Magnetic Sensors, Volume 5, Sensors: A Comprehensive Survey

1

Introduction R ICHARD BOLL. Vacuumschmelze GmbH. Hanau. FRG

Contents 1.1 1.2 1.3 1.4 1.4.1 1.4.2 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.6 1.6.1 1.6.2 1.7 1.7.1 1.7.2 1.7.3 1.8 1.8.1 1.8.2 1.8.2.1 1.8.2.2 1.8.3 1.9

. . . . . . . . . . . . Definition of Magnetic Sensors . . . . . . . . . . . . . . . . . . . Magnetic Terms and Units .................... Natural and Technical Magnetic Fields and Their Order of Magnitude . . Introductory Remarks. Historical Background

Natural Magnetic Fields . Technical Magnetic Fields

. . . . . . . . . . . . ............ Soft and Hard Magnetic Materials for Sensors . . Soft Magnetic Materials . . . . . . . . . . . . . Hard Magnetic Materials . . . . . . . . . . . .

Mechanical Properties of Magnetic Materials . Supplementary Remarks . . . . . . . . . . .

. . Magnetic Noise . . . . . . . . . . . . . . . . Thermal and Thermomagnetic Noise . . . . . Barkhausen Noise . . . . . . . . . . . . . . .

. . . . .

. . . . .

. . . . .

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

. . . . . . . . . . ......... . . . . . . . . . . . . . . . . . . . ......... Coil Systems to Produce Definite Magnetic Fields . . . . . . . . . . Coils for Homogeneous DC Fields up to Approximately 100 A/cm . . . Coils for Higher Fields (Electromagnets) . . . . . . . . . . . . . . . Superconducting Coils . . . . . . . . . . . . . . . . . . . . . . . Shielding Magnetic Fields . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles of Magnetic Shielding . . . . . . . . . . . . . . . . DC Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . AC Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 3 5

6 6 8 9 10 13 15 16 16 16 19 20 21 23 24

Materials for Magnetic Shieldings and Design

24 24 25 25 26 27

References

29

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

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

2

1 Introduction

1.1 Introductory Remarks, Historical Background The expression magnet or magnetic originates from the region Magnesia in Thessaly (Greece) where magnetic loadstone (Magnetite, Fe, 0,) is found as a natural resource. The first reports in Europe of the attraction and repulsion forces arising between magnetic loadstones were made by Thales of Miletus around 600 B. C. The expression “sensor” is derived from the Latin “sensus” meaning capable of sensitivity. It is gradually replacing previously used expressions such as “measurement pick-up” and “probe”. The directional compass can really be regarded as the first magnetic sensor since it reacts to the Earth’s magnetic field. Its history stretches back over 4000 years and can be traced to the Chinese who first discovered magnetic loadstone as a natural source of magnetism and used it as a directional aid for orientation [l, 21. Other early sensors can be found in the world of wildlife where nature has equipped certain birds and fish with “magnetic sensors” providing them with the capability to orientate themselves in the Earth’s magnetic field and hence providing them with a sense of direction. The compass became significantly more important in Europe from about 1200 A. D. onwards, and in particular around the time of the great seafaring adventurers and explorers. On his transatlantic voyages Christopher Columbus observed the behavior of the compass as he sailed westward and famous compass-makers are known to have lived in London and Nurnberg around 1500. At that time the production of “steel’’ suitable for compass needles was a closely kept secret. In 1820 Oersted discovered that a current carrying wire deflected a compass needle in its vicinity, and with that the age of electromagnetism had arrived. The first mathematical formula describing the correlation between electric current and magnetism through the deflection of a magnetic needle was Biot-Savart’s law. Then Faraday repeated and extended Oersted’s experiments and while doing so discovered the Law of Induction in 1831. The first magnetometer to be constructed was the bifilar magnetometer built in 1831 by Gauss and Weber and in 1841 the Weber-Bussole compass which included a magnetic needle was used to measure powerful currents. In 1862 Maxwell created the common theoretical basis for electromagnetism with the laws which were named after him [3], though the expression “permeability” can be traced to Lord Kelvin. Throughout the history of this topic it is evident that the availability of different types of sensors operating on a magnetic basis is very closely linked to the development and the availability of special magnetic materials and to the discovery of new physical and magnetic effects. Some of these effects were very soon exploited to make new magnetic sensors, others were not used until much later and some are yet to be utilized in sensors. Table 1-1 gives a brief survey (see also [4]).

1.2 Definition of Magnetic Sensors

3

B b l e 1-1. Magnetic effects for sensors. Year

Effect

Explanation

Technical Use

1842

Joule effect

Change in shape of a ferromagnetic body with magnetization (magnetostriction)

In combination with piezoelectric elements for magnetometers and potentiometers

1846

AE effect

Change in Young’s modulus with magnetization

Acoustic delay line components for magnetic field measurement

1847

Matteucci effect

Torsion of a ferromagnetic rod in a longitudinal field changes magnetization

Magnetoelastic sensors

1856

Magnetoresistance (Thomson effect)

Change in resistance with magnetic field

Magnetoresistive sensors

1858

Wiedemann effect

A torsion is produced in a current carrying ferromagnetic rod when subjected to a longitudinal field

Torque and force measurement

1865

Villari effect

Effect on magnetization by tensile or compressive strength

Magnetoelastic sensors

1879

Hall effect

A current carrying crystal produces a transverse voltage when subjected to a magnetic field vertical to its surface

Magnetogalvanic sensors

1903

Skin effect

Distance sensors, proximity sensors

1931

Sixtus Tonks effect

Displacement of current from the interior of material to surface layer due to eddy currents Pulse magnetization by large Barkhausen jumps

1962

Josephson effect

lbnnel effect between two superconducting materials with an extremely thin separating layer; quantum effect

Wiegand and pulse-wire sensors SQUID magnetometers

1.2 Definition of Magnetic Sensors

The expression “Magnetic Sensors” is not commonly used. However, when the concept for a book series on sensors was formed and the volumes and chapters were being planned it appeared that the term “magnetic sensors” described quite succinctly a clearly defined group of sensors.

4

1 Introduction

This description is sensible when one considers that the category is not limited solely to magnetic-field sensors, but is allowed to include all magnetic sensors some of which have previously fallen into different groups. Here, magnetic sensors are understood to be sensors which in one way or another are associated with the laws and effects of magnetic or electromagnetic fields. The latter group covers those sensors which utilize the laws of induction, whilst the former group includes sensors in which certain material properties are influenced by a magnetic. field. Magnetic materials, i. e., soft and hard magnetic materials and all other materials, which are sensitive to magnetic fields, play a principal role in the nature and operation of magnetic sensors, but at this stage it is not relevant to consider whether metals, metal oxides or semiconductors are concerned or which physical properties are being influenced by the magnetic field. Previous attempts at classification and grouping of sensors have been inconsistent and not uniform. In textbooks on measurements and control, but also from other books on sensors or from review articles sensors have been classified using the following methods [5-141:

-

‘Ijrpes of sensors Physical principles Properties measured Sensor applications Sensor technologies.

For this edition of Volume 5 , a classification system has been selected which is essentially based on physical principles and effects, as follows:

- Magnetogalvanic sensors - Magnetoelastic sensors

-

Magnetic-field sensors: saturation-core magnetometers (flux-gate magnetometers) and induction-coil and search-coil magnetometers Inductive sensors (including eddy-current sensors) Wiegand and pulse-wire sensors Magnetoresistive sensors SQUID sensors.

Each chapter of this volume individually deals with the fundamentals, measurement magnitudes, sensor components and devices, new technologies, and also partially with sensor electronics. In addition, technical design and the main fields of application are also discussed. A more complete survey of applications is presented in Chapter 11, whilst Chapter 12 outlines future trends in the field. This volume does not include sensors based on a magneto-optical basis, i. e., fiber-optic sensors. These are discussed in Volume 6 as their intrinsic physical properties are primarily derived from the field of optics and optical effects (e.g. Faraday effect). Moreover, Volume 5 does not cover magnetic heads of the sort used to read magnetic memories of audio, video and data devices like magnetic tapes, magnetic cards, Winchester disks etc. Strictly speaking though, magnetic heads which react to the stray fields of information carriers are actually magnetic sensors. However, they form a special group which does

1.3 Magnetic Terms and Units

5

not readily fall under the subject matter discussed in this volume, and this applies equally to magnetic heads operating on an induction or magnetoresistive basis as well as to those sensors operating magneto-optically. Also excluded are magnetic sensors using magnetic resonance effects or the Zeeman effect. Some special magnetic sensors based on integrated circuits technology will be covered by Volume 1.

1.3 Magnetic Terms and Units The subject of magnetism generates a number of terms and units which are commonly used, the more important ones being included in Table 1-2. Nowadays, magnetic terms and units are given using the MKSA system, a subsystem of the SI system (Systtme International d’unites), Table 1-2. Magnetic terms and units. Term, quantity

MKSA unit

subunits

CGS unit

conversion

Magnetic field strength H

A/m

1 A/cm = 100 A/m 1 mA/cm = 0.1 A/m 1 kA/m = 1000 A/m

Oe (Oersted)

1 Oe = 79.58 A/m = 0.796 A/cm

Magnetization M Magnetic induction B (flux density)

A/m T (Tesla)

G (Gauss)

v.s --

see field strength 1 mT = T 1 pT = 1 0 - 6 T 1 nT = 1 0 - 9 T 1 pT = T 1 yl) = 1 nT

1G = T 1 kG = 0.1 T 1 mG = iO-’T

Magnetic flux

Wb (Weber)

-

Mx (Maxwell)

1 Mx = lo-* Wb

m2

@

=v*s Magnetic polarization Permeability

T

J

(absolute)

P

= 10-5 G

see induction -

T.m

G -

A

Permeability of vacuum (magnetic constant) ,uo

1 yl)

4n.10-’

-

Oe

T.m

T.cm

- 0 , 4 ~ . 1 0 - ~ -A A

1

-

I) y is a special unit used in geomagnetism, there is a necessity to distinguish between yH and ye (related to H and B )

The most important basic equations are: B =/J~,.(H+M)=P~.H+J

B M = - - H = -

J

PO

PO

P

=

p,, . p r

p , = relative permeability

6

1 Introduction

and they are based on the four basic units of meter, kilogram, second and amptre (see also [ISl). Although the previously used electromagnetic system of dimensions (CGS electromagnetic units - emu), also known as the Gauss system, is officially no longer acceptable it is still sometimes found in the literature and so a conversion table for the CGS units has been included (Table 1-2) [16- 181. Specialized terms pertaining to particular materials are explained in the individual chapters.

1.4

Natural and Technical Magnetic Fields and Their Order of Magnitude

Both our natural environment and our technical surroundings provide magnetic fields of many different types and orders of magnitude. Many magnetic sensors detect such fields either directly or indirectly using diverse principles, hence it is important to take a closer look at the types and magnitudes of the various fields.

1.4.1

Natural Magnetic Fields

The firth’s Magnetic Field The most ubiquitous natural field of all is the magnetic field of the Earth which surrounds us perpetually. It is a dipole field, whose field lines originate at the magnetic poles in the interior of the earth, escaping through the surface and reaching into outer space (Figure 1-1). The Earth’s magnetic field is used everyday by people with compasses to determine direction or at altitudes of several hundred kilometers to stabilize satellites [19], and on the Earth’s sur-

Figure 1-1. Magnetic field of the Earth.

1.4 Natural and Technical Magnetic Fields and Their Order of Magnitude

7

face it can be employed as a constant reference field within certain ranges and times. The precise determination of the parameters of the Earth’s magnetic field, namely its magnitude and direction was one of the great pioneer acts in the field of magnetism and goes back to the works of Gauss and Oersted [20]. Table 1-3 gives examples of data on the Earth’s magnetic field for several towns in the Federal Republic of Germany. As a rough guide we may consider the magnitude of the field or flux density at the poles of the Earth to be approx. 0.5 A/cm (0.06 mT) and at the equator to be roughly 0.25 A/cm (0.03 mT).

Magnetic Fields in Outer Space With the aid of satellites and sensitive magnetic-field sensors, magnetic fields in the vicinity of planets and in outer space can also be determined directly (see Table 1-4 and [21, 221). Table 1-3. Components of the Earth’s magnetic field (values from German Hydrographical Institute, Hamburg, 1986). Town Berlin Dusseldorf Frankfurt Hamburg Munich

H= A/cm

H, A/cm

0.1480 0.1536 0.1580 0.1441 0.1662

0.3590 0.3964 0.3466 0.3375 0.3404

8

go

+ 0.42

61.6 68.8 65.6 66.9 63.9

-2.20 - 1.42 - 1.03 -0.18

H = = Horizontal component, H , = Vertical component, 8 = Declination, r9 = Inclination. Positive declination 8 means a deviation to the east referred to the geographic direction north T = 0.1256mT = 1.256 * lo5 nT in air, respectively in a vacuum. 1 A/cm corresponds to 1.256 .

Table 1-4. Magnetic field strengths of celestial bodies and objects in outer space. Celestial bodies Galaxies Mercury (poles) Jupiter (poles) Mars Saturn (equator) Sun (surface) Earth (poles) A-stars 1 m T a 10 Gauss

Field strength A/cm

Flux density mT

0.15 ... 0.25 * = 3 10-3 up to 6

I :

2.4 ... 16 4 8

0.2 . .. 0.3 * 0.35 . 10-3 up to 0.8 0 0.3 .., 2 0.5 .., I

I :

0.5

0.06

4

.

0 I :

...

up to 28 . lo3 A/cm

up to 3.5 T

8

1 Introduction

Biomagnetic Fields Human beings also produce small magnetic fields which are primarily caused by microcurrents in cardiac, brain, and muscle tissue. They can nowadays be measured with highly sensitive magnetic-field detectors such as flux-gate magnetometers, SQUIDS, and gradiometer coils (see Chapter 10) on the surface of the body, whereas in the past, it has only been possible to measure these currents indirectly by attaching electrodes to the skin and measuring the relevant voltage drops - a technique which forms the basis for the electrocardiogram (ECG). The magnitude of the field strengths and flux densities produced by heart and brain currents are nT and 1 nT, respectively [23, 241. approximately 50 .

-

Magnetic Noise Fields in Magnetic Components Magnetic and thermomagnetic noise fields are caused by thermal fluctuations in every magnetic component, as they are in magnetic cores. In particular, Barkhausen noise is significant in magnetic materials (see Section 1.6).

1.4.2 Technical Magnetic Fields Magnetic Fields in the Vicinity of i7-ansformers and Electric Motors Magnetic fields produced in electrotechnical devices, equipment, and plants are usually in to 1 T). In most cases these would be the field-strength range of 0.1 to lo4 A/cm (ca. AC fields emitted by overhead lines, electrified lines (train or tram lines etc.), transformers and electrically powered machinery. Transformers and machinery are mostly operated near the saturation limit of their iron cores, and as such the polarization in the core material attains a level of about 2 T. Similarly, both flux densities in the air gaps of big choke coils or in the gaps between rotors and stators of electric machinery and the stray fields in the vicinity are, as a rule, not much lower.

Fields of Permanent Magnets With the exception of electromagnets, permanent magnets and magnet systems are frequently used to produce static magnetic fields, particularly in measurement devices. In such cases, the field is mostly concentrated into a specified volume (eg, operating air gap) through appropriate design of the magnet and the magnetic circuit. The magnitude of the field strengths or flux densities attainable depends on both the remanence and the energy density of the magnetic materials as well as on the geometry of the magnetic circuit (see Section 1.5 and [25, 261).

1.5 Soft and Hard Magnetic Materials for Sensors

9

Fields of Conventional and Superconducting Coils Solenoids with a conventional design, iron cored coils (electromagnets), and superconduction (solenoid) coils can produce flux densities in the region of 1 to 100 T depending on their dimensions, their magnitude and their mode of operation [27-291. Superconducting coils in medical scanning machines (NMR systems) with a practical diameter of roughly 1 m can produce fields of 1 to 2 T, and special coils with large diameters are used for specified tasks in elementary particle physics and nuclear fusion producing flux densities anywhere from 2 to 10 T. The schematic diagram in Figure 1-2 presents the entire field strength and flux density scale for natural and technical magnetic fields which extends over 16 to 18 orders of magnitude [30].

Blomagnet ic fields

'FG 'FG I

1

I I

1 1

I

I

;

1 I

1 1

I

10-16

Hi gh-current Convent 1 ona 1 and transmission, superconductive cot 1s short power transformers, Devices chokes, I nith I I motors permanent; II I magnets I

Long distance from earth

:stance

!

I

10-14

I

I

,

10-12

,

I

I

,

,

I

10-l~

,

,

I

,

;

10-~

I

,

,

1

!

,

lo2 T

Figure 1-2. Scale of magnetic field strength and flux density.

1.5 Soft and Hard Magnetic Materials for Sensors Almost all magnetic sensors include magnetic materials in the form of active or passive components, and to a large extent, they determine the concept, construction, and ultimately the sensitivity of the sensors. In view of this, a brief survey of magnetic materials and their most important characteristic is presented in Tables 1-5 and 1-6. These materials are classified according to the IEC system for soft and hard magnetic materials [31, 321. For textbooks on materials refer to 133-451. The magnetic materials listed in Tables 1-5 and 1-6 are closely related to the main classes of magnetic sensors shown in Table 1-7 although some special materials have been added.

10

1 Introduction

Table 1-5. Soft magnetic materials [31]. Group

Code

G

Irons Low carbon mild steel Silicon steel, mainly with 3% Si Other steels Nickel-iron alloys (5 groups E l .. . E5 with 30% Ni) Iron-cobalt alloys (3 groups F1 . . F3 with 23% CO) Other alloys as AlSiFe-alloys

H

Soft ferrites as NiZn and MnZn oxides and others

Amorphous metals

I

Amorphous alloys (Fe-based and Co-based alloys)

Powder composite metals

-

based on Fe and iron alloy powders

Crystalline metals

A B C D E F

Oxides

.

. . . 83% . . . 50%

~

Table 1-6. Hard magnetic materials (31, 321, see also [33, 35, 37, 44,451. Group

Code

~

Crystalline metals

R1 I) R2 R3 R6 R5 I) R7')

Amorphous metals

-

Alloys of AlNiCo-type Platinum-cobalt alloys Iron-cobalt-vanadium (Chromium) alloys Chromium-iron-cobalt alloys Rare earth cobalt alloys Rare earth iron alloys Rare earth iron alloys

Oxides

S1

Hard ferrites as Ba- and Sr-ferrites

T

Other hard magnetic materials, e. g., magnetically semihard metals

I)

also as powder composite materials

1.5.1

Soft Magnetic Materials

Shape of the Hysteresis Loop The most typical characteristic of a soft magnetic materials is its hysteresis loop. The shape of the loop can vary greatly and is determined by the type of material and its structure which can be changed by processing and annealing. This is valid for both metals and oxides. The three main types of loop are shown in Figure 1-3 [36]. As the number of magnetic materials currently available is vast, there seems little point in providing extensive tables of materials data. This information is published in standard monographs and company catalogues. Instead, we have chosen to present the ranges of variation of the most important magnetic material terms found in survey diagrams.

1.5 Soft and Hard Magnetic Materials for Sensors

11

Table 1-7. Magnetic materials for sensors (materials defined in Tables 1-5 and 1-6). magnetically hard

magnetically soft Sensor class magnetogalvanic

material

Ic, E D El, I

magnetoelastic

C, El

useful for

material

useful for

I slotted cores yokes I R1, R5, R7 1 magnetic circuits shafts, surface layers for shafts, laminated core packages, pot-cores

fluxgate

El, H, I

strips and rods, toroidal cores

inductive, eddy-current

C, E2, E3

rods, yokes, laminated cores pot cores, rods

parts magnets as rods for switching

Wiegand, pulse-wire alloys magnetoresistive

resistors NiCo, NiFeCo

R

Z

premagnetizing layers

R2, R5, CoCr

F

Figure 1-3. Shapes of hysteresis loop.

Saturation Polarization J, and Coercivity H, Two of the most important material terms are saturation polarization J , , which gives an idea of the amount of material required for a certain component and coercivity H , , which provides the basis for classification of the magnetic material with regard to its hard and soft

12

1 Introduction

magnetic qualities. Figure 1-4 shows a plot of saturation polarization J, versus the coercivity H, where J, is plotted on a linear scale and H, on a logarithmic scale, since the materials currently available range from extremely soft alloys, such as permalloys, to commercial iron and steel, covering approximately four to five orders of magnitude.

soft magnetic alloys carbon steels alloys

\

0.001

0.1

0.01

10 A/cm 100

1

Coercivity

/f,

Figure 14. Survey on soft magnetic materials.

