 25, No. 4, pp. 195-201, 1990. [57] M. A. K. Hamid, Survey of radio frequency techniques for teledetection of soil moisture, J. Microwave Power, Vol. 8, No. 3, pp. 217-225, Nov. 1973. [58] A. Klein, Microwave determination of moisture in coal: Comparison of attenuation and phase measurement, J. Microwave Power, Vol. 16, Nos. 3/4, pp. 289-304, Dec. 1981. [59] N. Cutmore, D. Abernethy, and T. Evans, Microwave technique for the on-line determination of moisture in coal, J. Microwave Power, Vol. 24, No. 2, pp. 79-89, 1989. [60] B. L. Dalton, Microwave non-contact measurement and instrumentation in the steel industry, J. Microwave Power, Vol. 8, No. 3, pp. 235-244, Nov. 1973. [61] H. Soga, A new microwave thickness gauge, J. Microwave Power, Vol. 8, No. 3, pp. 253-266, Nov. 1973. [62] M. Tiuri and P. Liimatainen, A microwave method for measurement of fiber orientation in paper, J. Microwave Power, Vol. 10, No. 2, pp. 141-145, July 1975. [63] V. Prakash and J. A. Roberts, Perturbation of resonant microwave cavity by select alcohol vapors, J. Microwave Power, Vol. 4, No. 1, pp. 45-50, 1986. [64] M. Bramanti, A slot line microwave dielectric permittivity sensor for measure and control of laminated materials, J. Microwave Power, Vol. 26, No. 2, pp. 67-71, 1991. [65] J. Kurian, K. Jose, K. Balakrishnan, and K. Nair, Microwave non-destructive flaw/defect detection system for non-metallic media supported by microprocessor-based instrumentation, J. Microwave Power, Vol. 24, No. 2, pp. 74-78, 1989. [66] T. K. Ishii, Microwave sensing technique of surface hair-line cracks on fast moving objects, J. Microwave Power, Vol. 23, No. 3, pp. 176-182, 1988. [67] Alpha Industries, Inc., "Diodes, Modules, & MMICS," Publ. No. 50010010 R, pp. 5-15-5-40. Woburn, MA, 1990. [68] AM Sensors, Inc., "Microwave Sensors." Sale, NH, 1991. [69] M. I. Skolnik, Introduction to Radar Systems, 2nd Ed. New York: McGraw-Hill, 1980. [70] S. Haykin, An Introduction to Analog and Digital Communications. New York: John Wiley & Sons, 1989. [71] J. G. Proakis, Digital Communications. New York: McGraw-Hill, 1983. [72] W. Tomasi, Electronic Communications Systems. Englewood Cliffs, NJ: Prentice-Hall, 1988. [73] Miteq, Inc., "Signal Processing Components." Hauppauge, NY, 1991. [74] T. K. Ishii, Practical Microwave Electron Devices. San Diego: Academic Press, 1990. [75] T. K. Ishii, Microwave Engineering. Washington, DC: Technology Publications, 1989. [76] Avantek, Inc., "Modular and Oscillator Component," Data Book, 2nd Ed. Milpitas, CA, 1990. [77] Mini-Circuits, Inc., " R F / I F Signal Processing Guide." Brooklyn, NY, 1992.

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[78] I. Ahmad, R. Dalton, and D. Clark, Unique application of microwave energy to the processing of ceramic materials, J. Microwave Power Electromagn. Energy, Vol. 26, No. 3, pp. 128-138, 1991. [79] K. Khalid and Z. Abbas, A microstrip sensor for determination of harvesting time for oil palm fruits, J. Microwave Power Electromagn. Energy, Vol. 27, No. 1, pp. 3-10, 1992. [80] D. Patil, B. Mutsuddy, and R. Garard, Microwave reaction sintering of oxide ceramics, J. Microwave Power Electromagn. Energy, Vol. 27, No. 1, pp. 49-53, 1992. [81] P. Antony and F. Paoloni, Heating of Lossy films on a metal surface using a dielectric loaded T-septum waveguide, J. Microwave Power Electromagn. Energy, Vol. 27, No. 2, pp. 112-116, 1992. [82] T. Labuza and J. Meister, An alternate method for measuring the heating potential of microwave susceptor films, J. Microwave Power Electromagn. Energy, Vol. 27, No. 4, pp. 205-208, 1992. [83] A. Murphy, R. Morrow, and L. Besley, Combined radio-frequency and forced-air drying of alfalfa, J. Microwave Power Electromag. Energy, Vol. 27, No. 4, pp. 223-232, 1992. [84] U. Shivhare, V. Raghavan, R. Bosisio, and M. Giroux, Microwave drying of soybean at 2.45 GHz, J. Microwave Power Electromagn. Energy, Vol. 28, No. 1, pp. 11-17, 1993. [85] W. Tinga and W. Xi, Design of a new high-temperature dielectrometer system, J. Microwave Power Electromagn. Energy, Vol. 28, No. 2, pp. 93-103, 1993. [86] N. Cutmore, T. Evans, and A. McEwan, On-conveyor determination of moisture in coal, J. Microwave Power Electromagn. Energy, Vol. 26, No. 4, pp. 237-242, 1991. [87] G. Adams, Microwave blood plasma defroster, J. Microwave Power Electromagn. Energy, Vol. 26, No. 3, pp. 156-159, 1991. [88] G. Windgasse and L. Dauerman, Microwave treatment of hazardous wastes: Removal of volatile and semi-volatile organic contaminants from soil, J. Microwave Power Electromagn. Energy, Vol. 27, No. 1, pp. 23-32, 1992. [89] N. Zhu, L. Dauerman, H. Gu, and G. Windgasse, Microwave treatment of hazardous wastes: Remediation of soils contaminated by non-volatile organic chemicals like dioxins, J. Microwave Power Electromagn. Energy, Vol. 27, No. 1, pp. 54-61, 1992. [90] E. Sedhom, L. Dauerman, N. Ibrahim, and G. Windgasse, Microwave treatment of hazardous waste: "Fixation" of chromium in soil, J. Microwave Power Electromagn. Energy, Vol. 27, No. 2, pp. 81-86, 1992. [91] S. Nelson, K. Lawrence, and C. Kandala, Sensing moisture in peanut and pecan kernels by RF impedance measurements, J. Microwave Power Electromagn. Energy, Vol. 27, No. 3, pp. 171-174, 1992.

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CHAPTER

I I Biomedical Applications of Microwave Engineering Joseph H. Battocletti

I. Electrical Properties of Biological Materials Bulk electrical properties of biological materials are important to the thrust of this chapter for the following reasons: (1) quantification of exposure to nonionizing electromagnetic fields (EMFs); (2) determination of potential hazards of these EMFs; (3) explanation of diagnostic and therapeutic medical applications of EMFs; and (4) in nonmedical applications, such as food processing and agriculture, which include pasteurization, sterilization, drying, thawing, heating, and the application of insecticides. Bulk electrical properties of matter may be described in terms of four physical quantities. ~, magnetic permeability ( H / m ) , E, electric permittivity (F/m), ~r, conductivity (mho / m, or S / m), and p, resistivity (ohm-m). ~r and p are reciprocals of each other at low frequencies. The general

Handbook of Microwave Technology, Volume 2

309

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

310

Joseph H. Battocletti

definitions of these quantities arise from three field relationships of the familiar vector electric and magnetic field quantities. D=eE

( C / m 2)

(1)

J=o'E

( A / m 2)

(2)

B =/zn

( W b / m 2, or T).

(3)

For biological materials, /z is constant and equal to the permeability of free space (/z 0 = 4rr × 10 -7 H / m ) . However, due to dielectric polarization and relaxation processes, permittivity and conductivity vary with frequency. The complex relative dielectric constant is o"

gr = e' - jE" = e' - j

= E'(1 - j tan S),

(4)

a~E0 where e 0 is the permittivity of free space (107/4rrc 2 = 8.854 × 10 -12 F / m ) . The ratio e"/e' - tan S is called the "loss tangent." The frequency variation of Er of biological materials is very complicated because of the various ways by which water is bound to proteins and other molecules. Also, the coupling of the electromagnetic fields to the biological material affects the complex permittivity. In general, the complex relative dielectric constant may be represented by a sum of Debye functions. m~?i

g r - ' E ~ k- E i

f\ 1+j~ )

O"s

-j--, O~e0

(5)

where ~Xei = oJ(e s - eoo)Pi is the contribution for the ith Debye function, whose relaxation frequency is f~l. Coo and e s are relative dielectric constants at infinite and zero frequencies, respectively. ~rs is the conductivity at zero frequency, p~ is an amplitude factor. A good example of Equation (5) is the frequency variation of pure water. It has been found that the sum of two Debye functions of equal amplitude yields curves of e' and e" which very closely fit the experimental data [56], with the following values at 25°C: coo = 4.5, e s = 78.3, o"s = 0, f~l = 15.3 GHz, and f c 2 - - 25.2 GHz. ^

Es

-

= Er

E°°

+

2

E~

1

1 f + f 1 +J~cl 1 + Jr-72

crs -j--. ~°e°

(6)

311

II. Biomedical Applications

Equation (6) may be separated into real and imaginary components, yielding the following equations for relative dielectric constant and conductivity as a function of frequency. esS

-

eo~

1

1

e w = e~ +

f) 2+ 1+

f Cs - SE~ Orw

=

fc2

[ 1+

~ c2

f

fcl

O'S -q- ('OE0

(7)

2

2

at-

2

f

"

(8)

~ c1

Equations (7) and (8) are plotted in Figures 1 and 2, respectively, on a log frequency scale from 0.1 to 10 GHz. The loss tangent quantity is also

(/')(3 3E

=

0 ~-,

Ul

IIIII IIII IIIli ~°

LI3

0

,11•

LJ.~

c;

r.3

~

I1[111 IIIll[ It1111,/J/]llll...~

~1-

'Fill llllll lllllP/,/IIII!!~ llii iil[ll ii~/ nUBBin~° Jiili ~ °

°~_

~

(I2

"

=

~ ~ 03

oI.~_

Rel.

£ ie !.

IN~-.

'~11 I]111°"

"

-r"

~

tilll~ ~~" I]ii"

f_9

inuli~n

_.1 o!",1

......

~_~-o° iiil]ii Ill.... iii111\ "~ki11il ~ ,- ~ .~~ __1

to o

lo'

I0'

FREQUENCY ( 8ISFIHERTZ

Io ~

}

Figure I. Relative dielectric constant [Equation (7)], magnitude of impedance [Equation (13)], and relative wavelength [Equation (14)] as a function of frequency, for pure water.

312

Joseph H. Battocletti

/I

ii

II

E

:I

i,,-

/1

:i!

iW

"

, d,,,i;,!~

DeF ~h

i::

I

Z uJ

'_/

Z

__

I

i

r

m m l l II,', =.

~ngeJ t

IIP.lli m~r

-,,-o

aaron.,,

f d m m n u p,~iimmmm m u m • mR

© ._.1

I I1~i

ill

o T

F->

-'ll

IIl,d

0

/

i

IIiil

IIIlllo=

ill

Ill

Ill

a Z

o oe~ .-0

•

~

y!

-/i-" "1, -1

,-0

% "

toO

to 1

t0 2

tos"

FREQUENCY (GIGAHERTZ) Figure 2. Conductivity [Equation (8)], loss tangent, and skin depth [reciprocal of c~, Equation (11)] as a function of frequency, for pure water.

plotted in Figure 2. A log scale is used for conductivity and the loss tangent because of their wide variation. A Cole-Cole relationship [20, 56] which closely fits the experimental data has also been derived. It is a single-Debye function, but with ( f / f c ) (1-°~) in Equation (5), in which a = 0.014, e~ = 4.6, e s = 78.3, and fc = 19.7 GHz. For soft tissue, such as muscle, four distinct relaxation frequencies have been identified (Table 1). Figure 3 shows the variation of relative dielectric constant for muscle whose zero-frequency conductivity is 0.02 m h o / m (resistivity, 500 ohm-m). For the delta dispersion, f c 4 = 1.5 GHz and m E 4 --- 15 were chosen. (Figure 4 shows conductivity and loss tangent curves. Figures 3 and 4 are typical for many types of biological

313

II. Biomedical Applications TABLE I Typical Debye Parametric Values for Muscle Tissue

fc

AE

A~r (mho/m)

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substances. F i g u r e 6, in the next section, shows a g r a p h of e' a n d tr for several types of tissue for t h r e e f r e q u e n c i e s below 1 G H z , at which variation as a function of f r e q u e n c y is not very large.)

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314

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a,

Equation ( I I ) ] as a

Space does not permit the inclusion of tables of dielectric constant and conductivity for biological and other materials at various microwave frequencies. References which are identified by an asterisk ( , ) are excellent sources of this information in both table and graph form. The propagation constant, 3/, and wave impedance, Z, can be derived from basic relationships in wave theory.

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(10)

315

II. Biomedical Applications

Upon substituting for e r from Equation (4) and simplifying, a=

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where c is the velocity of light and Z 0 is the wave resistance of free space, equal to 377 ohm. The wavelength in the dissipative medium is given by 2rr//3. By using Equation (12) and substituting Ao for 27rc/o9 (the flee-space wavelength), the wavelength in the material is r

a = a0

~/E

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(14)

Because e' is usually much larger than unity for biological material, the wavelength and wave impedance are much smaller than the free-space values. The skin depth ( l / a ) is plotted in Figures 2 and 4 for water and tissue, respectively. The wavelength ratio (A/A 0) and magnitude of wave impedance (IZI) are plotted in Figs. (1) and (3). The conductivity-related curves for pure water and tissue were drawn to different scales and different axes because of the widely different values of conductivity, loss tangent, and skin depth between them. The loss tangent was better plotted on a linear scale for tissue, whereas a four-cycle log was best for pure water. Skin depth had to have five log cycles for water in spite of eliminating data below 0.125 GHz. These differences are attributed to assuming "zero" conductivity at "zero frequency" for pure water, whereas it is 0.02 m h o / m for tissue.

2. Heat Deposition in Biological Material, Particularly Man Exposure of biological material to electromagnetic fields is of three types depending on the distance, d, from the source of the field, the largest dimension, D, of the radiating source, and the wavelength (a).

Joseph I-I.

316

Battocletti

Far Field: Normal Radiation

The distance, d, is greater than 2D2/A. E and H are perpendicular to each other and to the direction of propagation, given by the vector, E × H. The field is radiative, comprising a plane wave whose power decreases inversely with d 2. E and H are related to each other by the intrinsic wave resistance, Z 0 - 377 ohm. Near Field: Inductive or Fresnel Region

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does not yield plane-wave radiation. Wave impedance varies with distance. Radiation decreases inversely with d 4 and d 6. Near Field: Quasistatic or Reactive

The distance, d, is less than A. Most often the E field or the H field predominates, depending on the nature of the source of the field. Although the space variation of the field may be complex, analysis is often made by assuming a uniform field. Only that part of the field which enters the biological material generates heat by eddy currents when the equivalent conductivity of the biological material is nonzero. The energy absorbed depends on many factors, such as the shape, size, orientation, and heterogeneity of the object, as well as the frequency and nature of the excitation source. The frequency of the incident field determines the properties of the conducting medium, as discussed in the previous section. Heterogeneity may lead to localized heating. Polarization relative to the orientation of the object, as well as the free-space and internal wavelengths relative to the size of the object (resonance effect), is a factor to be considered. Although resonance effects do not occur at microwave frequencies for the human body due to the very short wavelength, resonance of parts of the body may occur. The generally accepted measure of heat generation is the specific absorption ratio (SAR) [64]. SAR is defined as the "time derivative of the incremental energy (AW) absorbed by, or dissipated in, an incremental mass (AM) contained in the incremental volume (AV) of a given density (p)." In equation form it is d(AW) SAR = -~- - ~

1 d(AW) = P ~ -~

(W/kg),

(15)

317

II. Biomedical Applications

the entire mass of the object. Or it can be applied to a local region of the object, in which case AM is the mass of the selected AV volume. In the latter case, Or

SAR = ~plEI 2 ( W / k g ) ,

(16)

where IEI is the peak magnitude of the electric field in AV. The SAR figure can be measured in a smaller volume (animal) and extrapolated to a larger volume (man). The SARs for different-size objects are similar for a constant product of frequency ( f ) and dimension (L) of the object, i.e.,

fiLl =f2L2 .

(17)

Of course, this does not take into account the difference in the material properties at the two different frequencies. The SAR figure can be evaluated in closed form only for simple geometries, such as semi-infinite slabs, cylinders, spheres, prolate spheroids, and ellipsoids [41]. The development involves the solution of LaPlace's Equation by the method of separation of variables in a coordinate system natural to the geometry of the object [45]. Sometimes, a Schwarz-Christoffel transformation can yield a new geometry amenable to a usable coordinate system [35]. Although the closed-form solution of simple geometries yields qualitative insight into the location of heat generation, SAR must be determined by approximate analytical or experimental methods for real-life geometries. A second complicating factor is the necessity to consider the layered and heterogeneous nature of the object. The differing electrical properties of each layer or region often cause a peaking of the SAR inside the object. There is a large amount of literature which treats the many different models which have been used to assess the degree of deposition of heat in biological material caused by electromagnetic fields. For example, see a special issue on "Electromagnetic-Wave Interactions with Biological Systems" in the IEEE Transactions on Microwave Theory and Techniques, Vol. 32, No. 8, August 1984. Here, we will consider only full-scale human models. Models for mathematical analyses are constructed of a large number of blocks, slices, or both. The relative permittivity and conductivity of each block are selected to correspond to those of the tissue being modeled. Over a period of years, a full-scale heterogeneous model of a 162-cmtall man (Figure 5a) was developed by S. S. Stuchly et al. [66, 67]. It was

318

Joseph H. Battocletti

b

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(Run No. I) [59].

319

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FREOUENC't' (MEGFIHER'I'Z) Figure 6. Dielectric properties of four types of simulated tissue used in the experimental model of Figure 5c at three frequencies (I 60, 350, and 915 HHz). (a) Relative dielectric constant; (b) Conductivity, and (c) Skin depth [67].

constructed of the following: (a) 1-mm-thick fiberglass shell; (b) a simulated skeleton, comprising a skull, spinal cord, rib cage, and all major bones, except for those in the feet and hands, and fabricated from epoxy

320

Joseph H. Battocletti

and potassium chloride (KC1); (c) simulated brain, lung, and muscle, made from mixtures of hydroethyl cellulose, NaC1, and sucrose in such proportions to obtain the desired dielectric constant and conductivity (hollow silica microspheres were added to the lung mixture to simulate air passages); and (d) a semiliquid material having the dielectric properties of muscle. Measured dielectric constants and conductivities are plotted in Figure 6 for frequencies of 160, 350, and 915 MHz; these values fall within the range plotted in Figures 3 and 4 for muscle. Miniature triaxial electric field probes were placed at 38 locations inside the model to measure the electric field and thus the SAR from Equation (16). The locations are shown in a CT scan of the model (Figure 5b). A dipole antenna was positioned in front of the model and far enough away to generate approximate plane-wave radiation. It was oriented either vertically, i.e., parallel to the long dimension of the model (E-polarization), or horizontally (H-polarization). SAR values normalized to 1 m W / c m 2 of incident radiation are plotted in Figure 7 for locations along the central axis of the model ( A - A in Figure 5b), for all three frequencies, and both polarizations. The following are observed in Figure 7: (a) SAR values peak in the neck region, due to a smaller cross section with the accompanying higher current density; (b) SAR values are an order of magnitude less at 915 MHz than at 160 MHz; (c) SAR values for H-polarization are an order of magnitude less than those for E-polarization. Near-field SAR values were measured by M. A. Stuchly et al. [66, 67] in a similar experiment. The antenna was placed a small fraction of a wavelength in front of the model. Curves similar to those in Figure 7 were obtained; however, the SAR values were about one half as large, compared with far-field values, for the same incident power. The same heterogeneous model of man was used to obtain finer SAR measurements in the head, neck, and lung regions [59]. Measurement scans were made from back to front at 350 MHz for E-polarization. In addition, finite-difference time-domain analyses were made of a block model of 128,300 cubical cells. There were 8300 2-cm cubical cells for the body and 120,000 cells for the volume surrounding the body (Figure 5c). Boundary values of the variables computed for this model (called Run No. 1)were used in a finer-model analysis (called Run No. 2). Figure 8 shows the finer model which includes both the head and the neck regions. There was good agreement between the SAR values of the models and those of the experiment for the lung region and between the values obtained from the studies described above. However, measurement SAR values were generally larger than theoretical values for the head and neck regions. Experimental difficulties arose because of the simulated bone in the measurement path.

321

II. Biomedical Applications a

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322

Joseph H. Battocletti

Brain

Air

Brain

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Guy and Chou [26] obtained SAR values of about the same magnitude in homogeneous models of man, woman, and child. Material electrical parameters were E ' = 51 and ~r = 1.24 m h o / m at 916 MHz. Radiation was obtained from a mobile radio antenna at 835 MHz. Again, maximum SAR values occurred in the neck region. The Biomedical Engineering group at the University of Utah, Salt Lake City, has developed another type of full-scale man mathematical model for analysis using the F D T D method [68, 69]. The model is based on cross sections taken from the classic book by Eycleshymer and Schoemaker [18]. Whereas the book divided the torso into 24 horizontal layers, Sullivan et al. [69] divided the entire body (typically 175 cm tall and 70 kg) into a larger number of cross sections. Each layer was subdivided into cubical cells of one or more of 14 tissue types, each with its own E' and ~r values. Table 2 gives information for two models, one for 100 MHz and the other for 350 MHz. SAR values were calculated on the basis of a density of 1 g / c m 3. Maximum values occur in the narrow sections, such as the neck and ankles. At 350 MHz, maximum SAR values were 160 m W / k g for 1 m W / c m 2 incident power density. All the above examples are for frequencies below 1 GHz. Gandhi and Riazi [22] discuss biological implications of millimeter-wave absorption above 1 GHz, up to 300 GHz. For tissue (see Figures 3 and 4), conductivity increases rapidly in this range, whereas the dielectric constant and skin

323

II. Biomedical Applications TABLE 2 Full-Scale Man Model Parameters for Two Different Frequencies (Biomedical Engineering Group, University of Utah) Item Number of layers Number of tissue cells Cube cell size (cm) Total number of cells (including air)

100 MHz

350 MHz

68 5,889 2.62 23 x 12 x 68 = 18,768

135 40,067 1.31 45 x 24 x 135 = 144,800

depth decrease rapidly. Consequently, most of the heat deposition (largest SAR values) occurs in the skin; thus, there may be thermal sensations similar to those caused by far-infrared radiation (,~ > 3 ~), since heatsensing nerve endings are distributed at depths from 0.1 to 1 ram. Gandhi and Riazi calculated SAR values greater than 15,000 m W / k g for an incident power of 1 m W / c m 2. They state that the threshold of heat perception occurred for incident power of 0.6 m W / c m 2, and sensations of "very warm to hot," at 8.7 m W / c m 2. The cornea of the eye is of particular and continuing concern at millimeter wavelengths as has been true for all microwaves in the past [4, 42]. Paulsen et al. [93] developed three-dimensional finite element analysis (3DFEA) techniques to calculate SAR in anatomically based human models, derived from CT scans. The formulations center on Helmholtz weak forms. With proper choice of algorithms and preconditioning, reliable convergence of the solution was achieved for matrix ranks of 200,000. Reduced instruction set computer (RISC)workstations were used; run times were on the order of hours.

3. Exposure Guides and Standards Concern over the potential deleterious effects of microwave radiation on man did not reach a critical stage until over 10 years after the end of World War II. The invention and use of high-power radar may have first led to occurrences of cataracts in radar operators and repairmen, even though an early study did not find any changes in the eyes of 45 military radar operators [14]. The first identification of cataracts in radar workers was not reported until 9 years later [28]. In subsequent studies, although some possible occurrences of cataracts may have been identified, more often subjects showed no ocular effects from normal activity in the vicinity of radar and other radiation sources [4].

324

Joseph H. Battocletti

The first exposure standard to gain widespread usage was formulated in 1957 at the Tri-Service Conference by the U.S. Armed Forces. This and subsequent standards and guides are listed and briefly described below with some commentary. For details regarding the more recent standards in the United States and in other countries, see Polk and Postow [49] and Stuchly [65]. The first four standards were applicable to the entire frequency spectrum [70]. Gradually, time duration of exposure was introduced. 1. The Tri-Service Conference (1957), sponsored by the U.S. Army, Navy, and Air Force, stated that the incident power density should be less than 10 m W / c m 2. 2. The Bell Telephone Laboratories (1960) stated that for indefinite exposure, the incident power density should not be more than 1 m W / c m 2. For incidental, occasional, or casual exposure, this level could be increased to 10 m W / c m 2. 3. The U.S. Army and Air Force specified a variable incident power density, P (mW/cm2), dependent on the exposure time, T, in minutes per hour of exposure. The following equation for this condition is applicable up to 55 m W / c m 2, since a minimum of 2 m i n / 1 h of exposure is considered to be practicable, T = 6000/P 2 (minutes per hour of exposure).

(18a)

For continuous exposure, T = 60 m i n / h ; so P = 10 m W / c m 2. 4. The U.S.A. Standards Institute (1966) Standard C95.1 set a limit similar to that of Equation (18a), but expressed the time of exposure averaged over 0.1 h. One form of the equation is T = 60/P

(minutes per 6 min of exposure).

(18b)

For continuous exposure, T = 6 m i n / 6 min; so P = 10 m W / c m 2. In addition, it was stated that this standard could be relaxed at extreme cold temperatures, but should be more severe for moderate-to-severe heat stress. 5. The research outlined in Section 2 led to the introduction of a variable incident power density as a function of frequency. For example, Figure 7 shows that SAR values are frequency dependent. Several Eastern European countries had already introduced frequency dependence into .

.

.

.

325

II. Biomedical Applications

their standards at the time the American National Standards Institute (ANSI) C95.1-1982 Standard was published [4]. The C95.1-1982 Standard is based on metabolic rates in humans and on a typical-size man weighing 70 kg and having 1.9 m 2 of surface area. Basal metabolic rates (BMR) of various organs and conditions are given in Table 3 [71]. More specifically, this standard is based on a whole body SAR of 0.4 W / k g , which is one tenth of what is considered to be a hazardous level. The frequency variation of incident power density (P), electric field intensity (E), and magnetic field intensity ( H ) is plotted in Figure 9. The ratio, E/H, in this Standard is 400 ohm; the ratio of E/H of a plane wave in free space is 377 ohm. The ANSI C95.1-1982 Standard is applicable for the general public and the workplace. The guidelines may be exceeded if the SAR does not exceed 0.4 W / k g . Time of exposure per 6 min is determined by Equation (18b). 6. Since the above-mentioned standards were not regulatory, being voluntary and advisory, several political entities in the United States passed laws, usually more stringent the ANSI C95.1-1982. The State of Massachusetts ad Multnomah County (Oregon) mandated a maximum SAR of 0.08 W / k g ; the State of Connecticut chose the ANSI standard; New York City ordered a maximum SAR of 0.02 W / k g [17]. 7. Reports and proposals proliferated in the 1980s by various organizations [17], such as the World Health Organization (1982), National

TABLE 3 Basal Metabolic Rates of Humans (W/kg) Averaged over whole body (sleeping) Skeletal muscle Skin Heart muscle Brain Kidney Liver Diathermy equivalent Young men in heat stress studies Noticeable to most individuals, primarily in the skin and skeletal muscle Theoretical values, assuming no thermoregulation Raise muscle 0.00024°C / s Raise muscle 1.5°C Raise head core temperature 0.2°C

1.05 0.7 1 33 11 20 6.7 50 5 1 1 1.4 1.4

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II. Biomedical Applications

327

Institute for Occupational Safety and Health (1985), Environmental Protection Agency (1986), National Council on Radiation Protection and Measurement (1986), and Committee on Interagency Radiation Research and Policy Coordination (1986). 8. In 1987, the International Non-Ionizing Radiation Committee (INIRC) of the International Radiation Protection Association (IRPA) approved guidelines for both occupational and general public exposure limits. The occupational standard is based on a maximum S A R of 0.4 W / k g , but for the general public was reduced to 0.08 W / k g . Graphs of both standards are plotted in Figure 10 [2]. 9. The ANSI exposure standard of 1982 was revised by the IEEE Accredited Standards Committee No. 28 on Non-Ionizing Radiation Hazards to include guidelines on RF-pulsed power. The new guideline, C95.1-1991, covers exposure to both RF-pulse trains and single pulses. It includes the frequency range from 3 to 100 kHz and divides the balance of the frequency spectrum (up to 300 GHz) into seven frequency ranges. The new standard covers exposure criteria for both controlled and uncontrolled environments [30]. The graph is not very different from that in Figure 10.

4. Microwave Hyperthermia for Cancer Treatment Although not routinely used clinically at the present time, probably the most important and widely known application of microwave energy in medicine is cancer treatment by means of localized hyperthermia. This therapeutic technique involves the use of elevated temperatures in the 42 to 50°C range to hasten the destruction of cancerous tissue. At the elevated temperature, cells lose their ability to divide. However, the temperature limit for healthy tissue is 45°C due to pain and toxicity for the patient [79]. Review articles, with many references, were published by Cheung and A1-Atrash [13], Steeves [81], and Field and Hand [82]. Hyperthermia is often more effective when used in combination with another method of anticancer therapy, such as radiation or drugs. The combination effects may be additive, multiplicative, or complementary. An example of multiplicative effects is that after 1000 rad of X-ray radiation 100 of 10,000 cells survive, whereas only 1 of 10,000 survive when heat is added. An example of complementarity is that hypoxic cells are largely immune to X-ray radiation, whereas heat is equally efficient on both hypoxic and oxygenated cells. The combination of heat and chemotherapy or electrontherapy is additive [83].

328

Joseph H. Battocletti

Three parameters of critical importance in hyperthermia are temperature, time, and focusing of heat. Focusing is dependent on the type of applicator used and will be discussed later in this section. Desirable temperature and time relationships depend on physical and physiological characteristics of the cancerous tissue. For example, for therapeutic effect on a tumor, the period of heating at 42°C should be 45 min. It is important that heating be rapid and that the temperature distribution over the region of the cancerous tissue be as uniform as possible. For microwave heating, this requires that the local SAR be sufficiently large to compensate for thermal dissipation due to both heat conduction and blood perfusion. Hahn [27] identifies two thermal-time effects: Step-down heating: if cells are exposed to 43°C or higher for a short

time, the cells are much more susceptible to subsequent exposure below 43°C. Thermotolerance" if cells are exposed to mild heat or to slow heating. during patient setup, the cells become resistant when later exposed to 43°C or higher.

The Bioheat Equation A general form of the bioheat equation for the approximate modeling of the heating process in tissue is (e.g., [62]) OT

ptCt Ot (storage)

=

kcV2T (conduction)

- P b C b P t m ( T - Tb) + Q ( x , y , z , t ) (perfusion)

(deposition)

+

Wm

,

(metabolism)

(19) where each term is identified according to its action in the heating process. The individual parameters in Equation (19) are defined as follows: Pt, tissue density (kg/m3); ct, specific heat of tissue ( W . s / k g / ° C ) [PtCt = 2 × 10 6 to 4 × 10 6 W" s / m 3 / ° C for various tissue]; Pb, blood density (kg/m3); Cb, specific heat of blood ( W . s / k g / ° C ) ; k c, thermal conductivity of tissue ( W / m / ° C ) , 0.20 to 0.64; m, volumetric flow rate of blood per unit mass of tissue (m3/kg/s); Tb, temperature of the blood entering the region (°C); Q ( x , y, z, t), power absorbed from the impinging M-field per unit volume of tissue (W/kg3), cr[E(x, y, z, t)[2;

II. Biomedical Applications

329

Wm, power generated by metabolism per unit volume of tissue ( W / kg3); and I~72T, Laplacian of the temperature, T. Except for highly vascularized regions, the conduction term is much larger than the perfusion term. The conduction term also governs the time constant of the system, i.e., the time from onset of Q(x, y, z, t) to the steady state. Knudsen and Overgaard [34] solved Equation (19) as the one-dimension model of a semi-infinite homogeneous volume of tissue. They also applied surface cooling by means of circulating water in a plastic bag. This adds another term to the right-hand side of Equation (19), involving a heat transfer coefficient between the cooling water and the tissue. They showed that, by balancing the heat, Q(z, t), deposited by a plane wave traveling into the medium (z-direction)with cooling by all methods, the temperature could be maximized at a prescribed distance, z, below the surface. Strohbehn et al. [60] solved Equation (19) in polar coordinates, approximately applicable to a cylindrical model in which there is no temperature variation in the z-direction. Their model used N identical antennas equally spaced around the circumference of the cylinder. Isotherms were calculated for various conditions: (a) time following the onset of power deposition, (b) blood flow, (c) frequency of the plane wave, (d) number of antennas, and (e) electrical tissue characteristics, i.e., different types of tissue. The following results of the numerical analysis were obtained. (a) Four antennas excited at a frequency of 1 GHz were used to excite a 2.828-cm-diameter cylinder simulating skeletal muscle (e = 50, ~r = 1.3 m h o / m , Pt 1000 k g / m 3, c t = 3500 W . s / k g / ° C , and k c = 0.63 W / m / ° C ) , with a resting blood flow of 2.7 m l / 1 0 0 g / m i n = 0.45 × 10 -6 m S / k g / s . Therapeutic temperatures were obtained over a large portion of the cylinder after 15 min. (b) As blood flow was increased (e.g., by exercise), therapeutic temperatures were obtained only in the immediate vicinity of the antennas. Externally, cooling is often used to reduce the heating near the antennas [34]. (c) Excitation at 1 GHz gave the best hyperthermia for the multiantenna array for the 2.828-cm-diameter cylinder. (d) The uniformity of hyperthermia is improved as the number of antennas in the array is increased. (e) The region of therapeutic heating of tissue depends on the properties of the tissue. With skeletal muscle considered "unity," the volumes of =

330

JosephH. Battocletti

therapeutic heating of brain tissue and fat obtained in a four-antenna array are given in the following table.

Skeletal muscle Brain tissue Fat

e

tr (mho/ m)

Volume ratio

50 42 5.6

1.3 0.9 0.085

1.00 1.44 1.74

Mechling and Strohbehn [86, 87] solved the bioheat transfer equation for three-dimensional steady-state temperature distributions using a finite element method. Homogeneous and nonhomogeneous blood flow models were considered at 915 and 2140 MHz. Applicators

The majority of hyperthermia equipment for the cancer clinic has been of the "magnetic inductive" type, operating at frequencies around and below 100 MHz. Oleson [47] reviewed clinical applications prior to 1984. Most of the systems involved simple coils. One such system is the Magnetrode [61], developed by Henry Medical Electronics (Los Angeles, CA). A one-turn coil formed from a single sheet of copper was excited at 13.56 MHz. In another type, the CDRH Helix-I (Center for Devices and Radiological Health, FDA), the coil acts as a double-wavelength resonant device, operating at about 82 MHz ([25, 50]). A second type of sub-100-MHz applicator is the "annular phased array" (AA or APA). An example is an octagonal structure with 16 apertures, developed by BSD Medical Corporation (Salt Lake City, UT) [24, 61, 76, 77, 85]. Of the higher frequency hyperthermia applicators, the Interstitial Microwave Antenna Array (IMMA) is probably the one which fulfills the requirement of focusing the microwave radiation in the tumor [58]. The first type of IMMA which had practical clinical usage was four individual dipole antennas located at the corners of a square, typically 2 cm on a side [43, 79]. Each was inserted into the diseased tissue through an individual catheter. The antenna is made of coaxial cable, in which the outside portion of the end is detached. Figure l la shows a simple probe [43, 80]. This simple arrangement is not very efficient, having a cold zone near the tip, so that the probe must be inserted beyond the tumor. A better design was suggested by Turner [78] and is shown in Figure llb. Lyons et al. [43] used 915 MHz (A 0 = 32.8 cm), Winter et al. [79] used 2450 MHz (A 0 = 12.2 cm), and Turner [78] used 640 MHz (A 0 = 46.9 cm) for their applicator systems.

331

II. Biomedical Applications Metal Collar

Plastic Catheter

Outside Conductor

on

Center Conductor

I

]

b Metal Collar Metal Tube

I

l

Metal Collar

Outer Conductor

....

Center Conductor and Insulator

c

Pang Sl~

Coaxial Cable

Figure II. Three types of probes for interstitial microwave hyperthermia. (a) Simple end-loaded coaxial, showing the catheter; (b) an improved design used at frequencies up to 2450 MHz in a four-antenna phased array; and (c) a "ring-slot" probe proposed by Terakawa et al. [72].

Another design, the "ring-slot" applicator (Figure llc), has been proposed by Terakawa et al. [72]. A typical configuration, however, had a cool spot in front of the tip similar to those of the other two probes. Terakawa et al. proposed an equivalent circuit model, which might enable one to design a more efficient applicator. Driving the four antennas simultaneously and coherently yielded the most efficient operation. Although tuning each antenna produced maximum output at the antenna, it also produced unequal phase shifts which reduced the total power deposited in the tissue [80]. A better strategy is to design the antennas to match 50 ohm as closely as possible and then to use attenuators before the antennas to maintain the match. Of course, the effect of the tissue electrical properties must be taken into account in the tuning process. Typical clinical evaluations of the effectiveness of combined hyperthermia and radiation therapy in head and neck tumors are given by Seegenschmiedt et al. [58, 88]. Work is commencing on microwave waveguide applicators [89], in which beam shaping is accomplished by using absorbing saline/gelatin pad boluses. These pads could be designed to yield a uniform heating pattern over a large area or, alternatively, to generate complex heating patterns for specific clinical applications. In a different approach, a multiapplicator array is set up inside a large rectangular waveguide, operating below its cutoff frequency [94]. The human torso is positioned so that it acts as a post inside the waveguide.

332

Joseph H. Battocletti

5. Microwave Monitoring, Imaging, and Sensing Microwave radiation and detection techniques are being developed for the monitoring, imaging, and sensing of biological and physiological function of the human body. Although most of these techniques are being implemented with the transmitting antenna in contact with the body, remote sensing at a distance, even from behind a barrier, has also been accomplished. Some of the applications, which may have overlapping features, are related to the following: (a) (b) (c) (d) (e) (f) (g) (h) (i)

lung water [31], pulsatile blood flow [48], remote life detection [11], thermography or radiometry [37, 90], thermal imaging [7], permittivity imaging [23], breast cancer detection [16], neuronal activity in the brain [29], and cerebral blood flow [21].

Only several of the applications are discussed below, since most of them are based on similar principles and circuitry. Some applications use separate transmitter and receiver systems, whereas others use the same antenna for both transmitting and receiving. For the latter, interferometric techniques are used to obtain the desired information. In these cases, active sources are used. In some radiometric thermographic applications, detection is passive; i.e., the antenna or antenna array detects the electromagnetic energy naturally radiated by the object being scanned. The applications listed above are based on one of three parameters: (1) motion, (2) temperature, and (3) material variability. An example is given for each parameter.

One-Antenna, Active Sensing, Remote Life Detection An example of a one-antenna, active sensing system is described by Chen et al. [11]. They showed an X-band remote life-detection system, which

could detect slight movements of a living being, including respiration and heart beat. It is an interferometric system utilizing phase shift differences to obtain a signal caused by the motion. "Clutter" was canceled by subtracting some of the power applied to the antenna, properly attenuated and phase shifted, from the total signal picked up by the antenna, as

333

II. Biomedical Applications 10 GHZ SIGNAL SOURCE

J

~mTTERI_

VAR.

-i t

7-7 1

Pkl"

-~ERl

1

3a

j VAR. PHASE _[ - [ ATTEN. " " - " ~ SHIFTER - ~ ' ~

l

NA BODYTO BE SCANNED

] ~ o

II

CLUTTER REMOVALCIRCUIT I 10 GHZ SIGNAL SCATTERED FROM OBJECT

10 GHZ REFERENCE

iwRi J°oue-I I I!'

ATTEN I

--I

BALANCED ~ MIXER

,,PRE AMF

1

BASE-BAND SIGNAL

Figure 12. Block diagram of a Microwave Remote Life Detection System using an active single antenna [11]. It senses motion, even from behind physical barriers.

shown in Figure 12, a simplified block diagram of the life-detection system. Clutter has to be random to be cancelable; other moving objects, such as trees and bushes, will deteriorate the signal from the living being. The operation of the system is independent of the polarization of the radiation, and clothing has no effect. Lin [91] reviews the subject of noninvasive detection and monitoring of movement of tissue and organs from outside the body. One-Antenna, Passive Scanning, Thermography or Radiometry All warm objects radiate electromagnetic energy according to Planck's black-body radiation formula, E(u,T)

-

2h u 3 du C2 e h , , / k r _ 1 '

(20)

where E is the energy per unit volume between v and v + d~, (j/m3); h is the Planck's constant, 6.626 x 10 -34 J/s; c is the velocity of light, 2.997925 x 108 m / s ; k is the Boltzmann's constant, 1.38 x 10 -23 J / K ; T is the temperature (K); and u is the frequency (Hz). [Some books and articles use obsolete units and consequently have 8 r c h / c 3 as the factor in Equation (20).] A graph of E / E m a x as a function of frequency at a body temperature of 37°C is given by the solid curve in

334

Joseph H. Battocletti

Q W -t-

(x)

/I

z w

D

°

/ ,

,--

' , // /

// I I

~

/

-

/

"

i /

oo

i0 °

\\ 101

10 2

FREOUENCY ( 818RHERTZ I Figure 13. Normal Planck's black-body radiation spectrum (solid curve) at a temperature of 37°C. The dashed curve is the relative sensitivity from muscle tissue, using the "skin depth" curve of Figure 4. The normal emissivity of the muscle is assumed to be constant over the frequency range.

Figure 13. Note that maximum radiation occurs at about 18 GHz, with one-half energy points at 7.4 and 35 GHz. However, when temperature below the surface of the tissue is to be measured, the solid curve of Figure 13 must be combined with the frequency-dependent attenuation constant, a, and normal emissivity of the tissue. (Normal emissivity is determined by the physical properties of the tissue surface.) The effect of the tissue is taken into account by employing the truism, "a good radiator is also a good absorber." Therefore, the tissue which absorbs microwaves the best is the best radiator. Consequently, the tissue which has the larger a is the better radiator. For example, assuming that the normal emissivity is not frequency dependent, when a, the reciprocal of the "skin depth" curve of Figure 4 for muscle tissue, is combined with Equation (20), the overall relative sensitivity is given by the dashed curve in Figure 13. The optimum

335

II. Biomedical Applications

sensitivity now occurs at about 25 GHz, with half-energy points at 14.5 and 45 GHz. These frequencies will vary for different tissues, since the attenuation constant varies differently with frequency for different tissue, as seen in earlier parts of this chapter. The attenuation constant, c~, of the tissue affects the overall emissivity of the radiating object, as already described. Carr [9] showed relative experiment emissivities of various materials including muscle and bone phantoms, saline, and water at 4.76 GHz. He pointed out that the emissivity of muscle, with a larger a, is much greater than that of bone. In the application of the black-body radiation phenomenon to microwave thermography, the inverse problem has to be solved. Through the measurement of radiated microwave energy, W(v), from a "warm body," the temperature, or temperature distribution a(T), of the warm body is to be determined uniquely. The radiation power spectrum is given by the equation, 2hv 3 ,.~ a( T) dT W ( v ) - C2 [Jo eTgvTiT5-i"

(21)

Many papers have been written on the subject of inversion of the blackbody problem, including Bojarski [6], Bevensee [5], and Chen and Li [12]. Solutions generally involve the use of the inverse LaPlace transform. Invariably the data which are obtained by W(v) are insufficient to obtain a(T)precisely [5]. To provide medically useful information, however, microwave thermography must have a temperature resolution of about 0.1°C [37]. Direct temperature measurement cannot meet this requirement. But, the requirement can be met by (a) measuring only differences in temperature and (b) using a Dicke-type comparison radiometer, in which the radiation signal is compared with a known thermal noise signal whose temperature is close to the temperature to be measured. A simplified functional block diagram of a microwave radiometer is shown in Figure 14. The temperature resolution, AT, is given by the equation [37]

Q ( Tref nt- Lig ) AT =

BvrB _

,

(22)

where Q is the radiometer constant whose value lies in the range of 4.6 to 6.6, Tre f and Tsig are the reference and signal temperatures, B is the receiver bandwidth (Hz), and r is the response time of the postdetection filter. Frequently, a commercial lock-in amplifier is used as the coherent detector in Figure 14; the filtering takes place in its postdetector filter. For

336

Joseph H. Battocletti LOW-FREQ. (1O0HZ) SWITCHER I I I

'

~h~ II "

Tso L o~RCE. ..... T,.o~IIn

J MICROWAVEH " 1 RECEIVER

BANDPASS H FILTER

DETECTOR& H LFAMPL.

l

COHERENT ~ DETECTOR

1

i 'OST-° FILTERT. I

1

RADIOMETER OUTPUT (Tref-Tsig)

Figure 14. Functional block diagram of a Microwave Thermography System using a passive single antenna. The Dicke-type comparison radiometer is used to obtain a temperature resolution on the order of 0. I°C.

example, for Q = 5.6, Tre f = 293 K, Zsig = 310 K, BW = 500 MHz, and ~- = 2 s, AT is calculated to be 0.107 K. Three examples of the use of the microwave thermograph follow. 1. Abdul-Razzak et al. [1] described a scanning microwave thermograph operating in the range of 9 to 10 GHz. An 80- x80-cm area was sampled to give a 64- x 64- x 4-bit image. With an integration time of 0.1 s, the time of the scan was 6.5 min. The antenna was located about 1 m from the subject. This system has been applied in a vascular surgery department to determine the best location for amputation of lower limbs. 2. Carr et al. [10] developed a dual-mode microwave system that combined an active transmitter for localized heating at 1.6 GHz and a passive microwave radiometer at 4.7 GHz. Carr [9] described a similar radiometer. A small-size antenna was placed in contact with the subject. The active transmitter, which provided localized heating, enhanced the early detection of cancer. The radiometer was also used in a study of 61 human volunteers for the following conditions: a. variation of temperature due to the menstrual period in women; b. changes of thermal patterns with age; and c. bilateral thermal symmetry between left and right breasts in women. 3. Land [37] built and tested a compact clinical microwave thermography system at 3 GHz. The antenna was placed in contact with the skin of

II. Biomedical Applications

337

the subject. Temperature profiles have been taken of the following situations: a. across the left and right breasts to verify the presence of a 1.5-cm-diameter carcinoma; b. across the left and right knee joints to show rheumatoid arthritis; and c. across the lower anterior abdominal wall to show the presence of an inflamed appendix. One problem which has been encountered in the design of microwave radiometers for biomedical applications is impedance matching between the antenna and the tissue. Remote measurement (e.g., Abdul-Razzak et al. [1]) is not as good as contact measurement. Land [37] used a low-loss dielectric loaded TEll-mode circular waveguide with a broadband fin-line transition to a coaxial cable. Carr [9] used a simple TEl0 mode with dielectric loading to reduce the antenna's physical size. In studying the sensitivity of microwave radiometry, Cheever and Foster [92] used a dielectric-loaded waveguide antenna in contact with a lossy dielectric.

Two-Antenna, Microwave Imaging The dielectric properties of biological tissue have been measured, in vivo, by means of characteristics of a transmission line. Some of asterisks [ , ] in front of them describe and specifically, refer to the following.

at microwave frequencies the tissue's effect on the the references which have use this technique. More

a. Stuchly et al. [63] used an 8.3-mm Teflon-filled open-ended coaxial transmission line, described by Athey et al. [3], to measure various tissue in a cat up to 1 GHz. b. Kraszewski et al. [36] used an open-ended 3.6-mm Teflon-filled coaxial transmission line up to 8 GHz, also in a cat. c. Burdette et al. [8] used a 2.2-mm coaxial probe at 2.45 GHz to measure permittivity in the brain (both gray and white matter) of dogs. d. Thansandote et al. [73] used an interferometer system with a horn antenna at the end of the X-band waveguide to monitor biological impedance qualitatively at 9.3 GHz. These efforts led to the idea of performing microwave imaging of intact biological systems [32, 38]. See also the publication Medical Applications of Microwave Imaging, edited by Larsen and Jacobi [39].

338

Joseph H. Battocletti

In computed tomography (CT) using soft X rays, the scanning beam is collimated, so that its scattering is well defined. On the other hand, the electromagnetic radiation used in microwave imaging has a finite beam width and a diverging wavefront, resulting in complex diffraction, interference, and scattering patterns. This characteristic of microwave radiation has led to poor results in the images obtained so far, primarily because the same kind of reconstruction algorithms [algebraic reconstruction technique (ART)] used in X-ray CT were employed. This problem has been magnified by the use of the Born approximation, which assumes that scattering acts as only a small perturbation on the illumination, so that the field within the body is approximated by the incident field. This approximation breaks down in biological bodies due to their high contrast characteristics and large size compared with those of wavelength [33]. Datta and Bandyopadhyay [15] have suggested an improved algorithm, called the "simultaneous iterative reconstruction technique (SIRT)"; however, they concede that further work is needed to obtain a more refined algorithm. Resolution is also a problem, since it is approximately equal to one wavelength (inside the tissue); this problem is not as great as it could be since the wavelength in tissue is a fraction of the flee-space wavelength, '~0 [see Figures 1 and 3, and Equation (14)]. However, the wavelength is different in the various organs of the body. Spatial resolution is improved by immersing the body to be imaged in a medium of deionized water. The cylindrical imaging system described here was built and tested by Jofre et al. [33]; both absolute and differential images of tissue-simulating phantoms and of the arms of human volunteers were obtained. A functional block diagram is shown in Figure 15. Each of the 64 water-loaded waveguide antennas is flared in the E-plane to form a sectorial horn, 2.5 cm high by 2.5 cm long. The radiated field is approximated 2 cm high in the vertical plane of the cylinder. The H-plane is nearly omnidirectional, since it is not flared. In operation, one of the 64 horns serves as the emitter, and 32 horns opposite it on the cylinder wall are scanned sequentially. This is repeated 64 times; the measurement time is 3 s for human tests and 45 s for arm and head phantoms, to obtain better resolution. The following results were obtained. 1. In tests on the human arm, the resolution was much better for the imaginary part of the complex permittivity; the real part was unsatisfactory, which was attributed to the limitations of the Born approximation. 2. The resolution of temperature in water flowing through a 3-cm-i.d. rubber tube was 0.5°C.

339

II. Biomedical Applications

i S

WM POWER

OSC.

|

1 waet:

AMPLIFIER~

I A CR

I IX N G H

Referenae

I/Q

DET I~

~Q |

-

TWIN

[

SYNCHR ~ _ ~ ~ E DATAOUTPUT DETECTO~I (MAGNITUDEAND PHASE)

Figure 15. Functional block diagram of a Microwave Imaging System using two sets of antennas in a cylindrical model. Best results are obtained when the object imaged is immersed in water.

3. The changing blood flow in the human arm, in a cuffing-release experiment, was imaged in the differential mode. The sequence of images as a function of time showed both the storage of blood in the vascular system distal to the location of the cuff and the outflow at the release of the cuff. The reference image was that of result No. 1. 4. Differential imaging of a phantom head was performed to show changes within the brain, such as simulation of a hemorrhage. The reference was an image obtained by the reconstruction numerically simulated data. Changes of 1% were detectable. Jofre's system is limited in its application because the object must be immersed in water to provide impedance matching between the antennas and the object. Larsen and Jacobi [38] showed that spatial resolution could be improved by a factor of 9 when water immersion was used.

340

JosephH. Battocletti

Acknowledgments This work was supported in part by the Department of Veterans' Affairs Medical Center Research Funds and by the Department of Neurosurgery, Medical College of Wisconsin, Milwaukee, Wisconsin. Appreciation is extended to the Computing Center at Marquette University for the constant availability of its VAX cluster for the data analysis and graph generation used to prepare this chapter.

References [1] M. M. Abdul-Razzak, B. A. Hardwick, G. L. Hey-Shipton, P. A. Matthews, J. R. T. Monson, and R. C. Kester, Microwave thermography for medical applications, lEE Proc., Part A, Vol. 134, No. 2, pp. 171-174, 1987. [2] Anonymous, Guidelines on limits of exposure to radiofrequency electromagnetic fields in the frequency range from 100 kHz to 300 GHz, Health Phys., Vol. 54, No. 1, pp. 115-123, 1988. [3] T. W. Athey, M. A. Stuchly, and S. S. Stuchly, Measurement of radio frequency permittivity of biological tissue with an open-ended coaxial line: Part I, IEEE Trans. Microwave Theory Tech., Vol. MTT-30, No. 1, pp. 82-86, 1982. [4] J. H. Battocletti, Electromagnetism, Man and the Environment, Table 4.1, pp. 50-53. London: Paul Elek, 1976. [5] R. M. Bevensee, Comments on recent solutions to the inverse black-body radiation problem, IEEE Trans. Antennas Propag., Vol. AP-37, No. 12, pp. 1635-1638, 1989. [6] N. N. Bojarski, Closed form approximation to the inverse black body radiation problem, IEEE Trans. Antennas Propag., Vol. AP-32, No. 4, pp. 415-418, 1984. [7] J. C. Bolomey, L. Jofre, and G. Peronnet, On the possible use of microwave-active imaging for remote thermal sensing, IEEE Trans. Microwave Theory Tech., Vol. MTT-31, No. 9, pp. 777-781, 1983. *[8] E. C. Burdette, P. G. Friederich, R. L. Seaman, and L. E. Larsen, In situ permittivity of canine brain: Regional variations and post mortem changes, IEEE Trans. Microwave Theory Tech., Vol. MTT-34, pp. 38-50, 1986. [9] K. L. Carr, Thermography, in Encyclopedia of Medical Devices and Instrumentation (J. G. Webster, ed.), Vol. 4, pp. 2746-2759. New York: John Wiley & Sons, 1988. [10] K. L. Carr, A. M. El-Mahdi, and J. Shaeffer, Dual-mode microwave system to enhance early detection of cancer, IEEE Trans. Microwave Theory Tech., Vol. MTT-29, No. 3, pp. 256-260, 1981. [11] K.-M. Chen, D. Misra, H. Wang, H.-R. Chuang, and E. Postow, An X-band microwave life-detection system, IEEE Trans. Biomed. Eng., Vol. BME-33, No. 7, pp. 697-701, 1986. [12] N.-X. Chen and G.-Y. Li, Theoretical investigation on the inverse black body radiation problem, IEEE Trans. Antennas Propag., Vol. AP-38, No. 8, pp. 1287-1290, 1990. [13] A. Y. Cheung and J. AI-Atrash, Microwave hyperthermia for cancer therapy, IEE Proc. Part A, Vol. 134, No. 6, pp. 493-522, 1987. [14] L. A. Daily, A clinical study of the results of exposure of laboratory personnel to radar and high frequency radio, U.S. Nay. Med. Bull., Vol. 41, pp. 1052-1056, 1943. [15] A. N. Datta and B. Bandyopadhyay, An improved SIRT-style reconstruction algorithm for microwave tomography, IEEE Trans. Biomed. Eng., Vol. BME-32, No. 9, pp. 719-723, 1985.

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[16] J. Edrich, Microwaves in breast cancer detection, Eur. J. Radiol., Vol. 7, No. 3, pp. 183-193, 1987. [17] J. A. Elder, Radiofrequency radiation activities and issues: A 1986 perspective, Health Phys., Vol. 53, No. 6, pp. 607-611, 1987. [18] A. C. Eycleshymer and D. M. Schoemaker, A Cross-Section Anatomy. New York: Appleton, 1911. *[19] K. R. Foster, J. L. Schepps, R. D. Stoy, and H. P. Schwan, Dielectric properties of brain tissue between 0.01 and 10 GHz, Phys. Med. Biol., Vol. 24, pp. 1177-1187, 1977. [20] K. R. Foster and H. P. Schwan, Dielectric properties of tissues, in CRC Handbook of Biological Effects of Electromagnetic Fields (C. Polk and E. Postow, eds.), pp. 27-96. Boca Raton, FL: CRC Press, 1986. [21] E. S. Gabrielyan, L. A. Khachatryan, S. G. Nalbandyan, and F. A Grigoryan, Microwave method of determining cerebral blood flow, Bull. Exp. Biol. Med., (Engl. Transl.) Vol. 103, No. 5, pp. 713-715, 1987. [22] O. P. Gandhi and A. Riazi, Absorption of millimeter waves by human beings and its biological implications, IEEE Trans. Microwaue Theory Tech., Vol. MTT-34, pp. 228-235, 1986. [23] D. K. Ghodgaonkar, O. P. Gandhi, and M. J. Hagmann, Estimation of complex permittivities of three-dimensional inhomogeneous biological bodies, IEEE Trans. Microwave Theory Tech., Vol. MTT-31, No. 6, pp. 442-446, 1983. [24] F. A. Gibbs, Jr., M. D. Sapozink, K. S. Gates, and J. R. Stewart, Regional hyperthermia with an annular placed array in the experimental treatment of cancer: Report of work in progress with a technical emphasis, IEEE Trans. Biomed. Eng., Vol. BME-31, No. 1, pp. 115-119, 1984. [25] M. K. Gopal, T. C. Cetas, and P. S. Ruggera, The CDRH Helix-I: A physical evaluation, IEEE Eng. Med. Biol. Mag., Vol. 9, No. 2, pp. 58-64, 1990. [26] A. W. Guy and C.-K. Chou, Specific absorption rates of energy in man models exposed to cellular UHF mobile-antenna fields, IEEE Trans. Microwaue Theory Tech., Vol. MTT-34, pp. 671-680, 1986. [27] G. M. Hahn, Hyperthermia for the Engineer: A short biological primer, IEEE Trans. Biomed. Eng., Vol. BME-31, No. 1, pp. 3-8, 1984. [28] F. G. Hirsch and J. T. Parker, Bilateral lenticular opacities occurring in a technician operating a microwave generator, AMA Arch. Ind. Hyg. Occup. Med., Vol. 6, pp. 512-517, 1952. [29] D. S. Holder, Feasibility of developing a method of imaging neuronal activity in the human brain: a theoretical review, Med. Biol. Eng. Comput., Vol. 25, pp. 2-11, 1987. [30] D. E. Hudson, Standard defines safe RF pulsed-power levels, Microwaves RF, Vol. 31, pp. 83-86, June 1992. [31] M. F. Iskander, R. Maini, C. H. Durney, and D. G. Bragg, A microwave method for measuring changes in lung water content: numerical simulation, IEEE Trans. Biomed. Eng., Vol. BME-28, No. 12, pp. 797-803, 1981. [32] J. H. Jacobi and L. E. Larsen, Microwave time-delay spectroscopic imagery of isolated canine kidney, Med. Phys., Vol. 7, pp. 1-7, 1980. [33] L. Jofre, M. S. Hawley, A. Broquetas, E. de los Reyes, M. Ferrando, and A. R. Elias-Fuste, Medical imaging with a microwave tomographic scanner, IEEE Trans. Biomed. Eng., Vol. BME-37, No. 2, pp. 303-312, 1990. [34] M. Knudsen and J. Overgaard, Identification of thermal model for human tissue, IEEE Trans. Biomed. Eng., Vol. BME-33, No. 5, pp. 477-485, 1986. [35] H. Kober, Dictionary of Conformal Representations. New York: Dover, 1952.

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*[36] A. Kraszewski, M. A. Stuchly, S. S. Stuchly, and A. M. Smith, In vivo and in vitro dielectric properties of animal tissues at radio frequencies, Bioelectromagnetics, Vol. 3, pp. 421-432, 1982. [37] D. V. Land, A clinical microwave thermography system, IEE Proc., Part A, Vol. 134, No. 2, pp. 193-200, 1987. [38] L. E. Larsen and J. H. Jacobi, Microwave scattering imagery of isolated canine kidney, Med. Phys., Vol. 6, pp. 394-403, 1979. [39] L. E. Larsen and J. H. Jacobi, eds., Medical Applications of Microwave Imaging. New York: IEEE, 1986. *[40] C. P. Lawinski, J. C. W. Shepherd, and E. H. Grant, Measurement of permittivity of solution of small biological molecules at radiowave and microwave frequencies, J. Microwave Power, Vol. 10, pp. 148-162, 1975. [41] J. C. Lin, Computer methods for field intensity predictions, in CRC Handbook of Biological Effects of Electromagnetic Fields (C. Polk and E. Postow, eds.), pp. 273-313. Boca Raton, FL: CRC Press, 1986. [42] R. M. Lipman, B. J. Tripathi, and R. C. Tripathi, Cataracts induced by microwave and ionizing radiation, Surv. Ophthalmol., Vol. 33, No. 3, pp. 200-210, 1988. [43] B. E. Lyons, R. H. Britt, and J. W. Strohbehn, Localized hyperthermia in the treatment of malignant brain tumors using an interstitial microwave antenna array, IEEE Trans. Biomed. Eng., Vol. BME-31, No. 1, pp. 53-62, 1984. (Spec. Issue Hyperthermia Cancer Ther.) *[44] A. C. Metaxas and J. L. Driscoll, A comparison of the dielectric properties of paper and board at microwave and radio frequencies, J. Microwave Power, Vol. 9, pp. 80-89, 1974. [45] P. Moon and D. E. Spencer, Field Theory for Engineers. Princeton, NJ: Van Nostrand, 1961. *[46] T. Ohlsson, N. E. Bengtsson, and P. O. Risman, The frequency and temperature dependence of dielectric food data as determined by a cavity perturbation technique, J. Microwave Power, Vol. 9, pp. 130-145, 1974. [47] J. R. Oleson, A review of magnetic induction methods for hyperthermia treatment of cancer, IEEE Trans. Biomed. Eng., Vol. BME-31, No. 1, pp. 91-97, 1984. [48] M. A. Papp, C. Hughes, J. C. Lin, and J. M. Pouget, Doppler microwave: A clinical assessment of its efficacy as an arterial pulse sensing technique, Invest. Radiol., Vol. 22, No. 7, pp. 569-573, 1987. [49] C. Polk and E. Postow, CRC Handbook of Biological Effects of Electromagnetic Fields. Boca Raton, FL: CRC Press, 1986. [50] P. S. Ruggera and G. Kantor, Development of a family of RF helical coil applicators which produce transversely uniform axially distributed heating in cylindrical fat-muscle phantoms, IEEE Trans. Biomed. Eng., Vol. BME-31, No. 1, pp. 98-105, 1984. *[51] M. A. Rzepecka, A cavity perturbation method for routine permittivity measurement, J. Microwave Power, Vol. 8, pp. 3-11, 1973. *[52] M. A. Rzepecka and R. R. Pereira, Permittivity of some dairy products at 2450 MHz, J. Microwave Power, Vol. 9, pp. 277-288, 1974. *[53] M. A. Rzepecka and M. A. K. Hamid, Modified perturbation method for permittivity measurements at microwave frequencies, J. Microwave Power, Vol. 9, pp. 317-328, 1974. *[54] J. L. Schepps and K. R. Foster, The UHF and microwave dielectric properties of normal and tumour tissues variation in dielectric properties with tissue water content, Phys. Med. Biol., Vol. 25, pp. 1149-1159, 1980.

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*[55] H. P. Schwan, Determination of biological impedances, in Physical Techniques in Biological Research (G. Oster et al., eds.), Vol. 6, pp. 323-377. New York: Academic Press, 1963. [56] H. P. Schwan, R. J. Sheppard, and E. H. Grant, Complex permittivity of water at 25°C, J. Chem. Phys., Vol. 64, pp. 2257-2258, 1976. [57] M. H. Seegenschmiedt, R. Sauer, R. Fietkan, U. L. Karlsson, and L. W. Brady, Primary advanced and local recurrent head and neck tumors: Effective management with interstitial thermal radiation therapy, Radiology (Easton, Pa.), Vol. 176, pp. 267-274, 1990. [58] M. H. Seegenschmiedt, L. W. Brady, and R. Sauer, Interstitial thermoradiotherapy: Review on technical and clinical aspects, Am. J. Clin. Oncol., Vol. 13, No. 4, pp. 352-363, 1990. [59] R. J. Spiegel, M. B. A. Fatmi, S. S. Stuchly, and M. A. Stuchly, Comparison of finite-difference time-domain SAR calculations with measurements in a heterogeneous model of man, IEEE Trans. Biomed. Eng., Vol. BME-36, pp. 849-855, 1989. [60] J. W. Strohbehn, B. S. Tembely, and E. B. Douple, Blood flow effects on the temperature distributions from an invasive microwave antenna array used in cancer therapy, IEEE Trans. Biomed. Eng., Vol. BME-29, No. 9, pp. 649-661, 1982. [61] J. W. Strohbehn and E. B. Douple, Hyperthermia and cancer therapy: A review of biomedical engineering contributions and challenges, IEEE Trans. Biomed. Eng., Vol. BME-31, No. 12, pp. 779-787, 1984. *[62] M. A. Stuchly, T. W. Athey, S. S. Stuchly, G. M. Samaras, and G. Taylor, Dielectric properties of animal tissues in vivo at frequencies 10 MHz-1 GHz, Bioelectromagnetics, Vol. 2, pp. 93-103, 1981. *[63] M. A. Stuchly, T. W. Athey, G. M. Samaras, and G. E. Taylor, Measurement of radio frequency permittivity of biological tissue with an open-ended coaxial line: Part I I - Experimental results, IEEE Trans. Microwave Theory Tech., MTT-30, pp. 87-92, 1982. [64] M. A. Stuchly and S. S. Stuchly, Experimental radio and microwave dosimetry, in CRC Handbook of Biological Effects of Electromagnetic Fields (C. Polk and E. Postow, eds.), pp. 229-272. Boca Raton, FL: CRC Press, 1986. [65] M. A. Stuchly, Proposed revision of the Canadian recommendations on radiofrequency-exposure protection, Health Phys., Vol. 53, No. 6, pp. 649-665, 1987. [66] M. A. Stuchly, A. Kraszewski, S. S. Stuchly, G. W. Hartsgrove, and R. J. Spiegel, RF energy deposition in a heterogeneous model of man: near-field exposures, IEEE Trans. Biomed. Eng., Vol. BME-34, pp. 944-950, 1987. [67] S. S. Stuchly, A. Kraszewski, M. A. Stuchly, G. W. Hartsgrove, and R. J. Spiegel, RF energy deposition in a heterogeneous model of man: far-field exposures, IEEE Trans. Biomed. Eng., Vol. BME-34, pp. 951-957, 1987. [68] D. M. Sullivan, D. T. Borup, and O. P. Gandhi, Use of the finite-difference timedomain method in calculating EM absorption in human tissues, IEEE Trans. Biomed. Eng., Vol. BME-34, pp. 148-157, 1987. [69] D. M. Sullivan, O. P. Gandhi, and A. Taflove, Use of the finite-difference time-domain method for calculating EM absorption in man models, IEEE Trans. Biomed. Eng., Vol. BME-35, pp. 179-186, 1988. [70] J. R. Swanson, V. E. Rose, and C. H. Powell, A review of international microwave exposure guides, in "Electronic Product Radiation and the Health Physicist," pp. 95-110, Publ. No. B R H / D R P 70-26, U.S. Dep. Health, Educ., Welfare, Washington, DC, 1970.

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[71] R. A. Tell, "An Analysis of Radiofrequency and Microwave Absorption Data with Consideration of Thermal Safety Standards," O R P / E A D 78-2, U.S. Environ. Prot. Agency, Off. Radiation Programs, Las Vegas, NV, 1978. [72] T. Terakawa, K. Ito, K. Ueno, M. Hyodo, and H. Kasai, Design of interstitial ring-slot applicator for microwave hyperthermia, l lth Annu. Conf. Eng. Med. Biol., Seattle, WA, pp. 1147, 1989. [73] A. Thansandote, S. S. Stuchly, A. M. Smith, and J. S. Wight, Monitoring variations in biological impedance at microwave frequencies, IEEE Trans. Biomed. Eng., Vol. BME-30, No. 9, pp. 561-565, 1983. *[74] W. R. Tinga and S. O. Nelson, Dielectric properties of materials for microwave processing-Tabulated, J. Microwave Power, Vol. 8, pp. 24-65, 1973. *[75] E. C. To, R. E. Mudgett, D. I. C. Wang, S. A. Goldblith, and R. V. Decareau, Dielectric properties of food materials, J. Microwave Power, Vol. 9, pp. 303-316, 1974. [76] P. F. Turner, Regional hyperthermia with an annular phased array, IEEE Trans. Biomed. Eng., Vol. BME-31, No. 1, pp. 106-114, 1984. [77] P. F. Turner, Mini-annular phased array from limb hyperthermia, IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 5, pp. 508-513, 1986. [78] P. F. Turner, Interstitial equal-phased arrays for EM hyperthermia, IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 5, pp. 572-578, 1986. [79] A. Winter, J. Laing, R. Paglione, and F. Sterzer, Microwave hyperthermia for brain tumors, Neurosurgery, Vol. 17, No. 3, pp. 387-399, 1985. [80] T. Z. Wong, J. W. Strohbehn, K. M. Jones, J. A. Mechling, and B. S. Tembely, SAR patterns from an interstitial microwave antenna-array hyperthermia system, IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 5, pp. 560-567, 1986. (Spec. Issue Phased Arrays Hyperthermia Treat.) [81] R. A. Steeves, Hyperthermia in cancer therapy: where are we today and where are we going? Bull. N.Y. Acad. Med., Vol. 68, No. 2, pp. 341-350, 1992. [82] S. B. Field and J. W. Hand, An Introduction to the Practical Aspects of Clinical Hyperthermia. Philadelphia: Taylor & Francis, 1990. [83] J. B. Dubois, M. Hay, and G. Bordure, Superficial microwave-induced hyperthermia in the treatment of chest wall recurrences in breast cancer. Cancer (Philadelphia), Vol. 66, No. 5, pp. 848-852, 1990. [84] C. K. Chou, Evaluation of microwave hyperthermia applicators, Bioelectromagnetics, Vol. 13, No. 6, pp. 581-597, 1992. [85] R. J. Myerson, L. Leybovich, B. Emami, P. W. Grigsby, and W. Straube, Phantom studies and preliminary clinical experience with the BSD 2000, Int. J. Hyperthermia, Vol. 7, No. 6, pp. 937-951, 1991. [86] J. A. Mechling and J. W. Strohbehn, Three-dimensional theoretical SAR and temperature distributions created in brain tissue by 915 and 2410 MHz dipole antenna arrays with varying insertion depths, Int. J. Hyperthermia, Vol. 8, No. 4, pp. 529-542, 1992. [87] J. A. Mechling, J. W. Strohbehn, and T. P. Ryan, Three-dimensional theoretical temperature distributions produced by 915 MHz dipole antenna arrays with varying insertion depths in muscle tissue, Int. J. Radiat. Oncol., Biol. Phys., Vol. 22, No. 1, pp. 131-138, 1992. [88] M. H. Seegenschmiedt, R. Sauer, C. Miyamoto, J. A. Chalal, and L. W. Brady, Clinical experience with interstitial thermoradiotherapy for localized implantable pelvic tumors, Am. J. Clin. Oncol., Vol. 16, No. 3, pp. 210-222, 1993. [89] M. D. Sherar, F. F. Liu, D. J. Newcombe, B. Cooper, W. Levin, W. B. Taylor, and J. W. Hunt, Beam shaping for microwave waveguide hyperthermia applicators, Int. J. Radiat. Oncol., Biol. Phys., Vol. 25, No. 5, pp. 849-857, 1993.

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[90] K. R. Foster and E. A. Cheever, Microwave radiometry in biomedicine: a reappraisal, Bioelectromagnetics, Vol. 13, No. 6, pp. 567-579, 1992. [91] J. C. Lin, Microwave sensing of physiological movement and volume change: a review, Bioelectromagnetics, Vol. 13, No. 6, pp. 557-565, 1992. [92] E. A. Cheever and K. R. Foster, Microwave radiometry in living tissue: what does it measure? IEEE Trans. Biomed. Eng., Vol. BME-39, No. 6, pp. 563-568, 1992. [93] K. D. Paulsen, X. L. Jia, and J. M. Sullivan, Finite element computations of specific absorption rates in anatomically conforming full-body models for hyperthermia treatment analysis, IEEE Trans. Biomed. Eng., Vol. BME-40, No. 9, pp. 933-945, 1993. [94] A. Boag, Y. Leviatan, and A. Boag, Analysis and optimization of waveguide multiapplicator hyperthermia systems, IEEE Trans. Biomed. Eng., Vol. BME-40, No. 9, 1993.

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CHAPTER

12 Chemical Applications of Microwaves Thomas C. Ehlert

I. Microwave Absorption Spectroscopy Introduction

This section

is limited to molecular gases. Absorption by atomic gases is extremely rare. Absorption by solids and liquids is not amenable to the following treatment.

Classifications of Molecules Molecules can be classified by their relative inertial moments about mutually perpendicular axes a, b, and c. These moments are represented by I A, I B, and I c , respectively. The classes are as follows. Linear molecules: I A -- I B and I c = O. Symmetric top molecules: I A = I B 4: I c (e.g., N H 3 and CHC13 ). Spherical top molecules: I A = I B = I c (e.g., SF 6, U F 6, and CC14). Asymmetric top molecules: I A 4: I B 4: I c (e.g., H 2° and CH 3OH).

Conditions For a molecular gas to absorb microwave radiation, three conditions must be met.

Handbook of Microwave Technology, Volume 2

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Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

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Thomas C. Ehlert

Resonance The radiation frequency v must satisfy the resonance condition Vtu = ( E u - E t ) / h ,

(1)

where h is the Planck's constant, E u is the upper energy state, and E l is the lower energy state. In all cases of practical import, u and 1 are rotational energy states. Rotational energy states are quantized; only certain energies are allowed.

Transition Probability The u ~ I transition must have a nonzero probability. This probability will be zero unless the molecule has a permanent electric dipole moment (see below).

Population Some of the sample molecules must be in state 1. Each of these requirements is discussed in detail below.

Rotational Energies The molecule's classification determines the formula to be used to predict the energies E u and E l used in Equation (1). Energy formulas are expressed in terms of rotation constants A, B, and C, related to the three inertial moments I A, I n, and I c, respectively, as A = h/(8rr2IAc)

(2a)

B = h / ( 8 7 r 2 I n c)

(2b)

c = h/(8¢%c),

(2c)

where c is the speed of light.

Linear Molecules For linear molecules E is given by E = J(J + 1)Bhc,

(3)

where J is a positive integer having values from zero upward and B ( = A) is a rotational constant for the nonzero inertial moment. Values of B

349

12. Chemical Applications of Microwaves

(rotational constants) for some diatomic molecules are given in the following table. Molecule BrH CN CO CS

B/cm -1

Molecule

B/cm -1

8.4657 1.8989 1.9302 0.8200

CIH FH HI HO

10.5884 20.9557 6.512 18.871

Values are averaged over isotopic varieties.

Symmetric Top Molecules The energy levels are given by

E = J( J + 1)Bhc + KZ( A - B),

(4)

where K is limited to integer values from 0 to J.

Spherical Top Molecules The energy formula is immaterial because these molecules do not undergo electric dipole transitions.

Asymmetric Top Molecules The formula for E is E = 0 . 5 J ( J + 1 ) ( A + C)hc + 0.5(A - C ) f ( E ) ,

(5)

where A is the largest and C is the smallest of the molecular constants A, B, and C. See Reference [1] for a tabulation of values of the function

f(E). Resonant Frequencies

In general, resonant frequencies are given by Equation (1). In some cases, simplifications are possible.

Linear Molecules Absorption occurs only when J increases by 1 so from Equation (1) resonant frequencies are given by ~, = ( 2 J + 2)Bc.

(6)

Symmetric Top Molecules Only transitions in which K does not change are allowed. As a result, resonant frequencies are given by Equation (6).

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Thomas C. Ehlert

Spherical Top Molecules Under ordinary conditions (see Limitations), these molecules do not undergo electric dipole transitions.

Asymmetric Top Molecules Transitions for which J changes by 0, + 1, or - 1 are allowed. In general, Equation (6) applies. However, symmetry considerations may be important. See Reference [1].

Probability of Absorption---Attenuation of Microwaves Upon passing distance dx through a sample, the radiation intensity at frequency 2'lu, Ilu, decreases by dI~u: -- d i l u

= (Ilu)(absorber number density) ( transition cross section) dx.

(7) The dimensionless product (absorber number density) (transition cross section) dx represents the probability of absorption. The transition cross section and therefore the absorption probability are zero unless two requirements are met. (1) The molecule has a permanent dipole moment. Spherical top molecules cannot have a permanent dipole moment. (2a) For linear and symmetric molecules, Ju = Jl + 1, where Ju and Jl are the rotational quantum numbers for states u and 1, respectively. (2b) For asymmetric tops, Ju -- Jl + 1 or 0.

Transition Cross Section First, quantum mechanical methods are used to calculate the transition moment/Xlu. Then (transition cross section) = (h/c)[87r3tX2u/(127reoh2)]

(me), (8)

where c is the velocity of light and E0 is the permittivity of space. The quantity in brackets is called the Einstein coefficient of induced absorption Blu. EXAMPLE: If /Xlu for a certain transition is 1 × 10 -30 Cm, then Blu

= 8T/'3 X

(1 × 10-3°)2/((3 X 1.11 × 10 -1°) × (6.6 × 10-34) 2}

- 1.9 × 1018 mkg -1,

12. Chemical Applications of Microwaves

351

and by Equation (8) the transition cross section is 1.9 × 1018 × 6.6 × 10-34/3.0 x 10 8 = 4 × 10 -24 m 2. With the above relations, the attenuation equation [Equation (7)] can be restated as dllu -'-

Ilu(Nl/V)(h/c)Blu d x .

(9)

Alternatively, the number of times (S -1) that a molecule undergoes absorption transitions per second in a unit volume of a sample and in a frequency band 1 Hz wide at Vlu is rate of induced absorption = (4hv/c)flu (N1/V)Blu.

(10)

If N 1/ V is constant between x = 0 and x, the intensity change is the integral of Equation (10), In( I / I o)~,u = - ( N1 / V ) ( h / c ) ( Blu ) X,

(11)

where I 0 is the intensity at x = 0.

Population of the Lower Quantum State The absorber number density is the number of absorbers in state 1 per unit volume V. Under equilibrium conditions, N 1/ V is given by the Boltzmann equation which for the J t h rotational state is

Nj/V=

(N/V)(2J + 1)giexp(-Ej/kT)/z,

(12)

where N / V is the number of sample molecules per unit volume, g i, called the nuclear spin statistical weight, is discussed below, and z is the partition function. The following expressions for z are valid except when the temperature is very low. Linear Molecules

For linear molecules having a permanent dipole moment z is given by

z = Bhc/(~rkT),

(13)

where ~r, called the symmetry number, is defined to be unity for nonlinear molecules with no axis of symmetry and n for molecules with an n-fold axis of symmetry. Examples include ~r = 1 for CO, 2 for H 2 0 , and 3 for NH 3. In some cases, e.g., H 2 0 , the nuclear statistical weight gi must be included in z (see below).

352

Thomas C. Ehlert

Symmetric Top Molecules Excluding the possible need for the g i factor, discussed below, the partition function is given by J=~ Z

=--

K=J

E E J=O

(2J + 1)exp(-S(J + 1)Bhc/kT + (A - B)K2/kT).

K=-J

(14)

Asymmetric Top Molecules In this case z is given by Z -- " f f l / 2 0 r - l ( 8 ' w 2 k T h

-2]3/2fl/2fl/2II/2 ] *A "B

~C

"

(15)

Special Cases

For molecules in which one part can rotate with respect to another, as CH 3 can rotate relative to CH2C1 in CH3CH2C1, or which can turn inside out like an umbrella, e.g., NH3, see Reference [1].

Nuclear Statistical Weight The weighting factor g i is needed only in certain cases: molecules having symmetrically positioned identical nuclei with half-integral nuclear spins. Examples are H 2 0 , HzS , and NH 3. See Reference [2] for details.

Limitations The above requirements are valid only for perfectly rigid molecules. Real molecules are not exactly rigid; transitions which these rules forbid occur but with low probability. Due to centrifugal distortion, more complicated formulas are required to more precisely describe energy states. Also, "constants" A, B, and C vary slightly with the vibrational state of the molecule. Finally, at increased pressures interactions with neighbors induce dipole moments, obviating the requirement of a permanent dipole moment.

Widths and Shapes of Spectral Lines All transitions between quantum states occur over a finite range of frequencies. The more important causes include the following.

353

12. Chemical Applications of Microwaves

Doppler Broadening Translational motion of the absorber causes "Doppler" broadening of a spectral line. The frequency v' of radiation from a source moving at velocity v is v'=

v(a

-

v/c) ×

(1 -

v2/c2) -1/2,

(a6)

where v is the frequency when the source is at rest. Usually v << c so the frequency shift Av = (v - v') is

Av = - v ( v / c ) .

(17)

Molecular motion toward or away from the detector is determined by the one-dimensional velocity distribution

dn/dv - g(m/2rrl~r)l/2exp(-mv2/21~r).