Initial Permeability pi Another important property of soft magnetic materials is the (relative) initial permeability pi, which in a similar manner to coercivity covers several orders of magnitude and is shown in Figure 1-5. The diagram is subdivided in order to correlate with the material groups shown in Table 1-5. metals amorphous crystalline

ui oxides,

ponder composite materials

ferr 1tes I06

co based

-

I o5 E2

E3

Febased

-c

E4

c

c

1 o4

1o3

A, C. F B,O[

1o2

10

3

-

NiZn ferrltes

NiFe powder and Fe ponder hexagonal cores ferrltes

-

Figure 1-5. Range of initial permeability of soft magnetic materials (materials defined in

Table 1-5).

13

1.5 Soft and Hard Magnetic Materials for Sensors

The highest initial permeability, with a value of more than 100000, is seen in crystalline 72 to 83% NiFe alloys and in cobalt-based amorphous alloys. Mid-range permeabilities in the region of 2000 to 15000 occur in NiFe alloys with 36 to 50% Ni and also in ferrites. Low initial permeability values of 300 to 1500 are typical for iron, silicon-iron, cobalt-iron, and some ferrites. Even lower values, in the region of 50 to 300 occur with powder composite materials and ferrites and very low permeabilites (down to values of 5 to 10) are typical for some special powder composite materials and special ferrites.

Specific Electrical Resistivity p, Curie temperature T, The difference between the specific electrical resistivity of metals and that of ferrites is several orders of magnitude as a result of which, for AC-field applications metals require laminated cores whereas ferrites and powder composites can be used directly as compact cores and parts. Figure 1-6 shows the range of the specific electrical resistivity p for metals, ferrites and powder composites. The Curie point is another important parameter for a magnetic material. At the Curie temperature the saturation polarization decreases to zero and ferromagnetic materials become paramagnetic. Figure 1-7 shows the range of Curie temperatures T, of soft magnetic materials. P

metals

-

R cm 10’0

106

TC

ferrites

1

1000 OC!

.:.:$:

.... :::.

102

....

:.... .: ... .... .... .... .... ,.. ...

1o-2

Figure 1-6. Specific electrical resistivity p of soft magnetic materials.

1.5.2

10-6

a

Figure 1-7. Curie points of soft magnetic materials.

O t

Hard Magnetic Materials

In a similar manner to Figure 1-4 for soft magnetic materials Figure 1-8 shows a separate survey of permanent magnetic materials. Since in this case, however, the coercivity H,, and the remanence B, are the most important terms, both of these values have been included in

1 Introduction

14

1.5

1.5 FeNiCo

NdFeB

FeCoCr

T

I'

Qc

1.0

1 .o

E

/

FeCoVCr

I

Y

a

0

.-

0

Y

a

f

c

AlNlCo

0.5

L

PtCO

1

I

1

10

3

100

3

Coercivity

HCI

-

3

0.5

I

1000 A/m

0

Figure 1-8. Survey diagram of permanent magnetic materials.

NdFeB V = 0,32 cm3

Sm Co5 V = 0,86 cmS

Al Ni Co 500

H

5mm

Figure 1-9. Magnets which produce a field of 0.1 T at a distance of 5 mm from the face.

15

1.5 Soft and Hard Magnetic Materials for Sensors

the diagram. The maximum energy density ( B H),,,= depends on B, and H, and also on the shape of the demagnetization curve. The schematic representation in Figure 1-9 illustrates the significance of the energy density with respect to the volume V of a magnet by showing the volume of various magnetic materials that is required to achieve a flux density of 0.1 T, at a distance of 5 mm from the face of the magnet. The differences in magnet volume required are quite marked.

1.5.3

Mechanical Properties of Magnetic Materials

In certain sensor types, the mechanical properties of materials are also important, for example, in magnetoelastic sensors the hardness, yield strength, compressive strength, Young’s modulus etc. must all be considered. Several of the mechanical properties of soft and hard magnetic materials have been compiled in Table 1-8.

’Pable 1-8 Mechanical Properties of magnetic materials I). _____

~

Vickers hardness HV

Material Group

80 800

Yield strength N/mm

... 200 ., , 1000

150 1500

Magnetically soft

100

... 230

ca. 150

compressive strength N/mm2 soft ferrites powder composite metals

malleable alloys like FeCoCr, FeCoV Magnetically hard

800

75 60

-

450

... 950

1

... loo

... 250

150

ca. 50

Yield strength N/mm2 1000

... 1500

245

... 255

compressive strength N/mm2 metals, cast AlNiComagnets RE magnets (SmCo, NdFeB) hard ferrites

I)

... 500 . . . 2000

Young’s modulus kN/mm

in the magnetically optimized state

110 ... 150 150

16

I Introduction

1.5.4 Supplementary Remarks Section 1.5 provides a short review of essential background information on magnetic materials. Each chapter of this volume deals with a particular class of magnetic sensors discussing the specific materials and material properties which are practically important to the mode of operation of each group of sensors, e. g., thin-film materials and semiconductor materials.

1.6 Magnetic Noise The sensitivity limits of measurement and detection are determined by the noise effect of the electronic components. Noise in electronic components and devices is a reflection of fundamental statistical fluctuations and results from a number of different physical effects. These limitations are equally encumbered on magnetic sensors, and for this reason the phenomenon of magnetic noise, i.e., noise in magnetic materials, is considered here.

1.6.1 Thermal and Thermomagnetic Noise Resistance noise is the best known form of this and was first calculated by Nyquist [46]. He discovered that every effective resistance must be considered as a source of noise regardless of the degree of complexity of the circuitry involved. The most practical method for the investigation of noise in a magnetic material is to use an equivalent circuit diagram in which a coil is considered to be a pure inductance and a resistance [47]. Thermomagnetic noise is actually created by directional fluctuations in the magnetization which result from thermal effects that cause the magnetic moments to perform a type of Brownian molecular movement, i. e., small torsional movements around their position of equilibrium. This gives rise to local fluctuating fields which cause wall movements and jumps. These processes give rise to losses in the material due to eddy currents, after-effects etc. Nee1 has shown theoretically that such fields are the result of thermal fluctuations [48]. Macroscopically, the external magnetization or polarization of a magnetic sample is basically constant, and it can also be zero. However, this is not valid on a microscopic scale. There are constant minute temporal fluctuations of the overall magnetization or polarization which produce stray fields on the surface of the sample. Although the sample is not externally magnetized, these fields will create a noise voltage in a winding around the sample, and the noise voltage itself, in turn, generates a noise current. Figure 1-10 shows the equivalent circuit diagram of a noise voltage source feeding resistance R (a) and a coil with pure inductance L and resistance R (b). The noise voltage source can I”, since it consists of statistical fluctuations about the arithmetical be described by (2) mean value zero. Similarly, the noise current is described by (2)”’.

1.6 Magnetic Noise

17

Figure 1-10. Resistance and coil with a noise voltage source U, and noise current I,.

According to Nyquist [46] the spectral distribution of the noise voltage of a resistance R (Figure 1-10a) is given by:

where k ,

=

Boltzmann’s constant = 1.38

.

W . s/K, T = absolute temperature, and

w = 2 x f , circular frequency.

In the frequency interval dw the noise current in Figure 1-10a is given by: ti; d o iidw = R2 *

For a coil (Figure 1-lob) with an impedance Z,

Z 2 = R 2 + w 2 *L 2 .

(1-7)

Thus, it follows that the noise current in dw is

The noise now must not only be considered for the frequency interval d o , but also for the entire frequency range of 0 + 03; it is therefore necessary to integrate. From Equation (1-8) we obtain for the noise current in [O,w]: w

This integral has the solution (see also [49]):

.

2 k,*T wL R (arc tan x), R . R R L

= -

~

(1-10)

18

I Introduction After inserting the boundary values ultimately, we obtain: (1-11)

Now L (at low excitation) can be replaced by (1-12) where A , = iron core cross section, lFe= magnetic path length, N = number of windings, and pi = initial permeability. Introducing the noise field strength Hn

(1-13)

-

we obtain, after elimination of N and L and introduction of the core volume VFe = lFe A , for a constant temperature of the specimen: (1-14)

The same result can also be obtained from an energy calulation, where the magnetic field energy Em in the volume VFe equals the thermal energy Ethper degree of freedom [50]:

Eth =

I 2

- * k, T .

(1-16)

From Equations (1-15) and (1-16) it is possible to obtain Equation (1-14) directly. A summary interpretation of these results is that the higher the permeability of the core, the smaller the fluctuating stray fields arising on the surface of the specimen because the magnetic flux is almost entirely contained in the interior of the material. With larger specimens, it is worth noting that the volume of the specimen close to the surface where the fluctuating stray fields arise is a smaller portion of the whole volume of the specimen. For a core made of Permalloy with pi = 50000, VFe = 1 cm3, and T = 295 K (room temperature), the numerical value for Equation (1-14) is:

H,,=

* 295 A2 1.38 * 1.256 lo-* . 50 lo3 1 cm2

-

=

2.55

- 10-gA/cm.

1.6 Magnetic Noise

Near the surface of the specimen (in air) this corresponds to a noise induction of B,,

19 =

po * H,, = 0.32 fl.

The noise field strength H,, within the core material itself is equivalent to an induction of B = ,uo. pi H,, = 16 nT. If the specimen is cooled to the temperature of liquid helium (4 K), then H,, is reduced to 0.29 10 -9 A/cm, i. e., reduced by one order of magnitude. In this example, this corresponds to the minimum thermomagnetic noise field strength which cannot be further reduced. An alternative method for reducing H,, is to increase the permeability of the specimen or to enlarge the volume. If a thermomagnetic specimen is not kept at a constant temperature but rather subjected to temperature variations, then additional noise effects known as “excess noise” will occur in addition to the normal thermomagnetic noise which will be present [SO]. Mechanical vibrations of the material are a similar source of excess noise. In both cases additional noise is caused by inherent mechanical stress in the material which becomes noticeable with temperature variations and vibrations and in turn give rise to Bloch wall jumps.

-

1.6.2 Barkhausen Noise After the discovery of Barkhausen noise in the year 1917 it became clear that the existence of Weiss domains and spontaneous change of magnetization were the factors responsible for magnetic noise. Since these domains have a finite magnitude, change of magnetization of a ferromagnetic material is an unstable process on a microscopic level, thus a magnetization curve is not ideally smooth but rather shows steps. Figure 1-11 shows the hysteresis loop of an AlFe alloy as an example from [51].

Figure 1-11. Hysteresis loop of a 12% AlFe alloy.

As soon as the magnetization of a ferromagnetic material is no longer characterized by reversible (elastic) wall displacements, which only occurs with very low field strengths, but is in the form of step-like irreversible wall displacements, then Barkhausen noise becomes clearly noticeable. It is most pronounced in the region of coercivity, i. e., in the steep parts of the magnetization curve, and it depends strongly on the nature of the material. It is, however,

20

I Introduction

nearly independent of the velocity of remagnetization as long as quasi static conditions are fulfilled. This behavior can be described by a model where the Bloch walls are located in energy minima which are a result of the structure of the material, and as such they act as pinning centers. An externally applied magnetic field will lift the Bloch wall over the nearest energy barrier where it falls into another (higher potential) energy minimum. This process causes a spontaneous step-like Bloch wall movement which contributes to the Barkhausen noise. In the quantitative treatment of Barkhausen noise its energy spectrum is considered a function of the frequency. Figure 1-12 is an example of the energy spectrum (energy density) for a narrow strip approximately 300 mm . 2 mm 0.1 mm of 3% SiFe, for an extremely slow cycle of the hysteresis loop (roughly 2 hours) after [50]. There is a relatively constant energy density in the range of 0.1 Hz to 10 Hz, then this drops proportionally to f - 1 . 6 .

Figure 1-12. Energy spectrum of Barkhausen noise for 3% SiFe [501.

(q)”2

From Figure 1-12 a noise voltage of V,,= = 80 pV is obtained for the frequency 10 Hz with a band width of 1 Hz and for a coil with 3860 turns, i.e., 20 nV per turn, with a core volume V,, = 0.06 cm3. It should be noted that the purely resistive noise voltage according to Equation (1-5) for a resistor of 100 SZ at 295 K and with a band width of 1 Hz is approximately 1.3 nV. Barkhausen noise is a very complex phenomenon on which extensive literature is available. It is strongly dependent on the material itself, the state of the material, and the shape of the specimen. The reader should refer to review articles, papers and books for further details [50-551.

1.7 Coil Systems to Produce Standard Magnetic Fields Standard magnetic fields - whether homogeneous or gradient fields - are frequently required to allow comparable measurements to be made and to enable calibration of magnetic sensors. Such fields are produced most effectively with pure air-cored coils, since in this case the inhomogeneities caused by nonlinearity in the magnetic curves of iron cores do not arise. Depending on the configuration and the dimensions of the coils, in some limited areas relatively high homogeneity in the range of 10 - 2 to 10 - 4 can be achieved.

1.7 Coil Systems to Produce Standard Magnetic Fields

21

Larger air-cored coils, with diameters of some meters, are used to compensate for the Earth's field in situations where a space free of a magnetic field is required but shielding cannot be used for some reason. Examples of some of the better-known coil systems are described below. Initially, simple air-cored coils will be discussed, and also coil systems for field strengths with magnitudes up to 100 A/cm which can be produced without any special provisions such as water cooling etc. will be considered. Also more recent data is provided on coils for high fields including the superconducting coils.

1.7.1

Coils for Homogeneous DC Fields up to Approximately 100 A/cm

The best-known coil arrangement for homogeneous fields is the Helmholtz coil. It ideally consists of two circular rings with radius r, which are arranged concentrically and parallel to each other with a separation distance r (Figure 1-13a). As a rule, flat multi-layer coils are used (Figure 1-13b) and the magnetic fields of Helmholtz coils are described in detail in the literature [56].

Figure 1-W. Helmholtz coil schematically.

The following equations are derived from the ideal arrangement as shown in Figure 1-13a, for the field components H, and H, at the point P with the coordinates x, z, at a distance r' from the center of the coil:

H,

=

Hz0 * - - -

(1-18)

22

I Introduction

At the center of the axis:

H,,

= 0.715

*

I r

-,

(1-19)

where I is the current in the coil. The situation is slightly more complex for the arrangement shown in Figure 1-13b (multilayer winding with cross section a x b) where in order to avoid impairing the high degree of homogeneity certain relationships with respect to a and b must be maintained [57]. In multi-coil arrangements such as the one shown in Figure 1-14 where the radius decreases towards the outside, the region of high homogeneity can be made larger than that achievable by Helmholtz coils [58].

Figure 1-14. Multi-coil arrangement.

Relatively homogeneous fields can also be created in the coil center of longer cylindrical coils. The following mathematical formulas are applied along the axis for evenly wound cylindrical coils such as that shown in Figure 1-15 [56]: (1-20) Thus, for the coil center (x = 112): (1-21) and for the coil ends (x = 0 and x = 1, respectively) (1-22)

23

1.7 Coil Systems to Produce Standard Magnetic Fields

-

+.-

-

---

-.+L

H-

I

I

Figure 1-15. Cylindrical coil.

The smaller the ratio r/l, the more homogeneous is the field. It follows that for r/l 5 1/80 the field is constant within +0.1%0 over 2/3 of the length of the coil. Fields up to approximately 0.5 T can also be produced with cylindrical coils in which the winding density increases towards the ends (Figure 1-16), once again, when compared to the fields generated with Helmholtz coils, this kind of coil produces both higher field strengths and improved homogeneity [60].

I

Figure 1-16. Production of homogeneous fields in a cylindrical coil where the winding density increases towards the ends; (a) linear, (b) quadratically increasing winding density.

I

.. U

Refer to references [61] and [62] for more information on circular coils with very high homogeneous magnetic fields. Finally, in addition to the simple cylindrical coil it is worth mentioning an arrangement which involves two additional moveable coils (Figure 1-17). For further details and more information on the mathematical formulas involved see [58, 591.

Figure 1-17. Production of homogeneous coil fields in a cylindrical coil with adjustable additional coils at each end.

1.7.2 Coils for Higher Fields (Electromagnets) Magnetic fields of up to about 3 T are produced in the air gap of electromagnets since, in this case, the magnetic field strength is concentrated primarily along the relatively short length of the air gap, whilst the iron return circuit of the magnet system only requires a small part

24

I Introduction

of the field strength. By mounting pole shoes made of CoFe alloys and using computer-aided calculations to select the shape of the pole shoe, it is possible to generate relatively high homogeneous fields whilst still only creating low stray fields. Before the advent of superconducting coils, it was necessary to use specially constructed Bitter coils in order to generate stationary fields with flux densities of up to 15 T [61-641. Under pulse operation, these are capable of producing flux densities of the order of 50 to 100 T over brief periods (milliseconds) [65].

1.7.3 Superconducting Coils Magnetic fields in the range of 10 to 20 T can only be continuously produced using superconducting coils which actually, in principle, are air-cored coils. Currently the only suitable conducting materials for such coils are the hard Q p e 111 superconductors which are capable of carrying the high critical field strengths that are required. The most commonly used materials are NbTi alloys (up to 10 T) and Nb,Sn alloys (up to approximately 20 T). These materials must be cooled to approximately 4 K to be effective [61, 621. Currently, new superconducting materials of metallic oxides capable of achieving superconductivity above 90 K are under investigation. The superconducting wires are either embedded in a metallic matrix, i. e., of Cu or surrounded with Cu to ensure that in the event of failure the high currents can still be carried even if only for a brief time. In order to improve the dynamic behavior of the coils, using a special twisted cable conductor construction the conductors are made up into filaments [66, 671. Figure 1-18 shows a schematic design for a superconducting coil [68].

Superconduct ing coi 1 Liauid Helium

Figure 1-18. Superconducting magnetic coil in a cryostat (for NMR spectrometer, outside diameter ca. 1 m).

1.8 Shielding Magnetic Fields 1.8.1 General In order to ensure that accurate measurement and calibration can be achieved it is often necessary to exclude magnetic interference fields or at least to eliminate them as far as possible. This can be achieved in several different ways:

1.8 Shielding Magnetic Fields

25

- by maintaining sufficient distance between the source of interference and the object of interest,

- by ensuring suitable orientation of critical objects with respect to the direction of the interference field, e. g., orientation perpendicular to the Earth’s field,

- by using different types of compensation, i.e. coil systems or permanent magnet arrangements, - by using gradiometer coils as sensing coils, - by use of magnetic and electromagnetic shielding.

The methods given above are all limited in some way or cannot be always fully realized. For instance, it is easier to compensate a constant static magnetic field than to compensate fluctuating AC fields of different field strengths, frequencies and directions. Similarly, compensation of spatially homogeneous fields is much easier in small volumes than in large volumes, and for multi-sensor configurations. The most effective method is electromagnetic shielding, where either the object or the source of interference is shielded. The basic principles and possible applications of shielding are described below [69-721.

1.8.2

Basic Principles of Magnetic Shielding

1.8.2.1 DC Fields

The use of soft magnetic materials for shielding of static magnetic fields is based on the fact that these materials possess an extremely high magnetic permeability: their magnetic permeability is in fact higher by a factor of between lo3 and lo5 than that for either air or a vacuum. Shielding made of soft magnetic materials provides very effective shunts for the magnetic interference field which will preferentially concentrate in the walls of the shielding leaving the interior space effectively free of magnetic field (Figure 1-19).

Figure 1-D. Shielding static magnetic fields.

26

I Introduction The shielding factor Sin a static field is defined as the ratio of the external interference field

Heto the residual field Hiin the interior of the shielding. That is: (1-23) The shielding attenuation a, is often used instead of S:

.

a, = 20 log S

(1-24)

,

These shielding factors can be fairly accurately calculated for simple geometric shapes (closed housing) [69-71, 731. Several examples illustrating the use of high permeability material and small wall thicknesses are stated below:

- Hollow sphere: 4 Pr*d s = -3

0

+,

p r : relative permeability of shielding material, usually denoted as pi or p4

d : wall thickness

(1-25)

D: diameter

- Cube:

a : edge length of cube (1-26)

- long cylinder

N : demagnetization factor dependent on

perpendicular to axis:

s,

Pr*d =-

+

1

(1-27)

D

parallel to axis: =

L/D

L : length of cylinder

- 1) + 1 + D/2 . L

4N(S 1

(1-28)

- Double cylinder

S,, Sz shielding factors S, of cylinder 1 and

S = S, * Sz * [1 - (D2/D1)2] +

+s, +s,+

1

2 according to Equation (1-27)and D, > D, (1-29)

The above formulas apply to entirely closed shieldings or infinitely long cylinders. The shielding factors of short cylinders and housings with openings are smaller and, moreover, the calculations are more complex [73-751.

1.8.2.2 AC Fields When AC fields are being shielded, field displacement in the shielding wall plays a major role due to the eddy currents which are induced in the material as a result - the so-called skin effect. The penetration depth 6 is significant and is calculated as follows [69-731:

1.8 Shielding Magnetic Fields

p = specific electrical resistivity ,uo= magnetic constant

f

(1-30)

= frequency.

For a 75% nickel iron alloy with p = 0.55 serted in Hz as

6=

27

a mm2/m 6 is obtained in mm when f is in-

f-. 139400 Pi

*f

Example: when pi = 50000 and f = 50 Hz follows 6 = 0.24 mm. For a closed magnetic shield, e. g. a sphere or a long cylinder the shielding factor s, in an AC field is given by [69, 701: (1-31)

With open shielding, the formulas are again more complex [74+751, but for shielding with small homogeneously distributed openings, e. g., braided shielding, cable wrapping etc., the equation is: (1-32)

In this case the permeability pr from Equation (1-26) is replaced by the modulus of the complex permeability lp 1. The important difference between Equations (1-31) and (1-32) is the fact that in the closed shielding case the shielding factor increases exponentially with the frequency, whereas in shielding with openings it decreases at a rate of l / f l [69, 711. Thus, it can be concluded that static magnetic fields can only be shielded with soft magnetic materials. These materials are also extremely effective at shielding in AC fields, especially in the lower frequency range. Shielding with soft magnetic materials is limited to fields or flux densities up to 0.5 T due to the onset of saturation effects above this value. Pure conducting shielding (copper and aluminium) can be used for higher frequencies, and indeed, in many cases a combination of magnetic and conducting shielding is recommended.

1.8.3 Materials for Magnetic Shieldings and Design The materials most commonly used for magnetic shielding are crystalline nickel-iron alloys, followed closely by silicon-iron and iron. The full shielding effect is only obtained from these materials in their final annealed state after which the shielding must not be mechanically deformed. The group of suitable materials has recently been extended by the advent of the amorphous alloys, in particular the low magnetostriction Co-rich alloys which can be exposed to mechanical stress without impairing their shielding effect. A survey of suitable materials is given in Table 1-9.

28

I Introduction

Table 1-9. Materials for magnetic shielding [73]. Group

Alloy

crystalline

77% 50% 36% 3% Iron

amorphous

NiFe NiFe NiFe SiFe

Co-based

Code

BUi

J. (TI

El E3 A

30000 to 50000 6000 3000 1000 300

0.8 1.55 1.3 2.0 2.1

I

25 000

0.55

E4 c2

To complete the picture it should be pointed out that superconductors can also be used to shield against magnetic fields. Superconductors can force magnetic fields out of the interior of the material (Meissner-Ochsenfeld effect), and it, therefore, follows that the interior of a superconducting hollow sphere is absolutely free of magnetic field. Superconductors are suitable for use in high field strengths, such as flux densities up to 10 T. Magnetic shieldings are available in many diverse designs, e. g. as round or square shaped cans, cylindrical and conical housings as well as in flexible metal hose and foil forms. A further variant is the use of multi-layer shielding. Table 1-10 gives several examples of the shielding factors of simple housings.

Table 1-10. Shielding factors of different housings [73];(material 77% NiFe with pi = 30000; 6 = 0.30 mm at 50 Hz;6 = 0.11 mm at 400 Hz). Design

Diameter D Wall thickness d

Sphere

D = 100mm d = d =

Double cylinder

400

1000

> 105

300

900

> 105

lmm

D,= 150 mm D, = 100 mm d =

400 Hz

lmm

D = 100mm

Single cylinder

Shielding factor 50 Hz

static

= 34000

lmm

A design which arouses particular interest in biomedical and industrial circles is the socalled “walk-in” magnetically shielded room which has interior measurements of approx. 2.5 m 2.5m 2.5 m. Depending on the required degree of suppression or shielding factor, either single or multi-layer shields can be used [76-791.The latter are used in diagnostics to facilitate interference free measurement of the magnetic fields produced by the human body using SQUIDS which are a highly sensitive family of magnetic field sensors (see Chapter 10). As an example Figure 1-20 shows the measured shielding factors as a function of frequency for five different designs of shielded room.

-

-

29

1.9 References

120

106

dB lo5

100

104

8o

S

t

as

lo3

60

100

40

10

20

1

0

0.01

1

0.1

10

1000

100

No.

Number of shields (Shells) Total Magnetic Conducting shields shields

1 2 3 4 5

2 2 3 6 7

2 1 2 3 6

1 1 2 x 3 1

Hz

References [781 1731 [731 [791 [771

Figure 1-20. Shielding factor S and shielding attenuation a, of different shielded rooms; interior measurements approx. 2.5 m x 2.5 m x 2.5 m.

1.9 References [l] Meyer, H.W., A History of Electricity and Magnetism; CambridgdMass.: The MIT Press, 1971. [2] Enz, U.; “From loadstone to ferrite: A survey of the history of magnetism!’ In: Wohlfarth, E. P. (ed.), Ferromagnetic Materials, Vol. 3; Amsterdam, New York, Oxford: North Holland Publishing Co., 1982, pp. 3-36. [3] Krafft, F., (Ed.), GroJe Nuturwissenschaftler. 2nd Edition; Dttsseldorf: VDI Verlag, 1986. [4] Schubert, J., Dictionary of Effects and Phenomena in Physics; Weinheim: VCH Verlagsgesellschaft, 1987.

30

1 Introduction

[5] Rohrbach, C. Handbuch fur elektrisches Messen mechanischer GriJen; Dtisseldorf VDI-Verlag, 1967. [6] Profos, P. (Ed.), Handbuch der industriellen MeJtechnik. 4th Edition; Essen: Vulkan-Verlag, 1987. [7] Bently, J. P., Principles of Measurement Systems; London, New York: Longman, 1983. [8] Heywang, W., Sensorik (Halbleiter-Elektronik 17); Berlin, Heidelberg, New York, Tokyo: Springer Verlag, 1981. [9] Seippel, R. G., Transducers, Sensors and Detectors; Reston/Virginia: Reston Publishing Co. Inc., 1983. [lo] Schanz, G. W., Sensoren - Fuhler der MeJtechnik: Heidelberg: Huthig-Verlag, 1986. [ll] Hederer, A. et al., Dynamisches Messen (Kontakt + Studium, Band 32); Grafenau: Lexika-Verlag, 1979. [12] Bonfig, K. W., Bartz, W. J., Wolff, J. (Ed.), Das Handbuch fur Zngenieure. Sensoren, MeJauJ nehmer. 2nd Edition; Ehningen: expert verlag, 1988. [13] Usher, M. J., Sensors and Transducers; London: Macmillan Publishers Ltd. 1985. [14] Fiz-technik, In,formationsdienst Sensoren; Berlin: ZDENDE-Verlag, 1988. [15] Recommendations in the Field of Quantities and Units Used in Electricity; IEC Publication 164, 1964. [16] German, S., “Das internationale Einheitensystem”. In: Kohlrausch, F., Praktische Physik, Vol. 1, 23rd Edition; Stuttgart: B.G. Teubner, 1985, pp. 6-13. [17] Chen, C. W.: “Magnetism and Metallurgy of Soft Magnetic Materials”. In: Wohlfarth, E. P.: Selected topics in Solid State Physics, Vol. V, Appendix I; Amsterdam: North-Holland Publishing Co., 1977. [l8] “Units for magnetic quantities”, Magnets in your Future 1/6 (1986) 15. [19] Mager, A., “Diimpfungsstilbe fur magnetfeldstabilisierte Satelliten”, Z. Flugwiss. 15 (1967) 91 -98. [20] Fanselau, G. (Ed.), Geomagnetische Instrumente und MeJmethoden; Berlin: VEB Deutscher Verlag der Wissenschaften, 1960. [21] Parker, E. N., Kosmische Magnetfeder, Spektrum der Wissenschaft 10 (1983) 82-94. [22] Acuna, M. H., “Fluxgate magnetometers for outer planets exploration”, ZEEE Trans. Magn. MAG10 (1974) 519-523. [23] Ern& S. N., Hahlbohm, H. D., Lllbbig, H. (Ed.), Biomagnetism; Berlin, New York: de Gruyter, 1981. [24] Williamson, S. J., Kaufman, L., “Biomagnetism”, J Magn. Magn. Mat. 22 (1981) 129-201. [25] Schuler, K., Dauermagnete. Werkstoffe und Anwendungen; Heidelberg: Springer, 1970. [26] McCaig, M., Permanent Magnets in Theory and Practice; Plymouth: Pentech Press, 1977. [27] Parkinson, D. H., Mulhall, B. E., The Generation of High Magnetic Fields; London: Plenum Press, 1967. [28] Zijlstra, H.: Experimental Methods in Magnetism. Part 1: Generation and computation of magnetic fields; Amsterdam: North-Holland Publishing Co., 1967. [29] Montgomery, D. B., Solenoid Magnet Design, New York: Wiley-Interscience, 1969. [30] Boll, R., “Magnetische Schirmung, eine wichtige MaBnahme zum Schutz gegen StBrungen und Umweltbelastung durch elektromagnetische Felded’ In: Jahrbuch fur Ingenieure; Grafenau: expert verlag, 1981, pp. 436-447. [31] “Magnetic materials”. Part 1: “Classification”, ZEC Publication 404-1(1979). [32] “Magnetic materials”. Part 8: “Specifications for individual materials!’ Section 1: “Standard specifications for magnetically hard materials”, ZEC Publication 404-8-1(1986). [33] Bozorth, R. M., Ferromagnetism; Toronto, New York, Londong: Van Nostrand Co. Inc., 1955. [34] Heck, C., Magnetic Materials and their Applications; New York: Crane, Russack & Co. Inc., 1974. [35] Kneller, E., Ferromagnetismus. Berlin, Gdttingen, Heidelberg: Springer Verlag, 1962. [36] Boll, R. (Ed.), Soft Magnetic Materials; Berlin, Miinchen: Siemens A G London: Heyden, 1979. [37] Wohlfarth, E. P. (Ed.), Ferromagnetic Materials. A Handbook on the Properties of Magnetically Ordered Substances. Vol. 2; Amsterdam: North-Holland Publishing Co., 1980.

1.9 References

31

[38] VDEh (Ed.), Werkstoffkunde Stahl. Vol. 2: Anwendung; Berlin, Heidelberg: Springer Verlag, 1985, Sec. D 20. [391 Chen, H. S., “Glassy metals”, Rep. Prog. Phys. 43 (1980) 353-432. 1401 Luborsky, F. E. (Ed.), Amorphous Metallic Alloys; London: Butterworth, 1983. [411 Smit, J., Wijn, H. P. J., “Ferrites”, Philips Tech. Rev. (1962). 1421 Snelling, E. C., Soft Ferrites; London: Iliffe Books Ltd. 1962. [43] Kampczyk, W., Rdss, E., Ferritkerne. Berlin, MUnchen: Siemens AG, 1978. [44] Schlller, K., Brinkmann, K., Dauermagnete. Werkstoffe und Anwendungen; Heidelberg: Springer Verlag, 1970. [45] Tebble, R. S., Craig, D. J., Magnetic Materials; London, New York, Sydney, Toronto: Wiley-Interscience, 1969. [46] Nyquist, H., Thermal agitation of electric charge in conductors, Phys. Rev. 32 (1928) 110-113. [47] Nonnenmacher, W., Schweizer, W., “Die Bestimmung der Permeabilittit ferromagnetischer Stoffe aus der thermischen Rauschspannung von Spulen”, Z. Angew. Phys. M (1957) 239-243. [48] Ntel, L., Theorie du trainage magnktique des substances massives dans la domaine de Rayleigh, J. Phys. Radium ll/8 (1950) 49-61. [49] Kleen, W., Pdschl, K., “Rauschen”, in: Meinke, M., Gundlach, F. W. (Eds.), Taschenbuch der Hochfrequenztechnik, 3. Aufl.; Berlin: Springer Verlag, 1968, pp. 1242- 1244. [50] Bittel, H., Storm, L., Rauschen; Berlin, Heidelberg, New York: Springer Verlag 1971. [51] Lambeck, M., Barkhausen-Effekt und Nachwirkung in Ferromagnetika; Berlin: de Gruyter, 1971. [52] Hdhler, G. (Ed.), Der magnetische Barkhausen-Effekt (Springer Tracts in Modern Physics, Vol. 40); Berlin: Springer Verlag, 1966. [53] McClure, J. C., Schrdder, K., “The magnetic Barkhauseneffect”, CRC Crit. Rev. Solid State Mater. Sci. Jan. 1976, 45-83. [54] Heiden, C., Storm, L., GrundsBtzliches zur Bestimmung der GrbRenverteilung der Barkhausenvolumina in Ferromagnetika. Z. Angew. Phys. 21 (1966) 349-354. [55] Bertotti, G., Fiorillo, F., Sassi, M. P., Barkhausen noise and domain structure dynamics in SiFe at different points of the magnetization curves, J. Magn. Magn. Mater. 23 (1981) 136-148. [56] Braun, E., “Erzeugung und Messung magnetischer Felder”, in: Kohlrausch, F., Praktische Physik, Vol. 2, 23rd Edition, Stuttgart: B. G. Teubner, 1985, pp. 399-401. [57] Berger, W., Butterweck, H. J., “Die Berechnung von Spulen zur Erzeugung homogener Magnetfelder und konstanter Feldgradienten”, Arch. Elektrotechnik XLII (1956) 216-222. [58] Neumann, H., “Herstellung raumlich und zeitlich konstanter Magnetfelder fur MeRzwecke”, Part 11, ATM Z 60-2 (1940). [59] Fanselau, G., “Die Erzeugung weitgehend homogener Magnetfelder durch Kreisstrdme”, Z. Phys. 54 (1929) 260-269. [60] Heddle, T. A., “A method of designing compensated solenoids giving approximately uniform field”, BZ Appl. PhyS. 3 (1952) 95-97. [61] Parkinson, D. H., Mulhall, B. E., The Generation of High Magnetic Fields; London: Plenum Press, 1967. [62] Zijlstra, H., Experimental Methods in Magnetism, Part 1: Generation and Computation of Magnetic Fields; Amsterdam: North-Holland Publ. Co., 1967. [63] Montgomery, D. B., Solenoid Magnet Design; New York: Wiley-Interscience, 1969. [64] Braun, E., “Elektromagnete”, in: Kohlrausch, F., Praktische Physik, Vol. 2, 23rd Edition, Stuttgart: B. G. Teubner, 1985, pp. 405-407. [65] Knoepfel, H., Pulsed High Magnetic Fields; Amsterdam, London: North-Holland Publ. Co., 1970. [66] Hillmann, H., “High Field Superconductors”. Lecture Notes in Physics 177, in: Landwehr, G. (Ed.); Berlin, Heidelberg: Springer Verlag, 1983, pp. 517-530. [67] Krauth, H., “Multifilamentary NbTi and Nb,Sn superconductors for pulse magnets and electrical machines”, Cigre symposium 05-87, Vienne 1987, Sec. 1, 100-08, 2-6.

32

1 Introduction

[68] VACUUMSCHMELZE GMBH, “High field superconductors”, IB SLOl; Hanau, 1986. [69] Kaden, H., Wirbelstr6me und Schirmung in der Nachrichtentechnik, 2nd Edition; Berlin, Heidelberg: Springer Verlag; Miinchen: J. F, Bergmann, 1959. [70] Mager, A., “Magnetic shields”, IEEE Trans. Magn. MAG4 (1970) 67-70. [71] Boll, R., Borek, L., “Elektromagnetische Schirmung”, NTG-Fachber. 76 (1980) 187-204. [72] Mager, A., Magnetostatische Abschirmfaktoren von Zylindern mit rechteckigen Querschnittsformen, Physica SOB (1975) 451-463. [73] VACUUMSCHMELZE GMBH, Magnetic Shielding, FS-M9; Hanau, 1989. [74] Kaden, H., “Die Ausbreitung elektrischer und magnetischer Wechselfelder in offenen Abschirmrohren”, Frequenz 24 (1970) 27-32. [75] Mager, A., “Magnetic shielding efficiencies of cylindrical shells with axis parallel to the field”, J. Appl. Phys. 39 (1968) 1914. [76] Mager, A.: “The Berlin magnetically shielded room (BMSR) Section A. Design and construction”, in: Erne, S. N., Hahlbohm, H. D., Liibbig, H. (Eds.), Biomagnetism; Berlin, New York: de Gruyter, 1981, pp. 51-78. [77] Cohen, D. et al., “Magnetocardiogram taken inside a shielded room with a superconducting pointcontact magnetometer”, Appl. Phys. Lett. 16/7 (1970) 278-280. [78] Cohen, D., “Large volume conventional magnetic shields”, Rev. Phys. Appl. 5, (1970) 53-58. [79] KelhB, V. A., “Construction and performance of the Otaniemi magnetically shielded room”, in: Erne, S. N., Hahlbohm, H. D., Liibbig, H. (Eds.), Biomagnetism; Berlin, New York: de Gruyter, 1981, pp. 33-50.

2

Physical Principles KENNETH J. OVERSHOTT. Brighton Polytechnic, Brighton. UK

Contents 2.1 2.2 2.3 2.4 2.5 2.6 2.1

........................... Galvanomagnetic Effects . . . . . . . . . . . . . . . . . . . . . . Magnetostriction and Magnetoelastic Effects . . . . . . . . . . . . Electromagnetic Systems . . . . . . . . . . . . . . . . . . . . . . Movement of Domain Boundaries . . . . . . . . . . . . . . . . . Josephson Effect . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction

34

35 36 38

39 42 42

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

34

2 Physical Principles

2.1 Introduction The basic principle of all sensors is transduction - that is, the transmission of energy from one system to another. In general, an electric signal is produced by the change of a physical property induced by the applied change of a second parameter (see Figure 2-1). In the case of magnetic sensors either the property or the parameter would have a magnetic context. For example, in a magnetoresistive device the induced change of a physical property, resistance, caused by the applied change of a magnetic field is used to produce an electrical signal (see Figure 2-2). The linearity, magnitude, sensitivity, repeatability, etc, of the relationship between the electrical output, E, and the physical property defines the quality of the sensor

E

=

f(R, H ) .

Ease of measurement and processing makes an electrical signal the preferred output. APPLIED second parameter

1

1-

kb

INPUT

OUTPUT

physical property

in general: electrical signal

Figure 2-1. Schematic diagram of sensor.

field

R

resistance

Figure 2-2. Schematic representation of a magnetoresistive sensor.

The physical effects useful for magnetic sensors have been developed over 120 years with the Joule effect being discovered in 1842, the latest discovery being the Josephson effect in 1962. Over these 120 years many other physical effects suitable for magnetic sensors have been investigated, as shown in Figure 2-3. These physical effects can be classified into four categories, although the position of magnetostrictive effects in c. below and not b. is debatable: a. electromagnetic systems ; b. effects of magnetic fields on material properties, eg, Hall, galvanic, resistance ; c. interrelationship of stress and magnetic properties, eg, magnetostriction and magnetoelastic ; d. superconductivity, eg, Josephson effect.

2.2 Galvanomagnetic Effects

Figure 2-3. Physical effects useful for magnetic sensors and year of discovery.

35

W 1865

It would be logical to describe the physical effects used in magnetic sensors under these four categories. However, the description of the physical principles used in magnetic sensors will be presented in the same order as the later chapters to facilitate cross-referencing. In addition, the description of these physical effects presented here is brief in order not to duplicate the information included in later chapters.