(18)

Solving Equation (17) for v and substituting it in Equation (18) give the line shape function f ~ characteristic of Doppler broadening:

fA,, Ct N ( m / 2 r r k r ) exp(-mc2Av2/2kTv2).

(19)

Perturbation/Pressure Broadening Collisions can shift the energy levels of an absorber, causing the photon it absorbs to differ in frequency from the unperturbed case. The characteristic line shape function in this case is fay Of, (1

+ CA/,,2) -1,

(20)

where C is a constant related to the time required for the system to "relax" to the lower quantum state.

2. Nuclear Magnetic Resonance Spectroscopy Introduction The proton and many kinds of nuclei behave as if they spin about an internal axis. This spin is characterized in part by a nuclear spin quantum number, I [3, 4].

Nuclear Magnetic Dipole Moment A spinning nucleus possesses a magnetic dipole moment tt M, the magnitude of which is given by tt M = I ( I + 1) 1/2 gN/3N,

(21)

354

Thomas C. Ehlert TABLE I Spin Properties and Isotopic Abundances of Some Light, Stable Nuclei

I

gN

1H 2H I°B

71 1 3

5.585 0.857 0.600

99.985 0.015 19.8

42.58 6.54 4.57

11B

3

1.792

0

80.2 98.9

13.66

12C 13C

1

14N 15N

1 1

1.405 0.403

1.1 99.6

10.71 3.08

0.4

4.31

160

0

170

5

180 19F

0

Abundance (%)

NMR frequency v in a 1.0-T Field (MHz)

Nucleus

-0.567

99.76 -0.757

0.04

5.77

0.20

1 3

5.257

100.

23Na

1.480

100.

11.27

27A1

5

1.457

11.11

2Ssi 29Si 3°Si 31p

0 12 0 1

100. 92.2 4.7 3.1 100.

17.23

- 1.111 2.263

40.05

8.47

Note. Data from G. Fuller, J. Phys. Chem. Ref. Data, Vol. 5, p. 835, 1976. The superscript denotes the isotope's mass number.

where ~N, known as the nuclear magneton, equals 5.0508 × 10 -27 JT -1 and g N is a dimensionless factor characteristic of the nucleus. Table 1 lists g N and I values of some light nuclei.

Magnetic Dipole Moment Components In the presence of an externally applied magnetic field, B, t h e / x M vector assumes an angle, 0, relative to the field's direction such that its components, /x M cos 0, in the field direction are quantized. These components are given by ~ M COS 0 -- m l g N f l N ,

where the quantum number m I can take on values from I to - I steps. That is, m I = + I , I - 1 , . . . , 1 - I , - I .

(22) in unit

355

12. Chemical Applications of Microwaves

1 1 1 EXAMPLE: For the 1 H nucleus ( I - 5) m i can be + 5 and - 5- There are 2 I + 1 such components since m I has 2 I + 1 possible values.

Magnetic Dipole Energy States In the absence of a magnetic field all components have the same energy. Nuclear magnetic resonance (NMR) spectroscopy makes use of the fact that in the presence of a magnetic field, 13, each component has a different energy, E, allowing transitions between these energy states. E is given by E = - ~ M cos 0B = --mlgN[3 N.

(23)

Allowed Transitions between Energy States Quantum rules limit transitions to those for which A m I = + ] (emission) or - 1 (absorption). Substances containing spinning nuclei absorb electromagnetic radiation if the frequency u satisfies the resonance equation u = (E u -El)/h

= gN X ~N X 1 3 / h ,

(24)

where h is Planck's constant. EXAMPLE: U for a proton in a 1.4-T field is u = gN~NB/h

= 1 X 5.585 X 5.0508

x

10 -27

x

1.4/6.626 x 10 -34

= 59.6 MHz.

Details of Spectra Chemical Shift

An applied magnetic field causes diamagnetic circulation of the electrons orbiting the nucleus. This produces a magnetic field opposing the applied field, albeit about a million times smaller. As a result, the effective magnetic field 13ef at the nucleus differs from the applied field by a few parts per million. The size of this difference increases with increasing electron density on the nucleus. Because the electron density on the nucleus varies with the chemical environment, the N M R frequency does likewise. This is known as the chemical shift. The amount of magnetic "shielding" this opposing field offers a given nucleus is proportional to t , so ~ef

=

~

-- O'~

=

(1 - tr)B,

(25)

where tr 13 is the chemical shift and the proportionality constant cr is called the shielding or screening constant. The smaller is tr, the less 13 and

356

Thomas C. Ehlert

~ e f differ. Thus, in C 2 H s O H , shielding of the hydroxyl H is slight because oxygen, having a large electron affinity, reduces the electron density on this H. Then the hydrogen atom in the O H group reaches resonance at a lower B than either the CH 2 or CH 3 hydrogens. Although the O in O H also tends to lower the electron density on the hydrogens in the CH 2 group, shielding effects are not efficiently transmitted through bonds; the effect of O on the CH 2 protons is but a few percent of that on the H in the O H group. Equation (5) is inconvenient because it is difficult to make precise, absolute measurements of B and because tr values are very small. One alternative is to define a chemical shift parameter, 6, ai =

106 X

(Bre f -

Bi)//Bref,

(26)

where Bre f is the field strength which satisfies the resonance condition for a reference substance and B i is the corresponding value for substance i. O'ref)106" Equation (26) is convenient for use with a Note that ~ i - - ( O ' i fixed-frequency, variable-magnetic-field N M K spectrometer. For a fixed-magnetic-field, variable-frequency instrument, an equivalent but more convenient form is ~i --

106 X

( l,'i -- l,'ref)//,'re f.

(27)

To avoid negative values of ~i for proton NMR, chemical shifts relative to the (highly shielded) protons in tetramethyl silane, Si(CH3)4, are also used. This ~- scale takes t~ for Si(CH3) 4 to be 10.00 so that the ~" and the t~ scales are related by 7"i = 1 0 . 0 0 -- ~i" Table 2 lists some proton chemical shifts.

Spin-Spin Splitting There is a second way B and Bef can differ. The magnetic field "seen" by a given nucleus is altered by the tiny magnetic field associated with each of the 21 + 1 components of/~ m of any other spinning nuclei nearby. Each neighboring nucleus which spins modifies B in 21 + 1 ways. Since a component's magnitude varies with the spinning particle's charge, the

TABLE 2 Observed Proton Chemical Shifts as z Values in ppm

Methyl Methylene Methinyl Olefinic

5.5 to 1 0 . 0 5.4 to 9.8 5.5 to 6.0 4.4 to 5.4

Acetylenic Aromatic Aldehydic Carboxylic

7.5 to 8.0 1.7 to 2.7 0.0 to 0.2 -2. to 0.5

357

12. Chemical Applications of Microwaves

extent of this modification depends, albeit weakly, on the environment. Nuclei in identical environments are said to be equivalent. For example, the hydrogens in the CH 3 group of C2H 5 are equivalent; those in the CH 2 group are equivalent to one another but not to those in the CH 3 group. When interactions with neighbors are random in time and position, usually the case in liquids, their effects average to zero; only the spinning nuclei within the molecule have an effect. In principle every nucleus is affected by every other spinning nucleus in the molecule, although the extent diminishes rapidly with the number of intervening bonds, a notable exception being double bonds.

Relaxation Processes Relaxation is any nonradiative process which limits the lifetime of an energy state. Magnetic dipole energy may be changed to translation or vibration energy via collisions with neighbors (called "spin-lattice" or "longitudinal" relaxation) and may be lost by transfer to neighboring nuclei (called "spin-spin" or "transverse" relaxation.) In either case, the lifetime of the magnetic dipole energy state is shortened, increasing the transition line width.

Power Saturation Under the conditions prevailing in magnetic resonance spectroscopy the population of the upper state, N u, is only slightly less than that of the lower state, N~. EXAMPLE: N u / N l for a proton system in a 1.4-T field at 300 K is

N u / N l = exp( - A E / k T ) = exp(-gy~yB/kT)

= e x p ( - 0 . 0 0 0 0 1 ) = 0.99999.

Absorption of radiation at U~u forces N u / N ~ closer to 1, whereas relaxation tries to maintain the ratio at the value set by the Boltzmann equation. Only when the radiation intensity is sufficiently low does net absorption occur. With increasing intensity the relaxation processes are eventually overwhelmed and the net absorption decreases, a phenomenon known as line reversal.

High-Field NMR A stronger magnetic field increases all resonant frequencies, as required by Equation (24). This simplifies the spectrum by separating transitions

358

Thomas C. Ehlert

which overlap due to similar chemical shifts. However spin-spin splitting is unaffected by larger B because spin-spin coupling constants depend only on the efficiency of coupling spin information from nucleus to nucleus. NMR Spectra of Solids

For lack of averaging effect, the conventional NMR spectrum of a solid consists of very broad absorptions. There are several means to reduce broadening. One is spinning the solid about an axis of 54° 44", called the "magic angle," with respect to B. Another, in Fourier transform NMR, is a special sequence of RF pulses that eliminates the broadening due to other kinds of dipoles in the neighborhood. Finally, when the perturbing dipoles are part of the molecule under study it is possible to "decouple" their spins by irradiating the sample at their resonant frequency. Fourier Transform NMR

To find the resonant frequencies of several tuning forks, one could irradiate the array of forks with radiation from a slowly swept audio oscillator. This is equivalent to the technique known as "slow passage" NMR; the tuning forks are the spin systems, the oscillator is the RF transmitter, and the listener is the RF receiver. Alternatively, one could irradiate the array of tuning forks with a brief blast of noise and then listen as the forks simultaneously emit their characteristic frequencies. A listener with a good ear could then identify each fork's frequency. This is equivalent to Fourier transform NMR (FtNMR); the noise is a band of RF radiation and the listener is a receiver and Fourier transform analyzer. In pulsed FtNMR, the transmitter produces brief pulses of RF radiation, e.g., around 60 MHz for protons in a 1.4-T field. Fourier's theorem shows that shortening the pulse duration At broadens the band of frequencies Av contained in the pulse, as given by the lifetime broadening formula Av X At > 1/2zr. Thus, a broad pulse can simultaneously excite all the resonances, e.g., of hydrogen, in the sample. After irradiation, some nuclei return to the lower energy state by emitting the same frequency they previously absorbed, so the receiver "hears" an interference signal called an interferogram. The interferogram is digitized and Fourier transformed from amplitude vs time to amplitude vs frequency. The interferogram's amplitude decays with time as relaxation by spin-spin, spin-lattice, and emission reduces the number of emitters.

359

12. Chemical Applications of Microwaves

3. Electron Spin Resonance Spectroscopy Introduction The electron behaves as if it spins about an internal axis. This spin is characterized in part by a spin quantum number, s, the only allowed value 1 of which is ~ [5, 6].

Electron's Magnetic Dipole Moment As a spinning charge, the electron possesses a magnetic dipole moment (/XM)e, the magnitude of which is given by (/'ZM)e =

1 --ge~B[(5)(g

1

nt-

1)]1/2

(28)

•

The constant /3 B, called the Bohr magneton unit, is 9.274078 × 10 -24 JT -1. The ge term is a dimensionless parameter which depends on the electron's environment but is typically about 2 in molecular substances.

Magnetic Dipole Moment Components In In 0, in

the absence of a magnetic field all components have the same energy. the presence of a magnetic field, D3, the (/XM)e vector assumes an angle, relative to the field's direction such that its components, (/XM)e COS 0, the field's direction are quantized. The components are given by 1 m s g e ~ B, where the quantum number m s can take on the values -~ 2 1 and - 5 only.

Magnetic Dipole Energy States In a magnetic field, ~3, the dipole moment components differ in energy, as given by (EM)

where

m s

1

is either + 5 or

e -

msge~B03,

(29)

1

2"

Allowed Transitions between Energy States Q u a n t u m rules limit transitions to those for which A m or + 1 (absorption). Substance-containing unpaired

s

= - 1 (emission) electrons absorb

360

Thomas C. Ehlert

electromagnetic radiation if the frequency u satisfies the resonance equation v = (E u - E1)/h

= ge~B[B,

(30)

where h is Planck's constant.

Spectra In addition to the splitting of energy states caused by B, any of the magnetic dipoles associated with spinning nuclei sufficiently near the unpaired electron alter the g factor and cause further splitting of the energy states. This is called "hyperfine" splitting because it is much weaker than that caused by B. The effect of a second such nucleus which is located in a position chemically equivalent to the first is to split each of the states again, giving a triplet, the relative amplitudes of which are in the ratio 1:2:1. Two nonequivalent neighbors would give a 1:1:1:1 quartet. EXAMPCS: The magnetic dipole moments of the three equivalent protons of the methyl radical CH 3 can couple in four ways to produce four modifications of the magnetic field seen by the unpaired electron. These four slightly different values of the field cause a 1:3:3:1 hyperfine pattern.

Relaxation Processes Electron spin systems relax by essentially the same mechanisms as nuclear spin systems, although the rate is in general much faster due to the smaller mass of the electron.

4. Chemical Synthesis and Analysis Using Microwave-Produced Plasmas Apparatus Microwave power applied to a resonant cavity of metal produces an electrodeless discharge in glass or quartz tubing containing a carrier gas such as argon. The cavity shape and size are chosen so as to establish standing waves in various modes. Typically, dimensions are on the order of centimeters but there is no unique design. Raytheon Microtherm (diathermy) units providing up to 200 W at 2.45 GHz have been used. In synthetic applications, the reactant gas is mixed with the carrier. In analytical applications, the analyte is entrained in the carrier as an aerosol. See References [7] and [8].

361

12. Chemical Applications of Microwaves

Theory Ionization of the carrier is initiated by a cosmic ray, natural radioactivity, a spark, etc. The freed electron, when sufficiently accelerated by the RF field, ionizes reactant molecules, freeing more electrons. The plasma state forms quickly as these, in turn, cause the formation of more ions and more free electrons, etc. Rotationally, vibrationally, and electronically excited states of the reactant or analyte molecules are produced through energy transfer processes. Excitation energy may be emitted at frequencies characteristic of the emitter, or it may serve to dissociate the reactant molecules. The probabilities of forming various excited states and of dissociating depend upon the reactant and, for a given reactant, on the electron energy. Unfortunately, these processes are very complex and the data needed from making predictions are seldom available. Assuming a steady state, isotropic scattering, and that the collision frequency is independent of electron speed, the mean energy of electrons in an RF field of V Vcm-1 is approximately E e -- 0 . 5 ( M / m ) 1 / 2 q V A ,

(31)

where m, q, and A are the electron's mass, charge, and mean free path, respectively, and M is the collision partner's mass. In the plasma, electron speeds assume a quasi-Maxwellian distribution with an effective temperature of 30,000 K, typically. If s is speed, the distribution is

f ( s ) ds ct s 2 exp(-6m3s4/(8MA2q2V 2) ds.

(32)

In the absence of collisions, the maximum energy attained by the free electrons is Emax =

2 (2 m to2 ) q 2 Vmax/

(33)

and is parallel to the field. In Equation (33) Vmax is the field's maximum amplitude and to is the field's angular frequency. Thus, for 1 GHz and 300 W/cm, Emax is only about 2 eV, equivalent to about 25,000 K. However, collisions eventually transfer to energy in all directions relative to the field.

Synthesis Commonly, the dissociation and recombination products are cryogenically trapped downstream. There is no simple way to selectively produce a particular product with great efficiency.

362

Thomas C. Ehlert

Analysis The visible-region radiation emitted is subjected to spectroscopic analysis. Comparison with known emission patterns [9] serves to identify atomic emitters. Examples of some characteristic atomic emissions include sodium at 588.995 nm and potassium at 766.023 nm. Emission intensity can be related to elemental abundance in the sample via calibration procedures. This method works for most elements.

5. Thermal Effects Introduction Microwave heating is used to speed chemical processes which proceed too slowly at ambient temperatures. Examples include annealing semiconductors, bending and bleaching wood, bonding polymers, calcining nuclear waste materials, cross-linking and curing polymers, decomposing nitrates of nuclear fuel elements, dehydrating zeolites used as driers, dissolving, drawing thermosetting polymers, dyeing textiles, esterifying, hardening mold coatings, polymerizing, sintering, and vulcanizing. Applications in which the microwaves are used to produce a plasma in order to form highly reactive species are not considered here.

Heating Let tan S be the loss tangent and e ' r be the relative dielectric constant of the material to be heated. Then, upon exposure to microwave radiation of frequency u and intensity V (Vm-~), microwave power P, absorbed in watts per cubic meter of material, is approximately P = 2'n'~,e0E'r tan 6V 2,

(34)

where e 0 is the permittivity of free space, 8.86 × 10 -12 Fm -1. Equation (34) is approximate in that it neglects the interdependence of v, e'r, tan 6, and V. Further, V depends on the size, geometry, and location of the material within the microwave cavity as well as the cavity design and volume. To the extent that heat losses by the sample may be neglected, the absorbed power, sustained for At seconds, causes a temperature rise given by AT = PAt/(Cpp),

(35)

12. Chemical Applications of Microwaves

363

where Cp is the material's heat capacity (JK -1 kg -1) and p is its density (kgm-3). For most substances both e'r and Cp increase slowly with temperature, tan 8 generally rises almost exponentially with power. As a result, AT tends to do likewise. Equation (36) is approximate in at least three ways. 1. It neglects the possibility of a phase change, e.g., melting. In such a case, the temperature remains constant until microwave energy equal to that needed to bring about the phase change has been added. 2. Cp in almost all cases rises with increasing temperature. 3. Some energy is lost to the surroundings. Reaction Rate Enhancement

The conversion of a reactant to a product generally obeys an equation of the form product formation rate = (constant) × (amount of reactant) n, (36) where the exponent n is called the "order" of the reaction and the constant is called the "rate constant." The reactant amount(s) may be expressed in mass, mole, or concentration units. Then the product formation rate will be expressed as the corresponding amount per unit time. Usually, both n and k must be found experimentally. In addition, k may be strongly temperature d e p e n d e n t m s e e below. Increasing the temperature increases the reaction rate, mainly by increasing the rate constant. If k l is the reaction rate constant at some temperature, T 1, then the rate constant at temperature T 2 is given approximately by k 2 -- k 1 e x p ( - A E / R T ) ,

(37)

where A E is the (molar) activation energy and R is the (molar) gas constant. The mechanism of the reaction determines A E and may differ between microwave and other means of heating. For example, for sintering A120 3 containing 0.1% MgO, AE by microwave heating is 170 kJmo1-1 but is 575 kJmo1-1 by conventional heating [10]. References

[1] Microwave Spectroscopy, C. Townes and A. Schawlow. New York: McGraw-Hill, 1955. [2] Infrared and Raman Spectra of Polyatomic Molecules, G. Herzberg. New York: Van Nostrand, 1945. [3] High Resolution Nuclear Magnetic Resonance, J. A. Pople, W. G. Schneider and H. J. Berstein. New York: McGraw-Hill, 1959.

364

Thomas C. Ehlert

[4] Spectrometric Identification of Organic Compounds, R. Silverstein and C. Bassler. New York: John Wiley and Sons, 1967. [5] Electron Paramagnetic Resonance: Techniques and Applications, R. S. Alger. New York: Wiley (Interscience), 1968. [6] Electron Spin Resonance: Elementary Theory and Practical Applications, J. E. Wertz and J. R. Bolton. New York: McGraw-Hill, 1972. [7] Chemical Reactions in Electric Discharges, Advances in Chemistry Series No. 80. Washington, DC: American Chemical Society, 1969. [8] Inductively Coupled Plasma Emission Spectroscopy, Part I, P. W. J. M. Boumans, ed., Chemical Analysis, Vol. 90. New York: John Wiley & Sons, 1987. [9] Massachusetts Institute of Technology Wavelength Tables, G. R. Harrison. Cambridge, MA: MIT Press, 1969. [10] W. H. Sutton, Ceram. Bull., Vol. 68, No. 2, pp. 376-386, 1989.

CHAPTER

13 Electron Paramagnetic Resonance James s. Hyde

I. Introduction F. Bloch in his Nobel prize paper [1] wrote the following differential equations to describe nuclear magnetic resonance (NMR) phenomena: dM x

dt

Mx

--~ ~/[MyH° -[- M z g l sin wt] - -~2'

dMy dt dM z dt

= T [ M ~ H 1 cos w t - M x n o ]

-

(1)

My ~,

(2)

T2

- 7 [ - M x H 1 sin cot - M y H 1 cos cot] +

Mo - M z

(3)

T1

Here M o is the static magnetization M o = XoHo,

(4)

with X0 being the static susceptibility arising from nuclear magnetic moments if a sample is placed in an applied static magnetic field, H 0. H a is an applied radio frequency (w) magnetic field that is perpendicular to H 0 and is circularly polarized in the laboratory frame. M x and M y are radio frequency components of magnetization that are coherent with H~.

Handbookof MicrowaveTechnology,Volume2

365

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

366

James S. Hyde

if H 1 is turned off, this coherence disappears exponentially in a characteristic time, T2, M~ is the instantaneous magnetization. If H 1 is turned off, M z approaches M 0 exponentially with a characteristic time, T 1. The gyromagnetic ratio 3' is a constant of nature that differs for each nuclear isotope that has a nuclear spin. These differential equations have the following stationary solutions:

1

[

( ¢.00 -- ¢.0)T 2

X'=

-2X°°')°T2 1 + (w 0 - o9)2T 2 + T2H2T1T2 '

(5)

X"=

1 [ -2x°T2 1 +

(6)

1 (~o 0 - w)2T2 + T2H2T1T2 "

These are the real and imaginary parts of the complex radio frequency susceptibility. Here a)o - TH o.

(7)

If o~ = ~o0, the denominator becomes small, and resonance can be said to occur. The differential equations of Bloch, Equations 1 to 3, and the stationary solutions, Equations 5 and 6, closely parallel those describing a resonant RLC circuit; however, there is no parallel in engineering to the introduction of two relaxation times, T 1 and T2. The analysis of Bloch applies equally well to electron paramagnetic resonance (EPR, also called electron spin resonance, ESR). However, 3' is about 1000 times greater for a free electron. Because of Equation (7), magnetic resonance experiments, whether NMR or EPR, can be performed at any applied field H 0 by finding the right value of w for the value of 3' that is of interest. Typically, however, EPR experiments are performed at microwave frequencies (e.g., X-band or 9.5 GHz with a value of H 0 of 0.35 T), and NMR experiments, at radio frequencies. It is noted, however, that the highest frequency currently used for NMR is 750 MHz ( H 0 of 17.6 T), approaching the microwave region. The quantity X" is called "absorption" and is associated with the concept of "loss" or heating of the sample. The quantity of X' is called dispersion. X" and X' can be related to each other by a Hilbert transform if the t e r m TZH2T1T2 in the denominator is zero, as is well known for the stationary solutions of resonant RLC circuits. These quantities X' and X" are small, and much effort has gone into the development of microwave circuits that will facilitate their detection. These circuits are the subject of this section. A sample, which may be liquid, solid, or gas, is placed in a resonator, and microwave power is applied at the resonant frequency of the resonator. Obviously from Equa-

TTT

tion (7), one might sweep either co or H 0 in order to satisfy the resonance condition o)0 = co and thereby to obtain a "spectrum." In CW EPR spectroscopy, the static field H 0 is always swept. When resonance occurs, the Q of the resonator decreases slightly because of the loss associated with X". In addition, the resonant frequency of the resonator changes because of the dispersion X'. These changes give rise to changes in both terms of the complex reflection coefficient F of the resonator. The magnitude of the changes in F depend not only on the concentration of spins and sample volume, but also on T 1, T2, and the dielectric loss of the sample (aqueous samples being particularly lossy). The microwave engineering problems are first to maximize the change in F for a particular class of samples, which can also be visualized as improving the match of a transmission line to a spin system, and second to arrive at an optimum microwave circuit for detection of the changes in F. Various transient magnetic resonance experiments can be performed, and the differential equations of Bloch (1-3), used to describe the results. Essentially all NMR experiments performed today are of this class. Most EPR experiments remain in the CW category for a variety of technical reasons. Pulse EPR experiments are, however, of increasing importance. An important early paper on EPR was written by Feher [2], using an engineering vocabulary. Wilmshurst, himself trained as an electrical engineer, wrote a general treatise on EPR spectrometers [3]. Alger's book [4] contains many useful technical details. The reader is referred specifically to both the first and the second editions of Poole's book [5, 6]. These editions contain considerable differences and, together, constitute a comprehensive literature survey of essentially all technical aspects of EPR spectroscopy to 1982. Applications of EPR are more or less equally divided among chemistry, biology, and physics. The paramagnetic species of most interest are transition metals such as Cu and Fe with various organic ligands, free radicals, and nitroxide radical spin labels that are used as extrinsic probes. Approximately 2000 citations of EPR appear each year in Chemical Abstracts. The Journal of Magnetic Resonance (Academic Press) is an important primary source of information. The field of EPR is reviewed regularly in a comprehensive manner in the series Specialist Periodical Reports [7]. An exceptionally comprehensive compilation of EPR data has been published in the Landolt-B6rnstein series [8]. General books for use in a classroom setting on EPR spectroscopy have been written by Carrington and McLachlan [9] and by Pake and Estle [10]. Several general books on EPR spectroscopy have been written from the perspective of the physical chemist: Weil, Bolton, and Wertz [11], Atherton [12], Ayschough [13], and Harriman [14]. The last is theoretical. General books from the

368

JamesS. Hyde

perspective of the physicist have been written by Al'tshuler and Kozyrev [15], Gordy [16], Low [17], and Poole and Farach [18]. General books from a biological perspective include Ehrenberg et al. [19], Swartz et al. [20], and Feher [21]. References [19-20] are rather old. An important book on EPR as applied to biological systems has been edited by Hoff [22]. It contains considerable engineering detail at an advanced level. See also the book by Dalton et al. [23]. The number of books on various specialized aspects of EPR spectroscopy is considerable. They can be categorized as follows: Pulse EPR [24-26] Nitroxide radical spin labels [27-29] Double resonance [30-32] Electron-nuclear double resonance (ENDOR) Electron-electron double resonance (ELDOR) Relaxation (spin-spin and spin-lattice) [33-35] Transition metal ions [36-38] High-resolution EPR [39] Solid-state EPR [40] EPR imaging [41].

2. Continuous W a v e Bridges: 0 . 5 - 35 G H z It is customary to modulate the static magnetic field at a sinusoidal frequency, tom, often at 100 kHz, which from Equations (5)-(7) is equivalent to modulating the incident microwave frequency to. This process produces, at resonance, modulation sidebands at to + n t o m. The theory of modulation sidebands in magnetic resonance is developed in the Appendix of Re~rence [42]. After microwave detection, the signal is amplified and fed to a phase-sensitive detector (alternatively called a lock-in amplifier). From the point of view of analysis of the microwave detection system, it is appropriate to describe the receiver as a superheterodyne system. A carrier is supplied to the microwave detector at to, which serves as the local oscillator (LO). The signal information of interest is at to + tom. These two very low amplitude microwave signals are the signal oscillator (SO) frequencies. The intermediate frequency (IF) is at tom. The microwave detector is a mixer operating in the linear range, and the usual vocabulary of the noise temperature, noise factor, noise figure, conversion gain (or loss), noise figure of the preamplifier, and overall receiver noise figure is appropriate. See Reference [43] for an analysis of an EPR "front end."

369

13. Electron Paramagnetic Resonance

Under One-Arm Bridges and Reference-Arm Bridges, we review the various types of bridges that have been used for general purpose EPR spectroscopy. These are of the so-called one-arm type and reference-arm (or two-arm) type and are used with sample-containing resonators in reflection. The literature [5, 6] contains descriptions of other microwave circuits for use with transmission resonators. Detection of Dispersion and Reference-Arm Bridge with a Low-Noise Microwave Amplifier extend the discussion by describing more recent developments of reference-arm bridges as used for general purpose EPR spectroscopy at a somewhat advanced level. Notes on Advanced Microwave Bridges gives access to the literature on three- and four-arm bridges and as well as to the literature on millimeter-wavelength bridges. The literature on microwave bridges for EPR is very large. A particular selection has been made here of gradually increasing complexity: one-, two-, three-, and four-arm bridges, always with reflection-resonator geometry. The various texts cited here (References [24]-[41]) provide essentially complete access to the literature on EPR microwave bridges.

One-Arm Bridges We review six bridge designs of the one-arm category. They are seldom used today, but have the advantages of simplicity and low cost. They were all developed originally at the X-band. Figure 1 shows the simplest magic tee bridge. (The microwave notation used here is given in Table 1). Oscillator

Reflex klystrons of the type developed during World War II were used (e.g., V153C). A mechanical tunability of 8.8 to 9.5 GHz was required

X

Figure I. Basic magic tee bridge.

James s. Hyde

370 TABLE I

Definition of Microwave Symbols

@

f I I ISOLATOR

r-J)

.~LIDE SCREW TUNER

MICROWAVE OSCILLATOR

?/~

~AMPLE CAVITY I fflTtl AI).IU£TAIILE IRISI

DIRECTIONAL COUPLER :3 ATTENUATOR

C I RCULATOR 1

PHASE SHIFTER MATCHED LOAD

__JL_ ---1 [-

DETECTOR

I n ("d

MAGIC TEE MICROWAVE DELAY LINE

because it is customary on occasion to insert small sample-containing quartz dewars into the cavity resonator for temperature control of the sample, which lowers the resonant frequency of the resonator by about 500 MHz. The oscillator power is in the range of 200 mW. Tee

The tee should be " magic," with both pairs of opposite arms isolated from each other.

Adjustable Attenuator The adjustable attenuator is required because of the appearance of

TZHZT1T2 in the denominator of Equations (5) and (6). Experiments are typically carried out with incident powers such that this term = 1, or perhaps somewhat lower. A "level-set" attenuator of 30 dB is adequate.

Slide Screw Tuner The slide screw tuner is adjusted to accomplish two purposes: (1) to 1 1 provide LO power at the detector of about ~ to ~ mW and (2) to buck-out or cancel any power reflected from the sample resonator.

Detector Crystal The detector crystal in early bridges was a point-contact diode of the 1N23 series, with late models such as 1N23H preferred because of reduced " l / f " noise at 100 kHz.

13. Electron Paramagnetic Resonance

371

In Figure 1, an automatic frequency control circuit (AFC) locks the resonant frequency of the resonator to the oscillator. It follows that the dispersion X' [Equation (5)] cannot be observed. The range of powers over which experiments could be performed was not sufficiently large because of the need to keep the LO level high enough for good conversion. The overall receiver noise figure was probably not better than 15 dB because of 1 / f noise. It was necessary to readjust the slide screw tuner each time the incident power was changed, which not only is inconvenient but also reduces the quantitative accuracy of the experiment. A further disadvantage is that half of the available incident microwave power is lost in the tee, and, also, half of the available EPR signal power reflected from the sample resonator is lost. Figure 2 shows a slight variation. The slide screw tuner is now in the sample resonator arm. A standing wave is set up between the resonator and the tuner, changing the coupling to the resonator and thereby altering the power "seen" by the sample. In Figure 1, the power at the sample is not affected by the slide screw tuner. Figure 3 shows an improvement over both Figures 1 and 2. An adjustable iris is introduced at the sample resonator in order to match it. The range of coupling adjustment should be such that the resonator can be matched if the dielectric loss of the sample reduces the Q to a value of about ~1 of its value with the sample removed. With the resonator well matched, one of the two functions of the slide screw tuner in the opposite arm is eliminated, bridge adjustment is facilitated, and quantitative accuracy isimproved. This structure was sold commercially by Varian Associates circa 1960. Figure 4 is the bridge of Rempel and Weaver [44]. It contains an interesting custom-made component in the resonator arm: an adjustable

X

Figure 2. Modified magic tee bridge.

372

James S. Hyde

ADJUSTABLE IRIS

Figure 3. Magic tee bridge with an adjustable iris.

isolator. It could be used to reduce the power incident on the resonator by an additional 30 dB, giving a total of 60 dB for the range of incident power. In modern research bridges, a 90-dB attenuation range is sometimes available, but 60 dB is sufficient for most purposes. The reflected signal containing E P R information passes back through the isolator with minimal loss. At low microwave powers incident on the resonator, the AFC does not work well and a reference cavity is used. The bridge then becomes very flexible, but quite difficult to use for the inexperienced operator. Each adjustment of the variable isolator causes a phase change. Therefore, it is usually left in a preset range and the power is adjusted by the level-set

REFERENCE CAVITY

X ADJUSTABLE FERRITE ISOLATOR

Figure 4. Magic tee bridge for use at very low powers.

373

13. Electron Paramagnetic Resonance

attenuator. It is possible to observe either dispersion or absorption by changing the phase shifter, but the AFC locks on some combination of the reactivity of the sample resonator and the reference cavity, which is a complication. Temperature drift of the difference in resonance frequencies of the resonator and reference cavity can be troublesome. This bridge was marketed by Varian Associates for use when experiments are carried out at liquid helium temperature, at which T 1 values are long and microwave power saturation must be considered because of the term TZHZTIT2 in the denominator of Equations (5) and (6). A particular disadvantage of this bridge is that serious complications occur if the product tomT1 > 1. If T 1 is long, okm must be small and 1 / f detector noise is very high. It is noted that the basic idea of Rempel and Weaver can be used in the bridges of Figures 1-3 by inserting an ordinary isolator just before the sample resonator. Figure 5 shows a true superheterodyne version of the bridge of Figure 4. It was developed by the author and available from Varian as an accessory. The advantage is that the intermediate frequency of 30 MHz overcomes the 1 / f noise problem of the circuit of Figure 4. It is interesting to note that experiments with balanced mixers failed to show any benefit, and thus single-ended mixers continued to be used. Poole's book [5,6] shows numerous superheterodyne bridges. The author constructed a particularly elaborate one in 1959 [45] in which the two klystrons were phase locked. However, this technology, elegant as it is, has become obsolete.

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Figure 5. Superheterodyne magic tee bridge.

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James S. Hyde

X 6 dB COUPLER

ADJUSTABLE IRIS

Figure 6. Low-cost bridge.

Figure 6 shows one of the lowest cost bridges ever developed. It was used in a low-cost Varian EPR spectrometer that was designed to facilitate the teaching of EPR spectroscopy.

Oscillator The oscillator is a Gunn diode with the operating voltage carefully selected such that an incremental change in voltage changes the frequency, but not the power. This feature was key to the AFC system.

Six-Decibel Coupler A 6-dB coupler reduces the amount of available power by a factor of 4, which is certainly not desirable. However, 75% of the signal power reaches the detector crystal, and, since a voltage detector is employed, the signal voltage is actually 87% of a perfect s y s t e m ~ a very significant advantage. This circuit lends itself to coaxial transmission-line technology.

Adjustable Iris The adjustable iris is used to mismatch the resonator deliberately in order to bias the detector crystal into the linear range.

Detector Crystal A Schottky diode is used, which, because of its low 1 / f noise, provided about 3 dB in improved receiver noise at 100 kHz from the carrier relative to a 1N23H point-contract diode. Figure 7 shows the final stage in the evolution of one-arm bridges. It was introduced by Varian Associates in 1966 in their E-3 table-top EPR spectrometer.

Oscillator The oscillator is an external cavity reflex klystron with a long-life cathode.

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375

Figure 7. Basic circulator bridge.

Circulator

Except for insertion losses, all microwave power generated by the oscillator reaches the sample resonator and all signal power reaches the detector crystal. Variable Iris

The variable iris provides microwave power to bias the detector into the linear region. Detector

The detector is a Schottky barrier diode. This bridge, simple as it is, makes few compromises with sensitivity and meets most of the needs of biologists and chemists. It is seriously deficient at helium temperatures and fails as a core bridge for the many so-called advanced E P R experiments such as those discussed in Hoff's book [22].

Reference-Arm Bridges Figure 8 illustrates the classic reference-arm bridge. It is the basic configuration employed in the great majority of E P R bridges in use today. Specifications and remarks on the various components of the bridge are as follows. Oscillawr

An external-cavity reflex klystron is normally employed, although Gunn diode oscillators have been used. The power is 400 mW over a 10% bandwidth. Sometimes a power leveling circuit is employed with a voltage-controlled attenuator as part of a feedback circuit such that the power actually available in the bridge is held at a constant 200 mW. The purpose is to compensate for a gradual drop of oscillator power output as

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James s. Hyde

Figure 8. Basic reference-arm bridge.

the device ages. A crucial specification is the phase noise. Typical values at the X-band are - 1 2 0 d B c / H z in a 1-Hz bandwidth 100 kHz from the carrier. At 35 GHz the desired power is 100 mW and the phase noise specification is - 107 d B c / H z . Precision Attenuator

Attenuators of the rotary-vane type are used because of the low phase shift. The nominal attenuation range is 60 dB. Sometimes an additional 30-dB pad is available that can be switched into the bridge in series with the precision attenuator, giving a 90-dB range. It is noted that microwave power that reaches the sample resonator spuriously can be on the order of 90 dB below the oscillator output. Circulator

Four-port circulators of the best available quality are employed. All isolations specified by the manufacturer should be 40 dB.

Reference Arm The two directional couplers are nominally 10 dB such that the maximum power available at the detector crystal is a few milliwatts. It is desirable that the path length in the reference arm from the first directional coupler to the second be the same as the path length in the sample arm between directional couplers, including the path from the circulator to the sample resonator and the return path. The latter is between 1 and 2 m; a delay line in a semirigid coaxial cable of this length is therefore inserted in the reference arm. Above 18 GHz the delay line can be made from a waveguide. Figure 9 shows a pattern used for a 35-GHz delay line

13. Electron Paramagnetic Resonance

377

1 2 . 2 em

Figure 9. Delay line for use at 35 GHz,

in the author's laboratory. Mirror image troughs 0.140 in. wide and 0.140 in. deep were machined in aluminum using a numerically controlled mill and bolted together. Arm-length equalization results in an unchanged bridge lineup over the 10% bandwidth of the bridge at X-band. At lower frequencies, bridge bandwidths tend to increase up to an octave, and therefore arm-length equalization is still necessary. Similarly at 35 GHz the bridge bandwidth decreases to 3%, but the wavelength relative to X-band changes a corresponding amount and arm-length equalization remains necessary. The level-set attenuator in the reference arm is set for optimum conversion gain of the detector crystalwor sometimes at a higher microwave level. Higher levels reduce the sensitivity of the bridge to oscillator phase noise. A troublesome ambiguity in the setting of the reference-arm phase shifter for detection of absorption [X", Equation (6)] is found depending on whether the path length difference is 180 ° or 360 ° . It should be 360 ° , such that microwave power reflected from the sample resonator is in phase rather than 180 ° out of phase with respect to the reference-arm phase at the detector crystal. It is noted that if the reference plane is defined at the detuned short position, the detection of absorption corresponds to the detection of the imaginary part of the sample resonator complex reflection coefficient. It is customary for the microwave engineer to set up the bridge such that the scientist-user cannot reach the 180 ° position with the reference-arm phase shifter.

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James S. Hyde

Detector

Crystal

All possible detector diodes have been evaluated. A common error is to select video or square-law diodes rather than mixer diodes, failing to recognize that the bridge is effectively a superheterodyne system. Diodes intended for Doppler radar are good choices. Generally modern bridges employ Schottky barrier diodes.

Detection of Dispersion Because the AFC locks the resonant frequency of the sample resonator to the oscillator frequency and because dispersion is manifested by a change in the resonant frequency of the sample resonator when magnetic resonance occurs, it might be thought that dispersion cannot be detected when an AFC is used. However, it was pointed out in Reference [46] that if the AFC feedback circuit does not have significant gain at the field modulation frequency, this apparent incompatibility of dispersion detection and use of AFC circuits is overcome. Figure 10 illustrates one possible circuit for dispersion detection. The phases of the microwave references signals (LO) at the two detector crystals differ by 90 ° . Magnetic resonance information always comes from the left-hand detector crystal. AFC information comes from this same detector crystal for detection of absorption and from the right-hand detector crystal for detection of dispersion. When shifting from absorption detection to dispersion detection, or vice versa, the phase shifter in the

90° PHASE SHIFTER~ /

1

Figure I0. Reference-arm bridge with a dispersion detection option.

379

13. Electron Paramagnetic Resonance

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reference arm must also be shifted by 90 ° . This scheme sacrifices 10% of signal power or 5% of the signal-to-noise ratio, assuming a linear detector. Figure 11 illustrates an alternative closely related AFC circuit for detection of dispersion. The idea is to use a sample-and-hold AFC circuit. The separation of the PIN diode and the adjustable short in arm 3 of the circulator is 45 ° . AFC information is collected during 10% of the available time with the PIN diode conducting, for example, and magnetic resonance information during 90% of the available time with the PIN diode open. This circuit has an advantage over that of Figure 10 in that no signal information is lost in normal detection of the absorption signal. Figure 12 illustrates another possible circuit for detection of dispersion. Only the circulator and sample resonator are shown for simplicity. A 10-dB directional coupler diverts 10% of the resonance information reflected from the sample resonator to a detector crystal selected for best sensitivity at very low microwave power (i.e., square-law detector). The resonator is assumed to be perfectly matched. One simply passes between dispersion and absorption by introducing 90 ° shifts using the phase shifter

380

James s. Hyde

•

1 ~-~,,~

3

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Figure 12. Scheme for dispersion detection with an AFC.

in the reference arm. The schemes of Figures 10 and 11 use 10% of the available power for AFC, resulting in an AFC signal-to-noise ratio that is 32% of the value when absorption is detected, which is probably an acceptable disadvantage. The scheme of Figure 12 is very easy to implement, but suffers further loss of the AFC signal because of the use of a square-law detector rather than a mixer. Figure 13 illustrates the use of a reference cavity in an AFC circuit. Because the full power of the oscillator is available for the AFC system, the sensitivity disadvantage of the circuit of Figure 12 is largely overcome. However, drift of the resonance frequency of the reference cavity relative to that of the sample resonator can be a problem. The various compromises and technical problems encountered in these schemes for detection of either the real or the imaginary magnetic resonance signals are largely overcome when a low-noise microwave signal amplifier is introduced into the bridge, as discussed in the next section.

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Figure 13. Scheme for dispersion detection with an AFC lock to a reference cavity.

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13. Electron Paramagnetic Resonance

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Figure 14. Basic reference-arm bridge with a low-noise microwave amplifier,

Reference-Arm Bridge with a Low-Noise Microwave Amplifier

EPR bridges employing low-noise microwave amplifiers have been described in References [43, 46-49]. This advance makes all other microwave bridge designs obsolete in situations in which performance rather than cost are important. Figure 14 illustrates one possible microwave circuit taken from Reference [43] (author's laboratory)which was developed at 35 GHz. The overall receiver noise figure using the classic circuit of Figure 8 was about 11 dB at X-band (recall that the effective intermediate frequency is 100 kHz). It was estimated in Reference [43] to be 25 dB at 35 GHz. The introduction of a low-noise microwave amplifier improves the overall receiver noise figure to that of the amplifier itself. However, in order to achieve realizable system improvement over the wide range of conditions employed in EPR spectroscopy, a number of additional improvements were required, as follows. Oscillator

In the classic reference-arm bridge, receiver noise usually limits performance, but phase noise in some circumstances must be considered also. Phase noise becomes more apparent as the receiver noise figure improves. It is often dominant when detecting dispersion and enters in quadrature when detecting absorption. See Reference [43] for a detailed discussion. It was shown in References [50] and [51] that phase noise could be reduced by more than 20 dB relative to that of the klystrons previously employed by using a Gunn diode locked to a high-Q tank circuit. Lowering of oscillator phase noise is required in order to realize improved system performance expected from introduction of low-noise microwave amplifiers.

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James S. Hyde

Microwave Amplifier The minimum gain required to lift amplifier noise above that of the remainder of the receiver system should be employed.

Mixer Medium- or high-barrier Schottky diodes in a balanced mixer should be used. Since the SO levels are higher by the amplifier gain, it is desirable that the LO level (i.e., reference-arm power) be correspondingly higher. This will give the bridge a similar "feel" to the spectroscopist as that of the classic bridge (Figure 8). A balanced mixer cancels oscillator AM noise, which is now more apparent.

Circulator A possible concern is that microwave power at the carrier frequency will reach the amplifier because of poor isolation or a slightly mismatched sample resonator. It would then be amplified and might compete with the reference-arm power. Introduction of slide screw tuners to match the arms of the circulator could be appropriate. Reference [52] describes such an approach using a drop-in circulator in a microstrip EPR bridge. Figure 15 replaces the balanced mixer of Figure 14 with a balanced quadrature mixer. The LO level must, of course, be correspondingly higher. Since the noise floor is established, dispersion and absorption, i.e., the I and Q signals, can be simultaneously detected using two lock-in amplifiers. AFC information is obtained without compromise. Because the I and Q signals [see Equations (5) and (6)] are related to each other by a Hilbert transform at low microwave powers, an additional 3 dB in the

I

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> >

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Figure 15. Reference-arm bridge with simultaneous detection of absorption and dispersion,

13. Electron Paramagnetic Resonance

383

signal-to-noise ratio can be obtained by transforming the dispersion to absorption and adding. This procedure fails at high powers, which is why it is of interest to the EPR spectroscopist to detect both the dispersion and the absorption signals. These signals in fact contain different information at high powers but not at low powers. Notes on Advanced Microwave Bridges

In the preceding sections on reference-arm bridges, a single arm was used to deliver power to Port 1 of the circulator and, hence, to the resonator. It is convenient in some advanced experiments to form the incident irradiation by combining several microwave signals, which are then fed to Port 1. Among the experiments of this kind are the following. (1) Electron-electron double resonance (ELDOR), in which two rather well-separated (ca. 30 MHz) microwave frequencies are incident on a low-Q resonator [53]. (2) Multiquantum EPR, in which at least two closely spaced frequencies (ca. 10 kHz) are incident [54]. (3) Multiquantum ELDOR, in which a closely spaced pair of frequencies and also a third well-separated frequency are incident [55]. (4) Saturation recovery, in which a very intense pulsed-microwave frequency and also a weak CW frequency are incident. The source either may be at the same frequency or may be incoherent. An early circuit for saturation recovery using incoherent sources was described by Davis et al. [56], who originated this technique. Reference [57] describes an alternative strategy in which the intense and weak signals were fed to the two inputs of a sample-containing bimodal cavity. (5) Pulse ESR, in which the irradiation strategy requires a train of pulses, each of carefully controlled amplitude, microwave phase, and duration. A bridge with two excitation paths for pulse EPR is described in Reference [58]. The Bruker Pulse EPR Bridge, ESP380-1010, contains four excitation paths. A circuit diagram of this instrument appears in Reference [26, p. 84]. From Equation (7), it is apparent that EPR experiments can be carried out at very high frequencies using very high magnetic fields. There is currently a growing interest in high-field EPR spectroscopy. A chapter by Budil et al. in Reference [22] describes instrumentation for EPR at 250 GHz and 1 mm. Quasioptical techniques are used. Eaton and Eaton [59] review applications of high magnetic fields in EPR spectroscopy and provide access to the current literature.

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James S. Hyde

3. Resonators for EPR Spectroscopy Microwave cavity resonators have been used in nearly all EPR experiments until recently. The sample is placed in the cavity in a region in which the microwave magnetic field, H1, is a maximum and the cavity is oriented such that the static magnetic field, H 0, is perpendicular to H~. Although every microwave resonant mode can, in principle, be used for EPR spectroscopy, the modes of practical significance are the rectangular TEl02, the cylindrical TE011, and the cylindrical TMll 0. In this section, the rectangular TE~02 cavity is considered in some detail. Extension of the key ideas to other modes is straightforward. Selected material relevant to other modes is also presented. However, the literature is very large. The reader is referred to Poole's books [5, 6] for access. Other types of microwave structures, including slow wave or lumped circuits, have been introduced. These structures are discussed briefly at the end of Section 3.

Multipurpose TE 102 Cavity By far the most common cavity mode for X-band ESR is the rectangular TEl0 2. A system of accessories, collets for sample support, and facilitated conversion to other closely related modes has evolved. This flexibility is the reason that the adjective "multipurpose" is used to describe the cavity. Probably in excess of 2000 Multipurpose TEl02 EPR X-band cavities have been sold commercially. The system was developed by Varian Associates and remains in production by Bruker Instruments. The basic design was described in the patent literature [60]. A photograph is shown in Figure 16. The inner cross section corresponds to waveguide dimensions of 0.9 x 0.4 in., with a length of 1.7 in. The resonance frequency is 9.5 GHz. For convenience of further discussion, let these dimensions be called A, B, and C with indices 1, 0, and 2 along coordinates x, y, and z, respectively. In Figure 16, the yz plane is horizontal and the x direction is vertical. Features of the Varian design are described below.

Sample Access Stacks Sample access stacks are hollow brass tubes, 11 mm i.d., centered on both the upper and the lower yz surfaces and press fitted into a brass cavity body. All cavity surfaces including stacks are silvered, with a gold-flash on external surfaces to avoid tarnishing. The diameter of the

13. Electron Paramagnetic Resonance

385

Figure 16. Multipurpose TE io2 X-band EPR cavity,

stacks is close to cutoff for the fundamental propagation mode in the cylindrical waveguide, TE~I, but the symmetry of the fields in the resonator is such that this mode is not excited. A system of collets supports the sample. The microwave magnetic field is parallel to x and is at a maximum in this sample position; the microwave electric field is of zero amplitude in the xy plane that bisects the sample.

Variable Iris

Figure 17 shows the iris structure of the Varian cavity. It was bolted to one xy face using a silver gasket. It is probably the most frequently used variable iris structure in the world, but to the author's knowledge has

386

JamesS. Hyde

Teflon Tuning Screw

©

I I

© -- Disk

©

©

Figure 17. Variable iris for the multipurpose cavity.

never been described in the patent or scientific literature. (The patent, cited in Reference [60], describes a different iris.) Coupling increases as the copper "disk" at the end of the Teflon tuning screw (visible in Figure 16) approaches the center of the iris hole. It moves in a hollowed out "bathtub." The range of coupling can be increased by increasing the thickness of the disk. Demountable Sidewalls

In order for lO0-kHz magnetic field modulation to penetrate the cavity, the xz faces must be electrically thin. Two different sidewall geometries were employed: silver plated thin stainless steel and ceramic sidewalls with baked silver paint. Silver gaskets were placed between the resonator and sidewalls, and the assembly was carefully bolted together using a torque screwdriver. Microwave currents cross the edges of the sidewalls, and this might, therefore, be considered an unreliable design. Careful attention to detail made it commercially viable. Field modulation coils made from Litz wire and mounted on the side plates in a Helmholtz geometry are resonant at 100 kHz and provide up to a 20-G peak-to-peak field using a power supply with about 8 W of capacity. Unloaded Q-values of 7500 are typical. Light Irradiation Slots

Figure 16 shows slots with 50% transmission cut into an end plate that is bolted to the xy face opposite the iris. There are numerous EPR experiments requiring illumination of the sample.

EPR Cavity Problems Problems associated with cavity design include the following.

13. Electron ParamagneticResonance

387

Background Contamination, Usually from Iron and Copper Salts in the Walls Strict attention to purity of plating materials is required. A gold flash was used for appearance, but was excluded from the cavity interior. More difficulty was experienced with contamination during gold plating procedures than for silver. The silver salts (tarnishing) forming on the interior are, in spite of their appearance, not deleterious for EPR spectroscopy.

Acoustic Vibrations at 100 kHz Current passing through the modulation coils at 100 kHz gives rise to forces because of the static magnetic fields. An acoustic analysis of brass structures of typical X-band dimensions reveals numerous mechanical resonances in the 100-kHz range. Care must be taken not to excite these acoustic modes. If they are, modulation of Q and spurious cavity resonance frequency modulation occur that are very troublesome. Modulation coils are embedded in epoxy such that displacements from the forces are minimal.

Eddy Currents Time-varying magnetic fields at 100 kHz induce eddy currents in metal structures that in turn give rise to forces because of the static magnetic field. The resulting complications are similar to direct forces on the lO0-kHz modulation coils. Multipurpose Cavity Accessories

Liquid Nitrogen Dewar A dewar made from the highest purity synthetic fused quartz (outer wall, 10 mm o.d. and 8 mm i.d.; inner wall, 7 mm o.d., and 5 mm i.d.) is placed in the resonator passing through the stacks. Quartz sample tubes of 3 mm i.d. and 4.5 mm o.d. are used. Of course, silvering on the dewar is omitted in the region of the microwave field. Liquid nitrogen has a dielectric constant of 1.454, and bubbling can be troublesome. The dielectric properties of quartz shift the resonant frequency of the cavity from 9.5 to 8.8 GHz, necessitating retuning of the microwave bridge. Ultraviolet irradiation sometimes induces background signals (color centers) in the dewar. They can sometimes be removed by annealing. It was observed that quartz in this dewar geometry increases the peak microwave magnetic field at the sample by 21/2. It may be thought surprising that a dielectric can alter a magnetic field distribution, but this observation is a natural consequence of Maxwell's equations, which connect all electromagnetic field vectors.

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James S. Hyde

Dewar Insert

In order to avoid liquid nitrogen bubbling, temperature-regulated nitrogen gas can be made to flow over a transmission dewar with an opening at the bottom for the gas and at the top not only for sample access but also for escaping gas.

Mixing Chamber Figure 18 shows a plastic mixing chamber. Two chemical reactants flow into the tubes at the bottom of the chamber, and the product of the reaction flows into a curvette that is inserted into the resonator. It is observed that flow from the bottom to the top reduces bubble formation. Under favorable circumstances a transient EPR signal can be observed in times as short as 1 ms. Both continuous flow (for observing the spectrum

Figure 18. Mixing chamber with an attached "flat" cell.

13. Electron Paramagnetic Resonance

389

of a short-lived species) and stopped flow (for studying the kinetics) can be used. Flat Cell

An approach to handling aqueous samples (which have an exceptionally high loss tangent) is to contain the sample to the central xy plane, in which the microwave electric field goes to zero and the RF magnetic field is a maximum. As Stoodley has shown ([61], and references therein) a flat quartz cell of a 1-cm × 0.4-mm inner cross section gives optimum sensitivity. Careful positioning jigs and collets are needed in order to place the flat cell precisely in the nodal surface, resulting in the highest possible Q. The mixing chamber of Figure 18 is shown connected to a flat cell for the observation of short-lived species in an aqueous solution. It was discovered

Figure 19. Tissue ceil,

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James S. Hyde

that if the electric field is perpendicular to the surface, the cavity Q is high and experiments are also possible [62].

Tissue Cell

The idea is the same as that for the flat cell~namely, to accommodate a tissue sample with a high dielectric loss in the nodal plane (see Figure 19).

Electrochemical Cell

Maki and Geske [63, 64] first demonstrated in situ electrochemical generation of free radicals for electron paramagnetic resonance studies. Shortly thereafter, Piette et al. [65] developed an electrochemical cell for use with the Varian Multipurpose TEl0 2 microwave cavity. This cell

Figure 20. The TE Jo4dual-sample cavity.

13. Electron Paramagnetic Resonance

TO 400 CYCLE FIELD MODULATION POWER SUPPLY

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remains in commercial production by Wilmad Glass Co. and by Bruker and is by far the most widely used geometry. See Reference [66] for an article on electrochemical generation of free radicals. Conversion to Other Rectangular TE Modes

Dual-Sample Cavity Two multipurpose cavity bodies are bolted together to form a rectangular TE~04 cavity (Figures 20 and 21). Two samples can be inserted, one for calibration and the other for examination. Different field-modulation frequencies are employed, permitting the simultaneous independent detection of the EPR spectra from both samples. This is accomplished by feeding the output of the microwave detector in the bridge to two separate lock-in amplifiers. Quantification of signal intensities and precision in measurement of EPR spectral positions are greatly facilitated by this direct comparison of an unknown spectrum with a reference spectrum.

Optical Transmission Cavity An extra half-wavelength section is bolted to a multipurpose cavity body, thereby converting it to a rectangular TEl03 cavity (Figure 22). Short sections of a higher frequency waveguide are placed in the end walls of the cavity, as illustrated. These sections are beyond cutoff and protrude slightly into the cavity such that the resonant frequency is not shifted. There is a "straight through" optical pathway that permits simultaneous EPR and optical spectroscopy measurements. The purpose of the extra half-wavelength is only to provide space for a microwave coupling structure. Figure 22 also shows the demountable field modulation coil assembly.

392

James S. Hyde

Figure 22. Optical transmission cavity.

//,11//o Sometimes in E P R spectroscopy it is desirable to be able to examine a sample not only with H 1 _L H 0, but also with HI lIH0. The inner cross section of the standard multipurpose cavity in the xy plane is, as previously stated, 0.9 by 0.4 in. The microwave frequency in the y direction corresponding to the 0.4-in. dimension and the 0 index is independent of this dimension. In the cavity under consideration in this section, the cross section was changed to 0.9 x 0.81 in. The frequency of the standard mode was unaffected, and a n e w T E l 0 2 mode could be observed with x and y axes interchanged and with H 1 at the sample position parallel to H 0. Resonance frequencies are 9.502 GHz for H 1 _1_

13. Electron Paramagnetic Resonance

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Figure 23. Diagonal variable iris for use in the H~IIH 0 cavity.

and 9.645 GHz for H 11[. When a quartz dewar insert is placed in the cavity, these frequencies shift: 9.250 GHz for H 1 _1_ and 8.903 GHz for Hill. Figure 23 illustrates the iris used in this cavity. The structure of Figure 17 has essentially been rotated by 45 ° and the incoming waveguide has a 45 ° twist. Either mode could be excited by setting the frequency of the microwave bridge to the frequency of the desired cavity resonance. The variable iris worked well for both modes. The experimentalist could easily shift from H~ _1_H 0 to H~lIH0 by readjusting the bridge frequency without touching the sample setup. One discovery in the development of this structure is that 11-mm-diameter sample-access stacks can be placed not only in the center of the yz plane, but also in the center of the xz plane. ELDOR cavity (see Notes on A d v a n c e d M i c r o w a v e Bridges)

A one-half wavelength section as in the optical transmission cavity is bolted to the HI I[H0 cavity. Two "crossed" modes result: a TEl02 crossed with a TEl03 (see Figure 24 and Reference [66]). The microwave fields of both modes are present at the sample, but of only one mode in the extra half-wavelength section. Introduction of a dielectric into that section shifts the resonance frequency of that mode, but not the resonance frequency of the other mode. This permits the sweeping of one resonant frequency without affecting the other resonant frequency.

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Other EPR Microwave Cavity Designs In this section several novel microwave cavity ideas are discussed. Bimodal Induction Cavities

I n this application, one assumes the existence of two microwave modes that are degenerate in frequency with the microwave magnetic fields at the sample orthogonal. Moreover, both fields should be orthogonal to the static magnetic field H 0. Two incoming microwave waveguides are organized with accompanying irises such that microwave power can be introduced or received from each mode independently. Microwave power for excitation of the sample is coupled into one of the modes. If the two modes are perfectly isolated from each other, no power is found in the crossed mode; however, when magnetic resonance takes place, power is coupled to the orthogonal mode and, therefore, to the output waveguide. The sample can be said to induce a signal in the crossed mode. This is the microwave analogy of the Bloch crossed-coil induction experiment [1]. EPR induction was first described by Teaney et al. [67]. Moore has provided a particularly definitive theoretical analysis, including a discussion of isolation between modes [68]. Spurious leakage between modes can be described by a microwave vector of some phase and amplitude. It must be canceled by introducing an equal and opposite signal using suitable perturbing elements. In the author's experience, 30-dB isolation is achieved easily by careful machining, 50-dB isolation can be obtained and held using perturbing elements, and 80-dB isolation can be demonstrated on the microwave test bench, but is too unstable to be the basis of an experiment. Figure 25 illustrates a bimodal cavity designed by the author [66]. In this structure, two TEl03 modes are crossed, but only overlap for two half-wavelengths. The extra half-wavelength sections that are not "shared" contain the iris structures and provisions to tune the two resonant modes to the same frequency. The static magnetic field must be parallel to the long axis (z axis) of the cavity, which necessitates a rather large magnet gap.

Wire-Wound TEon Cavity Figure 26 illustrates a "wire-wound" TE011 cavity [69]. It is effectively transparent to transverse magnetic fields including not only magnetic field modulation at 100 kHz, but also radio frequency fields used in E N D O R (up to about 100 MHz). Microwave cavities based on this design were available commercially from Varian at both X-band, at which the wire diameter was 0.010 in. and the spacing, 0.010 in., and also at Q-band

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g z~W~ ~Z~w

w~o~ E

.~n"

E

c'-

>,,, ..0

(D -(D 0 4-0

O ._C '~

tr~ >,,,

---

I--- -

o

0 E ~' 0

(D -[D

s-

U

oE

'0

~z

-o d

c-

>~

(D

0

c-

E

u~ c-

8

~ W

wO "1-0

Z

Dill

/

c~

'[3 (D

~o L

o~

i_

(D

~-- . _ ._u g-

'0

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cA

0 X

o -o E

E

13. Electron Paramagnetic Resonance

397

Figure 26. Wire-bound TEol~ cavity,

(35 G H z ) w i t h 0.005-in. wire diameter and spacing. The microwave coupling structure as well as sample access stacks were on one end, requiring careful attention to layout. Some microwave leakage was observed, apparently arising from the radiation field associated with the microwave coupling structure. This was reduced by surrounding the structure of Figure 26 by an insulated layer of closely spaced wires parallel to the axis of the cavity.

Large Sample-Access Cavity Figure 27 illustrates an exploded view of the so-called "large sampleaccess" cavity developed by Carrington et al. [70]. It is well known that very large holes can be placed on axis of TE011-mode cavities. The symmetry of this mode is such that the low cylindrical transmission line modes are not excited. The design employed a 2.5-cm sample-access stack. There was then no longer sufficient access at the ends for a coupling structure. Therefore, a TE012 mode was employed; the first half-wavelength along the z axis of the cavity was used for side coupling, and the second was a wire-wound structure as described in Figure 26.

398

James s. Hyde

Figure 27. Exploded view of the large sample access cavity of Carrington and Hyde for use with gas-phase samples.

Other Types of EPR Sample-Containing Structures Hefices

The traveling wave helix was introduced into EPR spectroscopy by Webb [71]. Resonant helices were analyzed by Volino et al. [72]. Sokolov and Benderskii describe the use of a helix for ELDOR [73]. These workers continued their studies of slow-wave structures for EPR spectroscopy as reported in the specialized Russian literature. Hausser and colleagues describe the use of a helix inserted into a microwave cavity for ELDOR experiments [74, 75]. Loop-Gap Resonators

This lumped-circuit device was introduced into EPR by Froncisz and Hyde [76], and numerous variations were subsequently developed. The subject has been reviewed [22]. The bridged loop-gap resonator of Pfenninger et al. [77] was analyzed by full-scale electronmagnetic field calculations. Anderson et al. [78] and Britt and Klein [79] describe experiments in which loop-gap resonators were inserted into TEl02 cavity resonators. Loop-gap resonators consist of discernable capacitances and inductances with overall dimensions of the order of 1/10th of a wavelength. Thus, they are in fact intermediate between distributed and lumped circuits. In the author's judgment, microwave geometries of this kind remain underdeveloped.

13. Electron Paramagnetic Resonance

399

Slotted- Tube Resonator

This structure was introduced into EPR by Mehring and Freysoldt [80] following a design for use at much lower frequencies by Schneider and Dullenkopf [81]. The microwave magnetic-field pattern resembles that of the TMll 0 cavity mode. However, the entire structure is miniaturized by introducing curved conducting surfaces that are in the electric-field regions. The slotted-tube resonator has been widely used in pulse-EPR spectroscopy. Dielectric Resonators

The earliest use of dielectric resonators for EPR appears to be that by Rosenbaum [82], and this paper is recommended to the reader. Further access to the literature is provided by Poole [5, 6]. Typically, the EPR dielectric resonator oscillates in the cylindrical TE011 mode with a hole on-axis for the sample. A severe criticism of dielectric resonators for EPR usage is that background signals from trace impurities in the dielectric are very objectionable.

References [1] F Bloch, Nuclear induction, Phys. Rec., Vol. 70, pp. 460-474, 1946. [2] G. Feher, Sensitivity considerations in microwave paramagnetic resonance absorption techniques, Bell. Syst. Tech. J., Vol. 36, pp. 449-484, 1957. [3] T. H. Wilmshurst, Electron Spin Resonance Spectrometers, Monographs on Electron Spin Resonance. London: Adam Hilger, 1967. [4] R. S. Alger, Electron Paramagnetic Resonance: Techniques and Applications. New York: Wiley (Interscience), 1968. [5] C. P. Poole, Electron Spin Resonance: A Comprehensice Treatise on Experimental Techniques. New York: Wiley (Interscience), 1967. [6] C. P. Poole, Electron Spin Resonance: A Comprehensive Treatise on Experimental Techniques, 2nd Ed. New York: John Wiley & Sons, 1983. [7] Electron Spin Resonance, Specialist Periodical Reports. London: Chemical Society. [8] C. Daul, H. Fischer, J. R. Morton, K. F. Preston, and A. v. Zelewsky, Magnetic Properties of Free Radicals, Landolt-B6rnstein, Vol. 9. Berlin: Springer-Verlag, 1977. [9] A. Carrington and A. D. McLachlan, Introduction to Magnetic Resonance, with Applications to Chemistry and Chemical Physics. New York: Harper & Row, 1967. [10] G. E. Pake and T. L. Estle, The Physical Principles of Electron Paramagnetic Resonance, 2nd Ed., Frontiers in Physics. Reading, MA: Benjamin, 1973. [11] J. A. Weil, J. R. Bolton, and J. E. Wertz, Electron Paramagnetic Resonance: Elementary Theory and Practical Applications. New York: John Wiley & Sons, 1994. [12] N. M. Atherton, Electron Spin Resonance: Theory and Applications. New York: John Wiley & Sons, 1973.

400

JamesS. Hyde

[13] P. B. Ayschough, Electron Spin Resonance in Chemistry. London: Methuen, 1967. [14] J. E. Harriman, ~n Theoretical Foundations Of Electron Spin Resonance. New York: Academic Press, 1978. [15] S. A. Al'tshuler and B. M. Kozyrev, Electron Paramagnetic Resonance (trans. by Scripta Technica). New York: Academic Press, 1964. [16] W. Gordy, Theory and Applications of Electron Spin Resonance. New York: John Wiley & Sons, 1980. [17] W. Low, Paramagnetic Resonance in Solids. New York: Academic Press, 1960. [18] C. P. Poole and H. A. Farach, The Theory of Magnetic Resonance. New York: Wiley (Interscience), 1972. [19] A. Ehrenberg, B. Malmstr6m, and T. Viinng~rd, eds., Magnetic Resonance in Biological Systems. Oxford: Pergamon Press, 1967. [20] H. M. Swartz, J. R. Bolton, and D. C. Borg, eds., Biological Applications of Electron Spin Resonance. New York: John Wiley & Sons, 1972. [21] G. Feher, Electron Paramagnetic Resonance with Applications to Selected Problems in Biology. New York: Gordon & Breach, 1970. [22] A. J. HolT, ed., Advanced EPR: Applications in Biology and Biochemistry. Amsterdam: Elsevier, 1989. [23] L. R. Dalton, EPR and Advanced EPR Studies of Biological Systems. Boca Raton, FL: CRC Press, 1985. [24] L. Kevan and R. N. Schwartz, eds., Time Domain Electron Spin Resonance. New York: John Wiley & Sons, 1979. [25] L. Kevan and M. K. Bowman, eds., Modern Pulsed and Continuous-Wave Electron Spin Resonance. New York: John Wiley & Sons, 1990. [26] C. P. Keijzers, E. J. Reijerse, and J. Schmidt, eds., Pulsed EPR: A New Field of Applications. Amsterdam: North-Holland Publ., 1989. [27] L. J. Berliner, ed., Spin Labeling: Theory and Applications. New York: Academic Press, 1976. [28] L. J. Berliner, ed., Spin Labeling H: Theory and Applications. New York: Academic Press, 1979. [29] L. J. Berliner and J. Reuben, eds., Spin Labeling: Theory and Applications. New York: Plenum, 1989. [30] L. Kevan and L. D. Kispert, Electron Spin Double Resonance Spectroscopy. New York: John Wiley & Sons, 1976. [31] H. C. Box, Radiation Effects: ESR and ENDOR Analysis. New York: Academic Press, 1977. [32] M. M. Dorio and J. H. Freed, eds., Multiple Electron Resonance Spectroscopy. New York: Plenum, 1979. [33] P. C. Poole and H. A. Farach, Relaxation in Magnetic Resonance: Dielectric and M6ssbauer Applications. New York: Academic Press, 1971. [34] L. T. Muss and P. W. Atkins, eds., Electron Spin Relaxation in Liquids. New York: Plenum, 1972. [35] K. J. Standley and R. A. Vaughan, Electron Spin Relaxation in Solids. New York: Plenum, 1969. [36] A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions. Oxford: Clarendon Press, 1990. [37] J. R. Pilbrow, Transition Ion Electron Paramagnetic Resonance. Oxford: Clarendon, 1990. [38] T. F. Yen, ed., Electron Spin Resonance of Metal Complexes. New York: Plenum, 1969. [39] F. Gerson, High Resolution ESR Spectroscopy. New York: John Wiley & Sons, 1970.

13. Electron Paramagnetic Resonance

401

[401 J. A. Weil, M. K. Bowman, J. R. Morton, and K. F. Preston, eds., Electron Magnetic Resonance of the Solid State. Ottawa: Candaian Society for Chemistry, 1987. [41] G. R. Eaton, S. S. Eaton, and K. Ohno, EPR Imaging and In Vitro EPR. Boca Raton, FL: CRC Press, 1991. [42] W. A. Anderson, Nuclear magnetic resonance spectra of some hydrocarbons, Phys. Rev., Vol. 102, pp. 151-167, 1956. [43] J. S. Hyde, M. E. Newton, R. A. Strangeway, T. G. Camenisch, and W. Froncisz, EPR Q-band bridge with GaAsFET signal amplifier and low noise Gunn diode oscillator, Rec. Sci. Instrum., Vol. 62, pp. 2969-2975, 1991. [44] R. C. Rempel and H. E. Weaver, Low-power microwave reflection bridge, Rev. Sci. Instrum., Vol. 30, p. 137, 1959. [45] J. S. Hyde, "Magnetic Resonance, Relaxation, and Rapid Passage Phenomena in LiF F Centers," PH.D. Thesis, MIT, Cambridge, MA, 1959. [46] J. S. Hyde, "Gyromagnetic Spectrometer Having Separate Dispersion and Absorption Mode Detectors," U.S. Pat. 3,350,633, Oct. 1967. [47] C. Hoentzch, J. R. Nikals, and J. M. Spaeth, Sensitivity enhancement in E S R / E N D O R spectroments by use of microwave amplifiers, Rev. Sci. Instrum., Vol. 49, p. 1100, 1978. [481 G. Grampp, Application of microwave preamplifier to an ESR spectrometer, Rev. Sci. Instrum., Vol. 56, pp. 2050-2051, 1985. [49] S. L. Dexheimer and M. P. Klein, Sensitivity improvement of a Varian E-109 EPR spectrometer with a low noise amplifier, Rev. Sci. Instrum., Vol. 59, pp. 764-766, 1988. [50] R. A. Strangeway, T. K. Ishii, and J. S. Hyde, Low phase noise Gunn diode oscillator design, IEEE Trans. Microwave Theory Tech., Vol. MTT-36, pp. 792-794, 1988. [51] R. A. Strangeway, T. K. Ishii, and J. S. Hyde, Design and fabrication of a 35 GHz 100 mW low phase noise Gunn diode oscillator, Microwave J., Vol. 31, pp. 107-111, July 1988. [52] D. A. Knoll, "Tuning of Microstrip Circulators for Maximum Sensitivity in ESR Bridges," M.S. Thesis, Marquette Univ., Milwaukee, WI, 1989. [53] J. S. Hyde, J.-J. Yin, W. Froncisz, and J. B. Feix, Electron-electron double resonance (ELDOR) with a loop-gap resonator, J. Magn. Reson., Vol. 63, pp. 142-150, 1985. [54] P. B. Sczaniecki, J. S. Hyde, and W. Froncisz, Continuous wave multiquantum electron paramagnetic resonance spectroscopy II. Spin-system generated intermodulation sidebands, J. Chem. Phys., Vol. 94, pp. 5907-5916, 1991. [55] H. S. Mchaourab, T. C. Christidis, W. Froncisz, P. B. Sczaniecki, and J. S. Hyde, Multiple quantum electron electron double resonance, J. Magn. Reson., Vol. 92, pp. 429-433, 1991. [56] C. F. Davis, Jr., M. W. P. Strandberg, and R. L. Kyhl, Direct measurement of electron spin-lattice relaxation times, Phys. Rev., Vol. 111, pp. 1268-1272, 1958. [57] M. Huisjen and J. S. Hyde, A pulsed EPR spectrometer, Rev. Sci. Instrum., Vol. 45, pp. 669-675, 1974. [58] R. W. Quine, G. R. Eaton, and S. S. Eaton, Pulsed EPR spectrometer, Rev. Sci. Instrum., Vol. 58, pp. 1709-1723, 1987. [59] S. S. Eaton and G. R. Eaton, Applications of high magnetic fields in EPR spectroscopy, Magn. Reson. Rev., Vol. 16, pp. 157-181, 1993. [60] R. C. Rempel, C. E. Ward, R. T. Sullivan, M. W. St. Clair, and H. E. Weaver, "Gyromagnetic Resonance Method and Apparatus," U.S. Pat. 3,122,703, Feb. 1964. [61] L. G. Stoodley, The sensitivity of microwave electron spin resonance spectrometers for use with aqueous solutions, J. Electron. Control, Vol. 14, pp. 531-546, 1963. [62] J. S. Hyde, A new principle for aqueous sample cells for EPR, Rev. Sci. Instrum., Vol. 43, pp. 629-631, 1972.

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[63] A. H. Maki and D. H. Geske, Detection of electrolytically generated transient free radicals by electron spin resonance, J. Chem. Phys., Vol. 30, pp. 1356-1357, 1959. [64] D. H. Geske and A. H. Maki, Electrochemical generation of free radicals and their study by electron spin resonance spectroscopy; the nitrobenzene anion radical, J. Am. Chem. Soc., Vol. 82, pp. 2671-2681, 1960. [65] L. H. Piette, P. Ludwig, and R. N. Adams, EPR and electrochemistry. Studies of electrochemically generated radical ions in aqueous solution, Anal. Chem., Vol. 34, p. 916, 1962. [66] J. S. Hyde, J. C. W. Chien, and J. H. Freed, Electron-electron double resonance of free radicals in solution, J. Chem. Phys., Vol. 48, pp. 4211-4226, 1968. [67] D. T. Teaney, M. P. Klein, and A. M. Portis, Microwave superheterodyne induction spectrometer, Rev. Sci. Instrum., Vol. 32, pp. 721-729, 1961. [68] W. S. Moore, The design, analysis, and performance of resonant and nonresonant microwave transmission devices with theoretically infinite rejection, Rev. Sci. Instrum., Vol. 44, pp. 158-164, 1973. [69] J. S. Hyde, ENDOR of free radicals in solution, J. Chem. Phys., Vol. 43, pp. 1806-1818, 1965. [70] A. Carrington, D. H. Levy, T. A. Miller, and J. S. Hyde, Double quantum transitions in gas-phase electron resonance, J. Chem. Phys., Vol. 47, pp. 4859-5860, 1967. [71] R. H. Webb, Use of traveling wave helices in ESR and double resonance spectrometers, Reu. Sci. Instrum., Vol. 33, pp. 732-737, 1962. [72] F. Volino, F. Csakvary, and P. Servoz-Gavin, Resonant helices and their application to magnetic resonance, Rev. Sci. Instrum., Vol. 39, pp. 1660-1665, 1968. [73] E. A. Sokolov and V. A. Benderskii, Binary electron-electron resonance spectrometer with a spiral resonator, Prib. Tekhn. Eksp., Vol. 3, p. 232, 1969. [74] K. Hausser, "Electron Double Resonance Spectrometer with a Microwave Cavity Bridge Arrangement," U.S. Pat. 3,798,532, Mar. 1974. [75] E. Stetter, H.-M. Vieth, and K. H. Hausser, ELDOR studies of nitroxide radicals: discrimination between rotational and translational correlation times in liquids, J. Magn. Reson., Vol. 23, pp. 493-504, 1976. [76] W. Froncisz, and J. S. Hyde, The loop-gap resonator: a new microwave lumped circuit ESR sample structure, J. Magn. Reson., Vol. 47, pp. 515-521, 1982. [77] S. Pfenninger, J. Forrer, A. Schweiger, and Th. Weiland, Bridged loop-gap resonator: a resonant structure for pulsed ESR transparent to high-frequency radiation, Rev. Sci. Instrum., Vol. 59, pp. 752-760, 1988. [78] J. R. Anderson, R. A. Venters, M. K. Bowman, A. E. True, and B. M. Hoffman, ESR and ENDOR applications of loop-gap resonators with distributed circuit coupling, J. Magn. Reson., Vol. 65, pp. 165-168, 1985. [79] R. D. Britt and M. P. Klein, A versatile loop-gap resonator probe for low-temperature electron spin-echo studies, J. Magn. Reson., Vol. 74, pp. 535-540, 1987. [80] M. Mehring and F. Freysoldt, A slotted tube resonator STR for pulsed ESR and ODMR experiments, J. Phys. E: Sci. Instrum., Vol. 13, pp. 894-895, 1980. [81] H. J. Schneider and P. Dullenkopf, Slotted tube resonator: a new NMR probe head at high observing frequencies, Rev. Sci. Instrum., Vol. 48, pp. 68-73, 1977. [82] F. J. Rosenbaum, Dielectric cavity resonator for ESR experiments, Rev. Sci. Instrum., Vol. 35, pp. 1550-1554, 1964.

CHAPTER

14 Microwave Navigation Aids Stephen Hatcher and Goson Gu

Microwave

navigation systems are moving away from systems requiring ground stations which offer variable performance to systems offering worldwide coverage with high performance in all weather conditions. Two such systems utilizing satellite telemetery and Doppler measurements are summarized in this chapter.

Part A: THE GLOBAL POSITIONING SYSTEM

The Gobal Positioning System (GPS) is a satellite-based position-fixing system under development by the U.S. Department of Defense since 1973. The purpose of GPS is to provide any user at any place on or near the surface of the earth with highly accurate three-dimensional position and velocity information and the time. With as many as 21 high-altitude satellites orbiting the earth, the coverage of GPS is worldwide and its precision is on the order of 10 m rms for position and 0.1 m / s rms for velocity in each dimension. Also it is tolerant of nonintentional or intentional interference. Compared with the existing systems like Loran-C or Transit System, GPS has shown its outstanding performance in precision,

Handbook of Microwave Technology, Volume 2

403

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

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Hatcher and Gu

coverage, and user access. There is no doubt that GPS has become the dominating system for land, water, and air navigation.

I. General Description The GPS has three segments: the space segment, the control segment, and the user segment.

Space Segment (1) The Space Segment consists of 21 satellites orbiting the earth with a period of 12 sidereal hours at an altitude of 20,200 km. (2) In addition to 3 active spare satellites, the 18 operating satellites form a constellation of six orbits with 3 satellites equally spaced on each (see Figure 1). (3) Each orbit is inclined by 55 ° with respect to the equatorial plane and is offset from one another by 60 ° in longitude. (4) The 18 operating satellites continuously broadcast navigation messages which include satellite positions, satellite clocks, clock correction parameters, and other navigation information. (5) The number of in-view satellites above the horizon is at least four at any place on earth.

9 3

5

1

8

4 Figure I. GPS satellite configuration: six orbits with three satellites equally spaced on Earth.

405

14. Microwave Navigation Aids

Control Segment (1) The control segment consists of a master control station, an upload station, and four monitor stations (more stations are planned). (2) The master control station completely controls the operation of the control segment. It performs the computations necessary to determine satellite ephemeris and atomic clock errors, generates user navigation data, and maintains a record of satellite navigation processor contents and status. (3) The upload station provides the interface between the control segment and the satellites. It utilizes an S-band uplink to upload data into satellite navigation processors. The monitor stations are unmanned remote data-collection stations under direct control of the master control station. (4) Each monitor station receives a satellite's broadcast signals for processing and collects local meteorological data for tropospheric signal delay correction.

User Segment (1) The user segment includes any GPS user equipment capable of receiving and demodulating navigation signals broadcast from GPS satellites. (2) A GPS user equipment comprises four major components: antenna, receiver, computer, and i n p u t / o u t p u t device. It receives navigation signals from satellites, selects the satellites with the best geometry and computes the pseudoranges to them, and determines its position, velocity, or both.

2. Position Fixing The coordinate system used in this article is the earth-centered inertial coordinate system shown in Figure 2, in which the positive-x axis goes from the earth center through the intersection of the equator and Greenwich meridian, the positive-z axis goes from the earth center through the North Pole, and the y axis completes the right-handed coordinate system. Because of earth rotation, the x and y coordinates change in longitude about 15° per hour.

Concept of Position Fixing (1) By measuring the distance rl to a satellite at position (x ~, y 1, Zl), we can narrow down our position (x, y, z) from the whole universe to a

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Hatcher and Gu

NORTH POLE GREENWICH

Y

Figure 2. Earth-centered inertial coordinate system.

sphere specified by the following equation (see Figure 3a): ¢(X-

XX) 2 -I- ( y -

y l ) 2 -]- (Z -- Z 1)2 = F1.