2.2 Galvanomagnetic Effects One group of magnetic sensors is based upon the galvanomagnetic effects that occur in semiconductors. These galvanomagnetic effects are caused by the interrelationship that occurs between the electrical currents flowing in a material which is being subjected to a magnetic field. The two most important galvanomagnetic effects are the magnetoresistive (or Thomson) effect [l] and the Hall effect [2]. The effects can only be exploited in semiconductor materials in which a high carrier mobility and a low free carrier concentration is achieveable. However, sensors based upon the magnetoresistive effect in thin ferromagnetic films are also of commercial importance. Under the influence of a magnetic field, an increase in the resistivity of a material occurs and this phenomenon is called the magnetoresistive effect. The exploitation of this effect in sensors has only been worthwhile since the development of III/V semiconductors. A free charge carrier in a semiconductor is deflected by the Lorentz force which acts perpendicular to the direction of the motion and the magnetic flux density. The charge carrier even-

36

2 Physical Principles

tually collides with the crystal lattice and the rotation of the current direction occurs which results in an increase in the length of the path of the current flow. This increase in the path length produces an increase in the resistivity of the material, magnetoresistance, which is the physical basis of a family of magnetic sensors. If a very long strip of strongly extrinsic and homogeneous semiconductor material carries a current, I,, in the x direction and when the strip plane is in the xy plane then an applied field in the z direction, manifested as a flux density, B,, produces a transverse electric field in the y direction, the Hall field (see Figure 2-4).

Figure 2-4. Schematic diagram of Hall effect.

The Hall voltage, U,, is approximately proportional to the product of the flux density perpendicular to the strip plane, B,, and the current I,.

The theoretical basis of the Hall effect - that is, the effect of the Lorentz force on the charge-carrier transport phenomenon occuring in condensed matter - is well described in Chapter 3.

2.3 Magnetostriction and Magnetoelastic Effects In 1842 Joule observed that when a magnetic rod was subjected to a longitudinal magnetic field then the length of the rod changed. This longitudinal magnetostrictive (change of dimensions due to effect of the magnetic field) phenomenon is called the Joule effect [3]. If there is an increase in length in the longitudinal direction then a decrease in dimensions takes place in the transverse direction and, in general, a change in the volume of the material occurs. Four years after the initial discovery of magnetostriction it was found the Young’s modulus, E, of a material is changed by the application of the magnetic field to a material. Young’s modulus is the ratio of stress to applied strain and hence this A E effect is a ramification of the property that a change of stress in a material occurs when it is magnetized and is dependent on the magnetostrictive properties of a ferromagnetic material.

2.4 Magnetostriction and Magnetoelastic Effects

37

The magnetostrictive change in dimensions is caused by rotation of the magnetization or displacement of 90" walls. When a mechanical stress is applied to a demagnetized ferromagnetic, two kinds of strain are produced : (i) mechanical elastic strain, I , , which occurs in any material, and (ii) magnetoelastic strain, A,, due to the reorientation of domains by the applied stress, n. The Young's modulus for this demagnetized state is given by

For a saturated sample the magnetoelastic strain is zero because no domain reorientation can occur. therefore

Hence it follows:

The magnetoelastic strain, I , , depends on the applied stress and the magnitude of the anisotropy present. The latter half of the nineteenth century saw the discovery of other magnetoelectric effects which are often in contemporary literature described as obscure magnetostrictive effects. The best known of these effects are named after their discoverers - that is, the Matteucci effect, the Wiedemann effect and the Villari effect. Villari [4] found that an elastic elongation of a ferromagnetic material produces a permeability change in the direction of the applied tension. Materials which have a positive magnetostriction increase their permeability under tensile stress and conversely materials with negative magnetostriction reduce their permeability under the influence of a tensile stress. The Matteucci effect [ 5 ] and the Wiedemann effect [6] are closely related. The Matteucci effect was discovered in 1847 when Matteucci stated that the torsion of a ferromagnetic rod in a longitudinal field changes the magnetization of the rod. Wiedemann stated this effect more precisely by saying that if a ferromagnetic rod is subjected to a longitudinal magnetic field (produced by a solenoid) and a current is passed through the rod (producing a circular field) then the rod will twist (see Figure 2-5). There are obviously two inverse Wiedemann effects such that : (a) when the circularly magnetized ferromagnetic rod is twisted a longitudinal magnetic field is produced, (b) when a longitudinally magnetized ferromatic rod is twisted a circular magnetic field is produced. This latter inverse Wiedemann effect can be seen to be essentially similar to the Matteucci effect. It has been shown [7] that the Wiedemann effect is a consequence of the tensorial relationships of magnetostriction in a material. The theoretically-derived formula for the angle of a twist, 8, of a rod has been related to the longitudinal and transverse magnetostriction con-

38

2 PhysicaWrinciples solenoid producing longitudinal magnetic field 00000000000000000000000000000000

n

current producing circular magnetic field OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO~

twist

Figure 2-5. The Wiedemann effect.

stants, I , and I , , of the materials and the magnitude of the longitudinal and circular magnetic fields, H, and Hci,. I 9= - 2( A , I r

- A,)

4 Hcir H : + Hf,, '

where 1 is length of rod and r is radius of rod. This theoretical derivation has been experimentally verified [8] and further work on the effect has recently been performed [9].

2.4 Electromagnetic Systems The most simple type of magnetic sensor is based upon electromagnetic principles. Faraday's Law states that a voltage is induced in a closed electric circuit when the rate of flux linkage, N@,is changed with time:

U = - d 0") dt

The most important aspect of Faraday's Law of electromagnetic induction is that it is the rate of flux linkage in a sensing coil which produces the induced voltage. Hence, the flux linkage can be changed with respect to time by changing the flux linking with a stationary coil or by changing the flux linking with a coil by moving the coil. The former method of changing the flux linking with a stationary coil can be achieved in two principal ways: (a) the generation of a flux which changes periodically with time (b) the magnetic flux varying within a magnetic circuit due to variation of an air gap or changes in the direction of magnetization. The most common use of system (a) above is the generation of a sinusoidal flux by exciting a primary coil with a sinusoidal current and using a search (secondary) coil to measure the flux density in a specific area. The electromagnetic induction equation can be then used to calculate the peak flux density, B, in Tesla, for the specific area of search coil, A in m2, when the flux is changing at a frequency off in Hz . The rms voltage U (in Volt) induced in a search coil of N turns is given by

U

= 4.44

-

B, A N * f .

2.5 Movement of Domain Boundaries

39

One has to make sure carefully that the impedance of the search coil does not load the measuring system. However, the search coil, being the most simple magnetic sensor, has many advantages and, in fact, whole careers in magnetism have been founded upon its extensive use [lo]. An alternative method of changing the flux linkage in the coil is to change the magnetic domain structure in the region of the magnetic material close to the search coil and is described in Section 2.5. Variable reluctance sensors also use a change of the configuration of the magnetic flux in a magnetic circuit to induce voltage in a coil. A permanent magnet is used in variable reluctance sensors to produce a magnetic flux in a magnetic circuit. A change in the length of an air gap in the circuit or some other method of producing a change in the reluctance of the magnetic circuit causes a change in the magnetic flux in the circuit. This change of flux generates a voltage in a search coil by electromagnetic induction. The second family of electromagnetic sensors is based upon moving a coil so that the flux linkage of the winding changes with time. This necessary change of flux linkage can be made to occur by

- moving the coil in a controlled method or by taking the coil into and completely out of a DC field - varying the electromagnetic coupling between coils - changing the inductance of coils by the relative motion of coils or by moving a soft

magnetic core within the coils. A secondary method of utilizing electromagnetics in a sensor is the use of eddy currents. If the conducting material is subjected to an alternating magnetic field then emf’s are induced in the material which cause eddy currents to circulate in the material because of resistive property of the material. These eddy currents produce a secondary magnetic field in the material. The interaction of this secondary magnetic field with the original alternating magnetic field can be used as the basic principle of magnetic sensors. These devices, which can also be based upon the detection of the eddy currents, are generically called eddy current sensors, see Chapter 7, Section 7.5.

2.5 Movement of Domain Boundaries In 1931 Sixtus and Tonks [ll] performed a classic experiment which showed that hard-drawn nickel-iron wires, having between 10% and 20% nickel, positive magnetostriction and relatively low magnetic anisotropy, when magnetized and under tension would form a single domain with the saturation magnetization along the axis of the wire. Reversal of the magnetization field produced no effect on the single domain until a critical value H,, was exceeded. For greater fields it was possible to start a reversal of the domain magnetization at one end of the wire by means of a local magnetizing coil. Figure 2-6a shows the experimental scheme, D is the starting coil while coils C and F were used to determine the velocity with which the domain boundary passed along the wire, and also to give some information about the shape of the advancing domain boundary.

40

2 Physical Principles

wire in tension

H

-

main coil

V

a

IB

b

C

Sixtus-Tonks experiment.

Figure 2-6b shows an hysteresis loop for the unstressed multi-domain condition and a loop when the wire is stressed. The high rate of change of flux density with field, dB/dH, corresponds to the reversal of magnetization produced by the movement of the domain wall from one end of the wire to the other. The travelling wall was deduced to have a trumpet shape, as shown in Figure 2-6c [12]. The discontinuous magnetization reversal of a small magnetic specimen, which in the ideal case comprises a single magnetic domain, can be used for sensing purposes if the resulting induced voltage pulse in a coil associated with the reversal is utilized. This magnetic switching effect is due to large reproducible Barkhausen jumps in ferromagnetic wires under tensile stress. The most common practical use of the Sixtus-Tonks phenomenon was proposed by Wiegand [13] who twisted wires made of Vicalloy (Co 52, V 10, Fe 38). These Wiegand wires, which have a soft magnetic inner core and a harder magnetic outer zone, supply high reproducible pulse-voltages. In the initial status, it is ensured that the inner core and outer zone are magnetized to saturation in mutually opposite directions (Figure 2-7a). The hard magnetic outer zone keeps the magnetization of the inner core under a magnetic strain. If an

41

2.5 Movement of Domain Boundaries

additional field is generated - for example, using a permanent magnet - in the direction of the magnetization of the outer zone, then after a particular threshold value has been exceeded (threshold field strength > coercive field strength H , ) a domain wall propagation is triggered in the inner core which induces a voltage of several volts if a 1000 turn coil is used. At the end of this procedure, the inner core and outer zone are magnetized in the same direction (Figure 2-7b). For the next reversal procedure the wire is reset to its original status (Figure 2-7a) by a magnetic field of the correct magnitude. In the ideal case the amplitude and shape of the voltage pulse are only dependent on the velocity of the moving domain wall propagation (Sixtus-Tonks wave), but not on the rate of change, dH/dt, of the driving field. For an induced voltage, generally the relation holds

where A B is the flux density change of a large Barkhausen jump, v is the velocity of the domain wall propagation and n is the number of domain walls. Figure 2-7c explain the magnetization reversal mechanism using the hysteresis loop and shows a typical voltage pulse. The use of these physical principles of domain wall propagation is used in Wiegand sensors and pulse-wire sensors as described in Chapter 8.

I

I

a

b

B

/-

I

large I Barkhausen

I

t IAB

*

C

Figure 2-7. The Wiegand effect.

H

42

2.6

2 Physical Principles

Josephson Effect

A whole new family of magnetic sensors has been developed over the last 25 years. These sensors are called SQUIDs (Superconducting Quantum Interference Devices) and are based upon a superconducting phenomenon named the Josephson Effect. SQUIDs are the most sensitive magnetic sensors and have achieved a magnetic field resolution in the order of several femto-Tesla (fT). The operation of these sensors is based upon the properties of the superconducting state - namely, flux quantization and the Josephson effect. The superconducting state which occurs in materials at low temperature (approaching 0 K) - although superconduction at higher temperatures (circa 100 K) has been reported - is categorized by perfect conduction of current without power loss, the expulsion of magnetic flux (Meissner effect) and the quantization of flux with the occurence of an energy gap, etc. In 1962, Josephson [14] published a theoretical prediction that it should be possible for electron-pairs to tunnel between closely spaced superconductors even with no potential difference. An experimental demonstration of the effect was made in 1964 [15]. The theoretical basis and application of the Josephson effect in sensors, SQUIDs, are described in Chapter 10.

2.7 References [l] Thomson, W., “On the effects of magnetization on the electric conductivity of metals”, Philos. Trans. R. SOC.London A 146 (1856) 736-751. [2] Hall, E. H., “On a new action of the magnet on electric current”, Am. J. Math. 2 (1879) 287-292. [3] Joule, J. P., “On a new class of magnetic forces”, Ann. Electr. Mugn. Chem. 8 (1842) 219-224. [4] Villari, E., “Change of magnetization by tension and by electric current”, Ann. Phys. Chem. 126 (1865) 87-122. [5] Matteucci, C. H. ,“Memoire sur le magnetisme developpi par la courrant electrique”. Comptes Rendus 24 (1847) 301-302. [6] Wiedemann, G . , Lehre von der Elektrizitut 3 (1883) 680-684. [7] Yamamoto, M., Sci. Rep. Tohoku Univ. /AJ 10 (1958) 219-239. [8] Smith, I. R. and Overshott, K. J., “The Wiedemann effect, a theoretical and experimental comparison”, Brit. J, Appl. Phys. 16 (1965), No. 12, 47-50. [9] Ruzek V. J., “Untersuchung des Wiedemann’schen Effektes zur Kraft- und Drehmomentmessung”, Feinwerktechnik & Messtechnik 92 (1984) 415-416. [lo] Overshott, K. J., Private communication (1989). [ll] Sixtus, K. J., and Tonks, L., “Propagation of large Barkhausen discontinuities”, . Phys. Rev. 37 (1931) 930-958. [12] Brailsford, F., “Physical Principles of Magnetism”, New York: Van Nostrand 1966, pp. 183f. [13] Wiegand, J. R . , “Switchable Magnetic Device”, U S. Patent No 4247601, 1981. [14] Josephson, B. D., “Possible new effects in superconductive tunnelling”, Phys. Lett. 1 (1962) 251 -253. [15] Anderson, P. W., and Rowell, J. M., “Probable observation of the Josephson superconducting tunnelling effect”, Phys. Rev. Lett. 10 (1963) 230-232.

3

Magnetogalvanic Sensors RADNOJEPOPOVIC. Landis & Gyr. Zug. CH WOLFGANG HEIDENREICH. Siemens AG. Regensburg. FRG

Contens 3.1 3.2 3.2.1 3.2.2 3.2.3 3.3 3.3.1 3.3.2 3.3.3 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.5 3.5.1 3.5.2 3.5.3 3.6 3.6.1 3.6.2 3.6.3 3.6.4 3.7 3.8

. . . . . . . . . . . . . . . . . . . . . . . . . . . Galvanomagnetic Effects . . . . . . . . . . . . . . . . . . . . . . The Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . . The Hall Coefficient . . . . . . . . . . . . . . . . . . . . . . . Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . Hall Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structures and Technology . . . . . . . . . . . . . . . . . . . . . Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetoresistors . . . . . . . . . . . . . . . . . . . . . . . . . Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetoresistor Technology . . . . . . . . . . . . . . . . . . . . Properties of Magnetoresistors . . . . . . . . . . . . . . . . . . . Differential Magnetoresistors . . . . . . . . . . . . . . . . . . . . Other Semiconductor Devices as Magnetic Sensors . . . . . . . . . . Magnetodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetotransistors . . . . . . . . . . . . . . . . . . . . . . . . Carrier-Domain Magnetic Sensors . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Measurement . . . . . . . . . . . . . . . . . . . . . . Noncontact Position Sensing . . . . . . . . . . . . . . . . . . . . Selected Examples . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction

44 45 46 48 51 52 54 56 57 61 61 64 67 68 71 72 73 74 75 75 76 81 87 91

92

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

44

3 Magnetogalvanic Sensors

3.1 Introduction

This chapter is devoted to magnetic field sensors whose operating principle is based on the galvanomagnetic effects that occur in semiconductors. Galvanomagnetic effects are the physical phenomena that arise in matter which is carrying an electrical (galvanic) current whilst at the same time being exposed to a magnetic field. The best known fundamental galvanomagnetic effects are the Hall effect and the magnetoresistive effect. These effects are most conveniently exploited in materials that possess a high carrier mobility and a relatively low free carrier concentration, and since these two criteria are best met in a number of semiconductors, only the semiconductor galvanomagnetic sensors are of practical importance. The only exception are the sensors based on the magnetoresistive effect in thin ferromagnetic films (see Chapter 9). Hall discovered the effect which was subsequently named after him in 1879 [l]. The magnetoresistive effect, however, was discovered even earlier in 1856 by Thomson [2], but was little known until the advent of Hall’s discovery. For a long time, both effects were used in solid-state physics as powerful tools for studying carrier transport phenomena [3, 41, and it was only the developments occurring in semiconductor technology that enabled the additional use of the galvanomagnetic effects for sensor applications. In 1948, Pearson proposed a germanium Hall device as a magnetic sensor [5], and it was then only a few years after the discovery of the high-mobility compound semiconductors [6], that Hall devices and magnetoresistive sensors became readily available commercially. A detailed account of the early work done on the galvanomagnetic semiconductor sensors can be found in references [7-91. The current microelectronic revolution still strongly influences and stimulates further development of new galvanomagnetic sensors, because, generally, sensors that show as high a performance-to-price ratio as the microelectronic circuits themselves are highly desirable [lo]. This also applies, of course to magnetic-field sensors and similarly determines trends in their development. An obvious way to achieve the goal then, is to make use of an available mainstream technology. Accordingly, most new developments in the field of galvanomagnetic sensors take advantage of the availability of high-quality materials and the well-established sophisticated fabrication methods that are used in integrated circuit production. Such a trend has been further motivated by the possibility of being able to integrate a magnetic-field sensor and some signal-processing circuitry on the same chip. These integrated sensors, with “on chip”-signal processing, are called smart sensors [ll]. It is interesting to note, however, that only the semiconductor magnetic-field sensors have the potential to be fully compatible with contemporary integrated circuits [12], and thus they are the natural choice for the realization of smart magnetic sensors. The first directly integrated galvanomagnetic sensor, an MOS-Hall element, was proposed by Gallagher and Corak in 1966 [13]. In 1968, Bosch proposed the incorporation of a Hall device into a standard silicon bipolar integrated circuit [14], and this idea formed the basis of a number of commercially successful products [15, 161. By 1980, over 150 million smart Hall sensors had been manufactured and put to use as position or current sensors [15]; the new results on such integral semiconductor galvanomagnetic sensors will form one of the main topics of this chapter.

’

3.2 Galvanomagnetic Effects

45

Another way in which microelectronics has influenced the development of galvanomagnetic sensors is through the full employment of the abundance of physical effects available in semiconductor devices. The basic galvanomagnetic effects may be combined in any number of ways with the well-known phenomena inherent to semiconductor devices, such as carrier drift, diffusion, injection, recombination, etc., thus producing new, combined galvanomagnetic effects. In 1949, for example, Suhl and Shockley studied the carrier transport phenomena in point-contact transistors exposed to an external magnetic field [17] and discovered a combined galvanomagnetic effect, which is now called the magnetoconcentration effect or Suhl effect. Many interesting magnetic sensors have been proposed over the last 30 years which exploit such combined galvanomagnetic effects in somewhat modified conventional semiconductor devices such as transistors, diodes, and thyristors. They are now referred to as magnetotransistors, MagFETs, magnetodiodes, and carrier-domain magnetometers for more information refer to the review papers [12] and [MI. A part of this chapter also deals with these promising devices.

3.2 Galvanomagnetic Effects In this section, we have summarized the most important theoretical ideas and experimental results concerning the two basic galvanomagnetic effects, the Hall effect and the magnetoresistive effect, concentrating on the issues which are the most important for magnetic-field sensors. More detailed treatments of the subject can be found in many textbooks, for example references [19-211, monographs [3, 41, and review papers [22-251. Isothermal conditions have been assumed for this theoretical consideration and only the basic effects have been dealt with here. The combined effects will be discussed in Section 3.6, along with the corresponding devices. Generally, galvanomagnetic effects are manifestations of the charge-carrier transport phenomena occurring in condensed matter, when the carriers are subject to the action of the Lorentz force F :

F = eE

+ e[u x

B]

.

(3-1)

Here e denotes the carrier charge (for electrons e = -4, and for holes e = q, where q = 1.6 10-l9C and represents the magnitude of the electron charge), E denotes the electrical field, u the carrier velocity and B the magnetic induction. For nondegenerate semiconductors exposed to transverse electrical and magnetic fields, ie, (E * B) = 0, the carrier transport equation for one type of carrier reads (after [19]):

where j denotes the total current density. The term j , = aE

- eDVn

(3-3)

46

3 Magnetogalvanic Sensors

is the current density due only to the electric field and the carrier-concentration gradient V n ; ie, j , does not depend explicitly on the magnetic field. However, j , # j ( B = 0), since a magnetic field generally influences the electric potential and carrier-concentration distributions. Equations (3-2) and (3-3) take into account both carrier drift and diffusion phenomena (the terms proportional to E and V n , respectively), and also the transverse transport caused by the magnetic field (the term proportional to B ) . The transport coefficients pH (the Hall mobility), 0 (the conductivity), and D (the diffusion coefficient) are determined by the carrier scattering processes and generally depend on electric and magnetic fields. Both the galvanomagnetic effects we are interested in can be derived from the solutions of Equation (3-2) subject to the appropriate boundary conditions. The Hall mobility is given by

where r is the Hall scattering factor and p is the drift mobility. The Hall mobility has the sign of the corresponding carriers, ie, pHp > 0 and p H n < 0, p and n denoting holes and electrons, respectively. The Hall scattering factor, a number close to unity, is defined by

where tion.

( 7 )denotes

the average value of the carriers relaxation time over their energy distribu-

3.2.1 The Hall Effect Let us now consider a special case of carrier transport in a very long strip of a strongly extrinsic and homogeneous (Vn = 0) semiconductor material (Figure 3-1). For simplicity we assume that the strip axis is along the x-axis, the strip plane is in the xz-plane, and that B = (0, By, 0). If we expose the strip to an external electric field E,,, = (Ex, 0, 0) a current Z will flow through it with current densityj = ( j x ,0, 0). Since j , = 0, an internal transverse electric field EH must build up in order to counteract the “magnetic” part of the Lorentz force (the second term in Equation (3-1)). The field EH is called the Hall field and can be determined from Equation (3-2), by substituting E = E,,, + EH , under the condition that the transverse current density vanishes, ie:

Figure 3-1. The Hall effect in a long sample. If a strip of conducting material, placed in the xz-plane along the x-axis, is exposed to an electric field Ex and magnetic induction B y , a transverse electric field E, appears.

3.2 Galvanomagnetic Effects

47

A macroscopic and tangible consequence of the existence of the Hall field is the appearance of a measurable transverse voltage, namely the Hall voltage:

where w denotes the strip width. The generation of the transverse Hall electric field and the consequent Hall voltage under conditions similar to those in Figure 3-1 is usually collectively referred to as the Hall effect. Another way to characterize the Hall effect is by the angle of inclination of the total electric field in the sample with respect to the external field. This angle 0, is called the Hall angle and is given by Ez = - p , ~ . tan@, = EX

(3-9)

In weak magnetic fields, the Hall voltage is proportional to the Hall angle (Equations (3-8) and (3-9)). The intensity of the Hall effect in a material is best characterized by the Hall coefficient. By definition, the Hall coefficient R H is given by: EH RH = - [ j x B ]

(3-10) *

However, in our case:

[J

X

Bl = (O,O,j , B )

(3-11)

so that now: (3-12) Sincej = aE, we can obtain within the limit of B = 0: RH - pH c 7

=-

en

(3-13)

using Equation (3-4) and the relation a = q p n . It is thus possible to express the Hall voltage (3-8) as UH = R , j x B w

where the negative sign has been omitted.

(3-14)

48

3 Magnetogalvanic Sensors

Consider now another form of the galvanomagnetic effect, arising in an unlimited sample. For the sake of ease, an arrangement such as that shown in Figure 3-1 has been used, but with w 03, see Figure 3-2a). If an electric field E = (Ex, 0, 0) is applied, the current density (Equation (3-2)) becomes +

j x = aEx

(3-15)

j, = p H B a E x .

(3-16)

Since there are no boundaries, the current is not solely confined to the field direction. Consequently, the total current density vector rotates with respect to the applied electric field. The angle of rotation is the Hall angle, given by tan@, = p H B .

(3-17)

Exept for the opposite sign, this is the same as in the conventional Hall effect (Equation (3-9)). In infinite samples the Hall effect is sometimes referred to as the carrier deflection effect. The essential condition for its appearance is obviously the nonexistence of the Hall field. This condition also can be realized approximately in a short sample, using highly conductive contact electrodes on the larger faces (see Figure 3-2 b), which provide a partial short-circuiting of the Hall voltage.

= b)

Figure 3-2. The Hall effect in an unlimited sample - the carrierdeflection effect. a) If a plate of conducting material, placed in the xz-plane, is exposed to an external electric field Ex and magnetic induction By, the current density vector j covers with Ex the Hall angle 0,.b) The same effect can be obtained in a short sample with highly conducting contacts at the large faces.

3.2.2 The Hall Coefficient The Hall coefficient is the proportionality factor relating the Hall field or the Hall voltage to the current-magnetic field product in a Hall-effect experiment (Equations 3-10 and 3-14).

3.2 Galvanomagnetic Effects

49

The value and stability of the Hall coefficient directly determines the magnitude and the stability of the sensitivity of the sensors based on the Hall effect. For a material with both types of carriers, ie, electrons and holes, the Hall coefficient is given by RH =

1 r p p - b2r,n 4 (p + b n ) 2

(3-18) (3-19)

Here rp and r, denote the Hall scattering factors, ,upand p, are the mobilities, and p and

n are the concentration of holes and electrons, respectively. The coexistence of both types of carriers reduces the Hall voltage: the carriers tend to accumulate at the same side of the plate and partially compensate each other’s fields. This situation arises in two cases, namely, in intrinsic semiconductor materials and under high-injection conditions. In the intrinsic semiconductors, p = n = n, , where n,is the intrinsic carrier density, given by: -

ni = A T 2 e

-~E8

(3-20)

2kgT

and where A is a coefficient, dependent on the carriers’ effective masses and the energy bands’ structures, A = (0.2/4) . 10’’ m - 3 K -3’2, T is the absolute temperature, Eg is the band-gap energy and k, is the Boltzmann constant. The high-mobility semiconductors, such as InSb and InAs, tend to have small band gaps and are nearly intrinsic at room temperature. The Hall coefficient (Equation (3-18)) thus becomes: 1 I rp - b 2 r , RHi = -q n, (I + b ) 2

(3-21)

and is highly temperature dependent. High-injection conditions arise in a sample if a strong nonthermal carrier-generation mechanism supplies the nonequilibrium carriers to the sample. Such mechanisms may, for example, be the internal photoeffect or carrier injection via a p-n junction. In an extreme case, p = n, Equation (3-21) applies again, with n + n,; the carrier concentration, however, is now Z [26], then defined predominantly by the generation rate. For example, n

-

RHinj

C

-

zinj

rP-b2rn (1+b)2

(3-22)

where Zinj denotes the injection current and C is a coefficient, which depends on the recombination process. Should the higher mobility carriers strongly prevail, eg, if

50

3 Magnetogalvanic Sensors

then Equation (3-18) reduces to

R,, = --rn

(3-24)

9n

which is the same as Equation (3-13). The condition (3-23) is best fulfilled in strongly extrinsic semiconductors, when n&p, n =Nd

(3-25)

where Nd is the donor density. Both of these equations are valid only within the saturation temperature range [26]. The values of the Hall scattering factors rp and rn in Equations (3-18) and (3-24) are always close to unity. However, their exact values depend on many parameters, such as temperature, magnetic field and mechanical stress, and so they are important determinants of the performance of the galvanomagnetic sensors. In the simple case of semiconductors with spherical constant-energy surfaces in weak magnetic fields (defined by p 2 B 2 4 1) the Hall scattering factor is given by the ratio of the appropriate relaxation-time averages (Equation (3-5)). For acoustic phonon scattering, this expression gives r = 1.18, and for ionized impurity scattering r = 1.93. In strong magnetic fields, defined by p 2 B 2 %- 1, or in degenerate semiconductors and metals, r = 1. Generally, in weak magnetic fields, the Hall scattering factor may be represented by [27] r

= ro(l - a p c B 2 )

(3-26)

where r, = r ( B = 0) and a is a parameter, a complicated function of the scattering process. For lightly doped silicon, r,, = 1.15 and rop = 0.7, for electrons and holes, respectively, at 300 K [28, 291. Within the temperature range 200 K to 400 K, r,, varies approximately linearly with temperature, the temperature coefficient being (l/ron) (8ro,/i3 T ) = 10 - 3 K - I . The nonlinearity coefficient a for n-type silicon is a, t: 0.3 to 1 [27], the lower values being found in more highly doped samples (Nd = 10l6 cm-3) and at lower temperatures ( T = 250 K). A value of a = 1 was found in low-doped samples (Nd = 1.7 . 1014 ~ m - at ~ higher ) temperatures ( T = 400 K), a result corroborating the theoretical predictions for the case involving the phonon scattering process. For n-type GaAs with electron concentrations in the range from lOI5 to lo1' cm-3, it was found that r,, = 1.1 to 1.2 at T = 300 K and l(l/ron) (aro,/aT)I < 0.5 also a, = 0.1 for n < 1015 cm-3 at 300 K (extracted from [30]). Semiconductors such as silicon, with many-valley band structures and anisotropic energy minima, generally exhibit piezo effects in the carrier-transport phenomena. A change in the Hall coefficient occurring as a function of the mechanical stress X i s referred to as the piezoHall effect. For lowdoped n-type silicon, the coefficients relating to piezoresistance and the piezo-Hall effect are of almost equal size and sign and depend strongly on the crystal orientation [31]. For example, A R , , / ( R H , X ) = 0.45 . bar-' for a device in the (100) plane, bar-] for a current along the ( 1 1 1 ) directions in the (110) and A R , , / ( R , , X ) < 0.1 . plane.

3.2 Galvanomagnetic Effects

51

3.2.3 Magnetoresistance Under the influence of a magnetic field, an increase in material resistivity is generally observed and this phenomenon is called the magnetoresistive effect. In weak magnetic fields, the change in resistivity is proportional to the square of the magnetic-field component perpendicular to the current-density vector, ie. CJB

=

CJO

1

+ HB:

(3-27)

where po is the resistivity at B = 0, CJ = l/p, gois the conductivity at B = 0, and H i s the coefficient of magnetoresistance. The coefficient of magnetoresistance can be obtained by solving the general transport equation (3-2), subject to the appropriate boundary conditions. For example, for an infinite sample of the type discussed at the end of Section 3.2.1, Figure 3-2a, in small magnetic fields [19] one obtains: (3-28)

In the case of the long strip (see Figure 3-1): HL = p2(C - r2)

(3-29)

where r is the Hall scattering factor, Equation (3-5). For spherical energy surfaces and acoustic phonon scattering, C = 1.77, r = 1.18, so that H,, P h = 1.77 p 2 and HL,P h = 0.38 p 2 ; for ionized impurity scattering, C = 5.89, r = 1.93, so that H,, = 5.89 p 2 and HL,= 2.17 p 2 . The increase in resistivity of the carrier transport under the influence of a magnetic field arises because of the shorter distance which a carrier can travel between two successive collisions, along the direction of the external electric field. An obvious macroscopic consequence of this observation is that the current-density vector is rotated with respect to the electric field (Figure 3-2). Since the current lines in a short sample like the one in Figure 3-2b become longer when a magnetic field is present, the magnetoresistive effect under such conditions is sometimes referred to as the geometrical magnetoresistive effect. However, even if the pure in Figure 3-l), the geometrical effect vanishes, such as occurs in the long strip (i 1 magnetoresistive effect generally still exists, Equation (3-29). This is a consequence of the fact that the Hall field compensates for the action of the magnetic field only in average, while the carriers are spread over all energies, and they generally travel along curved lines. The magnetoresistive effect will only vanish (to a first approximation) in a long sample and in degenerate materials if the relaxation time does not depend on energy: C = r = 1, and HL = 0 (Equation (3-29). Since the Hall field diminishes the magnetoresistive effect, it is common practice to design the magnetoresistive sensor in such a way that the generation of a Hall field therein is inhibited. To this end, the most effective design is that of the Corbino disc [32] (Figure 3-3) which is a practical realization of an effectively infinite sample. Other such practical realiza-

,

,

52

3 Magnetogalvanic Sensors

0

Figure 3-3. The Corbino disk is a round plate of semiconductor material with one electrode at the center and the other round the circumference. As there are no nonconducting boundaries, the Hall field cannot build up, and the electric field E is always radial. The current density j covers everywhere with E an equal Hall angle 0,.

tions are based on the short-circuiting effect of the Hall voltage in short samples such as the one in Figure 3-2 b. The coefficients of magnetoresistance are proportional to the square of the carrier-mobility term, Equations (3-28) and (3-29). Therefore, high mobility materials are strongly preferred for magnetoresistive sensor applications. (At T = 300 K, ,u: (in m2/V2 s2) is 0.022 for Si, 0.15 for Ge, 0.72 for GaAs, 10.9 for InAs and 64 for InSb.) The intrinsic behavior of small bandgap materials at around room temperature is not of great importance to the magnetoresistive effect. Indeed, the presence of both types of charge carrier even helps to reduce the Hall field, see Equation (3-21), and simplifies realization of magnetoresistive sensors with H = H a .

3.3 Hall Sensors A Hall sensor is a magnetic-field sensor based on the Hall effect much in the form as Hall discovered it. Usually, such a sensor composes of a thin rectangular plate of a semiconductor material, fitted with four electrical contacts (Figure 3-4). A bias current I is supplied via two of the contacts (the current contacts, CC, and CC,), and the other two contacts (the sense contacts, SC, and SC,) are placed on two equipotential points at or close to the plate boundary. If a magnetic field is applied to the device, the Hall voltage, which is the sensor output signal, appears between the sense contacts. The Hall voltage is approximately proportional to the product of the component of the magnetic induction perpendicular to the plate plane B, and the bias current I.

Figure 3-4. Rectangular Hall plate. CC, and CC, are the current contacts, SC, and SC, the sense contacts, Z the bias current, U the voltage drop over the plate and U, the Hall voltage.

In the ideal case o f a very long plate, such as the strip described in Figure 3-1, with very small sense contacts, the Hall voltage is given by Equation (3-14). Since the current density j is given by j = I/tw

(3-30)

53

3.3 Hall Sensors

where t is the plate thickness and w is its width, Equation (3-14) can be rewritten as: U,, =

3 BI t

(3-31)

where the suffix L stands for long plate. In the general case of a plate with finite dimensions and a finite contact size, the Hall voltage is given by: U , = -RG,B I t

(3-32)

where G is the geometrical correction factor. By definition, the geometrical correction factor is the ratio of the Hall voltage in an idealized, point-contact device to that of an actual device: G = UH/UHL,

(3-33)

It accounts for the diminution of the Hall voltage due to the short-circuiting effect caused by the finite current and sense contacts. Obviously, the geometrical correction factor may vary between 0 (for a device with large contacts, covering its whole periphery) and 1 (for the above described very long or point-contact device). In most practical realizations of Hall sensors, the electron conductivity is strongly prevalent, ie, condition (3-23) is fulfilled. Thus it is possible to substitute for the Hall coefficient in Equation (3-32) with R , = R,, (see Equation (3-24)) and obtain:

rn G B I

IuHl

(3-34)

This Equation explains why Hall sensors are usually thin plates and are made of a low-carrier-concentration material, since the Hall voltage is inversely proportional to both the plate thickness t and the carrier concentration n. However, a thin plate with a low carrier concentration generally has a high sheet resistance. Using such a material for the sensor may cause the voltage drop across the sensor current contacts

U = RI

(3-35)

to become unacceptably high. (R denotes the resistance between the current contacts.) For example, for a rectangular plate, like in Figure 3-4,

I

1

1

R = p- = -wt q p n wt

(3-36)

where p is the resistivity of the plate material. By substituting Equations (3-35) and (3-36) into (3-34), the Hall voltage can be expressed in terms of the voltage U applied between the current contacts: (3-37)

54

3 Magnetogalvanic Sensors

Combining equations (3-34) and (3-37), it is possible to obtain the Hall voltage in terms of the power P = U s Z dissipated in the plate: (3-38) It is important to note in both of the last equations the dependence on the mobility. For a given Hall voltage, both the voltage drop and the dissipated power will be minimized if a high-mobility material is used for the Hall plate.

3.3.1

Geometry

A Hall device does not have to have a rectangular shape such as the example shown in Figure 3-4, or indeed any other regular shape. Actually, any finite plate, provided with a least three contacts, may be used as a Hall device. (The fourth contact may be replaced by a potentiometer [33].) Some examples of Hall-plate shapes are shown in Figure 3-5. Using conformal mapping theory, Wick [34] demonstrated the invariance of Hall plate electrical efficiency with respect to geometry (“. . . there are no properties . . . that cannot be obtained from a circle, square, or any other simple shape by proper size and position of the electrodes!’) That said however, some of the shapes may have some technological or application advantages over the others. For example, a vertical Hall device [35] is much easier to fabricate in IC technology if all contacts are situated on one side of the plate, as shown in Figure 3-5 h. Alternatively, achieving a high value for the geometrical factor G in small-size devices is much easier in a cross-shaped configuration (Figure 3-5 c) than in a rectangular one (Figure 3-5 a) [36]. Still another example is the application of devices which are invariant under rotation through

sc/cc

O b

GCed SC/CC

SC/CC

rnf sc cc sc cc

Fieure 3-5. Some shapes of Hall plates. CC represents the current contact, SC the sense contact, and S C K C indicates that the current and sense contacts are interchangeable.

3.3 Hall Sensors

55

90°, such as those in Figure 3-5b, c, and d, for cancelling the offset voltage [15] (see Section 3.3.3). The influence of the Hall-plate shape on its efficiency is summarized in the geometrical correction factor G (Equations (3-32) and (3-33)). The problem has been studied using conformal mapping technique and numerical simulation [34, 37-42] and for some conventional shapes of Hall plates, the following approximate analytical expressions were found: For relatively long rectangular Hall plates, with I/w > 1.5, small sense contacts, s/w CO.18, and small Hall angles 0, (Equation (3-9)) the geometrical correction factor can be approximated by [38]

2 s O H ] n w tan@,

G = [t - + enx p ( - + $ ) + ] . [ i

(3-39)

with an accuracy better than 4%. Here I, w, and s are the characteristic dimensions of the plate, as defined in Figure 3-4. The function (3-39) approaches unity if I/w > 3 and s / w < 1/20. For short rectangular Hall plates, with vanishingly small sense contacts, it was found [37] that: 1

W

+ 2.625 - 3.257

W

This expression is accurate to within 1% if the plate length-to-width ratio I/w + 0 and 0 , + 0,

(3-40)

< 0.35 and

0, < 0.45. In the limit of I/w G

I

0.742 -

(3-41)

W

By substituting this expression into Equation (3-37), the maximum value for the Hall voltage

U,, = 0.742pH,BU

(3-42)

that can be obtained in a Hall sensor biased by a given voltage U. For Hall plate shapes which are invariant under a rotation through 90°, such as a square (Figure 3-5 b), cross (Figure 3-5 c), circle, and octagon, the geometrical correction factor can be approximated by the following function [40]: (3-43) Here g(1) is a function of the ratio A of the (all) contacts length and the total length of the plate boundary. The approximation is valid for small Hall angles and small ratios A. For example, for a symmetrical octagon,

g(1) = 1.940

(

1 1

+ 0.4141)

2

(3-44) *

56

3 Magnetogalvanic Sensors

This leads to an accurate value of G (A, OH)to within 0.5% if A I0.73, ie, g (A) I0.61, and OH = 0.016. If the term @,/tan OH in Equation (3-43) is expanded into a series and only the first two terms are retained, it leaves us with [27]:

After some rearrangements, the geometrical correction factor can be described by:

G = Go(l + p , u i B 2 ) ,

(3-46)

ie, in the same form as Equation (3-40). Here Go = 1 - g (A) is the value of the geometrical correction factor at B = 0, and is a numerical coefficient dependent on the plate geometry. For devices with a weak short-circuiting effect, using Equations (3-45) and (3-46) one can obtain an expression for /3:

p z - . 1 - Go

(3-47)

3 GO

For devices with a strong short-circuiting effect such as a short rectangular plate, one finds from Equations (3-40) and (3-46) that:

p

%

0.604 - 0.732Go

.

(3-48)

In view of the equivalency of Hall plates with different shapes [34], it was concluded in [27] that expressions (3-46), (3-47) and (3-48) are generally valid. In particular, according to Equations (3-40) and (3-44), they are accurate to within 1% if Go I 0.260 or Go 2 0.39, respectively.