(1)

(2) By measuring the distances r I and r e to two satellites at (x 1, Yl, Zl) and (x a, Ya, Za) respectively, our position is confined on a circle specified

Position Locus .....................

2

i

Figure 3. (a) One range puts the user on a sphere. (b) Two ranges puts the user on a circle. (c) Three ranges puts the user on two points.

407

14. Microwave Navigation Aids

by the following joint equations (see Figure 3b):

1,/" x -V

- xI

)2

2+

+ ( ~ - yl)

( z - Zl)

2

-- r 1

(2)

V/(x . x:) :+(y . .

.

/-2.

(3) Theoretically, knowing three satellite's positions and the distances to them, we can locate our position on earth (see Figure 3c). The position is determined by solving the following joint equations (there are two possible solutions, but one would be obviously wrong): V/(x -Xl)

.

2 + (y -yl)2

.+ ( y .

¢ ( x . x3) 2. + ( y .

+ (z - Zl)2

.+ ( z y3).2 + ( z

= rl

r2 z3) 2

(3)

/'3"

Satellite-Position Acquisition and Radio Ranging (1) The GPS satellites continuously broadcast their positions to GPS users. After a broadcast signal is received and demodulated, the position of the broadcasting satellite can be obtained. (2) The distance to a satellite is based on radio ranging. The distance between two points is measured using a radio signal which travels between these two points. Since radio waves travel at the speed of light, c - 300,000 km per second, the distance to a satellite would be r = c × t, where t is the time a radio signal takes to travel from the satellite to us. The distance to a satellite is measured in terms of the radio signal travel time from the satellite to user.

Clocks (1) To precisely measure the signal travel time requires knowing the exact times at which the signal is transmitted and at which time it is received. Since there are two different "times" involved, the timing system has to be unified. (2) The GPS standard time is indicated by the very accurate clocks at the master control station, which is almost equal to Universal Time Coordinated. With highly stable clocks such as cesium or hydrogen laser clocks, a resolution of 1 ns (10 -9 sec) can be reached. (3) The time of a satellite clock is called the "space vehicle time" (SV time). Although each satellite carries four atomic clocks, the SV time may

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deviate slightly from the GPS standard time. This deviation is broadcast to GPS users via the satellite clock correction parameters contained in the navigation message. (4) The user clock is normally a quartz clock with lower accuracy than the satellite clocks.

Pseudoranges and Navigation Equations (1) Since the user clock is not accurate enough, the measured signal travel time would be incorrect. For example, a 10-3-s error will result in a distance error of 300 km. (2) To compensate the user clock error requires using four inaccurate satellite ranges called "psuedoranges." (3) Assume the user clock is tbias seconds faster than the GPS standard time. If the i th navigation signal is transmitted from the i th satellite at GPS time tsv i and received at user clock time tusi, the pseudorange to the ith satellite is /~i "- ¢ X (tus i --tsv i) and the true range is ri =

c X ( t u s i - - t b i a s - - tsv i) - - ri - - ¢ X t b i a s .

(4) Consider the following joint equations:

V/ ( x -

Xl) 2 + ( y -

yl) 2 + ( Z -

Z1)~ --/~1--C X tbias

V/(x - x2) 2 + ( y - y2) 2 + (z - z2) 2 = F2 - c X

/bias

(4)

V/(x-x s (X

-- X 4

2

+ (Y-Ys)

)~ -3t- ( Y

-- Y 4 )

2

2

+ (z-zs) -~- ( Z

-- Z4)

2 -- /~3 -- C X t bias 2

= r4 -- C X t b i a s .

Based on the known information, xi, yi, zi, and Fi, the four unknown terms, x, y, z, and t b i a s , c a n be solved. (5) Thus to derive a position a receiver must receive the navigation signals transmitted from four different satellites, get the satellite position information, measure the pseudoranges, and solve the navigation equations [Equations (4)].

3. Time Measurement (1) The pseudorange is determined by the inaccurate signal travel time (tus - tsv)which is measured by shifting and matching pseudorandom (PRN) codes.

14. Microwave Navigation Aids

409

(2) The GPS satellites broadcast their navigation messages using two data links: Link 1 (L1) at a center frequency of 1575.42 MHz and Link 2 (L2) at a center frequency of 1227.6 MHz. (3) The L1 and L2 signals are modulated by two PRN codes: a coarse acquisition code ( C / A code) and a precision code (P code). (4) The purpose of using PRN codes is for (a) the identification of the satellites, via code division multiplexing, and (b) the measurement of the signal travel time, via phase-shift measurement. (5) The C / A code is a Gold code with a length of 1023 bits and a chip rate of 1.023 MHz. It repeats every millisecond. (6) The P code is a long precision code with a complete cycle of 267 days and a chip rate of 10.23 MHz. Each satellite uses the exact one-week period of the P code which is nonoverlapping with the codes of other satellites. The P code is reset once a week. (7) The C,/A code is short, slow, and easily acquired. The P code is difficult to acquire but provides more precise timing. (8) Usually the C / A code is acquired first and then a transfer to P code is made. The transfer is made possible using the handover word (HOW). (9) Each 6-s navigation data subframe contains a new HOW (see Navigation Message). The H O W multiplied by 4 gives the Z-count at the beginning of the next 6-s subffame, where the Z-count is defined as the number of 1.5-s epochs since the beginning of a week. (10) Knowing the Z-count in the next subffame is equivalent to knowing the incoming P code in the next subframe. (11) The signal travel time is measured by the phase shift of the received signal with respect to the replica of the C / A code, P code, or both generated by the GPS receiver. (12) Although the measured signal travel time is inaccurate, it can be corrected by solving the navigation equations.

4. Velocity Measurement (1) The determination of the user's velocity is based on the measurement of the Doppler shift. (2) The velocity vector of a satellite at any time can be calculated by the user computer. (3) Knowing the position of the user and the position and the velocity of the satellite, the user's computer can determine the satellite's velocity along the direction of the user to the satellite.

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(4) The measurement of the Doppler shift gives the satellite's velocity relative to the user along the direction of the user to the satellite. The difference between the satellite's velocity and the satellite's relative velocity is the user's velocity along the direction of the user to the satellite. (5) A similar measurement from two other satellites provides the user with two other velocity vectors. (6) However, the signal frequency is not exactly known. Hence, four satellites and four Doppler-shift measurements are necessary to determine the user's velocity.

5. Signal Structure (1) The GPS signal carries information about satellite position, the satellite clock, clock correction parameters, and other components. (2) There are two data links, L1 and L2. Both the L1 and the L2 signals contain the same navigation data stream. (3) The L1 signal has two components: the in-phase component modulated by the P code and the quadrature-phase component modulated by the C / A code. (4) The L2 signal is modulated by the P code. (5) The C / A code is the product of two 1023-bit PRN codes with certain phase offset. It has a chip rate of 1.023 MHz and a period of 1 mso (6) The P code is the product of two long PRN codes with certain phase offset: one has a length of 15,345,000 bits and the other is 37 bits longer. It has a chip rate of 10.23 MHz and a complete period of 267 days. However, each satellite uses only a seven-day period of the P code. (7) Each satellite has it own C / A code and a seven-day period of the P code. (8) The navigation data stream has a bit rate of 50 bps with a subframe period of 6 s and a frame period of 30 s. (9) The spectra of L1 and L2 signals are shown in Figure 4.

6. Navigation Message (1) The navigation message is contained in a data frame 1500 bits long. (2) There are a total of five subframes in each data frame. (3) Each subframe consists of 10 words of 30 bits each. (4) The first two words are the telemetry word (TLM) and HOW, which are generated by the satellite. The remaining eight words of each subframe are user navigation data generated by the control segment.

411

14. Microwave Navigation Aids a L1 Signal dBW i

~

iq

, i,i

-1601-

2.046 MHz

~,,,,,, C/A Code

1575.42 MHz -

20.46 M H z - - - . ~

b L2 Signal

dBW

-166 1227.60 MHz 20.46 MHz

:-

Figure 4. The spectra of the L t and L2 signals,

(5) The TLM contains an 8-bit preamble, 14 bits of TLM message, 2 noninformation bearing bits, and 6 parity bits. (6) The HOW contains 17 bits of Z-count, a 1-bit synchronization flag, a 3-bit subframe identification, 2 noninformation bearing bits, and 6 parity bits. (7) The first subframe contains the satellite's clock correction parameters and ionospheric propagation delay model parameters, which are generated by the control segment. (8) The second and third subframes contain the satellite's ephemeris. (9) The fourth subframe contains a message of alphanumeric characters. (10) The fifth subframe contains the almanacs of all satellites (one per frame). (11) The format of the navigation message is shown in Figure 5.

7. Navigation Solution and Dilution of Precision The Navigation Solution (1) The navigation equations shown in Equations (4) are nonlinear equations of four unknown terms: x, y, z, and tbias.

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Hatcher and Gu

10 30-bitwords,6-secsubframe

Subframe No.

v

TLM

I HOW

I Block l - Clock Correction

TLM

l HOW

[ Block2-Ephemeris

TEa

I HOW I B'°ck3"Ephemen~(c°ntinued)

TLM

I HOW

TLM

HOW

]

l Block4-Message

1 frame 30 seconds 1500 bits

,

I BlockS-Almanac (25 framesto complete) ]

Figure 5. The format of a navigation message.

(2) A linearized version of Equations (4) can be derived, which is shown in the following, (x°-xl) A x + ( y O _ y a ) A y + ( Z 0 -- Z1) A Z + C • Atbias = A r 1 ~ o 0 0 r 0 -- C " tbias r~ o _ c • tbias r- ° -- C • tbias

(xO _

(yO -Ya) Ay +

X2) Ax +

0 ~0 _ C" tbias

(xO_X3)

-" 0 r 0 -- c " tbias

Ax +

~0 __ C" t0ias (X0--X4)

~0

(yO-Y_3_) Ay + ~0 _ C" t bias

Ax +

(yO_

Y4)

-

(Z° --z3) Az + c'Atbias 0 ~0 C " tbias z

Ay +

o

-

~o

r ° -- C" tbias

~O __ C" t0ias

( Z 0 -- Z 2 ) A Z -t- C" Atbias = A r 2 _ _ C . t0ias

= Af 3

z4)

c • t0ias

A Z + C • Atbias = A t 4 ,

(5) where x = x ° + Ax y=y°+Ay z=z°+Az

0

t bias : t bias -t- A t bias ¢

) 2 ( X 0 --

X i

+

(y

0

-

yi)2

+

(z

0

-

z i

)2

-

~ r° -

c

0 "/bias"

.413

14. Microwave Navigation Aids

(3) A matrix representation of Equations (5) is (6)

A .X=R,

where

A -

0-11

O'12

0"13

C

O'21

0"22

°'23

C

O"31

0"32

0"33

C

0"41

0"42

0"43

C

X=~ [Ax

Ay

Az

R = [A/~ 1

AE 2

AF 3

Atbias] T z~r4] T.

(4) The navigation solution is X=A

-1 . n ,

(7)

which gives the incremental relationship between pseudorange measurements and the user position and user clock bias. (5) The element 0-ij of A is the direction cosine of the angle between the range to the ith satellite and the jth coordinate, which affects the precision of navigation solution. Dilution of Precision (DOP)

(1) The matrix A is determined by the geometry of the four selected satellites. In the worst case, A-1 does not exit, which implies the unique navigation solution does not exit. (2) The covariance matrix of X is COV(X) = [A T. COV(R) -1 "A] -1. By normalizing COV(R) as the unity matrix, COV(X) = [ATA] -1, which implies the error variance of the user position and user clock bias is determined by the geometry of the four selected satellites. (3) The geometric dilution of precision (GDOP) is defined as oooP-

(4) In order to get the best navigation solution with the smallest error variance, the four satellites with the smallest GDOP should be selected.

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(5) Other DOP factors are defined in terms of Vx, Vy, Vz, and Vt, where V~, Vy, Vz, and Vt are the diagonal elements of COV(X). (a) Vertical dilution of precision (VDOP): VDOP = fVz(b) Horizontal dilution of precision (HDOP): HDOP = CV x + Vy. (c) Position dilution of precision (PDOP): PDOP

CV~ + Vy + V~.

(d) Time dilution of precision (TDOP): TDOP = ~ t -

8. Error Sources The errors of GPS are primarily from three major sources: the space segment, the user segment, and the propagation link.

Space Segment The errors coming from the space segment include satellite ephemeris error, satellite delay, and satellite clock error. (1) Ephemeris error: The satellite position error results from the difference between the actual satellite positions and the ephemeris data contained in the navigation message received by the user. (2) Satellite delay: The satellite delay is the signal propagation time delay caused by the processing and passage of the signal through the satellite equipment. (3) Clock error: The individual satellite clock may deviate as much as 976 /xs from GPS standard time. The deviation is corrected by transmitting the clock correction coefficients to the user as part of the navigation message.

User Segment The errors coming from the user segment include user receiver measurement error and user mechanization error. (1) Receiver measurement error: This error primarily is contributed by the receiver noise and the receiver quantization error. (2) Mechanization error: The mechanization error is due to finite resolution of user computers, mathematical approximation, algorithm uncertainties, and execution/computation timing delays.

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Propagation Link The propagation link errors have been identified as being due to ionospheric delay, tropospheric delay, and multipath. (1) Ionospheric delay: The propagation delay of radio signals passing through the ionosphere is due to a reduction in speed and the bending of the ray. The overall delay in the signal is nearly inversely proportional to the square of the signal frequency. (2) Tropospheric delay: The tropospheric delay is the propagation delay of the signal when it passes through the troposphere, which is independent of signal frequency. (3) Multipath: Multipath error results from the combination of data from more than one propagation path that distorts the signal characteristics. This error depends on the environment and the specific location of the user.

9. Differential GPS Concept of Differential GPS (1) The concept of differential GPS is derived from the fact that the measurement errors are highly correlated among different GPS users in the same local area. (2) This correlation is because the satellites are so high up that the paths of satellite signals to different users in the same local area and the signal propagation delays will almost be the same. (3) By canceling the common errors experienced by different users in the same local area, the measurement accuracy can be increased to the order of centimeters.

Implementation of Differential GPS The implementation of differential GPS is shown in Figure 6. (1) A reference receiver at a known location is set up in the area in which greater accuracy is desired. (2) The reference receiver measures the correlated errors which are common to all users in the same local area. (3) The reference receiver broadcasts an error correction message to GPS users in the same local area. (4) The GPS users receive the error message and use it to correct their navigation solutions.

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Hatcher and Gu

ReferenceReceiver

~

H

/

Figure6. ConfigurationofdifferentiaGPS. l I0. Summary (1) The GPS is a satellite-based position-fixing system which provides the user with highly accurate three-dimensional position and velocity information and the time. (2) The GPS has three segments: the space segment, the control segment, and the user segment. (3) The space segment of the GPS consists of 21 satellites orbiting the earth at a high altitude. (4) The control segment of the GPS consists of a master control station, an upload station, and several monitor stations. (5) The position fixing is based on measurements of pseudoranges. It needs four satellites to get four navigation equations in order to solve four unknowns: three-dimensional position plus time. (6) The pseudorange is determined by the signal travel time which is measured via shifting and matching PRN codes. (7) The velocity measurement is based on the measurement of Doppler shifts. It needs four satellites to determine the user's threedimensional velocity vector. (8) The GPS navigation message is broadcast through two data links: L1 and L2. The L1 and L2 signals are modulated by the P code and the C / A code. (9) The C / A code is short, slow, and easily acquired. The P code is fast and difficult to acquire, but provides more precise timing. (10) The GPS navigation message contains the satellite's ephemeris, the clock correction parameters, the satellite's almanacs, and other components.

14. Microwave Navigation Aids

417

(11) The precision of navigation solution is determined by the geometry of the four selected satellites. This factor is called GDOP. (12) The best four satellites to be selected for solving the navigation solution are the four with the smallest GDOP. (13) The errors of GPS are primarily from the space segment, the user segment, and the propagation link. (14) With the operation of differential GPS, much more accurate measurements can be obtained.

Part B: DOPPLER NAVIGATION SYSTEM

A Doppler navigation system, or Doppler navigator, is a completely self-contained, dead-reckoning system requiring no ground stations. It is an all-weather system (except in certain conditions of rain) and can provide continuous position and velocity information anywhere on earth. The Doppler navigator obtains the velocity information from a Doppler radar and the direction information from a directional sensor. By combining these two pieces of information, the quantities such as along-heading velocity, cross-heading velocity, vertical velocity, ground speed, and drift angle can be determined. The Doppler navigator continuously integrates the velocity information into the distance traveled from the point of departure and resolves the present position. With the information of points of departure and destination or desired course and distance, the Doppler navigator can provide the autopilot information such as bearing to destination, distance to destination, track-angle error, and cross-course deviation.

I. General Description (1) A complete Doppler navigation system has three major components: the Doppler radar, the heading reference and vertical reference, and the navigation computer. The block diagram of a Doppler navigation system is shown is Figure 7. (2) The Doppler radar measures the aircraft velocity with respect to its antenna frame coordinate system.

418

Hatcher and Gu Departure position & destination or desired course & distance

Doppler Radar

Velocity ~__

Pitch Roll and

Vertical Reference

Track-angle

Computer

Heading

-..__

~

CurrentBearinposition g Distance error Cross-course deviation

Navigation

1

To displays and to autopilot

1

Heading

Reference

Figure 7. Diagram of the Doppler navigation system.

(3) The heading reference and vertical reference fix the direction of the antenna frame with respect to the navigational coordinate system. (4) The navigation computer accepts the velocity information from the Doppler radar and the heading information from the heading reference, continuously integrates the velocity information into the distance traveled from the point of departure, and resolves the present position. By comparing the information of the current position with destination coordinates, the quantities such as bearing to destination, distance to destination, track-angle error, and cross-course deviation can be continuously computed. These quantities can be output to displays and to the autopilot.

2. Fundamental Principles of Doppler Radar (1) The Doppler effect is a phenomenon in which, when there is relative motion between a wave source and an observer, the observed frequency is different from the transmitted frequency. This change in observed frequency is called the Doppler shift, which can be expressed by

vRf fD=

C

vR -- h '

(1)

where fD is the Doppler shift, f is the wave frequency, c is the wave speed (speed of light for Doppler radar), VR is the relative velocity between the source and the observer, and h - c / f and is the wavelength.

419

14. Microwave Navigation Aids

(2) Consider an aircraft moving with a horizontal velocity, V~, and radiating a beam at an angle, 4~, with the velocity vector, as shown in Figure 8. The Doppler shift observed after the beam bounces back to the aircraft is 2f

2

f~' = - 7 V. cos 4' = 7 V. cos 4,.

(2)

If ~b and fD are known, V~ can be determined by v~ =

c .f,, a .fo = . 2 f cos & 2 cos ~b

(3)

Equation (3) is the fundamental expression for the measurement of velocity by means of Doppler radar. (3) Since velocity is a three-dimensional vector, it contains three orthogonal components. Therefore, a minimum of three noncoplanar beams are required to measure these three velocity components. A beam configuration, called a Janus configuration, is designed to accomplish this. It has both forward- and rearward-looking beams. A Janus configuration with four beams is shown in Figure 9 in which the beam Doppler frequencies f~ and the velocity components Vi have the following relationships. fA=

2f c[Vx cos 6

+ v, cos 0 - v~ cos 12 ]

f~=

2f 7[Vx cos 4,

- v,, cos 0 - v~ cos a ]

fc=

2_f [-Vx cos 6 - vy cos 0 - Vz cos a ] c

f~

2f = c[-Vx

cos 4, + v,, cos o - v~ cos a ]

c

D -I~ Vx = 8 f cos q5 (f°A + fB

-,"2)

c

v~ = 8 l c o s 0 ( f A - I ~ -

f~ +I5)

--c

v~ = 8 f c o s a ( f ~ +fF, + f c

+f~).

420

Hatcher and Gu

Vx

Figure 8. Basic Doppler radar beam.

VZ

Vx

Vy

•

-\

Figure 9. Four-beam configuration.

42 I

14. Microwave Navigation Aids

(4) Since three noncoplanar beams are enough to measure the velocity components, we can drop beam D from Figure 9. The remaining configuration is a three-beam Janus configuration in which the beam Doppler frequencies f~ and the velocity components V/ have the following relationships. foA = 2 f f~=

c[Vx c o s

4, +

Vyc o s 0

2f c[Vx cos

4, -

Vyc o s

fDc = --~2 f [ -- V x

C O S (~ -

Vy

-

Vz

cos f~ ]

0 -

v~

cos f~ ]

cos

0 -

V z cos f~ ]

c

Vx = 4 f cos 05 ( f ~ - fc°) C

Vy = 4 f cos 0 ( f ~ - f ~ ) --C

V~ = 4 f cos f~ ( f DA + f cD) "

3. Functional Description of Doppler Radar A typical Doppler radar consists of four major units: the antenna, transmitter, receiver, and frequency tracker. The diagram of a Doppler radar is shown in Figure 10.

Antenna (1) From stabilization consideration, there are two types of antennas used for Doppler radars: one is fixed to the aircraft frame and the other is continuously stabilized to the local horizontal. (2) The fixed antenna has the advantage of simplicity. It can be made as an integral part of the aircraft's skin or a rigid assembly. However, extra computation is required to obtain the ground speed and drift angle. (3) The stabilized antenna produces simple velocity data and offers better accuracy at large drift, pitch, or roll angles. (4) From physical consideration, the antennas used for Doppler radars include linear slotted arrays, planar slotted arrays, paraboloids and cut

Hatcher and Gu

422

Antenna

Transmitter

Receiver

>~ FrequenCYTracker

Data

Converter

Velocity

Output Figure I0. Diagram of Doppler radar.

paraboloids, and dielectric and metal-plate-lens antennas fed by horns. Linear slotted arrays produce conically shaped fan beams, and the other types of antennas produce pencil or near-pencil beams. Transmitter and Receiver

(1) The radar signal is generated in the transmitter and radiated via the antenna system toward the ground. The signal is then backscattered by the ground, intercepted by the antenna system, and fed to the receiver. (2) In the receiver, the received signal is mixed with the transmitted signal or the signal generated by a local oscillator, and the resulting Doppler signal is amplified and then fed to the frequency tracker. (3) The basic types of signals generally used for Doppler radars are incoherent pulse, coherent pulse, continuous wave, and frequencymodulated continuous wave. (4) Doppler radars use frequencies in the X-band and Ke-band. Frequency Tracker

(1) The function of the frequency tracker is to track the center frequency of the noiselike Doppler signal output from the receiver. (2) The frequency tracker is a closed-loop system consisting of a frequency discriminator, an integrator, and a tracking oscillator. The block diagram of the frequency tracker is shown in Figure 11. (3) In Figure 11, the frequency discriminator measures the frequency difference between the Doppler signal and the signal generated by the tracking oscillator. The output of the frequency discriminator is fed to the integrator, whose output is used to control the tracking oscillator. Using

423

14. Microwave Navigation Aids Doppler Signal (from receiver)

Frequency Discriminator

Integrator

Tracking Oscillator

Doppler Frequency (to data converter) Figure II. Block diagram of a Doppler frequency tracker.

the frequency difference information, the tracking oscillator generates the feedback signal and outputs the Doppler frequency.

4. Doppler-Radar Performance and Errors Doppler-Radar Performance (1) The performance of a Doppler radar is a function of the Doppler signal-to-noise ratio ( S / N ) and the sensitivity of the frequency tracker. (2) The Doppler S / N per beam for a coherent system in which each beam is separately demodulated is given by

S)

PtGoaLrLaWEA 2

d=

, 16-n-2r2Bd k T ~ + PtQi 7

(4)

cos 0

where ( S / N ) d is the Doppler S / N , Pt is the average transmitted power per beam, G o is the one-way maximum antenna gain relative to an isotropic radiator, a is the scattering coefficient, L r are the losses in the radar transmitter and receiver paths, L a are the losses in the atmosphere, w is the antenna-pattern factor, E is the efficient factor, A is the wavelength of transmission, r is the range to the scattering surface along the beam, B a is the bandwidth of interest, k is the Boltzmann's constant, T is the absolute temperature, • is the noise figure of the receiver, Qi is the

424

Hatcher and Gu

effective transmitter-receiver isolation coefficient, (N/S) t is the ratio of transmitter-generated noise to the transmitter power, and 0 is the central beam incidence angle with respect to a normal to the surface. (3) In most well-designed systems, Qi is SO small that the term PtQi(N/S) t in Equation (4) is negligible. In this case, Equation (4) becomes

(S)

Ptaoagrga WEA2

-N d -- 167r2r2BdkTdp COS 0"

(5)

Equation (5)can be rewritten as S

S

S

if

if

where (S/N)iz is the intermediate-frequency S / N in the intermediatefrequency bandwidth BiT of the receiver, expressed by

(S) -N if

_

PtGoaLrLawA 2 16rc2r2BifkTd# cos 0 '

(7)

and U is called the utilization factor which is the ratio of the Doppler S / N to the intermediate-frequency S/N. (4) The sensitivity of the frequency tracker is usually expressed by two quantities: the acquisition sensitivity and the tracking sensitivity. The acquisition sensitivity is the Doppler S / N with which the Doppler signal can be acquired and tracking begins. The tracking sensitivity is the Doppler S / N with which the signal-to-noise detector is set to cause the frequency tracker to stop tracking.

Doppler-Radar Errors (1) There are two types of Doppler-radar errors: random errors and bias errors. (2) Random errors are defined as those errors that vary during a flight or flight leg. There are two types of random errors: those with relatively long correlation times and the Doppler-fluctuation noise, which has a correlation time of 0.25 to 1 s. (3) The major sources of random errors are Doppler fluctuation, beam direction, transmission frequency, altitude hole, sea current, surface wind water motion, and attitude stabilization. (4) Bias errors are those that are constant for the duration of a flight. Known bias errors can be calibrated out, before the start of a flight, after

14. Microwave Navigation Aids

425

equipment installation in the aircraft, or even before shipment from the factory. All uncompensated bias errors must be taken into account in an error analysis of a Doppler radar. (5) The major sources of bias errors are beam direction, frequency tracker, land terrain, over-water calibration shift, installation, calibration, and readout.

5. The Navigation Computer (1) The navigation computer, fed with velocity information and the heading reference, can evaluate current position, ground speed and drift angle, course and distance to destination, and other navigation information. (2) If Doppler information is lost, the computer can continue to function on memory, using the latest-stored ground speed and drift angle. (3) The computer is required to allow the human operator to feed in the reliable position information any time during a navigation. (4) The computer can be designed as an integral part of the Doppler navigation system or as a separate unit capable of receiving standard inputs and performing the required computations.

Additional Reading R. J. Milliken and C. J. Zoller, Principle of operation of NAVSTAR and system characteristics, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 3-14. Washington, DC: Institute of Navigation, 1980. J. J. Spilker, Jr., GPS signal structure and performance characteristics, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 29-54. Washington, DC: Institute of Navigation, 1980. A. J. Van Dierendonck, S. S. Russell, E. R. Kopitzke, and M. Birnbaum, The GPS navigation message, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 55-73. Washington, DC: Institute of Navigation, 1980. S. S. Russell and J. H. Schaibly, Control segment and user performance, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 74-80. Washington, DC: Institute of Navigation, 1980. B. G. Glazer, GPS receiver operation, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 81-86. Washington: DC: Institute of Navigation, 1980. E. H. Martin, GPS user equipment error models, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 109-118. Wasl~ington, DC: Institute of Navigation, 1980. P. S. Jorgensen, Navstar/Global Positioning System 18-satellite constellations, in Global Positioning System Papers Published in Navigation, Vol. II, pp. 1-14. Washington, DC: Institute of Navigation, 1984.

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Hatcher and Gu

K. P. Yiu, R. Crawford, and R. Eschenbach, A low-cost GPS receiver for land navigation, in Global Positioning System Papers Published in Navigation, Vol. II, pp. 44-60. Washington, DC: Institute of Navigation, 1984. M. A. Sturza, GPS navigation using three satellites and a precise clock, in Global Positioning System Papers Published in Navigation, Vol. II, pp. 122-132. Washington, DC: Institute of Navigation, 1984. R. M. Kalafus, J. Vilcans, and N. Knable, Differential operation of NAVSTAR GPS, in Global Positioning System Papers Published in Navigation, Vol. II, pp. 197-214. Washington, DC: Institute of Navigation, 1984. J. Ashjaee, GPS Doppler processing for precise positioning in dynamic applications, in Global Positioning System Papers Published in Navigation, Vol. III, pp. 54-69. Washington, DC: Institute of Navigation, 1986. E. G. Blackwell, Overview of differential GPS methods, in Global Positioning System Papers Published in Navigation, Vol. III, pp. 89-100. Washington, DC: Institute of Navigation, 1986. D. Klein, The use of pseudo-satellites for improving GPS performance, in Global Positioning System Papers Published in Navigation, Vol. III, pp. 135-146. Washington, DC: Institute of Navigation, 1986. R. W. King, E. G. Masters, C. Rizos, A. Stolz, and J. Collins, Surveying with GPS, School of Surveying, Univ. of New South Wales, 1985. D. Wells, N. Beck, D. Delikaraoglou et al., Guide to GPS Positioning. Canadian GPS Associates, 1986. E. Lassiter and M. Ananda, The GPS overview and navigation system concept, in "The NAVSTAR GPS System" AGARD Lecture Ser. No. 161, pp. 1-1-1-13, AGARD, 1988. M. Ananda, The Global Positioning System (GPS) constellation and coverage, in "The NAVSTAR GPS System," AGARD Lecture Ser. No. 161, pp. 3-1-3-17, AGARD, 1988. M. Ananda, The Global Positioning System (GPS) accuracy, system error budget, space and control segment overview, in "The NAVSTAR GPS System," AGARD Lecture Ser. No. 161, pp. 4-1-4-17, AGARD, 1988. P. W. Nieuwejaar, GPS signal structure, in "The NAVSTAR GPS System," AGARD Lecture Ser. No. 161, pp. 5-1-5-6, AGARD, 1988. R. P. Denaro, Differential operation of Navstar GPS for enhanced accuracy, in "The NAVSTAR GPS System," AGARD Lecture Ser. No. 161, pp. 10-1-10-18, AGARD, 1988. J. Hurn, GPS: A Guide to the Next Utility, Trimble Navigation, 1989. A. Leick, GPS Satellite Surveying. New York: John Wiley & Sons, 1990. T. Logsdon, The Navstar Global Positioning System. New York: Van Nostrand-Reinhold, 1992. B. Hofmann-Wellenhof, H. Lichtenegger, and J. Collins, Global Positioning System: Theory and Practice. New York: Springer-Verlag, 1992. R. R. Hatch, ed., Global Positioning System: Papers Published in Navigation, Vol. IV. Washington, DC: Institute of Navigation, 1993. F. B. Berger, The nature of Doppler velocity measurement, IRE Trans., Vol. ANE-4, pp. 103-112, Sept. 1957. F. B. Berger, The design of airborne Doppler velocity measuring systems, IRE Trans., Vol. ANE-4, pp. 176-196, Dec. 1957. D. J. Povejsil, R. S. Raven, and P. Waterman, Airborne Radar. Princeton, NJ: Van Nostrand, 1961. _

.

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M. I. Skolnik, Introduction to Radar Systems. New York: McGraw-Hill, 1962. W. R. Fried, Doppler navigation, in Avionics Navigation Systems (M. Kayton and W. R. Fried, eds.), Chap. 6. New York: John Wiley and Sons, 1969. E. G. Walker, Airborne Doppler, in Navigation Systems: A Survey of Modern Electronic Aids (G. E. Beck, ed.), Chap. 7. Princeton, NJ: Van Nostrand-Reinhold, 1971. J. L. Farrell, Integrated Aircraft Navigation. New York: Academic Press, 1976. G. J. Sonnenberg, Radar and Electronic Navigation. London: Butterworth, 1988.

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CHAPTER

15 Microwave Applications for Law Enforcement John Tomerlin and John Fuhrman

I. Introduction l J o p p l e r - b a s e d radar has been in use for traffic speed enforcement since 1947. This application requires a microwave antenna for sending and receiving, signal-processing circuitry, and an LED display for the target speed. When a signal is transmitted on one of the four frequencies presently assigned to traffic enforcement agencies by the Federal Communications Commission (FCC), a portion of that beam is reflected to the antenna by a moving object (target). In accordance with the Doppler principle, the frequency of the reflected energy will be higher than the energy that was transmitted. This difference is proportional to the speed of the target and can be converted into an equivalent value in miles per hour. There are important differences between radar devices designed for police traffic enforcement and those used by the military and commercial aviation. Whereas the latter employ an omnidirectional signal capable of detecting multiple targets and locating them directionally with great precision, traffic radar focuses energy into a relatively narrow beam~typically from 8° to 26 ° in width--in an effort to isolate individual targets. When only a single target is present in the radar's beam and in the absence of various types of interference, police radar is considered accurate to within + / - 1 mph of the target's speed.

Handbookof MicrowaveTechnology,Volume2

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Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

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Tomerlin and Fuhrman

Inasmuch as traffic radar measures only the difference in energy between the transmitted signal and the reflected signal, not whether one is higher or lower, it cannot determine whether the reflective surface is moving toward it or away from it, only the speed at which it is doing one or the other. A further difference is that, whereas large commercial radar devices measure changes in frequencies (Doppler shift) directly, police radar interprets changes after they are filtered through a phase-lock loop (PLL). This process is intended to stabilize the signal long enough for an operator to identify its source, but may result in other forms of error. Depending on design, traffic radar can be used in either the stationary or the moving modes, with some units being capable of both. Some moving radar can be operated simultaneously to the front and rear of the patrol car by means of dual antennas. In an attempt to defeat radar-detection devices, most recent radars can be operated in the instant-on mode which suppresses the signal until the last instant before a measurement is taken. When operated in this mode, there is no way for the operator to detect false speed readings due to various types of interference. Modern traffic radar produces an audible tone that varies in pitch according to the speed reading being obtained. This feature is known as "audio Doppler" and is extremely important to determine which of several possible vehicles within the radar's beam is responsible for a given speed reading. When more than one target is available, pointing the antenna does little to ensure the resultant reading. This holds true whether the targets are distributed laterally across several lanes of traffic or longitudinally at various distances along the highway. The signal emitted by the radar leaves the antenna in an expanding cone, like the beam of a flashlight, and grows wider (and weaker) as it spreads. At less than one quarter of a mile, the beam of a typical radar unit will cover all four lanes of oncoming traffic on a freeway. At a half of a mile it will pick up readings from all traffic in both directions. At one mile it will cover an expanse wide enough to land and take off in a small airplane. Because radar seeks out the "best" target in its field of reception, i.e., the best reflector it can find, it will readily ignore vehicles closer to it ~ r e g a r d l e s s of their s p e e d ~ t o fix on one more distant. Tests have shown that a small target may remain "invisible" to radar up to 500 ft from its antenna, whereas a large reflective target, such as a semi-tractor-trailer truck may produce a clear reading for up to a mile and a half. Weather conditions have a strong effect on police radar, with precipitation of any sort rendering it ineffective. Reduced visibility exacerbates target-identification problems, and high temperatures can cause erratic signal propagation. Radar cannot read the speed of targets around corners

15. Microwave Applications for Law Enforcement

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or over the tops of hills, and its microwave radiation is readily absorbed or deflected by common objects in the highway environment such as trees or signs in the median strip. Such limitations make radar unreliable except along unobstructed roadways with relatively light traffic in good weather.

2. Historical Following the development of radar for military uses during World War II, traffic agencies began using a simpler form of the technology to compute traffic speeds. In 1947, the State of Connecticut employed radar to determine average traffic speeds in order to set speed limits and shortly afterward for enforcement. Several legal challenges ensued, all of which were successfully resolved in favor of the enforcement use of radar. In Dantonio v New Jersey, in 1955, the court determined that an officer needed no special training or proficiency in the use of traffic radar in order to measure traffic speeds and make arrests. Connecticut v Tomanelli, in 1966, established that the accuracy of the radar device could be reliably determined by holding a tuning fork of a known frequency in front of the radar's antenna and striking it. If the speed reading obtained by means of this simulation matched the fork's assigned frequency, the radar was presumed to be functioning properly. Honeycutt v the Commonwealth of Kentucky, also in 1966, added that, when more than one vehicle was present in the radar's beam and when a speed reading higher than the legal limit was obtained, the vehicle "out front by itself" and closest to the radar was responsible for the reading. Although, scientifically and factually, all three decisions were wrong, they remain the legal basis of radar speed enforcement. In truth, traffic radar is subject to many types of false speed readings due to interference. Such interference can be of an electromagnetic (radio) or mechanical type. Radio interference will be more commonly encountered in actual field use than in controlled classroom situations, with the result that police officers often underestimate the probability of such interference. The widespread proliferation of transmitting equipment increases the problem. For example, in the past five years alone, more than five million cellular telephones have gone into use, not counting the necessary base stations to support these mobile units. The problem of interference has become so acute that the U.S. military has assigned a special research and development group to do nothing but study this problem. When traffic radar is subjected to moderate to strong radio energy fields, different makes and models respond in nonstandard ways. Some will

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boost the indicated speed up or down, whereas others may blank the display. When a mobile radio transmitter is within approximately 200 ft of the radar, false speed readings can be produced. Other sources of interference include CB radios, ham equipment, airport radar, and several types of door opening systems and bank alarms. High-intensity discharge also creates radio interference. Mercury vapor and neon lights, high-tension power lines, and electrical power stations are representative of external sources of interference, whereas police-band radio, air-conditioner fans, radiator fans, and even faulty battery connections inside the patrol car can cause false speed readings on police radar.

3. Moving Radar The use of police radar from a moving patrol car, so-called moving-mode radar, is accomplished by measuring two components of the transmitted signal. One component, referred to as the high beam, is directed at a target vehicle approaching the radar whose speed is determined in the usual way by interpreting the shift in frequency of the reflected signal. A second, "low" component of the beam is read from the ground or pavement ahead of the patrol car; this portion of the beam is taken to represent the speed of the patrol car, and is subtracted from the target speed. The sum of the two readings is taken to be the true target speed. The most common source of error in moving-mode radar results from incorrect readings of the low, or patrol car, portion of the beam. If moving radar locks onto a larger, slower moving vehicle instead of the ground, it will compute a lower-than-actual patrol speed; the difference in this reading will be added to the speed reading in the radar's target-speed display. This is known as "shadowing error." Here is an example of shadowing error. Imagine a typical four-lane highway with average traffic. A patrol car equipped with moving radar is traveling in the No. 1 lane (closest to the center divider). The posted speed limit is 45 mph. In the right-hand lane and slightly ahead of the patrol car is a semi-tractor-trailer truck in the process of slowing to turn right; as its speed decreases to 10 mph, the patrol car's radar locks onto the truck's strong reflective surface instead of the ground reference. In these circumstances, the radar will compute the patrol car's speed as 10 mph slower than it really is (actual speed minus truck speed). At the same moment, an automobile approaching from the opposite direction becomes the target of the patrol car's radar. It is traveling at the speed limit of 45 mph. The patrol car itself is moving 40 mph, so the radar

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computes a closing speed of 85 mph. It then subtracts the (incorrect) low-beam speed reading of 30 mph and displays a target-speed reading of 55 mph. If the officer fails to observe an incorrect reading in the patrol speed window of his radar during the approximate 4-s interval available to him to (a) observe the target, (b) check its speed reading, (c) check his speedometer, (d) match the speedometer reading with the patrol speed reading of the radar, and (e)verify the correct target by means of a change in Doppler tone as it passes, then there is a high probability that the motorist in question will get a ticket for driving 10 mph above the legal speed. All radar is "line of sight." It cannot display the speed of any vehicle out of its direct "view." However, hills, dips in the road, or shallow valleys can cause difficulties in target identification. First of all, the radar unit must be carefully positioned in, or attached to, the patrol car. The antenna must be aligned in the direction of travel and parallel to the ground. This was easier to do when the antenna was incorporated with the console and operated from the dashboard; but increasing concerns for the harmful effects of stray microwave radiation have led to a preference for externally mounted antennas. Such antennas can reduce the amount of electromagnetic contamination reaching radar operators, but complicates the task of proper target alignment. When the patrol car crests a hill the radar beam does not conform to the ground contour, but instead tends to fall on traffic farther away. To visualize this effect, recall how your car's headlights illuminate the road while being driven in rolling or hilly terrain. Under such circumstances, police radar will not travel to the nearest approaching vehicle, but will overshoot it to display the speed of a vehicle or other moving object in the distance. Curves in the highway present a different problem in that moving radar can add speed to a target that approaches its antenna along an inside arc. This error is due to an increase in the frequency shift caused by reading the target along an angle cotangent to its true direction and is known as cosine error.

4. Mechanical Errors Mechanical interference can be defined as the reflection of a radar signal from any moving object other than the target vehicle that produces a speed reading. Traffic radar is designed to measure the relative motion or velocity of objects. The tuning forks used to perform the most basic field

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testing of a radar device utilize the unit's ability to respond to any moving object included in a non-Doppler reflection. It is important to note that the frequency of the return echo has not in this case been frequency shifted; instead, the radar echo has been phase modulated by the vibrating tines of the fork (the frequency of the return echo itself has not been changed). Thus, there are two mechanisms that can cause a reading in the display, the frequency shifted Doppler return echo and the modulation of the unshifted echo, the latter of which may be caused by any vibrating or rotating object. The tuning fork test, it should be noted, verifies only the operation of the radar unit's counting circuits and its display. Tuning fork accuracy is thus only part of the calibration evidence that must be referenced in order to ensure accuracy. Another source of error in police radar is a change in frequency of the microwave oscillator due to age or mishandling. Although the tuning fork is able to verify the accuracy of the timebase used to convert Doppler frequencies into digital readings, it does not ensure that the microwave generator itself is operating on the correct frequency. Inasmuch as the Doppler difference is proportional to the transmitted frequency, if the transmitter produces a higher frequency than that assigned, the radar unit will read high. Lower frequencies will result in lower speed readings, but in neither case will the error be observed during the tuning fork calibration test. Some manufacturers employ quartz crystals for internal signal verification as a sort of self-test. At least one, however, uses a reed device that is suspected of being sensitive to temperature changes. Such units may give unreliable readings in conditions of extreme heat or cold; indeed, this unit failed government tests under these conditions (see below).

5. Mechanical Interference Police radar is highly susceptible to various types of mechanical interference, the most commonly occurring of which is the patrol car's own A C / h e a t e r fan. Depending on the type of radar unit~single piece or m u l t i p i e c e ~ o r the method of mounting, fan reflection can vary from weak to strong. Operation requires care and knowledge by the operator because the fan location is not obvious in most automobiles. Just placing the antenna away from any vents or ducts is not enough; the operator should perform a test by turning the fan on and off and by operating it at different speeds to ensure that "ghost" readings are not being produced.

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Certain roadside objects may also cause undesirable readings on the radar display. Large ventilating fans, rotating ventilators, signs, or turbines are examples of sources of mechanically induced interference. Not only is radar used in the moving mode susceptible to all these sources of interference, many or most of these sources are difficult to identify due to the transient nature of their occurrence. Another situation in which the target's speed can be misread is when the patrol car carrying radar slows down abruptly while performing a reading. This situation may occur often if the police officer begins to slow down prematurely during the reading in order to turn around to begin pursuit. The resulting effect, which is known as "batching," or target-speed bumping, results because the readout for the patrol car's speed is slightly dampened to avoid random fluctuations. Sudden deceleration may confuse the unit and cause it to add several miles per hour to the target speed (or fail to subtract enough patrol car speed, which is the same thing). Because most moving-radar units are built in two pieces, an antenna and a control console, the antenna can be turned in such a way as to scan its own console. This produces very high speed readings. It can occur accidentally when the officer changes from taking readings in one direction to reading traffic coming from the opposite direction.

6. Photo Radar A variation of the use of radar, so-called "camera radar," or "photo radar," has been in use in Japan and some countries of Western Europe for several years. It has been adopted by several smaller U.S. cities. The system consists of a radar speed gun and a still camera. Positioned along the road, or in some cases suspended directly above a lane of traffic, the radar is set to trigger the camera whenever a higher speed is detected. A photograph is taken to capture the license plate and, in U.S. versions, the face of the driver. The license plate number is then used to locate the vehicle's owner from Department of Motor Vehicle records, and the picture is used for identification in case the ticket is protested in court. Photo radar differs from conventional radar in several ways. Instead of being aimed parallel to the road to pick up oncoming or receding traffic, it is directed across one or more lanes of traffic at a shallow (22 °) angle. Its narrow beam width and low power output make it all but invisible to present-day radar detectors. Some detector manufacturers offer " K a " band (34 Ghz) sensitivity, but as a rule they are useful only to tell the driver when he has been through a stakeout, not to warn him ahead of time.

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The effective range of photo radar is about 120 ft, or approximately three lanes of traffic. This makes it susceptible to registering--and photographingmmore than one car at a time. Distributors of photo radar claim that it can reliably distinguish between vehicles under these conditions, but technically speaking this is untrue. Basic lane discrimination depends on the unit being set up with great precision and kept free from such disturbances as wind gusts from passing cars and trucks. When multiple targets are present, no present type of police radar can be relied upon to tell which is traveling at a particular speed. Photo radar devices are manufactured by several companies in Western Europe and Japan, but none are built in the United States at present. This makes it difficult to ensure performance specifications, and to date none has been tested or approved by the National Bureau of Standards. The film is exposed through an optical matrix containing the time, date, location, and radar speed reading of the target vehicle. A magazine holds enough film for about 800 exposures, which can be taken at a rate of up to 260 frames per hour. Once the film has been retrieved and developed, each photo is examined to make certain that the license plate is legible and the driver's face is recognizable. If either has been obscured for any reason, the evidence is thrown away. Otherwise, the registered owner (not necessarily the driver of the car at the time of the violation) is notified by mail and advised of the amount of the fine. Because photo radar is operated from the side of the road, and directed across it at a fairly sharp angle, it is necessary to correct for cosine error. This is done by calculating the amount of cosine effect included in the reading and correcting to produce the vehicle's presumed actual speed. Unfortunately, this method does not allow for sudden changes in vehicle direction, as when it changes lanes, a circumstance that may result in as much as 5 mph being added to or subtracted from the actual speed. Inasmuch as there is no witness to the act of speeding other than the radar itself and since the equipment is not subject to crossexamination, motorists accused of speeding by photo radar have no means of defense.

7. Testing for Accuracy No federal performance standards for police radar exist, nor is regular testing done to ensure accuracy. However, the National Bureau of Standards (NBS) tested the six most commonly used radars in 1980, and the International Association of Chiefs of Police (IACP) tested all available

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brands and models in 1984. Both programs indicated that the reliability of current police radar technology is inadequate. A total of 24 models were tested for compliance to the Model Performance Specifications for Police Traffic Radar Devices developed for the National Highway Traffic Administration (NHTSA) in the Law Enforcement Standards Laboratory (LESL). The specifications had been adopted by the IACP and the program was conducted under their supervision during the period June 1983 to January 1984. The radar devices were subjected to examination, including documents and accessories, laboratory evaluation, and operational testing. During the period of testing the radar manufacturers were allowed to make minor modifications to their products to achieve compliance with the model specification requirements. Upon the completion of the initial testing it was found that many of the individual radar devices failed to comply with the model specifications because the required manufacturer information was not provided. For example, some devices lacked operating or installation instructions, whereas for others the required tuning fork certificate was either incomplete or not provided. In several instances model specifications were misleading or unrepresentative of actual performance, either exceeding the limits for signal processing sensitivity or claiming nonexistent sensitivity in certain speed ranges. Overall, few of the radar units provided for testing were in full compliance with the labeling and manufacturer-provided information requirements at the time of initial testing. In addition, there were some areas of noncompliance with the requirements of the model specification that required "minor modifications" to the test units to achieve compliance. The most common deficiency was failure to meet the signal processing channel sensitivity requirements. This deficiency was corrected, in most cases, by a change in the values of the filter components. The second most common deficiency was in the display readability capability of the units, i.e., character height and luminance contrast. Other areas of noncompliance included frequency stability under conditions of high and low temperature or of high humidity. After modifications were made to the test units under IACP supervision, all five participating manufacturers were judged to be in full compliance with model specifications. This decision was somewhat arbitrary, as the following summary of test results indicates.

Tuning Fork Calibration This test required measurement of the frequency of the tuning fork to ensure that it was within + / - 0 . 5 % of the frequency specified in the

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certificate of calibration. This could not be accomplished with 12 of the radar units as no certificate was supplied by the manufacturer. Tuning Fork Tests

The tuning forks supplied for use in checking the operating condition of the radar device were tested. If the radar is functioning properly, the speed for which the tuning fork is calibrated should appear in the speed display with a tolerance of + / - 1 mph. With moving radar devices, both the target and the patrol speed displays must show correct speed readings. The tuning fork tests were conducted under standard conditions, specified low- and high-temperature conditions, high-humidity conditions, and high-vibration conditions. All of the radar devices were found to be in compliance at ambient temperature; however, four of the devices failed to comply during the environmental tests. Three radar units did not function properly at low temperature. One of the three also did not function properly under the high-temperature test conditions, and another of the three failed during the high-humidity test. The speed display on one additional unit showed erroneous readings during vibration tests. Microwave Transmission

These tests checked the stability of operation of the radar devices under conditions that could be encountered in the operational environment. The tests were repeated a number of times to record performance data under standard test conditions (68 to 80°F) and under conditions of low temperature (-22°F), high temperature (140°F), and high humidity (90% at > 99°F). All tests were repeated at three voltage levels; nominal voltage (13.6 V), nominal voltage plus 20% (16.3 V), and nominal voltage minus 20% (10.8 V) or any lower voltage specified by the manufacturer. Five of the radar devices did not maintain frequency stability within the allowable tolerances during testing. One failed under all conditions, whereas three others failed the low-temperature test. A fifth device failed during the high-humidity test. Three of the radar units that did not meet the frequency stability requirement also did not meet the input current requirements of less than 10% variation and no change in numerical display under one or more of the test conditions. Three additional units were unstable during the low-temperature tests, whereas four failed at high temperature. Four units failed the high-humidity tests.

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Four units did not maintain radiated power output within + / - 1.5 dB from nominal as required by the standards; two did not comply under low-temperature conditions, and one failed the high-temperature test. Two devices were not in compliance under high-humidity conditions. The maximum horizontal beam width allowed by the model specifications--18 ° for X-band radar and 15° for K-band radar--was initially exceeded by three X-band and one K-band unit, and four radars failed the requirement for near-field antenna power density.

Low-Voltage Supply Radar devices are required to operate to a specific low-voltage point and to have a low-voltage indicator capable of being heard or seen by the operator. Low voltage to the radar device is capable of causing incorrect high target speed readings. The required low-voltage operating point is 10.8 V or the lowest voltage specified by the manufacturer. Seven radar units did not meet the performance standard; five units met the requirement of the model specifications, but not the lower voltage claimed by the manufacturer.

Doppler Audio Radar devices are required to emit a Doppler audio tone that correlates with the received Doppler signal and to have an audio volume control. The audio tone helps the operator correlate a visual observation of a target vehicle with the radar speed display and can warn the operator of the presence of electromagnetic interference. Three of the radar units tested were not in compliance with requirements for audio output and volume control. Two units failed to meet requirements for audio squelch and squelch override. One radar did not meet the auto track-through lock test.

Electromagnetic Interference Operational testing was carried out with the radar device properly installed in a patrol vehicle of the type normally used for law enforcement purposes. The test vehicle had an FM transceiver and antenna and a citizens band transceiver and antenna, each installed in accordance with the manufacturer's instructions. A handheld vM transceiver was also positioned in the vehicle for use by the driver. Although the radar was tracking an acquired target vehicle traveling at 50 mph, audio tones from 500 to 3000 Hz generated by a slide whistle were transmitted via the

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microphone of the FM and CB transceivers. The radar display was observed for any erroneous readings caused by the slide whistle transmission from the transceiver. The tests were repeated similarly with the patrol vehicle in the stationary mode, tracking a target vehicle while another vehicle with the FM and CB transceivers passed within 10 ft, first on one side of the patrol car and then on the other. One radar device was subject to interference from the FM transceiver when it was initially tested, and two others were interfered with by the CB transceiver.

Speed Accuracy Tests were conducted on a half-mile measured course over which the target vehicle was driven at constant speeds of 20, 50, and 70 mph. The true speed of the target vehicle for each test was calculated from the elapsed time to travel the known distance or measured with a fifth wheel speed measuring device. The speed displayed on each radar device during the runs was compared with the true target vehicle speed to determine whether or not the radar-displayed speed was within the allowable variation of + 1 and - 2 mph in the stationary model and of + / - 2 mph in the moving mode. Five radar devices were reported as not complying with the speed accuracy requirements of the model specifications; three in the stationarymode/moving-mode target test and one of these t h r e e - - i n addition to two others--in the moving-mode/approaching target test. The three radar devices that were not in compliance in the stationary-mode/movingmode target test situation at 70 mph were in compliance when tested at speeds of 20 and 50 mph, greatly increasing the probability of false speeding tickets at the higher speeds. Notwithstanding these deficiencies, the IACP found all of the units tested to be in full compliance with the agency's requirements and suitable for use in speed enforcement. Earlier tests by the National Bureau of Standards were less forgiving. These tests were designed to determine whether it was possible to affect target speed measurements in several environments and under several conditions that had been identified as the cause of radar inaccuracy during proceedings before the Eleventh Judicial Circuit Court of Florida in 1979. During these tests there was no observed degradation in the performance of any of the six units tested arising from (1) cosine angle effect, (2) automatic lock, (3) heat buildup, (4) mirror switch aiming, and (5) high-tension power wire interference. Only one of the six units tested was affected by police radio transmission at distances beyond 30 ft from the radar.

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Certain of the units were affected in varying degrees by internal electrical interference from the patrol car's ignition and alternator, as well as interference from air conditioner and heater fans. Although transmission from police radios in the same vehicle as the radar was found to have a limited effect on the radar units, CB transmission in the same vehicle affected nearly all radars. Patrol car shadowing was found to affect all but one of the radars, and target speed bumping was observed to affect half of the units. In all cases, the two-piece radars were affected by panning the antenna beam through the display console. In some instances, the performance of the radar units was not degraded by the environments or use situations described above so long as the target vehicle was present. Specific test results included the following.

Shadowing Shadowing, better identified as patrol speed shadowing, is the tendency of a moving vehicle mode radar to use a slow moving large vehicle rather than the ground to measure the speed of the patrol car. This effect was observed, in varying degrees, for several of the radars during testing.

Radar Unit A (Kustom MR-9) The patrol speed reading went from an actual 26 mph to an indicated 22 mph as a large oil tanker passed the patrol car. Radar Unit B (MPH K-55) A large truck came to a stop 50 yards in front of the patrol car, and the patrol car reading changed from 40 to 28 mph. Radar Unit C (Decatur MV-7125) The actual patrol speed of 25 mph was reduced to 17 mph when the patrol car was following a large truck. The actual patrol speed of 34 mph was reduced to 11 mph for a long time when a pickup truck passed the patrol car. The pickup passing the patrol car decreased the patrol speed reading by 10 mph and increased the target speed by same amount. Radar Unit D (CMI Speedgun 6) This particular unit demonstrated very severe shadowing effects from moving vehicles in the vicinity of the radar. A 44-mph patrol speed momentarily dropped to 11 mph with a pickup truck 100 ft in front of the patrol car. While traveling at actual

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patrol speeds of 30-40 mph, with target speeds of 50-60 mph, the following readings were observed as the patrol car was passed by trucks. Patrol speed (mph)

Target speed (mph)

12 16 20 17

80 72 57 68

Radar Unit E (CMI Speedgun 8) While the patrol car was traveling at a patrol speed of 50 mph, shadowing from passing large trucks caused the following radar readings. Patrol speed (mph)

Target speed (mph)

17 11

74 41

This effect did not occur every time a truck passed. Patrol readings decreased momentarily several times when a passenger sedan passed the patrol car.

Radar Unit F (MPH K-55) While the patrol car was traveling at 35 mph, readings of a 20-mph patrol speed and 76-mph target speed were observed. When a pickup truck passed the patrol car and pulled back into the lane, the actual patrol speed of 47 mph dropped to 35 mph. Radar Unit G (Kustom MR-7)

This unit showed no effects from

passing large trucks.

Batching Batching, better identified as target speed bumping, occurs if the target vehicle speed display varies when the patrol car changes speed. This effect was observed for some of the radars during testing.

Radar Unit A (Kustom MR-9) There was no effect on target speed readout due to acceleration or deceleration of the patrol car. Radar Unit B (MPH K-55) The radar occasionally subtracted 2-3 mph from the target reading when the patrol car was accelerating. This was not consistent. There was no effect from deceleration. Radar Unit C (Decatur MV-715) Acceleration or deceleration of the patrol car had no effect on target readings.

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Radar target speeds decreased with

both acceleration and deceleration.

Radar Unit E (CMI Speedgun 8) No effect on target speed reading from accelerating or decelerating of the patrol car could be observed. Radar Unit F (MPH K-55) On rare occasions, target speed readings increased 2-3 mph when the speed of patrol car was increased or decreased. Radar Unit G (Kustom MR-7) No effect on target readings from a sudden increase or decrease of the patrol car speed was observed. Panning Error Panning error occurs when the radar antenna is used to pan through its own display. The two one-piece units used in these tests could not do that; using the two-piece units in this manner always produced an erroneous reading.

Radar Unit A (Kustom MR-9) Panning the antenna across the radar readout console produced 101-mph speed readings. Radar Unit B (MPH K-55) Panning the antenna across the radar readout console produced 75-mph speed readings. Radar Unit C (Decatur MV-715) Panning the antenna across the radar readout console caused readings of over 100 mph. Radar Unit D (CMI Speedgun 6)

This radar unit was not applicable.

Radar Unit E (CMI Speedgun 8)

This radar unit was not applicable.

Radar Unit F (MPH K-55) Panning the antenna across the radar readout console produced various speed readings. Radar Unit G (Kustom MR-7)

Panning the antenna across the radar readout console produced 95-mph speed readings.

Scanning Error Scanning errors can result when the radar operator moves his antenna too quickly. The results obtained by positioning the radar in commonly used positions or pointing it in several directions included the following.

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Radar Unit A (Kustom MR-9)

There was no effect from the A C /

heater fan motor.

Radar Unit B (MPH K-55) The unit picked up the A C / h e a t e r fan intermittently while it was mounted on the dash. When the heater fans were on, scanning the dash with the handheld antenna caused readings proportional to the fan speed. No readings from the fans were detected when the antenna was pointed out the side windows. The unit picked up fan readings when the radar was pointed out the rear window. Radar Unit C (Decatur MV-715) When mounted, the antenna was pointed slightly downward toward the dash with the heater fans on high" stationary modemtarget, 34 mph; patrol, 55 mph. No readings from the fans were detected when the antenna was pointed out the side or rear window. The antenna mounted outside the rear passenger window, slightly aimed at the dash with the fans on picked up readings of 24-25 mph in the stationary mode. Radar Unit D (CMI Speedgun 6) This handheld radar when pointed at the dash picked up the A C / h e a t e r fans. There was no effect from the fans, and no readings were detected when the unit was pointed out the side or rear windows. Radar Unit E (CMI Speedgun 8) This handheld radar antenna pointed at the dash picked up readings from the A C / h e a t e r fans. This unit seemed to pick up the fan extremely easily when the antenna was aimed forward but not mounted on the dash mount; no readings were detected when the antenna was aimed out the side or rear windows. Radar Unit F ( MPH K-55) No fan readings were detected when the unit was dash mounted. When the radar antenna was pointed at the dash, the radar picked up the fan readings. No speed readings were detected when the antenna was pointed out the side or rear windows. Radar Unit G (Kustom MR-7) Scanning the dash with the radar antenna did not pick up the A C / h e a t e r fan. No readings were detected when the antenna was pointed out the side or rear windows with all the fans on. Cosine Angle Effect Cosine error, better named the cosine angle effect, was closely observed during the testing, for this effect is present any time that the radar

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and the target vehicle are not headed directly toward each other. The speed that the radar displays when it is in the stationary mode is equal to the actual speed times the cosine of the angle between the direction of travel of the target vehicle and the radius vector from the radar to the target vehicle. No erroneous readings were noted during these tests due to the cosine angle effect.

Automatic Lock The advantages and disadvantages of the automatic lock feature were observed. The advantage is in enabling the officer to automatically obtain a speed on the display console using a present threshold value. The disadvantages far outweigh this advantage. The primary one is that the automatic lock prevents the radar operator from obtaining a tracking history, i.e., what the vehicle being tracked does after it is detected traveling over the speed limit. Also, the radar may automatically lock on a stray abnormal reading which appeared only momentarily due to an unobserved interference source. Another disadvantage is that use of the automatic lock feature makes it almost impossible to compare the patrol car speed with its radar measured counterpart to ensure that the two agree at the time that the display is locked in or at times of possible interference such as that brought on by patrol speed shadowing.

External Interference Theoretically, defective high-tension wires may affect radar speed measuring devices by causing stray readings or by decreasing the sensitivity of the radar and thereby reducing its range of operation. However, no stray readings were noted by the NBS in testing near and under high-tension wires. Four of the radars did not display false readings due to external police radar transmission, and only one radar was affected by external CB operation.

Radar Unit F (MPH K-55) A CB radio mounted in a pickup caused readings of 60-70 mph at distances of up to 175 ft from the patrol car. The 100-W transmitter caused radar readings at 5 ft from the left rear of the patrol vehicle to 30 ft from the right of the patrol vehicle.

Internal Interference The radar units were operated in their usual configuration in a patrol car, and electrical interference due to the patrol car ignition system, alternator, and air condition and heater fan motors was investigated. Some of the radar units displayed a reading when the air conditioner and heater

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fans were operated with no radar target present, and one type displayed a reading during the ignition and alternator testing.

Radar Unit C (Decatur MV-715) With the radar mounted in a pickup, erratic patrol speed readings from the engine alternator, ignition, or both in the moving mode were displayed. Extreme interference from the heater fan motor in the moving mode was observed. When a CB radio was installed in the same vehicle as the radar unit, operating from the same battery, several of the radar units were subject to interference during CB transmission. Radar Unit A (Kustom MR-9) When the CB radio and the radar were mounted in the same truck and connected to the same battery, interference from the CB radio was evident. Interference from the tone whistled into the microphone caused speed readings to be displayed. Radar Unit B (MPH K-55) When the radar and the CB radio were connected to the same battery, readings were observed on the radar target readout. The magnitude of the readings depended on the frequency of the CB radio. Radar Unit C (Decatur MV-715) The radar and the CB radio connected to the same battery caused readings in the stationary mode. Radar Unit D (CMI Speedgun 6) There was interference from the CB radio when the radar and the CB radio were powered by the same battery. Radar Unit E (CMI Speedgun 8) There was no effect when the radio and the radar were both connected to the same battery. Radar Unit F (MPH K-55) This unit was not tested because the unit was found to be "extremely sensitive to external CB transmission." Radar Unit G (Kustom MR-7) The radar and the CB radio connected to the same battery caused a reading on the radar target speed display. Under these conditions, the radar picked up the correct reading on the passing target car, and whistling in the CB microphone had no effect on the correct reading until the target was out of range. Two of the radars were affected by operating the police radio in the same car as the radar.

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Radar Unit D (CMI Speedgun 6) A 100-W transmitter had no effect on large targets or strong signals, but it boosted target speeds as much as 20 mph for distant weak signals or small targets. Radar Unit G (Kustom MR-7) A 100-W transmitter caused increases or decreases of 10 mph in target speed readings intermittently. Several observations were made by the NBS as a result of its radar test program. 1. Two-piece radars can produce erroneous readings when an antenna is panned through the display console. The radar should not be mounted with the display console in the antenna beam. 2. Air conditioner and heater fans and alternator or ignition noise can interfere with the radar when no bona fide radar target is present. The radar antenna should be mounted so that it is not pointed toward the air conditioner or heater fans. If possible, the antenna should be mounted outside of the patrol vehicle. 3. Patrol speed shadowing can occur during move-mode radar operations. Operators should be aware of this, should recognize its symptoms, and should know its cause and that its effect can best be detected by checking the radar patrol car speed with the patrol car speedometer. 4. Target speed bumping can occur during moving-mode radar operations. Operators should know what it is, how it occurs, and that its effect can be avoided by maintaining a constant speed when making speed measurements. 5. The cosine angle effect can occur during stationary radar operation when the target is off axis within the antenna beam. Operators should understand the cosine angle effect and recognize when it is occurring. 6. Transmission from 100-W VM police radios can produce erroneous speed readings. Operators should be aware of this and not transmit on CB radios while using the radar. 7. Use of the automatic speed lock feature (still found on many older-model police radars) may result in wrong target identification. Operators should be aware of this and not use the automatic lock feature, but instead use the manual lock feature and then only when they have observed a sufficient "tracking history" to ensure that the correct target vehicle is being tracked. 8. When two or more vehicles are in the radar beam, it can be difficult to select the correct target. Operators should continue radar tracking until the proper target is positively identified. It may be necessary to wait until the vehicles pass by the radar source and the one being tracked no longer registers a speed reading on the display console.

448

Tomerlin and Fuhrman

8. Does Radar Increase Safety? Contrary to generally held opinion, police radar has little ability to influence traffic speeds or safety. Studies show that enforcement that is not visible to the motoring public does not affect its behavior; inasmuch as radar is visible, in a sense, only to users of radar detectors, it cannot be considered a safety measure. Studies by the Texas Transportation Institute (TTI) at Texas A & M and by the Highway Safety Research Center (HSRC) at the University of North Carolina have shown that police radar has no measurable influence on traffic speeds or accident experience apart from the effect of the visible patrol car that is employing it. Conversely, hidden enforcement including regular radar and photo radar are effective at entrapping motorists traveling at or near the 85th-percentile speed of traffic. Inasmuch as the 85th percentile speed is generally greater than the national maximum speed limit, the use of hidden enforcement results in large numbers of speeding tickets and generate substantial revenues for agencies of local and state government. In light of the many sources of error affecting police traffic radar, the absence of performance standards for the radar or training standards for its operators, and the secondary role of hidden enforcement in improving traffic safety, it seems probable that the value of radar in traffic enforcement has been generally misunderstood and greatly overrated.

Additional Reading P. D. Fisher, Shortcomings of radar speed measurement, IEEE Spectrum, Vol. 17, No. 12, pp. 28-31, Dec. 1980. U.S. Department of Transportation, "Model Minimum Performance Specification for Police Traffic Radar Devices," No. DOT HS-807-415, May 1989. J. F. Campbell, P. D. Fisher, and D. A. Mansfield, Defense of Speeding, Reckless Driving and Vehicular Homicide. New York: Matthew Bender, 1984. P. D. Fisher, Improving on police radar, IEEE Spectrum, Vol. 29, No. 7, pp. 38-43, July 1992. T. K. Ishii, Analysis of target speed determination with Doppler radar, IEEE Trans. Instrum. Meas., Vol. IM-19, No. 2, pp. 85-91, May 1970. T. K. Ishii, Critical analysis and proposal for improvement of vehicle speed radar telemetry, IEEE Natl. Telemetering Conf. Proc., Los Angeles, CA, p. 37, Apr. 1970. T. K. Ishii, Error of Doppler radar in target speed determination for traffic control, IEEE Trans. Microwave Theory Tech., Vol. MTT-13, No. 3, pp. 389-390, May 1965.

CHAPTER

16 Microwave Radio Communication George Kizer

I. I n t r o d u c t i o n

In

the mid-1930s multiple channel point-to-point radio relay transmission using 12 frequency division multiplexed voice channels on an amplitude modulated (AM) very high frequency (VHF) carrier was introduced. During World War II, this technology was extended to ultra high frequency (UHF). In addition to AM systems, frequency modulation (FM) and digital pulse position modulation (PPM)were used. The first transcontinental microwave radio system was the AT & T TD-2 route from New York to San Francisco. This system employed 100 repeater stations operating in the 4-GHz band using a 20-MHz channel bandwidth to relay 480 voice channels on a frequency modulated radio carrier. This system, eventually upgraded to 1800-channel operation, was the forerunner of the many radio systems in operation today between 2 and 11 GHz. By the middle 1970s many of the major radio routes had reached their capacity of 1800 or 2400 analog channels using FM. Several routes were converted to single-sideband amplitude modulation permitting up to 6000 voice channel operation in a 30-MHz wide radio channel. As the microwave transmission network matured, the switching systems were converting from analog to digital operation. In the early 1960s

Handbook of Microwave Technology, Volume 2

449

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

450

George Kizer

digital cable transmission using pulse code modulation (PCM)was introduced. Shortly thereafter, the introduction of digital switches using this technology for voice circuits was begun. In 1965 the first digital switch, the lESS, was placed in service for local metropolitan use. This worked so well that, in 1976, the first four-wire toll switch, the 4ESS, was introduced. By 1979 the 4ESS was upgraded to handle over 100,000 lines serving over 600,000 calls per hour. This all-digital switch, together with the D4 digital voice channel bank, offered a significant economic advantage to the use of digital transmission systems. By the mid 1970s the conversion of analog transmission systems to digital operation had began. Initially the digital radio systems used the simpler digital modulation methods (e.g., 4 PSK, 8 PSK, or 9 QPRS). What these systems had in common was inefficient use of the frequency spectrum for voice transmission, compared with analog radio systems. Substantial improvements in spectral efficiency have been made over the last decade by the near universal adoption of quadrature amplitude modulation (QAM). The most commonly used criterion, b i t / s / H z , for the spectral efficiency of a digital radio is the number of payload bits per second divided by the 99% transmit spectrum power bandwidth. The first QAM radios used two orthogonal sets of four amplitude states. This 16-QAM signal had a spectrum efficiency of 2.5 to 3.5 b i t / s / H z . Later 64 QAM (4.5 to 5.2 b i t / s / H z ) and 256 QAM (5.5 to 6 b i t / s / H z ) w e r e developed. Using 64 kbit/s PCM, the spectral efficiency of a 256-QAM radio is comparable to that of an analog FM radio. The increasing technical difficulties encountered in the design of digital radios at the higher modulation levels have fostered investigations into the feasibility of cross-polarized cochannel frequency transmission. If this can be made practical, the 256-QAM radio, with frequency reuse, would have a spectral efficiency of 12 b i t / s / H z . Using 64 kbit/s PCM, this would make the radio system nearly as spectrally efficient for telephone circuits as a single-sideband analog radio. Of course, the digital radios are far more efficient for digital circuits than their analog radio counterparts. Microwave system design is a tradeoff of many factors. Some of those are a function of state-of-the-art equipment parameters. Other factors are independent of equipment design. These include interference and radio path fading. Design is complicated by the fact that most systems are designed as multiple transmitter/receiver pairs ("hops") cascaded to provided transmission between two remote locations. The effect of cascading the equipment significantly complicates designing systems to meet specific end-to-end performance objectives. This chapter will overview the major factors.

451

16. Microwave Radio Communication

2. Equipment-Dependent Radio Performance Analog Systems Most analog radio systems are FM frequency division multiplex (FDM) configurations. Detailed analog radio system design is done on the basis of a detailed end-to-end noise performance objective. Final noise performance objectives are determined based on appropriate domestic or CCIR objectives. The performance is determined by the worst-case noise. This noise occurs when one or more of the radio system paths is experiencing a partial loss of the received signal level ("fading"). Therefore, most of the design of analog systems revolves around designing the system to minimize the effects of interference and receive signal level fading. However, the designers must confirm that the system performance is not limited by intermodulation noise on an unfaded end-to-end basis. To ensure this, the system designer takes an equipment specification noise power radio (NPR). That specification is converted to a noise value, N. N (dBm0) = NLR (dBm0) - BWR (dB) - N P R (dB), where N L R is the noise loading ratio, - 1 5 + 10 log (number of voice channels) for CCIR systems and - 1 9 . 6 + 10 log (number of voice channels) for North American systems; BWR is the bandwidth ratio, 10 log ([ fb (kHz) - fa (kHz)]/3.1), where fa is the lowest baseband frequency and fb is the highest baseband frequency; and N P R is the noise power ratio. The calculated noise is the sum of the thermal and the intermodulation noise. Using the radio path and radio parameters the thermal noise for a hop of radios is calculated. A convenient method is to use Figures 1 and 2. Obtain a graph value, Ng, from Figure 1 based on C/N.

C/N

(dB) -- RSL (dBm) + 114.0 - NF (dB) - 101ogB ( M H z ) ,

where C/N is the carrier-to-noise ratio, RLS is the received signal level, NF is the receiver noise figure at the location at which RSL is specified, B is the receiver 3-dB bandwidth prior to the FM demodulator (typically the IF bandwidth), and log(x) is the common logarithm (base 10) of x. The received FM receiver thermal noise N is given from the following formula, N (dBm0) = Ng + 29.6 - 20 log [df (kHz)] + 10 log[B (MHz)] - W ( d B ) -

P (dB),

452

George Kizer

-20

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where Ng is the graph value from Figure 1, df is the per channel RMS deviation (for a 0-dBm0 test tone at the emphasis crossover frequency), B is the receiver 3-dB bandwidth prior to the FM demodulator (typically the IF bandwidth), W is the noise weighting (typically 2 dB), P is the preemphasis value from Figure 2, and f is the baseband test tone frequency of interest. The thermal noise is subtracted (on a power basis) from the total NPR noise (using a chart such as Figure 3) to yield pure intermodulation noise. The end-to-end noise is the power summation of the end-to-end thermal and intermodulation noise components. Thermal noise is generated by each radio receiver front end. Since each receiver is independent of each other, the thermal noise is uncorrelated from radio hop to radio hop. Therefore, the anticipated end-to-end thermal noise caused by N identical radio paths would be end-to-end thermal noise (dBm) = single-hop thermal noise (dBm) + 10 log N. Intermodulation noise is a function of composite baseband voltage level. It would be the same on each hop since the composite baseband voltage

453

16. Microwave Radio Communication

+5 1

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would be identical on each hop. Theoretically intermodulation noise adds on a highly correlated basis. For N identical radio paths the anticipated end-to-end intermodulation noise would be 20log N if all noise was enhanced or 0 if every other hop noise canceled. As a practical matter, intermodulation noise addition will vary considerably. Actual measurements of cascaded systems yield results which vary from 10 to 171og N. Use of 13 log N to 16 log N addition are reasonable practical estimates. Therefore end-to-end intermodulation noise (dBm) = single-hop intermodulation noise (dBm) + 13 log N. This entire process is explained in considerable detail in Reference [24].

454

George Kizer

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Digital Systems The digital signal is called a "bit" which is a contraction of "binary digit." A bit represents the state of a single binary symbol. That state is generally represented as "0" or "1 . , . or. .as. . - . . or . . + . The average transmission capacity of a system is generally expressed as bits per second (bit/s). A symbol or single signaling element represents a single transmission event. The term "baud," the unit of signaling speed, is equal to the number of symbols per second. If a symbol can assume any of "m" states with equal probability, then the number of bits "n" that can be transmitted by that symbol are given by the relationship. m=2

n

or

n = log2(m) = 3.321 loglo ( m ) . The transmission capacity of the system ( b i t / s ) is the baud rate (symbols/ s) multiplied by the average symbol capacity (bit/symbol). The transmitted information (bit) is the transmission capacity ( b i t / s ) multiplied by the transmission duration (s).

16. Microwave Radio Communication

455

The design and operation of communication networks and equipment are based on various performance objectives. The introduction of digital transmission has caused new performance criteria to be introduced. The criteria may be grouped into three main categories. The first is absolute transmission delay. This is of particular importance to the telephony service in which significant subscriber difficulties arise as the delay increases. Round-trip transmission delay values in excess of 400 ms are presently considered unacceptable for telephony without special measures. Digital radio systems introduce smaller absolute delays than coaxial cable, optical fiber, and satellite systems. Geostationary orbit satellite systems introduce a round-trip transmission delay of 560 ms. The smaller transmission delay for radio systems is an advantage. For radio systems virtually all delay is introduced by multiplexes and time slot interchangers in electronic digital cross-connects. The second is variation in timing position of each bit from the expected position, as defined by the clock interval. This is normally expressed as wander or jitter. Wander is very low frequency jitter. It is the long-term fluctuation of the significant transition instants of a digital signal (with respect to their ideal time position). Wander is generated by changes in propagation delay of the transmission path. This is usually a function of cable length variation with temperature and clock drift. Jitter is the random phase modulation of a digital signal. It is a measure of the short-term frequency and phase stability of a digital signal. Its two principal sources are digital regenerators and digital multiplexes. Regenerator jitter is introduced by imperfections in the timing recovery period, whereas multiplex jitter is introduced in the pulse stuffing mechanism used to synchronize the low-speed incoming pulse stream. Jitter accumulation through the network is a complicated process because the stuffing-destuffing process interacts with the input jitter in a nonlinear way. The interaction alters the frequency of the input jitter as well as its amplitude. Jitter may introduce a number of impairments such as errors, slips, cross-talk, and distortion to the original signal. Thus, jitter can be a particularly important parameter for the types of digital terminals which may be interconnected to asynchronous circuits because the terminal loop timing circuits must work in the presence of jitter. The third is a series of criteria relating to errors in transmission. These criteria follow. Bit Error Ratio (Rate) The most common measurement of error performance is the bit error ratio (BER), sometimes stated as the bit error rate. The BER is the ratio

456

George Kizer

of the number of measured digital errors to the total number of observed digits. No error detection scheme (short of an out-of-service bit-by-bit comparison) can detect all bit errors. The measurement of long-term BER gives little information about short-term error performance. For example, if errors are occurring in short bursts, the error performance might be acceptable. Single random errors (dribbling errors) leading to the same BER could severely affect data throughput. The terms error-free seconds and errored seconds address this problem. The number of error-free seconds is the number of seconds during a defined measurement period when no errors occurred. Conversely, the number of errored seconds is the number of seconds during the same measurement period when any error occurred.

Errored Seconds (ES) An ES is a second during which at least one error has occurred. An important reason for counting ES is the quality statements in data service tariffs are generally given in terms of percentage of error-free seconds. In addition, by combining the count of ES and the effective BER, a measure of the error distribution can be obtained. Distinguishing between bursty and randomly distributed errors can be important in diagnosing a facility problem. Errored second measurements may be made synchronously or asynchronously. For synchronous errored seconds, an errored second begins with the detection of an error. All errors falling within a 1-s window synchronized to the beginning error are included in that error second. Asynchronous measurements use a free running clock to measure the errored seconds. The asynchronous measurement has the potential to give different readings for different test sets connected to the same digital signal. Synchronous measurements avoid this potential problem. Errored seconds are to be measured only when service is available.

Severely Errored Seconds (SES) An SES is a second which contains more than N coding violations. The value of N will vary with the frame size and bit rate and should be chosen to correspond to a bit error ratio of approximately 10 -3, assuming errors are randomly distributed. This count may be used to ascertain problems for particular types of services. It may also be used as a measure of facility outage duration. In conjunction with ES and effective BER, the SES count yields additional information on error distributions. In the case of ESs, SESs should be measured during available time alone (less than 10 s in duration).

16. Microwave Radio Communication

457

Consecutive Severely Errored Seconds (CSES) This is a new performance parameter proposed by AT & T which defines a sequence of SESs lasting from 3 to 10 s. Such interruptions can be very disruptive to customer services because they can cause complete loss of the connection due to initiation of carrier group alarm (CGA).

Unavailable Seconds (UAS) Service is said to become unavailable if 10 consecutive SESs occur. Once the service becomes unavailable, it remains unavailable until 10 consecutive nonseverely errored seconds occur, after which it becomes available. The parameter UAS measures the duration for which the service was unavailable, in seconds. Unavailable time is a service-quality measure used in data service tariff specifications. More detailed information may be needed to adequately describe the performance of a error ratio of 10 -4 for an extended period of time. If there is only a facility alarm at a 10 -3 bit error ratio threshold, the degraded performance may not be detected, although this level of service may not be acceptable to a data customer. In effect, this alarm can be used to determine availability but not quality of service. Quality of service is measured only when the circuit is available.

Degraded Minutes (DMs) Available time, with all SESs removed, is grouped into 1-min. intervals. If the average BER of this minute is worse that 1.0 -6, the minute is counted as a degraded minute. As an in-service measurement, this is typically measured as any such minute with m or more CRC violations. The ~¢alue of m must be defined depending on the bit rate and the number of bits per CRC-protected block.