3.3.2 Structures and Technology The fabrication technology of Hall sensors has always been influenced by the state of the art of semiconductor technology. Early devices were made as bulk or thin-film discrete components [5, 7, 81; later, with the development of integrated-circuit technology, devices were proposed based on the silicon MOS process [13], the silicon bipolar process [14], GaAs epitaxy [43], and, recently, a superlattice structure fabricated by molecular beam epitaxy [44]. Most of the currently available commercial Hall sensors are based on the bipolar integrated circuit process [15, 161, as shown in Figure 3-6. The active region of the plate is realized as a part of the n-type epitaxial (collector) layer, its planar geometry being defined by the deep p-(isolation)-diffusion regions and the n -(emitter)-diffusion regions. The n + layers are used to provide good ohmic contacts between the low-doped n-type active region and the metal layer (the contacts). The isolation between the Hall plate and the rest of the chip is achieved using reverse-biased p-n junctions surrounding the plate, a technique commonly employed in monolithic integrated circuits. +

3.3 Hall Sensors

sc

57

cc

Figure 3-6. Rectangular Hall plate in bipolar IC technology. The notation for the contacts is the same as that used in Figure 3-4. D L denotes the depletion layer surrounding the n-type active device region.

Typical electron densities and thicknesses for the epitaxial layer are n = 10l5 to 10I6cm - 3 and t = 5 to 10 pm, respectively, yielding an nt product (see Equation (3-34)) of 5 10" cm-2 to 1013cm -2. The active n-type layer can also be created by ion implantation, which provides better control and uniformity of doping density than epitaxy. The typical implantation dosages correspond to the nt products given above. Typical planar dimensions for integrated Hall plates are about 200 pm, but devices with submicron active-region dimensions have also been demonstrated [45]. The devices described so far have had the form of a discrete plate or an integrated plate merged into the chip surface. They are sensitive therefore, to the magnetic field perpendicular to the chip plane. For applications where sensitivity to the magnetic field parallel to the device surface is preferred, a so called vertical Hall device was devised [35]. In the vertical Hall device (Figure 3-7) the general plate shape is chosen in such a way that all contacts become available on the top surface of the chip, as in Figure 3-5 h. The active device volume is part of the n-type substrate material, surrounded by a deeply defused p-type ring. The sensitivity of the device is not affected by the unusual geometry, corroborating the considerations discussed in Section 3.3.1. A version of the vertical Hall device in bipolar technology [46] has been made successfully and a three-contact device [47] has also been realized. Figure 3-7. Vertical Hall device (see also Figure 3-5 h). The bias current Z flows between the two peripheral contacts, each carrying a half of the current (1/2), and the central contact. The Hall voltage appears between the two sense contacts SC, and SC,.

3.3.3 Performances Sensitivity: In modulating transducers, such as Hall sensors, absolute and relative sensitivities can be distinguished. Absolute sensitivity of a Hall sensor is defined as:

S, = I 8UH/i3BI I

=

Const

(in V/T = Volt/Tesla)

.

(3-49)

58

3 Magnetogalvanic Sensors

-

-

However, since in a Hall-effect device U, BZ and UH BU, (see Equations (3-34) and (3-37), a more useful feature is its relative sensitivity. Supply-current-related sensitivity of a Hall sensor is defined as: (in V/AT = volt/ampere

- tesla) .

(3-50)

From Equations (3-32) and (3-34) one can obtain:

(3-51) Current-related sensitivity depends solely on the plate-surface carrier density, nt, and the geometry. Its typical values range between 80 V/AT [16] and 400 V/AT [35], but the value becomes rather high in small-contact devices, where G = 1, if the nt product is made small. However, in integrated Hall devices, the minimum value of nt is limited by the junction field-effect. The highest sensitivity reported so far is S, = 3100 U/At, corresponding to nt = 2 10" cm-' [481. Analogously, supply-voltage-related sensitivity can be defined as:

(3-52) For a rectangular device, using Equation (3-37) one obtains:

(3-53) Typical values of voltage-related sensitivities are 0.07 T for silicon [16] and 0.2 T for GaAs devices [49]. The maximum value is obtained in short Hall plates, the physical limit derived from Equations (3-42) and (3-52), being:

Sum, = 0 . 7 4 2 ~ ~ " .

(3-54)

This yields, at room temperature, 0.128 T - ' and 0.725 T - ' for low-doped n-type silicon and GaAs respectively. Noise: The noise-voltage spectral density across the Hall sensor contacts is given by [50]:

(3-55) where S,, stands for l/f noise and S,, for thermal noise. Two useful figures with respect to noise are: firstly, the equivalent input magnetic-field noise spectral density, which is defined as

(3-56)

59

3.3 Hall Sensors

where S, denotes the absolute sensitivity, Equation (3-49); and secondly, the detection limit, determined by 1

(3-57) in the frequency range between fland f2.The detection limit corresponds to a signal-to-noise ratio of SNR = 1. A low detection limit can be achieved in large devices, if they are made of a high-mobility material with a low Hooge a-parameter, operated at a high power level [12]. The detection limit of a Hall element made of a material with p H = 6 m2/Vs and operated at P = 0.5 W for a high frequency signal with Af = 1 Hz was assessed theoretically to be Bmin= 4 10 -I1 T [50]. The experimentally obtained SNB values of a silicon Hall device biased at Z = 0.5 mA are: 3 . 10 -I3 T*/Hz at 100 Hz (l/f noise) and 10 -I5 T2/Hz at 100 kHz (thermal noise) [51]. Cross-sensitivity can be defined as the undesirable sensitivity of the sensor to other environmental parameters or signals, such as temperature, pressure, light, etc. A convenient way to characterize the cross-sensitivities of a Hall device is to use relevant secondary sensitivities,

-

(3-58) where P denotes a parameter, such as temperature ( P = T ) or pressure ( P = p ) , and S, denotes a prime sensitivity, Equations (3-49), (3-50) and (3-52). For example, by taking S, = S,and P = T, it is possible to derive an important secondary sensitivity known as the temperature coefficient of current-related sensitivity. For a Hall plate made of strongly extrinsic n-type material, Equation (3-25), one can obtain from equation (3-51) and (3-58) the function:

(3-59) Similarly, the pressure coefficient of current-related sensitivity can be expressed as:

(3-60) Some experimental data on the temperature sensitivity of the Hall scattering factor, (3-59), and the pressure sensitivity of the Hall coefficient, (3-60), are quoted in Section 3.2.2. Offset of a sensor can be defined as a static or very slowly varying output signal in the absence of a measurand. The major causes of offset in Hall sensors are imperfections in the fabrication process and also piezoresistive effects producing an asymmetry voltage U, f (B) at the sense contacts [12, 521. Offset is usually characterized by an equivalent (offset) magnetic induction B, corresponding to the offset voltage U,, such that:

*

B, = Uo/S, , where S, denotes the absolute sensitivity (Equation 13-49)).

(3-61)

60

3 Magnetogalvanic Sensors

If a static magnetic field is to be measured with a Hall sensor, the application of an offsetreduction technique is usually required. Conventionally, offset can be reduced by trimming or calibration [7-91. Devices with a shape which is invariant under a rotation through 90" allow the application of the connection commutation technique, where diagonally situated contacts are alternately used as the current and sense contacts [15, 531. Since the Hall voltage rotates with the bias current and the offset voltage does not, the offset voltage can be cancelled out from the output voltage. A similar effect is obtained if two matched integrated Hall elements are biased orthogonally and their outputs connected in parallel [15]. Combining this idea with a buried active layer design, an equivalent offset induction as low as 1 mT has been achieved in silicon-integrated Hall elements [54]. Recently, an attempt was also made to apply the sensitivity variation method for offset reduction [55] on integrated Hall devices [52]. Nonlinearity is the ratio:

where U, is the measured Hall voltage and UHois a best linear fit to the measured values. Since UH = S, BZ, Equation (3-62) can be rewritten as:

(3-63) where S, (B,I) denotes the current-related sensitivity as a function of magnetic field and current. If one of the terms determining the sensitivity, namely RH , G, and t in Equation (3-51), varies with magnetic field or current, the sensor will exhibit a non-linearity, which is respectively called material, geometrical, or junction field-effect non-linearity [27]. Material non-linearity stems from the magnetic-field dependence of the Hall scattering factor (Equation (3-26)). It is characterized by the parameter a, whose value ranges between 0.1 and 1, (refer to the notes following (Equation (3-26)). Geometrical non-linearity is a consequence of the magnetic-field dependence of the geometrical factor G, see Equation (3-46). The coefficient p can vary from 0 (in devices with no short-circuit effect) to 0.604 (in devices with Go = 0, see Equation (3-48)) [27]. Junction field-effect nonlinearity is due to a feedback modulation of the Hall-plate thickness (t in Equation (3-51)) by the generated Hall voltage. It plays an important role in high-sensitivity integrated Hall devices, where it may be as high as a few percent [48]. The linearity of Hall sensors can be improved in several ways. Geometrical non-linearity can be compensated for by loading the sensor output with a resistor [7-91. More efficiently, material and geometrical nonlinearities can be made to mutually cancel in devices where a = 8, see Equations (3-26) and (3-46) [27]. Nonlinearity due to the junction field-effect can be compensated for using the very same effect in a feedback circuit [48], [27]. One of the lowest experimental nonlinearity values, N L = + 3 . at B c 1 T and room temperature, was reported for an ion-implanted, cross-shaped GaAs Hall device [43].

3.4 Magnetoresistors

61

3.4 Magnetoresistors 3.4.1 Fundamentals Magnetoresistors (MR) are passive semiconductor sensors which are based on the increase in resistance which occurs when they are exposed to a magnetic field. Although Thomson [2] observed the effect in metals in 1856, the effect only found a technical application after the discovery of III/V semiconductors by Welker [6]. The principle of Magnetoresistance has already been described in Section 3.2.3 and the following summary serves to recall the basis of the phenomenon. Magnetoresistive sensors which are based on the anisotropic magnetoresistive effect in thin films of ferromagnetic transition metals are the topic of Chapter 9. A free charge carrier experiences a deflection by virtue of the Lorentz force (Equation (3- l)), which acts perpendicular to the direction of the velocity v and the magnetic induction B. In a semiconductor material the charge carrier eventually collides with the crystal lattice, whereby it loses velocity and hence establishes the so called Hall angle 0, between the electric field Ex and the direction of the current. The Hall angle 0, as given in (3-17) is proportional to , , and to the magnetic induction B. the Hall mobility U This rotation of the current direction results in an increase in the length of the path of the current flow, which manifests itself as an increase in the resistance of the material. This magnetoresistive effect is exploited to produce MR devices. Further descriptions of the Magnetoresistive effect and components based on it are given in [8, 9, 79-82].

3.4.1.1 Basic Equations Equations (3-27) and (3-28) are valid for infinite geometries with low magnetic fields. They show a quadratic characteristic between specific resistance and magnetic field B. At large magnetic fields (0,--$ d 2 ) the function shows a linear dependence. Lippmann and Kuhrt [83] have reported the resistance of a square semiconductor plate in relation to Hall angle and to the geometry ratio I/w, where I is the length and w the width of the plate. For small Hall angles 0, 5 0.45 the quadratic dependence is valid, ie,

PB (1 + c,( P H B ) 2 )

RB -Ro

(3-64)

Po

where Ro is the resistance at B = 0, p B / p ois the relative specific resistance of an infinitely long rod (see Equations (3-27) and (3-29)) and C, is a geometry-dependent constant. For large Hall angles, 0, + d 2 , the linear relationship is valid, ie, RB PB = -(C,,U,B

Ro

Po

+ C3)

where C, and C3 are both geometry-dependent factors.

(3-65)

62

3 Magnetogalvanic Sensors

The resistance characteristic is symmetrical about the R, /R,axis and thereby independent of the magnetic field direction. In order to produce components which work by using the magnetoresistive effect it is necessary to optimize the geometry-dependent factors C, , C,, C, , and also the semiconductor material which determines p,, the Hall mobility.

3.4.1.2 Influence of Geometry If one considers the current paths in a real isotropic semiconductor plate when it is subjected to a perpendicular magnetic field, then it can be shown that the effects of the Hall angle OH are only significant in the region close to the contact electrodes. The supply-current terminals stretch over the full width w of the plate as is represented in Figure 3-8.

1

1 Y

H

O

X -

I

-

F

Figure 3-8. Rectangular semiconductor plate in a magnetic field perpendicular to the plane of the page. - represents current paths, -- represents equipotentials.

W

The current paths in the center of the plate run parallel to the edges and here, as already discussed in 3.2.3, the Hall field tends to reduce the magnetoresistive effect. The equipotentials are therefore rotated through the Hall angle OH,ie, a Hall voltage can be measured. The magnetoresistive effect is magnified as the ratio of the electrode separation along the length I to the electrode width w decreases. Figure 3-9 shows the relative resistance change for various length to width relations I/w as a function of the magnetic field B from tests made on similar doping grades of InSb [84]. //w =0 Korbino disk)

20

1

d \ d

15 I / w = 0.33

10 //w=l

5 1

0

I

I 0.1 0.2 0.3 0.4 0.5 0.6 03 0.8 0.9T1.0 1

I

B-

//w

10

Figure 3-9. Dependence of the relative resistance R , / R , on a magnetic field B, for various length-to-width ratios.

63

3.4 Magnetoresistors

From the results of [83] the geometry-dependent factors C,, C 2 , C3 (from Equations (3-64) and (3-65)) can be expressed in order to define the characteristic curve. For I/w 5 0.35 (3-66)

C, = 1 - 0 . 5 4 1 / ~ ,

hence the Equation for Hall angles 0, 5 0.45 can by using Equation (3-64) be given by: RB PB = -(1

Ro

Po

+ ( p H B)’(l - 0.541/~))

(3-67)

If I/w = 0 then the largest possible relation is obtained. This can only be practically realized in the form of the Corbino disc [32] (see Figure 3-3).

c2= w/l

(3-68)

using (3-65) the following expression for large Hall angles 0, + n/2 can be obtained: RB =

Ro

PB @H B w/l Po

+ C3) .

(3-69)

The dependence of the geometry factor C3 in on I/w gives the characteristic curve in Figure 3-10 after [83]. In Equation (3-69) the ratio w/l gives the gradient of the asymptote and C3 the point where it cuts the axis. 1 0 -1 -2 -3

5 \

z

-4

-5 -6

-7

Figure 3-10. Constant C, in Equation (3-69) showing its dependence on the length/width ratio I/w; from [83].

-8 -9

-10

0

05

1

1.5 I/

2

25

3

W

3.4.1.3 Selection of Material The influence of the material is strongly manifest in the Hall mobility pH and this is of special importance for the magnetoresistive effect. Table 3-1 shows a selection of suitable semiconductor materials. InSb shows the highest absolute value for mobility and is therefore the preferred material for magnetoresistive components. The very small band gap possessed

64

3 Magnetogalvanic Sensors

Table 3-1. Physical properties of some suitable semiconductor materials. unit cm2V-' s eV

P E8

ni(RT) a(RT)

InSb

-'

P@T)

Rn

3 . lo4 0.45 6 ' 1014 + i s 10-3 - 1 . 10-~ 100

7.7 104 0.24 2 * 10'6 -2 * 10-2 -1.5 . 380 +

K-' K-' cm3A-I s - '

Si

Ids

1.5. 103 1.12 1.5 * 10" + 5 . 10-~ +1.2. 1 0 - ~ 3000')

GaAs

8 * lo3 1.43

10' +8 - 5 . 10-4 60 I )

depending on doping

by InSb leads, even at room temperature (20°C), to a high temperature coefficient of resistance, a = -2%/K. This disadvantage can be overcome by the addition of foreign atoms, ie, doping, which shifts the intrinsic conductivity range to higher temperatures. The accompanying reduction in the gradient of the characteristic curve can usually be tolerated. The temperature dependence of the normalized internal resistance R,/R,, (0:Celsius temperature) of various semiconductor materials is shown in Figure 3-11.

,8.10-&

'

0-20 0

I

I

20

60

I

100 Temperature E

GaAs

I

I

140

180

-

'C

Figure 3 4 . Temperature dependence of the normalized resistance R,/R,, of various semiconductors.

3.4.2 Magnetoresistor Technology 3.4.2.1 Production of InSb Semiconductor Material InSb material for magnetoresistors is produced as a polycrystalline bar in a zone-melting process. The elements Indium, In, and Antimony, Sb, are purified and powdered and then melted together in stoichiometric proportions in an inert atmosphere. The melting point of InSb lies at 525 "C. The InSb bar is then refined to the required purity by zone melting, and then the pure material is doped as required with tellurium to about 2 loz2to 2 1023m- 3 [7].

3.4.2.2 Technology of Short-circuit Straps The basic requirement for the effective use of the magnetoresistive effect is the smallest possible ratio of I/w, Equations (3-67) and (3-69). Intrinsic or doped InSb has a very

3.4 Magnetoresistors

65

high specific conductivity, ie, 0 = 200-800 (SZcm)-'. The ideal form of the Corbino disc is therefore not a practical proposition. In order to obtain resistances in the range 100 - 1000 ohms a large number of I/w ratios must be connected in series, and the principle behind short circuit straps is shown in Figure 3-12.

Figure 3-U. Semiconductor plate with shortcircuit straps and current paths in a magnetic field acting perpendicular to the plane of the page.

3.4.2.2.1 Gridded Magnetoresistor Thin films of InSb are prepared either by grinding or by evaporation techniques. Short circuit straps of highly conductive metals are deposited perpendicular to the direction of the supply current flow either by evaporation or by galvanic growth into pre-prepared grooves [8], [91. The basic resistance R, can be determined to a reasonable degree by controlling the crosssection and length of the MR system, Figure 3-13 showing a possible configuration. Due to the high production effort required and the relatively small scale of the desired effect, the short circuiting process is restricted to the surface. This type of MR has been of little significance and as a result will not be considered further.

Figure 3-W. Connection example of a gridded magnetoresistor.

3.4.2.2.2 Magnetoresistors with NiSb Needles Using a process developed by Weiss and Wilhelm [76], highly conductive NiSb needles are built into the polycrystalline InSb rod. Formally, 1.8% mass fraction NiSb is added to the InSb rod which is then remelted far above the InSb melting point. At this point an eutectic exists, and on recrystallization of this eutectic the NiSb forms as long thin needles of approximately 1 pm diameter. As the growth of the needles extends perpendicular to the liquidholid phase boundary, a homogeneous distribution of needles is produced parallel to the axis of the bar by a specially designed temperature profile. The conductivity of NiSb is more than two orders of magnitude greater than that of InSb at room temperature and as such produces a very good short-circuiting effect. The average length of the needles is about 50 pm and they are separated by about 5 10 pm, so that throughout the entire cross section the resulting I/w ratio is about 50.2. Figure 3-14

66

3 Magnetogalvanic Sensors

a

b

c

Figure 3-14. Cross-section photograph of the InSb/NiSb eutectic a) parallel to needle direction, and b) perpendicular to needle direction; c) current path through the InSb/NiSb eutectic under the influence of a magnetic field directed into the plane of the page.

shows a cross-sectional view of the material parallel and perpendicular to the direction of the NiSb needles.

3.4.2.3 Construction of Magnetoresistors with NiSb Needles The bar of semiconductor material is sliced parallel to the NiSb needles, and the wafers are subsequently reduced to a thickness of 25 pm. In order to produce a resistance which is of practical value, the resistors are etched with a meander path using photolithography and acidetching processes. Some examples of this are shown in Figure 3-15. ,

Figure 3-15. Layout and contact pad examples of meander paths.

Indium is galvanically deposited onto the contact areas, the resistance meander is glued onto a soft iron or ceramic carrier and wire contacts are soft soldered onto the pads. Figure 3-16 shows the configuration of such a system. The systems are then covered in lacquer in order to provide some protection.

Figure 3-16. Layout and connection example of a magnetoresistor on a carrier using leadwires as connectors.

3.4 Magnetoresistors

67

In a newly developed production process the semiconductor wafers are coated with an insulating layer and bonded to a large ferrite substrate. The resistor meander paths are then produced by a similar photolith/etch process as before after which the chips can be separated by dicing on a wafer saw. The contacts are made using a modified impulse solder process whereby the InSb/NiSb resistance meanders are bonded directly to the Micropack frame. A ferrite system and a complete Micropack package are shown in Figure 3-17. The system is protected from mechanical damage by a protective lacquer, as above. Using special high temperature adhesives and lacquers and also pure tin solder contacts, the Micropack component can be implemented at operating temperatures up to 180°C [77].

Figure 3-17. Layout and connection example of a magnetoresistor on a ferrite substrate using Micropack as the connector.