Estimating End-to-End Digital Radio Performance Typically three parameters are most significant to end-to-end equipment performance. These are jitter, bit error ratio and errored (or error-free) seconds. Jitter takes two forms. The first is RMS phase jitter that builds up on cascaded radio hops between modulators and demodulators. Based on the RMS phase jitter of a transmitter/receiver pair (without a modulator or demodulator) the designer must estimate the composite RMS jitter presented to the demodulator prior to digital signal detection. The composite RMS jitter degradation is typically characterized as a system fade margin

458

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degradation (see Figure 4). Theoretically, if n is the number of cascaded identical regenerators, RMS phase jitter accumulations on a square root of n basis. Figure 4 compares actual data with this theoretical result. For small numbers of regenerators, this is a little optimistic. For a large number of regenerators, this is too pessimistic. For a large number of repeaters, the differences due to manufacturing tolerances begins to become apparent. Figure 5 graphs the impairment (C/I degradation) caused by carrier phase jitter at the input to the radio demodulator. The second form of jitter is the peak-to-peak waiting time jitter introduced into digital signals by asynchronous (plesiochronous) multiplexer/demultiplexer pairs (muldems). This jitter is introduced by the pulse stuffing process of the muldems. This jitter is introduced every time digital radios are cascaded unless the radios are back-to-back digital ("rail") repeaters (without digital detection and remodulation). Although like RMS jitter this jitter builds up on a square root of the number of tandem muldems basis, this process is highly nonlinear; considerable variation will exist from case to case. Figure 6 shows actual averaged results for a nine-DS-3 system (1:2 multiline system employing three DS-3 64-QAM radios) with up to eight switching sections spread out over a 1000-mile system. The system designer must make sure that the end-to-end peak-to-peak jitter does not exceed the input jitter specification of the terminating demultiplexer. All North American standard multiplexes must accept five unit intervals of peak-to-peak jitter and still operate properly [4].

459

16. Microwave Radio Communication

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The next digital quality factor considered is bit error ratio. BER has two interesting properties. Unlike other error measurements such as errored seconds, BER is constant regardless of the transmission rate or

460

George Kizer TABLE I Comparison of Various Digital Modulation Techniques (Based on Equal Data Rates) SYSTEM DESIGNATION

2-PSK 3-QPR 4-PSK, 4-QAM 8-QAM 8-PSK 9-QPR 16-QAM 16-PSK 25-QPR 32-QAM 32-PSK 49-QPR 64-QAM 64-PSK 121-QPR 128-QAM 128-PSK 225-QPR 256-QAM 256-PSK 512-QAM 529-QPR 961-QPR 1024-QAM 2209-QPR 2048-QAM 3969-QPR 4096-QAM

INFORMATION DENSITY (bps/Hz)

SIGNAL-TO-NOISE RATIOS FOR BER = 10 -6 CHANNEL Eb/N o (dB)

DECISION CKT S/N (dB)

10.6 12.6 10.6 13.5 14.0 12.6 14.5 18.6 15.5 17.5 23.8 16.6 18.8 28.8 19.5 21.8 34.3 21.0 24.0 39.8 27.2 24.0 26.0 29.0 29.4 32.5 31.0 34.0

13.6 17.6 13.6 18.3 18.8 17.6 20.5 24.6 22.3 24.5 30.8 24.6 26.6 36.8 28.5 30.3 42.8 30.8 33.0 48.8 36.8 34.3 37.0 39.0 40.8 42.9 43.0 44.8

PEAK TO AVERAGE RATIO (dB) (SQUARE ROOT FILTER PARTITIONING)

0.0 2.0 0.0 1.3 0.0 2.0 2.6 0.0 3.3 2.3 0.0 4.6 3.7 0.0 4.3 3.2 0.0 5.7 4.3 0.0 3.4 5.2 6.3 4.5 5.4 3.6 6.5 4.8

multiplexing level. The BER of the DS-3 input of a (M13) multiplexer is the same at the BER of the DS-1 multiplexer output. This assumes errors occur randomly. However, actual measurements using faded radios (which produce error bursts due to error correction and data scrambling)validate this theoretical result for practical systems. For typical BERs (10 -3 or smaller), the end-to-end BER of cascaded links is the sum of the individual link BERs [25]. These properties greatly simplify BER calculations. BER under faded conditions will be treated later. At that time, Table 1 will be useful to estimate faded BER. If Trellis encoding or forward error correction is used, these coding gains must be added to the results of Table 1. Under unfaded conditions the equipment BER performance is quite good. The typical system engineering problem is not how good the (unfaded carrier or non-RSL dependent) system performance is but how to verify that high level of performance during system signoff. The bit error ratio of a digital circuit is defined as the ratio of measured digital errors to the total number of observed digits. It is assumed that the measurement has been made over a statistically significant period of time. For high transmission rates and relatively large BERs (e.g., 10 -3 to 10-6), many errors are observed in a small period of time.

461

16. Microwave Radio Communication

For very small BERs (e.g., 10 -9 to 10-12) e v e n very long periods of time will yield only a few errors. For this situation, the question of measurement accuracy is important. The statistical problem of estimating the ratio of two possible discrete outcomes is called the Bernoulli trial problem. The binomial distribution characterizes the binary outcomes of the Bernoulli trials. For a large number of trials (in our case, a large number of transmitted digits), the discrete binomial distribution may be accurately approximated by the continuous Poisson distribution. Assume that n digits have been transmitted and e digits were found to be in error. For the following assume that n is at least 10,000. The median unbiased maximum likelihood estimator for B E R is BER=

1/(3n)

fore=0

BER =

e/n

for e > 0.

Since the number of observed errors (events) is so small statistically, variation of the result should be expected if the experiment is repeated. To determine the expected range of the measurement with a stated confidence level, one determines the upper and lower confidence limits (e.g., 95%) and determines the upper and lower limits of e based on the Poisson distribution (see Table 1). A confidence level of 95% means that, if the experiment were repeated many times, 95% of the time the results would fall within the upper and lower limits. For example, if 10 l° bits were transmitted, 10 errors were observed, and a confidence level of 95% is desired, the B E R lower (BER l) and upper (BER u) confidence limits would be the following: B E R u (95% confidence) =

eupper/n

= 18.4/101° = 1.84 × 10 .9 B E R (maximum likelihood) =

e/n

= 10/1010 = 1 . 0 0 × 10 .9 B E R l (95% confidence) =

elower/n

= 4.7/101° = 4.7 × 10-1°.

462

George Kizer TABLE 2 Error Confidence Limits Confidence Level Errors (e) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

95%

90% Lower Limit 0.0 0.1 0.4 0.8 1.4 2.0 2.6 3.3 4.0 4.7 5.4 6.1 6.9 7.7 8.4 9.2 10.0 10.8 11.6 12.4 13.2 14.0 14.9 15.7 16.5 17.4 18.2 19.0 19.9 20.7 21.6 22.4 23.3 24.1 25.0 25.9 26.7 27.6 28.5 29.3 30.2 31.1 31.9 32.8 33.7 34.6 35.4 36.3 37.2 38.1 39.0 39.9 40.7 41.6 42.5 43.4 44.3 45.2 46.1 47.0 47.9

Upper Llmlt 3.0 4.7 6.3 7.8 9.2 10.5 11.8 13.1 14.4 15.7 17.0 18.2 19.5 20.7 21.9 23.1 24.3 25.5 26.7 27.9 29.1 30.3 31.4 32.6 33.8 34.9 36.1 37.2 38.4 39.5 40.7 41.8 43.0 44.1 45.3 46.4 47.5 48.7 49.8 50.9 52.1 53.2 54.3 55.4 56.6 57.7 58.8 59.9 61.0 62.2 63.3 64.4 65.5 66.6 67.7 68.8 69.9 71.1 72.2 73.3 74.4

Lower Limit 0.0 0.0 0.2 0.6 1.1 1.6 2.2 2.8 3.5 4.1 4.7 5.4 6.2 6.9 7.6 8.4 9.1 9.9 10.6 11.4 12.2 13.0 13.8 14.5 15.3 16.1 17.0 17.8 18.6 19.4 20.2 21.0 21.9 22.7 23.5 24.4 25.2 26.0 26.9 27.7 28.6 29.4 30.2 31.1 31.9 32.8 33.7 34.5 35.4 36.2 37.1 38.0 38.8 39.7 40.5 41.4 42.3 43.1 44.0 44.9 45.8

99% Upper Limit 3.7 5.6 7.2 8.8 10.2 11.7 13.1 14.4 15.8 17.1 18.4 19.7 21.0 22.3 23.5 24.8 26.0 27.3 28.5 29.7 30.9 32.1 33.3 34.5 35.7 36.9 38.1 39.3 40.5 41.7 42.9 44.0 45.2 46.4 47.5 48.7 49.9 51.0 52.2 53.3 54.5 55.6 56.8 57.9 59.1 60.2 61.4 62.5 63.7 64.8 65.9 67.1 68.2 69.4 70.5 71.6 72.7 73.9 75.0 76.1 77.3

Lower Llmlt 0.0 0.0 0.1 0.3 0.7 1.1 1.5 2.0 2.6 3.1 3.7 4.3 4.9 5.6 6.2 6.9 7.6 8.2 8.9 9.6 10.3 11.1 11.8 12.5 13.2 14.0 14.7 15.5 16.2 17.0 17.8 18.5 19.3 20.1 20.8 21.6 22.4 23.2 24.0 24.8 25.6 26.4 27.2 28.0

28.8 29.6 30.4 31.2 32.0 32.8 33.6 34.5 35.3 36.1 36.9 37.8 38.6 39.4 40.2 41.1 41.9

Upper Limlt 5'.3 7.4 9.3 11.0 12.6 14.1 15.7 17.1 18.6 20.0 21.4 22.8 24.2 25.5 26.9 28.2 29.5 30.8 32.1 33.4 34.7 36.0 37.3 38.5 39.8 41.0 42.3 43.5 44.8 46.0 47.3 48.5 49.7 50.9 52.1 53.4 54.6 55.8 57.0 58.2 59.4 60.6 61.8 63.0 64.2 65.4 66.6 67.8 68.9 70.1 71.3 72.5 73.7 74.8 76.0 77.2 78.4 79.5 80.7 81.9 83.0

16. Microwave Radio Communication

463

(,Continued)

TABLE 2 Confidence Level

90%

95%

99%

Errors (e)

Lower Limit

Upper Limit

Lower Limit

Upper Limit

Lower Limit

Upper Limit

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91

48.8 49.6 50.5 51.4 52.3 53.2 54.1 55.0 55.9 56.8 57.7 58.6 59.6 60.5 61.4 62.3 63.2 64.1 65.0 65.9 66.8 67.7 68.6 69.5 70.4 71.4 72.3 73.2 74.1 75.0 75.9 76.8 77.7 78.7 79.6 80.5 81.4 82.3 83.2 84.2

75.5 76.6 77.7 78.8 79.9 81.0 82.1 83.2 84.3 85.4 86.5 87.6 88.7 89.8 90.9 92.0 93.0 94.1 95.2 96.3 97.4 98.5 99.6 100.7 101.8 102.9 103.9 105.0 106.1 107.2 108.3 109.4 110.5 111.5 112.6 113.7 114.8 115.9 117.0 118.0

46.6 47.5 48.4 49.3 50.1 51.0 51.9 52.8 53.7 54.5 55.4 56.3 57.2 58.1 59.0 59.9 60.7 61.6 62.5 63.4 64.3 65.2 66.1 67.0 67.9 68.8 69.7 70.6 71.5 72.4 73.2 74.1 75.0 75.9 76.8 77.7 78.6 79.5 80.4 81.3

78.4 79.5 80.6 81.7 82.9 84.0 85.1 86.2 87.3 88.5 89.6 90.7 91.8 92.9 94.0 95.1 96.3 97.4 98.5 99.6 100.7 101.8 102.9 104.0 105.1 106.2 107.3 108.4 109.5 110.6 111.7 112.8 114.0 115.1 116.2 117.3 118.4 119.4 120.5 121.6

42.7 43.6 44.4 45.2 46.1 46.9 47.8 48.6 49.5 50.3 51.1 52.0 52.8 53.7 54.5 55.4 56.2 57.1 58.0 58.8 59.7 60.5 61.4 62.2 63.1 64.0 64.8 65.7 66.5 67.4 68.3 69.1 70.0 70.9 71.7 72.6 73.5 74.3 75.2 76.1

84.2 85.4 86.5 87.7 88.8 90.0 91.2 92.3 93.5 94.6 95.8 96.9 98.1 99.2 100.4 101.5 102.7 103.8 105.0 106.1 107.2 108.4 109.5 110.7 111.8 113.0 114.1 115.2 116.4 117.5 118.6 119.8 120.9 122.0 123.2 124.3 125.4 126.6 127.7 128.8

92

93 94 95 96 97 98 99 100

The results of Table 2 were taken from Poisson distribution tables. For e > 30, the table values may be determined (or extended) by using the following formulas:

euppe r - e

elowe

r

--

+

1 Z2

e + (~)Z

+

:

-

Z(e

+ 1) ° '

Z ( e ) 0"5

_

+(-s)

1

464

George Kizer

For the above, Z is the number of standard deviations for a given confidence level based on a zero mean unity variance two-tailed normal distribution integral. For the listed confidence levels Z = 1.64 for the 90% confidence level Z = 1.96 for the 95% confidence level Z = 2.58 for the 99% confidence level. It has been assumed for the above that a period of time was chosen for the error measurements prior to evaluating BER. This is termed direct binomial sampling (DBS). If an arbitrary number of errors is defined prior to the experiment and testing is stopped when this level is reached, this testing procedure is termed inverse binomial sampling (IBS). The calculation procedure for BER estimation is the same with the following exceptions: e u p p e r (IBS)

=

e upper (DBS)

- 1

e,ower(IBS) = elower(DBS). The last digital quality factor considered is errored seconds or the related parameter, error-free seconds. For a measurement period, errored seconds is the sum total number of seconds containing at least one error. Error-free seconds is the difference between the measurement period (in seconds) and the errored seconds measured. Unlike BER, ES measurements do not remain the same at different multiplexing levels. The ES of the DS-3 input of a (M13) multiplexer is not the same as the ES of the DS-1 multiplexer output. If errors are uniformly distributed in a data stream, the theoretical percentage of a measurement period containing errored seconds, denoted ESt, would be given by the following: ES t (%) = (100 x BER x binary transmission rate)

or

(100),

whichever is less. Unfortunately error correction algorithms and descrambiers cause errors to be bunched rather uniformly distributed. Figures 7 and 8 compare theoretical and actual ES measurements made with test generators and fade RSL digital microwave radios.

16. Microwave Radio Communication

465

%

100 80

.................................................... ¢ ~ ...... "::"7" ..................... ii:::::

60

......................................

,/"//

................................ .

/," ,,'.: .................. ~.'"

.......--::.:::ii............................................... .... THEORETICAL

.:::::i .....................................................................................................

GENERATOR

...............

40 f'"

FADED RADIO

20

0 L,. 0.1

I

I

I

I

I

0.2

0.5

1

2

5

I ,

10

I

~

20

50

100

BER x 10^6 Figure 7. Percentage of seconds with errors (DS-I).

%

100 1 8o

r

. ~

.....................................................

.......~

7 / ...................................... •. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

S I~'/'"......

60[

...../

....[] .......................... ~,

/'/" ......El.... THEORETICAL

~

GENERATOR

40i ........................ ~...................................... ~':~................................................................................................ •"~

20 0 0.001

FADED RADIO

d:il............................................................................................................ i 0.01

i I 0.1 1 BER x 10^6

i 10

100

Figure 8. Percentage of seconds with errors (DS-3).

3. T r a n s m i s s i o n - P a t h - D e p e n d e n t

Radio P e r f o r m a n c e

The ultimate end-to-end performance of a microwave radio is limited by the nominal and time-dependent characteristics of the transmission path. Some of the characteristics of the path affect both analog and digital systems similarly. In other cases, the effects are different. General characteristics will be overviewed. Specific methods of calculating both analog and digital system performance will then be given.

GeorgeKizer

466 Transmission Path Loss

An isotropic source is a hypothetical radiator which transmits or receives power equally in all directions. In an infinite homogeneous lossless medium, the power density P at a distance, d, from an isotropic source is the total power transmitted Wt, divided by the surface area of a sphere with radius d. The power received Wr by a receiving antenna with effective a r e a A r is the product of A r and P. The free space loss is defined as W r / W t. L (dB) = 10 log( Wr / Wt). The formula is more commonly expressed in decibels in one of the following ways: L (dB) = - 7 4 . 3 + 20log f (GHz) - 20log d (miles) + 10log

A t (ft 2)

+ 10 log Z r ( f t 2) - t t (dB) - Z r (dB) = - 4 9 . 5 + 20 log f ( G H z ) - 20 log d (km) + 10 log A t (m 2) -k- 1 0 1 o g A

r ( m 2) - L t ( r i B ) - L r ( d B ) .

Transmission line losses are significant at microwave frequencies and must be accounted for. L t is the transmission line loss between the transmitter and the transmit antenna and L r is the transmission line loss between the receive antenna and the receiver. A x is the effective area of projection of the antenna aperture in the direction of transmission and 3 is the antenna efficiency. If the transmit antenna has axial gain (relative to an isotropic radiator) G t and effective a r e a A t and the receiving antenna has axial gain G r (relative to an isotropic radiator) and effective a r e a A r , the free-space transmission loss formula becomes L (dB) = - 96.6 - 20 log f ( G H z ) - 20 log d (miles) -- L t ( d B )

+ G t (dB)

+ G r (dB)

- L r (dB)

= - 9 2 . 4 - 20log f (GHz) - 20log d (km) - L t (riB) -k- G t ( d B )

+ G r (dB)

- L r (dB),

where the antenna gain is given by G~ (dB) = + 11.1 + 20 log f (GHz) + 10 log A (ft 2) + 10 log(6) = + 21.5 + 20 log f (GHz) + 10 log A ( m 2) + 10 log(a). The typical value of 6 varies from 0.45 to 0 . 5 5 for commercial parabolic antennas (see Table 3) and 0.90 to 1.0 for passive reflectors. For parabolic

467

16. Microwave Radio Communication

TABLE 3 Typical Worst-Case Commercial Parabolic Antenna Gain (Decibels Relative to the Isotropic Radiator) DIAMETER m (ft)

0.6(2)

1.2(4)

1.8(6)

2.4(8)

3.0(10)

3.7(12)

4.6(15)

24.3 25.0 25.8 26.3 27.2 27.9 27.9

27.8 28,5 29.3 29.3 30.9 31.0 31.1 34.5 34.9 34.9 36.4 38.4 38.5 39.4 40.0 40.7 40.8 41.0 43.1 44.0 44.8 45.1 45.1 46.1 47.9 49.7

30.0 31.0 31.9 32.2 33.3 33.5 33.6 36.7 36.8 37.3 38.9 41.2 41.3 42.0 42.5 43.3 43.3 43.5 45.8 46.4 47.3 47.6 47.6 48.6

32.0 32.9 33.8 34.2 35.2 35.2 35.4 38.7 38.8 39.0 40.8 42.9 43.1 43.8 44.5 45.2 45.2 45.4 47.8 47.8 48.5 48.8 48.8 50.5 -

33.7 34.5 35.4 35.7 36.9 37.4 37.4 40.4 40.4 41.0 42.4 44.5 44.8 45.4 46.0 46.7 46.7 47.0 49.2 49.8 50.6 50.9 50.9

35.7 36.4 37.3 37.6 -

Frequency 1.7 1.9 2.1 2.2 2.4 2.5 2.6 3.7 3.9 4.0 4.7 5.9 6.2 6.8 7.4 8.0 8.1 8.4 10.6 11.2 12.5 12.7 13.0 14.9 18.7 22.4

31.4 33.O

34. I 34.5 35.4 35.5 35.6 36.5 38.5 40.5

35.0 36.0 36.5 37.1 37.2 39.6 40.5 40.7 40.8 41.0 42.5 44.7 46.3

-

42.1 42.3 42,7 44.3 46.1 46,4 46,9 47.7 48.6 48.6 48.8 51,3 51.6 51.9

-

antennas, A is merely the frontal area (Tr × d i a m e t e r 2 / 4 ) o f the reflector since the antenna is aligned in the direction of transmission. For passive reflectors, A is the area of the passive reflector projected onto a plane passing through the passive reflector which is orthogonal to the direction of transmission. For a passive reflector, the effective area is the total surface frontal area multiplied by COS ( C / 2 ) , where C is the angle formed by the two transmission paths which converge at the reflector. The above loss formulas are commonly written as L (dB) = - L t (dB) + G t (dB) + c~ (dB) + G,. ( d B ) -

L r (dB)

(dB) = free-space loss = - 96.6 - 20 log f ( G H z ) - 20 log d (miles) = - 92.4 - 20 log f ( G H z ) - 20 log d ( k m ) . L t and L r may be estimated using Tables 4 and 5. It is possible to use one, two, or more passive reflectors between a transmitter and a receiver. In the far field one can treat each path independently. The reflector acts as a

468

George Kizer TABLE 4 Typical Copper Corrugated Elliptical Waveguide Loss FREQUENCY (GHz)

1.9 2.1 2.2 2.4 2.5 2.6 3.7 3.9 4.0 4.7 5.9 6.2 6.8 7.4 8.0 8.1 8.4 10.6 11.2 12.5 12.7 13.0 14.9 18.7

LOSS

WAVEGUIDE TYPE

EW20 EW20 EW20 EW20 EW20 EW20 EW37 EW37 EW37 EW44 EW52 EW52 EW63 EW64 EW77 EW77 EW77 EW90 EW90 EW127 EW127 EW127 EW132 EW 180

dB100 m

dB/100 ft

2.0 1.7 1.6 1.5 1.4 1.4 3.1 2.9 2.8 4.0 4.0 3.9 4.4 4.8 5.8 5.8 5.6 10.5 10.0 11.8 11.7 11.5 15.4 19.4

0.60 0.52 0.49 0.45 0.44 0.43 0.94 0.87 0.85 1.2 1.2 1.2 1.4 1.5 1.8 1.8 1.7 3.3 3.1 3.6 3.6 3.5 4.7 5.9

TABLE 5 Typical Copper Circular Waveguide Loss FREQUENCY (GHz)

4.0 4.7 5.9 6.2 6.8 7.4 8.0 8.1 8.4 10.6 11.2 12.5

LOSS

WAVEGUIDE TYPE

WC-281/-269 WC-281/-269 WC-281/-269 WC-281/-269/-205 WC-281/-269/-166 WC-281/-166 WC-281/-166 WC-281/- 166 WC-281/-166 WC-281/-166/-109 WC-281/-166/-109 WC-281/-109

dB100 m

dB/100 ft

1.2/1.3 1.0/1.1 0.91/0.99 0.91/0.98/1.6 0.89/0.97/2.5 0.89/2,3 0.89/2.1 0.89/2.1 0.89/2.1 0.91/1.9/4.5 0.92/1.9/4.3 0.95/4.2

0.36/0.41 0.32•0.35 0.28/0.30 0.28/0.30/0.50 0.27/0.30/0.76 0.27•0.70 0.27/0.65 0.27•0.64 0.27/0.64 0.28/0.57/1.4 0.28/0.57/1.3 0.29/1.30

receiver in one direction and a transmitter in the other. The gain is, of course, the same in either case. The two-way repeater gain referred to by some authors is the sum of the receive and transmit gain (expressed in decibels) of the repeater.

469

16. Microwave Radio Communication

The preceding formulas assume that all antennas are far enough from each other that far-field conditions apply. Lewis, as reported by Friis [18], suggested that far-field conditions exist as long as d > 2a2/A a = free-space wavelength - 1 / [1.0167 f (GHz)] in feet = 1/[3.3356 f (GHz)] in meters, where d is the distance between the antennas, a is the largest linear dimension (in the plane of projection of the wave) of the larger antenna, and a is the wavelength of the radio wave. As the antennas are moved closer together, the gain of the two antennas is reduced compared with the far-field gain. Parabolic antennas were addressed by Bickmore and Hansen [6] for the case in which one antenna is much larger than the other (only the large antenna is in the near field). Pace [42] gives an approximation for parabolic antennas of similar size. Based on these results, Figure 9 was produced. This figure graphs the loss in composite antenna gain relative to far-field gain as a function of D a and D b , the diameters of the two parabolic antennas. For this figure, D a >_ D b and the above parameter definitions apply.

0

-1

-2 dB -3 I

-4

-5

0

-9

-8

-7

-6 -5 -4 10 log( d/[2Da 2/2 ])

-3

-2

Figure 9. Dual-parabolic-antenna near-field correction factor,

-1

0

470

George Kizer

It is common to estimate the total path loss through a passive repeater as two independent paths. Often one end of the path has the reflector, parabolic antenna, or both in the near field, reducing effective free-space gain. Jakes [22] considered the case of a parabolic antenna and elliptical (cirular projection) reflector. Medhurst [37] produced a result for both the elliptical (circular projection) and the rectangular (square projection) reflector cases. Based on Medhurst's results, Figures 10 and 11 were produced. They represent the loss in composite antenna and reflector gain when the two approach each other. D r is the diameter or width of the projection of the reflector gain when the two approach each other. D r is the diameter or width of the projection of the reflector in a plane parallel

+6

-101-~ dB

2.5 3.0 DA~ DR 4.0 5.0

-15

I

~

6.0 7.0 8.0 9.0

-20

-25

-3O -10

0 10 log (d/[2DR2/;k])

+10

Figure I0. Circular reflector and parabolic antenna combined gain.

16. Microwave Radio Communication

471

+6

2.5 3.0 \ DA DR 4.0

-10 dB

5.0 6.0

-15

7.0

\

8.0 ~

-20

-25 [

f

-30 . -10

,

,

,

,

.

,

.

.

,

. . . .

0

.

.

,

.

.1

+10

10 log (d/[2DR2/X]) Figure I I. Square reflector and parabolic antenna combined gain.

to the parabolic a n t e n n a . D a is the diameter of the primary parabolic antenna. Sometimes a pair of rectangular passive reflectors are used to go over or around obstructions. Although this case may be analyzed as three independent paths, typically the two passive reflectors are in each other's near field. Yang [51] analyzed the case of two rectangular (square projection) passive reflectors in the transmission path. Figure 12 shows the loss in combined far-field gain (relative to the gain of a single smaller reflector) as the two passive reflectors are moved close together. It is assumed that the projection of each rectangular passive reflector in the plane orthogonal to the direction of transmission is square. A is the width of the square

472

George Kizer

•l O f , , , , , , , , , , , 1

,1,4

1 //

,3,4

I

lo dB

4

5 6

8

-10

-20 -20

-10

0 10 log

+10

+20

(d/[2Dae/~])

Figure 12. Dual-square-reflector combined gain (relative to a single smaller square reflector).

projection of the smaller reflector and B is the width of the square projection of the larger reflector. Using Figure 12, work the problem as the loss of two independent paths with the smaller reflector as a single reflector and add the loss from the figure. Note that all rectangular reflectors are assumed to have a square shape when they are projected into the path of transmission. If they are rectangular, the width used in the figures is the larger of the two rectangular dimensions. All elliptical reflectors are assumed to have a circular projection. If they are elliptical, the smaller dimension is used for the diameter. In all cases, however, the actual projection area is to be used to calculate far-field gain. The far-field radiation patterns of circular and rectangular reflectors, based upon Silver's results [45], are displayed in Figure 13.

Received Signal Variation ("Fading") The predicted values of received radio signal strength are usually based on a standard atmosphere (one which has no ducts, no refractive index

473

16. Microwave Radio Communication 0

-20~-

IY~

i

-20

0

I

q

I

|

//-CIRCULAFIAPERTURE" -"

"~

|

20 log

]

I

i

sin O]

i

.,o

.4o

Figure 13. Far-field patterns for uniformly illuminated apertures.

discontinuities, and no turbulence). Natural variations from the standard atmosphere that occur at various times and places are produced chiefly by variations in the temperature and water vapor content of the actual atmosphere. They can cause considerable variation (fading) in the actual signal strength received compared with that predicted from a theory which assumes a static standard atmosphere. These variations in the predicted values of signal strength produced by natural phenomena should be considered in the design of a radio communication system. Most fading can be categorized as atmospheric absorption (including rain attenuation), multipath, diffraction (shadow), loss (earth bulge), antenna decoupling, and ducting. Often, fading is a combination of these types. A general introduction is given in the following paragraphs.

Atmospheric (Nonrain) Absorption Path loss caused by atmospheric absorption is primarily due to atmospheric gases and rain. At frequencies below 60 GHz, attenuation due to frozen moisture (e.g., snow or ice crystals) can be neglected. The only significant loss due to precipitation is caused by liquid raindrops. This loss will be overviewed later. Atmospheric gas absorption is due to resonance of various molecules and a broad nonresonant loss due to oxygen and

474

George Kizer

0.8 " .

ABSOLUTE HUMIDITY

//.~

(gm/m3! ..................................//...,...~_ .....~.. . . . . . .

0.6

30 -

25

20 ,~

0.4

.................................

15 10

LI, I

...............................................

5.

0.2

0

|

I

I

10

20

30

40

FREQUENCY (GHz) Figure 14. Nonrain atmospheric transmission loss.

water vapor. Below 100 GHz, the only significant resonances are due to water vapor (H20) at 22 and 68 GHz, ozone ( 0 3) at 67 and 96 GHz, and a broad band of oxygen (O 2) resonances from 61 to 68 GHz. Due to atmospheric pressure, the absorption resonances are broadened so that significant absorption is observed near the resonance frequencies. Nonrain atmospheric losses for 15°C have been plotted in Figure 14. Rain Loss

At higher radio frequencies, large amounts of rain can have a significant effect on system radio interference (rain scatter), cross-polarization discrimination [39], and path attenuation. The interference and cross-polarization discrimination effects are short lived and generally are not a significant degradation to terrestrial paths. Path attenuation, however, has a significant impact on path design. Tillotson [46] observed the considerable effect rain can have on path design. He observed that for a rain rate of 100 mm (4 i n . ) / h , a normal 4- or 6-GHz path of 30 to 60 km (20 to 30 miles) designed for a 40-dB fade margin would be unaffected by rain. However, to maintain the path within the 40-dB fade range, the path length would have to be reduced to 9.2 km (5.7 miles) at 11 GHz, 3.7 km (2.3 miles) at 18 GHz, or 2.1 km (1.3 miles) at 30 GHz. Actual path lengths will vary from rain climate to rain climate. However, the considerable affect of rain on high frequency radio transmission is clear.

16. Microwave Radio Communication

475

The rain attenuation observed on a radio path is a function of the following three variables: c~ = (dB) =/3TL, where/3 (dB/kin) is the attenuation of a signal in rain of constant density and rate (attenuation due the point rain rate), y is the path correction factor (conversion factor from the point rain rate to the path averaged rate), and L (krn) is the path length. The attenuation of a signal due to rain is a function of the size distribution of raindrops as well as a function of rain rate and the terminal velocity of the drops. The size distribution is a function of the type of rain (e.g., thunderstorm and drizzle), and terminal velocity is a function of raindrop shape which is a function of rain type and wind. Olsen et al. [40] suggest that the Laws and Parsons [26] size distribution and the Gunn and Kinzer [19] terminal velocity results are the most reliable data to date. Medhurst validated these theoretical results by actual measurement [38]. Photographs have shown that rain, rather than being spherical, is actually flattened or concave. Because of this flattening, linearly polarized signals experience polarization-dependent attenuation. If the raindrops are assumed to be elliptical, /3 is given by the following [40], /3 ( d B / k m ) = aR b, where R ( m m / h ) is the rain rate and a and b are found in Table 6. Figure 15 plots/3 for various rain rates and transmission polarizations. For reference Bussey [8] observed that a rain rate of 1 m m / h represented

TABLE 6 Rain Attenuation Coefficients FREQUENCY 1 2 3 4 5 6 7 8 9 10 11 12 15 20 25 30 35 40 45 50 60 70 80 90 100

aHORIZONTAL

aVERTICAL

bHORIZONTAL

bVERTICAL

0.0000387 0.000154 0.000389 0.000650 0.000871 0.00175 0.00301 0.00454 0.00679 0.0101 0.0141 0.0188 0.0367 0.0751 0.124 0.187 0.263 0.350 0.442 0.536 0.707 0.851 0.975 1.O6 1.12

0.0000352 0.000138 0.000352 0.000591 0.000784 0.00155 0.00265 0.00395 0.00594 0.00887 0.0125 0.0168 0.0335 0.0691 0.113 0.167 0.233 0.310 0.393 0.479 0.642 0.784 0,906 0.999 1.06

0.912 0,963 1,029 1,121 1.291 1.308 1.332 1.327 1.301 1.276 1.243 1,217 1.154 1.099 1.061 1.021 0.979 0.939 0,903 0.873 0.826 0.793 0.769 0.753 0.743

0.880 0,923 0.987 1.075 1.248 1.265 1.312 1.310 1.287 1.264 1.229 1.200 1.128 1.065 1.030 1.000 0.963 0.929 0,897 0.868 0.824 0.793 0.769 0.754 0.744

476

George Kizer

20

H POL RAIN RATE

(mm/hr)

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FREQUENCY (GHz) Figure 15. Rain attenuation.

light rain; 4 m m / h , moderate rain; 16 m m / h , heavy rain; and 100 mm / h, a cloudburst. The attenuation measured at one point of a radio path is not totally representative of the attenuation of the path taken as a whole. The point rain rate attenuation is a complex function of rain gauge integration time and the probability of rain cell size and occurrence. A rain rate at one location may be low but it may be much higher elsewhere on the radio path. High rain rates, however, indicate that the observation point is near the center of maximum rain intensity. Several methods, such as Lin's [30] and CCIR's [11], have attempted to modify point rain attenuation for path length variation. The Crane method, given at the end of this chapter, has received the widest acceptance. Rain rate data are taken by measuring the total rain accumulated in a rain gauge in a period of time (integration period) and dividing this by the integration time. The measured rain rate varies considerably with rain gauge integration time [31]. A very short integration time produces widely varying results due to wind and spatial variations. A long integration time reduces the effect of a short-duration high rain rate. Two path rain attenuation calculation methods are popular. Rain loss calculations assume a point rain rate, R, which will not be exceeded more than a percentage of the time. The actual rain rate at any instant is quite erratic. A long-term rain rate gathered from a single rain gauge requires a very long time (several years) to yield stable statistics. If the time base is not sufficiently long, the short-term results tend to

16. Microwave Radio Communication

477

underestimate (or occasionally overestimate) the long-term, large sample average. Data taken over a period of less than 10 years [16] are generally unreliable for moderate rain rates. The incidence of high rain rates at a single point is so low that a much longer time base (a few decades) is required to obtain stable statistics [20]. Rain rate calculations assume rain rate distributions measured over one or two decades [33, 35]. The rain rates obtained from these data represent the rates that would have been measured if the radio path had been operating over the previous long time period. Exactly the same data will probably not be obtained if measurements are made over the next couple of decades. However, these data represent the best estimate of the rain rate which would not be exceeded over any one year. The actual rain rate measured over any one specific year will be different than the average value. Average values should not be confused with worst-case values. Osborne [41] observed that the worst-case one-year rain rates can exceed long-term averages by 2.5 to 10 times. Worst-case month or hour rates can exceed long-term averages by extremely large factors. Engineering paths based on worst-case statistics lead to very uneconomical radio systems. As Osborne [41] observed, at the present time there is no definitive proven solution to this problem. There is no practical method to limit the worst-case outage time for radio paths with loss dominated by rain attenuation. However, route diversity can be used to reduce outage time.

Reflection ("Fresnel Zone") Fading A common form of multipath fading is reflective fading (sometimes called Fresnel zone fading). This fading, like that caused by atmospheric multipath, is due to the reception of several signals from several different paths. The concept is exactly the same as one used in optics. Indirect signals arrive due to reflections from the ground, water, nearby objects, or stable atmospheric layers. Unlike atmospheric multipath, fading due to these reflective signals is relatively slow changing since the secondary paths are relatively stable. If the fading is due to cancellation between the main signal and a single reflected signal, the composite signal will be a minimum when the reflected signal is reflected from an obstacle that is an even Fresnel zone radius from the main path. The composite signal will be a maximum if the radius is odd. Generally, reflective fading is not a problem for paths over heavily wooded terrain or for paths so far above the reflecting surfaces that the transmit and receive antenna patterns discriminate against reflections. Flat paths can have reflections. Paths over water or salt flats almost always have reflections. Reflections can be reduced by blocking the reflection (using screen or high-low path design), tilting the antenna, or using spaced antennas. It is common to use two receive

GeorgeKizer

478

antennas (space diversity) to combat the effect of multipath. Another method is to reduce the antenna height at one end of the path while raising it at the other end to block the reflection or move it to a location less likely to be reflective (high-low path design). This technique makes one site elevated so as to provide the required clearance; the other site is located near ground level. The reflection point can be placed at a selected location by slight changes in the lower antenna height and geographical location. Even if the path is reflective, this technique reduces the difference between the direct and the reflected paths when compared with midpath reflection.

Obstruction ("Diffraction") Fading Radio waves normally travel outward along radial lines from their source, except when deviated by refraction or reflection. Another condition under which radio waves deviate from a straight line is called diffraction. Whenever radio waves encounter an obstructing object, some of the energy of the wave is diffracted at the edges of the object and becomes bent around the edge. This is a direct result of Huygens' principle of secondary radiation. This reduces the shadowing effect of objects which are opaque to radio waves. Diffraction fills part of the shadow area with some energy from the wave. The curved surface of the earth is the edge of one such object. Other objects may be buildings, trees, hills, mountains, or structural parts of a ship or airplane. If the obstructing object is small and subtends only a small angle, as seen from the source of radiation, the region at a considerable distance behind the object may become filled in and suffer little or no shadowing effect. Close behind the object, however, shadowing will be observed. Shadowing due to the earth causes the field strength to decrease rapidly with distance beyond the radio horizon. In general, an exact determination of signal strength for various path clearances is difficult. The obstruction loss generally falls somewhere between the knife-edge diffraction and the fiat-sheet reflection cases shown in Figure 16. The first Fresnel zone radius F 1 at any point on the radio path is given by the following: F 1 = first Fresnel zone radius Fn

= nth Fresnel zone radius = sqr(n) F 1

d I = distance from one end of path to reflection point t d e = distance from the other end of path to the reflection point

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d o = total length of path = d 1 4- d 2

f = frequency of operation, where n = 1, 2, 3 . . . and sqr is the square root. For F 1 in feet; d 0, d 1, and d 2 in miles; and f in gigahertz, F 1 = 72.1 ( d l d z / f d 0 ) a / 2 . For F 1 in meters; d 0, dl, and d 2 in kilometers; and f in gigahertz, F 1 = 17.3 ( d l d 2 / / f d 0 ) l / 2 . From a classical physics (optics) point of view, the quantity (h/F1)2 defines the Fresnel zone (or fraction of the zone) clearance of an obstacle as measured perpendicular to the line of wave propagation. In practice it is measured in a line perpendicular to the earth. For normal microwave paths, there is no significant difference. Bullington [7] used (h/F 1) to define path clearance. Since that time, common usage has been to define (h/F 1) rather t h a n (h/F1)2 as Fresnel zone clearance.

480

George Kizer

The speed of a radio wave varies inversely with the density of the medium through which it travels. The radio refractive index of air is the ratio of the speed of propagation in a vacuum to the radio wave's speed in the atmosphere. This ratio, n, is approximately 1.0003 under standard conditions near the earth's surface. For convenience, a factor, N, refractivity, given by N = (n - 1) X 10 6, is used in propagation studies. Refraction (bending) of a radio wave occurs when the wave speed on one side of the beam is reduced below that on the other. The bending is in the direction of the reduced speed, and its degree is directly proportional to the amount of speed reduction with distance (i.e., speed gradient) normal to the beam axis. Typically the atmosphere has a gradient of - 6 3 N units per mile or - 3 9 N units per kilometer. This gradient causes the radio wave to bend. The curvature of the nearly horizontal radio beam is slightly different from the curvature of the earth. If the actual earth with radius a were replaced by an equivalent earth with radius K a (see Figure 18), horizontal radio waves would travel parallel to the equivalent earth. For microwave radio frequencies, this equivalent earth factor, K, is given by K = 253/[253 + = 157/[ 157 +

(dN/dh)] for (dN/dh)in N units per mile ( dNIdh)] for ( d N I d h ) in N units per kilometer.

60

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The typical value of K is 5. 4 Figure 19 shows the range of possible refractivity when observed on a worldwide basis. To analyze a microwave path for conformance to the above guidelines, the profile of the earth along the transmission path is plotted. The microwave beam is then shown as a straight line between the two points. This represents the radio or light ray for K of infinity. An h value is then subtracted from the ray height to show beam bending due to various potential K values. The h correction value is given by the following: h = the change in vertical distance from a horizontal reference line p = location at which h is determined d 1 -- distance from p to one end of the path d 2 = distance from p to the other end of the path K = effective earth radius factor. For h in feet and d 1 and d 2 in miles

h - [did2]~[1.50 K].

482

George Kizer 300

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For h in meters and

d I

and

d 2

in kilometers

h = [dld2]/[12.74 K]. To adjust for ray curvature, subtract the above h value from the height of the ray above a flat earth or add the h value to the height of the earth below a straight ray. A particular form of diffraction loss is called obstruction ("earth bulge") fading. When the K factor becomes less than 1, the radio wave is bent upward. Under extreme cases the receive path can be partially or completely blocked. This type of loss is called earth bulging because the earth appears to bulge up into the radio path. The power fades that occur due to diffraction by the earth's surface are generally supported by a subrefractive (positive) gradient of refractive index. This type of fading can persist for several hours to depths of 20 or 30 dB. The fading is essentially independent of small-scale changes of frequency, but may be reduced or avoided by a proper choice of terminal antenna heights. Figure 20 shows areas of the world where this is common. From experience, various rules of thumb have been developed [50] to reduce obstruction fading to an insignificant effect. The following guide-

16.

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with a high probability of earth bulge (percentage of the worst month that the refractivity gradient > 0 N/kin).

Figure 20. W o r l d areas

lines for radio frequencies greater than 2 GHz are based on CCIR criteria [10]. These criteria were developed by Vigants and other in conjunction with Study Group 5 and represent an improvement to Vigants's original published guidelines [47]. The guidelines for 2-GHz radio frequencies and path length guidelines to minimize obstruction fading were developed based upon unpublished computer simulations and other studies. Guidelines for Radio Frequencies Greater Than 2 GHz For good propagation areas, allow obstruction clearance of 0.6 F 1

for K = 1

or

0.00

F 1 (grazing)

2

for K = 5,

whichever is greater clearance. For average propagation areas, allow obstruction clearance of 4

1.0F 1

forK=5

0.3 F 1

for K = 5,

or

2

484

George Kizer 0.9

Ki

CLEARANCE CRITERIA 0.8

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whichever is greater clearance. For difficult propagation areas, allow obstruction clearance of 4

1.0 F 1

for K = 5

0.00 F 1 (grazing)

for K = 3,

or 1

whichever is greater clearance. The preceding guidelines apply to the normal or main antennas for short to medium-length paths. For long paths, the clearance criteria may be relaxed, as shown in Figure 21. This accounts for the observation that obstruction fading is typically caused by localized refractivity gradient changes. For long paths, the average refrac4 tivity gradient is closer to the normal K value of 5.

Guidelines for 2-GHz Radio Frequencies Since Fresnel zones are much larger for 2 GHz than for higher frequencies, the above guidelines may be relaxed for low-frequency paths. For good or average propagation areas, allow obstruction clearance of 0.6 F 1 for K = 43 " For difficult propagation areas, allow obstruction clearance of 4

1.0 F 1 for K = g.

485

16. Microwave Radio Communication

Guidelines for Space Diversity Antenna Placement If space diversity is used, the criterion for diversity antenna clearance is less stringent. For the diversity antenna path, allow obstruction clearance of 0.60F 1 forK= 4 with at least 10 ft in the first 500 ft from the antenna. This usually permits placement of the diversity antenna at an appropriate level below the main antenna. If the path terrain is nonreflective, multipath fading improvement is achieved by placing the diversity antenna at least 200 wavelengths below (or above) the main antenna. See Figure 17 (page 480) for this distance.

Guidelines for Radio Path Lengths The above guidelines are designed to cover the vast majority of situations. In unusually severe propagation areas (such as the southern United States coastal areas), path lengths must be limited to reduce the occurrence of obstruction fading to a reasonable level. More detailed engineering may be required to design reliable paths in some areas. This engineering generally requires detailed knowledge of refractive index statistics for a given area. Such effort is costly and time consuming and should not be accomplished unless required. Based upon computer simulation, obstruction fading should be investigated if the following path lengths are exceeded. Maximum path length [kilometers (miles)] Frequency (GHz) Climate factors Good (C = 0.5) Average (C = 1.0) Bad (C = 2.0)

2

6

11

18

65 (40) 50 (30) 30 (20)

65 (40) 40 (25) 25 (15)

65 (40) 50 (30) 25 (15)

40 (25) 25 (15) 15 (10)

Refer to the following multipath calculations for further discussion regarding climate factor C. Worst-case conditions were investigated for each climate region. These path length guidelines assume that the preceding criteria for antenna placement were used. It is also assumed that adequate minimum thermal fade margins (35 dB for 2 and 6 GHz, 45 dB for 11 GHz, and 30 dB for 18 GHz)were engineered into the path.

Power Fading Power fading due to antenna decoupling refers to the loss of signal that occurs for transmission and reception of the signal outside of, or at the

486

George Kizer

extremities of, the main lobe of the antenna pattern. Variation of atmospheric refraction can cause changes in the apparent angle-of-arrival of the line-of-sight ray, particularly in the vertical plane, and can therefore effectively cause a reduction in gain in the antennas used at the radio path terminals. Measurements made in the United States over a path of 28 km, at frequencies of 4 and 24 GHz, show that the angle-of-arrival can change rapidly by as much as 0.75 ° above and below the normal line of sight. Another source observed 0.5 ° of angle-of-arrival variation on a 39-km path. Variations in the vertical angle-of-arrival of up to 0.5 ° have been observed on a 40-km path. This effect is proportional to the path length and can introduce several decibels of loss for high-gain antennas and long line-of-sight paths. Because of the vertical variations in angle-of-arrival, antennas having half-power beam widths less than 0.5 ° should generally be avoided for line-of-sight paths. This limitation can be used as one criterion to determine the maximum aperture size for antennas and the maximum vertical dimension for passive repeaters. This loss may be minimized by specifying a sufficiently broad antenna beam so that the expected variations of the angle-of-arrival are matched or exceeded.

Duct Fading Whenever a horizontal layer of air has its normal properties altered so that the refractive index decreases rapidly with an increase in height, strong downward bending of any nearly horizontal rays traversing the layer will occur. The curvature of these rays often exceeds the curvature of the earth's surface. A layer of air having this property is called a duct. Ducts may be divided into two types, ground (surface) and elevated. The underside of a ground-based duct is in contact with the earth's surface, whereas the underside of an elevated duct is above the earth's surface and overlies a layer of normal air. Prolonged fading, or signal enhancement, can result from propagation through ducts, especially when either the transmitter or the receiver is located within the duct. Signals may be trapped within the duct and propagated far beyond the horizon. Ducts may also cause multipath fading. Two conditions are necessary to form a duct. The first is for the refractive index gradient to be equal to or more negative than - 1 5 7 N per kilometer ( - 2 5 3 N per mile). This means that K must be infinite (flat earth) or negative (extreme superrefractivity). The second necessary condition is that the gradient must be maintained over a height of several wavelengths. For ducts 100 to 30 ft thick, trapping will occur for frequencies between 2 and 13 GHz, respectively. Of course, the cutoff relationship is only approximate since ducts have vague boundaries. See Figure 22 for areas in which ducting is highly probable.

487

16. Microwave Radio Communication 180

120

60

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Atmospheric Multipath Fading Multipath fading generally takes one of two forms. The first, atmospheric multipath, is caused by the received signal being composed of several signals arriving at the receive site by slightly different paths from the transmitter. The different transmission paths are caused by slight timeand space-dependent variations in the atmospheric refractive index. This phenomenon is the same one that causes stars to twinkle at night. Since the relative time delay of the various received signals will change as the atmosphere varies randomly, the composite received signal will vary widely and rapidly. This fading will be worse if obstruction (earth bulge) or reflective fading has already reduced the level of the dominant receive signal. Figure 23 diagrams the multipath fading mechanisms. Figure 24 shows typical time domain received signal variation during multipath fading. DeLange [17] noticed that for a 22-mile path operating at 4 GHz, path differences were from a fraction of 1 to 7 ft, with 3 ft being the most common. Kaylor [23] made several observations for a typical 31-mile, 4-GHz path with no significant ground reflections. He observed that deep multipath fades (greater than 20 dB relative to normal propagation

488

George Kizer h h

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conditions) always showed definite frequency selectivity (great loss occurred only over a relatively narrow frequency range). The deep fading was caused by at least four to six different component rays. The amplitude of the short path signals was larger than that of longer path signals, but depth of fade was primarily a function of long-path signal amplitude. Deep fading was largely uncorrelated for frequencies separated by more than 160 MHz (4% separation) but was highly correlated for frequencies within 80 MHz (2% of the deep fade notch. Deep fading usually occurred with a wide frequency loss of at least 10 dB (for deep fades bf 30 to 40 dB, broadband losses were typically 10 to 20 dB.). Most multipath fading occurs at night. Frequency diversity helps reduce deep fading but has no effect on shallow fades. The space correlation of fading signals is large in the horizontal plane. However, it is small in the vertical plane under severe fading conditions. Therefore, vertically spaced (transmit or receive) space diversity antennas can be used to reduce fading. Space diversity is as good as or better than frequency diversity for multipath or reflective fading [47] and sometimes better for long, slow fades due to defocusing and ducting [49]. Atmospheric multipath fading is relatively independent of path clearance. The fading becomes more frequent, faster, and deeper as distance or frequency is increased [18]. As frequency or distance is increased, the

16. M i c r o w a v e

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60

Figure 24. Typical multipath fading,

statistics of the received signal approach the distribution of Rayleigh. After the multipath fading has reached the Rayleigh distribution, further increase in either distance or frequency increases the number of fades to a given depth but decreases the duration so that the product is essentially constant [7]. If a received signal envelope voltage, V, at an instant of time has a Rayleigh distribution (as measured over a long period of time), the probability, p, that it has a value less than or equal to L is given by

p(u
_L 2

,

where L 2 is the specific faded power level relative to the unfaded power. The instantaneous fade depth in decibels is - 2 0 l o g ( u ) = -10log(u2), where u 2 is the instantaneous received signal power relative to the unfaded power. The specific fade depth in decibels is - 2 0 l o g ( L ) - 1 0 log(L:). For L smaller than 0.1 (fade greater than 20 dB)

p ( u _< L) = L 2 =

1 0 - ( f a d e d e p t h in d e c i b e l s ) / lO .

490

George Kizer

To account for the fact that fading is not as severe as Rayleigh for short, low-frequency paths, Barnett [3] modified the probability to p = rL2/I,

where r is a correction factor to account for path variables and I is an improvement factor to account for various forms of diversity reception. As implied by Barnett's Figure 8 [3], r should be limited to the range 0.01 to 1.0 (1.0 indicating full Rayleigh fading). Lin's results [34] indicate fading is worse than Rayleigh only for paths with a relatively constant interfering reflection (such as over water paths). Fading is generally much better than Rayleigh for relatively short paths. This is illustrated in Figures 25 and 26. Atmospheric multipath fading is the primary limitation on the performance of fixed point-to-point microwave systems. As shown in Figure 23, multipath fading occurs due to the summation at the receive antenna of several signals which are time-delayed portions of the original transmitted signal. It is readily demonstrated that if a main and small delayed radio signal are combined, the result will display a sinusoidal amplitude versus frequency response. If the secondary signals are only delayed slightly in time relative to the main received signal, the received signal will appear to be enhanced or depressed in overall power level as the peak or the null of

10"1

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Figure 25. Theoretical cumulative amplitude distributions of fading signals.

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the sinusoidal passes through the restricted bandwidth of the radio receiver. This type of fading is termed "flat" fading and is estimated using a thermal fade margin. This type of fading affects both analog and digital radios. The thermal fade margin of a radio is readily determined by placing an adjustable attenuator between the radio transmitter and the radio receiver and increasing the attention until the specified level of performance is achieved. The attenuation is the thermal fade margin. If the time-delayed signals have a relatively long time delay, the sinusoidal amplitude versus frequency pattern will compress in frequency and several cycles of the ripple pattern will pass within the transmission bandwidth of the radio receiver. This will cause a significant distortion in the phase and amplitude of the received signal but will cause little loss in received signal power. In reality, several delayed signals appear at the radio receive antenna so the received amplitude versus frequency response of the transmission path, due to the summation of the multiple signals, is more complicated than a simple sinusoid. This type of distortion has little effect on analog radios but can be devastating to digital radios [36] due to the considerable distortion of the received signals' amplitude and phase. This phenomenon [43, 44] is termed "dispersive" fading and is estimated

492

George Kizer

using a dispersive fade margin. If the largest received signal is received ahead of smaller delayed signals, the resulting fade is called "minimum phase." Sometimes the main signal will become so depressed that the delayed signal may be larger in amplitude than the main signal. In this situation, the fading is termed "nonminimum phase." For shallow fading (less than 20 dB), minimum phase fading is predominate. For deep fading, both types of fading occur approximately equally. The dispersive fade margin is a complicated number which is calculated or measured based of an average of minimum and nonminimum fades to a specified BER with a pseudo-three-ray fade model of specified delays [5]. This fade margin is calculated using a measured "equipment signature." This measurement must be made in a laboratory. Since this measurement is so complicated, the calculated dispersive fade margin is typically supplied by the equipment manufacturer. Interestingly, both flat fading and dispersive fading are caused by the same mechanisms. Therefore, their statistics are similar. Although the previously mentioned faded received signal analysis was originally developed to describe flat fading, the same model has been shown to be applicable to dispersive fading as well.

4. Path Availability Calculations If a microwave system is properly designed to avoid obstruction and reflective fading, the major limitation to radio system performance will be atmospheric absorption, rain attenuation, and multipath fading. Availability objectives for analog systems are given in CCIR Recommendation 395 (permissible noise in real analog FM telephony circuits) [10]. See Kizer [24] for more detail. Objectives for digital systems are CCIR Recommendations 557, 634, and 695 with CCIR Report 930 [10]. The North American AT & T two-way path unavailability (due to rain or multipath) objective [24] is 0.01% for both long-haul (4000-mile circuit, half of the hops fading) and short-haul (250-mile circuit, all of the hops fading) reference circuits. These result in one-way path outage objectives of 0.800 s/mile (0.497 s / k m ) for long-haul or 6.40 s/mile (3.98 s / k m ) for short-haul circuits. The following equations represent the state of the art in estimating path availability. The total path outage time for a line-of-sight microwave radio is Ttota I -- Ttherma I -1- Tdigital + Train,

where Ttota 1 is the total one-way path outage in seconds assuming adequate path clearance and Ttherma 1 is the thermal multipath outage. This is the

493

16. Microwave Radio Communication

outage caused by multipath fading below the radio thermal noise threshold (typically for a 10 -6 bit error ratio for digital radios or a top-slot 30-dB unweighted S / N ratio for analog radios). It also includes the effects of cochannel interference from other microwave systems and adjacent channel interference from other radio channels on the same microwave path. Tdigital is the dispersive multipath outage (digital radios only). This is the outage caused by in-band distortion of the digital signal. Train is the rain outage. To calculate two-way outage, each factor except rain is calculated in both directions and added. Since rain outage occurs simultaneously in both directions of transmission, the rain outage is the same for a one-way or two-way calculation for equal fade margins. If the fade margins are different in the two directions of transmission, the rain outage is calculated for the smaller fade margin. To calculate availability, A = 100 × ( 1 -

Ttotal/Tref)

,

where A is the availability in percent and Tref is 3.15 × 107 s for yearly availability and 2.59 × 106 s for worst month availability. To calculate the outage time [43, 47] due to multipath fading,

Ttherma I -- (RT o × 10- FFM/,0)//thermal rdigital = ( R T o X lO- DFM / lO ) /Idigital,

where R is the fade occurrence factor; TO is the number of seconds in the heavy fading season, (8 × 106× (t/50) for yearly availability [47] and 2.59 × 106 for worst month availability); t is the average annual temperature in degrees Farenheit (used to adjust the length of the fading season from region to region) from Figure 27 or 28; FFM is the flat fade margin in decibels (composite fade margin not including the dispersive fade margin); DFM is the dispersive fade margin in decibels; /thermal is the improvement factor for thermal outages from frequency and space diversity; and /digital is the improvement factor for dispersive outages from frequency and space diversity. The fade occurrence factor is calculated using the basic outage equation [47] for atmospheric multipath fading, R = c(50/w)lS(f/4)D

3 × 10 .5 ,

where 0.01 < R < 1.0, f is the frequency in gigahertz, D is the path length in miles (0.621 the path length in kilometers), and w is the terrain roughness factor in feet (20 < w < 140) (3.28 the terrain roughness factor in meters). The terrain roughness factor is the square root of the average

494

George Kizer

~ 4 o

40

Z'~

Figure 27. Mean temperatures for the United States (°F).

180 WEST 135 6o-

90

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0

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~id~,~/J~lll t I ! ,[I.~ 45 !1{ I~ II I 40 40 45 4 0 .

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70 - J U

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I ~

/

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45 z

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,, =~ _ ~Iv'75--~

,

.../v rLLzc..j/ ~ ~t,~. ,,v

., '

^~.oU....o #~-~ Av.~ --"

~

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/~71 JTg

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)

\._ ..-") 7o/(

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/

'\

-u,

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_0 @

~,J . "-" /

~

if',..

~o

~

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7'O~',t,o

30 15

v.~.o~'~) ~ \/-

fk'"

f ~ 75 7~/ / ~

60-

-. _

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t',G..t

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•"'-" .I J I 70\ \, ~f'~j, 1 ,_...--~ 3'~"" 1 - 7s

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.v

\~,~ ,. ~ / , . , ~ ~ , , , ~ - . - ~ _ ~ ~_.~_~ ~ ~" // I

.<"

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~

\~ ~

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\-

,-_"Z""~ %-= 30 N

f'

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_1 90

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\

~ 65

/

\ I ~/r ~,~ ~,1 I,I/

45

0

~u

75

75 ~u .

I I~/i)1),4 45

90

LONGITUDE Figure 28. Worldwide mean temperatures (°F).

60 ~ / "

v t/,,ol .tss

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45 ~ 180

16. Microwave Radio Communication

495

square of the deviation from the mean of terrain heights (above an arbitrary reference) taken one mile apart along the radio path. c = climate and humidity factor = 0.5 for good (high altitude or dry climate) paths = 1.0 for average conditions = 2.0 for bad (coastal and over water) paths. A good path would generally occur in an area characterized by dry climate, hilly or mountainous country with rough terrain, rare occurrences of calm weather or atmospheric stratification, or launch angles exceeding 0.5 °. Mountainous areas such as the Alps, Andes, Atlas, Himalayas and Rockies have good propagation. Average paths would be hilly or flat country (not marsh or salt flats) with occasional calm weather or atmospheric stratification; coastal areas with moderate to low temperatures (not the Gulf Coast or over water); or hot, tropical regions with steep launch angles. Bad paths would have low launch angles over flat ground or in warm coastal regions or tropical regions, humid areas in which ground mist forms, wet or swampy terrain (e.g., irrigated fields), conditions favorable for atmospheric stratification (e.g., broad protected river valleys and moors), or over water (e.g., inland lakes and seas). In the United States good paths are in eastern Washington, eastern Oregon, northeastern Nevada, Idaho, Utah, northeastern Arizona, western Montana, western Wyoming, western Colorado, western New Mexico, and far west Texas. Bad paths are in southern California, southwestern Arizona, southeastern Texas, southeastern Arkansas, Louisiana, Mississippi, Alabama, Georgia, Florida, North and South Carolina, southeastern Virginia, eastern Wisconsin, northeastern Illinois, Michigan, northern Indiana, northern Ohio, far west Pennsylvania, and far west New York. The flat fade margin (FFM) is derived from the power addition of up to three individually contributing fade margins [43] per the following equation, FFM

=

-]01Oglo[10 -TFM/10 + 10 -EIFM/10 -Jr- l0 -AIFM/10]

where TFM is the thermal fade margin in decibels, EIFM is the external interference fade margin for all exposures in decibels ( E I F M ~ 101ogl0N), EIFM~ is the external interference fade margin for one exposure in decibels, N is the number of interference exposures, and AIFM is the adjacent channel interference fade margin in decibels. The

496

George Kizer

factors DFM, AIFM, and EIFM 1 are based on equipment specifications. The thermal fade margin (TFM) is determined as follows: TFM=G-L-Tn

(dB),

where G is the antenna gains (dB) plus the radio transmit power (dBm); L is the sum of the free space loss, waveguide losses, circulator losses, radome losses, attenuators, field margin, and atmospheric absorption loss (dB); and Tn is the radio thermal noise threshold (dBm, typically specified at a 10 -6 bit error rate for digital radios or a top-slot 30-dB unweighted S/N ratio for analog radios). To calculate free space loss in decibels, FSL = 96.6 + 20 log 10 f (GHz) + 20 log 10 D (miles) = 92.4 + 20 log

10 f

(GHz) + 20 log10 D (km),

where f is the operating frequency and D is the path length. Atmospheric absorption loss [12] is calculated as follows, L 0 = {(7.19/1000) + ( 6 . 0 9 / [ f 2 + 0.227]) +(4.81/[(f-57.0)2+ Zw

--

1.5])}(/VLOOO)

{0.050 + 0.0021p + ( 3 . 6 / [ ( f - 22.2) 2 + 8 . 5 ] ) + + ( 8 . 9 / [ ( f - 325.4)

(10.6/[(f-

+ 26.3])}( f

183.3)2+ 9.01)

loooo)

TO = 1.00 - 0 . 0 1 ( - 1 5 + [(~)(t - 32)]) T w = 1.00 - 0.006( - 15 + [(5)(t - 32)1 ) A t o t a I --

1.61([ToLo] +

[TwLw])D,

where f is the frequency in gigahertz ( f < 57 GHz), D is the path length in miles (0.621 the path length in kilometers), p is the absolute humidity of the region in g / m 3 (median value from Figure 29 or 30), t is the temperature of the region in degrees Farenheit (5 < t < 105) (median value from Figure 27 or 28) (32 + (9) [temperature of the region in degrees centigrade ( - 2 0 < T < 40)]), TO is the oxygen attenuation temperature correction factor, T w is the water vapor attenuation temperature correction factor, L 0 is the oxygen attenuation, L w is the water vapor attenuation, and Z tota I is the total atmospheric absorption in decibels for

497

16. Microwave Radio Communication

6

7

7

14 15 16

/

17 18 19 /

,,

)l p /

Figure 29. Mean absolute humidity for the United States (g/m3),

180

150

120

90

60

30

0

30

60

90

120

150

180 80 - 75

-70

o z

-45

-15 -

~

0

-15 -

~ 45

30

-45

70 180

~ o

"I" 60--

I

I

I

150

120

90 WEST

A - -

60

/

30

!

I

0 30 LONGITUDE

~

I

60

I

90 EAST

I

120

70

i x~

150

Figure 30. Worldwide greatest monthly mean absolute humidity (g/m3).

180

498

George Kizer

the path. The expected improvement due to space diversity [27, 47] is calculated using the following equations, IsD-thermal = 7 X IsD-digital "-

IO-5S2(f/D)

0.09(f/D) ×

X 10 FFM/10

10 DFM/IO,

where IsD-thermal is the space diversity improvement factor for thermal outages (1 _< IsD-thermal ~ 200), IsD-digital is the space diversity improvement factor for dispersive outages (1 _< IsD-digital -~< 200), S is the vertical separation of receiving antennas in feet, center to center (3.28 the vertical separation of receiving antennas in meters), f is the frequency in gigahertz, D is the path length in miles (0.621 the path length in kilometers), FFM is the flat fade margin in decibels, and DFM is the dispersive fade margin in decibels. When the two antennas have different gains, the thermal fade margin is calculated by using the average gain of the two antennas. The expected improvement due to frequency diversity [28, 29, 48] is calculated from the following equations, /FD-thermal = IFD-digital =

IO0(f/DG)

× 10 FFM/10

(468/f 2D) X

10 DFM/15

/FD-digital -- 9 3 2 4 ( f / D G ) X l0 DFM/15

for 1"1 systems for

M'N

multiline systems, N > 1,

where IFD-thermal is the frequency diversity improvement factor for thermal outages (1 < IFD-thermal ~ 200); IFD-digital is the frequency diversity improvement factor for dispersive outages (1 < IFD-digital -< 200); f is the frequency of operation in gigahertz; D is the path length in miles (0.621 the path length in kilometers); FFM is the fiat fade margin in decibels; DFM is the dispersive fade margin in decibels; G is f3/(fchfeq); feb is the frequency in gigahertz between the two channels for a 1:1 system and the frequency in gigahertz between two adjacent channels for an M:N system; feq is 1 for a 1"1 system, 1/sqr(N) for a I ' N system, 4 . 2 / N °8 for a 2:N system, l l . 2 / N for a 3:N system, and 24.2/N 1"1 for a 4:N system; and sqr(x) is the square root of x. The improvement in a four-receiver system [48] with space diversity and frequency diversity (i.e., quad diversity) is /thermal -" IsD-thermal X IFD-thermal /digital = /SD-digital X /FD-digital"

499

16. Microwave Radio Communication

One word of caution. As noted earlier, paths over water have a 1/L, rather than a typical 1 / L 2, fading characteristic. For these paths, space diversity should be considered to have normalized the path to a 1 / L 2 fading characteristic. Therefore, only the frequency diversity improvement factor should be applied to this type of quad diversity path. The improvement in a two-receiver system with space diversity and frequency diversity (i.e., hybrid space diversity using a different frequency on each antenna) is

/thermal-- maximum (/SD_thermal, /FD-thermal) /digital -" maximum (IsD.digital, IFD-digital)" For angle diversity antennas, research results are divided. For some paths, angle diversity outperforms space diversity [6]; for others, angle diversity is little better than no diversity [1]. For some paths, angle diversity will be better than space diversity part of the time and worse other times [21]. When the path thermal noise fade margin is not substantially greater than the dispersive fade margin, vertical space diversity improvement is at least an order of magnitude better than that of angle diversity [32]. Lacking more definitive data, the following provisional improvement factors are suggested:

lAD-thermal --" ( IsD-thermal / 10), lAD-digital--- IsD-digital,

] ~ 1AD_thermaI ~ 20 1 ~ lAD_digital ~ 200.

The thermal improvement /SD-thermal is calculated using a 30-ft equivalent space diversity spacing. Using the Crane path attenuation model [15, 16], rain attenuation is calculated from the following equations, A

R

--

aRb[(e ubD - 1)/ub]

A R = aRb[((e "ha-

for 0 _< D _< d km

1)/ub}-

{(B%Cba)/cb} + ((B%cbD)/cb}] for d < D _< 22.5 km,

where u is ln[BeCd]/d, B is 2.3 R -°17, c is 0 . 0 2 6 - 0.03In(R), d is 3 . 8 - 0.6In(R), A R is the path attenuation due to rain in decibels and equals TFM - WRL, TFM is the thermal fade margin in decibels, WRL is the wet radome loss in decibels, R is the point rain rate in r a m / h , D is the path distance in kilometers (Dmi~¢~ × 1.609), Dmiles is the path distance in miles, and In is the natural (base e) logarithm. For paths longer than 22.5 km, the attenuation A R is calculated for a 22.5-km path and the resulting rain outage time is multiplied by a factor of (D/22.5).

500

George Kizer TABLE 7 Point Rain Rate Distribution Values RAIN CLIMATE REGION

PERCENT OF YEAR RAIN RATE EXCEEDED

1.0 0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 0.0005 0.0002 0.0001

B

1.7 2.5 4.0 5.5 8.0 12 15 19 24 28 32 37 41

1.8 2.7 4.8 6.8 9.5 14 19 26 40 54 68 87 101

C

D1

1.9 2.8 4.8 7.2 11 18 28 41 62 80 98 122 140

2.2 4.0 7.5 11 16 27 37 50 72 90 108 132 150

D(2 )

3.0 5.2 9.5 15 22 35 49 64 86 102 118 139 155

D3

E

F

G

H

4.0 7.0 14 22 31 48 63 81 107 127 147 174 194

4.0 8.5 21 35 52 77 98 117 144 164 184 211 231

0.8 1.2 3.2 5.5 8.0 14 23 34 51 66 81 101 116

3.7 7.0 14 22 33 51 67 85 109 129 149 176 196

6.4 13 31 51 77 115 147 178 220 251 282 323 354

EXPECTED STANDARD DEVIATION OF MEASUREMENTS ABOUT MODEL %

Table value shows rate in mmlhour measured with 1-minute rain gauge integration time.

The coefficients a and b are functions of frequency and polarization [13] and are listed in Table 6. R values are determined from Table 7 based on the rain climate region determined from Figure 31 or 32. To calculate rain outage, an iterative computer program is used to vary the rain rate R until the calculated path attenuation is equal to the rain attenuation margin, A R = T F M - WRL. This rain rate is then applied to a distribution of rain rate vs time for a particular geographic

C

B

Figure 31. Rain rate climate regions within the United States.

501

16. Microwave Radio Communication 180

150

75

120

90

60

A

60

-'"

-~ 0

0

30

"

~ ~~~-~B

45

90

120

150

~~__~ . ~ " ~ 150

75

0

~

.

,~ . ~

--

~.~ .~~~~

45

~ 0

"'~-""

180

180

DR ~ 7 ~ ~

C

60

G

I-."1"45 0 6O co

30 ~

120

90

60

30

WEST

' --"" ~

~'-A

[[I]]B

[~C

0

ITJJD

-451:~1'-

,=,,

A 30

60

90

120

LONGITUDE [TA

,~

"

[]E

I~F

[]G

O 60 m 150

180

EAST

IH

Figure 32. Worldwide rain rate climate regions.

area to find the rain outage time. Annual rain outage Train in s / y e a r may be converted to worst-month outage Train__mont h in s / m o n t h as follows [14]:

Train__month = 1.22(Train) 0"87.

5. Conclusion Microwave radio system performance is highly dependent on the choice of the appropriate transmission equipment and careful path design. No single chapter can treat the topic exhaustively. This chapter aquaints the reader with the most significant system design topics and overviews the most important calculations necessary to estimate line-of-sight microwave radio performance.

Acknowledgments The author acknowledges and appreciates the assistance of Bill Knight, Chief Transmission Engineer for Alcatel Network Systems, with the guidelines outlined in this chapter.

502

George Kizer

References [1] E. W. Allen, Angle diversity vs. space diversity at 6 GHz: Results of a 3.5 year test, Int. Telecommun. Symp., Taipei, Feb. 1992. [2] G. D. Alley, W. C. Peng, W. A. Robinson, and E. H. Lin, The effect on error performance of angle diversity in a high capacity digital microwave radio system, IEEE/IEICE Global Telecommun. Conf. Rec., pp. 31.5.1-31.5.4, Nov. 1987. [3] W. T. Barnett, Multipath propagation at 4, 6, and 11 GHz, Bell Syst. Tech. J., Vol. 51, pp. 321-361, Feb. 1972. [4] Bellcore Technical Advisory TA-TSY-000009, "Asychronous Digital Multiplexes, Requirements and Objectives," Issue 1, pp. 4-6-4-9, Dec. 1984. [5] Bellcore Technical Reference TR-TSY-000752, "Microwave Digital Radio System Criteria," Issue 1, pp. 6-16, Oct. 1989. [6] R. W. Bickmore and R. C. Hansen, Antenna power densities in the Fresnel region, Proc. IRE, Vol. 47, pp. 2119-2120, Dec. 1959. [7] K. Bullington, Radio propagation fundamentals, Bell Syst. Tech. J., Vol. 36, pp. 593-626, May 1957. [8] H. E. Bussey, Microwave attenuation statistics estimated from rainfall and water vapor statistics, Proc. IRE, Vol. 38, pp. 781-785, July 1950. [9] CCIR Recommendations, Doc. XVIIth Plenary Assem. CCIR, Vol. 9. Geneva: Int. Radio Consultative Comm., 1990. [10] CCIR Rep. 338-6, "Propagation Data and Prediction Methods Required for Terrestrial Line-of-Sight Systems, Annex I, Table II," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 355-420, 1990. [11] CCIR Rep. 563-4, "Radiometerological Data," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 105-148, 1990. [12] CCIR Rep. 719-3, "Attenuation by Atmospheric Gases," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 189-204, 1990. [13] CCIR Rep. 721-3, "Attenuation by Hydrometeors, in Particular Precipitation, and Other Atmospheric Particles," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 226-245, 1990. [14] CCIR Rep. 723-3, "Worst Month Statistics," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 262-274, 1990. [15] R. K. Crane, Attenuation due to rainmA mini-review, IEEE Trans. Antennas Propag., Vol. AP-23, pp. 750-752, Sept. 1975. [16] R. K. Crane, Prediction of attenuation by rain, IEEE Trans. Commun., Vol. COM-28, pp. 1717-1733, Sept. 1980. [17] O. E. DeLange, Propagation studies at microwave frequencies by means of very short pulses, Bell Syst. Tech. J., Vol. 31, pp. 91-103, Jan. 1952. [18] H. T. Friis, Microwave repeater research, Bell. Syst. Tech. J., Vol. 27, pp. 183-246, Apr. 1948. [19] R. Gunn and G. D. Kinzer, The terminal velocity of fall for water droplets in stagnant air, J. Meteorol., Vol. 5, pp. 243-248, Aug. 1949. [20] D. C. Hogg, A. J. Giger, A. C. Longton, and E. E. Muller, The influence of rain on design of ll-GHz terrestrial radio relay, Bell. Syst. Tech. J., Vol. 56, pp. 1575-1580, Nov. 1977. [21] R. W. Hubbard, Angle diversity reception for LOS digital microwave radio, IEEE Mil. Commun. Conf. Proc., pp. 19.6.1-19.6.7, Oct. 1985. [22] W. C. Jakes, Jr., A theoretical study of an antennamReflector problem, Proc. IRE, Vol. 41, pp. 272-274, Feb. 1953.

16. Microwave Radio Communication

503

[23] R. L. Kaylor, A statistical study of selective fading of super-high frequency radio signals, Bell. Syst. Tech. J., Vol. 32, pp. 1187-1202, Sept. 1953. [24] G. M. Kizer, Microwave Communication, pp. 315-440. Ames: Iowa State Univ. Press, 1990. [25] G. M. Kizer, Multiple hop radio system design to meet end-to-end performance objectives, Bellcore Nat. Radio Wireless Eng. Conf., D5.1-D5.30, May 1991. [26] J. O. Laws and D. A. Parsons, The relation of raindrop-size to intensity, Am. Geophys. Union Trans. 1943, Part II (Apr. 1943), pp. 452-460, Jan. 1944. [27] T. C. Lee and S. H. Lin, A model of space diversity improvement for digital radio, Int. Union Radio Sci. (URSI) Open Symp. Wave Propag.: Remote Sensing Commun., Durham, NH, Symp. Vol. pp. 7.3.1-7.3.4, July/Aug. 1986. [28] T. C. Lee and S. H. Lin, A model of frequency diversity improvement for digital radio, Int. Symp. Antennas Propag., Kyoto, pp. 7.3.1-7.3.4, 1985. [29] T. C. Lee and S. H. Lin, More on frequency diversity for digital radio, IEEE Globecom Conf. Rec., pp. 36.7.1-36.7.4, 1985. [30] S. H. Lin, A method for calculating rain attenuation distributions on microwave paths, Bell Syst. Tech. J., Vol. 54, pp. 1051-1086, July/Aug. 1975. [31] S. H. Lin, Dependence of rain-rate distribution on rain-gauge integration time, Bell Syst. Tech. J., Vol. 55, pp. 135-141, Jan. 1976. [32] S. H. Lin, Measured relative performance of antenna pattern diversity, antenna angle diversity, and vertical space diversity in Mississippi, IEEE Globecom Conf. Proc., pp. 44.1.1-44.1.5, 1988. [33] S. H. Lin, Nationwide long-term rain statistics and empirical calculation of ll-GHz microwave rain attenuation, Bell Syst. Tech. J., Vol. 56, pp. 1581-1604, Nov. 1977. [34] S. H. Lin, Statistical behavior of a fading signal, Bell Syst. Tech. J., Vol. 50, pp. 3211-3269, Dec. 1971. [35] S. H. Lin, H. J. Bergmann, and M. V. Pursley, Rain attenuation distributions on Earth-satellite paths--Summary of 10-year experiments and studies, Bell Syst. Tech. J., Vol. 59, pp. 183-228, Feb. 1980. [36] C. W. Lundgren and W. D. Rummier, Digital radio outage due to selective fadingq Observation vs prediction from laboratory simulation, Bell Syst. Tech. J., Vol. 58, pp. 1073-1100, May/June 1979. [37] R. G. Medhurst, Passive microwave mirrors, Electron. Radio Eng., pp. 443-449, Dec. 1959. [38] R. G. Medhurst, Rainfall attenuation of centimeter waves: Comparison of theory and measurement, IEEE Trans. Antennas Propag., Vol. AP-13, pp. 550-564, July 1965. [39] W. L. Nowland, R. L. Olsen, and I. P. Shkarofsky, Theoretical relationship between rain depolarization and attenuation, Electron. Lett., Vol. 13, pp. 676-678, Oct. 1977. [40] R. L. Olsen, D. V. Rogers and D. B. Hodge, The aR b relation in the calculation of rain attenuation, IEEE Trans. Antennas Propag., Vol. AP-26, pp. 318-329, Mar. 1978. [41] T. L. Osborne, Application of rain attenuation data to ll-GHz radio path engineering, Bell Syst. Tech. J., Vol. 56, pp. 1605-1627, Nov. 1977. [42] J. R. Pace, Asymptotic formulas for coupling between two antennas in the Fresnel region, IEEE Trans. Antennas Propag., Vol. AP-17, pp. 285-291, May 1969. [43] W. D. Rummler, A comparison of calculated and observed performance of digital radio in the presence of interference, IEEE Trans. Commun., Vol. COM-30, pp. 1693-1700, July 1982. [44] W. D. Rummier, More on the multipath fading channel model, IEEE Trans. Commun., Vol. COM-29, pp. 346-352, Mar. 1981.

504

George Kizer

[45] S. Silver, Microwave Antenna Theory and Design, pp. 169-199, 413-542, 574-592. New York: McGraw-Hill, 1949. [46] L. C. TiUotson, Use of frequencies above 10 GHz for common carrier applications, Bell Syst. Tech. J., Vol. 48, pp. 1563-1576, July-August 1969. [47] A. Vigants, Space-diversity engineering, Bell Syst. Tech. J., Vol. 54, pp. 103-142, Jan. 1975. [48] A. Vigants and M. V. Pursley, Transmission unavailability of frequency diversity protected microwave FM radio systems caused by multipath fading, Bell. Syst. Tech. J., Vol. 58, pp. 1779-1796, Oct. 1979. [49] R. F. White, Space diversity on line-of-sight microwave systems, IEEE Trans. Commun. Technol., Vol. 16, pp. 119-133, Feb. 1968. [50] R. F. White, "Engineering Considerations for Microwave Communications Systems," pp. 51-52, GTE Lenkurt, San Carlos, CA, 1975. [51] R. F. H. Yang, Passive repeater using double flat reflectors, IRE Natl. Cony. Rec., pp. 36-41, Mar. 1957.

CHAPTER

17 M icrowave Instrumentation and Measurements Aksel Kiiss

I. Scattering P a r a m e t e r s S-Parameter Measurements S-parameters are complex quantities containing both amplitude and phase information. There are two measurement techniques that are in general use in the industry. One measures both the amplitude and phase of the S-parameters, and the other measures only the amplitude (normally presented in logarithmic form). The first instrument is called a vector network analyzer, and the second, a scalar network analyzer. Vector analyzers are mostly used in design and development work, whereas the scalar analyzers are in wide use as production test equipment. In the United States vector analyzers are manufactured by HP and Wiltron, and scalar analyzers, by HP, Wiltron, and Wavetek among others. Before, we presented vector analysis and its associated uncertainties. Below we will discuss scalar analysis and its associated uncertainties.

Handbook of Microwave Technology, Volume 2

505

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

506

In high-frequency measurements, we know we can characterize a device under test (DUT) by measuring the input and output signals of the device after we have applied the proper stimulus signals. We take this information (the incident waves being a waves and the output waves being b waves) and define a set of equations using the device's S-parameters and the a and b waves. For a two-port device, we define two linear equations.

Aksel Kiiss

SCATTERING

PARAMETER

DEFINITION Incident

S=l

Transmitted

fr so

Reflected

C~

Port 1

Port 2

Transmitted

I I Reflected

II

St2 bl =

S.

b= = S=l

(,

a2

Incident

a 1 +S12

a=

a 1 + $22

a2

To determine the four S-parameters we first terminate port 2 with SCATTERING PARAMETER a Z 0 load, eliminating the a 2 signal. The resulting equations yield MEASUREMENT Sll and S21. S~ is the ratio of S =1 Transmitted b2 Incident biJa I when a 2 is zero, and S2a is 81 ! the ratio of b2/a I. What is the physical meaning of Sll? $1~ is bl ~eflected b~= S. al + ~ 2 a2 a~ equivalent to F since its magnitude b e - S ~ l a t + S , ~ a2 and phase response are identical to those of F (notice that F is also Reflected b1 Sll " I a= = 0 defined a s Vinc/Vrefl or bl/al). Incident a1 That means that the magnitude of Transmitted b2 Sfj is equal to p. In a like manner I a= : o $21 ---- m Incident al , the forward transmission coefficient is equivalent to $2~. The S-parameter numbering convention is, the first number represents the port at which the energy is emerging from the device, and the second number is the port at which energy is entering the device. So S21 means the ratio of the energy emerging at port 2 to the energy incident at port I (gain or loss is indicated by values greater or less than unity).

]j

507

17. Microwave Instrumentation and Measurements

By placing the source at port 2 and terminating the input with a Z 0 load, the a~ term now becomes zero so that S22 and Si2 can be determined. Notice that the S-parameters are referenced to the Z 0 impedance of the network analyzer and in most cases are 50 ,Q. However, a Z 0 impedance of 75 D, is possible with 75 ~ test sets. AN 95-1 and AN 154 give additional details on designing with S-parameters and converting them to other useful quantities.

One of the nice things about S-parameters is that they are intuitive. That is not true for other parameters such as Y-parameters at high frequencies. $2~ is simply the forward gain or loss of the device, expressed in linear form. With this 20-dB attenuator, we see that our familiar measurement loss of the attenuator is transformed to an S-parameter voltage ratio of 0. I. Since these are complex parameters, there is a phase angle associated with each S-parameter. Likewise the more familiar measurement of SWR on the device translates over to an S~ or input voltage reflection coefficient of

REVERSE MEASUREMENT

°'

''

b=

~I

:>

82 b~ Transmitted

St=

Incident

b= Szz =~--= I a , = O

bl St= =~'-= I 8 , = O

ATTENUATOR S - P A R A M E T E R S S~ 20 dB ~ 0.1 ..,,:.~ 1.2 SWR I S~ O.09J~

O.05z~ ~~s22 1.1 SWR

¢ <

0-1"~'e $1=< ~ 20 dB

0.09. Basically we have been making S-parameter measurements all along. We have just used different names for the same quantities. This attenuator is a bilateral device' i.e., it has approximately the same loss whether one measures it from port I or port 2 ($2~ -= S~2).

508

Aksel Kiiss

TRANSISTOR

S-PARAMETER

S:~ c = ~ 3 Z 54 °

A microwave transistor is a nonbilateral device; its reverse transmission coefficient is markedly different from its forward coefficient. Also, its S-parameter varies rapidly with frequency so the S2i of 3 (9.5 dB) applies only at I GHz. In addition, its reflection coefficients are very high, as is typical of small-signal high-frequency transistors.

o.~-16¢

~ o.4sz_63o

S~. 0.07 Z 18 o <~= $1= 2N5103 @ 1 GHz

Scalar Analysis A typical test setup for a scalar network analyzer consists of a signal source, normally a sweeper; a directional element that separates the transmitted and reflected signals; a detector; and an oscilloscope or power meter. The oscilloscope in today's equipment contains a logarithmic video amplifier that converts the detected signals into a logarithmic output to be displayed on the oscilloscope. It is also called a scalar analyzer, hence the term scalar analysis. A block diagram of the setup is shown in Figure 1. Possible sources of error are (1) Imperfect source and load impedances, (2) Directivity and the test port V S W R of the directional coupler or the directional bridge,

n SWEEP GENERATOR (Zo SOURCE)

SWR BRIDGE

v

AMPLIFIER UNDER TEST

I~1

DETECTOR SCALAR ANALYZER

I LOGARITHMIC I LEVEL

J

"--

SCOPE (DIRECT-

I c

Figure I. Typical arrangement of a basic swept reflectometer system.

,

509

17. Microwave Instrumentation and Measurements PERFECT TERMINATION

INPUT

.<~i~,;

Eo

~Ed

ii II

OUTPUT .0178 (35 dB)

Zo

Ed

Figure 2. Directivity of a directional device, Ed is the output with no reflection from the termination

(3) Harmonics and spurious outputs of the signal generator, (4) Inaccuracies of the power meter or the logarithmic detector-scalar analyzer, and (5) Imperfections of various adaptors used in the test setup.

Reflection Measurement ($11 and $22 ) Reflection measurements involve Sll and $22. The heart of a reflection measurement setup is a reflectometer that separates the incident signal into transmitted and reflected components. There are two possible sources of error caused by the reflectometer; directivity and the test port VSWR. Reflectometers consist of directional couplers or directional bridges. The couplers use either 10- or 20-dB decoupling and the directional bridge uses 12-dB decoupling. A functional schematic of a directional coupler is shown in Figure 2. If the test port is terminated in a resistive 50-~ load, there should be no output at the reflected port output. Because of imperfections in the coupler or in the bridge there is always an output signal. The ratio of that signal to the totally reflected signal is defined the directivity of the reflectometer and is normally expressed in decibels. The effect of the directivity error can be calculated by assuming that the signal caused by the directivity vector can add or subtract in any phase from the main reflected signal. Let us assume that we want to measure a 20-dB return loss with a reflectometer with 35 dB of directivity. Again if we assume that the desired reflected signal has an amplitude of 1, then the contribution from the directivity vector is 15 dB below the main signal. This can add to or subtract from the main vector, resulting in a possible maximum + 1.4 and - 1 . 7 dB of error to the actual 20-dB return loss. Figures 3, 4, and 5 depict the dependence of directivity errors on the input return loss of the device under test (DUT).

510

Aksel Kiiss ,,,%Z x 1.22 SWR .10 REFLECTION

INPUT

I

1

.0178

I

520 dB RETURN L O S S e s /

II II I

; I

Ed

tI

//

%

//E_, 1 ,/

35 dB

18.58 dB (1.27 SWR)

20 dB

"""~""""

JL Ex

I

21.70 dB (1.18 SWR)

RIPPLERESULTING FROM PHASE CHANGES AS FREQUENCY IS SWEPT

Figure 3. Uncertainty of a 1.22 SWR caused by directivity.

-6-

DIRECTIVITY

-4-

/

-2-

0

-

~

24-

6-

0

20

30

40

REFLECTION MEASUREMENT IN dB Figure 4. Reflection measurement uncertainty in decibels caused by a directivity of 35 dB.

Errors Caused by Test Port Mismatch The second possible error resulting from an imperfect directional device is caused by the VSWR of the test port because it causes multiple reflections between the device under test and that of the test port. Its contribution can be calculated similarly to that of the procedure used above. Figure 6 depicts the possible errors caused by test port mismatch and directivity. As one can see, the test port mismatch error decreases rapidly as the return loss increases.

511

17. Microwave Instrumentation and Measurements

DIRECTIVITY IN dB -4

I

T.P. M A T C H -

I

I

I

SWR: 2 . 0 0 -5

/

-2 1.50 --

m

-1

I >-

1.2o -

z <

I-rY b.J (D z

1.10 -0

1.10 --

1.20 -1 1.50 --

\\ \\\

2 2.00--

0

40 RETURN

Figure

LOSS

MEASURED

-dB

5. General uncertainty curves for a directional

/•

INPUT I

1

BEING

~

/

device.

1.22 SWR .112 REFLECTION TEST PORT MATCH 20 dB RETURN LOSS

~

f--

zx1"22 SWR

f

dOB

98 dB

Ex

BELOW Ex/

Figure

6. Uncertainty of a 1,22 SWR caused by a test port match,

Errors Due to Imperfect Signal Source Impedance The third possible error is caused by signals reflected from the unknown, traveling back to the signal generator, being partially reflected by the imperfect source impedance, and then adding to or subtracting from the main reflection.

512

AkselKiiss 20 dB

~ A

50 d B ---~"X (9 =.031 p/~ dopter

~

(~ =.I )

Detector~

Figure 7. Effecton the match. Effective = eA +e B =0.0316 +0.1 =0.1316 = 17.61 dB.

Uncertainties Caused by Adaptor VSWR The effect of mismatches caused by adaptors to the reflection measurement is to decrease the effective directivity of the reflectometer. The reflections caused by the adaptors can add to or subtract from the reflections caused by the test port VSWR. Figure 7 illustrates the effect of using a fairly good adapter (30-dB reflection loss and 1.065 SWR) on a detector (20-dB reflection loss and 1.222 SWR). The results of the calculation show that the effective match becomes 17.6 dB, 1.3 SWR, much worse than either device. One should always refer to the manufacturer-supplied operation manual for the actual test limits of the test setup and adaptors.

Uncertainties Caused by the Harmonic Content of the Test Signal The detectors used for the reflection and also for transmission measurements are wide-band devices and measure the total power of the test signal. To estimate the error bounds resulting from the test signal harmonic and spurious contents one has to know the actual harmonic content of the test signal, the directivity of the reflectometer as a function of frequency, and the match of the unknown at the fundamental and also of harmonic frequencies. Figure 8 shows the second harmonic error contribution limit.

Errors Caused by the Readout The output of most of today's test equipment is presented in logarithmic form (return loss in decibels). Typically the minimum sensitivity is in the order of - 5 0 dBm. Typical logarithmic accuracy is + 0.3 dB. Refer to the manufacturer manuals for detailed information.

Inaccuracies in Transmission Measurements (S2u and S, 2) Defining gain (loss) as the ratio of power delivered to the load to power available from the source we can measure power available by connecting our source to the detector and establishing our power reference. If the source and load impedance differ from Z 0 (50 fI), then the uncertainty in

17. Microwave Instrumentation and Measurements

513

+4bO t---

+2O EK

0-

L~ pr-/ -D

J -2

-4

I

-

-

OdB

lOdB

20dB

30dB

40dB

SECOND HARMONIC IN dB BELOW TEST SIGNAL Figure 8. Second harmonic error contribution limits. Error is the apparent change in the test signal in a broadband peak responding detector when the second harmonic is added. The magnitude of error is dependent upon the phase relationship of the harmonic in the test signal.

our reference can be expressed by peak to peak = 20 log

(1 + GeL)

+ detector frequency,

(1 --GEL) where

VSWRs - 1 e s --

VSWR s + 1

and

(VSWRL eL =

(VSWR

--

]-)

L nt- 1 ) '

where the subscript S signifies the source and the subscript L signifies the load. When the device under test is inserted between the source and the load we introduce two more u n c e r t a i n t i e s ~ t h a t between the source and the input of the D U T and that between the output of the D U T and the detector. input uncertainty (peak to peak) = 20 log

( 1 + es FDUTin) (1

output uncertainty (peak to peak) - 20 log

-

esFDuTin)

( 1 if- F D U D o u t e 2 )

(1

+ rDUDout¢2)

"

514

Aksel Kiiss

2. Transmission M e a s u r e m e n t s Transmission Measurement Magnitude Transmission measurements are a function of the incident signal and the transmitted signal. The linear transmission coefficient is the ratio of transmitted voltage to incident voltage (assuming the same Z 0 environment) and is normally given as T at some phase angle, T being the magnitude portion of this transmission coefficient.

Transmitted

Incident

DUT

Reflected

Vinc,en,, I DUT I V,..... ,ted)

transmission coefficient - t =

insertion loss (dB) = 20 log

gain(dg) = 20 log

Vtransmitted

Vinci.en~ vtransmitted / Vincident

vtransmitted / Vincident .

Before we make the transmission TRANSMISSION MEASUREMENT measurement of our test device, we will want to establish the magStep #1 - Establish "O dB" Reference nitude and phase reference data of Response Calibration our system. In this example, we "Thru" are using an S-parameter test set Network OH,S~,.IOgMAG5dB/ REF0dB which provides the signal separaAnalyzer C0r tion we need to make ratio measurements. We use a simple transTest Set I mission "through" response calibration to remove any signal path / ........ j loss differences in our reference Thru and test paths. (Otherwise, we are CH1CENTER200.000000MHz SPAN50.000000MHz assuming a perfect measurement system.) After we measure the through, we end up with a fiat line which is our 0-dB magnitude reference.

17. M i c r o w a v e

Instrumentation

515

and M e a s u r e m e n t s

5

MA8

log

CH ! e S 2 1

riB/

REF

0

dB

Cot

/

By connecting a filter as our DUT, we can then directly measure the insertion loss over the specified frequency range.

~-.

/

/

/

\

18

m "

.-

\

/"

O t-

.5

Z)

2

./

/

,,"

~-" '

j

/- ,,~ J-

o es---

;

_~.e2 ~ el,

I

J /" ~

/ ,,-" ~

./"

/

/ "

FPeq (GHz) 4.e.~.o__.se . . . .

,,/

'

aeto,e

.. .." /

.840 t o

28

.845

.840

t;o

'~---

--'--h~. I

18

-18

-3B

-58

-TS

-98

S21 Measurement Level (dB from Ref)

8510C accuracy

/.,,,,,f , ' "

8

./

0

,/

.f'

0C 1 30C

-..

Typical _ - - ~

0 -10 -20 -30 -40 -50 -60 70 -80 -90-100

Transmission Level (dBm) 8752 accuracy.

516

Aksel Kiiss

!111111 II!1111 IIII IIIII!111 !ii1111 i111111 IIII IIIIIIIII Iii1111 !111111 IIII I i~lll

,3.o

+2.0

o IIIIIII "1"111111 IIII

-1.0

IIIIII IIIIII III!11 IIII!i

IIIIIII IIIiill IIii 1111111 IIIIIII IIII 1111111 II!1111 IIII

-2.o -3.o

300 kHz

_

3MHz 30 MHz 300 MHz 6GHz

Dynamic accuracy: <6GHz <3 GH2

(-.

8

M ~ B M

IN;;;;; i'-'~------~

Munro

rn

"0 +I

.001 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100

Input Level (dBm)

8753C accuracy.

Transmission Measurement Phase

Phase measurements are accomplished by comparing the phase of the transmitted (or reflected)IF signal to that of the incident signal. Note that an incident or reference signal is required for phase measurements. Many phase detectors measure up to a + 180° difference in the phase of the two IF signals. This results in the traditional display with the + 1 8 0 ° transitions. Of course this is entirely equivalent to the Bode plot format, in which phase is displayed continually.

PHASE MEASUREMENTS Phase Requires a Reference IF (From DUT)

v IF (Incident)

~ ....

!

;

I •

~--I-'18°"

Frequency--~ o° 180 ° 360 °

~

517

17. Microwave Instrumentation and Measurements

Let us investigate this relationship among phase, device length, and PHASE CHANGE WiTH LENGTH frequency by looking at the phase 0° 720 ° 1440 ° 0 change as a function of length (of • , "--:-" • 360" CW . an airline in this case) at a single Signal Since C ,= )~f frequency. Notice that phase varies Airline ,, J as a function of physical length of Length L ~) I ) i the transmission line and as a funcoo I ,g tion of the wavelength of the CW 360° I frequency. This can be seen intu720 ° I itively from the diagram using a == ~o8oo ~ I CW signal and an airline. Although a. 1440 ° the signal amplitude remains un360" - f ~--(~ C )-" changed, the phase, using the input as a reference, varies linearly with physical length depending on how many wavelengths have been traversed to the point of interest. The formula can be rewritten in terms of frequency, f, by substituting c / f for wavelength (I). The propagation velocity for the speed of light in an airline is c = 3 x 108m/s.

Since our original transmission measurement problem involved phase change with frequency, let us now consider the case in which our phase measurements are made at the end of the airline. Because physical length is now a fixed quantity, the formula can be rewritten with frequency as the variable.

=

-(360°.f/c)./

PHASE CHANGE WiTH FREQUENCY

I

Swept

Source

..

."

.-

.. .

•

.,,,oe0,Len,hL /k~=

= -(360°.11c).

Phase

" '°e'ic'°r

-360 ° C

O_~

:_

I"x. I '_ F__'<.o-

'

.Af -L

f.

We see that if frequency from a swept source changes linearly, the phase will also change linearly. This looks somewhat like our measurement problem.

AkselKiiss

518

Let us look at the electrical length of a cable with a nonair dielectric. The dielectric slows the propagaCable of Physical Length. tion velocity from c to where Er is the relative dielectric - 360°e L constant and /~r is the relative 0"Up magnetic permeability. If we again Lengthe " C • f rewrite our equation for phase, we see that a length of the airline is equal to ~(/~lrE~) times the Airline of physical length of our cable and Length 0 that both would produce the same Physical phase shift with frequency. Thus Where is the Equivalent length of Aidine V/(/~E~)L is said to be the cable's equivalent electrical length of the airline. By referencing all electrical lengths to the airline the confusion between physical lengths and dielectrics is avoided.

c~~-~E~,

,L

360/c = 1.2 x 10-6 = - 360°/~ • length = Vp/frequency.

The simple transmission through response calibration we performed earlier for our magnitude measurements also establishes the CH1 821 phase 10°/REF 0° H1 S21 phase 10°/REF 90° phase reference for our system. Notice that the phase response of our "uncalibrated" through measurement is not even close to 0 ° response at all frequencies. This is due to the differences in path R M ENTER200000(300MH SPAN40.000(300MH; length of the reference and test Uncorrected Corrected signal paths. The through response calibration uses this phase measurement as the phase reference. After our response calibration, the displayed phase reference is our desired 0 ° phase line.

~c

ResponseCalibration

tt"

LIl,tt

t,l, [

I

17. Microwave Instrumentation and Measurements

A simple example of a device whose magnitude response does not vary much but whose phase response does is a section of coaxial cable. Measuring this section of coaxial cable shows the insertion phase response over the specified frequency range, Note that the phase response of this device changes linearly as a function of frequency. This phase response is a function of both the length of the cable and the frequency span over which the phase response is measured.

519

Coax Cable (.6 m)

I

I

CH1 S21 phase 20°/ REF-100 ° m INSERTIONPHASE

l

Cor

CENTER 200.000 000 MHZ

SPAN 40.000 000 MHZ

Why Does The Phase Response Have A Slope?

I

! oo so

/"

"-'~ 20

_~ l e ~

!,

r~

/" .//'

.,~"

,,/

,.'/

l:'reCl (6Hz) 40 to 50

--"' "/..- ..' " ,.. I i ,,. -. """ ..

2

.,

..+"

=~==._._..

...045 .......to_o....... .040

+--------~--~~.,,--.---_~-

110

-10

-30

-50

-

-;O

-90

$21 MeasurementLevel(dB fromRef)

85 I0 accuracy

100 10

E

~ o

_=

X,

, . ' /

O01 '

8752.

/ ~

0-10-20-30-40-50-60-70-80-90-100

Transmission Level (dBm)

520

Aksel Kiiss

+1 -t -t

IllllllillllllllilUlllliilllllllBI IIIIIIlilllllll/illllllliilllllllil IIIllllBIIIIIIIlillllllllmllllllllill

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I I I I I I I m m l l l l l l l l B B I I i l l l l i m B I I I I I I I m m B ~

I

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Iillllllllllllllinllllllllllllllllnll Illllllilllllillillllllllillllllllil I

-1

300 kHz

'~

100

g

~o

3MHz 30 MHz 300 MHz 6GHz

w

<6GHz <3 GHz _

_-

\.-" / !

¢-

1 I~

m

, ~

,j

a. : / i

i

-J

__-

.1

121 +1

.01

0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100

Input Level

8753C.

dBm

3. Reflection M e a s u r e m e n t s

MEASUREMENT

APPLICATIONS Transmitted

In

Reflected

DUT

17. Microwave Instrumentation and Measurements

521

What causes the reflected signals that we want to measure? If we have a source of RF or microwave ==Z o : -! energy with a source impedance ZL=Z o Z L=OI Z L = co of 50 ~ , then that source will Z o SHO OPEN deliver its maximum power available to the transmission line if the • transmission line's impedance is the ,, > same as or equal to the source impedance. In this case, our transmission line is of infinite length and C:v" i is a 50-~ impedance transmission I line. If we terminate the transmisC:v, v, = =) sion line with a 50-~ termination, then all of the energy flowing from the source will be absorbed by the termination (i.e., the signal cannot tell the difference between a Z 0 load and a Z 0 transmission line of infinite length). What happens to all of that energy if we now terminate the transmission line with a short circuit? Since a short circuit has 0 ~,, it cannot dissipate any power (the energy cannot be absorbed in the short), and since there is nowhere else for the energy to go, it is "reflected" back toward the source. Since a short circuit cannot support any voltage (Vshor t = 0 V), the reflected voltage wave must be of equal magnitude and of opposite polarity compared with the incident voltage wave for the voltage sum at the short to be equal to zero. Opposite polarity with a sine wave means being 180° out of phase. Similarly, when we terminate the transmission line with an open, there is nowhere for the energy to go since an open can support no current and thus can dissipate no power. A reflected wave is again launched back toward the source but the reflected voltage wave is "inphase" (or of the same polarity) and of the same magnitude as the incident wave at the open.

v.

/X~= v,=v,~lz~=o)

Having established that the reflected signal is a function of both the load impedance and the charZL--Z 0 acteristic impedance, let us use this Vn = V I.c relationship to see if we can preZL+Z o dict what the reflected signal will be if we terminate our transmission line with a 25-~ resistor (an impedance somewhere between a LET Z k= 25 Ohms, Z o = 50 Ohms short and an open). We find that VR =-2_._55VINC= _ 113 V:.c our reflected voltage wave at the 75 impedance will have an amplitude VR of ~ of that of the incident wave - -1/3 V=NC and will be 180° out of phase with it. If we take the ratio of the reflected signal to the incident signal, we have a relationship which accounts for the difference beween the load impedance and the characteristic impedance which we will refer to as the reflection coefficient.

522 The reflection coefficient (F) has both a magnitude and a phase value. The magnitude of the reflection coefficient is defined as (p) and varies between 0 and I. The return loss in decibels is equal to -201ogp. This results in a positive decibel number even though p is less than I. Values range between 0 dB (p = I) and oo dB (p = 0). The standing wave ratio (SWR) is the ratio of the maximum standing wave voltage to the minimum standing wave voltage (Emax/Emin). It is also related to p by the equation shown. SWR varies between I and oo.

Aksel Kiiss

REFLECTION TERMINOLOGY [.

Reflection

=

Coefficient

.p

VR

ZL--

VINC

Z t "4" Z o

Zo j D Z (~

= Irl

Return L o s s = - 2 0

Log.13

I+P SWR -

1-.1:) l p

O

O RL ( dB ) oo SWR

1

As with transmission measureRFRAB Response Calibration ments, we also want to establish a magnitude and phase reference Short Circuit CHI $11 log MAG 5 clB/ REF 0 dB ~,-12.014dB point for reflection measurements. I '= 5.861 010 MHz l DUT] In a simple reflection response cal,~ ~or ° I ibration we normally use a short Reference circuit because its response (F = Hld Plane 1 / 1 8 0 °) is well known. This response calibration compensates for the differences in the measurement signal paths (both magnitude and phase). When the DUT is START .300 000 MHz STOP 10.000 000 MHz then connected the return loss in decibels is the difference between the 0-dB reference line and the measurement.

The measurement calibration with the short circuit also establishes the phase reference plane for our reflection measurements. Notice that a polar display of a measurement of a short circuit before any measurement calibration does not indicate the true response of a short. After the response calibration, the polar display now indicates the proper reflection coefficient of a short circuit.

Re R A B °

Phase

.

Reference IResponse

-~i

X I

!

il Sh°rtl

Uncorrected c,1 s111u FS = 971.81.U 178.66° R e f e r e n c e " ~ 0 10..z Plane Hld

~

START .300000MHZ

STOP10.000000MHZ

Calibration

"Short"

Corrected c,~ slll u Fs = 9~9~,u ~799~ " 10MHz co,

Hdl

START .300000MHZ STOP10.000000MH2

523

17. Microwave Instrumentation and Measurements The polar format displays the reflection coefficient resulting in a two-dimensional vector representation. The concentric circles are p = scaled in units of linear magnitude /_ ~ = F = from 0 at the center to I at the outer circle. The radial lines scale the phase angle from 0 ° to + 180° or - 1 8 0 °. Values read from the polar chart consisting of a linear magnitude ratio and a phase angle. The ideal short circuit has a reflection coefficient of 1 / 1 8 0 °, an ideal open circuit has a reflection coefficient of I / 0 °, and a perfect termination ( Z 0 characteristic impedance) produces a response at the center of the chart, 0 / 0 °. Since there is no frequency axis, frequency measurements.

POLAR FORMAT Linear Magnitude Ratio Relative Phase Angle

90° _.1__..~

p Z~ o

Zo 50 Ohms ~ 0o oz

+ Sho

oL,l

:-,o o

(

~ ~ ~ ~ " ~ ~ / / ~ i O pt e n- . . _ y,

1 / O°

/ + 180 °

-90 °

information must be read from markers or by CW

IMPEDANCE MEASUREMENTS Reflection data can also be displayed in an impedance format. Recall that [', the reflection coefficient, is related to the characteristic impedance and the unknown load impedance. If we know F and Z 0, we can calculate and display the load impedance. The unknown impedance we wish to display is a complex impedance; that is, it has both resistive and reactive components associated with it.

VREFL

Z L- Z0

VIN c

ZL'IL Zo

(1 + 17) Z L

~'~

Zo

(1 -- F ) ZL =

lg

Resistive (R

+ +

Reactive iX)

\

o

Freq

8,

8 5 4 ~ . ~

,,---

(GHz)

28 t o 4B

B

.2

.4

....

.6

$11 Reflection Coefficient

.8

,840 to

20

,e45 t o

,84Q

524

Aksel Kiiss

> , .84 "~

.~.. , / " ,i

.83 ..i .//

8

-2

~)

---

8

.2

.

.

.

.

I-

"-

.4

F'req (GHz)

4o to 50 ~--&-;~....

.. i - . ~ .

_. . . . . . . . . .

.6

. . .840 to

20

I

.8

1

S l l Reflection Coefficient 85 I0 accuracy

0

J/ E

1

j

j ' Jj j / /

8 0I 0.( 1

iypical

/

_~ ~'4/

3.0( 1

0 -10 -20 -30 -40 -50 -60 -70 -80 -90-100 Reflection Level (dBm)

I00 10

y J

0.1

0.010 8752/8753

accuracy.

Tyl:!ical _,,,,,J

-." J

J

-10 -20 -30 -40 -50 -60 -70 -80 -90-100

ReflectionLevel(dBm)

525

17. Microwave Instrumentation and Measurements

4. Electrical Delay An equivalent method of determinCH1 $21 phase 30°/REF 0° , ,119.97 ° ~-- ~ ~-_,.... _ 200.000 000 MHz ing electrical length with modern Cor ~ ~ network analyzers is to use an internal electrical length adjustment feature which varies (mathematically) the length of the reference CENTER 200.000 000 MHz SPAN 40.000 000 MHz signal path to vary the phase reCH1 29.91°/REF 0= ~ 335.44 m° Cor sponse of our device. The internal De 1 3.3401 ns 1.0013 m electrical delay function can quickly Electrical I Cable balance the phase response of our 3.35 I... device under test. Once the phase 1.004 M is balanced, the amount of equivaCENTER 200.000 000 MHz SPAN 40.000 000 MHz lent length we have electronically added to the reference path then is equal to the electrical length of our device under test. In addition, the electrical delay time is displayed in seconds and distance is displayed in meters. By entering in the proper value of dielectric material or the relative phase velocity, the distance displayed can be physical length.

5. Group Delay

Group delay is defined as the derivative of the phase response with respect to frequency. That is, it is the rate of change of the phase response as a function of frequency. A perfectly linear phase shift would have a constant rate of change with respect to frequency (a constant slope with no variations) and therefore a constant group delay, Units for group delay are seconds which indicates that group delay is a measure of transit time through the device under test for a particular frequency.

Phase

UJ

_F,equenc, " duj ~

Group Delay = t= -

-d~

in Radians UJ In Radians/Sec

dUJ -1 360 °

d~ df

In degrees f In Hz (uJ=2 7Tf)

The group delay differentiation process reduces the linear portion of the phase response to a constant value and transforms the deviations from the linear phase into deviations from constant group delay. Since the deviation from constant group delay corresponds to deviations from the linear phase, it is these variations that indicate distortion. Because differentiation effectively removes the linear component of the phase shift, high-resolution measurements are again possible. Total or absolute delay indicates the signal transit time through the device.

GROUP DELAY AS A D I S T O R T I O N P A R A M E T E R Deviation From Constant

Frequency

Grtougpl

Gr°uplDelay

Phase to

Y

Frequency Deviation From Constant Group Delay Indicates Distortion Total Delay Indicates Transit

Of the several group delay measurement techniques, phase slope is probably the most straightforPHASE-SLOPE GROUP ward. It is a static or CW techMEASUREMENT nique that involves measuring the phase at two closely spaced frefl f2 quencies and then computing the I ! " slope (which is an approximation of the derivative). This is the techQ1 nique used exclusively in modern @2 network analyzers since it yields the best resolutions. Depending 1 Zl(~ upon the source, the user has alTg = 3 6 0 ° A f most complete control over the frequency step Af (aperture). The group delay range then is a function of how stable the frequency source is. A source with I-Hz frequency resolution has a maximum delay range of about 500 ms.

PHASE SAMPLES

A ~ =-90"

DELAY

<180 ° APART

+ 180"~

The only network analyzer limitation which we need to account for is that the D4 measured between two adjacent frequency points must be < 180° . If the phase is > 180°, incorrect delay information may result.

Time

A ~ ~ 170"

Z~~ = -190"

527

17. Microwave Instrumentation and Measurements

6. Noise Figure/Noise Temperature Measurements Definitions of the Noise Figure/Noise Temperature There are various ways of defining the noise figure. Historically it was defined as the signal-to-noise ratio at the amplifier input to the signal-tonoise ratio at the amplifier output. Noise temperature has gained in popularity and is fairly widely used in the industry today. From physics we know that the maximum thermal noise power available from a resistor into a matched load is PN = K T B ,

where K is the Boltzmann's constant (K = 1.374 x 10-23j/K), T is the physical temperature of the resistor in kelvins, and B is the noise bandwidth. For example, the noise power available from a resistor at 290 K is - 1 1 4 d B m / M H z . If one now takes a low-noise amplifier, terminates the input with a resistor at 0 K, and then measures the output noise power, one can find the equivalent noise temperature of the amplifier by dividing the output power by the amplifier gain, as shown in Figure 9. The equivalent noise temperature can be interpreted as an input resistor at temperature T~ followed by a noiseless amplifier. In these assumptions the amplifier gain has to be sufficiently high to make the noise contribution from the load resistor negligible. If one now connects a resistor at To = 290 K to the amplifier input port (or raises the temperature of the resistor from T = 0 K to T = 290 K), then the total noise power available at the amplifier output is N T = ( T o + T ~ ) K B G since the noise powers from the two sources are completely uncorrelated and can, therefore, be added. The amplifier noise figure can now be defined as NF (dB) = 10 log -~o + 1

)

50 OHMS AT T=O'K

OUT = KeT (3 B N OUT

Te= KGB Figure 9. Equivalent Te of a low-noise amplifier.

528

Aksel Kiiss

or expressed as noise factor =

T0

+ 1

It is of interest to point out that using T o = 290 K as a reference temperature for expressing the noise figure in decibels is completely arbitrary. Any other temperature, including normal room temperature, could have been chosen. We can now turn our attention to the practical noise figure/noise temperature measurements.

Noise Figure The most widely used, and probably the most accurate, method of measuring noise figure is the Y-factor method. The measurement consists of connecting two noise sources with known available noise power to the amplifier input port and then measuring the difference or change in the output power. That difference is called the Y factor. Mathematically y

_~

Te+ Th

+ Tc' where Te is the equivalent amplifier noise temperature; T h is the higher of the two known input noise temperatures, usually called Thot; and Tc is the lower of the two known input noise temperatures, often called Tco~d. There are two commercially available noise sources-noise standards that are generally used for noise figure measurements. The first one is a hot and cold load and the second is a noise diode. In the case of the h o t / c o l d loads the hot standard is usually a 50-~ well-matched termination heated and maintained at 373 K (100°C), and the cold standard is a 50-1-/well-matched termination immersed in liquid nitrogen (77.3 K). The loads should be identical and well matched (return loss higher than 25 dB). The other, and more widely used, reference is a solid-state noise diode. When a diode is reverse biased beyond the breakdown voltage, the available noise power from the diode is fairly constant as a function of frequency and is higher than that available from a resistor at temperature T 0. The excess noise ratio (ENR) is defined as follows:

E N R = 10 log

Th

where T h corresponds to the equivalent noise temperature of the diode in the on condition and T o = 290 K.

529

17. Microwave Instrumentation and Measurements

Sll i

IMAGE REJECT

'

~

L

~

r~

OLI

MIXER

STATE

HP 8970B

SOU RC E

LOCAL

NOISE

,,OSO,L TO., D.U.T. GAINS < 20 dB

FIGURE

ANO ,D. 4 MHz

i1_ ! I TOTALRMS NOISE POWER <-15dBm

Figure I0. Test setup for low-noise amplifier noise figure measurement with solid-state noise diodes,

Diodes normally have excess noise ratios of 30 dB. Unfortunately, there is a large variation in the diode impedance from the off to the on condition (almost from an open to a short circuit). To mask that impedance change, the diode output port is padded with an attenuatormthe higher the attenuator value is, the lower the ENR. Commercially available diodes have ENRs in the 15- and 5-dB range. In actual noise figure measurement there are two possible categories of measurement errors-measurement uncertainties. One set pertains to the test setup itself, whereas the other is related to the noise sources and the interface between the noise source and the low-noise amplifier under test. To ensure that the test results are limited to the uncertainties of the noise sources/standards and the interface, and not the measurement errors related to the remaining test setup, one should eliminate, or at least minimize, errors commonly known as operator errors. Typical test setups are shown in Figure 10 and Figure 11. Figure 10 shows the setup for h o t / c o l d standards and Figure 11 shows that for solid-state noise diodes. The following steps should be taken to eliminate operator errors. (1) Test setup saturation by noise peaks. To eliminate test setup saturation by noise peaks (also referred to as the crest factor) the system should be operated 12-15 dB below its 1-dB compression point. This precaution accommodates at least 99.9% of the noise peaks without compression.

,.,

.

STANDARD II

I

II L ~

HOT

STANDARDI I

'1

FILLER FOR HARMONIC RESPONSE REJECTION

Sll

I r-I

II s

_

I

I'

I

"

TOTAL RMS NOISE I POWER < -15 dBm

1,w

NOISE RGURE < 3 db FOR D.U.T. GAINS < 20 dB

- -

£, ~

IL I ~ REJECT MIXER

TEST RECEIVER

_

,, I +10 dBmM,N I OSCILLATOR ,oo~1 I OSCILLATORI I

ALL TYPE

I

.°~

BANDWlD'IH ~ 1 MHz

Figure II. Test setup for low-noise amplifier noise figure measurement with hot/cold noise standards.

530

Aksel Kiiss

(2) Multiple responses. To eliminate the image response, image reject mixers should be used. Less than octave-band filters will reject the mixer harmonic responses. (3) Temperature dependence. Both the amplifier noise figure and the solid-state noise diode ENR are temperature dependent. In the test setup the amplifier as well as the noise diode is kept close to the 23°C ambient temperature. The entire test setup should have sufficient warmup time to minimize system gain changes during measurement. Since the diode is calibrated at 290 K (approximately 17 C), the diode ENR should be corrected for the actual room temperature. (4) Mixer conversion loss modulation when the noise diode is switched from the off to the on condition. This can happen especially with high ENR diodes, when the mixer is not properly energized by the local oscillator. (5) To minimize uncertainties caused by second-stage noise contribution, well-matched low-loss isolators and low-noise amplifiers should be used. (6) In the h o t / c o l d test setup one should minimize the time required to switch the loads at the amplifier input and to eliminate backlash errors in the waveguide beyond the cutoff attenuator by rotating the attenuator in the same direction during the measurement. Assuming that the above-listed steps/precautions eliminated, or at least minimized, the operator-induced errors, we are left with uncertainties resulting from the noise sources themselves and from the source/ amplifier interface. These uncertainties can be caused by three principal effects. (1) Uncertainties regarding the absolute available noise power from the noise source. The noise diodes are calibrated by the manufacturer in terms of the available noise power into an ideal 50-l-I resistive load. This calibration compensates for the reflection coefficient of the noise diode itself. The cold standards are calibrated by assuming the 50-fl termination at 77.3 K and then theoretically correcting for the losses and temperature gradients of the cables connecting the load to the outside reference port. When the load impedance changes from the ideal resistive 50 ~ used for the diode ENR calibration to the complex input impedance of the low-noise amplifier, the uncertainty in the available noise power from the diode, and consequently the value of the ENR, also changes. Typical calibration/ correction data for noise diodes and h o t / c o l d noise standards are given in Tables 1-3 and Figure 12. (2) Source impedance-reflection coefficient variations. The change in the source impedance, as the noise diode is switched from the off to the on

531

17. Microwave Instrumentation and Measurements

condition or amplifier input port termination noise standards are switched from cold to hot, can affect the amplifier measured noise temperature in three ways. (a) The change in the source impedance can change the estimated available noise power from the noise source. (b) The change in the source impedance can change the amplifier noise temperature. (c) The change in the source impedance can change the amplifier gain. To minimize the gain modulation effect caused by the diode impedance change, HP a few years ago introduced the low-ENR diodes. HP added an additional 10-dB attenuator to the output of existing 15-dB E N R noise diodes. This additional attenuator further masks the diode impedance changes as the diode is switched from the off to the on condition. The model number of the low-ENR diode is HP346A.

TABLE I

Manufacturer-Specified "Worst-Case Uncertainty" and "Root Sum of Squares Uncertainty" for Cardinal Frequencies from 10 MHz to 18 GHz for HP346A, B and C Solid-State Noise Diodes

Frequency (MHz)

Worst-case uncertainty (dB)

Root sum of squares uncertainty (dB)

10 100 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000 16,000 17,000 18,000

0.34 0.34 0.34 0.34 0.34 0.34 0.35 0.35 0.37 0.37 0.38 0.39 0.39 0.40 0.50 0.51 0.52 0.54 0.55 0.57

0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.13 0.13 0.14 0.14 0.18 0.18 0.18 0.18 0.18 0.19

Aksel Kiiss

532 TABLE 2 Calibration Report - - Cryogenic Termination

Frequency (GHz) 3.95 7.50 12.40 18.00

Calibration equation for the input noise temperature (K) ( T ' = Tc + X A P + YATo~ +

Z ATo2)

Input noise temperature T' (K)

Input

Repaired

VSWR

VSWR

81.47

1.01

1.01

82.16

1.05

1.05

84.10

1.04

1.04

85.29

1.03

1.02

T ' = 80.84 + 0.01080 AP + 0.01587AT01 + 0.00192 AT02 T ' = 81.43 + 0.01077AP + 0.01917AT01 + 0.00162 AT02 T ' = 83.11 + 0.01068 AP + 0.02404 AT01 + 0.00532 AT02 T ' = 84.13 + 0.01062 AP + 0.02744 AT01 +0.00714 AT02

(3) U n c e r t a i n t i e s c a u s e d by a d a p t o r s in o r d e r to a c c o m m o d a t e diff e r e n t t y p e s of c o n n e c t o r s . T h e s e a d a p t o r s c a n c a u s e a d d i t i o n a l V S W R u n c e r t a i n t i e s a n d also a d d to t h e loss b e t w e e n t h e n o i s e s o u r c e a n d t h e a m p l i f i e r u n d e r test. It is v e r y difficult to i n d i v i d u a l l y s e p a r a t e t h e t h r e e effects. Q u i t e o f t e n l o w - n o i s e a m p l i f i e r s a r e n o i s e m a t c h e d for t h e l o w e s t n o i s e figure. T h i s r e s u l t s in a h i g h - i n p u t r e f l e c t i o n coefficient b e c a u s e t h e n o i s e m a t c h a n d t h e p o w e r m a t c h do n o t n o r m a l l y c o i n c i d e . S i n c e t h e a v a i l a b l e n o i s e p o w e r

TABLE 3 Calibration Report - - Thermal Termination

Input noise Calibration equation for the input noise temperature T' Frequency temperature (K) (K) (GHz) (T' = T + 0.23026 (TO - T)[½ LI(dB) + L 2 (dB)]) 3.95 7.50 12.40 18.00

1 T ' = 373.16 + 0.23026[7(0.09150) + (0.01695)] (295.66- 373.16) T ' = 373.16 + 0.23026 (295.66 - 373.16)[½(0.11270) + (0.03845)] T ' = 373.16 + 0.23026 (295.66 - 373.16)[½(0.12375) + (0.04705)] T ' = 373.16 + 0.23026 (295.66 - 373.16)[½(0.13790) + (0.06655)]

Input VSWR

372.04

1.02

371.47

1.08

371.22

1.05

370.74

1.03

533

17. Microwave Instrumentation and Measurements 12 == ,=,=='''"' _.,, =,==~'~== = ~

10

4 Z i--

2

<1

~

===-.m====,k

......

-2

=-..=. ~

-

....................

~ ~ ~ ~ ~ ' - " " |=====p.==

-4

2

3

4

5 6 7 FREQUENCY IN GHz

8

9

10

Figure 12. Corrections in hot and cold termination temperatures due to internal RF losses for AlL hot/cold standards. Dashed lines indicate the overall uncertainty of the plotted correction curves,

from the noise diode is calibrated into a 50-~ nonreflective load, the power available to a highly reflective load from a reflective nonresistive 50-~ source can be different from that claimed on the calibration chart. Normally, low-noise amplifier noise performance is optimized with the noise diode as the amplifier input termination. In that optimization process, in obtaining the lowest amplifier measured noise figure, the noise diode impedance becomes part of the actual input noise matching network. Practical experience has shown that when a low-noise amplifier is simultaneously noise and power matched, or low-loss isolators are used between the noise source and the amplifier, small source impedance variations have only a second-order effect on the amplifier noise temperature. The change in amplifier gain, sometimes referred to as gain modulation, is caused by the changes in the source impedance of the noise diode as the noise power is changed. This change can affect the noise figure in two ways. If the amplifier gain increases as the diode is turned on, one obtains an optimistic noise figure. When the gain decreases, the measured noise figure is higher.

534

Aksel Kiiss

Absolute Accuracy of Noise Figure Measurements It is very difficult to establish the absolute accuracy of the measured noise figure. In addition to the uncertainties discussed above, the calibration uncertainty when the noise standard is calibrated by the National Institute of Standards and Technology (NIST) is on the order of 0.1 dB. Based on past practical experience, one can assume that, when using h o t / c o l d noise standards from the same manufacturer, the noise figure measurement can be repeated to within +0.1 dB. H o t / c o l d standards from different manufacturers increase the measurement uncertainty. Table 4 gives comparative noise figure measurement data on a 8- to 12-GHz low-noise amplifier. The amplifier noise figure was measured at MITEQ by using 21 HP noise diodes (both high and low ENR) and Maury Microwave h o t / c o l d standards. The measurements were performed only at frequencies at which the diode manufacturer provided ENR calibration data. At a later date, the amplifier noise figure was measured at NIST with more sophisticated methods. Mismatch Uncertainties

Below we will investigate the uncertainties related to the Y factor caused by the mismatch uncertainties at the noise source output and amplifier input interface. In Figure 13 we have depicted the noise source output, the amplifier input port interface, and the resultant signal reflections. The available noise power from the noise source is normally calibrated by the manufacturer as the power from the noise source delivered from the source with its reflection coefficient, Fs, to a 50-1"~ resistive load. There are two noise voltages to be considered: one emanating from the noise source and the other being the reverse radiation from the amplifier input port. As the noise emitted from the noise source impinges on the amplifier input port, part of that noise is transmitted and part of it is reflected. The reflected part of the noise signal is retransmitted to the noise source output port. Again, part of it is absorbed by the noise diode and part is rereflected back to the amplifier input port. Likewise, the reverse radiation signal as it impinges on the noise diode output impedance is reflected by the noise diode and retransmitted to the amplifier input port. If we assume that the reflected noise signals are coherent with the original signal, then we can treat these noise voltages by vectorial addition and subtraction to obtain the worst-case scenario. The relative value of the noise signal reflected from the amplifier port is FA, and the part rereflected from the noise diode is FAFs. If the original signal is 1, then we can add the reflected signal vectorially. When the reflected signal adds in

Q_

E

| c~

w~ mJ ~ac~ 0 L LL . v~ ~ O

z

Z

!

m~

~t

Lr~

c~O Lr~

Lr~ Lr~

Lr~

c~0 Lr~

~

Lf~

C~

Lr~

~"

Ir~

if~

t'~

Cr~

L~

~

~Qo • I~

°

536

Aksel Kiiss

REFLECTED FROM NOISE DIODE ~A ~S

NOISE SOURCE

L

REFLECTED FROM AMP. INCIDENT SIGNAL

50 OHM

Figure 13. Mismatch uncertainties at the noise figure amplifier interface.

phase we obtain 1 + FAFs, and when it is 180 ° out of phase we get 1 - FAFs. Likewise for the reverse radiation signal we obtain 1 + F s and 1 - F s. The uncertainty can be expressed in decibels by 20 log(1 + F sFn). Figures 14a and 14b show the measurement uncertainties of a h o t / c o l d noise source and a 5-dB E N R noise diode, respectively.

Uncertainties in the Available Noise Power from the Noise Source All commercially available noise standards, be they solid-state noise diodes or h o t / c o l d noise standards, are calibrated by the manufacturer and traceable through secondary or primary standards to NIST, formerly known as the Bureau of Standards. If the noise source is calibrated by NIST, the calibration data are accompanied by the uncertainty information. If the calibration is performed by the noise source manufacturer and refers to its secondary or primary standards, the uncertainty as it relates to NIST calibration data increases. Table 1 represents the calibration uncertainties for the HP346A diode. Figure 12 has the same information for the AIL h o t / c o l d standard. Tables 2 and 3 present calibration data for Maury Microwave h o t / c o l d standards.

Uncertainties Caused by Test Instrument Y Factor Readout Noise diodes are normally used with noise figure meters that measure the noise figure directly from 10 to 2000 MHz. Above these frequencies mixers are used to convert the signals to the above-stated frequency range. Manufacturers' guaranteed uncertainty to the Y-factor readout is +0.1 dB. With h o t / c o l d measurements one can also use the noise figure meter as a Y-factor readout or use a precision waveguide attenuator to obtain the Y factor. The absolute accuracy of the attenuator is +0.005 d B / 10 dB + 0.03 dB, and the resolution is 0.01 dB/division. One advantage of the attenuator is that it removes the uncertainties of the detector since

17. Microwave Instrumentation and Measurements

537

the output meter reading is used only as a reference and is the same for the h o t / c o l d inputs. Figures 15a and 15b plot the noise temperature uncertainty as a function of amplifier noise temperature for a 0.1-dB Y-factor uncertainty for a h o t / c o l d diode and a noise diode, respectively.

7. M i c r o w a v e P o w e r M e a s u r e m e n t s Microwave power meters are the fundamental measurement tools of microwave engineers and technicians. Because of the high rate of signal oscillation at microwave frequencies, direct measurement of voltage and current is impractical; therefore, power meters are used to determine microwave signal levels. Power meters are differentiated according to measurement technique. The dominant commercial power measurement techniques are thermal-based power detection and diode-based power detection.

Thermal-Based Power Detectors Most thermal-based power detectors are either thermistors or thermocouples. Both types exhibit similar characteristics. A thermal detector's voltage response corresponds to the heat generated by the microwave signal energy. These detectors have good linear characteristics over a dynamic range of - 3 0 to + 20 dBm; however, the upper 10 dB of the detector range suffers from moderate output voltage compression. This condition is normally identified with detector specifications. The dynamic range of these detectors can be shifted upward by adding an attenuator at the detector i n p u t - - a technique which will also improve measurement uncertainty. Power meters using these detectors incorporate considerable noise filtering and averaging to compensate for the low sensitivity of the voltage response from the thermal detector. The lower 15 dB of a thermal-based detector's range tends to be especially noisy; furthermore, the average noise level tends to drift due to thermally induced potential variations at connector interfaces and detector temperature variations. For this reason, thermal-based power meters have measurement settling times and incorporate a "zero" function which is activated from the power meter's front panel. Power meters should be zeroed prior to performing measurements at low power levels. The zeroing process requires that the source signal be turned off, so the meter can measure and compensate for the noise. Thermal-based power meters provide a calibration source to which the absolute response of the d e t e c t o r / p o w e r meter combination can be ad-

538

Aksel Kiiss

a,o /

/ /

/ / /

12

/ ./ /

/ /

== 1o

/ /

i /

/

~

/

8

/

/

//

f

/

/ • /

/

6

f

/ //

_

/

/ /

/

/

/

/

4

/

....

/

2

-

. , . - -

. .......

-

0

-

'

°-

'

'

'

,

L

i

L

i

i

i

i

i

i

L

i

l

N O I S E T E M P E R A T U R E (KELVINS) . . . .

2:1

INPUT

RETURN

-

-

1.5:1

LOSS

INPUT

90

.......

1.22:1

INPUT

RETURN

AMPLIFIER

b

RETURN

LOSS

LOSS

INPUT

. I s

mm

mm

I

70

t I t

I

,. ~...'

60 I t

uu

5O

4O

I I

v

20

........

o

I

I

I

I

I

I

I

I

I

I

I

I

o

o

o

4,--'1

o

oO

o

o

o

=o

~

o

o

o

o

~

o

o

N O I S E T E M P E R T A T U R E (KELVIN) . . . .

2:1

INPUT

VSWR

-

-

1.5:1

AMPLIFIER

INPUT

VSWR

.......

1.22:1

INPUT

VSWR

I

INPUT

Figure 14. (a) Uncertainties resulting from the mismatch at the hot/cold noise source and amplifier interface for a 30-dB hot/cold standard input return loss. (b) Uncertainties resulting from the mismatclat the noise source and amplifier interface for a 20-dB diode return loss.

539

17. Microwave Instrumentation and Measurements

a 60.00 50.00 t

I

-

40.00

\

30.00

i ~

\

20.00

\ \ \

10.00

0.00

AM~IFIER NOISE T E M P E ~ R E

Ill

AM~IFIER NOISE T E M P E ~ R E

IK)

b 80.00 70.00

\ \ \

u. a

50.00

\ ~

4O.00

\

\ \ \

30.00

20.00 10.00

0.00

Figure 15. Amplifier noise temperature measurement uncertainties for a 0, I-dB Y-factor uncertainty as a function of the amplfier noise temperature for (a) a hot/cold diode and (b) a noise diode.

540

Aksel Kiiss

justed. These calibrators are typically traceable to an accepted national standards organization to within 0.7% at their specified output levels. D e t e c t o r / m e t e r response should be verified at least once every 4 h or whenever the detector is removed and reconnected to the detector cable.

Diode-Based Power Detectors Diode detectors have two operating regions from - 7 0 to + 20 dBm: the square-law region, which the output voltage is directly proportional to the input power, and the linear region, in which the voltage response is noticeably nonlinear.

f

/ /

I mV

lgv

k.ll'~wr"..,,~1~1"11

/

OUTPUT VOLTAGE

I

/

0.I J.LV - 7 0

-60

-50

- 40 INPUT

- 30

- 20

POWER

- I0

0

+10

+20

(dBm)

Ti.~:-~"~..~ ........ ,.ii.i:,......:;"() iil)iil;:i.W

Diode Based Microwave Power Detectors Have Two Operating Regions The square-law ~region from - 7 0 dBm to just above - 3 0 dBm exhibits good linear operation. Diode based detectors operating in this region respond to the true RMS level of incident microwave power--similarly to thermal-based detectors. For this reason, diode detectors can be operated with thermal-detector-compatible power meters to provide an additional power measurement range down to - 7 0 dBm. However, the thermaldetector-compatible power meter's filtering and built-in averaging restrict the potential measurement rate relative to that of power meters which are designed specifically for diode-based detectors.

17. Microwave Instrumentation and Measurements

541

Diode-Based Power Meters The fundamental problem of using the full 90-dB dynamic range and measurement speed (nearly instantaneous) is compensating for the diode's nonlinear response to input power above - 3 0 dBm. This can be accomplished with a power sweep calibrator. Although all diode sensors show the same general response patterns, nonlinearities vary from diode to diode due to junction etch pattern variations and impurities introduced into the diode's substrate during fabrication. An accurate calibrator can automatically account for these variations.

Photo of a calibrator. This power

sweep calibrator from Wavetek Microwave

steps through

51

precise I-dB steps to provide a compensation reference for the balanced diode sensors.

A power sweep calibrator provides compensation above the diode sensor's square-law region and allows the power meter to measure power levels as accurately as traditional thermal-based power meters. The calibrator steps through each power level from - 3 0 to + 20 dBm and corrects the power meter's displayed reading similarly to the fixed-level calibrator on thermal-based power meters. A power sweep calibration system also serves as a test system to prevent damaged sensors from generating erroneous power readings.

Frequency Calibration Factor Both thermal-based and diode-based detectors exhibit a measurable frequency response. This frequency response is determined when the detector is calibrated. The correction factors are either printed on the side of the d e t e c t o r - - a s is the case with most manufacturers of thermal detecting d e t e c t o r s m o r programmed into an E E P R O M within the sensor housing. Using an E E P R O M to store the frequency calibration data allows the power meter to automatically correct the displayed power reading rather than necessitating manual interpolation and data entry of the frequency

542

Aksel Kiiss

calibration data via the instrument's front panel. Accurate power measurement requires periodic calibration of the detector (measurement of the frequency calibration factors)with a vector network analyzer.

Photo of a 8542 power meter. A diode-based power meter like the one shown can utilize both C W and pulse detecting diode sensors.

Peak Power Meters Peak power meters utilize the measurement speed of diode sensors to sample and display the amplitude profile of pulsed microwave signals. The peak power sensors utilize low-barrier Schottky diodes in a balanced configuration. The balanced configuration virtually eliminates even-order harmonic errors, which are generally associated with single-diode sensors and crystal detectors. A balanced design also provides a 3-dB improvement in sensitivity.

Accuracy: How to Calculate Your Measurement Uncertainty The uncertainty of microwave power measurements depends on several factors, the most important of which is the impedance mismatch of both the power sensor and the RF source. A high return loss (low-reflection coefficient) minimizes impedance mismatch errors and improves accuracy. Error in absolute power measurement originates from six general sources. In order of importance, these are source (measurement port)-to-sensor mismatch uncertainty; thermal noise, which is dominant at the low end of a detector's dynamic range; instrument and sensor linearities; calibration factor uncertainty; calibrator power reference uncertainty; and calibratorto-sensor mismatch uncertainty. Tables 5 and 6 itemize the components of

17. Microwave Instrumentation and Measurements

543

TABLE 5 Sources of Measurement Uncertainty for a Typical Thermal Detecting Power Meter

Mismatch uncertainty, source to sensor Noise, dominant in the lower 15 dB of sensor range Sensor linearity, dominant in the upper 10 dB of sensor range Calibration factor uncertainty Power reference uncertainty Calibration pad error, where necessitated by sensor range Power reference mismatch uncertainty Instrument linearity Zero set and noise drift, only in the lower 15 dB of sensor range

Note. Listed by error magnitude.

TABLE 6 Sources of Measurement Uncertainty for a Typical Diode Based Power Meter

Mismatch uncertainty, source to sensor Noise, dominant in the lower 7 dB of sensor range Calibration factor uncertainty Power reference uncertainty Sensor linearity, only in the upper 20 dB of sensor range Power reference mismatch uncertainty Instrument Linearity Zero set and noise drift, only in the lower 7 dB of sensor range

Note. Listed by error magnitude.

measurement uncertainty for thermal-based and diode-based power meters, respectively. Mismatch uncertainty is calculated from the sensor reflection coefficient, Pl, and the measurement port reflection coefficient, P2, in either percentages or decibels according to Equation (1) or (2). M ( % ) = +_2 × (Pl)(P2) x 100% M(dB) = 201o810{1 _+ (Pl)(P2)}.

(1) (2)

Reflection coefficients are frequency dependent and may be calculated from manufacturers specifications according to Equation (3), (4), or (5). Pn = ( V S W R -

1 ) / ( V S W R + 1)

(3)

Pn = lO-(return Loss/20)

(4)

On = { 1 -

(5)

lO-(mismatchL°ss/lO)) 1/2.

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Aksel Kiiss

RSS and Worst-Case Calculations Measurement uncertainty values are typically stated in terms of the worst-case uncertainty and the root sum square uncertainty, (RSS). Worst-case uncertainty specifications assume that every source of error is at its maximum value and that the errors are cumulative. Since most measurement errors are statistically independent, this approach is a conservative indication of measurement uncertainty. worst case = ±(leal + le2l + le31 + "'" + I%l).

(6)

The RSS approach assumes that the sources of error are independent and that their individual effects on the total value are random. RSS=

+v/e 2+e 2+e 2+...

+ %2.

(7)

The RSS calculation yields a probabilistic quantity that is interpreted as the expected value of measurement uncertainty. The actual value of uncertainty (measurement error) can be g r e a t e r - - u p to the value of the worst-case uncertainty.

Measurement Techniques for Improved Measurement Accuracy Some sources of error can be minimized with good microwave measurement practice. For example, impedance mismatch between the source and the sensor can be reduced by placing an attenuator between them. The impedance of a microwave attenuator is very close to 50 ~ ; the improvement in return loss due to the addition of attenuator will effectively reduce the VSWR at the source and sensor connectors [Equations (3) and (4)]. When performing measurements at the low end of a sensor's dynamic range, the dominant source of error is noise. In this case, the sensor should be replaced with a high-dynamic-range sensor. Diode sensors are available with 90 dB of dynamic range. When it is impractical to switch sensors, the s e n s o r / m e t e r should be zeroed and the measurement should use a large averaging value. The zeroing function should be performed just before taking a final reading. The detector should remain connected to the signal source. By turning off the RF source instead of disconnecting the detector, the zeroing process automatically accounts for connector interface thermal EMFs.

17. Microwave Instrumentation and Measurements

545

8. Microwave Frequency Measurements

(CW and Pulsed) The use of various types of electronic counters for measuring and analyzing frequency, phase, and time interval signal characteristics is common in most high-tech industries. Today complex waveforms require sophisticated frequency counters. An example is the testing of a voltage-controlled oscillator (VCO): • • • • • •

Stability/draft, Frequency pushing / pulling, Step response, Past tuning drift, Tuning linearity, and Frequency setting repeatability.

Single-Shot, Precision VCO Characterization VCO switching characteristics can be key to optimal system performance. Often VCOs are used in a single-shot application, so it is critical to test the device in a similar manner. Conventional test techniques are cumbersome and temperature sensitive, require repetitive signals, or lack sufficient measurement resolution in single-shot modes. The HP 5372A can profile a VCO step and directly display the step response in a single pass. Settling time, overshoot, and post-tuning drift can easily be obtained from the frequency or phase vs time display. This time variation display can be referenced to a trigger edge, giving one a consistent reference point for settling time measurements. The optional channel C extends the measurement range from 500 MHz to 2 GHz. The addition of the HP 5364A Microwave Mixer/ Detector and an appropriate local oscillator offers 2- to 18-GHz measurements. When repetitive techniques can be used, HP 5372A time variation plots can be averaged, improving resolution for better analysis and characterization. • Frequency and phase vs time display: single shot or averaged for improved resolution; • 2-GHz channel C; • 8K measurement memory; • Pretrigger to view data prior to the VCO step; and • Measurements referenced to the trigger edge.

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Aksel Kiiss

A plot of frequency time is a simple, yet powerful way to examine a VCO step response.

HP 5372A Specification Summary

A detailed description of specifications, as well as operating characteristics, can be found in the HP 5372A Specification Guide, HP Literature No. 5952-8012.

Frequency Measurements For a single-measurement result, perform the following equations. Least significant digit displayed: 200 ps + × frequency - sample interval Resolution: _+

150 ps rms + (1.4 × trigger error) sample interval

× frequency

Accuracy: +_resolution _+ (time base aging x frequency) For continuous frequency measurements (mean estimation), perform the following equations. rms resolution (for the number of measurements/block >_ 3): ~/-~.5 × (150 ps rms + 1.4 × trigger error) (No. of blocks) 1/2 × (No. of measurements/block) 3/2 x sample interval x frequency

17. Microwave Instrumentation and Measurements

547

Accuracy: _+resolution +_ (time base aging × frequency) Graphs 1 and 2 may serve as an aid to quickly determine the approximate resolution and accuracy, respectively, of a frequency measurement. Random Uncertainties

100 kHz

¢= 0 0.. ==

1 kHz IOOHz

0 ee

f,l

= ~, LL

10 Hz 1Hz--1 100 mHz lOmHz lOOps

.....

pleinterva,*--

I

-- 10 msiample --

__..~

-

_..~v

f

-

-

-

I

-int. . . . I*

100 ml sample interval*l

_..~w~_j /

,s s~p,e ~n,erv.,"

. I"

.

j -

10 pHz 100 Hz

1 kHz

10 kHz

100 kHz

1 MHz 10 MHz

100 MHz

1 GHz

10 GHz

Measured Frequency Graph I. Frequency resolution is a function of the measured frequency, sample interval, and input

signal noise,

Time Base Aging

lOHz

,•

/

1 Hz

¢D

tJ 100 mHz ¢D ¢I" (D M.

10 rnHz

dd/ 100pHz 100 Hz

1 kHz

10 kHz

100 kHz

1 MHz 10 MHz

100 MHz

1 GHz

10 GHz

Measured Frequency

Graph 2. Time base crystal aging affects the frequency and period measurement accuracy,

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Aksel Kiiss

EXAMPLE: Measure a 100-MHz, 2-V, peak-to-peak sine wave. The input signal noise (across the HP 5372A's 500-MHz bandwidth) is 1 mV rms. A sample interval of 100 ms has been selected. It has been one year since the time base was calibrated. The resolution of a frequency measurement is influenced by noise on the input signal, the selected sample interval, and the measured frequency as shown above in the resolution equation for a single measurement. From Graph 1 it can be determined that the measured resolution will be approximately 100 Hz for each frequency measurement. As one can see, reducing the input noise or choosing a longer sample interval will improve the measurement resolution. If the signal is being downconverted, mixing to a lower input frequency will also improve resolution. Averaging may also be used to improve frequency resolution. Time base aging as well as resolution must be calculated to determine measurement accuracy. For this example, Graph 2 shows that the uncertainty due to time base aging is approximately + 11 Hz. Using an atomic standard such as the HP 5061B or calibrating more frequently will improve this uncertainty. The total accuracy uncertainty is approximately + 111 Hz.

Input Characteristics Channels A and B

The following refers to an HP 5372A with

HP 54002A pods installed. Range: DC coupled to 500 MHz Sensitivity ( × 1 attenuation, and minimum hysteresis): 15-mV rms sine wave (45 mV peak to peak), typically 10 mV rms, and 45 mV peak to peak for pulse input. Hysteresis control is available to reduce input sensitivity to trigger noise. Dynamic range: For × 1 attenuation, 45 mV peak to peak to 2 V peak to peak; for × 2.5 attenuation, 115 mV peak to peak to 5 V peak to peak. Minimum pulse width: 1 ns for all measurement modes except holdoff arming and 1.5 ns with holdoff arming

Channel C (Option 030) The following refers to a type N connector. Range: 100 M H z - 2 GHz (divide-by-four prescaler) Sensitivity (0-dB attenuation): 100 MHz to 1.5 GHz, - 2 5 dBm; 1.5 to 2 GHz, - 20 dBm

549

17. Microwave Instrumentation and Measurements

Dynamic range: 100 MHz to 1.5 GHz; - 2 5 to + 7 dBm; 1.5 to 2 GHz, - 2 0 to + 7 dBm. The trigger level is fixed at 0 V nominal. Impedance" Ac coupled, 50 ~ , VSWR < 2.5

External Arm Range: DC coupled to 100 MHz Minimum pulse width: 5 ns Impedance: 1 M ~ nominal, shunted by < 50 PF. Triggering: Adjustable in 20-mV steps. Range, _+5.00 V MEASUREMENT MODES

Function Frequency A and B a

Range 125 to 500 MHz (8 kHz to 500 MHz) b

Ca

100 MHz to 2 GHz 250 to 500 MHz (A and B), 16.0 kHz to 500 MHz (A and B)]b; 100 MHz to 2 GHz(C) 2 ns to 8s (2 ns to 131~) a

AandB, AandC, BandC, A+B,A+ C, B - A, C - A , B + C, C - B, A / B , B / A , A / C , C / A , B / C and C / B Period A and B a Ca AandB, AandC, BandC, A+B,A+C, B-A,C-A,B+ C,C-B,A/B,B/A, and A / C , C / A , B / C , and C / B Totalize A, B, A and B, A + B, A - B, B - A, A / B, and B / A Time interval A, B, A ~ B, and B ~ A Continuous time interval A and B a _+Time interval ( _+) A --* B, B ~ A, A and B Time deviation A and B a Rise and fall time A c Positive and negative pulse width A C Duty cycle A C Phase A rel B, B rel A, A and B a Peak amplitudes A and B

500 ps to 10 ns 2 ns to 4.0 s (A and B) [2 ns to 65 tzs (A and B)]a; 500 ps to 10 ns (C) 0 to 232 - 1 events, each channel 10 ns to 8.0s (10 ns to 131/~s) b 100 ns to 8.0 s (75 ns to 131 ~s) a - 4.0 to + 4.0 s including 0 ( - 65 to + 65/zs, including 0s) b 100 ns to 8.0 s (75 ns to 131 ~t/~S)b 1 ns to 100/zs (autotrigger) 1 ns to 1 ms (autotrigger) 0 to 100% for pulse widths > 1 ns and periods < 1 ms (autotrigger) Period < 4s ( < 65/zs) b 1 kHz to 200 MHz, 200 mV peak to peak to 2V peak-to-peak

aThe maximum sample rate for these measurements is 10 MHz (100 ns) and up to 13.3 MHz (75 ns) using the HP 5372A fast measurement mode. For all other measurements the maximum sample rate is 5 MHz (200 ns) in the normal measurement mode and 7.4 MHz (135 ns) in the fast measurement mode. bFast measurement mode values. CRequires 8 ns of setup time between each measurement.

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Aksel Kiiss

INPUT PODS

HP54002A

HP54001A

H P 5003A with 10:1 probe

H P 54003A without 10:1 probe

Coupling

DC

DC

DC

DC

Input capacitance (nominal)

N/A

2 PF

8 PF

10 P F

50 1)

10 k l )

1 MI~

1 Mf~

DC to 500 M H z

DC to 500 M H z

DC to 300 M H z

D C to 300 M H z

_+2 V

_+20 V

_+20 V

+_2V

Input resistance (nominal) Bandwidth ( - 3 dB) Maximum input voltage (xl)

Specifications INPUT SPECIFICATIONS

Frequency range Sensitivity (GHz) 0.5-12.4 12.4-20 0.5-26.5 (options 026 and 040) 26.5-40 (option 040) Maximum input Damage level

Connector (standard) (options 026 and 040)

SWR (typical) (GHz) 0.5-10 10-20 20-26.5 (options 026 and 040) 26.5 -40 (option 040)

Input 1 (50 f ~ ) 500 MHz - 20, 26.5 and 40 GHz

Input 2(1 MI), 11, 70 PF) 10 Hz-80 MHz

Input 2 (50 12) 10 MHz-525 MHz

25 mV rms

25 mV rms

- 28 dBm - 23 dBm - 20 dBm dBm = 0.37 x f (GHz) - 29.8 + 7 dBm + 25 dBm

Type N, female, 2.92 mm, and male, ompatible with APC 3.5 and Type A < 2:1 < 3:1 < 3:1 < 3.5:1

1 V rms + 10 dBm DC < 5 kHz, 250 V(DC + peak AC); DC > 5 kHz, 5.5 V rms + 1.25 10 +6 V r m s / (frequency) BNC, female (with replaceable fuse)

NA

NA

551

17. Microwave Instrumentation and Measurements

Frequency (Input 1) Automatic acquisition: 500 MHz-20 GHz, 500 MHz-26.5 GHz (options 026 and 040), and 12-40 GHz (option 040, high band), for CW and pulses > 100 ns. Manual acquisition: For 500 MHz-1 GHz, the entered value equals the input signal _+ 3 MHz; for 1-30 GHz, the entered value equals the input signal _+20 MHz; for 30-40 GHz, the entered value equals the input signal _+10 MHz; and for pulses < 100 ns, the entered value equals the input signal _+3 MHz. Least significant digit: 1 MHz to 1 Hz for frequency and 0.001 Hz for PRF Residual stability: 0.3 LSD rms typical for 1-Hz resolution at 25°C and 0.7 LSD rms for 26.5-40 GHz (option 040), when the counter and source use a common 10-MHz time base or when the counter uses an external high-stability time base.

Pulse Frequency Measurements Pulse width (minimum): 60 ns ( < 100-ns mode, manual acquisition) and 100 ns (autoaquisition) Pulse representative frequency: Minimum (low-PRF mode), 1 Hz (0 to 30°C), and minimum /maximum (default), 50 H z / 2 MHz O n / o f f ratio (typical): > 15 dB Maximum video (typical): > (signal level + 20 dB) TABLE 7 Pulse Acquisition Time a

Pulse width M a n u a l acquisition ( < 100 ns) 100 to 250 ns 250 to 500 ns 500 ns to 1.00 ~ s 1.0 to 5.0 ~ s > 5.0 ~ s

K~ 10 1200 250 120 30 12

K 2 ms (high band, option 040) 180 1700 360 (1700) 360 (1700) 360 360

Note. P u l s e / C W assess, 780-1300 ms. ( J x K1) x P R I + K 2 (ms) + assess, where J = 1 unless the signal carrier frequency is moving, in which case J = 10; the P R I minimum is 200 /zs for equations; and assess needs to be added only when a change from p u l s e / C W is made. F o r example, a P R I of 1 ms, a pulse width of 10 ~s, and a resolution set to 10 kHz, for a standard H P 5361B using automatic acquisition, gives a gating time of (3) × (1 ms + 0.4 ms) = 4.2 ms, an acquisition time of (1 × 1 2 ) × 1 m s + 3 6 0 ms=372 ms; and a m e a s u r e m e n t time of 4.2 ms + 372 ms + 200 ms = 576 ms.

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Aksel Kiiss

kk z ~,oo~

3000 1000

\ \ ~

100

\ ~,o lOns

lOOns liJs lOps lOOps 1ms PulseWidth/ExternalGateWidth/ Internal ProfileGateWidth

lOms

Graph 3. Resolution number of pulses (N)-vs, pulse width/external gate width/internal profile gate width. Gating time = N(PRI + 0,4 ms),The PRI minimum is 200 s for equations,

FM chirp tolerance: Manual acquisition 50 MHz peak to peak (when the entered value equals the center frequency _+1 MHz); auto acquisition, 10 MHz peak to peak Rise,/fall time (typical, to remain in the pulse mode): < 20/~s Measurement time (typical): Gating time + acquisition time + 200 ms (Graph 3) and Table 7) Resolution: 1 Hz-1 MHz (Graph 4) Accuracy: Time base uncertainty (Graph 5) + gate error (Graph 6)

1 MHz

10 kHz

~

with SmoothingOn

Maximum Resolution

" ~

10 Hz

1 Hz lOns

lOOns

lps

lOIJS

lOOps

1ms

lOms

Graph 4. Maximum resolution as a function of pulse width/external gate width/internal profile gate width.

553

17. Microwave Instrumentation and Measurements

10MHz 1 MHz

xx

100 kHz

\

10kHz

40 GHz

1 kHz

20GHz ~ ~ . -

100 Hz 10 Hz 10ns

100ns

lps

10ps

100ps

1ms

10ms

Graph 5. Maximum gate error as a function of pulse width/external gate width/internal profile gate width. 100kHz 1 kHz 10Hz ,

," '~ ~~~'°"~,x,~

~'

II,, II

100mHz o ==

1 mHz

iliI ilit

10pHz 0.1pHz

~

0

I 1K

Jill 100K

10M

Input Frequency (Hz) Graph

6.

1G

20G 26.5G 40G

Time base uncertainty.

CW Frequency Measurements

AM tolerance (typical): < 40% to 5 kHz; < 16% above 5 kHz FM deviation [typical (see Graph 7)]: Manual acquisition (when the entered value equals the center frequency +_1 MHz), 60 MHz peak to peak and 55 MHz peak to peak (option 040); automatic acquisition 20 MHz peak to peak and 12 MHz peak to peak (option 040) FM rate (maximum): 10 MHz Tracking speed: Fast acquisition track, 800 M H z / s ; normal FM rate, 1 M H z / s ; and, low FM rate, 80 k H z / s Acquisition time (manual acquisition): < 40 ms Acquisition time (automatic acquisition): Fast acquisition track, < 100 ms; normal FM rate, < 170 ms; and, low FM rate, < 1.3 s

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Aksel Kiiss

20 MHz m,

a. 12 MHz z _o u~ l

15kHz

r[

O0 kHz

sss e ss, , ss Is ,$s I

DC

.33 Hz 7.5 Hz 2.2 kHz

i 45 kHz FM LOW 10 MHz 1 kHz FMNORMAL 10MHz 300 kHz TRACK 10 MHz RATE

Graph 7. FM rate vs deviation rate.

Gate times (1-Hz resolution): For 500 MHz-5.7 GHz, 200 ms; for 5.7-11.3 GHz, 400 ms; for 11.3-16.9 GHz, 600 ms; for 16.9-22.5 GHz, 800 ms; and for > 22.5 GHz, 1000 ms Measurement time (typical): Gate time + acquisition time + 100 ms Resolution: 1 Hz-1 MHz, selectable Accuracy: +_1 LSD rms _+ time base uncertainty (Graph 6)

Profile (Input 1) Frequency range (minimum/maximum for the y axis; see FM chirp tolerance for the span): 500 M H z / 2 0 GHz, 500 MHz/26.5 GHz (option 026), and 500 M H z / 4 0 GHz (option 040) FM chirp tolerance (maximum span for the y axis) Manual acquisition, 50 MHz peak to peak (when the entered value equals +_1 MHz of the center frequency); auto acquisition, 10 MHz peak to peak Time range (minimum/maximum span for the x axis): 100 n s / 1 0 ms Time resolution: 1 ns Internal gate width: Minimum, 11 to 23 ns; typical minimum, 14 ns; and maximum, 10 ms External gate width (Minimum): Manual acquisition, 20 ns; auto acquisition, 60 ns Gating/arming: Pulse, internal, external arming, and external gating; CW, external gating Number of data points: Auto profile, up to 75; manual profile, 1 to 99

555

17. Microwave Instrumentation and Measurements

Profile Frequency Measurements Frequency resolution: Selectable, 1 Hz to 1 MHz, and dependent on the internal profile gate width (Graph 4) Printers supported: ThinkJet (HP 2225A), QuietJet Plus (HP 2227B), and PaintJet (HP 3630A, option 002)

Profile phase measurements A computer is required.

See Application Note 377-4 for details.

PULSE PARAMETERS (INPUT I)

Minimum / Maximum LSD Accuracy a (100 average)

Pulse width

PRI

Offtime

60 ns / 10 ms

500 ns / 1 s

400 ns / 1 s

(PW < 1 ms)-I ns; (PW > 1 ms)-100 ns +(20 ns + timebase error × measurement) _+LSD

PRF 1 Hz / 2 MHz To 0.001 Hz +(20 ns) × (PRF) 2 +_LSD _+ timebase uncertainty

Note Measurements are approximately 6 dB below the signal peak. aFor r i s e / f a l l times < 20 ns.

Time Interval Measurements Least Significant Digit Displayed: + -

200 ps ~

'

where N is the number of measurements averaged. Resolution" 150 ps rms _+ start trigger error + stop trigger error

where the start and stop trigger errors are illustrated in Graph 8. Accuracy: _+resolution _+ (time base aging × time interval) + trigger level timing error + 1 ns systematic error,

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Aksel Kiiss

Input Noise (random)

//

1 ms

100 ns Q

•1,1J I=

10 ns

.s+,y

o O.

._~

1 ns

|

w 100 ps

i 10 ps

1 ps 10 mV

100mV

1 mV

10 mV

100 mV

1V

Input Signal Noise (rms) Graph 8. Noise on the input signal will add uncertainty to time-interval measurements.

where the time interval is illustrated in Graph 9 and the trigger level timing error is illustrated in Graph 10. The systematic error can be reduced to < 10 ps with the HP J06-59992A Time Interval Calibrator.

Time Base Aging (systematic) 100 ns

10 ns

/

•~1

°

;

!/

,000s 1 ps 1m s e c

/

4-, ,,..~ ~/-

lOmsec

lOOmsec

100 msec

10 msec

Measured Time Interval

Graph 9. Time base crystal aging affects time interval measurements.

557

17. Microwave Instrumentation and Measurements

Trigger Level Timing Error(systematic) 1 ms

100 ns

•

-¢= I,M

10 ns

a_

~

1 ns

°-

|

m lOOps

\

10 ps

lps 100 mV/ms

1 V/ms

10 100 mV/ns mV/ns Input Signal Slew Rate

1 V/ns

10 V/ns

Graph I0. Trigger level timing error varies with the input signal slew rate, Uncertainty is associated with both start and stop edges,

Graphs 3, 4, and 5 may serve as an aid to quickly determine the approximate resolution and accuracy of a time interval measurement. EXAMPLE: Measure a single 500-ns interval, from a l-V, 10-ns rise time edge to a 1-V 10-ns edge (time interval, A --* B). The input signal noise (in a 500-MHz bandwidth) is 1 mV rms. It has been one year since time base calibration. The time interval resolution is influenced by trigger noise from the input signal (as well as the signal slew rate) and the internal timing jitter of the HP 5372A (150 ps rms). As shown in the resolution equation, averaging could be used to improve measurement resolution results ( v ~ ) . From Graph 8 it can be determined that the trigger noise contribution for both the start and the stop edges is approximately 10 ps rms. The single-shot time interval resolution is then _+(150 ps rms + 10 ps rms + 10 ps rms) = _+ 170 ps rms. To determine the accuracy of the time interval measurement, you must add time base aging effects, trigger level timing error, and internal systematic uncertainties to the resolution uncertainty. The time base aging uncertainty for this example is much less than 1 ps and can therefore be considered negligible (Graph 9). Graph 10 shows that the trigger level timing error uncertainty is also well below 1 ps. Once again, this effect is negligible with respect to resolution and internal systematic uncertainties.

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Aksel Kiiss

From the above equation, the total accuracy uncertainty is then approximately + 1.17 ns. Clearly, internal systematic uncertainties are the dominant effect in this measurement. This is due to differential path delays within the HP 5372A, as well as possible differential path lengths in the external measurement setup. The HP J06-59992A Time Interval Calibrator can be used to measure these systematic uncertainties. These uncertainty values can then be subtracted from results, improving measurement accuracy.

9. Measurement of Phase Noise Power Spectral Density An ideal signal source can be regarded as providing an output at a signal frequency or as an infinitely narrow line in the frequency domain. Unfortunately in the practical, real world, other factors enter the picture and degrade the performance of the frequency source. The infinitely narrow function assumption in the frequency domain applies only if the signal existed for an infinite time without any perturbations. Thermal, shot, and flicker noise randomly perturb the phase or frequency of the output signal. Since an oscillation is an inherently nonlinear physical phenomenon, it produces, besides the desired output signal, its harmonics. In a simple oscillator, the magnitude of the noise perturbations depends on the quality of the transistor and other active circuit elements used in the design and on the quality of the tuned circuit used as the frequency determining circuit element (Q of the circuit). As the complexity of the frequency source increases, other factors start to degrade the spectral purity of the signal. In frequency synthesizers, for instance, the output contains, besides the random noise perturbances, discrete outputs. These outputs are the result of frequency conversions and translations between the various signals which are necessary in the design of frequency synthesizers. In this discussion we will establish a simple theoretical basis for general noise perturbations in an oscillator. A signal can be mathematically represented by v(t) = [v 0 +

e(t)]sin[27rfot + A~b(t)],

where e(t) represents random amplitude variations and A~b(t) represents random phase variations. The random amplitude variations are less important in system applications. For instance, in a superheterodyne receiver, the amplitude fluctuations of a local oscillator are suppressed by the double balanced mixer.

559

17. Microwave Instrumentation and Measurements

The phase variations, on the other hand, are directly transferred from the local oscillator to the signal. For these reasons, and also for the much wider use of phase or frequency modulation in information transmission systems, the phase noise perturbations have a more pronounced degrading effect on the overall system performance. Assume that a small baseband noise voltage in a 1-Hz bandwidth at fm, with an amplitude of a l(t), is frequency modulating a carrier at frequency f0; then the instantaneous random frequency can be expressed as w = w 0 q- A w c o s w m t

,

where Aw = a(t)xc, where c is a modulation sensitivity constant of the oscillator. It should be noted that zXw itself is a voltage with random amplitude variation and with statistical peak and RMS values. The time varying signal can be expressed as

(

f ( t ) - A cos w0t +

sin Wm

Wmt

)

Aw =/3 - modulation index. Wm

This function can be expressed in the frequency domain as an infinite series of frequencies, + n , from the carrier f0. Their amplitudes are related to the corresponding Bessel functions. Since in our case/3 << 7r/2, we can use the narrow-band FM approximation in which only the carrier and the first sidebands, f0 -+ fm, exist. The amplitude of the carrier is A, and the amplitude of the sidebands is (A/2)Jl(13). But since /3 << r r / 2 , we can approximate J~(13)=/3/2. The amplitude of the sidebands becomes (A/2)(Aw/wm). Thus we can write the waveform (t) =A

cosw0t-

2w---~[ c o s ( w o -

Wm)t- COS(W0 +

Wm)t ] ,

and the ratio of phase noise spectral density to the carrier level can be expressed as AW AWrms 2 0 l o g 2Wm = 2 0 l o g ¢2Wm .