3.4.3 Properties of Magnetoresistors R , is the basic resistance at B = 0 and is determined by the geometry and conductivity of the system. The cross-section of the resistance paths is constant with a width of 80 pm and a thickness of 25 pm. The desired resistance is obtained by varying the length of the resistor (see Figure 3-15). The conductivity of InSb can be varied by adjusting the doping level. In practice three doping levels have found use [78, 71:

o o o

200 (C2 cm)-' 550 (a cm)-' = 800 (C2 cm)-'

=

=

-

undoped n = 2 loz2m - 3 D-type Te-doped n = 6 . loz2m - 3 Ltype Te-doped n = 2 . loz3m - 3 N-type

R , is the resistance of the element when it is subjected to a magnetic field. With small magnetic fields it takes a quadratic form (3-67) and at larger magnetic fields it is almost linear as defined by Equation (3-69). At increasing levels of doping the specific resistance and Hall mobility pH decrease, as can be seen in Figure 3-18, and this is manifested as a decrease in the sensitivity of the sensor. a is the temperature coefficient of the InSb which in its undoped form shows intrinsic conductivity at room temperature, and hence shows a very strong temperature coefficient of resistance of approximately - 2%/K. Increasing the levels of doping causes the point of tran-

68

3 Magnetogalvanic Sensors

Figure 3-18. The magnetic field dependence of the normalized resistance R,/R, of magnetoresistors in the InSb/NiSb eutectic for three different doping grades.

B-

sition to intrinsic conductivity to be raised to a higher temperature, although it simultaneously gives rise to a reduction in the magnetic field dependence as shown in Figure 3-19.

R

1

2 103

e d 5 n *

.D

2

LL

10'

5 2'

-20

I

0

I

20

1

I

40 60 Temperature 8

1

80

1

I

100 'C 120

Figure 3-19. The temperature dependence of the resistance of a magnetoresistor in the InSb/NiSb eutectic for two standard doping grades (D and N) shown with B = OT a n d B = 1T.

3.4.4 Differential Magnetoresistors

3.4.4.1 Magnetic Biasing The temperature dependence of InSb/NiSb magnetoresistors can be compensated for to a greater extent by placing them in a differential configuration. Differential sensors are described in [85, 86, 871. The magnetoresistors are arranged in pairs with a definite separation so that the field gradient produces a difference in their resistances which, when the arrangement is completed into a Wheatstone-bridge circuit, can be picked off as a voltage (Figure 3-20). The error arising from the asymmetry of the two resistors R , , R, when uninfluenced

69

3.4 Magnetoresistors

Figure 3-20. Signal conditioning of a differential magnetoresistor using a Wheatstone bridge arrangement; R , , R, : magnetoresistors, R,, R,: fixed resistors, Ui,: operating voltage, U,,,:

R1

output voltage; M = R 1 - R2 100%: middle symmetry. ~

ov

R,

by an external magnetic field gradient is called the middle symmetry A4 and shows up as an offset voltage U, in the bridge output. The output voltage Uo,,of a differential configuration of the type shown in Figure 3-20, depends not only on the magnitude of the effective magnetic field gradient AB but also on the value of the magnetic biasing field Bb due to the strong nonlinear R , characteristic, as shown in Figure 3-21.

Figure 3-21. Control of a biased differential magnetoresistor; B, : magnetic biasing level, A& actuation level, R,: resistance at working point, R , , R,: resistance of the MRs with an actuation of AB. With no actuation the resistances R , = R, = R,.

*

B-

The following is valid for low levels of actuation: B , = Bb

+ AB;

B2 = B,

- AB

dR dB

R,=Rb+AR=Rb+-AB

dR R, = Rb - AR = Rb - dB R,

=

(3-70) (3-71)

AB

R,

(3-72) (3-73)

and as (3-73) can be used to equate the output voltage (3-74) Thus together with (3-71) and (3-72) (3-75)

70

3 Magnetogalvanic Sensors

So then the sensitivity can be defined as: (3-76) The sensitivity Uo,, /AB is proportional to the relative magnetic-resistance change (dR/(R dB)), which itself is dependent on the level of magnetic bias and on the temperature. Figure 3-22 represents the dependence of the relative change in resistance on the level of magnetic biasing, the influencing parameters here being doping level and temperature.

D: 6 = 200 (Run)-’ N: 6 800 (Run)-’

-

1 dR R dB

0

0.2

0.4 Induction B

-

0.6

T

0.8

Figure 3-22. Dependence of the relative magnetic sensitivity on magnetic field at two temperatures and two standard doping grades (D and N).

Using (3-64) and C, = 1 it is possible to calculate the relative change in resistance for small Hall angles: (3-77)

As long as pH B I 0.45, then a proportional increase in the relative resistance change can be recognized, whereas when p H . B s- 1 a reduction proportional to 1/B is noticeable (Figure 3-22). The maximum lying between these values occurs at B i+ l/pH. If the Hall mobility p H is reduced through an increase in temperature or in doping level, then this maximum is shifted to higher field levels. It is necessary to choose a working point as close as possible to the maximum (see Figure 3-22) to produce the highest sensitivity in a differential system, and in order to obtain the smallest temperature dependence it should be subjected to a high level of bias field. The required levels of magnetic field are produced by permanent magnets which influence the magnetoresistors with a homogeneous magnetic field perpendicular to their plane. Rare earth/Cobalt magnets are the preferred biasing magnets, since as a result of their high energy density and small volume they can be used in open magnetic circuits to generate field strengths of 0.2 - 0.4 T on their pole faces. Differential MR systems then, have two advantages in addition to their improved temperature dependence in that the required magnetic bias does not

71

3.5 Other Semiconductor Devices as Magnetic Sensors

reflect itself in the output of the bridge circuit and the sensor therefore only reacts to a magnetic field gradient.

3.4.4.2 Temperature Compensation of Differential Sensors A differential sensor configuration only compensates for the individual magnetoresistors when they are both under the exact same conditions. However, when each MR is experiencing a different level of magnetic field strength then a difference in their temperature coefficients will be noted (Figure 3-22). In the simplest case, the temperature characteristic of the internal resistance itself is used as compensation. Figure 3-23 shows the relevant circuit arrangement for this mode of operation. The operational amplifier equates the output current from the bridge: (3-78) where U , is the open-circuit output voltage and Ri the internal resistance of the bridge. R,R2 R3R4 R. = ‘ R, + R, R, + R, +

(3-79)

R , and R , are independent of temperature, so that the temperature course of Ri is determined only by R , and R , . As the open-circuit output voltage U , and the internal resistance Ri decrease with increasing temperature, the quotient i in Equation (3-78) remains approximately constant. The output voltage U,,, can be stabilized over a defined range by the addition of a compensation resistor R, (Figure 3-23). The optimal value of R , is calculated empirically for the required temperature range and ( R , + R , ) / 2 can be taken as a good starting value for this.

3.5 Other Semiconductor Devices as Magnetic Sensors Generally, all “nonmagnetic” semiconductor devices, such as diodes and transistors, are sensitive to a magnetic field: via the Lorentz force, Equation (3-1), a magnetic field will modify the carrier-transport conditions in these devices and produce changes in their electrical output

72

3 Magnetogalvanic Sensors

characteristics. Normally, these changes are negligible. If, however, the device design and operating conditions are optimized with respect to the magnetic field sensitivity of the device characteristics, some useful magnetic sensors can be obtained. In this section we shall discuss the main operating mechanisms and design features of such devices. Additional details concerning various devices can be found in references [12] and [18].

3.5.1

Magnetodiodes

The operating principle of magnetodiodes is based on a combined galvanomagnetic effect (see Section 3.1) called the magnetoconcentration effect or Suhl effect [17]. It is a combination of three basic phenomena: carrier injection, Hall effect (in the form of carrier deflection, see Section 3.2.1), and surface recombination or generation of carriers. The general structure of a magnetodiode is shown in Figure 3-24. It is a long and thin semiconductor slab doped in such a way that a p-i-n structure along the long axis is formed. The two opposite surfaces of the slab S, and S,, have very different surface recombination velocities s, and s, say s, s,. In operation, the carriers are injected from the n + - and p +-contacts into the i-region, and drift there due to the electric field E along the long axis. If the device is exposed to a magnetic induction B parallel to S, and S, and perpendicular to E, both electrons and holes are deflected towards the same surface, S, or S,. If they are deflected towards the S, surface, their concentration at this surface increases, as does the generation rate, and the conductance between n and p increases. With the Lorentz force acting in the opposite direction, the carriers are deflected towards the S, surface where they recombine, the recombination rate and the resistance increase being roughly proportional to the magnetic induction [56]. +

p-or n - l i )

*

+

Figure 3-24. Basic magnetodiode structure. It is a long and thin p-i-n diode, with both low-recombination (S,) and high-recombination (S,) surfaces. .

I

I

52

In practical realizations, the low-recombination surface is prepared by polishing and surface passivation, for example by growing thermal SiO, on silicon. The high recombination surface can be effected via surface roughness (by grinding) [57], by use of surface crystal defects at the interface with another crystal (silicon-on-sapphire) [58], or by use of a reverse-biased p-n junction, where recombination is replaced by the collection of minority carriers [59]. Typical relative sensitivities of magnetodiodes are about 5 V/mA T at bias currents of 1 mA to 10 mA. Noise characteristics [60] are similar to those of the Hall devices (see Section 3.3.3).

3.5 Other Semiconductor Devices as Magnetic Sensors

73

3.5.2 Magnetotransistors Magnetotransistors are bipolar transistors whose structures and operating conditions are optimized with respect to the magnetic-field sensitivity of the collector current Z, . There are at least four effects which are fundamental to magnetotransistor operation: carrier deflection, injection modulation, modulation of the base-transport factor, and the magnetoconcentration effect. Usually, all these effects coexist, and understanding the operation of a specific magnetotransistor is rather involved. In the following discussion therefore some examples are considered where only a single magnetotransistor effect prevails. A semiconductor structure exhibiting a strong carrier deflection in a magnetic field was proposed originally as a model [61]. Later, a similar device, shown in Figure 3-25, was used as a magnetic sensor [62]. It is a drift-aided lateral double-collector bipolar transistor. Its base region (the large square), an isolated island in a bipolar integrated circuit, is obviously reminiscent of a Hall plate. As a result of the Hall field generated in the base region due to the drift of the majority carriers, the total electric field E in the base region is inclined with respect to the x-axis through a Hall angle of OH,,Equation (3-9). However, the current density vectorj, of the (injected) minority carriers rotates through an additional Hall angle OHp, Equation (3-17), with respect to E. As a result the upper collector C, receives more current than the lower one, the current difference being proportional to the total deflection angle: Mc

=

bHn

+ PHp) BzE

(3-80)

where K is a coefficient and ZE the emitter current.

Figure 3-25. Drift-aided lateral double-collector magnetotransistor. B, and B, are the contacts to the base region (n), E is the emitter, and C, and C, are the collectors.

The same double deflection phenomenon plays a key role in another lateral magnetotransistor devised for the CMOS process [63]. Relative sensitivities IZ;' . 8 Z C / 8 B I of up to 1.5 T were obtained in this device, and recently a relative sensitivity as high as 30 T - I was achieved in a similar structure [64]. Devices where only single deflection takes place generally show more moderate sensitivities of about 0.05 T - I [65, 661. The current-deflection mechanism can also be exploited in split-drain MOS transistors, called MagFETs. By incorporating a complementary Mag FET pair in a CMOS circuit, a sensitivity of 1.2 V/T has been achieved [67]. The injection modulation mechanism of magnetotransistor operation can be better understood with reference to Figure 3-26, which shows the cross-section of a lateral doublecollector magnetotransistor. Consider the Hall voltage generated in the base region between the two points A and B situated close to the emitter sidewalls, opposite to the collectors. The

74

I

3 Magnetogalvanic Sensors

c1

IE

cz

I Figure 3-26. Illustrating the injection-modulation mechanism in a lateral double-collector magnetotransistor. E denotes the emitter, N is the base region and C , and C , are the collectors.

Hall voltage is equal to the line integral over the Hall field along a line AB (see first part of Equation (3-8)). Assuming a very low emitter efficiency, ie, ZE t: ZB , ZE and ZB denoting the emitter and the base currents, respectively, one obtains [68]:

where t denotes the devices thickness (perpendicular to the figure plane). The Hall voltage (Equation (3-81)) produces an asymmetrical emitter-base bias, which leads to asymmetrical injection of the minority carriers. The resulting collector currents are

where I, denotes the collector saturation current, and U the emitter-base bias voltage. The corresponding relative sensitivity at B t: 0 reads

(3-83) The sensitivity is proportional to the emitter current, see Equations (3-81) and (3-82) as long as the device works at low injection levels. At high injection levels, the Hall coefficient of the base region drops (Equation (3-22)), as does the sensitivity. The relative sensitivities of magnetotransistors reported hitherto cover a surprisingly wide range, from 10 - 2 T - I to as high as 30 T - I . However, the high-sensitivity devices tend to require a large bias current not accounted for in the sensitivity definition, so that a fair comparison to other devices is not easy. In addition, low-frequency noise characteristics of some magnetotransistors seem to be superior to that of Hall plates [69]. In all other respects however, (offset, linearity, temperature coefficient), Hall plates are still better than magnetotransistors.

3.5.3 Carrier-Domain Magnetic Sensors A carrier domain in a semiconductor is a region of high nonequilibrium carrier density. It consists of an electron-hole plasma, where the carriers are permanently generated by a suitable mechanism, such as injection over a barrier or impact ionization. The formation of a carrier domain has been demonstrated in bipolar transistors [70], thyristor-like structures [71], and transistor-like structures operating in breakdown mode [72].

3.6 Applications

75

Figure 3-27 shows a vertical four-layer (n-p-n-p) device which can operate as a carrier-domain magnetic sensor [73]. It is a bipolar transistor with split-collector buried n +-contacts, and can be fabricated using bipolar IC technology. In operation, both emitter(1)-base(2) and substrate(4)-collector(3) junctions are forward-biased. Due to the lateral voltage drops, carrier injection occurs in two opposite small spots at the emitter-base and the substrate-collector junctions, and thus, a carrier domain forms which consists of electrons and holes moving in opposite directions. A magnetic field perpendicular to the figure plane produces a displacement of the domain, which in turn causes a change in the currents I, and I p . These variations in the base and collector currents can be interpreted as the sensor output signals. A variation in the current as large as 3 mA/T at 10 mA total current bias has been measured [73].

Figure 3-27. Cross-section of a vertical four-layer carrier-domain magnetic sensor. (1) is the emitter, (2) the base, (3) the collector, (4) the substrate, and the buried n +-regions, together with the two small n +-regions at the top, are the collector contacts.

In circular four-layer [74, 751 and three-layer [72] structures the carrier domain can travel around the circumference of the device, the rotation frequency being proportional to the magnetic field. A drawback of these devices, however, is a large offset: in the four-layer devices, the domain does not rotate unless the magnetic field exceeds a threshold value, which is between 0.1 and 0.4 T, but in the three-layer structure the domain rotates spontaneously even at B = 0. Moreover, these devices require rather large bias currents and are very sensitive to temperature changes.

3.6 Applications 3.6.1 Introduction Galvanomagnetic sensors convert a magnetic field value into an electrical signal. The major application for direct measurement of magnetic-field strength using Hall-effect probes is in instrumentation, and to fulfill the many types of function required of them, their packaging and also internal construction are matched to the necessary criteria. By measuring their magnetic-fields, electrical currents can be measured noninvasively using these devices,

76

3 Magnetogalvanic Sensors

and as a result of the multiplication factor characteristic inherent in Hall-effect generators, they can be used additionally to measure power. By suitable arrangement of the magnetic circuit, small physical movements of permanerlt magnets or of ferromagnetic materials can be detected by galvanomagnetic sensors via the field changes produced. As a result, these components find universal application in noncontact position sensing and are characterized by their reliability, high noise immunity and also their independence of actuating speed (contrary to inductive type sensors). Both areas of application, instrumentation measurement and position sensing, will be described in detail along with examples of practical applications.

3.6.2 Magnetic Measurement 3.6.2.1 Measurement of Magnetic Fields Hall-effect generators are used almost exclusively for the precise measurement of magnetic fields due to their linear and point-symmetrical characteristics. In addition they fulfill thc essential requirements of a small temperature coefficient, small and stable offset voltage as well as good linearity with sufficient sensitivity (see Section 3.3.3). When measuring alternating magnetic fields great care should be taken in the layout of the connection leads so that disruptive inductive components in the output signal are minimized, ie, avoiding loops, or twisted leads. The probes themselves are compensated internally to give a minimum residual component. Hall-effect generators are operated with a constant supply current so that the linear relationship U, B is used (as shown in Equation (3-32)). As the output signal U, of Hall-effect generators can be very small, they are often amplified by accurate voltage amplifiers or instrumentation amplifiers, usually coupled with temperature sensors to compensate for the temperature coefficient. Extensive application directions are given in [7, 8, 50, and 791. As mentioned above the internal construction and also the outer shape of Hall-effect probes are often matched to their use so that, for example, axial probes are constructed to measure axial fields in radial holes, tangential probes, and extremely thin probes for measuring in very small airgaps. Probes are also available which have a small active area so they can be used to give almost point measurements in magnetic fields and others have been developed for low temperature measurements in liquid helium [78].

-

3.6.2.2 Noninvasive Current Measurement Every electric current has an associated magnetic field. Hall-effect sensors are the preferred method for measurement of this magnetic field, since they can obtain a measurement of the current flowing yet remain potentially isolated from the current-carrying circuit. The current waveform is repeated identically in the output voltage of the Hall-effect sensor.

Measuring the tangential field strength of an electrical conductor A simple tangential field measurement produces a linear relationship between the measuring current Z and the magnetic induction B, as there are no nonlinear constituents like, for

3.6 Applications

77

Induction Liner

Figure 3-28. Principle of noninvasive current measurement in a circular conductor by measuring the tangential field strength at a distance r from the center of the conductor.

example, iron cores present. To effect such a measurement, a Hall effect probe is required which has its active area very close to the edge of the package. Figure 3-28 shows an example of a round conductor where:

I = $H*ds.

(3-84)

In a closed loop around the conductor the following is valid: I = H2nr; H = -

I 2nr

(3-85)

and in air: B=pO-

I 2711.

(3-86)

-'

where po is the permeability of vacuum and equals 4n * 10 H m - I . From (3-86) it can be seen that sufficiently large values of B will only be given for large values of I, the advantage of this method of current sensing being the good linearity obtainable in addition to its simple construction. A special application is described in [107].

Direct measurement using a core with an air gap Very large sensitivities can be obtained using a magnetic conductive core around the conductor [88],the sensor being located in an air gap in the core. Using multiple winding, an increased signal level can be obtained, such an arrangement being shown in Figure 3-29. Here:

In = Q H . ds

(3-87)

In = H L B + HFeIFe

(3-88)

where n is the number of windings, I , the mean path length of the iron and 6 the air gap.

78

3 Magnetogalvanic Sensors

Hall sensor

6 Figure 3-29. Arrangement for noninvasive current measurement using an iron core. The current to be measured produces a proportional magnetic field which can be measured in the air gap.

If the influence of stray magnetic fields are neglected then BFe = BFe =

and as: (3-89)

Pr PO

BL6 BL'Fe , then In=-+-

PO

BL =

BL,

(3-90)

Pr Po

PO In

(3-91)

'Fe

6+PI

Wh re B, is the air-gap induction nd p1the p rmeability of the core material. If pr is chosen to be sufficiently large (uI > 1000) then the following approximation can be used.

(3-92) The result of measurements with the arrangement in Figure 3-29 using an air gap of 6 = 1 mm is shown in Figure 3-30.

I

-30

-15

0 1.n

-

I

15

AW

Figure 3-30. Characteristic curve produced by the current measuring arrangement of Figure 3-29, where B = f ( I . n) with an air gap = 1 mm, and where n is the number of turns.

3.6 Applications

19

When large current values are being measured the nonlinear characteristic of the iron core must be taken into account as well as the occurrence of remanence effects. Using ferrite flux concentrators built into the sensor housing, Hall-effect sensors can be produced in GaAs or in InSb with effective air gaps of 6 = 0.2 to 1 mm, typical applications being current measurement probes in the range of 10 A to some kA.

Indirect measurement using the compensation method For very accurate measurements and also for very small measurand currents the compensation method, as represented in Figure 3-31, is employed. The iron core is kept free of induction by injecting a reverse current into the windings n, of the compensation coil. The current I2 required to compensate is then proportional to the measurand current I , . The Hall-effect sensor acts to indicate the null point, ie, B = 0, whereby the null voltage stability of the sensor is the determining parameter in the total accuracy of the measuring arrangement. When the field is zero, then

I , n,

+ I, n,

=

0,

(3-93)

and the output voltage is thus, given by

(3-94) whereby the strongly linear dependence between the measurand current and the output voltage can be seen. Hall-effect sensors in GaAs and InSb are used.