This is defined as the single-sideband noise power spectral density L(fm). Since it is a function of the random phase deviation Aw/wm, it is referred to as the phase noise power spectral density.

560

Aksel Kiiss

In addition to the multiplicative noise perturbations present in the oscillation process, degradation to the source performance can also result from external noise sources. The phase noise of a frequency source can be degraded by the thermal noise associated with amplifiers and frequency multipliers if the signal levels are allowed to drop below critical levels. For instance, if the output of a frequency multiplier is allowed to decrease to - 6 0 dBm and is then amplified by a 20-dB noise figure amplifier, the thermal noise floor is set at 94 dBc and no further improvement to the carrier-to-noise ratio is possible.

Short-Term Frequency Stability Phase Noise Measurement

Because of the extremely wide difference between the phase noise power spectral density and the carrier levels, utmost care must be taken to make sure the measured data relate to the device under test (Figures 16 and 17) and not to the limitations of the measurement setups. Quite often the phase and thermal noise limitations of the test setup are incorrectly interpreted as those representing the device under test. Below we will concentrate on three basic methods of phase noise measurement in general use in the industry and discuss their advantages and shortcomings. In the three methods of measurement, the sensitivity of the measurement is increased at the expense of the complexity of the test setup and

v1

~-~ v(t J

Figure 16. Delay line phase detector.

.~'- (t) - f I (t) x f2(t)

Figure 17. Phase detector.

17. Microwave Instrumentation and Measurements

.•

561

:- +voc (CLEN~I)

IIt

LOW-NOISE "-1 BASEBANDAMPL I

i',,T~m +

, --{zER

,I test

,oo.. ~ k _ RG214/U%

(TTIOli'U')/' ~ 0 VIX) l .. ,

'

'

~ ~-

°'v'°"l

~/

~ + l ' ' ' ~ . , . o . x l PDKTO1SPDK OREQUIVALENTPItASEDETECTOR

Figure 18. Typical delay line discriminator test setup.

1

I" SYNERGY~. fm=x'~a2 GHz STD. ~

/

UNDER TF~T

SECOND

SOURCE

J OREQUIVALENTPHASEDETECTOR

i

f BASEBANDAMPL, 5 HzTO5 MHz

.~

BASE-

Fo

"" /

-I THISAUXIUARYPHASE LOCKINGISUSEDWHENTHE SECONDSOURCEIS NOT COHERENTTO THEUNITUNDERTEST

"e

-I'I~ ..L ":'

I I I

~ 1 - - I ~

F

I I L

.

(71.5)

_ ~ .

.

.

.

.

OSclLLO-I

INTEREST

Figure 19. Typical phase detector two-source test setup.

the number of devices needed to perform the measurement. The necessary setups are shown in Figures 18 and 19; the approximate relative sensitivities of techniques are given in the following table. METHODS OF PHASE NOISE SPECTRAL DENSITY MEASUREMENT

Measurement technique Spectrum analysis at RF frequencies Delay line discriminator Coherent two-signal phase detector

Approximate sensitivity to L-band single-sideband phase noise at 10 kHz from the carrier (dBc) -110 - 140 - 180

562

Aksel Kiiss

The first method performs the actual measurement at RF frequencies, whereas the other two use carrier removal (nulling) and perform the measurement at the baseband (at the actual offset frequency from the carrier). Phase Noise Measurement with a Spectrum Analyzer The spectrum analyzer is the easiest and most direct method of phase noise spectral density measurement. Since it measures two quantities with wide differences in their levels, care must be taken to make sure that when measuring the carrier level one is still within the specified dynamic range of the test instrument and not in the saturation region of its RF front end. When measuring the phase noise spectral density, one has to ascertain that the test results represent the performance of the device under test and do not contain noise contributions from the test setup. There are two possible noise sources resulting from the spectrum analyzer. First, since the phase noise of the spectrum analyzer is directly imparted to the signal under measurement, it should be at least 10 dB below the phase noise spectral density of the device under test. Second, the phase noise spectral density is always referenced to the carrier level (dBc), but the spectrum analyzer input is limited by its noise figure. It is not uncommon to find spectrum analyzers with 30-to 40-dB noise figures at higher RF frequencies. Thus, if one tries to measure phase noise at a carrier level of - 4 0 dBm, the thermal noise floor of the spectrum analyzer is at - 134 dBm with a 40-dB noise figure. Any attempt to measure signals below the 94-dBc level will result in meaningless data. Another uncertainty results from the resolution bandwidth and its relation to the noise bandwidth of the spectrum analyzer. Normally manufacturers specify the applicable correction factors. Also, an important factor is the skirt selectivity of the frequency resolution determining filter (bandwidth). Normally the narrowest bandwidth in a typical spectrum analyzer is 10 Hz. If one attempts to measure the phase noise spectral density at 10 Hz from the carrier, one faces two problems. First, the frequency resolution at 10 Hz is equal to the bandwidth. Second, if the filter does not have sufficient rejection of the carrier, one measures the carrier contribution and not the actual phase noise level at 10 Hz from the carrier. Also, the measurement accuracy depends on the accuracy of the logarithmic amplifier and the accuracy of the RF input attenuator. Before interpreting the test results and determining performance limits, one has to take all the above factors into account. In general it can be said that the spectrum analyzer method gives conservative test data. If all the precautions and correction factors are properly applied, it can safely be interpreted as worst-case test data.

17. Microwave Instrumentation and Measurements

563

With modern-day microprocessor-controlled spectrum analyzers, both the single- and the double-sideband phase noise spectra can be displayed, recorded, or both. The microprocessor applies all of the correction factors (noise bandwidth, logarithmic detection, etc.) and displays the phase noise spectral density as a function of frequency in d B c / H z from the carrier.

The Delay Line Frequency Discriminator Method One of the advantages of the delay line phase detector method of phase noise measurement is cancellation of the high-level carrier by the phase quadrature of the two-phase detector inputs. This cancellation eliminates the need for the wide dynamic range setup that was required in the RF spectrum analyzer method. Since the delayed signal is always coherent to the undelayed signal at the phase detector input, measurements can be performed on free-running oscillators without having to resort to phase-locking techniques. The measurement is performed in two steps, as shown in the test setup in Figure 18. First, the oscillator under test is frequency modulated with a baseband signal at a frequency (fro) offset from the carrier for which the phase noise spectral density measurement is to be made. To preserve the small index of modulation requirements, the sidebands should be approximately 30-40 dB below the carrier. This ratio is measured for the RF spectrum analyzer and recorded. This measurement establishes the phase noise spectral density (Aw/w m) to carrier reference. This level of the modulating signal is also measured at the phase detector output on the baseband spectrum analyzer and recorded at frequency fm" The second step removes the modulating signal and measures the actual noise power spectral density at fm on the baseband spectrum analyzer in decibels. The sum of the two ratios in decibels with appropriate correction factors (noise bandwidth vs resolution bandwidth, noise detection by the logarithmic amplifier, etc.) results in the single-sideband phase noise-to-carrier power ratio. It can be shown that the theoretical measurement sensitivity of the technique is directly proportional to the delay of a lossless delay line (a detailed analysis can be found in Hewlett-Packard's Application Note 11729B-1). In a practical measurement setup, two constraints limit the sensitivity. One of the constraints is imposed by the assumptions and approximations used in the derivation. This limits the offset frequency fm to < 1/z. The other constraint is the insertion loss associated with any physical cable. The HP application note concludes that the optimum cable length is 1 with an 8.7-dB loss. Since the loss of the cable increases as a function of frequency, the adaptability of the method is limited at higher microwave frequencies by the losses associated with the delay line.

.$64

Aksel Kiiss

For easy reference, a summary of the mathematical derivation with a lossless cable follows. Let the two signals at the phase detector input be U1 = ~COS W ( t -- 7") + -~m COSWm ( t -- T)

1

V2 = ~ COS w t -- ~

COSWmt .

The desired output after some mathematical manipulations is

af

v ( t ) = k2- 7 - sin(rrfmr ) sin 2rrfm(t - r / 2 ) /m for 1 fm < ~ . 2rrr

Let Av = k 2 r r r A f , where k is the phase detector constant, A f is the peak frequency deviation in a 1-Hz bandwidth, and Af rrrfm Av = k 2-~m sin(rrfmr) = k 2 rr J sin rfmr = k 2 rr rA f . The Phase Detector Method The phase detector method is the most sensitive of the three presented here. Its drawback is that more than one source is required to perform the measurement. In the application described, we assume two sources with equal phase noise power spectral densities. However, the method can be used with a reference source with far better phase noise performance than that of the device under test, or it can be extended to involve three similar devices. As the first step of the measurement, the test setup is calibrated by establishing the carrier reference level. This can be done by offsetting the two sources or by phase locking them to slightly different frequency reference sources and then measuring the level of the difference frequency on the baseband spectrum analyzer. In the next step, the two sources are phase locked to the same reference signal in a narrow-band phase-locked loop. The loop bandwidth should be below the lowest offset frequency at which the phase noise spectral density is to be measured to avoid noise cancellation within the loop bandwidth that can result in erroneous data. The two inputs to the phase detector are adjusted to be in phase quadrature (carrier null), and the phase quadrature condition is maintained for the duration of the

565

17. Microwave Instrumentation and Measurements

m e a s u r e m e n t (by monitoring the pC level on the oscilloscope). T h e phase noise spectral density is m e a s u r e d directly on the spectrum analyzer. Possible sources of error that can d e g r a d e the accuracy of a measurem e n t are the phase detector conversion loss, the noise figure of the low-noise b a s e b a n d amplifier, and the i n h e r e n t phase noise of the baseb a n d spectrum analyzer local oscillators. A very short summary of the mathematical analysis of the m e t h o d follows. A s s u m e that two signals, AW 1

f l ( t ) = A 1 COS W1t +

sin w m wm

f z ( t ) = A 2 cos

Wzt +

AW 2

)

sinwmt Wm

,

are applied to a phase detector. T h e phase detector will multiply the two signals. T h e o u t p u t will consist of two terms: W 1 -- W 2 W 1 -~t-w 2 .

T h e difference t e r m is of interest to us:

f ( t ) =A1AzCsin[(

]

AW 1

sin w mt .

sin w mt

w 1 -- w 2 ) t +

Wm

Wm

If w 1 = w 2 (phase-locked condition), then AW 1

fo(t) = A1A2C sin

AW 2

sin wmt

)

sin wmt .

Wm

Wm

Since Aw~ << l s i n ® -- ® Wm

and we obtain Aw fm(t)

AW 2

sin Wmt

-- A I A z C Wm

)

sin Wmt , Wrn

A1AzC is the carrier level reference established with w 1 --

W 2 = AW, If we let Aw = w 1 - w 2 be within the frequency b a n d of interest, then the amplitude of the carrier (neglecting Aw/w m terms) becomes A1AzC , and the amplitude of the noise voltage in a 1-Hz bandwidth consists of two

566

Aksel Kiiss

terms,

Within the loop directly. Outside by independent uncorrelated and carrier is

AW 1

AW 2

Wm

Wm

bandwidth, these voltages are correlated and subtract the loop bandwidth, the noise perturbations are caused random noise sources and are, therefore, completely add randomly. The ratio of each of the sidebands to the

AW 1

AW 2

Wm

Wm

If we compare this amplitude with the amplitude resulting from the RF spectrum analyzer measurement, we observe that the voltage is higher by a factor of 2. Thus the power spectral density is 20 (log 2), or 6 dB higher. The second uncorrelated but equal signal increases the total noise power spectral density by an additional 3 dB. The above observations are the basis for the 6- and 3-dB correction factors tabulated in the test setup descriptions. The procedure for calibration follows. 1. Set the baseband generator at the frequency of measurement fm (for instance, 10 kHz). Adjust the amplitude for the 40-dB sideband level on the RF spectrum analyzer. Adjust the phase shifter 19 for 0 V of output on the oscilloscope. 2. Ascertain that the low-noise baseband amplifier is in the linear operating region. If necessary, adjust the level of attenuation (a) and record the change. Record the baseband analyzer resolution bandwidth B R. 3. Establish the sideband reference level on the analyzer at fm" Remove the baseband modulating signal fm and readjust the attenuator (a) to its original position and record the phase noise level N. 4. The noise spectral density is given by L(10 kHz) ( d B c / H z ) = - ( 4 0 + a + N + 10 log B N) + 2.5. The 2.5-dB correction is the result of logarithmic detection of noise. To correlate the noise bandwidth with the resolution bandwidth, consult the spectrum analyzer manual. For the Tektronix 7L5 the noise bandwidth B N = 0.7 × the resolution bandwidth B R. The procedure for calibration follows. 1. Frequency offset the two sources under test by fm and measure and record the level of the offset frequency fm on the baseband spectrum analyzer (PB).

567

17. Microwave Instrumentation and Measurements

2. Reestablish coherency adjust the phase shifter ® for 0 V of output. Measure the noise power (Pw) at fm within the established resolution bandwidth of the baseband analyzer. 3. The phase noise spectral density is given by L(fm)(dBc/Hz)Pw - PB - 10 log B N + 2.5 - 6 - 3. B N is the noise bandwidth. To correlate the noise bandwidth with the resolution bandwidth, consult the spectrum analyzer manual.

Integrating Phase Noise In some system analysis and applications the total noise power in a given information bandwidth might be required. This can be determined by integrating the total noise power spectral density over the total bands of interest (Figure 20). The L(f) can be characterized as a piecewise linear curve: K3 fl

L(f)

=

K 2 f2

K1 f3

f4

I+ I+ I+K01 -f~3 f ° Z f I Z f 2 f3

This quantity can be obtained directly from the oscilloscope readout in the test setup for phase noise measurement. If the oscilloscope bandwidth is wider than the noise integration bandwidth and if its noise does not add significantly to the output, then the peak or rms noise output represents the integrated noise. By using the reference calibration level, one can easily obtain the integrated noise-to-carrier ratio (dBc). Once the K's are determined (over their applicable regions), the basic definitions can be applied. Phase jitter: ®rms = V~fabL(f)clf in radians rms Residual VM jitter: A f rms = ~/~ f~L(f)f 2 df in hertz rms Noise-to-carrier ratio:

f3 2 Ko

Fo OFFSET FREQUENCY (Hz)

Figure 20. Piecewise linear phase noise power spectrum.

568

Aksel Kiiss

SHORTTERM FLUCTUATIONS

AGING

z

0,,~, z

j

0

<>-.> o," 0

I,

z

z

~ N5 2~ u_

I

10

I

I

100

1K

SAMPLE TIME (SECONDS) Figure 21. Long-term frequency stability.

2.1abL( f f) df

noise power carrier power

=

carrier power

in decibels

Long-Term Frequency Stability (Figure 2 I) So far we have limited our discussion to short-term perturbations of the output signal. In practical systems one has also to consider the effect of frequency changes over long periods of time. These variations are normally caused by component aging or component variations as a function of time. In the time domain, spectral purity is characterized by fractional frequency deviation. Frequency stability in the time domain is given by the Allan variance; 0 y ( r ) . 0y(r) is the statistical deviation of the fractional frequency fluctuations A f / f 0 over the interval of time T1 and for M samples. M

Allan variance & ( y ( r ) ) 2 ~ 2 ( M - 1) ~

2

(Yk-1 -- Yk)

K=I

af

Y = average-~-0 over time interval r. Crystal oscillators that are used for high-stability requirements have aging rates of 0.2 to 0.3 p p m / y e a r , whereas less stringent crystal oscillators have aging rates of 2 to 3 p p m / y e a r .

CHAPTER

18 Microwave Mathematics James Richie

I. P r e l i m i n a r y Definitions V e c t o r fields and matrices are in bold, and • denotes a complex conjugate. Unit vectors are written as ~?~. The complex number j=¢-l.

(1)

1 if ijk are an even permutation; it equals - 1 otherwise. 6ik is the Kronecker 6 function. ~ik is 1 if j = k; it equals 0 otherwise.

6.ij k is the Levi-Civita antisymmetrical symbol. Eij k

-

-

Phasor Notation and Fourier Transform [7, 14, 41, 46] Phasor notation is shorthand for frequency domain quantities. An example solution to the wave equation, A 0 cos(kx + w t), is written as A o cos(kx + ~ o t ) = IAolRe(e j(kx+'°'+~)) = IAole j(1'~+~) =Ao ejk~, (2) where IAol is the peak value, Ao-

Handbook of Microwave Technology, Volume 2

IAole jo,

569

(3)

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

570

James Richie

a n d e j°°t is assumed. Phasor notation implies harmonic analysis in which w is fixed. The Fourier transform relates the frequency domain with the time domain quantities:

f(t)

-

f_of(aJ)eS'°t

~

oo

do)

=

f-

f(t)e-S°°t dt

(4)

or

f(t)

=

,.~"-l[f((.O)]

f'(o))~- ~[f(t)].

Tables 1 and 2 summarize the properties of the Fourier transform.

TABLE I Properties of Fourier Series •Y r ( a g + ~ h ) = a,Yr(g) + ~.Yr(h)

Linearity

1 (o) 1

~-[g(at)l = -~-

Similarity

g -a

~ - ( g [ t - al) - ~ - ( g [ ~ ] ) e -j~°2~'~

Shift in time

~

Igl 2 dt =

Parseval's T h e o r e m

f _ j , ~ " ( g ) ] 2 do)

Convolution T h e o r e m

Autocorrelation

TABLE 2 Time Derivatives in the Frequency Domain Time Domain

Frequency Domain

0 Ot 02

jw ~0) 2

Ot 2

571

18. Microwave Mathematics

2. Mathematical Functions for Microwave Engineering Complex Functions [2, 6, 9, 35, 42, 44] Analyticity W( z ) = U( x, y) + j V ( x, y )( z = x + jy ) is a n a l y t i c if t h e r e exists t h e derivative

w ( ~ + h) - w ( ~ ) F'(z)

= lim

h

"

E q u i v a l e n t l y , W ( z ) m u s t satisfy t h e C a u c h y - R i e m a n n

OU Ox

OV =

Oy

OV and

relations:

OU =

Ox

(5)

Oy

.

(6)

Singularities and Cauchy's Integral Formula W ( z ) is n o t a n a l y t i c at s i n g u l a r p o i n t s . C l a s s i f i c a t i o n o f s i n g u l a r i t i e s is g i v e n in T a b l e 3 a n d C a u c h y ' s i n t e g r a l f o r m u l a is

f ' " ) ( a)

n! ,,c,

f(z)

T ~ j ~c (~ - a) ~+1

dz

n = 0,1,2,...,

(7)

TABLE 3 Types of Isolated Singularities (at z = z0), with Examples

1. nth-order pole

lim (z - Zo)nf(z) = A 4:0 Z---~ Z 0

Example 2. Branch points

Example 3. Removable singularity

1 (Z + 3) 4

fourth-order pole at - 3

Function is multivalued if encircling a branch point (z - 7) ~1/2) has a branch point at z = 7 lim f(z) exists Z---~ Z o

Example

sin(z)/z

4. Essential singularity Example

Singularities that are not poles, branch points, or removable exp(1/z)

5. Singularity at infinity Example

Characterized by investigating f(1 / w) at w = 0 f(z) = z 3 has a third-order pole at infinity

572

James Richie TABLE 4 Short Listing of Contour Integrals for the Evaluation of Real Integrals

Integral

Method

Contour

Solve ~cF(z) dz

See Figure 1

z = e j° dz = je j° dO

Unit circle

f Z F ( x ) a~ 2~F(sin O, cos O) dO

Z --Z -1

sin 0 =

Z +Z-

cos 0 =

2j

2

Solve ~cF(Z) dz Solve ~F(z)d jmz dz

f ~c F°( xs) [_ sin mxmX]dx

See Figure 1

Note. F(~) is rational in every case.

y

Iz

(3

,

>

x

Figure I. Contour used to evaluate some of the integrals in Table 4.

where f(z) is analytic inside C and O! = 1. Cauchy's integral formula may be used to evaluate definite integrals. See Table 4 and Figure 1.

Dispersion Relations [20; 30, p. 3111 Functions, f, analytic in the lower half plane, where f( z) =fl(Z)

-- j f 2( z ) ,

(8)

where fl and f2 are real functions, also satisfy 2 fl(Z)

= 77"

) dz' foooz'f2(z' Z t2 -- Z 2

f2(z)

2 dz' • 2 fo z,2 Z'f l(-- Z') Z

7I"

(9)

573

18. Microwave Mathematics

Residue Theorem A residue is given by (equivalent to a _ 1 in Laurent's series under series representations): 1

r~ = lim ( k

d k-1

1)! d z k - 1 r[(z --

z ----->a

a)~f(z)]:

(10)

The residue theorem states that, given f ( z ) inside some contour C which is analytic except at singularities a, b, c , . . . , ~f(z)

(11)

dz = 2rrj(r a + rb + rc + "'),

where r a is the residue at a, etc.

Principal Value Integrals [30, p. 368] Let F ( x ) be continuous on a < x _< b except at x 0. For el, e 2 > 0, bF(x)

dx -

lim

o ~lF(x) dx +

E 1 ---+0 E2 ---+ 0

Jx

F(x)

dx ,

(12)

0+e2

where ~4a denotes the principal value. Series Representations [35]

See Table 5. The Laurentz series is given in an anulus as shown in Figure 2, a_

f(z)

= a 0 + a l ( z - a) 2 + ' ' '

1

a_ 2

+ z - a + (z-a)2

+ "",

(13)

where f ( s ¢) a n = q~ ( ~ - - a ) n + l ds¢:

(14)

Jc

and the contour C is the union of C 1 and C 2. Convergence tests for the series are given in Table 6.

Generalized Functions [5, 39] Dirac ~ Function: ~(~) The definition, representations, and properties are given in Tables 7, 8, and 9.

574

James Richie TABLE 5 A Collection of Series Expansions for Functions, Including Examples x -- a ) 2

Taylor

x

f ( x ) = f ( a ) + (x - a ) f ' ( a ) + ~ f " ( a )

-- a) n

f(n)(a)

+ ... +

/ f(a + h,b + k)=f(a,b)

+ [h--

+...+--

( X + y ) n = X n ..[_ n x n - l y

f(x,

Y)I x=a

o)_?

y =b

n

1 h--

Ox

n!

Binomial

"at- k - Oy

OX

+

+ k--

(x, y)l

Oy

n(n-

1)

x

n-2y2

x =a

+ "'"

2!

Coefficients

J) = k p(p-

(1 + x ) p = l ! px +

Examples (1

+X)

~

eX=l+x+--+

X

2

2! X

3

-- + 3~

1)

X

2

"'"

Ixl _< 1

1 -T-x - + - x e ~ x e " " Ixl ~ 1

-1=

Miscellaneous

sin x = x -

Jt k~(j-k)~

X

5

X

3

+ •..

3! x 4

X2

+

cos x = 1 2~

5~ X

2

ln(1 + x ) = x 2

3 X .3I_ . . . . .

3

4!

Ixl < 1

J

I

Figure 2. Anulus for the evaluation of Laurent's series.

y2 < x 2

575

18. Microwave Mathematics TABLE 6 Convergence Tests for the Evaluation of Infinite Series

lUnl ~

Comparison test

If Elvnl converges and

Ratio test

If 2im [ Un+-------~] = L, then --,o~

N t h root test

If lim

IVnl, then Evn converges also L < 1 converges L > ldiverges L = lfails

Un

n~/lUnl = L,

then see above

H ----~oo

Integral test

If

f(z) > 0 for

z > a, then E l ( n ) c o n v e r g e s / d i v e r g e s as

f f f ( x ) dx converges/diverges

Note.

In the ratio and N t h root tests, when L = 1, the behavior of the series cannot be determined.

TABLE 7 Defining Qualities of the Dirac 6 or Impulse Function coo

J

6(x)=O

d(x) dx = 1 for a l l x 4 : 0

TABLE 8 Commonly Used Representations of the Dirac 6 Function

6(x)

=

lim

6~(x)

a ----) O

1

a

6~(x)---a

for [xl < -2-

~(x) = 0 otherwise

_x2)

-1

7 1

~(x)

a

-

7/" t~ 2 +

X 2

f eJxtd,

576

James Richie TABLE 9 Useful Properties of the Dirac t~ Function 1.oo

J_/(x)t~(x)

f~f(x)[cx~(X_

= f(O)

- a) + c2t~(x - b ) ] dx = Cxf(a) + c2f(b) 1 6(ax) = ~--~S(x)

~(-x) = ~(x) N t~(X -- ai) g'(ai)

t~(g[x])=

~1 i=

where g(a i) = 0 for i = 1, 2 . . . . N t~2(X) and e ~(x) are not defined

Unit Step Function: 0(~) T h e definition, r e p r e s e n t a t i o n s , and p r o p e r t i e s are given in Table 10.

3. Vectors and Matrices [5, 13, 45] Definition A = [ajk], w h e r e 1 < j < n rows and 1 < k < m columns. If n = m, A is square. T h e ajk are, in general, complex.

TABLE 10 Definitions and a Representation for the Unit Step Function O(~:)

Definition 1

f?/(x)O(x)

dx = f o f ( X ) dx

Definition 2 dO -

~(x)

dx Representation (e > O) O ( x ) = lim O~(x)

a--~O oo e TM O~ = 2 - ~ f -oo ~t -d Jet 1

577

18. Microwave Mathematics TABLE II

A Partial Listingof Vector Properties Multiplication by a scalar Addition

cA = [cajk] A + B = [ ajk + bjk ]

Multiplication (A is m × n, B is n × I)

C=[ck~,k 2 ] = A B =

n

]~akljbjk 2 i s m × I j=l

[AB]C = A[BC]; [A + B]C = AC + BC;

AB 4= BA in general Transpose

AT = [a~j]

Identity (I is the identity matrix, ajk = 6jk)

IA=M=A

Trace

Tr[A] = Eakk, Tr[AB] = Tr[BA]

Exponentiation (A must be square)

e A= 1 + A +

Unitary matrix

A-1 = AIq implies that A is a unitary matrix

a: 2~

+ -..

Properties S e e T a b l e 11.

Determinant If A is s q u a r e , d e t A = [A[ = [JAil = ~

+_ a l i f l 2 i 2 . . ,

ani,,

(15)

w h e r e { i l , . . . i n} is a p e r m u t a t i o n of { 1 , 2 , . . . , n}, _+ is for e v e n a n d o d d p e r m u t a t i o n s , a n d t h e s u m is over all possible p e r m u t a t i o n s , d e t A B = d e t A d e t B d e t cA = c n d e t A.

Minor T h e m i n o r of ajk is d e f i n e d as an ( n - 1) × ( n - 1) matrix, M j k , by d e l e t i n g t h e j t h row a n d k t h c o l u m n . T h e c o f a c t o r of ajk is given by cjk = ( - 1)(J+k)det Mj~.

(16)

Inverse

A A - 1 = A - 1 A = I. If d e t A = 0, t h e n t h e i n v e r s e d o e s n o t exist ( A is called singular). T h e i n v e r s e of a m a t r i x can be f o u n d u s i n g m i n o r s : [ a j k ] -1 _ -

Ckj

(a7)

578

JamesRichie

Hermitian Adjoint AI-I = [AT]*. If A = An, then A is Hermitian. [AB]/-/= B/-/A/-/.

Commutator and Anticommutator [A, B] = AB - BA is the commutator of A and B. The anticommutator is {A, B} = All + BA. A B = ~ I[A,B] + I{A,B} [All, C] = A[B, C] + [A, C]B.

(18) (19)

Solutions f o r x in A x = Y

Cramer's Rule is

IA/I xs= IAI'

(20)

where A i is defined as the matrix obtained by replacing the i th column of A with the vector Y. Solutions f o r x in A x = 0

There is a trivial solution if x = 0. There is a nontrivial solution if det A = 0.

Eigenvalue Problem If A is an n × n complex matrix and if x is an n × 1 vector, then A is an eigenvalue of A with eigenvector xA if Axx = Axx or [A - Al]xx = 0 (the characteristic equation).

The Cayley-Hamilton Theorem Every matrix satisfies its own characteristic equation.

Derivatives See Table 12.

Tensors and Dyadics [5, 27] A tensor of rank two is an object with nine components defined within a given orthogonal coordinate system. A second rank tensor can be thought

579

18. Microwave Mathematics TABLE 12 Derivitaves with Respect to Vectors

d --(xHx) = 2x dx d --(xUy) = y

dx

d

--(yHx)

=

y

dx d - - ( x H Q x ) = 2Qx

dx

Note. x and y, are vectors, and Q is a matrix.

TABLE 13 Defining Properties of the Elements of a Group

1. Closure 2. Associativity 3. There exists an identity for each element of the group such that I g i = 4. There exists a unique inverse for each element of the group such that

gi

I

gig~

= gi 1 _

g7 l g i

--

I

of as an o u t e r p r o d u c t of two vectors. A vector is a t e n s o r of r a n k o n e and a scalar is a t e n s o r of r a n k zero. A dyad or dyadic is a s e c o n d - r a n k t e n s o r defined as the juxtaposition of two vectors: AB. O n e can o p e r a t e in the usual vector fashion from the left or the right.

Group Theory [24, 27, 39] A g r o u p is a set of e l e m e n t s , {gl, g 2 , . . . }, a n d a binary o p e r a t i o n with the p r o p e r t i e s in Table 13. G r o u p t h e o r y is mostly used to formalize s y m m e t r y conditions.

4. Vector Spaces [5, 12, 20, 33, 45] Definition m A set of e l e m e n t s , V m a field of n u m b e r s , F (complex, in general) m a binary o p e r a t i o n of addition m s c a l a r multiplication defines a vector space (with e l e m e n t s x, y, z) if ~x

+y

=y +x

- - ( x + y) + z = x ( y + z) - - a n identity exists such that x + 0 = x m f o r each x t h e r e exists - x such that x + ( - x )

= 0.

580

JamesRichie TABLE 14 Properties of Scalar Multiplication and Vectors

a(/3x) = (a/3)x a(x + y) = a x + ay lx=x (a +/3)x = a x +/3x Note. a and/3 are elements of F.

See Table 14 for f u r t h e r properties. Vectors ( e l e m e n t s of V) can be written as [x) (bracket notation)

Linear Independence A set (x1, x 2 , . . . ,

Xn)

a l X 1 -k- a

is linearly i n d e p e n d e n t if +

2 x 2 + "'" + a n X n = 0 =~ ogi

=

0Vi

is the only solution.

Inner Product A m a p p i n g from V × V ~ F is written ( y [ x ) = F. T h e dual vector is written (y[ = [/31,/32,''',/3n]- Thus, if Ix) = [a 1 , a 2 , . . . , an] T, t h e n ( y Ix) = F.,ai~ i, w h e r e the sum is from i = 1 to n. See Table 15.

Orthonormality Ix) and [y) are o r t h o g o n a l if ( x l y ) = 0. {X1, X 2 , . . . , set if ( x i [ x j ) = 6is.

X n}

TABLE 15 Properties of the Inner Product between Two Vectors

( x l y ) = (y[x)* (ax +/3ylz) = a(xlz) +/3(ylz)

(x[x) = 0

if and only if I x ) = 0

is an o r t h o g o n a l

581

18. Microwave Mathematics TABLE 16 Vector Inequalities

Ix] 2= (x x) ~ ~ lail 2

Bessel inequality

i=1 If { Ixi )) is complete, then equality holds

I(xly) _< Ix yl

Schwarz inequality

G r a m - Schmitt Process The G r a m - S c h m i t t process is used to find an orthonormal set of vectors, {]yi)}, from a linearly independent set, {Ixi)}. [Yl) ----

IXl) IIx~)l

[x2)- lyl)(yllx 2) ly2> = IIx2>- lya>l

(21)

Inequalities See Table 16.

5. Linear Operator Theory [5, 12, 20, 40, 45] In this section, a physical system is related to a vector space with an assumed basis.

Definition A linear operator, A, on a vector space, V(F), is a mapping from V(F), written as A(x) = z, which satisfies

V(F)

to

A(ax

+/3y) = aA(x) +/3A(y). (22) EXAMPLE: V is a set of polynomials, and operator D is a derivative of a polynomial" Ix(t))"

~ a i ti = x(t)

(23)

i

y(t)

= Dx(t) =

~_~iaiti-1. i

(24)

582

JamesRichie TABLE 17 Properties of Linear Operators

1. AO = OA = 0 2. AI = I A = A 3. A(B + C ) = All + AC 4. A ( B C ) = (AB)C 5. AB :/: BA 6. [A, B] = AB - BA (commutator)

Properties S e e T a b l e 17. T o p r o v e r e l a t i o n s h i p s for l i n e a r o p e r a t o r s , o n e m u s t a p p l y t h e o p e r a t o r to a m e m b e r o f V.

Inverse A n o p e r a t o r is i n v e r t i b l e if 1. for e v e r y l y ) in V t h e r e exists a n Ix ) in V s u c h t h a t Alx) -

ly)

implies

Ix) = A - 1 l y )

2. A Ix 1) = A Ix2) i m p l i e s Ix 1 ) --" IX2 >" EXAMPLE: T h e o p e r a t o r D for d i f f e r e n t i a t i o n is n o t i n v e r t i b l e . A c o u n t e r e x a m p l e is Xl(t) = t + 7; x 2 ( t ) = t + 3 D x I = 1 = D x 2. T h i s viol a t e s t h e s e c o n d r e q u i r e m e n t . F o r t h e o r e m s , s e e T a b l e 18.

Similarity Transformation U s e d to c h a n g e t h e basis of t h e l i n e a r o p e r a t o r . A u n i t a r y m a t r i x , M, is used: At --- M - 1 A M .

(25)

T h i s t r a n s f o r m a t i o n p r e s e r v e s t h e d e t e r m i n a n t a n d t r a c e of A.

TABLE 18 Theorems on the Inverse Operator

If A and B are invertible, then (AB)- 1 = B- 1A- 1 If V(F) is finite dimensional, and Alx) - 0 if and only if Ix) = 0, then A is invertible Suppose that we have an orthonormal basis { I x 1 > . . . . [Xn>},we can specify any linear operator solely in terms of its operation on the basis

583

18. Microwave Mathematics TABLE 19 Properties of Projection Operators

rilx )oeilxi) Pilxj) = 0 if i 4= j, and Pilxj) =

Ixil

when i = j

Pi is idempotent: PiPi = Pi

PiPj = 0 Pi + Pj is a projection onto the subspace s p a n n e d by Ix i), ]xj) ~Pi = I, w h e r e the sum is over i = 1 to n

Projection Operators Pi = Ixi)(xil. See Table 19. EXAMPLE: We shall begin with a basis, Ix1), ]x 2 ), 1

and a second basis,

]Y 1),

0)

1 '

IX2) =

Y2),

(26)

1(2)

1 ( )2 1 V~

lY2) = ~ -

_1

"

(27)

The projection operators P1 and P2 can be found: P1=5

1

[

1

2

2

4

1[ 4 2]

p2 =

5

-2

(28)

1 "

Any Ix ) in the allowed set can be written in the "x" basis: Ix)=

1 "

(29)

Projecting Ix ) onto each of the elements of the "y" basis entails finding

Pl, lx ). For k = 1 and 2 we have P, lx) =

1()6

=

~IYl)

P2lx)=

1(12)

= --~-~lY2)

(30)

g3

or

3

1

Ix) = ~ - lYe) + ~ - l Y 2 ) =

1

~-

3] 1]

for the y basis

(31 )

584

James Richie TABLE 20 Properties of the Adjoint Operator A + exists for all A and is unique (A + B) += A + + B+ A + ( a x + fly)= aA+x + flA+y (All)+= B+A + (aA)+a*A + (A+) += A

TABLE 21 Theorems on Adjoint Operators If {Ix/)} is an orthonormal basis, then Aij = (xilAx j) A = 0 if and only if ( x l A x ) = 0 for all x Suppose that V is a complex inner product space; then A is self-adjoint if and only if ( x l A x ) is real for all Ix) Eigenvalues of self-adjoint operators are real

Adjoint Operators A + is the adjoint of A, where A+: ( x l A + y ) = ( A x l y )

for all x and y.

(32)

A summary of properties is given in Table 20. For theorems, see Table 21.

Unitary Operators A unitary operator, U, is one for which UU += I = U ÷ U. - - U n i t a r y operations preserve inner products: ( U x l U y ) - ( x l y ) . m l f {Ix/)} is an orthonormal basis, so is {IUxi)}.

Eigenvalue Problem Let A be a linear operator in V(F). Then A is an eigenvalue if and only if

Alxi) = Ailxi)

(33)

585

18. Microwave Mathematics TABLE 22 Properties of Eigenvalues

The geometric multiplicity of an eigenvalue is the number of linearly independent eigenvectors associated with the eigenvalue The algebraic multiplicity of an eigenvalue is the number of times that the eigenvalue appears as the solution to the characteristic equation:

IA-AII-0 If A is self-adjoint, then eigenvectors belonging to distinct eigenvalues are orthogonal If A is self-adjoint, then it can be diagonalized by a unitary matrix

for some nontrivial Ix i), where Ix i) is denoted the eigenvector. See Table 22. The solution to the nondegenerate inhomogeneous eigenvalue problem is Ax - Ax = y.

(34)

Suppose A is self-adjoint. The solution is

IX)

=

provided that A is not equal to

.

l~i

--

t~

'

(35)

/~i"

6. Function Spaces [5, 12, 23, 27, 30, 33, 34, 36, 40] Definition. An infinite-dimensional inner product space for which all Cauchy sequences converge is called complete and is denoted a Hilbert space. Definition. A function space is a space whose vectors are functions,

i.e., If): ( x l f )

= f(x).

(36)

Consider an interval (a, b) in variable sc with a denumerable set of functions [real or complex on (a, b)]. The definitions in Table 23 hold. This is useful for expanding arbitrary functions as a series of appropriate basis functions in the minimum mean squared error sense.

586

James Richie

TABLE 23 Definitions of the Properties of Sets of Functions Useful for Minimum Mean Squared Estimation oo

Y'. Un*(~t)Un(~) = t~(~ -- ~')

Complete

n=l

fba Un*(~)Um(~)d~ = 0

Orthogonal

for all m 4: n

fba Un~(~)Um(~) d~ = ¢~mn

Orthonormal

TABLE 24 Brief Summary of the Three Most Commonly Used Coordinate Systems

Coordinate systems Coordinates (Ul, U2, U3) Metric coefficients (hi, h 2, h 3) Unit vectors

Rectangular

Cylindrical

Spherical

X, y, Z 1, 1, 1 ~x, ey, ez

P, 4~, Z 1, p, 1 ep, e~, ez

r, 0, ~b 1, r, r sin 0 er 80, e~b

7. Vector Fields [3, 8, 18, 19, 25] A field is a quantity that depends on position. Scalar fields and vector fields are possible. Metric coefficients are multipliers to make length units consistent in some coordinate systems. See Table 24 and Figures 3 and 4.

P Z

x

Figure 3. Cylindrical coordinate system.

587

18. Microwave Mathematics Z

r

'

P

Y

Figure 4. Spherical coordinate system.

Operations Dot Product

A.B=f;A.B=B.A. (37)

ei " e~ = aij.

Cross Product AXB=C;A×B=

-BXA;A×(B+C)=AXB+A×C. ei x

(38)

ej = Eijkek .

Gradient: Vf is the maximum space rate of change of f, always directed toward increasing f.

1 Of ~el Vf = grad f - hi OUl -- ~

1 Of "+" ~ ~ 0 2

h2 0u2

1 Of "+-

~e3

-~3 0u3

"

(39)

EXAMPLE" Cartesian, Of^

Of

Of

(40)

588

JamesRichie

Divergence The flux per unit volume is V • F; V • (A + B) = V • A + V • B. V.F=

lim Av--~O

96F • dS (41)

AO

where dS encloses and is directed out of Av.

1 [e

( Flh2h3) + -~uz ( F2hlh3) + O--~3(F3h12) . (42)

V • F hlh2h3

EXAMPLE" Cylindrical 103

V "F = ---(pFp) p Op

+

103F~

F~

+ 03--. p o4, Oz

(43)

Curl The tendency of a vector to wrap around a point is V x F; V X (A + B)=V×A+VxB.

(VXF).~= lim

~F" dl u

s--,0

S

(44)

'

where c encircles S in the right-hand sense and t~ is the outwardly pointing normal to the surface.

V×F=

hlel 03

h2e2 03

h3e 3 03

hlh2h3 aUl hlFl

03//2

03//3

hzF2

h3F 3

(45)

EXAMPLE" Spherical, V X F-

1 [O rsinO

+--1[ r

~

l

(F~ sin 0)

aFr

sin 0 0 F ~

OFo ~-

er

l[a a ] Or (rF~) e o + -

aF~ (

Fo)

Laplacian V2f-

V • (Vf) and V2F - V(V • F) - V x V x F.

-

(46)

589

18. Microwave Mathematics

Theorems Divergence Theorem (47)

£V " A dV = ~sA " dS, where the surface S encloses the volume v.

Stokes' Theorem (48)

fs ( v X A)" dS = ~cA" dl, where the surface S is bounded by the closed contour C.

Helmholtz Theorem Any vector field in which the first derivitives exist is completely specified (up to an additive constant) by defining the divergence and curl of the vector field.

Vector identities See Table 25.

8. Differential Equations and Their Solutions

[4,

34, 35]

Series solutions are a straightforward method of solving differential equations. See Table 26.

TABLE 25 Vector Identities

V" (fA) = f ( V - A ) + A" Vf

V(fg) = f vg + g W

(,)

V -r

V x (fA)= Tfx A + I V x A

r2

V.(AX B)= B.(V XA)-A-(V

V x(VxA)=V(V.A)-

x B)

V.(VxA)=0

VxTf=O A.BXC=B.CXA=C'AXB

V2A

Ax(Bx

V(A.B)=(A.V)B+(B'V)A+Ax(Vx

C)=(A.C)B-(A-B)C

B)+Bx(V

XA)

590

James Richie TABLE 26 Functions Used for a Series Solution to Differential Equations

z 0 is a regular point oo

f ( z ) -" E Cm(Z -- Zo)m m=O z o is a regular singular point f ( z ) - ( z - zo)S ~

Cm(Z -- ZO)m

m=O

z o is an irregular singular point f(z) =

E Cm(z - Zo)m m._~-oo

Analytic Techniques [ I, 18, 23, 27, 30, 45] The wave equation

(49)

(V 2 d- k 2 ) ~ = 0

with boundary conditions, where k is the wavenumber, can be solved using separation of variables. Solutions in the standard three-coordinate systems are provided in Tables 27, 28a-28c, 29, and 30. A characteristic equation must also be satisfied. See Figures 5, 6, 7, 8, and 9. Boundary Conditions [30, Chap. 6] Cauchy Boundary Conditions T h e v a l u e a n d n o r m a l g r a d i e n t o f t h e function are specified on the boundary. This provides a unique solution o n l y in i d e a l s p e c i a l cases. TABLE 27 Characteristic Equations and Functional Form of the General Solution to Equation (41), the Helmholtz Equation

Coordinates Cartesian

)--'~kp2 = k 2 P

Cylindrical

Spherical

Solution, ~b, to

Characteristic equation

k2 +

~

(V 2 +

ke)~b = 0

~_,A~lkEF(klx)F(key)F(ke z)

kl k2 k2 = k2

>_ 0 -n n<m
E n

Ennk3Zn(klP)F(ndp)F(k3 z) k3

E E Cn zn(klr)Sn (cOs O)F(mdp) ,m n m

Note. The spherical case has no characteristic equation; however, only certain values of the indices m and n are allowed.

591

18. Microwave Mathematics TABLE 28a Possible Functions for the General Solutions in Table 27

F ( sc)

e j~

z.(~)

e -j~

cos ~

sin sc

Jn(~)

Nn(~)

n(1)(~) = Jn(~) + iNn(~)

sm(~)

n(2)(~) = Jn(~) - jNn(~)

pm(~)

Zn(~)

Jn(~) h(nl)(~) = Jn(~) + jnn(~)

Note. In addition, linear combinations anJ n + bnN~ is also a valid Z~.

nn(~) h(n2)(~)= Jn(~) -- jnn(~) are allowed. For example,

Dirichlet Boundary Conditions on the boundary.

The value of the function is specified

Neumann Boundary Conditions is specified on the boundary.

The normal gradient of the function

Green's Functions 13, 10, 16, 23, 30, Chap. 7; 36] Green's functions are derived from scalar or vector Green's identities. See Table 31. A Green's function can be thought of as "field of a point source" in a specified electromagnetic geometry. A generalized Green's function can be chosen in such a fashion that certain terms of the resulting integral equation vanish. EXAMPLE: Suppose we have a hertzian dipole

II = 47rc. If

(5o)

re:r',

V×V×G-k2G=0 then 47rc-VXE(r)

=~s(GXVXE(r')-E(r')

xVxG).ds

(51)

can be used to write an integral equation for E(r) in which e - j k Ir - r'l

G=V×c~b

05=

Ir-r'l

= g(r'r')

(52)

592

James Richie TABLE 28b:

Useful Relations RegardingAssociated Legendre Polynomials and the Spherical Harmonics (--1)

Pim(x)

Pim(x)

(m - I -

Recurrence relations p/m+l

2mx

+

V/1

-

1 -x

Ylm(O, ~)

t

Ix

(I + m)(Ix 2 pin +

rnx

1 --X

(X 2

-

1)'

m + 1)PIm-1 -- 0

2 [ - IxP[n + ( I + m )

2[(• + 1)xP[ n - ( I -

1-x

1 -

p~

dx l+m

1)e/~ 1 + (21 + 1)xP] n - ( m + l)e~n_l = 0

pin + (m + I)(I-

t

~

X2) m/2

1

'

mt

--

x 2

pin _

W

d l+m

m

2,i-----~(1

-"

V/1

__

pm

I-1]

m + 1)P/~ 1] m + 1) X2

p],,-

1

x

2 Pi m -

~

p

V/1

/

m

+ 1;

if m = O, then pX = _ V/1 _ x 2 p;

_ x 2

2I+ 1 (I-m)! 4"a" ( I + m ) ! P/m(c°s O)eJm4'

YIm(O, tiP) =

Yt ° ( O' qb) =

21 + 1 Pi°( c°s 0) 4 "a"

Y1_m(O, t~) -" (-- 1)mYffm(O, q~)

and G is the magnetic field of the hertzian dipole. The generalized G is G ' = G + F = V × cth + G 1,

(53)

where ×V×G~=0

onS,

(54)

will result in the Green's function for a hertzian dipole in the presence of a perfect conductor over S. The properties of Green's functions are given in Table 32.

Conformal Mapping [26, 31, 35] Conformal Mapping is a technique-from complex variables. If W(z) is analytic, then V2U = V2V = 0. If the transformation (z 1, z 2) -~ (Wl, W2)

593

18. Microwave Mathematics

TABLE 28c Useful Information Concerning the Cylindrical (Left) and Spherical (Right) Bessel Functions 2m +n

J n ( x ) = Y=0 m ! ( m

+ n)!

&(x)

-2

= (-x)"

(1 d)n(sinx) -

x~-

x

2 yx Jn(X) N n ( x ) = --log

1 ~ ~n-m-i,,(2)_ n --2m zr m-----O

m!

lk

x

,_l,m (x)

"n" m=O m ! ( m + n)!

nn(X ) =

--(--X) n

(1 d)n(cosx) --

x--~

x

n+2m

-2

x[&(m) + ~(m + n)] Small-argument formulas x--,o ~

IV.( x _ --+ -

jn( X ) --+

xn (

x--,O ( 2 n -

-5

(n- 1)!(2)

x~O

77"

x--,o

x2 t

1-

(21--1)!!( xI+i-

nn(x)-~_

X

1)!!

2(2] + 3) x) 2_ .

1 - 2(1

21)

Large-argument formulas L.(x)

-~

x ----)oo

~~x ( ~ ) 42

IV.( x ) --> x ---)oo

cos

~n~'~x~-g~ni(x--~) 1 (n~) nn(x) --" - - c o s

x

( 2~ ( sin 77"X

x

4

2

X ----)oo

x-

X

T

Recurrence n

Bn=Bn-1--Bn

X n

Bn =

- Bn + 1 + 7 Bn

2(n-

1)

z,,

2n + 1 [nZn-1

-- ( I +

2n+l

Bn = ~ B n _

1 - Bn_ 2

~

Z

n = Z n _ 1 -Jr- Z n + 1

Wronskian 2 J.Un

-

U.Jn

=

l)Zn+l]

7TX

1 j n n n -- nnJn =

594

James Richie TABLE 29 Accepted Names of the Functions Given in Table 28

Bessel function Jn Spherical Bessel function Neumann function nn Spherical Neumann function Modified Bessel function (first kind) K n Modified Bessel function (second kind) Hankel function (first kind) h{n1) Spherical function (first kind) Hn{2) Hankel function (second kind) h~ ~ Spherical Hankel function (second kind) Pnm Associated Legendre polynomials (first kind)

Jn Nn In n (1)

TABLE 30 Conventional Usage of the Special Functions for Wave Applications

Cartesian

Standing wave

Outgoing waves

Incoming waves

sin sr, cos ~"

exp(jsr)exp(-j~')

exp( -j~')exp(jsr)

Cylindrical

Jn(~), N n ( ~ )

Hn~2)(~")

Hn{1)(~")

Spherical

jn(~ ), n n(~ )

h(n2)(~)

h(nl)(~ )

.

0

J3(x)

i

i

5

10

i

15

i

x

Figure 5. Bessel functions of order 0 and 3.

preserves the magnitudes and the sense of all angles, then it is a conformal mapping. See Table 33. EXAMPLE: Map a unit circle to the z axis with the interior of circle mapped to the right half plane. See Figure 10. The mapping is written as W--1 = T(w)

=

w+l

(55)

595

18. Microwave Mathematics /

Yo(x)

o

x,,.><../

-1

-2

i

5

15

10

Figure 6. Neumann functions of order 0 and 3. Note how each function will be singular at the origin.

jo(x)

0.8

0.4

0

!

!

!

5

10

15

•

Figure 7. Spherical Bessel functions of order 0 and 3. Note the similarity to the cylindrical case (Figure 5),

and has an inverse mapping" l+z w = T-l(z,)

=

1 -

z"

(56)

Numerical Solutions

(Finite Element Analysis) (FEA) [11, 21, 28, 52] Finite element analysis is a discretization of space into small elements of variable size. Nodes of the elements are used as samples of the

596

James Richie

~(x)

° I

0

i

I

5

10

I

I

15

x

Figure 8. Spherical Neumann functions of order 0 and 3. Note the similarity to the cylindrical case (Figure 6).

2 p1

I

I

I

I

-1

I

I

0

1

Figure 9. Associated Legendre functions of various orders.

TABLE 31 Common Forms of Green's Identities

a~

ft,(~) V2~/ -- ~V 2 ~) dv = ~s (A x V x B - B x V x A ) - d s

=

f(B.

a~

~ -~

ds

v x v x A - A. 7 x V x B)du

Note. The first is the scalar form, and the second is the vector form.

597

18. Microwave Mathematics TABLE 32 Properties Useful in Obtaining the Green's Function

G(r, r') satisfies the homogeneous differential equation except at r = r'

G(r, r') -- G(r', r) G(r, r') satisfies the boundary conditions of the problem G(r, r') is continuous at r = r'

dG/dr is discontinuous at r - r'

TABLE 33 Procedure for the Implementation of Conformal Mapping to Solve Complicated Geometries

(1) Plane z is mapped to plane w (2) Solve problem in plane w (3) Inverse map the solution from w to z

w

r=1

ml

[l

Figure I0. Example conformal mapping.

f u n c t i o n s . T h e m e t h o d of s o l u t i o n is to find t h e l o w e s t v a l u e of a disc r e t i z e d e n e r g y f u n c t i o n a l . S e e T a b l e 34. T h e s t e p s to define a n F E A c o d e a r e given in T a b l e 35.

Finite Difference-Time Domain Analysis [28, 29, 49-51, 53, 54, 56] F i n i t e d i f f e r e n c e - t i m e d o m a i n analysis is a c e n t r a l d i f f e r e n c e a p p r o x i m a t i o n for s p a c e a n d t i m e d e r i v a t i v e s a p p l i e d d i r e c t l y to M a x w e l l ' s e q u a t i o n s in a d i s c r e t i z e d v o l u m e of s p a c e o v e r time. T h e g e o m e t r y of a single cell is given in F i g u r e 11.

598

James Richie

TABLE 34 Energy Functionals for Finite Element Analysis

Poisson equation V2(I) =

P E

Helmholtz equation - - V 2 C I ) = S 4- k 2 ~

d-f

([1

+

!k2~22

- ~s) dR

TABLE 35 Guidelines for Establishing a Finite Element Code

Division of region into elements Choice of functions defined over elements Choice of functional to minimize Matrix construction and solution

/

H

X

I

E

Z

EZ

H ~ X

Yx Figure II. Geometry of the unit cell in FD-TD analysis.

599

18. Microwave Mathematics TABLE 36 Tabulated Integrals

Elliptic Integrals (k 2 ( 1 ) d~

First kind

F(k, 05)= f : ¢ 1 - k 2 sin2 ~b E(49, k) = f : ¢ l - k2 sin2 dp ddp

Second kind

F(k, ~r/2), E(rr/2, k)

Complete elliptic integrals

Exponential integrals x sin u

Sine integral

Si(x)

= fo ~u dv

Cosine integral

Ci(x)

=f

Exponential integral

Ei(x)=f

x COS v

-

x

dv

e v

- dv

9. Integral Equations and Their Solution Tabulated Solutions [I, 15, 47] See Table 36 for the form of elliptic integrals and the s i n e / c o s i n e / exponential integrals.

Asymptotic Methods [30, Chap. 4; 43] The function f ( z ) is an asymptotic series if the series can be written

al

a2

z

z

f ( z ) = a 0 + - - + ---2"-',

(571

such that

( lim z ---~ oo

Nan]

zN

f(z)- E

-~

= 0.

(58)

rt=O

Saddle Point and Steepest Descent Methods These methods are useful for integrals such as l ( a ) + fabe o~f(z)at,

(59)

600

James Richie

where x is a large positive constant. Writing the Taylor series for f(z), where f'(z o) = 0, we produce oo

I ( a ) ~ e'~f(zo)f_ e -("/2)f'(z°Xz-z°)2 dz.

(60)

oo

Stationary Phase Methods These methods are useful for integrals such as l ( a ) = ~ e j~f(z) dz,

(61)

where a is a large positive constant. Writing the Taylor series for f(z), where f'(z o) = 0, we produce l ( a ) -~

ee(xo)f

oo

e -j(a/2)f'(z°Xz-z°)2 dz.

(62)

--00

Numerical Solutions

Numerical Integration [32, 38] See Table 37.

TABLE 37 Recipes for Numerical Integration of Functions Ax

T r a p e z o i d a l rule

bf(x)dx

= - - 2 - - [ f ( x 0 ) + 2 f ( x 1) + 2 " ' ' Z

+ 2 f ( X n _ 1) + f(Xn)]

M(b - a) 3 IEnl < -

Error

f;f

(x)dx

12n 2

If"(x)l

< M -

Simpson's rule nx = - - 2 - I f ( x 0 ) + 4 f ( x 1) + 2 f ( x 2) + 4 f ( x 3) + 2 f ( x 4) + 4 . . . ..5

a < x < b _ _

+ 4 f ( X n _ 1) + f(Xn)] a

(Ax)4(b -a)

En = -

Error

b-a Where A x - ~ , an must be even.

xi=a+iAx,

i=0,1,2

180 ..... n

f(4)(z),

w h e r e z ~ [a, b]

601

18. Microwave Mathematics

Method of Moments I17, 21, 28, 37, 48, 52, 55] The method of moments (MoM) is a procedure for solving integral equations. These integral equations can be written as:

Lf=e,

(63)

where L is a linear operator, f is the source function, and e is the response. Let N

f=

~7_.%fj,

(64)

j=l

where fj are basis functions and % are unknown coefficients. Project each side on to testing functions, {wi}, leaving the matrix equation, GA = E, where Gij = ( W i , Lfj); Aj = aj; and E i = ( W i , e). Common MoM integral equations are given in Table 38. Common basis/testing functions for the thin-wire MoM are given in Table 39. Guidelines for thin-wire modeling are given in Table 40.

TABLE 38 Commonly Used Integral Equations for the Method of Moments

l( s io)lx[J~(r')]g(r (1)

~2rrn x

'

Js(r)-

~

n ×

EFIE

)

r') - [n. E(r')lW(r, r') & ' = 2n x E'"~(r) MFIE J~(r') + V'g(r,r')da'= 2n × Hi"~(r) CFIE

a

a

2n X Hinc(r) + - - 2 n X Einc(r) = 2n X Hinc(r) + 2 - - n X Einc(r) ~7 ~7

TABLE 39 Commonly Used Basis and Testing Functions for the Method of Moments Galerkin Point matching Pulse Piece-wise sinusoidal

Basis functions are proportional to weight functions Basis and weight functions are impulse functions Basis and weight functions are constant over segment ajl + aj2 cos(~) + aj3 sin(sc)

602

JamesRichie TABLE 40 Guidelines for Thin-Wire Modeling of Wires, Surfaces, and Curves

Thin-wire modeling

L > 10d A>rrd A>d A > A/(2rr)

White mesh of solid surface

A × A: A < A/IO a = A/(2rr)

Curved wire modeling (R is the radius of curvature)

R>A

Curved surface modeling

R > V/A-7

Note. The wire length is L, wire diameter is d, wire radius is a, wavelength is A, and segment length is A.

References [1] M. Abramowitz, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Washington, DC: U.S. Gov. Print. Off., 1964. [2] L. V. Ahlfors, Complex Analysis, an Introduction to the Theory of Analytic Functions of One Complex Variable. New York: McGraw-Hill, 1953. [3] C. Balanis, Advanced Engineering Electromagnetics. New York: John Wiley & Sons, 1989. [4] W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 3rd Ed. New York: John Wiley & Sons, 1977. [5] F. Byron, Mathematics of Classical and Quantum Physics. Reading, MA: AddisonWesley, 1969. [6] C. Caratheodory, Theory of Functions of a Complex Variable. New York: Chelsea, 1954. [7] H. S. Carslaw, Introduction to the Theory of Fourier's Series and Integrals, 3rd Ed., Rev. and Enl. New York: Dover, 1930. [8] D. K. Cheng, Field and Wave Electromagnetics. Reading, MA: Addison-Wesley, 1983. [9] R. V. Churchil, J. W. Brown, and R. F. Verhey, Complex Variables and Applications, 3rd Ed. New York: McGraw-Hill, 1974. [10] R. E. Collin, Field Theory of Guided Waves, 2nd Ed. New York: IEEE Press, 1991. [11] R. L. Coren, Basic Engineering Electromagnetics: An Applied Approach. Englewood Cliffs, NJ: Prentice-Hall, 1989. [12] R. Courant and D. Hilbert, Methods of Mathematical Physics, 1st Eng. Ed. New York: Interscience, 1962. (Orig. publ. 1953.) [13] F. R. Gantmakher, The Theory of Matrices (K. A. Hirsch, transl.) New York: Chelsea, 1959. [14] J. W. Goodman, Introduction to Fourier Optics. New York: McGraw-Hill, 1968. [15] I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series, and Products New York: Academic Press, 1980. (A. Jeffrey, ed.). (Trans. from Russ. by Scripta Technica, Inc.)

18. Microwave Mathematics

603

[16] M. Greenberg, Application of Green's Functions in Science and Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1971. [17] R. F. Harrington, Field Computation by Moment Methods. New York: Macmillan, 1968. [18] R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961. [19] W. H. Hayt, Engineering Electromagnetics, 4th Ed. New York: McGraw-Hill, 1981. [20] F. B. Hildebrand, Methods of Applied Mathematics, 2nd Ed. Englewood Cliffs, NJ: Prentice-Hall, 1965. [21] S. Hoole and H. Ratnajeevan, Computer-Aided Analysis and Design of Electromagnetic Devices. New York: Elsevier, 1989. [22] A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering. Englewood Cliffs, NJ: Prentice-Hall, 1991. [23] J. D. Jackson, Classical Electrodynamics, 2nd Ed. New York: John Wiley & Sons, 1975. [24] D. L. Jaggard, H. N. Kritikos, and C. H. Papas, Recent Advances in Electromagnetic Theory. New York: Springer-Verlag, 1990. [25] M. Javid and P. M. Brown, Field Analysis and Electromagnetics. New York: McGraw-Hill, 1963. [26] A. I. Markushevich, Complex Numbers and Conformal Mapping. New York: Gordon & Breach, 1961. [27] J. Matthews and R. L. Walker, Mathematical Methods of Physics. New York: Benjamin, 1965. [28] E. K. Miller, A selective survey of computational electromagnetics, IEEE Trans. Antennas Propag., Vol. AP-36, pp. 1281-1305, 1988. [29] M. A. Morgan, ed., Progress in Electromagnetics Research. New York: Elsevier, 1989. [30] P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Parts I and II. New York: McGraw-Hill, 1953. [31] Z. Nehari, Conformal Mapping. New York: McGraw-Hill, 1952. [32] E. J. Purcell, Calculus with Analytic Geometry, 3rd Ed. Englewood Cliffs, NJ: PrenticeHall, 1978. [33] R. Shankar, Principles of Quantum Mechanics. New York: Plenum, 1980. [34] A. Sommerfeld, Partial Differential Equations in Physics (E. G. Straus, transl.). New York: Academic Press, 1949. [35] M. R. Spiegel, Schaum's Outline of Theory and Problems of Complex Variables, with an Introduction to Conformal Mapping and Applications. New York: McGraw-Hill, 1964. [36] I. Stakgold, Boundary Value Problems of Mathematical Physics. New York: Macmillan, 1967. [37] W. Stutzman, Antenna Theory and Design. New York: John Wiley & Sons, 1981. [38] E. W. Swokowski, Calculus with Analytic Geometry, 2nd Ed. Boston: Prindle, Weber & Schmidt, 1979. [39] M. Tinkham, Group Theory and Quantum Mechanics. New York: McGraw-Hill, 1964. [40] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations. Oxford: Clarendon Press, 1946. [41] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd Ed. Oxford: Clarendon Press, 1948. [42] E. C. Titchmarsh, The Theory of Functions. Oxford: Clarendon Press, 1932. [43] P. L. E. Uslenghi, ed., Electromagnetic Scattering. New York: Academic Press, 1978. [44] H. Wayland, Complex Variables Applied in Science and Engineering. New York: Van Nostrand-Reinhold, 1970. [45] H. W. Wyld, Mathematical Methods for Physics. Reading, MA: Benjamin, Advanced Book Program, 1976.

604

James Richie

[46] R. E. Ziemer, W. H. Tranter, and D. R. Fannin, Signals and Systems: Continuous and Discrete, 2nd Ed. New York: Collier Macmillan, 1989. [47] CRC Handbook of Mathematical Sciences. West Palm Beach, FL: CRC Press, 1978. [48] F. X. Canning, Protecting EFIE-based scattering computations from effects of interior resonances, IEEE Trans. Antennas Propag., Vol. AP-39, pp. 1545-1552, 1991. [49] K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics. Ann Arbor, MI: CRC Press, 1993. [50] R. J. Luebbers et al., A finite-difference time-domain near zone to far zone transformation, IEEE Trans. Antennas Propag. Vol. AP-39, pp. 429-433, 1991. [51] G. Mur, Absorbing boundary conditions for finite-difference approximation of the time-domain electromagnetic-field equations, IEEE Trans. Electromagn. Compat., Vol. EMC-23, pp. 1073-1077, 1981. [52] M. N. O. Sadiku, Numerical Techniques in Electromagnetics. Ann Arbor, MI: CRC Press, 1992. [53] A. Taflove and M. E. Brodwin Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations, IEEE Trans. Microwave Theory Tech., Vol. MTT-23, pp. 623-630, 1975. [54] A. Taflove, K. Umashankar, and T. Jurgens, Validation of FD-TD modeling of the radar cross section of three-dimensional structures spanning up to nine wavelengths, IEEE Trans. Antennas Propag., Vol. AP-33, pp. 662-666, 1985. [55] J. J. H. Wang, Generalized Moment Methods in Electromagnetics. New York: John Wiley & Sons, 1991. [56] K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propag., Vol. AP-14, pp. 302-307, 1966.

CHAPTER

19 Microwave Materials Hamid H. S. Javadi

I. I n t r o d u c t i o n

This

chapter will be of some value to the reader who needs to have a better understanding of the fundamental properties of passive microwave materials. It is clear that the present work is a compilation of data available in the literature, and this would not have been possible without the efforts of many individuals in industry and academia. References are cited for many tables and figures. The remaining data are compiled from more scattered sources and citations deemed impractical. Many empty sites in the tables remind us of needed work to be performed (perhaps in locating such data in the literature) in laboratories. This chapter starts with some useful formulas and approximate relations between dielectric parameters [1]. The atmospheric absorption of microwaves and millimeter waves is the subject of Figure 1, whereas Table 1 represents the thermal radiation transmittance of cold window materials [2]. Section 2 is allocated to the dielectric properties of compounds [bulk materials, Corning glasses [3, 4], substrates [5, 6] (plastic, ceramic, semiconductor, and ferrite), epoxies, and radomes [7]]. The anisotropy and power-handling capability of substrates [8, 9], temperature coefficients of some dielectrics [10], and irradiation effects on sapphire [11] are discussed. Section 3 focuses on the properties of manufactured compounds: dielectric resonators, surface acoustic wave materials [12], piezoelectrics [13], and ferrites [14, 15]. Section 4 concentrates on conductive, resistive, and capacitive thin films [16]. Section 5 addresses the physical properties of

Handbook of Microwave Technology, Volume 2

605

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

606

Hamid H. S. Javadi

Wavelength 30 100 1 40

15 i

I

l

( mm

10 8 6 5 i

I

l

l

I

4 3

)

2 1.5

0.8

i

I

IIII

I

I

I

I

l

l

l

l

..I

l

ljs~l

l l

I

/k /'d-

10 4

1 0.4~ 0 .H 4.1

ID

0.1

0.04 ~ 0.01 0.004

02

1:

'i

02

H2

......

O. 001 I

10

H

3000 ft Altitude I

I

20

I

I

I

I

30 40

Frequency

n nw,~ I I Ill

60

A il l i "1i

I i

100

i

200

( GHz

400

)

Figure I. Average atmospheric absorption of millimeter waves (horizontal propagation). Reproduced from a catalog of Hughes millimeter-wave products, Hughes Aircraft Co.

TABLE I Average Room-Temperature-Radiation Transmittance for Materials Cooled to 70 and 15 K Average transmittance at Material PTFE Fluorogold Styrofoam Stycast HIK (E r = 4.) Stycast 0005 (e r = 2.54) Rexolite Fused quartz Crystalline quartz TPX

Thickness (mm) 2.0 0.8 3.0 2.0 2.0 2.0 0.7 1.5 2.0

70 K 0.046 0.114 0.195 0.063 0.220 0.175 0.225 0.022 0.310

+ + + + + + + + +

0.003 0.006 0.010 0.003 0.010 0.010 0.010 0.002 0.015

15 K 0.442 0.005 0.202 0.010 0.185 0.238 0.094 0.910 0.105

+ + + + + + + + +

0.030 0.002 0.010 0.002 0.010 0.012 0.005 0.020 0.005

Note. Calculated from the measured temperature rise of an aluminum plate covered with a thin black drawing paper. Source. Reproduced with permission from Table 2 in [2], copyright © 1984 by Plenum Publishing Corp.

607

19. Microwave Materials

metals; the dependence of surface resistance of metals on their surface roughness is discussed [17], the temperature dependence of the surface resistance of copper is reviewed [18], the reflective losses of some metals are tabulated, and the circuit patterns utilized in radars are presented [19]. Section 6 covers conventional and high-temperature superconductors [20]. The frequency dependence of the surface resistances of YBazCu307_ ~ epitaxial films and single-crystal platelets is compared with that of Cu, Nb, and Nb3Sn at cryogenic temperatures. Finally, important substrates for the growth of epitaxial films of superconducting oxides are also reported in Section 6 together with their physical properties. The field of microwave materials benefits from the efforts of a multidisciplinary pool of researchers, and this chapter is only a very small drop [1-26] from a vast ocean of the current human knowledge. In a medium there may be many contributions to the microwave response which are characterized via (1) Complex conductivity o-* ( f ) = o-' + j'~r" from unbound charge carriers, etc. (2) Complex dielectric constant e * ( f ) = e'r + je r from bound charges, dipoles, polarizable molecules, the background lattice, etc. Due to the presence of free electrons, microwaves will penetrate a skin depth, rl, from the surface of a metal, 10 r / ( m m ) = ~ × [ f (GHz) × o"(~] -1 cm-1)] -1/2, where o-' is the real part of conductivity and r/is the skin depth (mm). The real part of conductivity o-' and the imaginary part of the dielectric constant e" can be interchanged to calculate the microwave loss tangent of a medium with free-charge carriers, tan 6 = e r / e ~ = 1.8 × 1012 X o"(D. -1 c m - l ) / [ f (Hz) × e;],

o"([~ -1 cm -1) = 5.563 × 10 -13 )< E~' x f (Uz), where tan ~ is the loss tangent, e'r is the real part of relative permittivity, and e~ is the imaginary part of relative permittivity. The approximate relation between e'r and tan 6 [1], for a change in the dielectric constant as a function of frequency is A e r / e ' r = 1.5 × tan 6 × log( f 2 / f l ) and for a change in the dielectric constant as a function of temperature is A e ' / e ' = 0.07 × tan ~ × (T 2 - T1).

608

Hamid H. S.Javadi

2. Dielectric Properties of Compounds Throughout this section the dielectric parameters of materials are reviewed. Schematics 1 and 2 are two-dimensional maps of materials in which the horizontal coordinates indicate relative permittivity and the 1.0 0.6 0.3 0.1 O. 08

.

.

.

.

.

.

.

0.06 0.04 Araldlte, CastingB

0.02

3=,

0.01 0.008 0.006 0.004 ~D c

I

0.002

Poraelal 3 GH=

,l~iIazn St.atit.3 GHz

0.001 0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 <0.0001 1.0

1.2

1.4

2.0

2.5

3.0

4.0

5.0

6.0

7.0

Schematic I. Dielectric properties of industrial products.

8.0

9.0

10.

609

19. Microwave Materials 1.0 0.6 0.3

Barium

Titanate

0.1 0.08 0.06 0.04 0.02 0.01 0.008 0.006 0.004 03 c-

GHz

Kerafar

Condensa i- 3TGH z

Negatit

I

i0 GHz

Cond~nsa

N

0.0009 0.0008

C

Hzl

10 GHz

0.0007 0.0006 1-3 GHz

11-3 GHz

0.0005 0.0004

0.0002 0.0001 #~

<0.0001 10

12.5

15

17.5

Id

35

40

45

50

80

90

100

200 >200

Schematic I. (Continued)

vertical coordinates represent the loss tangent. The size of each box corresponds to the range of uncertainty in the values or span of material characteristics. Table 2 reviews the dielectric, thermal, and physical properties of different classes of bulk materials (ceramics, glasses, plastics, waxes, rubbers, and miscellaneous materials). Tables 3 and 4 present the

610

H a m i d H. S. Javadi

1.0 0.6 0.3 0.1 0.08

Phenolic]

:2:~o::ol

0.06

] ,-ke~it- I S i l i c o n

0.04,

~-120

3~= 0.02

I I

Rubber Sodalime Glass

3 GHz

NylonI

0.01 0.008

Polychlro

othyzo.o

"

--

10 I

Teflex ~thyz rata

0. 004 oO

~.10X I

.........

0 006

a~z ]

o~ato

iiroonl I

Rubber

O. 0 0 2 0. 001

I

°

0.0009

®

N

t"

0.0008

~o ~

0. 0 0 0 7

"~ m 0 m

~0~

0.0006

0. 0005

. . . . 1,~-~

0 0004,

I "~'''-"

~1 0 I11

.

,,1,=o

,th¥1en.

0.0003

= N

o

iii

O~

0

Paw~ffin

i i0 ~nzl

/ .... .]_1 Styre~

ceram

30 GHz

I

0.0002 0.0001 <0.0001 2.0

2.2

2.4

2.6

2.8

3.0

3.5

4.0

4.5

5.0

6.0

7.0

8.0

Schematic 2. Dielectric properties of industrial products.

dielectric properties of more compounds. Table 5 is allocated to Corning glasses which are gaining considerable attention in millimeter-wave frequencies [3, 4]. Dielectrics in the form of substrates are used routinely in

10

0

~E

,,,.~ _1

U

._u ._~

0

~

o o t¢3 (",1

0

0

V~5

N

0

~ 0

0

•! . o ~ ~ . ~ ~ ~ ~

~ O 0 ~

O0

N

N 0

0

I~

~ ~~~~

~

i '.~

no

v

~o ~

O0

o~

o

0 o Pq

~h

0

0

N~

0

~ °

•

~

V

~

~'.~~.~'~-~~

oo

kO

~

""

,

612

~

~5

~o

'--'

.

o

br~

2

.

o

.

~

"C3 ~

.

,--,

0

oo

o.

"t3 . ,~.-,

.

N

0

0

.

~

~

"¢3

,.~ ©

~0

. . . .

-

c~

"T3

~,

q

b

"~

~

e

M

~

.

q q q ~

ee..ee

.,..~

e ~ e

M ~ M ~

c~

q q q q q q

M M ~

¢~

mMN

-

~=

~ m ~ m ~ M

¢)

~

,-~

~

~ ~

~'~" i ~ t¢3 ~-u

613

"r"

0

,,,.~ a.

t~ °~

g,

614

t",l

~

I'~

~-~

ec3~

bl

0 t¢3

° ~

~

I

I

©

t¢3

I~

i ~

._1 en

19

._m

0

T

19

I];

U I9

~9

0

o

N

o~

N

o

=I

o

•

"~~?~ ~,

o

/

~~

615

c=

=

~"

+1

~

×

~

o0

N

.

~

~

_

_J

°~ eL 0

u 0

u

._u

.~

u'l

._u e-

Sa

~o ~

~"

~

•~ .~ oo r~

o,,.~

<

.

cD • ,.--~

o

o

o

I

I

I

~:~ ~

.

~ ~

t"~

I~ .

o

~

.

~

o

.

v'~ ~

O0

~o

.

I~

°,=~

.,.~

o

v~ ~

o,~

:-~ .,~

~

~ ~

~

~

m

.

,--

~

o

~

~ ~

m

o,=~

~

.

~:~ ~!"

I" ~

°,~

616

t"-

r ~-

o

~

r ~-

r "~

N

~

I~-

617

0O

O'~

C~

I

z

O'~

A

o=.

z

I&l

i,.

IE

e-

.o

o

t~

_o

0

.o 0

0

Z

+

o

ZZZ

~.

i ~

+ +

~ +

A A~

c~

0 n~l

I

<

ZO0~

618

oo

~?'~o ~

+

+ ~

~

c~

O

C~

+

O

c~

O

O .,.~ .,~

.,..~

o

.,..~

a~

o

o

19. Microwave Materials

619

microwave devices [5, 6]. Integrated circuit patterns are incorporated over the substrate which is then packaged. The thermal conductivity of the substrate determines the heat dissipation of active microwave elements. The thermal expansion coefficient is decisive in the adhesion of a metal overlay on the substrate. The thermal variation of permittivity defines the stability of the circuit. This information can be found in Tables 6 and 7 for common substrates. Low-loss dielectric substrates incorporating Teflon or other plastics together with glass microfiber, woven glass, and ceramics are reviewed in Table 8. Some anisotropic substrates are considered in Table 9. Tables 10 and 11 discuss semiconductor and ferrite substrates, respectively. Low-loss epoxies are important for the everyday work of microwave engineers. The lack of comprehensive high-frequency data on adhesives is compensated by the compilation of the physical and (low-frequency) dielectric properties of adhesives and epoxies in Table 12. Table 13 covers radomes [7]. The anisotropy of composite substrates as a function of their dielectric constants is the subject of Figure 2. Less anisotropic substrates can be obtained utilizing Teflon composites incorporating random glass fibers. The next figure (Figure 3) discusses the power-handling capability of microwave strip lines. A 50-f~ line with 0.250-in. ground plane spacing is used up to 10 GHz, and the temperature rise is measured when microwave power is transmitted through the microstrip [8, 9]. The results of the measurements when different substrates are employed are shown in Figure 3. Relations between the temperature coefficient of capacitance

TABLE 7 Dielectric Properties of Substrate Materials

Material

A1N A1N (+3% Y203 ) AIN (+6% Y203 ) SiC BN (HP grade ) (The Carborundum Co.) BeO Sapphire a

Thermal conductivity (W/cm °C)

Thermal expansion coefficient (ppm/°C)

e

tan 6

8.5 (10 GHz) 7.77 (1-18 GHz) 7.81 (1-18 GHz) 40. (1 MHz) 4.1 (1 MHz)

0.004 (10 GHz) < 0.0023 (1-18 GHz) < 0.001 (1-18 GHz) 0.050 (1 MHz) 0.0045 (1 MHz)

1.40-2.30

4.40

2.70 0.25

3.7 0.0

6.7 (10 GHz) 11.5 (10 GHz)

0.004 (10 GHz) < 0.0001 (10 GHz)

2.60 0.46

9.0 5.3

aFor high-quality single-crystal sapphire, tan 8 ot T 475 (50 K < T < 300 K) and tan 8 ~ 10-8 (78 K, 9 GHz).

620

Hamid H. S. Javadi TABLE 8 Characteristics of Microwave Plastic Substrates

Laminate/substrate

Dielectric constant (X-Band)

Loss tangent (X-Band)

Dimensional stability

Chemical resistance

Temperature range (°C)

P T F E unreinforced

2.1

0.0004

Poor

Excellent

- 27 to + 260

P T F E glass woven web

2.17 to 2.55

0.0009 to 0.0022

Excellent

Excellent

- 27 to + 260

P T F E glass random fiber

2.17 to 2.35

0.0009 to 0.0015

Fair

Excellent

- 27 to + 260

P T F E quartz reinforced

2.47

0.0006

Excellent

Excellent

- 27 to + 260 - 15 to + 170

0.002

Excellent

Good

Cross-linked polystyrene

2.54

0.0005

Good

Good

- 2 7 to +110

Cross-linked polystyrene/ glass reinforced

2.62

0.001

Good

Good

- 2 7 to + 110

Cross-linked polystyrene/ quartz material

2.6

0.0005

Good

Good

- 2 7 to + 100

Cross-linked polystyrene/ woven quartz

2.65

0.0005

Good

Good

- 2 7 to + 110

Cross-linked polystyrene/

3 to 15

0.0005 to

Fair to good

Fair

- 2 7 to +110

Poor

Excellent

- 27 to + 260

Ceramic P T F E composite

10.2

ceramic powder filled

0.0015

Teflon/unreinforced (unclad)

2.1

0.0004

Teflon/glass reinforced

2.55

0.0015

Good

Excellent

- 27 to + 260

Teflon/ceramic

2.3

0.001

Fair to good

Excellent

- 27 to + 260

0.0006

Good

Excellent

- 27 to + 260

Teflon/quartz

reinforced reinforced

2.47

0.002

Good

Excellent

- 27 to - 260

Polyphenylene oxide ( P P O )

2.55

0.0016

Good

Poor

- 2 7 to + 193

I r r a d i a t e d polyolefin

2.32

0.0005

Poor

Excellent

- 27 to + 100

Excellent

- 27 to + 100

Excellent

- 27 to + 100

Teflon/ceramic

filled

10.3

Irradiated polyolefin/ glass reinforced

2.42

0.001

Fair

Polyolefin/ceramic powder filled

3 to 10

0.001

Poor

Note. Reproduced, with permission, from Table II in Bahl and Ely [6], copyright © 1990 by Horizon H o u s e - M i c r o w a v e , Inc.

and the dielectric constant of many compounds are depicted in Figure 4. The specific behavior of zirconates is the subject of Figure 5 [10]. Dielectric materials are very vulnerable to radiation effects [11]. This is particularly important in applications such as radomes, plasma, and nuclear reactor windows. Table 14 is an example of how neutron and a-particle radiation can affect the dielectric permittivity and loss tangent of sapphire.

19. Microwave Materials

621

TABLE 9 Dielectric Properties of Common Anisotropic Substrate Materials

E (GHz)

Material Sapphire (Union Carbide Corp.) Monocrystalline magnesium fluoride Pyrolitic boranitride Epsilam-10 ceramic-impregnated teflon a-Quartz Quartz, crystal (X-cut)

tan S (GHz) E ± c 0.00002 (8.5) E iic 0.00005 (8.5)

E ± c 9.39 (8.5) Elic 11.58 (8.5) Ell = 4.826 (kHz) E± = 5.50 (kHz) ell = 3.40 e ± = 5.12 Ell = 10.3 E± = 13.0 Ell = E± = e0 = Ee =

4.637 (kHz) 4.52 (kHz) 4.44 (35 GHz) 4.64 (35 GHz)

Thermal expansion coefficient (ppm/°C)

Thermal conductivity ( W / c m °C) 0.46 (60 ° orientation)

5.8 (60 ° orientation)

0.002

11 to 23

0.001 (35 GHz) 0.001 (35 GHz)

TABLE 10 Dielectric Properties of Semiconductor Substrates

Resistivity (f~ cm)

Electron mobility ( c m 2 / V s) (doping, 1017 cm - 3 )

(g / cm 3)

0.46

107-109

4300

5.32

14.0 11.7

0.68 1.45

'~ 107 103-105

3000 700

4.8 2.33

11.6

0.46

> 1014

700

3.9

Thermal Conductivity ( W / c m °C) 12.9

Material Active G a A s (doped) InP Active Si (doped) Silicon on sapphire

Density

(D)

TABLE II Dielectric Properties of Ferrite Substrates Material

tan S, ( G H z )

Mgl.18 Mno.o8 Fel.695 Alo.205 04+ s (spinel, magnetic ferrite)

< 0.0005 (9.3)

Mgo.9 Zno.1Mno.1Fel.2 Alo.8 O4 + (nonmagnetic ferrite)

< 0.0005 (9.3)

Y3 Fe 4.6 Alo.4 O 12 (garnet)

< 0.0002 (9.3)

Y2.9 Cao.1Fe3Alo.9 Si0.1012 (nonmagnetic garnet)

< 0.0003

e (GHz)

rc (°C) 185 (4,'n-Ms = 1900 G) 20 -

15.8

195 (47rM s = 1200 G) 20 -

_!

e-

X

0 1.1.1

,,,.~

f~l

0

~E ~d

u

t~

._

o

C 0

©

[-

~.~

.~-~ ~ ~

o

o

~

o~

o

II

o

c5c~

II

o

~ o -~.~

o

°

m

,..em c~ ~

"6 ~

~.o

0 0 ,-q

0

~

_o

~

X,.~

E-.--,

~n

~~.~

©

o~

~

~

©

""

N

19. Microwave Materials

623

TABLE 13 Room Temperature Dielectric Properties of Radomes

Material Erosion coating (Goodyear 1801C) Antistatic coating Honeycomb HRP, a 3 / 1 6 - 6 . 2 NP, b 3 / 1 6 - 9 . 0 Paper, 3 / 4 Foam Urethane, 10 l b / f t 3 Polystyrene, 10 l b / f t 3 E-glass organic laminates Selection 5003 Cordo H200C U.S. Poly P680 Epon 828 and tonox Cordo E-213M DC2106 DC7141 Pyroceram E-glass $994 glass D556 glass Plexiglas Polystyrene Teflon Duroid Aluminum oxide Beryllium oxide Fused silica Quartz Boron nitride Aluminum phosphate fiberglass laminate PBI S-glass laminate Quartz--DC2106 laminate Water Snow Ice Poly-4-methyl pentene-1 (TPX) High-density polyethylene Fused silica Alumina

Frequency (GHz)

Dielectric constant

Loss tangent

9.375 9.375

3.1 7.2

0.031 0.27

9.375 9.375 9.375

1.14 1.20 1.03

0.004 0.002 0.001

8.5 1.0

1.16 1.16

0.0024 0.0002

8.5 9.375 9.375 9.375 9.375 8.6 9.375 8.5 10.0 10.0 10.0 9.375 8.5 10.0 8.5 10.0 10.0 10.0 10.0 9.375 9.375

4.2 4.3 4.3 4.4 4.4 4.3 4.1 5.5 6.1 5.3 4.0 2.6 2.54 2.08 2.7 9.2 6.5 3.6 3.8 4.4 3.6

0.012 0.010 0.012 0.016 0.013 0.007 0.005 0.0003 0.006 0.007 0.003 0.015 0.0004 0.0004 0.003 0.0003 0.0003 0.0002 0.0001 0.0001 0.009

9.375 9 10 10 10 60 60 60 60

4.5 3.2 63 1.3 3.2 2.022 + 0.0004 2.3989 _+ 0.00005 3.9495 _+ 0.00005 9.575 _+ 0.00005

0.011 0.003 0.55 0.0005 0.0008 0.000785 0.001144 0.000421 0.001521

_+ 0.00005 _+ 0.00005 + 0.00005 _+ 0.00005

Note. Reproduced, with permission, from Table 5 in [7], copyright © 1970 by McGraw-Hill, Inc. aHeat-resistant phenolic. bNylon phenolic.

0

.,-I •1.)

~¢o

1.20 -,2

-

Woven

Glass-PTFE

1.15--

o~~ o 0 ~= •,-I 1.05

--

Random

1.00

I

'

2.20 Nominal

I

Fiber-PTFE

'

2.30 Dielectric

I

'

2.40 Constant,

£

r.7

I 2.50 @ I0 G H z

Figure 2. Anisotropy of Teflon-based dielectric substrates. Adapted from Figure I of product data sheet RT2.1.2. I, "The Advantage of Nearly Isotropic Dielectric Constant for RT/Duroid ® 5870-80 Glass MicroFiber- PTFE Composite." Rogers Corp., 1981, copyright © 1981 by Rogers Corp.

Temperature Rime for 0.250" Ground Plane Spacing

50 Ohm Line

Glas s-Polystyrene °~

I

Polysterene~

I II ~

~o

~

I

Woven Teflon Glass-. ~ ~ ~ Microfiber Teflon ~ ~ ~ ~ t ' i ~ m - ~ ~

| I

o /

0

1

2

3

4

5

6

Frequency,

7

8

10

9

GHz

Figure 3. Power handling capabilities of microwave strip lines constructed from various dielectric materials. Reproduced, with permission, from Figure I - 1 3 in Howe [8] and Figure 2 in Howe [9], copyright © 1971 by Horizon House-Microwave, Inc. u

400

/~

200

cz

\

•

MgO

~N\"g,Ti°,, .~'~11~i.~,%~ ~ 3 C a O , 3La =On, 6SIO2, Ca~'2 0',

~ ~ .-pho~~0.3 u (~j,o:zjo,°"' : si°",' 56 (Cao, La 203 44 (BaO, ZrO 2 )

.,.t

•~

.

.

0.23 (CaO, La202 ,2SiC 2 ) 0.77 (BaO, ZrO 2 )

!

-200

.

~

"~'o

,'x\',4

.

-400

~

.,4

I I

. . . . .~.~.v2CaO Ta 0 I --~.2CaO',:Ta2 05 +Laz ( I ~%.%.~Z~,~l~

1

6

9

13

17

21

Dielectric

25

29

Constant

33

37

41

45

49

£

Figure 4. Relations between the temperature coefficient of capacitance and the dielectric constant. Reproduced from Figure I in "New materials. 3. Improved compounds for microwave dielectrics." J. Electr. Eng., Vol. 21, p. 84, 1984, Dempa Publications, Inc.

625

19. Microwave Materials

U

+1oo r

.H

o~~-~-&~ G

U

o.o5 o.1 o.15

.~ o

_25~3~ ~

q4 ~

-50

0 U

-75

o

,,~-

~

-12sI37~

14

-150

G

s6, , , ' o's o.~o'6 o.'6s o ~7

SZT

"~ C o m p o s i t i o n

x,

Ba

or

Ti

38

s~z

(Sr~_Ba.)zre 3

o

SZT

Sr (Zrl_xTi . ) 0 3

,

CBZ

(C~_xBa x ) ZrO 3

•

CZT

Ca (Zrl_Ti x) 03

.

Figure 5. Variation of the temperature coefficient of capacitance with composition for various zirconate ceramics. Symbols along the lines indicate values of permittivity. All measurements were taken at 1.6 kHz. Reproduced, with permission, from Figure I in Kell et al. [10], copyright © 1970 by The Institute of Electrical Engineers.

TABLE 14 Dielectric Parameters of Irradiated Sapphire Disks (D = 30 mm) at 35 - 4 0 GHz

Type of irradiation Unirradiated Fission neutrons (E > 0.1 MeV) Spallation neutrons a-Particles (0-10 MeV)

Irradiation temperature (°C)

Quantity of dose

e'r ( + 0.02)

tan 6 [10 -4] ( + 1)

9.41a/11.59 b

1.5a/1.5 b

< 215

2.6 x 10 20 n / c m 2

9.49a/11.64 b

10a/ll b

250-400

5 X 1020 n / c m 2

9.43a/11.61 b

2.5a/2.0 b

200-500

0.3 X 1017a/cm 2 0.6 X 1017a/cm 2 1.6 X 1017a/cm 2

9.41a/11.61 b 9.42a/11.62 b

5a/5 b 4a/2 b 4a/3 b

9.43a/11.62 b

Note. Reproduced, with permission, from Table 2 in Heidinger and K6niger [11], copyright

© 1989 by the Society of Photo-Optical Instrumentation Engineers. aordinary ray. bExtraordinary ray.

626

Hamid H. S. Javadi

3. Properties of Manufactured Special-Purpose Compounds Dielectric r e s o n a t o r s are widely used in microwave filters, oscillators, and amplifiers. In such applications the t e m p e r a t u r e coefficients of expansion, of the dielectric constant, and of the r e s o n a n c e frequency are i m p o r t a n t . These, plus composition and o t h e r i m p o r t a n t information, are t a b u l a t e d in Table 15. Table 16 s u m m a r i z e s the i m p o r t a n t physical p r o p e r t i e s of surface acoustic wave materials [12]. T h e insertion loss of c o m m o n S A W materials vs the fractional b a n d w i d t h is the subject of Figure 6 [12]. Piezoelectrics are discussed in Table 17 [13]. T h e dielectric constant, dielectric loss tangent, and m a g n e t i c p r o p e r t i e s of c o m m e r c i a l ferrites are p r e s e n t e d in Table 18 [14]. Figure 7 illustrates the g e n e r a l behavior of s a t u r a t i o n m a g n e t i z a t i o n vs the Curie t e m p e r a t u r e for a l u m i n u m - s u b stituted Y I G [15].

TABLE 15

Dielectric Resonator Materials

Type

C D E F

C D E

•r

z~ (ppm/°C)

Manufacturer, Murata Erie North America, Inc. Brand, Resomics-S Series Composition" Ba(Zr, Zn, Ta)O 3 Minimum Qd, 10,000 (at 10 GHz) Thermal expansion coefficient, 11 ppm/°C Thermal conductivity, 0.0059 cal/cm s °C Water absorption, 0.01% maximuma 28.6 + 0.5 -20.4 + 4 29.2 + 0.5 -24.4 + 4 29.7 + 0.5 -28.4 + 4 30.1 + 0.5 -32.4 + 4 Manufacturer, Murata Erie North America, Inc. Brand, Resomics-E Series Minimum Qd, 20,000 (at 10 GHz) Thermal expansion coefficient, 10.7 ppm/°C Thermal conductivity, 0.0077 cal/cm s °C Water absorption, 0.01% maximuma 24.2 + 0.4 24.4 _+ 0.4 24.7 + 0.4

rf (ppm/°C)

0+ 2+ 4+ 6+

0 2 4

2 2 2 2

19. Microwave Materials

627

TABLE 15 (Continued) Type

Unspecified Unspecified

A B C D E F G H

E r

'r E

(ppm/°C)

rf (ppm/°C)

24.9 +_ 0.4 Manufacturer, Murata Erie North America, Inc. Brand, Resomics-K Series Composition: (Ba, Pb)NdzTi5014 Minimum Qd, 1000 (at 3 GHz) Thermal expansion coefficient, 8-9 p p m / ° C Thermal conductivity, 0.0039 c a l / c m s °C Water absorption, 0.01% maximum a 90_+ 2.7 - 2 9 _+ 4 90_+ 2.7 - 1 7 _+4 Manufacturer, Murata Erie North America, Inc. Brand, Resomics-M Series Composition: (Zr, Sn)TiO 4 Minimum Qd, 8000 (at 7 GHz) Thermal expansion coefficient, 6-7 p p m / ° C Thermal conductivity, 0.0046 c a l / c m s °C Water absorption, 0.01% maximum a 37.4 _+ 0.5 - 1 3 _+ 2 37.7 _+ 0.5 - 1 7 _+ 4 38.0 _+ 0.5 - 2 1 _+ 4 38.4 _+ 0.5 - 2 5 _+ 4

0_+2 2+2 4_+2 6_+2

Manufacturer, Murata Erie North America, Inc. Brand, Resomics-R Series Minimum Qd, 12,000 (at 10 GHz) Thermal expansion coefficient, 10.7 p p m / ° C Thermal conductivity, 0.0051 c a l / c m s °C Water absorption, 0.01% maximum a 29.6 _+ 0.5 30.3 _+ 0.5 30.9 _+ 0.5 31.5 _+ 0.5 Manufacturer, Murata Erie North America, Inc. Brand, Resomics-U Series Composition: (Zr, Sn)TiO 4 Minimum Qd, 6000 (at 7 GHz) Thermal expansion coefficient, 6-7 p p m / ° C Thermal conductivity, 0.0046 c a l / c m s °C Water absorption, 0.01% maximum a 36.6 _+ 0.5 b -5 + 4 37.0 _+ 0.5 b -9 + 4 37.4+0.5 b -13 +4 37.7 _+ 0.5 b -17 + 4 38.0 _+ 0.5 b -21 + 4 38.3_+0.5 b -25+4 38.6 _+ 0.5 b -29 + 4 38.9_+0.5 b -33+4

-4 + 2 -2 + 2 0+2 2 + 2 4 + 2 6+2 8 + 2 10_+2

0_+2 6_+2

(Continues)

Hamid H. S. Javadi

628 TABLE 15 (Continued) Type

•r

7"E

(ppm/°C)

D-8810 D-8811 D-8812

Manufacturer, Trans-Tech, Inc. Brand, Trans-Tech 8500 Series Composition: Z r / S n titanate Minimum Qd, 10,000 (at 4.5 GHz) Thermal expansion coefficient, 6.5 p p m / ° C Thermal conductivity, 0.005 c a l / c m s °C Water absorption, 0.01% maximum c 35.7 + 1.5% b 1.6 35.9 + 1.5% b -6.9 36.2 + 1.5% t' - 9.7 36.4 + 1.5% b - 13.1 36.4 + 1.5% b - 19.0 Manufacturer, Trans-Tech, Inc. Brand, Trans-Tech 8800 Series Composition: barium and titanium oxide Minimum Qd, 6000 (at 4.5 GHz) Thermal expansion coefficient, 9.2 p p m / ° C Thermal conductivity, 0.005 c a l / c m s °C Water absorption, 0.01% maximum c 36.6 + 1.5% 38.3 + 1.5% 38.3 + 1.5%

D-8621 D-8622 D-8623 D-8624 D-8625 D-8626

Manufacturer, Trans-Tech, Inc. Brand, Trans-Tech 8600 Series Composition: Ba, lanthanides, and Ti-oxide Minimum Qd, 3000 (at 3.0 GHz) Thermal expansion coefficient, 8.5 p p m / ° C Thermal conductivity, 0.005 c a l / c m s °C Water absorption, 0.01% maximum c 80.0 _+ 1.5% 80.0 _+ 1.5% 80.0 _+ 1.5% 80.0 _+ 1.5% 80.0 _+ 1.5% 80.0 _+ 1.5%

D-8516 D-8515 D-8514 D-8513 D-8517

Tf

(ppm/°C)

-3 0 3 6 9

-6 -3 0 3 6 9

19. Microwave Materials

629

TABLE 15 (Continued) Type

D-8731 D-8732 D-8733 D-8734 D-8735

E-1336 E-2036 E-2336 E-2636 E-2936

•r

I"E

(ppm/°C)

r r (ppm/°C)

Manufacturer, Trans-Tech, Inc. Brand, Trans-Tech 8700 Series Composition: Ba, Zn, and Ta-oxide (perovskite) Minimum Qd, 9500 (at 10 GHz) Thermal expansion coefficient, 10 p p m / ° C Thermal conductivity, 0.006 c a l / c m s °C Water absorption, 0.01% maximum c 27.6 _+ 1.5% 28.5 _+ 1.5% 29.4 _+ 1.5% 30.0 _+ 1.5% 30.6 +_ 1.5% Manufacturer, Thomson-CSF Components Corp. Brand, E36 Composition: (Zr, Sn)TiO 4 Minimum Qd, 4000 (at 10 GHz) Thermal expansion coefficient, 5 p p m / ° C 36.9 _+ 0.4 - 4 _+ 1 37.0 +_ 0.4 - 1 0 _+ 1 37.1 _+ 0.4 - 1 6 _+ 1 37.2 _+ 0.4 - 2 2 _+ 1 37.3 _+ 0.4 - 2 8 _+ 1

- 4 - 2 0 2 4

-3 0 3 6 9

_+ 1 +_ 1 + 1 +_ 1 _+ 1

aData reproduced, with permission, from catalog No. 095E-2 (1990) of Murata Erie North America, Inc. tAt 7.5 GHz. CData reproduced, with permission, from catalog No. 50010080, Revision 2 (1990), of Trans-Tech, Inc.

70

60El

"~ 50v I/l O

ST-Quartz..---.-.~~

"

40-

LiTa03BGO

J¢ - 30-

yZ_LiNb0s 0 "~ 20" T28° LiNbO L t#

/ /

__L

I/I

_~ 106 0

I

1

I

I

'

//

Z/ fAX

//,~/

' ,,.I

,

.

.

,

,.,.

10

100

Fractional Bandwidth ( % ) Figure 6. Optimal bandwidth of most commonly used surface acoustic wave materials. Reproduced, with permission, from Figure 6.14 in Penunuri et al. [ 12], copyright © 1989 by John Wiley & Sons, Inc.

ml I~D

"r, ~J

o_u ~J

Q~

E

0

o b E E 3

C

~L

0

c~

o

~

c~O~ .~

Q

o o, cJ

O

0 ~

L~

0

c~

~ i ~ I~

~

I i~

~

N

0

~

~ io

~

m

O

.,~ = 0

@ .~

8

=

.,~

E-

.,-~ .~

.~

=

19. Microwave Materials

631

TABLE 17 Piezoelectric Coupling and Frequency- Temperature Coefficients of Thin Plates of Microwave Acoustic Materials

Piezoelectric coupling (%)

Temperature coefficient (10-6/K)

Crystal

Class

Orientation

Mode

GaAs

43M

(110) (111)

Shear extension

6 4

- 34 - 72

Li2B40 7

4MM

49 °

z

Shear extension

26 19

0 + 191

(yxl)

LiTaO 3

3M

(xxl) 50 ° z

Shear extension

5 18

0 - 46

LiNbO 3

3M

x z

Shear extension

70 17

- 60 - 45

AIPO 4

32

(yxl)

31 °

x

Shear extension

12 8

0 - 65

(xyl) 35 ° x

Shear extension

9 10

0 - 20

SiO 2

32

Note.

R e p r o d u c e d , with permission, from Table 2 in Ballato and Lukaszek [13], copyright © 1990 by Horizon House-Microwave, Inc.

2.0 •

A

1.5

AMPEX

x

COUNTIS

o

XTALONIX

[]

TRANS-TECH

{n {n D 1.0 v

0.5

mm

0.0

!

I

i00

150 CURIE

I

200

TEMPERATURE

I

300

250 ( °C

)

Figure 7. Saturation magnetization versus Curie temperature for aluminum-substituted YIG. The data were published by Ampex, Redwood City, CA; Countis San Luis Obispo, CA; Trans-Tech, Adamstown, MD; and Xtalonix, Columbus, OH. Reproduced, with permission, from Figure 5.6 in Hord [15], copyright © 1989 by John Wiley & Sons, Inc.

._1

I11 !._ !._ tll u_

E E 0

t~ Q.

£ u

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~ .~o

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g.o

r~ 0

0

o

o

c',l

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c¢~

t'xl 1¢3 t'~

c¢~ c¢3 t¢3

VVVV

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19. Microwave Materials

6]]

TABLE 19 Properties of Conductor Materials for the Thin-Film Technique

Material Conducting layer material Ag Cu Au A1 Adhesion layer Cr Ta Ti Separation layer Pt Pd

Relative specific resistance, p/Pcu a

0.95 1.0 1.36 1.6

Skin depth, 6 (in micrometers, at 2 GHz)

Thermal expansion coefficient, AITh/(l AT) (in 1 0 - 6 / K )

Adhesion on A I 2 0 3 ceramic

Coating method b

1.4 1.5 1.7 1.9

21 18 15 26

Poor Poor Poor Poor

evap evap, galv evap, galv evap

Good Good Good

evap Sp, evap Sp, evap

7.6 9.1 27.7

4.0 4.5 7.8

8.5 6.6 9.0

6.2 6.2

3.6 3.6

9.0 11.0

Sp, evap Sp, evap

Note. Reproduced, with permission, from Table 1.14 in Hoffmann [16], copyright © 1987 by Artech House, Inc. g Pcu = 1.72 × 1 0 - 6 ~ cm. bevap, evaporation; galv, electrolytic deposition; and Sp, sputtering.

TABLE 20 Properties of Thin-Film Resistors

Material

Specific surface resistance (t << 6), R F = p/t (in ~ )

Temperature coefficient of the resistance, A R / ( R . AT) (in 1 0 - 6 / K )

Stability A R / ( R . AT) (in % / 1 0 0 0 h)

Production a

NiCr Cr Ta TazN Ti Cr-SiO cement

40-250 10-500 40-200 10-100 5-2000 500-2000

- 100 to + 100 - 300 to + 300 - 200 to + 200 - 6 0 to + 30 - 500 to + 500 - 250 to + 250

< 0.2 good Medium < 1 medium < 0.2 good Medium < 0.5 medium

evap evap Sp Reactive Sp evap Flash Sp

Note. Reproduced, with permission, from Table 1.15 in Hoffmann [16], copyright © 1987 by Artech House, Inc. aevap, evaporation; and Sp, sputtering.

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19. Microwave Materials

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4. Thin Films The physical characteristics of thin films fabricated via evaporation, sputtering, and electrolytic deposition are discussed in the following section [16]. Table 19 considers the specific resistance, thermal expansion, and adhesion on alumina substrate of conductive films. Resistive films are covered in Table 20. Table 21 presents the ranges of variation of the dielectric constant and loss tangent of thin-film capacitor materials vs their thicknesses. The temperature coefficients of capacitance, breakdown values, and specific surface capacitances are also included.

5. Electromagnetic Properties of Metals Particle-accelerator engineers, in their quest to produce high-Q resonators, are interested in the variation of the surface resistance of metals with surface roughness. A similar quest arises in the everyday implementation of the stripline when the microwave loss of metal films and the stripline's variation with the quality of the films (surface roughness, the ~A H

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636

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g r a n u l a r n a t u r e of t h e film, a n d t h e e l e c t r o n m e a n f r e e p a t h in m e t a l s as r e p r e s e n t e d by s u r f a c e c o n d u c t i v i t y ) a r e c o n s i d e r e d . F i g u r e 8 a d d r e s s e s t h e v a r i a t i o n of t h e s u r f a c e r e s i s t a n c e of m e t a l wires at 3 G H z us s u r f a c e r o u g h n e s s s c a l e d to skin d e p t h ( r e l a t e d to c o n d u c t i v i t y ) [17]. F i g u r e 9

TABLE 22 Reflective Losses of Common Metals

Resistivity Metal Aluminum Beryllium Brass (66 Cu and 34 Zn) Chromium Copper Gold Nickel Platinum Silver Tin

Skin depth (/xm)

Reflective loss

[(O-m) x 10 -8 ] 2 GHz 100 GHz 200 GHz 2 GHz 100 GHz 200 GHz 2.62 4.57

1.82 a 2.41

0.258 0.340

0.182 0.241

0.000152 0.0012 0.0015 0.000202 0.0014 0.0020

3.9 2.6 1.72 2.44 6.9 10.5 1.62 11.4

2.2 1.8 1.48 a 1.76 a 0.42 a 3.65 1.43a 3.80

0.31 0.26 0.209 0.249 0.059b 0.516 0.203 0.537

0.22 0.18 0.148 0.176 0.042b 0.365 0.143 0.380

0.000185 0.000151 0.000124 0.000148

0.0013 0.0011 0.0008 0.0010

0.0018 0.00151 0.00124 0.00147

0.000307 0.002 0.0031 0.000120 0.0008 0.0012 0.000319 0.0022 0.0032

Note. Reproduced from Table 1 of "Geosynchronous Microwave Atmospheric Sounding Radiometer Feasibility Study," Final Rep. Hughes Ref. No. D8647.SCG70532R, Contract NAS 5-24082, p. D-3 (1978). aVerified by comparison with published values; see Fink, Electronics Engineers' Handbook, p. 6-4. bAssumes /'/'r = 5 0 .

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depicts the temperature dependence of the surface resistance of copper at 1.2 GHz. As the temperature is lowered (and the conductivity is increased), the surface resistance approaches a minimum (determined by the surface quality and microscopic nature of electron transport in the vicinity of the surface boundary) [18]. Table 22 compiles the reflection losses of common metals at microwave frequencies. Figures 10 and 11 briefly introduce

638

Hamid H.S.Javadi

design patterns for surface element geometries employed as radar absorbers and in bandpass applications [19].

6. Physical and Electromagnetic Properties of Bulk and Thin-Film Superconductors Conventional and new high-temperature superconductors are gaining more recognition from the microwave community as high-frequency/low-power circuit designs are required for faster computers, broadband communications, and cryogenic/microwave-power-limited space applications. Tables 23, 24, and 25 present the physical properties of conventional TABLE 23

Superconductor Metals and Alloys Material

Crystal form

Tc (K)

Hc2(4.2 K)(T)

bcc alloy

9.5 10.8

11.5 10.5

18.0 20.3 20.7 23.0 15.2 17.0

21.5 33 41 37 22 21

Bi compound

15.7 16.5

13 28

V 2 (Hf, Zr)

C15 compound

10.1

23

Pb Mo 6 S 8

Chevrel

14.3

50

Nb-Ti Nb-Zr Sn Ga Nb 3 (A1, Ge) Nb 3 Ge V3Ga V3Si

Nb 3

Nb 3

A15 compound

NbN NbN film

TABLE 24

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Structure

Tc (K)

Sr-TiO 3- ~ BaPbl_ x BixO 3

Perovskite

0.55 13

TiO

NaCI

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1.25

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Bronze

6.7

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Superconductor Material Parameters

Material

2A0

kBTc

Tc

(K)

ALo(A)

v F (106 m/see)

so0 (A)

l (A)

3500 7,10010,000 200 100,000

Sn Pb

3.53 4.10

3.75 7.19-7.22

355 280-308

0.65 0.60-0.68

2390 990-1110

Nb AI

3.80 3.20

9.20 1.178

333 154

0.28 1.34

390 17,290

(metal, alloy, ceramic)superconductors. Tc represents the transition temperature of superconductors, Hc2 is the upper critical magnetic field for type-II superconductors, A 0 is the superconductor gap, AL0 is the London penetration depth, ~'F is the Fermi velocity, so0 is the coherence length, and l is the electron mean free path. Table 26 compiles the physical parameters of high-temperature superconductors [20]. Figure 12 illustrates the surface resistance of YBazCu307_ a (epitaxially grown films and single-crystal platelets) v s frequency. These data represent the work of pioneers in this new technology. It indicates that epitaxial films of

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Y B a 2 C u 3 0 7 _ , ~ can c o m p e t e with N b at 4.2 K. T h e q u e s t for t h e m o s t useful s u b s t r a t e on w h i c h to g r o w an epitaxial h i g h - t e m p e r a t u r e s u p e r c o n d u c t o r film was t h e m o t i v a t i o n for T a b l e 27. T h e crystal unit cell p a r a m e ters of s u b s t r a t e s n e e d to be m a t c h e d with t h o s e of s u p e r c o n d u c t o r s for t h e b e s t results. T h e dielectric c o n s t a n t s a n d loss t a n g e n t s of s u b s t r a t e s a r e i m p o r t a n t for m i c r o w a v e applications. T h e t h e r m a l coefficients of e x p a n s i o n are significant p a r a m e t e r s b e c a u s e t h e h i g h - t e m p e r a t u r e s u p e r c o n d u c t o r films have to be u s e d at c r y o g e n i c t e m p e r a t u r e s . M a n y e n t r i e s in T a b l e 27 a r e n o t final d u e to t h e c o n t i n u o u s r e s e a r c h in this n e w exciting field.

Acknowledgment I thank Professor T. Koryu Ishii for his support on this project and Professor Anti Raisanen for his critical reading.

References

[1] A. C. Lynch, Relationship between permittivity and loss tangent, lEE Proc., Vol. 118, p. 244, 1971. [2] J. Ibruegger, Transmission of room-temperature radiation by materials at low temperatures, Int. J. Infrared & Millimeter Waves, Vol. 5, p. 664, 1984. [3] A. Von Hippel, Dielectric Materials and Applications. New York: Wiley & Sons, 1954. [4] M. N. Afsar et al., Int. J. Infrared & Millimeter Waves, Vol. 3, p. 319, 1982. [5] F. E. Gardiol, Design and layout of microstrip structures, lEE Proc. Part H, Vol. 135, p. 153, 1988. [6] I. Bahl and K. Ely, Modern microwave substrate materials, Microwave J., 1990 State of Art Ref., p. 135, 1990. [7] V. J. Dicaudo, Radomes in Radar Handbook (M. I. Skolnik, ed.), Chap. 14, New York: McGraw-Hill, 1970. [8] H. Howe, Jr., Stripline Circuit Design, Chap. 1. Dedham, MA: Artech House, 1974. [9] H. Howe, Jr., Dielectric material development, Microwave J., Vol. 14, p. 26, 1971. [10] R. C. Kell, E. E. Riches, P. Brigginshaw, G. C. E. Olds, A. J. Thomas, R. F. Mayo, and D. F. Rendle, Novel temperature-stable ceramics for microwave dielectric resonators and microstrip substrates, Electron. Lett., Vol. 6, p. 614, 1970. [11] R. Heidinger and F. K6niger, Size parameter studies in Fabry-Perot resonators for dielectric measurements of irradiated specimens, Conf. Dig. 14th Int. Conf. Infrared & Millimeter Waves, SPIE No. 1240, p. 542, 1989. [12] D. Penunuri, K. H. Yen, andR. B. Stokes, Microwave surface acoustic wave devices, in Handbook of Microwave and Optical Components (K. Chang, ed.), Vol. 1, Chap. 6, page 289. New York: John Wiley & Sons, 1989. [13] A. Ballato and T. Lukaszek, Microwave acoustic material properties, Microwave J., Vol. 33, p. 106, 1990. [14] F. J. Rosenbaum, Ferrites control microwave energy, The Microwave System Designer's Handbook, First Ed., Chap. 6, p. 163. Cardiff Publishing Co., 1983.

19. Microwave Materials

643

[15] W. E. Hord, Ferrite control components, in Handbook of Microwave and Optical Components (K. Chang, ed.), Vol. 1, Chap. 5. p. 245, New York: John Wiley & Sons, 1989. [16] R. K. Hoffmann, Handbook of Microwave Integrated Circuits. Norwood, MA: Artech House, 1987. [17] R. D. Lending, New criteria for microwave component surfaces, Proc. Natl. Electron. Conf., Vol. 11, p. 395, 1955. [18] R. G. Chambers, Anomalous skin effect in metals, Nature (London), Vol. 165, p. 239, 1950. [19] M. T. Tuley, Radar absorbers in Radar Cross Section: Its Prediction, Measurement, and Reduction (E. F. Knott, J. F. Shaeffer, and M. T. Tuley, eds.), Chap. 9. Norwood, MA: Artech House, 1985. [20] P. Micnas, R. Janninger, and S. Robaszkiewicz, Superconductivity in narrow-band systems with local nonretarded attractive interactions, Rev. Mod. Phys., Vol. 62, p. 117, 1990. [21] H. H. S. Javadi, K. Cromack, A. J. Epstein, M. Angelopoulous, and A. G. MacDiarmid, Microwave transport in emeraldine form of polyaniline, Phys. Rev. B., Vol. 39, p. 3579, 1989. [22] H. H. S. Javadi, Polymers, exotic composite materials, Microwave J., Vol. 32, p. 162, Feb. 1989. [23] Z. H. Wang, H. H. S. Javadi, A. Ray, A. G. MacDiarmid, and A. J. Epstein, Electron localization in polyaniline derivatives, Phys. Rev. B., Vol. 42, p. 5411, 1990. [24] H. H. S. Javadi, A. Chakraborty, C. Li, N. Theophilou, D. Swanson, A. G. MacDiarmid, and A. J. Epstein, Highly conducting polyacetylene: Three-dimensional delocalization, Phys. Rev. B., Vol. 43, p. 2183, 1991. [25] D. W. Cooke, E. R. Gray, H. H. S. Javadi, R. J. Houlton, P. N. Arendt, N. Klein, G. Muller, S. Orbach, H. Piel, L. Drabeck, G. Gruner, J. Y. Josefowicz, D. B. Rensch, and F. Kiajenbrink, Frequency dependence of the surface resistance in high temperature superconductors, Solid State Commun., Vol. 73, p. 297, 1990. [26] H. H. S. Javadi, W. R. McGrath, B. Bubmle, and H. G. LeDuc, Dispersion in Nb microstrip transmission lines at submillimeter wave frequencies, Appl. Phys. Lett., Vol. 61, p. 2712, 1992.

This Page Intentionally Left Blank

Index

A boldface 1 or 2 before page numbers indicates the volume in which the entry is located.

A Absolute transmission delay, 2, 455 Absorber number density, 2, 351 Absorbing microstrip terminations, 1, 131-135 Absorption, 2, 366 atmospheric absorption, 2, 473-474, 496-498, 606 microwaves, 2, 350, 637 specific absorption ratio, 2, 316-323 Absorptivity, 2, 151 Active baluns, 1, 663-666 Adhesives, properties, 2, 622 Adjacent channel interference fade margin, 2, 495-496 Adjoint operators, 2, 584 Admittance, 1, 61-62, 620 Aeronautical mobile satellites, microwave propagation, 2, 240 Agricultural applications, 2, 293-296 AIN, properties, 2, 159, 160 Aircraft navigation, Doppler navigator, 2, 417-425 ALDAS (software), 2, 185 Algebraic reconstruction technique (ART), 2, 338 Allan variance, 2, 568

All-pass filters, 1, 161-162 All-pole bandpass transformations, 1, 164, 170 Alumina, s e e Aluminum oxide Aluminum (A1) inductors, 1, 96 microwave antennas, 2, 201-202 properties, 1, 369; 2, 158, 633, 636, 639 waveguides, 1, 19 Aluminum oxide (A1203), 1, 48, 95, 112 microwave heating, 2, 291 properties, 2, 159, 160, 611,623, 634 AM detectors, s e e Amplitude modulation detectors Ammonium dihydrogen phosphate, 2, 613 AM noise, s e e Amplitude modulation noise Amplifiers, 1, 391-392, 589-590 Amplitron, 2, 87 backward-wave amplifiers, 2, 77-78 bipolar amplifiers, 1, 405-406 cascade backward-wave amplifiers, 2, 78 crossed-field amplifiers, 2, 84-87 design, 1, 394-423 differential amplifiers, 1, 666 efficiency, 2, 86 GUNN amplifiers, 1, 346-350 gyroklystrons, 2, 98, 102-103, 114

645

646 IMPATT devices, 1, 377-381 impedance matching, 1, 630, 631,656 isolators, 1, 254-257, 408-410, 423 low-noise amplifiers, 1, 392-394, 405-428, 487; 2, 527-533 magnicons, 2, 98, 111-112 moderate bandwidth amplifiers, 1, 392, 393, 395, 426 noise, 1, 384-386, 407, 411,413, 415-419; 2, 527-528 octave band amplifiers, 1, 392-393, 412, 416, 428 parametric amplifiers, 1, 487 paraphrase amplifiers, 1, 663-666 power amplifiers, 1, 423-428 triode amplifiers, 1, 589-591 ultra-low-noise amplifiers, 1, 415, 428 ultra-wide-band amplifiers, 1, 394, 413, 414 wide-band amplifiers, 1, 405, 414, 657, 658 Amplitron, 2, 87 Amplitude modulation (AM) detectors, 1, 461-470 bridge detectors, 1, 462 coaxial line detectors, 1, 464-466 microstrip line detectors, 1, 467, 469-470 microwave FM detection, 1, 474-475 quadruple detectors, 1, 462-463 ring detectors, 1, 462 series diode detectors, 1, 461-462 shunt diode detectors, 1, 461-462 two-wire line detectors, 1, 463-465 waveguide detectors, 1, 465-468, 492 Amplitude modulation (AM) noise, 1, 487-489 GUNN oscillators, 1, 350, 351,353 Amplitude scintillation, 2, 230 AMPSYN (software), 1, 657 Analog radio system, 2, 301,449, 451-453 Angle diversity, 2, 499 Angle-of-arrival, 2, 230 Aniline-formaldehyde plastic, properties, 2, 612 Annular phased array (APA), 2, 330 Anodes gyrotrons, 2, 104 magnetrons, 2, 41-43, 47-48, 80, 82 strapping, 2, 42-43, 82 ANSYS (software), 2, 142 Antenna noise temperature, 2, 183 Antennas, s e e Microwave antennas Anticommutator, 2, 578 Antimony (Sb), diodes, 1, 371 Antipodal finlines, 1, 28-31 APA, s e e Annular phased array

Index

Appleton-Hartree equation, 2, 235 Applications biomedical, 2, 285, 288, 309-339 chemical, 2, 347-363 communications, 2, 9-11,207-241, 300-303, 449-501 consumer goods, 2, 249-273 foods, 2, 284-285, 290, 296 industrial, 2, 277-303 law enforcement, 2, 429-448 navigation aids, 2, 403-425 Applied magnetic field, 1, 235 Approximate narrow-band filters, 1, 168 Arbitrary loss, dielectric film capacitors, 1, 111-113 Arcing klystrons, 2, 28, 29 magnetrons, 2, 55 microwave oven, 2, 251 Argon, microwave heating, 2, 289 ARGUS (software), 1, 528; 2, 76 Arithmetic symmetry, bandpass transforms, 1, 171-172 Arsenic (As), diodes, 1, 371 Arsenic trichloride (AsC13), vapor-phase epitaxy, 1, 314-315 Arsine, vapor-phase epitaxy, 1, 314, 315 ART, s e e Algebraic reconstruction technique Asphalt, microwave curing, 2, 284 Asymmetric couplers, 1, 214-216 Asymmetric series gap capacitors, 1, 118-121 Asymptotic methods, 2, 599 Atmospheric absorption millimeter waves, 2, 606 radio path loss, 2, 473-474, 496-498 Atmospheric conditions, microwave propagation, 2, 212-228 Atmospheric ducting, microwave propagation, 2, 232 Atmospheric multipath fading, 2, 487-492 Atmospheric refractive index, 2, 212-213 Attenuation, 2, 214-228, 302, 351 circular waveguides, 1, 26 coaxial lines, 1, 12-13 earth-space paths, 2, 225-227 fog and clouds, 2, 227 gaseous atmosphere, 2, 215-219 imageguides, 1, 39-40 insertion loss, 1, 569 line-of-sight paths, 2, 214-228 low-pass filter prototypes, 1, 159-160 microstrip lines, 1, 51 microwave oven, 2, 260, 262-269 mismatch attenuation, 1, 159

Index

radio path loss, 2, 474-477, 499-500 rain, 2, 220-227 sand and dust, 2, 228 snow and ice crystals, 2, 227 specific attenuation, 2, 215, 217 terrestrial paths, 2, 225, 228-230 Attenuation constant, 2, 208, 211 biological materials, 2, 335 circular waveguides, 1, 22, 27 coaxial lines, 1, 6, 10 dielectric rectangular waveguides, 1, 38 imageguides, 1, 39-40 rectangular waveguides, 1, 18, 38 small-signal analysis, 2, 75 suspended substrate technique, 1, 143-144 TEM lines, 1, 3 Attenuation parameter, small-signal analysis, 2, 75 Attenuators, 2, 71-72, 376, 377 solid state, 1, 586-588 S-parameters, 2, 507 Audio Doppler, 2, 430, 439 AUTOGRID (software), 1, 519 Avalanche region, 1, 283, 363, 367 Average convection heat transfer coefficient, 2, 146 Average Nusselt number, 2, 148, 149 Average power, klystrons, 2, 15 Average power rating, waveguides, 1, 21-22, 27-28

B Back-bombardment, 2, 39 Backward diodes, 1, 261,262 Backward-wave devices, 2, 77-79, 87-90 amplifiers (BWA), 2, 77-78 oscillators (BWO), 2, 78-79 Balanced amplifier design, 1, 410-411 Baluns (balanced to unbalanced transformers), 1, 660-666 Bandpass filters, 1, 156, 164-170, 179-182 combline bandpass filters, 1, 181 dissipation loss, 1, 186 hairpin bandpass filters, 1, 180-181 interdigital bandpass filters, 1, 181-182 loaded Q definition, 1, 185 parallel-coupled half-wave resonator bandpass filters, 1, 179-180 surface element teometry, 2, 637 symmetric transforms, 1, 169-170 top-C-coupled, 1, 166-168, 171 top-L-coupled, 1, 168-169, 171-172 tubular, 1, 170 yttrium iron garnet, 1, 256-257

647 Bandpass loss, 1, 186 Bandpass networks, 1, 659-660 Bandpass transforms, 1, 164-172 Bandstop filters, 1, 165, 185 Bandstop filter transforms, 1, 165-166 BARITT diodes, s e e Barrier injection transittime diodes Barium ferrite spheres, 1, 341 Barium tetratitanate, properties, 2, 614 Barrier injection transit-time (BARITT) diodes, 1, 261,364, 365 Barrier potential, diodes, 1, 264 Batching, 2, 435, 442-'443 Baud, 2, 454 Bazooka baluns, 1, 661 Beam analyzers, 2, 23 Beam-coupling impedance, 2, 86 Beam-lead diodes, 1, 261-264, 268-269, 273 Beam shavers, 1, Beam-width, microwave antennas, 2, 170-171, 173 BER, s e e Bit error ratio Beryllium (Be), 1, 372 properties, 2, 636 Beryllium dioxide (BeO2), properties, 2, 159, 160, 623 Bessel functions, 1, 74; 2, 593-595 Bessel prototype values, 1, 161, 162 Bethe-hole couplers, 1, 202-205 Bethe holes, 1, 202 Bias current, 1, 277, 281 Biasing attenuators, 1, 586-588 direct current, 1, 585-587 phase shifters, 1, 582-586 transistors, 1, 396-397 Bias-tuned GUNN oscillators, 1, 340-341 Bias voltage, 1, 277, 281,282, 340, 582 Bilateral finlines, 1, 28-31, 33-34 Bimodal induction cavities, electron paramagnetic resonance spectroscopy, 2, 395 Binomial couplers, 1, 207, 208 Binomial transformers, 1, 641-645 Bioheat equation, 2, 328-330 Biological materials electrical properties, 2, 309-315 heat deposition, 2, 315-323 Biomedical applications biomass drying, 2, 288 electrical properties of biological materials, 2, 309-315 exposure guides and standards, 2, 323-327 frozen sample thawing, 2, 285

648 Biomedical Applications ( c o n t i n u e d ) heat deposition in biological materials, 2, 315-323 microwave hyperthermia for cancer treatment, 2, 327-331 microwave monitoring, imaging, and sensing, 2, 332-339 Biot number, 2, 145 Bipolar amplifiers, 1, 405-406 Bipolar junction transistors (BJT), 1, 284-293, 405, 419, 432 Bismuth telluride (BiTe), properties, 2, 161 Bistatic radar, 2, 300 Bit, 2, 454 Bit error ratio (BER), 2, 455-456, 460-464 Black-body radiation, 2, 333-335 Blinchikoff flat delay bandpass transform, 1, 172 Bohr magneton unit, 2, 359 Boiling heat transfer coefficient, 2, 149 Boltzmann equation, 2, 351 Boron (B), varactor diode, 1, 271 Boron nitride (BN), properties, 2, 159, 160, 633 Borosilicate glass, properties, 2, 611, 616-617 Boundary conditions, 2, 590-591 Branch-guide couplers, 1, 225-226, 228 Branch-line couplers, 1, 223, 225-228, 232 Brass microwave antennas, 2, 202 properties, 1, 344; 2, 158, 636 waveguides, 1, 19 Bridge detectors, 1, 462 Brillouin cloud, 2, 80 Brillouin field, 2, 7 Brillouin field level, 1, 539, 540 Brillouin focusing, 1, 548, 549; 2, 62-63 Broadband antennas, 2, 169 Broad beamwidth antennas, 2, 174 Broadcasting, s e e Transmission Broadside-coupled stripline coupler, 1, 218 Bronze, microwave antennas, 2, 203 Bulk resonators, 1, 196 Butterworth approximation, 1, 156-158, 160, 161 Butterworth filters, 1, 159 Butyl rubber, properties, 2, 613 BWA, s e e Backward-wave devices BWO, s e e Backward-wave devices

C CAD, s e e Computer-aided design Cadmium telluride (CdTe), 1, 276, 309

Index

CAEDS (software), 2, 142 Calcium titanate (CaZiO2), properties, 2, 611 Camera radar, 2, 435 Cancer treatment, hyperthermia, 2, 327-331 Capacitance, 1, 186-187 avalanche capacitance, 1, 283 capacitors, 1, 112, 115-121 coaxial lines, 1, 7 detectors, 1, 462, 463 diodes, 1, 263, 266, 269-271,273, 277, 279, 283 domain capacitance, 1, 279 end capacitance, 1, 122 equivalent capacitance, 1, 54 filters, 1, 167 ground capacitance, 1, 99, 101 inductors, 1, 99, 101, 106, 109-110 junction capacitance microstrip lines, 1, 53-58 quarter-wave transformers, 1, 651-652 solid-state devices, 1, 263, 266, 269, 270, 271,273-275, 276, 571 open-end capacitance, 1, 53, 121 package capacitance, 1, 277, 571 parallel capacitance, 1, 128 parasitic capacitance, 1, 263, 271,273, 413 shunt capacitance, 1, 462 temperature coefficient of capacitance, 2, 625 total capacitance, 1, 263, 273 transistors, 1, 301 two-wire lines, 1, 4 winding capacitance, 1, 106, 109-1 l0 Capacitors, 1, 186-188 capacitance, 1, 112, 115-121 chip capacitors, 1, 187 coupling capacitors, 1, 167 dielectric-film overlay capacitors, 1, lll-ll5 disk capacitors, 1, 115-118 materials, 2, 634 radio frequency choke, 1, 464, 466, 470 series gap capacitors, 1, 118-121 wafer capacitors, 1, 111 Carcinotron, 2, 87 Carpet backing, microwave drying, 2, 287 Carrier-to-noise ratio, 2, 214-215 Cascade backward-wave amplifiers, 2, 78 Catchers, microwave, 2, 303 Cathode heaters, 1, 516-518 Cathodes, 2, 57-60 computer-aided design, 1, 517

Index

dispenser cathodes, 1, 514-515, 517 heaters, 1, 516-518 klystrons, 2, 5, 20 loading, 1, 513-514 magnetrons, 2, 39-41, 54 oxide cathodes, 1, 515-516 type M cathode, 1, 515 Cauchy boundary conditions, 2, 590 Cauchy's integral formula, 2, 571-572 Cauer-Chebyshev prototypes, 1, 162-163 Cavity resonators, electron paramagnetic resonance spectroscopy, 2, 384-399 Cavity-stabilized GUNN oscillators (CSGO), 1, 342-346 Cavity-tuned oscillators, 1, 433, 435-436 Cayley-Hamilton theorem, 2, 578 C-band beacon antennas, missiles, 2, 198-199 CCIR, s e e International radio consulative committee Cellulose acetate-butyrate, properties, 2, 611 Center frequency bandpass filter prototypes, 1, 164 circulators, 1, 251-252 Ceramics, 1, 194-195 dielectric properties, 2, 611 properties, 2, 159, 160 superconductors, 2, 638 Ceresin wax, properties, 2, 613 CFA, s e e Crossed-field amplifiers Chamfered symmetric bend, 1, 130-131 Characteristic conductance, transmission lines, 1, 62 Characteristic impedance bilateral finlines, 1, 33-34 coaxial lines, 1, 6 dielectric waveguides, 1, 42-43 finlines, 1, 33-34 imageguides, 1, 41-43 microstrip lines, 1, 48, 49-52, 55 TEM lines, 1, 3 unilateral finlines, 1, 33-34 waveguides, 1, 13 Chebyshev approximation, 1, 159-161 Chebyshev couplers, 1, 208-210, 226-228 Chebyshev tapers, 1, 654-655 Chebyshev transformers, 1, 645-651,654 Chemical applications electron spin resonance spectroscopy, 2, 359-360 industrial applications, 2, 277-303 microwave absorption spectroscopy, 2, 347-353

649 microwave heating, 2, 289-293, 362-363 nuclear magnetic resonance spectroscopy, 2, 353-358 synthetic methods using microwaveproduced plasmas, 2, 360-362 Chemical shift, nuclear magnetic resonance spectroscopy, 2, 355 Child-Langmuir law, 1, 511-512; 2, 58 Chip capacitors, 1, 187 Chip diodes, 1, 273 Chip transistors, 1, 403 Choke structure, microwave oven, 2, 257-260 Chromium, properties, 2, 158, 633, 636 Circuit efficiency, amplifiers, 2, 86 Circular cylindrical waveguide cavities, 1, 73-80 Circular disk capacitors, 1, 115-116 Circularly polarized (CP) antennas, 2, 177-179 Circular ring indttctors, 1, 103 Circular spiral inductors, 1, 103-107 Circular waveguides, 1, 14, 22-28 attenuation, 1, 22, 26, 27 peniotron, 2, 131-132 phase shifters, 1, 244-246 Circulators, 1, 249-250 ferrites, 1, 249-254, 347 switches, 1, 257-258 Climate, microwave attenuation, 2, 220-227 C-L law, 1, 511-512 Clocks, Global Positioning System, 2, 407-408, 414 Closed ring resonators, 1, 87-88 Clothes, microwave drying, 2, 287 Clouds, microwave attenuation, 2, 227 Coal industry, microwave processes, 2, 288, 290-291,293, 298 Coarse-step frequency synthesizer, 1, 454 Coated films, microwave drying, 2, 287 Coaxial-cavity GUNN oscillators, 1, 326, 327-328, 336-338 Coaxial lines, 1, 1, 5-13 AM detectors, 1, 464-466 attenuation, 1, 12-13 baluns, 1, 660, 662, 663 capacitance, 1, 7 equations, 1, 6, 7, 12-13 microwave antennas, 2, 182-183 microwave mixers, 1, 479-480 modes, 1, 8-10 Q-factor, 1, 7 Coaxial magnetrons, 2, 83-84

650 Coaxial resonators, 1, 66-68, 196, 433, 436-437 oscillators, 1, 433, 436, 437, 445, 446 Coaxial-to-microstrip transitions, 1, 136-138 Codes, s e e Software Cole-Cole relationship, biological materials, 2, 312 Collector efficiency, transistors, 1, 288 Collectors Faraday cage collectors, 1, 552 klystrons, 2, 8 multistage depressed collectors, 1, 556, 558-559; 2, 73-74 secondary emission, 1, 559-560 single-stage collectors, 1, 552-555; 2, 72-73 spent beam models, 1, 553-556 Collimating antennas, 2, 180 Combline bandpass filters, 1, 181 Communication applications, 2, 300-303 fading, 2, 451,472-473, 477-492 klystrons, 2, 9-11 microwave propagation, 2, 207-241 radio communications, 2, 449-501 Commutator, 2, 578 Complex conductivity, 2, 607 Complex dielectric constant, 2, 208, 607 Complex dielectric permittivity, 2, 208 Complex functions, 2, 571-573 Complex to real impedance transformation, 1, 632-636, 637-639 Computed tomography, 2, 338 Computer-aided design (CAD) amplifiers, 1, 421 cathodes, 1, 517 electron gun design, 1, 502-503, 505-508 IMPATT oscillators, 1, 383 klystrons, 2, 23 transistors, 1, 292-293, 302 Computer simulation, s e e Simulation Computer software, s e e Software Conductance, characteristic, 1, 62 Conduction heating, 2, 279-280 Conduction shape factor, 2, 142-144 Conductive heat transfer, 2, 139-145 Conductivity, 2, 207-209 biological materials, 2, 310, 312, 314 complex conductivity, 2, 607 Conductivity modulation, 1, 275 Conductor attenuation constant, coaxial lines, 1,7 Conductor loss

Index

dielectric film capacitors, 1, 114-115 microstrip lines, 1, 51-52 Conductor quality factor, 1, 7 Conductors, microwave antennas, 2, 201-203 Conductor thickness, microstrip lines, 1, 50 Conductor width, microstrip line, 1, 55-56, 127-128 Confined flow focusing, 1, 549-550, 551; 2, 63 Conformal mapping, 2, 592-594, 597 Consecutively severely errored seconds (CSES), 2, 457 Constantan, properties, 2, 158 Constituent cavity, 1, 251,254 Consumer applications, 2, 249-273 Continuous coupling, 1, 211 Continuous wave bridges dispersion detection, 2, 378-380 electron paramagnetic resonance spectroscopy, 2, 368-383 one-arm, 2, 369-375, 381-383 reference arm, 2, 375-378 Continuous-wave (CW) frequency, measurement, 2, 553-554 Continuous-wave (CW) magnetrons, 2, 33-34, 39, 43,51 Continuous-wave (CW) oscillators, 1, 383, 384 Contour integrals, 2, 572 Controlled phase prototypes, 1, 160-162 Convective heat transfer, 2, 145-151, 161 Conventional elliptic bandpass transforms, 1, 170, 171 Convergence ratio, 2, 60-61 Convergence tests, infinite series, 2, 575 Converters, 1, 485-486 noise, 1, 487-489 packaging, 1, 494 Cooker oven magnetrons, 2, 34, 47 Cooling, magnetrons, 2, 43, 51-52 Coplanar waveguide coupler, 1, 218 Copper (Cu) attenuation, 1, 18, 20, 27 microwave antennas, 2, 203 properties, 1, 369; 2, 158, 633, 635, 636 Cores, 1, 195 Corona rings, 1, 539 Cosine error, 2, 433, 444-445 Cottonseed, microwave drying, 2, 293-294 Coupled-cavity circuit, 2, 67-70 Coupled-line couplers, 1, 200, 213-225 Coupled lines, suspended substrate technique, 1, 145, 149-153

651

Index

Coupled round rod couplers, 1, 218 Coupled slotline couplers, 1, 218 Coupled wave voltage, 1, 214 Couplers amplifier design, 1, 410-411,590 directional, 1, 199-201,232 branch-guide couplers, 1, 225-226, 228 branch-line couplers, 1, 223, 225-228, 232 coupled-line couplers, 1, 200, 213-225 rat-race couplers, 1, 229-232 waveguide aperture couplers, 1, 201-213 electron paramagnetic resonance spectroscopy, 2, 374 impedance, 1, 214, 223-224, 228 measuring RF leakage with, 2, 199-201 reflectometers, 2, 509 Coupling capacitors, bandpass filters, 1, 167 Coupling factors, 1, 62, 64 Coupling impedance, 2, 125 Coupling inductors, 1, 168 CP antennas, s e e Circularly polarized antennas Cramer's rule, 2, 578 Crepe rubber, properties, 2, 613 Crest factor, 2, 529 Critical microwave magnetic field, 1, 237 Crossed-field amplifiers (CFA), 2, 84-87 Crossed-field backward-wave oscillators, 2, 87-90 Crossed-field devices, 2, 57, 58 Crossed-guide coupler, 1, 212-213 Cross junction, microstrip lines, 1, 58 Cryogenically cooled low-noise amplifier, 1, 419, 421 Crystal oscillators, 2, 568 CSES, s e e Consecutively severely errored seconds CSGO, s e e Cavity-stabilized GUNN oscillators CT scans, 2, 338 Curing, industrial, 2, 281-284 Curl (mathematics), 2, 588 Current density, electron guns, 1, 513-514 Current sensitivity, diodes, 1, 265 Cutoff frequency bandpass filter prototypes, 1, 164 coaxial transmission lines, 1, 67 diodes, 1, 263, 264, 270, 272-274 distributed resonators, 1, 192 dynamic cutoff frequency, 1, 270 scaling prototype values, 1, 157 transistors, 1, 286, 290, 299 Cutoff wavelength

circular waveguides, 1, 23, 26 coaxial lines, 1, 7, 9, 10 rectangular waveguides, 1, 15, 18 resonant cavities, 1, 328 CW magnetrons, s e e Continuous-wave magnetrons CW oscillators, s e e Continuous-wave oscillators Cyclotron frequency, 2, 123 Cylindrical cores, 1, 195 Cylindrical resonators, 1, 73-80

D Damping factor, 1, 236 Data communications, 2, 232-240, 300-303 DC biasing, s e e Direct current biasing DDM HELIX TWT (software), 2, 76 Debye functions, biological materials, 2, 310 Deformable triangular mesh (DTM) gun codes, 1, 522-523, 525-526, 530 Degraded minutes (DMs), 2, 457 Delay, coaxial lines, 1, 7 Delay line frequency discriminator, 2, 563-564 DEMEOS (software), 1, 502, 518-525, 532-533, 535, 551,552, 556, 558 Depressed collectors, 2, 8 Depressed efficiency, 1, 558 Detector diodes, 1, 261-268 AM detectors, 1, 461,463, 465,467, 471 packaging, 1,491-492 Detectors amplitude modulation, 1, 461-470 capacitance, 1, 462, 463 electron paramagnetic resonance spectroscopy, 2, 374, 375, 378 frequency modulation, 1, 470-477 noise, 1, 487-489 packaging, 1, 491-492 phase detector, 2, 564-567 phase modulation, 1,477-478 power detectors, 2, 538-544 video impedance, 1, 265 Determinant, 2, 577 Deviation from omni, 2, 186 Diamond, properties, 1, 369; 2, 159, 160, 615 Dichloronaphthalene wax, properties, 2, 613 Dielectric antennas, 2, 188-189, 203 Dielectric attenuation constant, coaxial lines, 1, 7 Dielectric constant biological materials, 2, 311, 313 complex dielectric constant, 2, 208, 607 relative dielectric constant, 2, 362 software for, 1, 224

652 Dielectric couplers, scattering parameters, 1, 217 Dielectric film capacitors, 1, 111-115 Dielectric heating, 2, 280 Dielectric loaded TEM mode, 1, 196 Dielectric loss dielectric film capacitors, 1, 114-115 microstrip lines, 1, 51 suspended substrate technique, 1, 143 Dielectric loss angle, 2, 72 Dielectric permittivity, 2, 208 Dielectric properties, 2, 608-627 Dielectric resonators, 1, 80-83, 196, 346 electron paramagnetic resonance spectroscopy, 2, 399 oscillators, 1, 436-438, 445, 447 properties, 2, 620, 624, 626-629 Dielectric ring resonators, 1, 83 Dielectric substrates, 1, 48, 95 ceramics, 1, 194-195 Dielectric waveguides, 1, 34-35 characteristic impedance, 1, 42-43 losses, 1, 38-42 propagation constant, 1, 35-38 Dielectric windows, 2, 72 Differential amplifiers, 1, 666 Differential DPS, 2, 415 Differential equations, 2, 365, 589-599 Diffraction, microwave propagation, 2, 184-185, 231 Diffraction fading, 2, 478-482 Diffraction loss, terrestrial line-of-sight propagation, 2, 228-229 Digital radio systems, 2, 301,450, 454-457 path unavailability, 2, 492 transmission errors, 2, 455-465 Dilution of precision (DOP), 2, 413-414 Dimensional ratio, resonant cavities, 1, 344 Dimensionless Grashof number, 2, 147 Dimensionless Nussett number, 2, 147 Dimensionless P6clet number, 2, 147 Dimensionless Prandtl number, 2, 147 Dimensionless Reynolds number, 2, 146, 147 Dimensionless Stanton number, 2, 147 Diode-based power detectors, 2, 540-541 Diodes, 1, 307 backward diodes, 1, 261,262 B ARITT diodes, 1, 261,364, 365 beam-lead diodes, 1, 261-264, 268-269, 273 capacitance, 1, 263, 266, 269-271,273, 277, 279, 283 Child-Langmuir law, 1, 511-512 detector diodes, 1, 261-268

Index amplitude modulation, 1, 461,463, 465, 467, 471 packaging, 1, 491-492 DOVETI" diodes, 1, 365 forward-biased diodes, 1, 271,274 GUNN diodes, 1, 276-280, 307 amplifiers, 1, 424-435 design, 1, 316-325 oscillators, 1, 332-334, 337, 342 power combiners, 1, 354 IMPATT diodes, 1, 276, 280-284, 348, 354, 363-368 amplifier design, 1, 377-381 commercial specifications, 1, 373-377 fabrication, 1, 368-373 noise, 1, 384-386 oscillator design, 1, 382-386 impedance, 1, 283, 284 inductance, 1, 263, 273-274, 277, 283 Josephson junction diodes, 1, 261 junction diodes, 1, 268, 269, 271 MITATT diodes, 1, 365 mixer diodes, 1, 261-268, 478-485 noise diodes, 2, 528, 530, 536-538 packaged, 1, 463, 465, 467, 491-492 PIN diodes, 1, 272-276, 489, 491-492, 569-582, 586-588 point-contact diodes, 1, 261,262 QWITT diodes, 1, 365, 370 Read diodes, 1, 368 rectification, 1, 265, 266 resistance, 1, 263, 266, 270-271,273, 275, 582-583, 586 Schottky barrier diodes, 1, 261-268, 463, 465, 491-492; 2, 156, 189, 374, 375 SIS junction diodes, 1, 261 switches, solid-state, 1, 569-582 TRAPATT diodes, 1, 365 TUNNETT diodes, 1, 364, 365 varactor diodes, 1, 268-272, 487, 490, 582-586, 587 whisker diodes, 1, 261-264, 269 Diplexers, 1, 579-580 Dirac ~ function, 2, 573, 575, 576 Direct binomial sampling, 2, 464 Direct current biasing, 1, 585-587 Direct frequency synthesis, 1, 449-452 Direct grounded lumped terminations, 1, 132-133 Directional couplers, 1, 199-201,232 branch-guide couplers, 1, 225-226, 228 branch-line couplers, 1, 223, 225-228, 232 coupled-line couplers, 1, 200, 213-225 microwave mixers, 1, 481

653

Index

rat-race couplers, 1, 229-232 reflectometers, 2, 509 waveguide aperture couplers, 1, 201-213 Directivity couplers, 1, 200, 206-211 microwave antennas, 2, 171-174 reflectometers, 2, 509 Direct wave voltage, 1, 214 Discontinuities distributed filters, 1, 174-175 microstrip lines, 1, 53-58 impedance steps, 1, 55-56, 127-128 open-ended microstrip, 1, 121-123 right-angle bends, 1, 56-57, 128-130 short circuits, 1, 122, 124-126 quarter-wave transformers, 1, 651 simulations, 1, 183-184 Discriminator mode (resonator), 1, 474, 475 Disk capacitors, 1, 115-118 Dispenser cathodes, electron emission, 1, 514-515, 517 Dispersion, 2, 366 detection, 2, 378-380 microstrip lines, 1, 50-51 suspended substrate technique, 1, 143-153 transformer design, 1, 652 traveling-wave tubes, 2, 66 Dispersion relations, 2, 572 Dispersion shaping, 2, 66 Dispersive fade margin, 2, 492, 496, Dispersive fading, 2, 491 Dissipated power, 2, 138 Dissipation loss, 1, 184-186 Distortion bandpass transforms, 1, 171-172 coupled-cavity circuits, 2, 69-70 Distributed amplification, 1, 412-414, 422, 423, 666 Distributed element matching networks, 1, 656-658 Distributed emission crossed-field amplifiers, 2, 84, 87 Distributed filters, 1, 156, 172-182 Distributed resonators, cutoff frequency, 1, 192 Distributed terminations, 1, 131, 135 Divergence (mathematics), 2, 588 Divergence theorem, 2, 589 Diversity, 2, 180, 498, 499 DMs, s e e Degraded minutes Dolph-Tschebyscheff method, 2, 194-195 Domain capacitance, 1, 279 DOP, s e e Dilution of precision Doping profile, diodes, 1, 320-321,367 Doppler audio, 2, 430, 439

Doppler broadening, 2, 353 Doppler navigation system, 2, 417-425 Doppler radar, 2, 417-425 law enforcement applications, 2, 429-431 Doppler shift, Global Positioning System, 2, 409-410 Dot product, 2, 587 Double-drift IMPATT diodes, 1, 280, 370, 375 Double period permanent magnet (DPPM) focusing, 1, 553-554 Double stub impedance matching, 1, 622-623 Double-velocity transit-time (DOVETT) diodes, 1, 365 Down-converters, 1, 486 DPPM focusing, s e e Double period permanent magnet focusing Drain lines, 1, 413 Drain-source current, 1, 301,400 Drichlet boundary conditions, 2, 591 Drift region, impedance, 1, 283 Drying, industrial, microwave processes, 2, 285-289, 293-294 DTM gun codes, s e e Deformable triangular mesh gun codes Dual-mode electron guns, 1, 506, 507 Dual-mode phase shifters, 1, 244-245 Dual polarized antennas, 2, 179 Dual-sample cavity, electron paramagnetic resonance spectroscopy, 2, 391 Duct fading, 2, 486-487 Duct propagation, 2, 232 Dust, microwave attenuation, 2, 228 Dyadics, 2, 578-579 Dynamic cutoff frequency, 1, 270 Dynamic quality factor, 1, 270

E Earth-space paths microwave attenuation, 2, 225-227 microwave propagation, 2, 232-240 Edge-coupled stripline couplers, 1, 218, 219, 224-225 EEsof (software), 1, 421 Effective capacitance, 1, 115 Effective dielectric constant finlines, 1, 32 microstrip lines, 1, 48, 49-51 Effective gyromagnetic ratio, 1, 236 Effective inductance, 1, 189, 283 Effective isotropic related power, 2, 213 Effective permeability, core, 1, 195 Efficiency amplifiers, 2, 86 collectors, 2, 73

654 Efficiency ( c o n t i n u e d ) transistors, 1, 290 traveling-wave tube, 2, 67, 70 Efficiency gain, 1, 558-559 EGUN (software), 1, 522, 528, 532, 535, 551; 2, 77 Eigenvalue problem, 2, 578, 584-585 EIK, s e e Extended interaction klystron ELDOR, s e e Electron-electron double resonance Electrical delay, measurement, 2, 525 Electric field, waveguides, 1, 15-17, 23-25 Electric field intensity, 2, 208, 211 Electrochemical cell, electron paramagnetic resonance spectroscopy, 2, 390-391 Electromagnet, magnetrons, 2, 46 Electromagnetic properties metals, 2, 636-638 superconductors, 2, 638-642 Electromagnetic waves, in ferrite medium, 1, 237-241 Electron beams, 1, 497 beam optical design, 1, 518-530, 561 collection, 1, 552-560 collectors, 2, 8, 72-74 electron emission, 1, 511-518 focusing, 1, 498, 505, 506, 539-552 klystrons, 2, 7-8 traveling-wave thermionic devices, 2, 62-64 measurement, 1, 560-561 Electron cyclotron masers, s e e Gyrotrons Electron-electron double resonance (ELDOR), 2, 383, 393 Electron emission cathode heaters, 1, 516-518 cathode loading, 1, 513-514 dispenser cathodes, 1, 514-515, 517 microwave tubes, 1, 511-518 oxide cathodes, 1, 515-516 Electron guns, 1, 498-510 advanced centerpost guns, 1, 509, 510 beam optical design, 1, 518-530 cathodes dispenser cathodes, 1, 514-515, 517 heating, 1, 516-518 loading, 1, 513-514 oxide cathodes, 1, 515-516 design, 1, 502-503, 505-508, 530-539 dual-mode electron guns, 1, 506, 507 gridded guns, 1, 502-505, 519, 536-537, 539, 540; 2, 62 gun codes, 1, 522-528

Index

gyrotron electron guns, 1, 508, 509 high-perveance hollow-beam guns, 1, 507-508 high-perveance intercepting gridded guns, 1, 506 hollow-beam guns, 1, 507-510; 2, 62 hybrid grid electron guns, 1, 504, 505 intercepting gridded electron guns, 1, 503, 506 klystrons, 2, 5-6, 23 low-noise guns, 1, 505-506 magnetic centerpost guns, 1, 508-509 magnetron injection guns, 1, 507; 2, 62, 104, 108 measurement, 1, 560-561 mod anode guns, 1, 502 peniotrons, 2, 127-129 Pierce guns, 1, 498-504, 513-514, 519, 530-539; 2, 61-62 shadow-gridded electron guns, 1, 502-504, 505, 514 traveling-wave thermionic devices, 2, 60-62 Electronically tuned oscillators, 1, 335-342, 429-433 Electronic efficiency, amplifiers, 2, 86 Electron paramagnetic resonance spectroscopy, 2, 365-368 continuous wave bridges, 2, 368-383 resonators, 2, 384-399 Electron spin resonance spectroscopy, chemical applications, 2, 359-360 Elliptic approximations, filters, 1, 162-163 Elliptic bandpass transforms, 1, 170-171 Elliptic integrals, 2, 599 Ellipticity, 2, 176-177 Elliptic low-pass filters, 1, 175, 177 EM codes, 1, 528, 530 Emissivity, 2, 151-152, 279 EMSim (software), 1, 184 Enclosure, microstrip lines, 1, 52 End capacitance, 1, 122 End-coupled half-wave resonators, 1, 178-179 End effect length, microstrip lines, 1, 53 ENR, s e e Excess noise ratio Epitaxial growth, diode fabrication, 1, 313-316, 368, 370 Epoxy glass, properties, 2, 159, 160 Epoxy plastics, properties, 2, 622 Epoxy resin, properties, 2, 611 Equivalent amplifier noise temperature, 2, 528 Equivalent capacitance, 1, 54 Equivalent circuit analysis, 2, 68-69

Index

Equivalent dielectric constant, finlines, 1, 32 Equivalent earth factor, 2, 480-481 Equivalent end effect length, 1, 122 ER, s e e Errored seconds Errored seconds (ER), 2, 456, 464-465 Error-free seconds, 2, 464 ESYN (software), 1, 657 Ethyl cellulose, properties, 2, 612 Excess group delay, 2, 236 Excess noise ratio (ENR), 2, 528 Excess phase delay, 2, 237 Exponential integrals, 2, 599 Exponential taper, 1, 653 Extended interaction klystron (EIK), 2, 3, 4, 19, 28 External interference fade margin, 2, 495-496

F Fabry-Perot resonators, 1, 88-89 Fade margins, 2, 491-496 Fade occurrence factor, 2, 493 Fading, 2, 451,472-473 atmospheric multipath fading, 2, 487-492 diffraction fading, 2, 478-482 dispersive fading, 2, 491 duct fading, 2, 486-487 flat fading, 2, 491-492 Fresnel fading, 2, 477-478 minimum phase fading, 2, 492 obstruction fading, 2, 482-485 power fading, 2, 485-486 reflective fading, 2, 477-478 terrestrial line-of-sight propagation, 2, 229-230 Faraday cage collectors, 1, 552 Faraday rotation, 1, 237; 2, 235-236 FD-TD method, s e e Finite-difference timedomain analysis Feedback lossless, 1, 411-414 tetrode, thermionic, 1, 604-605 Ferrite devices bandpass filters, 1, 256-257 circulators, 1, 249-254, 347 Gunn oscillator, 1, 341 isolators, 1, 254-256 phase shifters, 1, 241-248 switches, 1, 257-258 waveguides, 1, 238-240 yttrium iron garnet devices, 1, 256-257 Ferrites, 1, 195 barium ferrite sphere, 1, 341 electromagnetic waves, 1, 237-241

655 ferrite/garnet, dielectric substrate, 1, 48 magnetized, 1, 235-236 microwave properties, 1, 235-237 partially magnetized, 1, 236 properties, 2, 621,632 FET, s e e Field effect transistors Field displacement isolators, 1, 255 Field distribution circular waveguide, 1, 23-25 rectangular waveguides, 1, 15-17, 36 Field effect transistors (FET), 1, 293-302, 419 amplifiers, 1, 413,419, 432 Field emission, 1, 511, 512 Field reversal focusing, 1, 552 Field simulators, 1, 183-184 Figure of merit, microwave antennas, 2, 183-185 Filament reduction curve, 2, 39-40, 47 Film boiling region, 2, 149 Film capacitors, 1, 111-115 Films microwave drying, 2, 287 properties, 2, 633 Filters all-pass filters, 1, 161-162 bandpass filters, 1, 156, 164-170, 179-182 dissipation loss, 1, 186 loaded Q definition, 1, 185 yttrium iron garnet, 1, 256-257 bandstop filters, 1, 165 loaded Q definition, 1, 185 capacitance, 1, 167 components, 1, 186-197 design, computer simulation, 1, 182-184 dissipation loss, 1, 184-186 distributed filters, 1, 156, 172-182 high-pass filters, 1, 156, 163-164 L-C filter transformation, 1, 163-171 low-pass filters, 1, 156, 159 dissipation loss, 1, 185-186 low-pass prototype, 1, 155-163 microwave mixers, 1, 484 radial line filters, 2, 260 radio frequency choke, 1, 464 surface acoustic wave (SAW) devices, 1, 197 yttrium iron garnet, 1, 256-257 Fine frequency synthesizers, 1, 454 Finite-difference time-domain (FD-TD) analysis, 2, 253-256, 597, 598 Finite element analysis, 2, 323, 595, 597 Finlines, 1, 29, 32-34

656 Flat cell, electron paramagnetic resonance spectroscopy, 2, 389-390 Flat fade margin, 2, 495, Flat fading, 2, 491-492 Flicker noise, 1, 488 Fluorogold, properties, 2, 606 FLUX (software), 1, 550 FM detectors, s e e Frequency modulation detectors FM noise, s e e Frequency modulation noise Foam, properties, 2, 623 Focusing electron beams Brillouin focusing, 1, 548, 549; 2, 62-63 computer codes, 1, 550-551 confined-flow focusing, 1, 549-550, 551; 2, 63 double period permanent magnetic focusing, 1, 543-544 field reversal focusing, 1, 552 klystrons, 2, 7-8 long-period focusing, 1, 552 magnetic, 1, 539-544, 561; 2, 7 periodic permanent magnet focusing, 1, 540-544, 547; 2, 7, 9-10, 62-64 solenoidal focusing, 1, 548-551 solution splicing and emittance growth, 1, 544-547 space-charge balanced flow focusing, 1, 549 traveling-wave thermionic devices, 2, 62-64 uniform field focusing, 1, 544-547 Fog, microwave attenuation, 2, 227 Folded waveguides, 2, 89 Food industry, microwave applications, 2, 284-285, 290, 296 Forced convection heat transfer, 2, 146, 148 Foreshortened coaxial line resonators, 1, 67-68 Forward-biased diodes, 1, 271,274 Fourier's law, 2, 139 Fourier transform, 2, 194, 358, 570 Four-ridge peniotron, 2, 122 Fowler-Nordheim equation, 1, 512 Fractional bandwidth, bandpass filter prototypes, 1, 164 Free convection heat transfer, 2, 146, 149 Free-running oscillators, 1, 429, 438 Free space, microwave propagation, 2, 213-214 Free-space resonant frequency, 1, 328-329

Index

Free space transmisssion loss, 2, 214, 466 Free stream mean velocity, 2, 146 Frequency, microwave antennas, 2, 169-170 Frequency agility, 1, 449 Frequency calibration factor, 2, 541-542 Frequency diversity, 2,, 499 Frequency domain, 2, 570 ' Frequency doubler, 1, 458-459 Frequency modulation (FM) detectors, 1,470--477 Frequency modulation (FM) noise, GUNN oscillators, 1, 342-343 Frequency multiplier, 1, 335, 458-460 Frequency of oscillation, 1, 278, 299 Frequency sweepers, GUNN voltage-controlled oscillators, 1, 341 - 342 Frequency synthesizers, 1, 448-458 Frequency tracker, Doppler radar, 2, 422 Frequency of unity current gain, 1, 290, 299 Fresnel fading, 2, 477-478 Fresnel zone clearance, 2, 479 Frics equation, 2, 213 Function spaces, 2, 585-589 Fused silica, properties, 2, 615, 623 Fusion experiments, gyrotrons, 2, 112-114 FVR (software), 1, 543

G Gain, 2, 512 amplifiers, 1, 399-400, 402, 403, 419; 2, 86 IMPATT diodes, 1, 382 microwave antennas, 2, 174-176, 183 peniotron, 2, 125 reflection gain, 1, 347 small-signal analysis, 2, 74, 76 transistors, 1, 290, 299 triode amplifiers, 1, 591 triodes, thermionic, 1, 591,594, 598 Gain modulation, 2, 533 Galactic noise, microwave frequencies, 2, 241 Gallium antimonide (GaSb), properties, 2, 161 Gallium arsenide (GaAs) amplifiers, 1, 405, 413 capacitors, 1, 112 dielectric substrate, 1, 48, 95 diodes, 1, 261-269, 271,276-277, 280, 367, 373-374, 377, 432 GUNN diodes, 1, 307, 308, 317-321, 323-325, 332-334, 337, 342, 348 epitaxial growth, 1, 314-315 metallization, 1, 371-372 negative differential mobility, 1, 309-313 properties, 1, 368, 369; 2, 161, 162

Index

transferred electron effect, 1, 308 transistors, 1, 284, 285, 287, 288, 293-295, 297, 298, 300, 302, 405, 419 Gallium arsenide phosphide (GaAsP) Gunn diodes, 1, 276 negative differential mobility, 1, 309 Gallium nitride (GaN), properties, 2, 161 Gallium phosphide (GAP), properties, 2, 161 Gap microstrip line, 1, 54-55 series gap capacitors, 1, 118-121 Gases, atmospheric, microwave attenuation, 2, 215-219 Gate lines, 1, 413 Generalized functions, 2, 573-576 General theory of diffraction, microwave antennas, 2, 184-185 Geomagnetic dip, 2, 235 Geostationary orbit, satellite communications, 2, 233-234 Germanium (Ge) IMPATT devices, 1, 371,372 properties, 1, 369; 2, 161 Glasses, properties, 1, 48; 2, 159, 160, 611, 614, 616-617, 623 Global Positioning System (GPS), 2, 403-417 Gold (Au) alloys, 2, 158 diodes, 1, 274 GUNN devices, 1, 319, 321,324 IMPATT devices, 1, 371,372 inductors, 1, 96, 99, 105 properties, 1, 369; 2, 158, 633, 636 solder, properties, 2, 162 G points, 1, 523 GPS, s e e Global Positioning System Gradient (mathematics), 2, 587 Gram-Schmitt process, 2, 581 Grashof number, dimensionless, 2, 147 Green's function, 2, 591-592, 596, 597 Gridded electron guns, 1, 502-505; 2, 62 design, 1, 519 focusing, 1, 539, 540 tunnel emittance, 1, 536-537 Ground capacitance, inductors, 1, 99, 101 Ground constants, 2, 210-211 Group delay, 1, 161 klystrons, 2, 17 measurement, 2, 525-526 Group range delay, 2, 236 Group theory, 2, 579 Group velocity, waveguides, 1, 15, 23

657 Growing wave parameter, small-signal analysis, 2, 76 GR-S rubber, properties, 2, 613 GTD models, 2, 184-185 Guide wavelength microstrip lines, 1, 48, 49 waveguides, 1, 15, 23 Gun codes, 1, 522-528 GUNN amplifiers, 1, 346-350 GUNN devices, 1, 307-308 design and fabrication, 1, 313-325 history, 1, 308-309 negative differential mobility, 1, 309-313 noise characteristics, 1, 350-354 power combiners, 1, 354-356 GUNN diodes, 1, 276-280, 307 amplifiers, 1, 424-435 design, 1, 316-325 electron paramagnetic resonance spectroscopy, 2, 375 oscillators, 1, 332-334, 337, 342 power combiners, 1, 354 GUNN effect, 1, 276 GUNN mode, 1, 278-279 GUNN oscillators, 1, 307, 324, 325-346 bias-tuned GUNN oscillators, 1, 340-341 cavity-stabilized, 1, 342-346 cavity tuned, 1, 433, 435-436 electronically tuned, 1, 335-342 injection-locked, 1, 348, 353, 382, 385 local oscillators, 1, 342 magnetically tuned, 1, 341 noise, 1, 342-343, 350-353 phase-locked, 1, 353-354, 438-448 voltage-controlled, 1, 335-340, 429-431 GUNPPMC (software), 1, 518-520, 530, 540 Gyroklystrons, 2, 98, 102-103, 114 Gyromagnetic ratio, 2, 366 Gyropeniotron, 2, 121, 122, 130-131 Gyrotron electron guns, 1, 508, 509 Gyrotrons, 2, 97 applications, 2, 112-115 design, 2, 103-104 fabrication, 2, 108-110 large-orbit gyrotrons, 2, 107 magnicons, 2, 98, 111-112 operation, 2, 98-103 performance, 2, 110-111 prebunched, 2, 111 quasi-optical gyrotrons, 2, 106-107 structure, 2, 104-108 ubitrons, 2, 98, 114-116

658 H Hairpin bandpass filters, 1, 180-181 Hairpin curves, 1, 537, 538 Half-wavelength baluns, 1, 661 Half-wave line, impedance, 1, 3 Harmonic autoresonant peniotron (HARP), 2, 132 Harmonic generators, 1, 489-491,494-495 Harmonic operation, GUNN diodes, 1, 332-335 HARP, s e e Harmonic autoresonant peniotron Hartree voltage, 2, 47-48 HBT, s e e Heterojunction bipolar transistors Heat, s e e a l s o Microwave heating bioheat equation, 2, 328-330 deposition in human tissue, 2, 315-323 in semiconductors, 2, 138 transient heat flow, 2, 145 Heaters cathodes, 1, 516-518 potted heaters, 1, 505, 516 Heating, s e e Microwave heating Heat sink GUNN diodes, 1, 325 temperature, 2, 138 Heat transfer boiling, 2, 149-151 by radiation, 2, 151-154, 161 conductive, 2, 139-145 convective, 2, 145-151, 161 Heat transfer coefficient, 2, 146, 149 Heat of vaporization, 2, 279 Helium (He), microwave heating, 2, 289 Helix circuit, 2, 67 Helmholtz equation, 2, 590, 598 Helmholtz theorem, 2, 589 HEMT, s e e High electron mobility transistors Hermitian adjoint, 2, 578 Heterojunction bipolar transistors (HBT), 1, 284-289, 292, 294, 295 Heterostructure field effect transistors (HFET), 1, 293 Hevea rubber, properties, 2, 613 HFET, s e e Heterostructure field effect transistors High electron mobility transistors (HEMT), 1, 285, 287, 288, 293-302, 405, 419 High-field nuclear magnetic resonance spectroscopy, 2, 357-358 High-frequency circuits, 2, 70-71 High-frequency crossed-field amplifiers, 2, 86-87

Index

High-pass filters, 1, 156, 163-164 hybrid, 1, 175, 177-178 High-perveance hollow-beam guns, 1, 507-508 High-perveance intercepting gridded guns, 1, 506 High-power antennas, 2, 182 High-temperature superconductors, 2, 641 Hilbert space, 2, 585 Hollow-beam electron guns, 1, 507-510; 2, 62 Homogeneous media, propagation, 2, 207-208 Horizontal polarization, microwaves, 2, 210-211 Hot/cold loads, 2, 528, 536-538 HOW, 2, 409, 410-412 Hull cutoff voltage, 2, 44 Hybrid grid electron guns, 1, 504, 505 Hybrid heating, 2, 280 Hybrid high-pass filters, 1, 175, 177-178 Hybrid microwave integrated circuits, 1, 95-96 Hyperthermia, cancer treatment, 2, 327-331

I Ice crystals, microwave attenuation, 2, 227 Ideality factor, diodes, 1, 263 I L O , s e e Injection-locked oscillator Imageguides attenuation, 1, 39-40 characteristic impedance, 1, 41-43 losses, 1, 39-42 propagation constants, 1, 35-38 Image impedance terminations, 1, 658-660 Imaging biological functions, 2, 332, 337-339 millimeter-wave imaging array, 2, 189-191 IMMA, s e e Interstitial microwave antenna array Impact-ionization avalanche transit-time (IMPATT) diodes, 1, 276, 280-284, 348, 354, 363-368 amplifier design, 1, 377-381 commercial specifications, 1, 373-377 double-drift IMPATT diodes, 1, 280, 370, 375 fabrication, 1, 368-373 noise, 1, 384-386 oscillator design, 1, 382-386 Impedance, s e e a l s o Characteristic impedance avalanche region, 1, 283 beam-coupling impedance, 2, 86 biological materials, 2, 313 capacitors, 1, 114

Index

coaxial lines, 1, 6 couplers, 1, 214, 223-224, 228 coupling impedance, 2, 125 detector video impedance, 1, 265 diodes, 1, 283, 284 drift region, 1, 283 half-wave lines, 1, 3 IMPATT devices amplifiers, 1, 378-381 oscillators, 1, 382 interaction impedance, 2, 66 klystrons, 2, 19 load impedance, 1, 624-625, 632, 637-638, 640; 2, 19 magnetrons, 2, 36 open wire lines, 1, 3 peniotron, 2, 125 quarter-wave lines, 1, 3 quarter-wave transformers, 1, 643-644 resonant cavities, 1, 329 short circuit post, 1, 124 small-signal analysis, 2, 74 software for, 1, 224 suspended substrate lines, 1, 145-147, 150-151 TEM lines, 1, 3, 4 total device impedance, 1, 284 video impedance, 1, 265 waveguides, 1, 13, 15, 23 Impedance matching, 1, 617 amplifiers, 1, 630, 631,656 baluns, 1, 660-666 microwave curing, 2, 282 narrow-band, 1, 618-640 wide-band, 1, 640-660 Impedance steps, microstrip line, 1, 55-56, 127-128 Impedance transformations complex to real, 1, 632-636, 637-639 quarter-wave transformers, 1, 652 real to complex, 1, 626-629, 636, 639-640 tapered transmission line transformers, 1, 652 Impulse function, 2, 575 Indirect frequency synthesis, 1, 452-458 Indium (In), 1, 372 properties, 2, 158 Indium antimonide (InSb) properties, 2, 161 transferred electron devices, 1, 308, 309 Indium arsenide (InAs) negative differential mobility, 1, 309, 310

659 properties, 2, 161 Indium phosphide (InP) epitaxial growth, 1, 315 GUNN diodes, 1, 276, 318-319, 321,323, 335, 341,348 negative differential mobility, 1, 309, 310 properties, 1, 369; 2, 161,621 transferred electron effect, 1, 308 transistors, 1, 287, 293-294, 296, 298 Inductance, 1, 188 diodes, 1, 263, 273-274, 277, 283 effective inductance, 1, 189, 283 inductors circular ring, 1, 103 ribbon, 1, 97-99 round wire, 1, 100, 101 spiral, 1, 103, 106 package inductance, 1, 277 parasitic inductance, 1, 263, 273 series inductance, 1, 187 short circuit post, 1, 124 static series inductance, 1, 128 transistors, 1, 301 transmission lines coaxial, 1, 7 microstrip, 1, 55-58 two-wire, 1, 4 Induction heating, 2, 279-280 Inductors, 1, 188-191 capacitance, 1, 99, 101, 106, 109-110 coupling inductors, 1, 168 permeability loaded, 1, 195-196 resistance, 1, 97, 100-103 ribbon inductors, 1, 96-99 ring inductors, 1, 101-103 spiral inductors planar circular, 1, 103-107 planar rectangular and square, 1, 107-111 wire inductors, 1, 99-101 Industrial applications agricultural, 2, 293-296 curing, 2, 281-284 data communications, 2, 232-240, 300-302 drying, 2, 285-289, 293-294 heating, 2, 277-281,289-293 lumber industry, 2, 296-297 moisture sensing, 2, 297-298 object recognition, 2, 300 sensing, 2, 297-299 thawing, 2, 284-285 Industrial heating, 2, 277-281,289-293, 362-363

660 Industrial heating (continued) klystrons, 2, 5-6, 11, 29 Infrared radiation, thermal resistance measurement, 2, 155 Initial loss factor, small-signal analysis, 2, 75-76 Injected-beam crossed-field amplifiers, 2, 84 Injection-locked oscillators (ILO), 1, 348, 353, 382, 385 Inner product, 2, 580 Input impedance dielectric film capacitors, 1, 114 TEM lines, 1, 3 Insecticide application, agricultural, with microwaves, 2, 295-296 Insertion loss, 1, 249, 409 phase shifters, 1, 584 switches, 1, 569, 571,573-575 Insular guides, 1, 44 Insulated finlines, 1, 28-31 Insulators, properties, 2, 159, 160 Integer frequency multiplication (division), 1, 450 Integral equations, microwave mathematics, 2, 599-602 Integral heat sink (IHS) devices, 1, 321-323 Integrated circuit dipole antennas, 2, 192-193 Intensity of magnetization, 1, 235 Interaction impedance, traveling-wave tube, 2, 66 Intercepting gridded electron guns, 1, 503, 506, 526, 529 Interdigital bandpass filters, 1, 181-182 Interdigitated couplers, 1, 218, 222 Interference fade margin, 2, 495-496 Intermodulating, klystrons, 2, 25-26 Intermodulation noise, analog radio, 2, 451-453 Intemal intensity of magnetization, 1, 235 Internal magnetic field strength, 1, 236 International Radio Consulative Committee (CCIR), 2, 207 International Telecommunications Union (ITU), 2, 207 International Thermonuclear Experimental Reactor (ITER), 2, 113 Interstitial microwave antenna array (IMMA), 2, 330 Invar, 1, 344 Inverse binomial sampling, 2, 464 Inverse (mathematics), 2, 577 Inverse operator, 2, 582 Inverted coaxial magnetrons, 2, 83

Index

Inverted stripguides, 1, 43, 44 Ionospheric effects, earth-space microwave propagation, 2, 234-237, 239-240 Ionospheric scintillation, 2, 234, 237, 238 Isolation circulators, 1, 249 switches, solid-state, 1, 570, 572-575 Isolators (isocirculators), 1, 254-257, 408-410, 423 Isotropic decibels, 2, 174-175 ITER, see International Thermonuclear Experimental Reactor ITU, 2, 207

l Janus configuration, 2, 419, 421 JFET, see Junction field effect transistors Jitter, 2, 455, 457-459 Josephson junction diodes, 1, 261 Junction capacitance quarter-wave transformers, 1, 651-652 solid-state devices, 1, 263, 266, 269, 270, 271,273-275, 276, 571 Junction diodes, 1, 268, 269, 271 Junction field effect transistors (JFET), 1, 293 Junction resistance, diodes, 1, 263, 266, 273, 571-573, 582-583, 586 Junction-type circulators, 1, 250-254

K Kirchoff's law, 2, 241 Kirchoff transform, 2, 142 Klystrons, 1, 515-517, 549, 553; 2, 1 applications, 2, 8-12 arcing, 2, 28, 29 design and fabrication, 2, 22-25 electron beam system, 2, 5-8 electron paramagnetic resonance spectroscopy, 2, 369, 373 extended interaction klystrons, 2, 3, 4, 19, 28 gyroklystrons, 2, 98, 102-103 noise, 2, 25-27 protection, 2, 29-31 RF circuit, 2, 1-4 specifications, 2, 12-22 stability, 2, 27-29

L Ladder circuits, 2, 70-71 Laminar flow, convective heat transfer, 2, 148, 149

Index

Land mobile satellites, microwave propagation, 2, 239, 240 Lange couplers, 1, 218 Laplacian, 2, 588 Large-orbit gyrotron, 2, 107 Large sample-access cavity, electron paramagnetic resonance spectroscopy, 2, 397 Large-signal analysis peniotron, 2, 126 traveling-wave tubes, 2, 76 Latent heat of vaporization, 2, 279 Launcher, microwave, 2, 302 Laurent's series, 2, 573, 574 Law enforcement, microwave applications, 2, 429-448 LC circuit, magnetrons, 2, 41 LC-tuned oscillators, 1,433-434 Lead (Pb) alloys, 2, 158 properties, 2, 158, 639 solder, 2, 162 Lead telluride (PbTe), properties, 2, 161 Leakage, magnetrons, 2, 46, 53 Leather, microwave drying, 2, 287 Legendre functions, 2, 596 Legendre polynomials, 2, 592 Length, open-ended microstrips, 1, 122 Lighthouse tubes, 1, 589, 591 Limited space-charge accumulation (LSA) mode, 1, 278-279 Linear accelerators (linacs), 1, 506, 528; 2, 8-9 Linear arrays, radiation pattern synthesis, 2, 194 Linear-beam devices, 1, 497-; 2, 57, 58 backward-wave devices, 2, 77-79 traveling-wave tubes, 2, 64-77 Linear colliders, gyrotrons, 2, 113 Linear independence, 2, 580 Linear operator theory, 2, 581-585 Line-of-sight paths (LOS), attenuation, 2, 214-228 Line resonators, two-wire, 1, 65-66 Line reversal, nuclear magnetic resonance spectroscopy, 2, 357 LINMIC+ (software), 1, 183 Liquid crystals, thermal resistance measurement, 2, 155-156 Liquid-phase epitaxy (LPE), 1, 315 Lithium fluoride, properties, 2, 611 Litton codes, 1, 519 Loaded quality factor

661 filters, 1, 185 resonant cavities, 1, 327, 344, 346 resonators, 1, 62-64 Load impedance, 1, 624-625, 632, 637-638, 640; 2, 19 Local oscillators, 1, 342 Locking bandwidth, 1, 353, 382 Locking frequency, 1, 353 Longitudinal electric field, waveguides, 1, 17, 23 Longitudinal magnetization ferrites, 1, 237, 239-240 waveguides, 1, 15, 23 Longitudinal relaxation, 2, 357 Long-period focusing, 1, 552 Loop coupled harmonic generator, 1, 489, 490 Loop-gap resonators, 1, 83-85; 2, 397 LOS paths, s e e Line-of-sight paths Losses, 1, 39-42 arbitrary loss, 1, 111-115 bandpass loss, 1, 186 dielectric film capacitor, 1, 111-115 dielectric waveguides, 1, 35, 38-42 dissipation loss, 1, 184-186 filters, 1, 184-186 finlines, 1, 34 insertion loss, 1, 249 low-pass loss, 1, 185-186 microstrip lines, 1, 51-52, 192 mixer conversion loss, 1, 264-265 suspended substrate technique, 1, 143-153 Loss factor, small-signal analysis, 2, 75, 76 Lossless feedback, amplifiers, 1, 411-414 Lossless matching network, 1, 618 Loss tangent, 2, 362 biological materials, 2, 310, 311-312, 314 calculation, 2, 607 Low-loss isolators, amplifiers, 1, 408-410 Low-loss lines, 1, 3 Low-noise amplifiers, 1, 392-394, 405-428; 2, 527-533 cryogenically cooled, 1, 419, 421 design, 1, 405-410 parametric amplifiers, 1, 487 Low-noise electron guns, 1, 505-506 Low-pass filters, 1, 156, 159 Butterworth approximation, 1, 156-158, 160, 161 Cauer-Chebyshev approximation, 1, 162-163 Chebyshev approximation, 1, 159-161 controlled-phase prototypes, 1, 160-162

662 Low-pass filters ( c o n t i n u e d ) dissipation loss, 1, 185-186 elliptic approximations, 1, 162-163 microwave mixers, 1, 484 Low-pass loss, 1, 185-186 Low-pass network, 1, 658-659 Low-power devices, 1, 321-324 LPE, s e e Liquid-phase epitaxy LSA mode, s e e Limited space-charge accumulation mode LSC (software), 1, 521,554, 555 Lumber industry, microwave applications, 2, 296-297 Lumped constant circulators, 1, 251 Lumped-distributed equivalents, distributed filters, 1, 172-174 Lumped-element matching networks, 1, 656-657 Lumped-element microwave integrated circuits absorbing microstrip terminations, 1, 131-135 capacitive components dielectric-film overlay capacitors, 1, 111-115 disk capacitors, 1, 115-118 series gap capacitors, 1, 118-121 coaxial-to-microstrip transitions, 1, 136-138 inductive components ribbon inductors, 1, 96-99 ring inductors, 1, 101-103 spiral inductors, 1, 103-111 wire inductors, 1, 99-101 microstrip discontinuities impedance steps, 1, 127-128 open-ended microstrips, 1, 50, 121-123 right-angle bends, 1, 128-130 short circuits, 1, 122, 124-126 unloaded Q definition, 1, 184-185 Lumped parameter microwave mixers, 1, 484-485, 493 Lumped parameter up-converters, 1, 486 Lumped terminations, 1, 131-135

M MAFIA (software), 2, 77 Magic angle, nuclear magnetic resonance spectroscopy, 2, 358 MAGIC (software), 1, 528 Magic-T, 1, 200-201; 2, 369-373 MAGLENS (software), 1, 558 Magnesium (Mg), properties, 2, 158 Magnesium fluoride (MgF2), properties, 2, 621 Magnesium silicate (MgSiO2), properties, 2, 611

Index

Magnesium titanate (MgTiO2), properties, 2, 611 Magnetically tuned GUNN oscillators, 1, 341 Magnetic centerpost guns, 1, 508-509 Magnetic dipole moment, 2, 353-355, 359 Magnetic field earth, earth-space microwave propagation, 2, 234-235 electron beam focusing, 1, 539-544, 561 klystrons, 2, 7, 23 magnetrons, 2, 43-44, 46, 48-50 waveguides, 1, 14-17, 23-25 Magnetic flux density, 1, 235 Magnetization, ferrites, 1, 235-241 Magnetron injection guns (MIG), 1, 507; 2, 62, 104, 108 Magnetron-like peniotrons, 2, 122, 129-132-133 Magnetrons, 2, 33-35, 33-55, 79-84 arcing, 2, 55 coaxial magnetrons, 2, 83-84 components, 2, 36-43 inverted coaxial magnetrons, 2, 83 magnetic field, 2, 43-44, 46, 48-50 magnetron-system interface, 2, 53 microwave oven, 2, 249-251 microwaves, 2, 35, 50, 51 power adjustment, 2, 46-50 power supplies, 2, 51-53 Rieke diagram, 2, 50-51 space charge, 2, 43-45 Magnicons, 2, 98, 111-112 MAGNUS-3D (software), 2, 77 MAGSYN (software), 1, 510, 519 MAGUN (software), 1, 526 MARC (software), 2, 77 Marine mobile satellites, microwave propagation, 2, 239-240 MASK (software), 1, 528, 553-554 Matched load, 2, 35 Matched terminations, 1, 131 Matching networks, impedance testing, 1, 618-666 MATCHNET (software), 1, 657 Mathematics microwaves, 2, 564-602 complex functions, 2, 571-573 differential equations, 2, 589-599 function spaces, 2, 585-589 generalized functions, 2, 573-576 integral equations, 2, 599-602 linear operator theory, 2, 581-585 vectors and matrices, 2, 576-579 vector spaces, 2, 579-581

Index

Matrices, 2, 576-579 Maximum device temperature, GUNN diodes, 1, 319 Maximum heat transfer coefficient, 2, 149 Maximum peak power coaxial lines, 1, 7 rectangular waveguides, 1, 18, 20 Maxwell's equations, 2, 253 MBE, s e e Molecular beam epitaxy MBWO, s e e Crossed-field backward-wave oscillators MDC, s e e Multistage depressed collectors Mean shear stress, 2, 146, 147 Mechanically tuned oscillators, 1, 433-438 Medical applications, s e e Biomedical applications Melamine-formaldehyde plastic, properties, 2, 612 MESFET, s e e Metal semiconductor field effect transistors Metallization inductors ribbon inductors, 1, 98-99 round wire inductors, 1, 99, 100 spiral inductors, 1, 105, 107, 111 materials, 1, 371-372 Metal-organic chemical vapor deposition (MOCVD), 1, 316, 368, 370 Metals properties, 2, 158, 633, 636-638 superconductors, 2, 638-642 Metal semiconductor field effect transistors (MESFET), 1, 285, 287, 288, 293-295, 297-302; 2, 156 Methane, microwave heating, 2, 289 Method of moments, 2, 601 MIC, s e e Microwave integrated circuits Micas, properties, 2, 611, 613 Microperveance, 1, 500; 2, 6 Microphase phase shifters, 1, 247-248, 252, 253 Microphonics, 2, 19 Microstrip antennas, 2, 169, 197 Microstrip coupled line couplers, 1, 218, 221, 224-225, 232 Microstrip disk capacitors, 1, 51, 115-118 Microstrip lines, 1, 47-58 AM detectors, 1, 467, 469-470 capacitance, 1, 53-58 characteristic impedance, 1, 48, 49-52, 55 coaxial-to-microstrip transitions, 1, 136-138 components capacitors, 1, 111 - 121 inductors, 1, 96-111

663 suspended substrate technique, 1, 143-153 terminations, 1, 131-135 cross junction, 1, 58 discontinuities, 1, 53-58 impedance, steps, 1, 56-57, 127-128 open-ended microstrip, 1, 121-123 right-angle bends, 1, 56-57, 128-130 short circuits, 1, 122, 124-126 dispersion, 1, 50-51 effective dielectric constant, 1, 48, 49-51 gap, 1, 54-55 losses, 1, 51-52, 192 microwave mixers, 1, 483-484, 492-493 properties, 2, 624 step changes, 1, 55-56, 127-128 T-junctions, 1, 57 up-converters, 1, 485, 486 Microstrip resonant cavity, 1, 327, 330-331 Microstrip resonators, 1, 86-88 Microstrip series gap capacitors, 1, 118-121 Microwave absorption spectroscopy, chemical applications, 2, 347-353 Microwave antennas, 2, 167 broadband antennas, 2, 169 broad beamwidth antennas, 2, 174 C-band beacon antennas, 2, 198-199 copper, 2, 203 dielectric antennas, 2, 188-189, 203 directivity, 2, 171-174 Doppler radar, 2, 421-422 figure of merit, 2, 183-185 gain, 2, 174-176, 183 integrated circuit dipole antennas, 2, 192-193 interstitial microwave antenna array, 2, 330 microstrip antennas, 2, 169, 197 microwave integrated circuits, 2, 187-193 missile antennas, 2, 195-199 monolithic microwave integrated circuits, 2, 187-193 omnidirectional antennas, 2, 186 parabolic antennas, 2, 466-467, 469 power fading, 2, 485-486 squint, 2, 180-181 stainless steel, 2, 202 transmission path loss, 2, 467-477 waveguides, 2, 182 Yagi antennas, 2, 189 Microwave catchers, 2, 303 Microwave devices applications biomedical, 2, 285, 288, 309-339 chemical, 2, 347-363

664 Microwave devices ( c o n t i n u e d ) communications, 2, 207-241,300-303, 449-501 consumer goods, 2, 249-273 industrial, 2, 277-303 law enforcement, 2, 429-448 navigation aids, 2, 403-425 electrical delay, 2, 17, 525-526 group delay, 2, 525-526 magnetrons, 2, 35, 50, 51 microwave frequency measurements, 2, 545-558 microwave power measurements, 2, 538-545 noise, 2, 527-538 phase noise power spectral density, 2, 558-568 propagation, 2, 207-215 attenuation, 2, 214-228 beyond the horizon, 2, 230-232 earth-space propagation, 2, 232-240 indoor, 2, 240-241 mobile propagation, 2, 240 noise, 2, 241 short-path propagation, 2, 240-241 terrestrial line-of-sight propagation, 2, 228-230 reflection measurement, 2, 509, 512, 520-524 scattering parameters, 2, 505-513 thermal enhancement, 2, 138, 156-163 thermodynamics, 2, 137-163 transmission, 2, 214-240, 225-227, 302 measurement, 2, 514-520 Microwave engineering mathematics, 2, 564-602 complex functions, 2, 571-573 differential equations, 2, 589-599 function spaces, 2, 585-589 generalized functions, 2, 573-576 integral equations, 2, 599-602 linear operator theory, 2, 581-585 vectors and matrices, 2, 576-579 vector spaces, 2, 579-581 Microwave frequency, measurement, 2, 545-558 Microwave heating bioheat equation, 2, 328-330 human tissue, heat deposition, 2, 315-323 hyperthermia, cancer treatment, 2, 327-331 industrial applications, 2, 277-281, 289-293, 362-363 klystrons, 2, 5-6, 11, 29

Index

thermodynamics, 2, 277-279, 362 Microwave imaging, 2, 332, 337-339 millimeter-wave imaging array, 2, 189-191 Microwave integrated circuits (MIC), antennas, 2, 187-193 Microwave launcher, 2, 302 Microwave ovens, 2, 34 arcing, 2, 251 design, 2, 249-252, 256-271 microwave field visualization, 2, 252-256 microwave leakage suppression, 2, 256-271 operation and use, 2, 271-273 Microwave power detectors, 2, 538-544 Microwave propagation, s e e Propagation Microwave radar, s e e Radar Microwave radiation, exposure guide, 2, 323-327 Microwave radio communications fading, 2, 451,472-473, 477-492 history, 2, 449-450 path availability calculations, 2, 492-501 transmission errors, 2, 455-465 Microwave radiometry, 2, 300, 333-337 Microwave receiver, 2, 303, 422 Microwave thermography, 2, 333-337 Microwave transmission, s e e Transmission Microwave transmitters, s e e Transmitters Microwave tubes, 1, 497-498 electron emission, 1, 511-518, 561-562 MIG, s e e Magnetron injection guns Millimeter-wave imaging array, 2, 189-191 Minimum interelectrode spacing, 1, 538 Minimum noise amplifiers, 1, 407, 411 transistors, 1, 290, 293, 299 Minimum phase fading, 2, 492 Mining, microwave processes, 2, 288, 290-291,293, 298 Minor (mathematics), 2, 577 Miram curves, 2, 29 Mismatch attenuation, 1, 159 Mismatch uncertainty, 2, 534, 536, 542-543 Missiles, antennas for, 2, 195-199 Mixed tunnel-avalanche transit-time (MITATT) devices, 1, 365 Mixer conversion loss, 1, 264-265 Mixer diodes, 1, 261-268, 478-485 Mixers, 1, 478-485 coaxial line mixers, 1, 479-480 down-converters, 1, 486 lumped parameter mixers, 1, 484-485 microstrip line mixers, 1, 483-484

665

Index

noise, 1, 487-489 packaging, 1, 492-494 up-converters, 1, 485-486 waveguide mixers, 1, 480-482 MMBC, s e e Moster-Molnar B-field code MMIC, s e e Monolithic microwave integrated circuits Mobile satellites, propagation effects, 2, 239-240 MOCVD, s e e Metal-organic chemical vapor deposition Mod anode electron guns, 1, 502 Mode, coaxial lines, 1, 8-10 Mode chart, resonators, 1, 81 Mode lattice, resonators, 1, 69, 75, 76, 329 Modeling GUNN devices, 1, 313 transistor design, 1, 292-293, 302 Moderate bandwith amplifiers, 1, 392, 393, 395,426 MODFET, s e e Modulation-doped field effect transistors Moding, 2, 41,249 Modulation-doped field effect transistors (MODFET), 1, 293-294 Modulator, microwave data communication system, 2, 301 Moisture sensing, microwave applications, 2, 297-298 Molecular beam epitaxy (MBE), 1, 315-316, 368, 370 Molybdenum (Mo), properties, 2, 158 Monitoring devices, biological functions, 2, 332-337 Monolithic microwave integrated circuits (MMIC), 1, 95-96, 342 antennas, 2, 187-193 Monostatic radar, 2, 300 Moreno cross-guide couplers, 1, 212-213 Moster-Molnar B-field code (MMBC), 1, 550, 551 Motion detector, 1, 324 Moving radar, 2, 432-433 M-type backward-wave oscillators, s e e Crossed-field backward-wave oscillators Multihole waveguide couplers, 1, 205-211 Multilayer couplers, 1, 232 Multiloop frequency synthesizers, 1, 454 Multipath fading, 2, 477, 487, 493 Multipath propagation, 2, 230 Multipliers, s e e Frequency multipliers Multipurpose TE~o2 cavity, 2, 384-394

Multiquantum electron paramagnetic resonance, 2, 383 Multistage amplifier design, 1, 415-418 Multistage depressed collectors (MDC), 1, 556, 558-559; 2, 73-74 Muscle, electrical properties, 2, 312-314

N Narrow-band bandpass transforms, 1, 166-171 Narrow-band impedance, lumped element matching, 1, 629-640 Narrow-band impedance matching distributed element technique, 1, 626-629, 636-640 double-stub matching, 1, 622-623 quarter-wave transformer, 1, 623-626 single-stub matching, 1, 619-622 NASA CC TWT (software), 2, 77 Natural noise, microwave frequencies, 2, 241 Navigation aids Doppler navigation system, 2, 417-425 Global Positioning System, 2, 403-417 Navigation equations, 2, 408, 411-413 Negative differential mobility (NDM), 1, 308-313 Negative resistance devices diodes, 1, 276, 277, 279, 280, 282, 363 history, 1, 308-309 Network theory, 1, 251 Neumann boundary conditions, 2, 591 Neumann functions, 2, 595, 596 Nickel (Ni), 1, 372 properties, 1, 369; 2, 158, 636 Niobium (Nb), properties, 2, 639 NMR, s e e Nuclear magnetic resonance spectroscopy Noise amplifiers, 1, 384-386, 407, 411,413, 415-419; 2, 84-87, 527-528 amplitude modulation noise, 1, 487-489 analog radio, 2, 451-453 carrier-to-noise ratio, 2, 214-215 converters, 1, 487-489 crossed-field amplifiers, 2, 84-87 Doppler radar, 2, 423-424 equivalent amplifier noise temperature, 2, 528 excess noise ratio, 2, 528 figure circles, 1, 407-409 flicker noise, 1, 488 galactic noise, 2, 241 klystrons, 2, 25-27 measurement, 2, 527

666 Noise (continued) microwave bridge designs, 2, 381 microwave devices, 2, 527-538 microwave frequencies, 2, 241 microwave mixers, 1, 479-485 oscillators, 1, 342-343, 350-353, 428, 439 GUNN, 1, 342-343, 350-353 IMPATT, 1, 385 phase-locked, 1, 439 parametric amplifiers, 1, 487 phase modulation noise, 1, 489 phase noise measurement, 2, 560-567 shot noise, 1, 487, 488 signal-to-noise ratio, 2, 423-424 solar noise, 2, 241 system noise temperature, 2, 183 tangential signal sensitivity, 1,463,488-489 tap noise, 1, 488 thermal noise, 1, 487-488 transistors, 1, 288, 290, 296, 401 Noise diodes, 2, 528, 530, 536-538 Noise figure, 2, 527-538 Noise peaks, 2, 529 Noise power ratio (NPR), 2, 451-453 Noise temperature, 2, 183, 527, 528 Noise temperature ratio, diodes, 1, 265 Nonchamfered symmetric bend, 1, 129-130 Nontransverse electromagnetic mode (nonTEM), 1, 1, 2, 13, 67 Normalized equivalent length, 1, 122 Notch radiator, 2, 190, 191 NPR, see Noise power ratio Nuclear magnetic resonance (NMR)spectroscopy chemical applications, 2, 353-358 differential equations, 2, 365 Nuclear magneton, 2, 354 Nuclear statistical weight, 2, 352 Nucleate boiling, 2, 149 Numerical integration, 2, 600 Numerical solutions differential equations, 2, 595-599 integral equations, 2, 600-602 Nusselt number, 2, 146 average, 2, 148, 149 dimensionless, 2, 147 Nylon monofilament, microwave heating, 2, 239 properties, 2, 612

O Object identification, microwave applications, 2, 300

Index

Obstruction fading, 2, 482-485 Obstructive clearance, 2, 483-485 Octave band amplifiers, 1, 392-393, 412, 416, 428 Offset-coupled stripline couplers, 1, 218, 220 Oil industry, microwave heating, 2, 291 Omnidirectional antennas, 2, 186 One-arm bridges, 2, 375, 381-383 One loop-one gap resonators, 1, 83-84 One-port reflection resonators, 1, 61-63 Open-end capacitance, 1, 53, 121 Open-ended microstrips, 1, 50, 121-123 Open ring resonators, 1, 87-88 Open wire lines, 1, 1, 3, 5 Optical transmission cavity, electron paramagnetic resonance spectroscopy, 2, 391-392 Optimum chamfer, 1, 130 Orthonormality, 2, 580 Oscillation, 1, 308, 591 klystrons, 2, 28 magnetrons, 2, 41, 47 Oscillator frequency, resonant cavities, 1, 327-328 Oscillators, 1, 428-429 backward-wave oscillators, 2, 78-79 carcinotron, 2, 87 cavity-stabilized oscillators, 1, 342-346, 433, 435-436 crossed-field backward-wave oscillators, 2, 84-87 crystal, 2, 568 electronically tuned oscillators, 1, 335-342, 429-433 electron paramagnetic resonance spectroscopy, 2, 374-376, 381 free-running oscillators, 1, 429, 438 frequency multipliers, 1, 458-460 frequency synthesizers, 1, 448-458 GUNN oscillators, 1, 307, 324, 325-346 bias-tuned, 1, 340-341 injection-locked, 1, 348, 353, 382, 385 local oscillators, 1, 342 magnetically tuned, 1, 341 gyrotrons, 2, 97-114 IMPATT diodes, 1, 382-384 LC tuned oscillators, 1, 433, 434 mechanically tuned oscillators, 1, 433-438 noise, 1, 342-343, 350-353, 428, 439 phase-locked oscillators, 1, 353-354, 438-448 pulsed IMPATT oscillators, 1, 374, 376

Index

switched oscillators, 1, 451 triode oscillators, 1, 591 voltage-controlled oscillators, 1, 335-340, 429-431; 2, 545-546 yttrium iron garnet tuned oscillators, 1, 341, 429-430, 432-433 Outage time, radio communications, 2, 492 Oxide cathodes, electron emission, 1, 515-516 Oxygen (O), microwave attenuation, 2, 215-217

P Package capacitance, 1, 277, 571 Packaged transistors, 1, 402 Package inductance, 1, 277 Packaging, 1, 491-495 Packaging industry, microwave heating, 2, 292 Palladium (Pd), 1, 372 properties, 1, 369; 2, 158, 633 Pancake heaters, 1, 517 PANDIRA (software), 1, 518-520, 528 Paper industry, microwave processes, 2, 286, 299 Parabolic antennas, 2, 466-467, 469 Parallel capacitance, 1, 128 Parallel capacitors, bandpass filters, 1, 167-168 Parallel-coupled half-wave resonators, 1, 179-180 Parallel resonators, bandpass filters, 1, 166-168 Parametric amplifiers, 1, 487 Paraphrase amplifiers, 1, 663-666 Parasitic capacitance diodes, 1, 263, 271,273 transistors, 1, 413 Parasitic inductance, diodes, 1, 263, 273 Parasitic resistance diodes, 1, 271 inductors, 1, 101, 107, 110-111 Particle acceleration, gyrotrons, 2, 113 Partition function, 2, 351 Pass-band characteristic, transformers, 1, 641 Pass-band ripple, 1, 159 Passive baluns, 1, 660-661,663 Passive reflectors, radio communications, 2, 467, 469-471 Pasteurization, microwave processes, 2, 296 Path attenuation, rainfall-induced, 2, 220-227, 474-477, 499-500 Path availability, 2, 492-501 Path loss, 2, 213-214, 466-471 atmospheric absorption, 2, 473-474

667 rainfall, 2, 474-477 Pattern recognition, microwave applications, 2, 300 PCM, s e e Pulse code modulation Peak power, klystrons, 2, 14 Peak power meters, 2, 542 Peak power rating, waveguides, 1, 18, 20, 27 Peak-to-peak waiting time jitter, 2, 458-459 Peclet number, dimensionless, 2, 147 Peltier cooling, 1, 419 Penetration depth, 2, 211-212 Peniotrons, 2, 102-103, 121-133 design, 2, 127-129 Percentage bandwidth, bandpass filter prototypes, 1, 164 Performance curve, magnetron, 2, 48 Periodic permanent magnet (PPM) focusing, 1, 540-544, 547 klystrons, 2, 7, 9-10 traveling-wave tubes, 2, 63-64 Permanent magnets, magnetrons, 2, 46 Permeability, 2, 195, 207-208 Permeability loaded inductors, 1, 195-196 Permeability tensor, ferrites, 1, 235-236 Permittivity, 2, 207-208, 619 biological materials, 2, 310 suspended substrate lines, 1, 145, 147-149, 152-153 Perveance, 1, 499-500, 537; 2, 6, 58, 60 Phase comparators, 1,472 Phase constant, TEM lines, 1, 3 Phase detector, 2, 564-567 Phase-error ripple, 1, 161 Phase-locked oscillators cavity oscillators, 1, 444-445 coaxial resonator oscillators, 1, 445, 446 dielectric resonator oscillators, 1, 445, 447 GUNN oscillators, 1, 353-354 noise, 1, 353-354, 438-448 VCXOs, 1, 443-444 Phase lock loop integrated circuits (PLL IC), 1, 470, 472-473; 2, 430 Phase modulation (PM) detectors, 1, 477-478 Phase modulation (PM) noise, 1, 489 Phase noise, 1, 433, 452 measurement, 2, 560-567 Phase noise power spectral density, 2, 559-567 Phase scintillation, 2, 230, 237 Phase shifters, 1, 241-248, 582-586 Phase shift keying (PSK) detectors, 1, 477-478

668 Phase velocity coaxial lines, 1, 7 waveguides, 1, 15, 23 Phasor notation, 2, 569 Phenol formaldehyde plastic, properties, 2, 612 Phenol-furfuraldehyde plastics, properties, 2, 612 PHOENICS (software), 2, 142 Phosphorus (P), 1, 371 Photo radar, 2, 435-436 PIC codes, 1, 528, 530, 553-555 Pierce electron guns, 1, 498-504, 529; 2, 61-62 current density, 1, 513-514 design, 1, 530-539 field enhancement, 1, 538 klystrons, 2, 6 peniotrons, 2, 128-129 synthesis codes, 1, 519 PIERCE (software), 1, 519, 531 Piezoelectric properties, 2, 631 PI mode, 2, 41-42, 44 Pinch-off voltage, 1, 270, 271,401 PIN diodes, 1, 272-276, 489 attenuators, 1, 586-588 packaging, 1, 491-492 switches, 1, 569-582 Planar circular spiral inductors, 1, 103-107 Planar dielectric-film overlay capacitors, 1, 111-115 Planar field, computer simulation, 1, 183-184 Planar rectangular spiral inductors, 1, 107-111 Planar ribbon inductors, 1, 96-99 Planar ring inductors, 1, 101-103 Planar square spiral inductors, 1, 107-111 Planck's law, 2, 151 Plane waves, 2, 208, 210 Plasma generation gyrotrons, 2, 112-113 magnetrons, 2, 34 microwave-produced, chemical synthesis using, 2, 360-362 Plasma frequency, small-signal analysis, 2, 75 Plastics, properties, 2, 611-613, 620 Platform geometry, microwave antennas, 2, 185 Platinum (Pt), 1, 369,372 properties, 2, 158, 633, 636 Platinum-gold alloy, properties, 2, 158 PLL IC, s e e Phase lock loop integrated circuits PM detectors, s e e Phase modulation detectors PM HEMT, s e e Pseudomorphic high electron mobility transistors

Index

p-n diodes, 1, 266 p-n junction varactors, 1, 268, 269, 271 Point-contact diodes, 1, 261,262 Poisson equation, 2, 140, 598 Poisson's equation, 1, 522-523, 526 POISSON (software), 1, 518-520, 528, 551 Polarization, 2, 176-180, 210-211,238 Polarization mismatch loss, 2, 177 Polarizers, phase shifters, 1, 245 Police radar, 2, 429-431 history, 2, 431-432 interference, 2, 434-435, 439-440, 445-447 moving radar, 2, 432-433 photo radar, 2, 435-436 testing for accuracy, 2, 436-447 Polybutene wax, properties, 2, 613 Polychlorotrifluoroethylene, 2, 615 Polyethylmethacrylate, properties, 2, 612 Polyimide, properties, 2, 159, 160 Polymethyl methacrylate, properties, 2, 613 Poly-4-methyl pentene-1, properties, 2, 623 Polyolefins, properties, 2, 614, 620 Polyphenylene oxide, properties, 2, 620 Polysilicon carbide, properties, 2, 159, 160 Polystyrene, properties, 1, 48; 2, 611,615, 620, 623 Polytetrafluoroethylene (PTFE), properties, 2, 606, 615, 620 Polyvinyl chloride (PVC) microwave heating, 2, 292 properties, 2, 612 Polyvinylcyclohexane, 2, 612 Polyvinyl formal, properties, 2, 612 Pool boiling, 2, 149 Position fixing, Global Positioning System, 2, 405-408 Potassium bromide (KBr), properties, 2, 611 Potted heaters, 1, 505, 516 Power antennas, 2, 181-183 dissipated power, 2, 138 effective isotropic related power, 2, 213 magnetrons, 2, 46-50 maximum peak power, 1, 7, 18, 20 peak power, 1, 18, 20, 27, 314, 542 Power-added efficiency, transistors, 1, 290, 294, 295, 299-300 Power amplifiers, 1, 423-428 Power capability, rectangular waveguides, 1, 18-22 Power combining, 1, 354-356, 381 Power-current ratio, 1, 13 Power density

669

Index

GUNN diodes, 1, 319-320 transistors, 1, 288, 295 Power detectors, 2, 538-544 Power dividers, 1, 423, 424 Power efficiency, amplifiers, 2, 86 Power fading, 2, 485-486 Power limiters, yttrium iron garnet, 1, 257 Power relaxation, nuclear magnetic resonance spectroscopy, 2, 357 Power sweep calibrator, 2, 540-541 Power transmission coefficient, 1, 64 Power-voltage ratio, 1, 13 PPM, s e e Pulse position modulation PPMFLD (software), 1, 558 PPM focusing, s e e Periodic permanent magnet focusing PPMG00 (software), 1, 518, 519 Prandtl number, dimensionless, 2, 147 Prebunched gyrotrons, 2, 111 Pressure broadening, 2, 353 Principal value integrals, 2, 573 Printed circuit dipole antennas, 2, 192 Printing industry, microwave drying, 2, 288 PRN codes, 2, 408-409 Probe coupled harmonic generators, 1, 490 Projection operators, 2, 583 Propagation microwaves, 2, 207-215 attenuation, 2, 214-228 beyond the horizon, 2, 230-232 earth-space propagation, 2, 232-240 indoor, 2, 240-241 mobile propagation, 2, 240 noise, 2, 241 short-path propagation, 2, 240-241 terrestrial line-of-sight propagation, 2, 228-230 refractivity, 2, 480 Propagation constants biological materials, 2, 314 equation, 2, 208 finlines, 1, 29, 32-33 imageguides, 1, 35-38 TEM lines, 1, 3 waveguides circular, 1, 23 dielectric, 1, 35-38 rectangular, 1, 15 Propagation loss, terrestrial line-of-sight propagation, 2, 228 Pseudomorphic high electron mobility transistors (PM HEMT), 1, 294, 296, 297, 405 Pseudoranges, 2, 408

PSK detectors, s e e Phase shift keying detectors PTFE, s e e Polytetrafluoroethylene Puck, 1, 436 Pulse code modulation (PCM), 2, 450 Pulsed Fourier transform nuclear magnetic resonance spectroscopy, 2, 358 Pulsed gyrotrons, 2, 110, 114 Pulsed IMPATT oscillators, 1, 374, 376 Pulsed klystrons, 2, 6 Pulsed wave magnetrons, 2, 33 Pulse electron spin resonance spectroscopy, 2, 383 Pulse frequency, measurement, 2, 551-553 Pulse position modulation (PPM), 2, 449 Pulsing, output power, magnetron, 2, 46-47 Pushing figures, 2, 18 PVC, s e e Polyvinyl chloride

Q Quadrature amplitude modulation (QAM), 2, 450 Quadrature hybrids, 1, 200 Quadruple detectors, 1,462-463 Quality factor (Q factor) capacitor, dielectric film, 1, 114, 115 coaxial lines, 1, 7 conductor quality factor, 1, 7 diodes, 1, 27 dynamic quality factor, 1, 270 inductors ribbon inductors, 1, 98 round wire inductors, 1, 100 spiral inductors, 1, 107, 111 loaded filters, 1, 185 resonant cavities, 1, 327, 344, 346 resonators, 1, 62-64 resonators, 1, 61, 63-65, 67, 88 unloaded capacitors, 1, 187-188 filters, 1, 184-185 inductors, 1, 189-191 resonant cavities, 1, 327, 328, 341 resonators, 1, 61-63, 65, 67, 88, 191-192 surface acoustic wave (SAW) devices, 1, 197 waveguides, 1, 192-193 Quantum-well injection transit-time (QWITT) diodes, 1, 365, 370 Quarter-wavelength baluns, 1, 661 Quarter-wave line, impedance, 1, 3 Quarter-wave plates, phase shifters, 1, 245 Quarter- wave transformers, impedance matching, 1, 623-626, 640-652

670 Quartz, 1, 48, 95 properties, 2, 159, 160, 606, 621,623, 630 Quartz glass, properties, 2, 614 Quasi-optical gyrotron, 2, 106-107 Quasi-optical peniotron, 2, 133 Quasi-TEM mode, 1, 191-192 couplers, 1, 216, 229 phase shifters, 1, 247, 253-254 QWITT diodes, s e e Quantum-well injection transit-time (QWITT) diodes

R Radar, 2, 300 bistatic radar, 2, 300 cataracts among operators, 2, 323 Doppler radar, 2, 417-425 law enforcement applications, 2, 429-431 gyrotrons, 2, 114 klystrons, 2, 12 microwave applications, 2, 300 Radial line filters, 2, 260 Radiation, heat transfer by, 2, 151-154, 161 Radiation frequency, 2, 348 Radiation pattern synthesis, microwave antennas, 2, 193-195 Radiation shape factor, 2, 153-154 Radiation transmittance, 2, 606 Radioactive ash, microwave heating, 2, 292 Radio communications, 2, 477-492 fading, 2, 451,472-473 history, 2, 449-450 path availability calculations, 2, 492-501 transmission errors, 2, 455-465 Radio frequency choke (RFC) detectors, 1, 464, 466, 470 microwave mixer, 1, 481 Radiometry, 2, 300, 333-337 Radio ranging, 2, 407 Radomes, properties, 2, 623 Rain microwave attenuation, 2, 220-227 radio path loss, 2, 474-477, 499-500 Rat-race couplers, 1, 229-232 Rat-race hybrid, 1, 201 RDEMEOS (software), 1, 525, 529 Reactance capacitors, 1, 187 shunt inductors, 1, 632 variable, varactor diodes, 1, 268-272 Reaction mode (resonators), 1, 474, 476 Reaction-type cavity-stabilized GUNN oscillators, 1, 343, 346 Read diodes, 1, 368

Index

Real frequency technique, 1, 657 Real to complex impedance transformation, 1, 626-629, 636, 639-650 Receivers Doppler radar, 2, 422 microwave, 2, 303 superheterodyne, 2, 558-559 Reciprocal dual-mode phase shifters, 1, 244-245 Rectangular-cavity GUNN oscillators, 1, 326, 328-330, 336, 337 Rectangular disk capacitors, 1, 116-118 Rectangular ring inductors, 1, 101-103 Rectangular spiral inductors, 1, 107-111 Rectangular waveguides, 1, 14-22 attenuation, 1, 18 cavities, 1, 68-72 dielectric, 1, 35, 38-39 equations, 1, 15 peniotron, 2, 122, 130-132 phase shifters, 1, 241-243, 246-247 Rectification AM detectors, 1, 461 diodes, 1, 265, 266 Reduced plasma frequency, small-signal analysis, 2, 75 Reduction factor, small-signal analysis, 2, 75 Reentrant coaxial cavity resonators, 1, 67-68 Reference-arm bridges, 2, 375-378 Reflection measurement, 2, 509, 512, 520-524 microwaves, 2, 210-211 Reflection coefficient, 1, 62; 2, 210-211 calculation, 2, 543-544 IMPATT devices, 1, 377, 380 measurement, 2, 522-524 oscillators, 1, 347 TEM lines, 1, 3 transformers quarter-wave, 1, 643, 645, 647 tapered transmission line, 1, 652, 654, 655 transistors, 1, 407 traveling-wave tubes, 2, 72 Reflection gain, 1, 347, 377 Reflection resonators, one-port, 1, 61-63 Reflection type cavity-stabilized GUNN oscillators, 1, 343-345 Reflective fading, 2, 477-478 Reflectivity, 2, 151 Reflectometers, 2, 509, 512 Reflectors, radio communication, 2, 467, 469-471

Index

Refraction, microwaves, 2, 210-211 Refractive index, atmospheric, 2, 212-213 Refractivity, 2, 480 Reggia-Spence phase shifters, 1, 246-247 Reinforced plastics, properties, 2, 620 Relative chamfer, 1, 130 Relative dielectric constant, 2, 362 biological materials, 2, 311, 313 Relative permittivity, 2, 208, 209 Relative wavelength, biological materials, 2, 311 Relaxation, nuclear magnetic resonance spectroscopy, 2, 357, 360 Relaxation frequencies, muscle, 2, 312 Remote life-detection system, 2, 332-333 Residue theorem, 2, 573 Resistance detectors, 1, 462, 463 diodes, 1, 263, 266, 270-271,273, 275, 582-583, 586 inductors, 1, 97, 100-103 junction resistance, 1, 263, 266, 273, 571-572, 582-583, 586 parasitic resistance, 1, 101, 107, 110-111, 271 series resistance, 1, 263, 267, 270, 271,273 spreading resistance, 1, 582 surface resistance, 2, 635, 636 transistors, 1, 301 Resistivity direct grounded lumped termination, 1, 132 ribbon inductors, 1, 98 Resistors microstrip terminations, 1, 131-135 sensitors, 1, 419 thin films, 2, 633 variable, PIN diodes, 1, 274 Resonance, 1, 65, 251-252; 2, 348 Resonance frequency, see also Resonators inductors, 1, 110, 190 Resonance isolators, 1, 255 Resonant cavities, 1, 326, 329 Resonant cavity combiners, 1, 354-355; 2, 41 Resonant cavity devices, 2, 97 Resonant frequency, 2, 349-350 free-space resonant frequency, 1, 328-329 Resonators circular cylindrical waveguide cavities, 1, 73-80 coaxial resonators, 1, 66-68, 196, 433, 436-437, 445, 446 dielectric resonators, 1, 80-83, 196

671 electron paramagnetic resonance spectroscopy, 2, 399 oscillators, 1, 436-438, 445, 447 properties, 2, 620, 624, 626-629 distributed, 1, 191 - 192 electron paramagnetic resonance spectroscopy, 2, 384-399 Fabry-Perot resonators, 1, 88-89 ferrites, 1, 256 filters bandpass filters, 1, 166-170 distributed filters, 1, 178-180 lighthouse tubes, 1, 589-591 line resonators, 1, 65-66 loop-gap resonators, 1, 83-85 materials, properties, 2, 620, 624, 626-629 microstrip resonators, 1, 85-88 microwave FM detectors, 1, 474-475 one-port reflection resonators, 1, 61-63 open-ended microstrips, 1, 121 properties, 2, 620, 624, 626-629 rectangular waveguide cavities, 1, 68-72 traveling-wave resonators, 1, 90 two-port transmission resonators, 1, 63-65 two-wire line resonators, 1, 65-66 yttrium iron garnet resonators (YIG), 1, 89-90, 256 Return loss ripple, 1, 159 Reverse-bias operation, diodes, 1, 271,272, 274, 282, 582-583 Reversed-phase couplers, 1, 211-212 Reynolds number, dimensionless, 2, 146, 147 R F C , see Radio frequency choke RF leakage, measuring with test couplers, 2, 199-201 Ribbon inductors, 1, 96-99 Riblet short-slot couplers, 1, 211 Rice-Holmberg model, 2, 220 Richardson-Dushman equation, 1, 511; 2, 58 Rieke diagram, 2, 50-51,249 Right-angle bend, microstrip lines, 1, 56-57, 128-130 Ring-bar circuit, 2, 67 Ring detectors, 1, 462 Ring inductors, 1, 101-103 Ring-slot probe, 2, 331 Ripple, 1, 159-161; 2, 18-19 Rising-sun magnetron, 2, 82 RMS phase jitter, 2, 457-458 Roberts balun, 1, 665 Rotational energy, 2, 348-349 Round metal post, short circuiting, 1, 124-126

672 Round wire inductors, 1, 99-101 Rubber dielectric properties, 2, 613 microwave curing, 2, 281-284 Ruby mica, properties, 2, 613

$ Saddle point method, 2, 599, 600 Sample access stacks, electron paramagnetic resonance spectroscopy, 2, 384-386 Sand, microwave attenuation, 2, 228 Sapphire dielectric film capacitors, 1, 111-112 dielectric substrate, 1, 48, 95 properties, 2, 159, 160, 619, 621,626 SAR, s e e Specific absorption ratio Satellite communications, 2, 301-303 geostationary orbit, 2, 233-234 Global Positioning System, 2, 403-417 microwave propagation, 2, 232-240 transmission delay, 2, 455 Saturated emission, 2, 58 SAW devices, s e e Surface acoustical wave devices SAW materials, s e e Surface acoustic wave materials S-band antennas, missiles, 2, 197-198 Scalar network analyzer, 2, 505, 508-509 Scalar permeability, 1, 236, 237 Scaling, filter prototype values, 1, 157-159 Scaling factor, imageguide, 1, 40, 41 Scattering matrix, directional couplers, 1, 200, 214 Scattering parameters, dielectric couplers, 1, 217 Schelkunoff method, 2, 194 Schottky barrier diodes, 1, 261-268, 463, 465; 2, 156 electron paramagnetic resonance spectroscopy, 2, 374, 375 microwave antennas, 2, 189 packaging, 1, 491-492 Schottky varactors, 1, 268-269, 271 Schwinger reversed-phase couplers, 1, 211-212 Scintillation, 2, 230 amplitude, 2, 230 ionospheric, 2, 234, 237, 238 phase, 2, 230, 237 tropospheric, 2, 238-239 Scintillation index, 2, 237 Screening constant, 2, 355-356 Screw tuners, 1, 327, 345, 465

Index

SDHT, s e e Selectively doped heterostructure field effect transistors Secondary emission, 1, 511,512-513, 559-560; 2, 60 Selectively doped heterostructure field effect transistors (SDHT), 1, 294 Selenium (Se), 1, 372 properties, 2, 611 Self-resonance frequency, spiral inductors, 1, 106-107

Semiconductor devices diodes GUNN diodes, 1, 276-280 IMPATT diodes, 1, 280-284 mixer and detector diodes, 1, 261-268 PIN diodes, 1, 272-276 varactor diodes, 1, 268-272 history, 1, 308-309 microwave mixers, 1, 478-485 transistors, 1, 419, 432 bipolar junction transistors, 1, 284-293, 405 field effect transistors, 1, 293-302 varactors, 1, 335 Semiconductors negative differential mobility, 1, 309 properties, 2, 161, 621 Sensing devices biological functions, 2, 332-337 microwave applications, 2, 297-299 Sensitors, 1, 419 SES, s e e Severely errored seconds Series diode detectors, 1, 461-462 Series gap capacitors, 1, 118-121 Series inductance, 1, 198 Series-operation combiners, 1, 355-356 Series representations, 2, 573, 574 Series resistance, diodes, 1, 263, 267, 270, 271,273 Series resonators, bandpass filters, 1, 169-170 Series solutions, 2, 589 Series stubs, 1, 621 Severely errored seconds (SES), 2, 456 Severs, 2, 71-72 SFPMIC+ (software), 1, 184 Shadow-gridded electron guns, 1, 502-504, 505, 514 Shadowing, 2, 432, 441-442 Shape factors, 2, 153-154 Shellac, properties, 2, 613 Shielding constant, 2, 355-356 Short circuits, microstrips, 1, 122, 124-126

Index

Short-path microwave propagation, 2, 240-241 Short-slot couplers, 1, 211 Shot noise, 1, 487, 488 Shunt diode detectors, 1, 461-462 Shunt stubs, 1, 619 Sidelobes, microwave antennas, 2, 180 Signal-to-noise ratio, Doppler radar, 2, 423-424 Silica, s e e Silicon dioxide Silicon (Si) dielectric substrate, 1, 48 diodes, 1, 261,262, 266, 268, 280-281, 373, 374, 463, 465 IMPATT oscillators, 1, 386 metallization, 1, 371 properties, 1, 369; 2, 161, 162 transistors, 1, 284-286, 288, 289-293 Silicon carbide (SIC), properties, 2, 161, 619 Silicon dioxide (SiO2) dielectric film capacitor, 1, 111-112 fused, properties, 2, 615, 623 microwave heating, 2, 291 properties, 2, 159, 160, 623, 634 Silicon-gold alloy, properties, 2, 158 Silicon nitride (SIN), properties, 2, 159, 160 Silver (Ag), 1, 372 properties, 1, 19; 2, 158, 633, 636 solder, properties, 2, 162 Similarity transformation, 2, 582 Simulation electron beam collection, 1, 552-553 electron gun design, 1, 502-503, 505-508 filter design, 1, 182-184 GUNN devices, 1, 312 transistor design, 1, 292-293 Simultaneous interative reconstruction technique (SIRT), 2, 338 Single-drift IMPATT diode, 1, 280, 370 Single-hole coupler, 1, 205 Single-loop frequency synthesizer, 1, 453-454, 455 Single-phase convective heat transfer, 2, 145-149 Single pull double throw (SPDT) switches, 1, 569-570, 575-577, 579, 581 Single pull multiple throw (SPMT) switches, 1, 569-570, 577, 578, 581 Single pole single throw (SPST) switches, 1, 569-571,573-575, 581 Single-stage amplifiers, 1, 407, 409 Single-stage collectors, 1, 552-553; 2, 72-73 Single-stub impedance matching, 1, 619-622

673 Singularities, 2, 571-572 Sink phase, 2, 51 Sintering, gyrotrons, 2, 113 SIRT, s e e Simultaneous interative reconstruction technique SIS junction diodes, s e e Superconductorinsulator-superconductor junction diodes Skin depth, 1, 65, 98 Slant paths, microwave attenuation, 2, 225-227 Slot-coupled stripline couplers, 1, 218 Slotted-tube resonators, electron paramagnetic resonance spectroscopy, 2, 399 Slow-passage nuclear magnetic resonance spectroscopy, 2, 358 Slow-wave devices, s e e Traveling-wave thermionic devices Small-signal analysis klystrons, 2, 22-23 peniotrons, 2, 124-126 traveling-wave thermionic devices, 2, 74-76 Small-signal gain, 2, 76 Smith chart, 1, 621,623, 630 Snow, microwave attenuation, 2, 227 Software, s e e a l s o specific programs amplifier design, 1, 421 cathode design, 1, 517 electron beam focusing systems, 1, 550-551 electron beam optical design codes, 1, 518-530 electron gun design, 1, 502 filter design, 1, 183, 184 GTD models, 2, 184-185 gyrotron and peniotron gain, 2, 126 impedance and dielectric constants, 1, 224 matching network synthesis, 1, 657 microwave antennas, 2, 185 platform geometry, 2, 185 thermal conductivity, 2, 142 traveling-wave tube analysis, 2, 76-77 Solar noise, microwave frequencies, 2, 241 Solders, thermal properties, 2, 161, 162 Solenoidal focusing, 1, 548-551 Solenoids, 1, 188-191 gyrotrons, 2, 108, 110 klystrons, 2, 7, 8, 10 SOLENOID (software), 1, 551 Solid-state devices attenuators, 1, 586-588 diodes GUNN diodes, 1, 276-280, 307, 316-325, 332-334, 337, 342, 354, 424-435

674 Solid-state devices (continued) IMPATT diodes, 1, 280-284, 348, 354, 363-386 mixer and detector diodes, 1, 261-268, 461,463, 465, 467, 471,491-492 PIN diodes, 1, 272-276, 489, 491-492 varactor diodes, 1, 268-272, 487, 490, 582-587 phase shifters, 1, 241-248, 582-586 switches, 1, 569-582 SPDT, 1, 569-570, 575-577, 579, 581 SPMT, 1, 569-570, 577, 578, 581 SPST, 1, 569-571,573-575, 581 transfer switches, 1, 577-579, 581 transistors, 1, 419, 432 bipolar junction transistors, 1,284-293,405 field effect transistors, 1, 293-302 vacuum triodes, 1, 616 Solution splicing, 1, 544-547 SOS (software), 1, 528; 2, 77 Space charge, magnetrons, 2, 43-45 Space-charge balanced flow focusing, 1, 549 Space-charge limited emission, 2, 58, 60 Space-charge loss factor, small-signal analysis, 2, 76 Space-charge parameter, small-signal analysis, 2,75 Space diversity, 2, 180, 485, 488, Space vehicle time, 2, 407 S-parameters, 1, 398-404, 584 measurement, 2, 505-512 Specific absorption ratio (SAR), 2, 316-323 Specific attenuation, 2, 215, 217 Specific heat, 2, 279 Spectroscopy electron paramagnetic resonance spectroscopy, 2, 365-399 electron spin resonance spectroscopy, 2, 359-360 microwave absorption spectroscopy, 2, 347-353 nuclear magnetic resonance (NMR) spectroscopy, 2, 353-358 Spectrum analyzer, phase noise measurement, 2, 562-563 Speedguns, 2, 432-447 Spent beam collectors, 1, 553-556 Spin-lattice relaxation, 2, 357 Spin-spin splitting, 2, 356-358 Spin-wave manifolds, 1, 236 Spiral inductors, 1, 103-111 Splicing, 1, 544-545 Spreading resistance, 1, 582 Spurious outputs, 1, 452-453

Index

Square spiral inductors, 1, 107-111 Square waveguides peniotrons, 2, 122, 130 phase shifters, 1, 244-246 resonators, 1, 69 Squint, microwave antennas, 2, 180-181 SSO (software), 1, 518, 521 Stability, klystrons, 2, 27-29 Stabilization factor, 1, 343 Stainless steel, microwave antennas, 2, 202 Standing-wave ratio phase shifter, 1, 584 resonators, 1, 64 TEM lines, 1, 3 voltage, 2, 36-38 Standing-wave rubber curing applicator, 2, 281-282 Stanton number, dimensionless, 2, 147 Static series inductance, 1, 128 Stationary phase methods, 2, 600 STB (software), 1, 518, 521 Steady-state heat conduction, 2, 139 Steel, properties, 2, 158 Steepest descent method, 2, 599-600 Stefan-Boltzmann law, 2, 151 Step-down heating, 2, 328 Stepped impedance low-pass filters, 1, 175-177 Steps, microstrip lines, 1, 55-56, 127-128 Stokes' theorem, 2, 589 Straight planar ribbon inductors, 1, 96-99 Strapping, anodes, 2, 42-43, 82 Strip conductors, 1, 96-99 Stripline phase shifters, 1, 247-248, 250, 252, 253 Strontium titanate (SrTiO4), properties, 2, 611 Stub matching, 1, 619-623 Styrofoam, properties, 2, 606, 613 Substrate mode, 2, 189 Substrates ceramics, 1, 194, 195 dielectric, 1, 48, 95 Sulfur (S), aqueous, microwave heating, 2, 290 Super Compact (software), 1, 421 Superconductor-insulator-superconductor (SIS) junction diodes, 1, 261 Superconductors, properties, 2, 638-642 SUPERFISH (software), 2, 77 Superheterodyne bridges, 2, 373 Superheterodyne receivers, 2, 558-559 Surface acoustical wave (SAW) devices, 1, 196-197 Surface acoustic wave (SAW) materials, properties, 2, 629-631

Index

Surface resistance, metals, 2, 635, 636 Surface resistivity direct grounded lumped terminations, 1, 132 ribbon inductors, 1, 98 Suspended substrate technique, 1, 143-153, 218 Sweepers, GUNN voltage-controlled oscillators, 1, 341-342 Switched oscillators, 1, 451 Switches ferrite, 1, 257-258 SPDT, 1, 569-570, 575-577, 579, 581 SPMT, 1, 569-570, 577, 578, 581 SPST, 1, 569-571,573-575, 581 transfer switches, 1, 577-579, 581 Switching cutoff frequency, diodes, 1, 273-274 Symmetric bandpass transform, 1, 172 Symmetric couplers, 1, 214-216 Symmetric series gap capacitors, 1, 119-120 Symmetric transform filters, 1, 169-170 Synchronization parameter, small-signal analysis, 2, 75 Synthesizers, s e e Frequency synthesizers System noise temperature, 2, 183

T Tangential signal sensitivity (TSS), 1,463, 488-489 Tantalum pentoxide (Ta2Os), dielectric film capacitors, 1, 112 Tantalum (Ta), properties, 2, 158, 633 Tapered baluns, 1, 660, 662 Tapered couplers, 1, 216 Tapered-slot antennas, 2, 189 Tapered transmission line transformers, 1, 652-656 Tap noise, 1, 488 Target-speed bumping, 2, 435, 442-443 Taylor line, source method, 2, 194-195 TBCATH (software), 1, 517 TDQL, s e e Thermal dielectric loss quotient TEGFET, s e e Two-dimensional electron gas field effect transistors Telephone systems, radio communications, 2, 449-450, 455 Tellurium (Te), 1, 372 TEM, s e e Transverse electromagnetic mode TE mode circular waveguide, 1, 23, 27 coaxial line, 1, 8-9 dielectric resonators, 1, 81 rectangular waveguide, 1, 14, 15, 18-22 waveguide cavities, 1, 70-80

675 Temperature, klystron performance, 2, 19, 29 Temperature sensor, 2, 156 Tensors, 2, 578-579 Terminations image impedance, 1, 658-660 microstrip, 1, 131-135 Terrain roughness factor, 2, 493, 495 Terrestrial paths, microwave attenuation, 2, 225, 228-230 TElo2 cavity, 2, 384-394 Tetrodes, thermionic, 1, 606-616 Thawing, industrial, microwaves, 2, 284-285 Thermal-based power detectors, 2, 538-540 Thermal beam model, electron guns, 1, 536 Thermal conductance, 2, 279 Thermal conductivity, 2, 139-142, 297, 619 Thermal dielectric loss quotient (TDQL), 2, 159, 163 Thermal fade margin, 2, 491 Thermal multipath outage, 2, 492-493 Thermal noise, 1, 487-488 analog radio, 2, 451-453 Thermal noise power, 2, 527 Thermal resistance, 2, 138, 158 measurement, 2, 155-156 Thermionic devices, traveling wave, s e e Traveling-wave thermionic devices Thermionic emission, 1, 511-512; 2, 57-60 Thermionic tetrodes, 1, 606-616 Thermodynamics microwave devices, 2, 137-163 microwave heating, 2, 277-279, 362 Thermography, 2, 333-337 Thermonic triodes, 1, 589-605 Thin-film capacitors, 1, 111 Thin films, properties, 2, 633, 634, 636 Thin-wire modeling, 2, 602 Thorium (Th), 2, 40-41 Three-branch couplers, 1, 225-228 3DFEA, 2, 323 Three-dimensional finite element analysis, 2, 323 Three-dimensional simulation, filter design, 1, 184 Three loop-two gap resonators, 1, 85 Three-port circulator, 1, 249-250 Threshold critical field, 1, 237 Time domain, 2, 570 Time measurement, Global Positioning System, 2, 407-409 TIMs, 1, 426 Tin (Sn), 1, 372 properties, 2, 158, 636, 639 Tin-gold alloys, properties, 2, 158

676 Tire industry, microwave processes, 2, 284, 299 Tissue cell, electron paramagnetic resonance spectroscopy, 2, 390 Titania, s e e Titanium dioxide Titanium (Ti), 1, 372 properties, 1, 369; 2, 158, 633 solder, properties, 2, 162 Titanium dioxide (TiO2), properties, 2, 159, 160, 634 T-junctions microstrip line, 1, 57 microwave mixer, 1, 481 TLM message, 2, 410-412 TMLBMC (software), 1, 518, 519, 530-531, 533-535 TM mode coaxial lines, 1, 8, 9 waveguide cavities, 1, 70-80 waveguides, 1, 15, 18, 23, 27 Top-C-coupled bandpass filters, 1, 166-168, 171 Top-C-coupled distributed resonators, 1, 175, 178 Top-L-coupled bandpass filters, 1, 168-169, 171-172 Toroidal phase shifters, 1, 241-243 Toroid cores, 1, 195-196 Total amplitude modulation noise, 1, 488 Total capacitance, diodes, 1, 263, 273 Total device impedance, 1, 284 Total node capacitance, bandpass filters, 1, 167 Total path outage time, 2, 492 Traffic radar, 2, 429-431 errors, 2, 433-434 history, 2, 431-432 interference, 2, 434-435, 439-440, 445-447 moving radar, 2, 432-433 photo radar, 2, 435-436 testing for accuracy, 2, 436-447 Transconductance, 1, 594, 597 Transductors, antennas, 2, 168 Transferred electron devices, 1, 307-308 amplifiers, 1, 346-350 design and fabrication, 1, 313-325 GUNN diodes, 1, 276-280, 301,313-325 GUNN oscillators, 1, 324, 325-346 history, 1, 308-309 negative differential mobility, 1, 308-313 noise characteristics, 1, 350-354 power combining techniques, 1, 354-356

Index

Transferred electron effect, 1, 276, 277, 308 Transfer switches, 1, 577-579, 581 Transformers balanced to unbalanced, s e e Baluns quarter-wave transformers, 1, 623-626, 640-652 binomial, 1, 641-645 Chebyshev, 1, 645-651 tapered transmission line transformers, 1, 652-656 Transient heat flow, 2, 145 Transistors amplifier design, 1, 394-402, 405,407, 426 biasing, 1, 396-397 BJT, 1, 284-293, 405, 419, 432 capacitance, 1, 301 chip transistors, 1, 403 collector efficiency, 1, 288 computer-aided design, 1, 292-293, 302 cutoff frequency, 1, 286, 290, 299 FET, 1, 293-302, 419, 432 gallium arsenide, 1, 284, 285, 287, 288, 293-295, 297, 298, 300, 302, 405, 419 HBT, 1, 284-289, 292, 294, 295 HEMT, 1, 285, 287, 288, 293-302, 405, 419 HFET, 1, 293 JFET, 1, 293 matched, 1, 426 MESFET, 1, 285, 287, 288, 293-295, 297-302 MODFET, 1, 293-294 packaged, 1, 402 PM HEMT, 1, 294, 296, 297, 405 power density, 1, 288, 295 resistance, 1, 301 SDHT, 1, 294 S-parameters, 2, 508 TIMs, 1, 426 ULTRA HEMT, 1, 405 voltage, 1, 401 Transition cross section, 2, 350-351 Transition moment, 2, 350 Transitions circuit to waveguide, 2, 72 coaxial to microstrip, 1, 136-138 Transit-time devices, 1, 363-365 BARITT, 1, 261,364, 365 DOVETT, 1, 365 IMPATT, 1, 276, 280-284, 348, 354, 363-386 MITATT, 1, 365

Index

QWITT, 1, 365, 370 TRAPATT, 1, 365 TUNNETT, 1, 364, 365 Transmission, 2, 302 broadcasting, 2, 207-241,300-303, 449-501 measurement, 2, 514-520 police radar, 2, 438-439 transmission errors, 2, 455-465 Transmission delay, 2, 455 Transmission line loss, 2, 466 Transmission lines, 1, 1 characteristic conductance, 1, 62 coaxial lines, 1, 1, 5-13 couplers, 1, 213 dielectric waveguides, 1, 34-44 finlines, 1, 28-34 lumped distributed equivalents, 1, 172-174 microstrip lines, 1, 47-58, 131, 135, 143-153 tapered, 1, 652-656 two-wire lines, 1, 2, 4, 12-13 waveguides, 1, 13-28 Transmission path loss, 2, 466-471 atmospheric absorption, 2, 473-474 rainfall, 2, 474-477 Transmission paths, 2, 465 earth-space, 2, 225-227, 232-240 line-of-sight path, 2, 214-228 terrestrial, 2, 225, 228-230 Transmission resonance method, 1, 271,474, 476 Transmission resonators, two-port, 1, 63-65 Transmission-type cavity-stabilized GUNN oscillators, 1, 343, 345 Transmissivity, 2, 151 Transmitters, 2, 301-302, 422 Transverse electric field, waveguides, 1, 17, 23 Transverse electromagnetic mode (TEM), 1, 1-2, 191-192 coaxial line mode, 1, 8, 9 coaxial line resonators, 1, 67 couplers, 1, 216, 223 dielectric loaded TEM mode, 1, 196 equations, 1, 2, 3 ferrite medium, 1, 237-239 Transverse magnetic field, waveguides, 1, 15, 23 Transverse split, microstrip line, 1, 55 Trapped imageguide, 1, 42-43 Trapped-plasma/avalanche-triggered transittime (TRAPATT) devices, 1, 365

677 Traveling-wave helix, electron paramagnetic resonance spectroscopy, 2, 397 Traveling-wave thermionic (TWT) devices cathodes, 2, 57-60 crossed-field amplifiers, 2, 84-87 crossed-field backward-wave oscillators, 2, 87-90 electron beam focusing, 2, 62-64 electron guns, 2, 60-62 linear-beam backward-wave devices, 2, 77-79 linear-beam traveling-wave tubes, 2, 64-77 magnetrons, 2, 33-55, 79-84 rubber curing, 2, 282 Triangular distribution taper, 1, 653-654 Triazine, properties, 2, 159, 160 Triodes, thermionic, 1, 589-605 Troposcatter (tropospheric scatter propagation), 2, 231 Tropospheric effects, earth-space microwave propagation, 2, 237-239, 240 Tropospheric scintillation, 2, 238-239 TRUE103 (software), 1, 518, 521,554, 556, 557 Tschebyscheff method, 2, 194-195 TSS, s e e Tangential signal sensitivity Tubular bandpass filters, 1, 170 Tumors, microwave hyperthermia as cancer treatment, 2, 327-331 Tuner screws, 1, 327, 345, 465 Tungsten (W), properties, 2, 158 Tungsten carbide (WC), 2, 40-41 Tuning capacitor diodes, 1, 583 Tuning fork calibration, microwave, 2, 437-438 Tunnel emittance, 1, 520-521,536-537, 546, 547, 556 Tunnel injection transit-time (TUNNETT) diodes, 1, 364, 365 Turbulent flow, convective heat transfer, 2, 148, 149 Twin-slab phase shifters, 1, 243 Two-branch couplers, 1, 224-226, 228 Two-dimensional electron gas field effect transistors (TEGFET), 1, 293-294 Two loop-one gap resonators, 1, 84-85 2.5D simulators, 1, 184 Two-port transmission resonator, 1, 63-65 Two-wire lines, 1, 2 AM detectors, 1, 463-465 attenuation, 1, 12-13 capacitance, 1, 4

678 Two-wire lines ( c o n t i n u e d ) equations, 1, 2, 12-13 resonators, 1, 65-66 TWT, s e e Traveling-wave thermionic devices Twystron, 2, 3-4, 19, 28 Type M cathode, 1, 515

U UAS, s e e Unavailable seconds Ubitron, 2, 98, 114-116 UHG antennas, missiles, 2, 196 Ultra high electron mobility (ULTRA HEMT) transistors, 1, 405 Ultra-low-noise amplifiers, 1, 415, 428 Ultra-wide-band amplifiers, 1, 394, 413, 414 Unavailable seconds (UAS), 2, 457 Unified theory of diffraction, 2, 185 Uniform field focusing, 1, 548-551 Uniform mesh (UM) gun codes, 1, 522-523, 525, 530 Unilateral finlines, 1, 28-34 Unilateral gain, transistors, 1, 290 Unitary operators, 2, 584 Unit step function, 2, 576 Unloaded quality factor capacitors, 1, 187-188 filters, 1, 184-185 inductors, 1, 189-191 resonant cavities, 1, 327, 328, 341 resonators, 1, 61-63, 65, 67, 88, 191-192 surface acoustic wave (SAW) devices, 1, 197 waveguides, 1, 192-193 Unsteady-state heat conduction, 2, 139, 142 Up-converters, 1, 485-486 Urea-formaldehyde plastics, properties, 2, 612 Urethane foams, properties, 2, 623 UTD, s e e Unified theory of diffraction

V Vaporization, thermodynamics, 2, 149-151, 279 Vapor-phase epitaxy (VPE), 1, 314-315 Varactor diodes, 1, 268-272 commercial, 1, 587 harmonic generator, 1, 490 parametric amplifiers, 1, 487 phase shifters, 1, 582-586 Varactors, 1, 335 Schottky varactors, 1, 268-269, 271 Varactor-tuned oscillators, s e e Voltagecontrolled oscillators

Index

VARGUS (software), 1, 528 Variable reactance devices, varactor diodes, 1, 268-272 VCO, s e e Voltage-controlled oscillators VCXO, s e e Voltage-controlled oscillators, crystal Vector fields, 2, 586-589 Vector identities, 2, 589 Vector inequalities, 2, 581 Vector network analyzer, 2, 505 Vectors, 2, 576-579 Vector spaces, 2, 579-581 Vehicular mobile satellites, microwave propagation, 2, 240 Velocity-field characteristics, GaAs, 1, 310-312 Velocity measurement Global Positioning System, 2, 409-410 police radar, 2, 440 Vertical-coupled stripline couplers, 1, 218 Vertical polarization, microwaves, 2, 210-211 VHF fine-tune frequency, 1, 451 Video impedance, detectors, 1, 265 Vinylidene-vinyl chloride copolymer, properties, 2, 612 Virtual grounded lumped terminations, 1, 134-135 Voltage bias voltage, 1, 277, 281,282, 582 couplers, 1, 214 direct wave voltage, 1, 214 Hartree voltage, 2, 47-48 Hull cutoff voltage, 2, 44 klystrons, 2, 19 magnetrons, 2, 47-48 pinch-off voltage, 1, 270, 271,401 ripple, 2, 19 transistors, 1, 401 Voltage-controlled oscillators (VCO), 1, 335-340, 429-431; 2, 545-546 crystal oscillators (VCXO), 1, 442-444 FM detectors, 1, 470, 472-473 Voltage coupling coefficient, 1, 214 Voltage-current ratio, 1, 13 Voltage reflection coefficient, 2, 210-211 Voltage standing-wave ratio (VSWR), 2, 36-38 microwave antennas, 2, 181, 185 Voltage standoff, electron guns, 1, 538 VPE, s e e Vapor-phase epitaxy VSWR, s e e Voltage standing-wave ratio

Index

W Wafer capacitors, 1, 111 Waiting time jitter, 2, 458-459 Wander, 2, 455 Water-cooled magnetrons, 2, 34, 43, 51-52 Water vapor, microwave attenuation, 2, 217-219 Waveguide aperture couplers, 1, 201-213 Bethe-hole couplers, 1, 202-205 Moreno cross-guide couplers, 1, 212-213 multihole waveguide couplers, 1, 205-211 Riblet short-slot couplers, 1, 211 Schwinger reversed-phase coupler, 1, 211-212 Waveguide branch-guide couplers, 1, 223, 225 Waveguide cavities, 1, 68-80 Waveguide devices AM detectors, 1, 465-468, 492 circulators, 1, 249-254, 257-258, 347 couplers, 1, 201-213, 223, 225 harmonic generator, 1, 489-491,494-495 IMPATT amplifiers, 1, 379 isocirculators, 1, 254-257, 408-410, 423 for microwave hyperthermia, 2, 331 microwave mixers, 1, 480-482, 492-493 peniotrons, 2, 102-103, 121-133 phase shifters, 1, 241-248, 582-586 resonators, 1, 68-72 up-converters, 1, 485, 486 Waveguides, 1, 13-14, 192-193 circular, 1, 14, 22-28, 244-246; 2, 131-132 dielectric, 1, 34-44 ferrites, 1, 238-240 folded, 2, 89 impedance, 1, 13, 15, 23 magic T, 1, 201 magnetic field, 1, 14-17, 23-25 microwave antennas, 2, 182 peniotrons, 2, 122, 130-132 rectangular, 1, 14-22, 35, 38-39, 241-243, 246-247; 2, 122, 130 square, 1, 69, 244-246; 2, 122, 130 Waveguide slot arrays, 2, 169 Wave impedance, biological materials, 2, 313 Wavelength microstrip line, 1, 48, 49, 49-50 small-signal analysis, 2, 74 waveguides, 1, 15, 23 Waxes, dielectric properties, 2, 613

679 Weighting factor, 2, 352 Whisker diodes, 1, 261-264, 269 Whispering gallery mode dielectric resonators, 1, 83 Wide-band amplifiers, 1, 405, 414, 657, 658 Wide-band impedance matching, 1, 640-660 image impedance terminations, 1, 658-660 matching networks, 1, 656-658 multisection quarter-wave transformers, 1, 640-652 tapered transmission line transformers, 1, 653-656 Wide-band matching networks, 1, 656-657 Wide-band tapered baluns, 1, 660, 662 Wilkinson power dividers, 1, 423, 424 Winding capacitance, spiral inductors, 1, 106, 109-110 Windows, 2, 72 Wire inductors, 1, 99-101 Wire-wound TE0~, 2, 395, 397 Wood industry, microwave applications, 2, 296-297 Woodward method, 2, 194 Work function, 2, 58 Wrap-around antenna, 2, 197 Y

Yagi antenna, 2, 189 Y-factor, 2, 528 YIG devices, s e e Yttrium iron garnet devices Y-junction circulators, 1, 251-254 Yttrium barium cuprate, properties, 2, 639, 640, 642 Yttrium iron garnet (YIG) devices ferrites, 1, 256-257 filters, 1, 256-257 oscillators, 1, 341,429-430, 432-433 power limiters, 1, 257 properties of materials, 2, 631,632 resonators, 1, 89-90, 256 7'

Zig-zag transformation, 1, 170-171 Zinc (Zn) IMPATT devices, 1, 371,372 properties, 1, 369; 2, 158 Zinc selenide (ZnSe), 1, 276, 309 Zirkonate, properties, 2, 614 ZY Smith chart, 1, 630

ISBN 0-12-374697-3 90038

23 7469