Figure 3-31. Arrangement for indirect noninvasive current measurement using the compensation principle. An iron core as represented in Figure 3-29 is held field free by injecting a current into a compensating coil wound on the core which offsets the field generated by the current being measured. The Hall effect sensor in the air gap serves as a null indicator.

“out

3.6.2.3 Noninvasive Power Measurement It is the multiplicative nature of Hall-effect sensors which is exploited in noninvasive power measurement (3-32). The load current consumption is measured using an arrangement like that shown in 3.6.2.2 with a magnetically soft-iron core. The load voltage is converted into a proportional control current from the AC supply using a transformer (Figure 3-32).

iL

-B

(3-95)

UL

-

(3-96)

‘in

80

3 Magnetogalvanic Sensors

T'

AC net

ure 3-32. Circuit diagram for AC-power measurement using a Hall effect sensor.

"out " PL

so using (3-32): UH

=

R H ii, B -

t

=

cuLi, = cp,

(3-97)

where c is a system constant. The arithmetic mean value is derived in the signal-conditioning circuit, ie, in a low pass filter, so that the disruptive offset voltage u,, of the Hall-effect sensor is eliminated. For resistive loads: u,(t) =

0,cos w t

(3-98)

i L ( t ) = 1, cos w t

uo(t) = UH

=

(3-99)

U0cos a t , then CU,

(t) i, (t)

(3-100)

+ u0 (t)

(3-101)

together with (3-98) through (3-IOO), then cos w t

.

(3-102)

Figure 3-33. Circuit diagram for DC-power measurement using a Hall effect sensor.

3.6 Applications

81

The term oocos w t does not contribute to the arithmetic mean. In reference [lo51 a complete application has been described. In DC systems, the supply current Ii, proportional to the load voltage U, is read directly from a high impedance, eg, impedance convertor, this principle being shown in Figure 3-33.

3.6.3 Noncontact Position Sensing Position sensors based on galvanomagnetic components detect the position of a permanent magnet by a localized measure of its magnetic field strength. To determine the position of a magnetically conductive material (eg, iron, ferrite etc.) the sensor is mounted directly onto a permanent magnet, which generates a constant bias field at the sensor, and by moving the magnetically conducting target within the field, localized changes in the magnetic field are produced which are converted by the sensor into electrical signals, and with suitable output circuitry the signal can then be further processed in analogue or in digital form. In silicon sensors this signal conditioning is integrated monolithically on the same chip (smart sensors). Figure 3-34 is a representation of the various configurations used with their respective output signal forms; a-d show sensors which are actuated by permanent magnets while e-f show those which are magnetically biased and are actuated by magnetically conductive materials. In each case the single and differential sensor configuration is represented. In arrangement a), actuation can take place along two axes. In one case the magnitude of the air gap can be changed by A d or the displacement As. This configuration is suitable for use in conjunction with electronic switching circuits to produce digital position sensors, limit switches etc. Arrangement b) shows the basic principle used in the construction of a brushless DC motor using a diametrically magnetized cylindrically formed permanent magnet, which is described below in more detail. In arrangement c), a linear position sensor with a range of up to 2 mm is shown. The arrangement can be optimized for each application by selecting suitable values for the air gap and the magnet dimensions. The differential arrangement shown in d) produces the same output waveform as in c). Arrangement e), where the sensor is magnetically biased and can therefore be actuated by magnetically conductive target materials, has the inherent disadvantage in both axes of actuation, that the usable nonlinear output signal is much smaller than that produced by the biasing magnetic field. Arrangement f) avoids the disadvantages of arrangement e) and produces an output signal with a linear portion similar to that obtained by c) and d). It is, however, a bit more difficult to realize due to the vertical assembly required. An additional area of application for this type of arrangement besides linear position sensing, is in the detection of cams and gearwheels, eg, in revolution measurement. The output signal which is similar to a sinusoid produced by each geartooth is digitalized as a square wave by a comparator. An example of a closed magnetic circuit is shown in arrangement g). Using a slotted disc as an actuator, one element is alternately short-circuited so that the opposing element effectively becomes field free. When combined with a comparator this arrangement can be used as a digital-output orientation/position indicator.

82

3 Magnetogalvanic Sensors

Arrangement

Preferred sensors

Output signal form

a1

Active area Sensor

s = constant = 0

Permanent magnet

Hall sensor Magnetoresistor

, -

d

5

bI

A,

E; I

-

dI

+ + d = constant

Hall sensor

5

d i constant

Hall sensor Magnetoresistor

Figure 3-34. Galvanomagnetic components for sensing the position of permanent magnets and magnetically conductive materials.

3.6 Applications

Arrangement

Preferred sensors

Output sigaal form

el

1

I

Unut

d = constant

s =constant

Hall sensor Magnetoresistor

d

fl I I I

E L

Magnetically conductive materiai

% d = constant

Hall sensor

Iron core /

Hall sensor

hI

+ d = constant

Hall sensor Magnetoresistor

83

84

3 Magnetogalvanic Sensors

Arrangement h) shows the classical construction used to detect magnetically conductive materials. As a result of its differential construction there is no electrical offset and an additional advantage is that the assembly is also realized with little effort. The output signal corresponds to that of arrangements c), d) and f) described above and the applications are identical to those described in f). When designing magnetic circuits it must always be kept in mind that the magnetic induction of permanent magnets falls off very rapidly with increasing distance from the pole face. For cubic magnets such as Figure 3-35, the relationship for the fall-off in the z-axis is given as follows (this is valid for rare earthkobalt magnets which are recommended for the applications mentioned above) [104]:

(3-103)

where the magnetization M lies in the z-direction.

Z-

Figure 3-35. Cuboid permanent magnet with square pole faces (a . a). The magnetic axis is along the length c.

The characteristic curve for Equation (3-103) is shown in Figure 3-36. The magnet geometry can be fixed for optimal effectiveness by choosing the magnetic length c to be about half as large as the diagonal of the poleface. As Equation (3-103) shows, an increase in the magnetic length will not produce a corresponding increase in magnetic induction since the contribution from magnetic length is approximately proportional to its square root and as such can be regarded as negligible for higher values of length. The strong dependence of the air gap on magnetic induction, which can also be seen from arrangement a) in Figure 3-34 implies that movements perpendicular to the axis of operation are to be avoided. When designing magnetic circuits, the air gap 6 should be kept as small as possible, or flux linking parts such as concentrators shoud be used, to help obtain as large an output signal as possible.

85

3.6 Applications

1 4

0.35 T

0.30 0.25 0.20 0.15

0 .lo 0.05

Figure 3-36. Fall-off in magnetic induction found with increasing distance z from the pole face of a cuboid magnet of SmCo (Vacomax) as represented in Equation (3-103).

0

mm

5

10

z-

Even for analogue position indication, nonlinear output signals are often used, if they are well reproducible. With modern electronics and with the availability of microprocessors for signal processing, such characteristics can be linearized very easily, hence the usable range of the galvanomagnetic position sensor can be significantly increased, eg, by using the arrangement in Figure 3-34a. A brief study of the collection of arrangements in Figure 3-34 will show that a great many of the configurations can be realized using either Hall-effect or MR sensors. Hall-effect sensors can be completed in the form of a differential system, as shown by Figure 3-37, and such components are also currently available. Iin

0

Figure 3-37. Connection of two Hall-effect sensors for use as a differential sensor.

The following discussion aims to help decide which sensor type is best suited to a given application. MR sensors of an InSb/NiSb eutectic mixture (see Section 3.4) connected as differential sensors have the advantage that they produce a large output signal when operated in the steep

86

3 Magnetogalvanic Sensors

portion of their characteristic curve (Figure 3-21). Differential MR sensors are therefore usually offered with a built-in permanent magnet. Their major applications are in digital position detection, e. g. presence indicators, limit switches, revolution/speed detectors, and also incremental angular encoders using magnetically conductive gearwheels or cams, in arrangements such as those shown in Figure 3-34h. The high temperature package (Micropack) designed for use up to +18O"C has already been described in 3.4.2 and plastic package devices with built-in permanent magnets are usable up to +150"C. Hall-effect sensors can be produced very economically using standard semiconductor processes such as epitaxy, ion implantation, or evaporation, and together with the choice of available materials a whole new area of applications can be addressed. Although silicon is not an ideal material in which to produce galvanomagnetic effects it can be integrated monolithically with signal conditioning electronics to give analogue or digital outputs [12, 14-16, 18, 94, 951. Gallium arsenide with its large bandgap of Eg = 1.43 eV presents itself as an ideal candidate for use up to temperatures in excess of 200°C and the relatively low output signal can be amplified by building a magnetic flux concentrator into the package [loll. Indium antimonide can be deposited in very thin layers onto ferrite or ceramic substrates by evaporation, or can be worked from bulk material by grinding. Very high output signals can be achieved with small magnetic fields if the active material is sandwiched between a ferrite substrate and a ferrite flux concentrator. Hall-effect sensors offer the user the opportunity of realizing a cost-effective sensor system for his individual 'use, simply by using a suitable arrangement of magnetic circuit (Figure 3-34). Due to their good stability over temperature (ie, GaAs) and their linear characteristics, Hall-effect sensors are amongst the most suitable components available for analogue position detection, and in addition to simple detection of position, other physical parameters such as force, pressure, flow, torque, acceleration etc. can be measured as a function of continuous displacement sensing. Further details of these are given in [89-92, 1061. A summary of the range of the magnetic induction for galvanomagnetic semiconductor sensors is given in Table 3-2. lsble 3-2. Range of the magnetic induction for semiconductor sensors. Magnetic induction B

Hall-effect sensors - measurement applications, open loop: with linearization:

-

0 0

position sensors with biasing, open magnetic circuit: bias : levels of actuation closed magnetic circuit: bias : levels of actuation

0.1 0 0.3 0

Magnetoresistors bias levels of actuation The detection limit (SNR = 1) for Af = 1 Hz: Bmi, s

0.2 0

T

... 1 T

... > 2 T

... 0.4 T

... 0.1 T

... 0.8 T

... 0.3 T ... 0.4 T ... 0.2 T

3.6 Applications

81

3.6.4 Selected Examples The following is a more detailed description of four of the applications mentioned earlier.

3.6.4.1 Revolution Counter Using a Differential MR Sensor The principle of the differential MR sensor has been described already in Section 3.4.4. Using the arrangement shown in Figure 3-34 h, magnetically soft gearwheels can be used to produce output signals as shown in Figure 3-38. In the construction of these differential sensors two magnetoresistors are mounted onto a magnetically conductive flux linking base of ferrite or soft magnetic alloys. The magnetic bias field is delivered by a rare earthkobalt permanent magnet. Magnetic materials for sensors have already been described in Chapter 1.5. If the sensor is completed into a Wheatstone bridge configuration such as in Figure 3-20 and actuated by a ferromagnetic gearwheel then a signal of the type in Figure 3-38 would be generated.

Gearwheel

material

$,_I

',>I

Permanent magnet Position:

I

I1

I11

"out

Position:

I

I1

I11

Figure 3-38. Sensing of a gearwheel using a differential MR sensor for revolution sensing or angular rotation measurement, showing also the corresponding output waveform.

The optimal signal amplitude is achieved when the intercenter separation x of the individual MRs corresponds to exactly half of the tooth period I (maximum value of AB). At present sensors are available with intercenter separations of x = 0.4 mm to x = 2.4 mm. However, the exact dimension of x / l = 0.5 is not always required, for a mismatch of up to

88

3 Magnetogalvanic Sensors

25% produces a reduction in the maximum obtainable signal of only 10%. Note that in cases

where x / l c 0.5, sharp tooth flanks should be used. The sinusoidal output waveform from the bridge is usually digitized by a comparator, either at the zero crossover or at a predetermined switching level, and the impulses are counted over a set time period. Figure 3-39 shows the principle block diagram of a suitable signal conditioning circuit. If two differential sensors phase shifted by 90" to each other are used then it is also possible to determine the sense of the rotation by combining the output signals. Rotation sensors based on MRs for automotive applications are also described in [93].

I

I

Figure 3-39. Block diagram showing the output signal conditioning of a differential MR sensor for revolution sensing as shown in Figure 3-38. The sinusoidal output is digitized, the impulses counted over time, and the output displayed numerically.

3.6.4.2 Noncontact Interrupter for Automotive Use, based on a Silicon Hall-Effect IC The potential for silicon to be monolithically integrated gives rise to the interesting possibility of being able to produce smart sensors. Using a Hall-effect sensor as the basic element, intelligent sensors in the form of magnetic switches [94] have been produced, some with additional temperature compensation or with analogue outputs [95], see also [96]. Digital sensors which latch on reaching a predetermined flux level and which have built-in hysteresis so that they release at a lower flux level are especially suitable for use in position detection, eg, as noncontact switches or as wear-free contact breaker points in automotive applications. The block diagram in Figure 3-40 shows the separate units which are required: constant voltage supply, Hall-effect sensor, amplifier, Schmitt trigger, output stage with open collector and protection circuitry. The Hall-effect IC is packaged together with a permanent magnet into a closed magnetic circuit as shown in Figure 3-34g, and is used extensively in automotive applications as a contact breaker (magnetic vane switch [97]). The sensor is actuated by a magnetically conductive vane with four slots which is passed through the air gap of the magnetic circuit. The switching

89

3.6 Applications

I I I I

I

-

Protection Us I t

circuit

- Regulator -

I

Hall genera tor

-

-

Protection circuit

-

-

I 1 L---,--------------------------------------~

0

1output I I

, t

I I

I I

signal of the sensor is then distributed at the required ignition point to each of the four spark plugs in the cylinders. Figure 3-41 is a schematic representation of this device. One arm of the core comprises the permanent magnet the other arm contains the digital Hall IC, and the actuating vane moves in between the two arms. When there is no vane present the Hall IC sees the maximum undisturbed magnetic-field level and its open collector output is conducting (low), Figure 3-41 a. Once the vane is inserted into the magnetic circuit, the circuit is effectively short-circuited and the arm of the magnetic circuit containing the Hall IC becomes field free, at which point its output is nonconducting (high), Figure 3-41 b. Due to the mode of operation the sensor still produces sharp edges even at low speeds of operation.

Package Hall

IC

Magnetically conductive material

b

Perrnan'ent magnet

Figure 3-41. Functional representation of a magnetic vane switch, a) without, b) with the actuating vane.

3.6.4.3

Brushless DC Motors

A brushless DC motor is based on a diametrically magnetized permanent-magnet rotor with coils in the stator [98, 991. The position of the rotor relative to the stator coils is detected by two Hall-effect sensors, and the four stator coils are then powered via the resultant Hall-effect

90

3 Magnetogalvanic Sensors

voltages from the sensors, so that a torque is produced by the magnetic field of the rotor. As a result of the polarity dependence of the Hall voltage, two Hall-effect sensors, displaced through 90°, suffice to control four stator coils. The operation principle is represented in Figure 3-42.

Control range

I

I

I

I

I

*

Figure 3-42. Representation of a brushless electronic motor using Hall-effect sensors. W, . . . W, are the stator coils, H , , H, are Hall-effect sensors, T, .. . T, are transistors, and U2... U8are typical characteristics of the control voltages for the coils belonging to the Hall voltages.

The two Hall-effect sensors are located either directly in the air gap between rotor and stator and are acted on directly by the magnetic field of the permanent-magnet rotor, or they are located outside the motor windings, eg, on a printed circuit board (PCB), and are acted upon by a control magnet mounted directly onto the motor shaft. By using Hall-effect sensors, smooth current change over in the windings is possible as the stator fields are reduced proportionally; this gives these motors good rotational characteristics. In noncritical cases where digital change over is sufficient, silicon Hall-effect ICs can be used without seriously affecting the rotational behaviour. At present Hall-effect sensors based on InSb or GaAs are being used. The advantage of these brushless motors lies in their long life, which is limited only by the lifetime of the bearings. Also worth mentioning is their low noise level, the absence of disruptive brush sparking and their good controllability. In addition to the obvious industrial applications, eg, in drive units, this form of electric motor is also used in commercial equipment, eg, HiFi and video machines etc.

3.6.4.4 Pressure Can Bused on Hall-Effect Sensing In a pressure can a Hall-effect sensor is actuated by a permanent magnet mounted onto a pressure sensitive diaphragm. The diaphragm flexes under pressure and thereby moves the magnet relative to the Hall-effect sensor, so that a change in pressure is effectively measured through a change in position. This application is described by the arrangements shown in Figure 3-34a and c. The characteristic curve W H = f(p) does not need to be linear but must be reproducible to the required level. Using the microelectronics that is currently available, it

3.7 Conclusions

91

is a relatively simple procedure to linearize a curved output characteristic through signal conditioning. The principle of the pressure can is shown in Figure 3-43. Electromechanical pressure sensing cans using Hall-effect sensors are a cost effective alternative to piezoresistive silicon pressure sensors, especially for automotive applications [loo]. The mechanical diaphragm affords complete separation between the media being measured and the electronic circuitry. At present Hall-effect sensors in GaAs are being used for this application.

Figure 3-43. Construction of a pressuremeasuring can based on a mechanical diaphragm moving a permanent magnet over the face of a Hall-effect sensor. The output waveform is also shown.

/

P e r m a n e n t magnet H a l l sensor

3.7 Conclusions Although the Hall effect and the magnetoresistive effect have been known for over 100 years, it has only been since the discovery of III/V semiconductors in 1953 that they have been of any commercial significance. Galvanomagnetic devices in InSb and InAs were produced, and after the discovery of the InSb/NiSb eutectic in 1961 whereby NiSb short-circuit needles can be grown in a InSb base crystal, a breakthrough into semiconductor magnetoresistors was achieved. Through the rapid development of integration techniques since 1968, silicon has also presented itself as an interesting material for Hall-effect IC sensors, and since 1980 GaAs has been added to the palette of useful materials. A wide range of applications for these devices has been built up on this basis and they have, as yet, not been fully exploited. With newer semiconductor/technologies available, cost effective sensors can be produced which meet the stringent requirements of high operating temperature, high sensitivity with small and stable offsets, and high reliability. In addition, they can also be integrated with intelligent signal conditioning. Magnetoresistors of InSb/NiSb eutetic, which have already proved themselves to be very reliable, are being developed further by new production techniques in which ferrite substrates are used to rationalize the process steps. In addition, the electrical and mechanical contact to the sensor is achieved through a copper/Kapton “Micropack” package which allows very high operating temperatures. A new high demand application for example, is in the automotive industry where it is employed as a wheel speed sensor in anti-lock braking systems with an operating temperature up to 180°C. The flexibility of the Micropack-packaged component is further demonstrated in that simply by changing the photomask sets the layout of the sensor can be adapted in intercenter

92

3 Magnetogalvanic Sensors

spacing, in basic resistance, and in geometry to match a number of applications, hence double differential systems for the detection of the sense of rotation in incremental linear and angular encoders can also be produced. A further advantage of the Micropack package is the extremely flat package outline which allows operation in very small air gaps allowing high resolution and high output-signal amplitude to be achieved. Future Hall-effect sensors for measurement and position sensing will, in addition to having small offsets and stable, linear output signals, offer the user an output signal suitable conditioned by integrated electronics. Such “smart sensors” will either offer a temperature compensated analogue signal or a digitized signal with stable switching levels. The greatest opportunities in this area lie with silicon. Hall-effect generators, magnetic transistors and magnetic diodes then, can all be combined together with electronics; Hall-effect arrays would also be possible as would multi-dimensional sensor systems, however, the maximum operating temperature sets the boundaries for silicon. GaAs is the ideal material for high temperature applications (as the intrinsic conductivity starts at over 400°C).Elementary sensors are being produced at present by ion implantation in semi-isolating substrates [loll or through epitaxial growth. Future developments will provide higher output signals, and sensors are already available in which a ferrite concentrator is built into the housing which acts to increase the field level at the active area. At present there is world-wide activity in development laboratories aiming to produce a monolithically integrated GaAs Hall-effect IC with analogue and digital outputs [102, 1031. The major application areas for such “smart sensors” in GaAs lie in the automotive industry due to their potentially high operating temperature range. Hall-effect sensors in InSb are produced by evaporation or by grinding from bulk on ferrite substrates, and in addition, a magnetic concentrator can be mounted onto the active area. As well as trying to optimize evaporation technology, other technologies are being investigated to facilitate the production of thin InSb films. The priority requirements being placed on the new generation of Hall-effect chips then, must be: high sensitivity, small offset, high operating temperature, good long term stability, good thermal stability, high reliability and also the ability to be integrated. Microelectronics and modern semiconductor technology already play a strong role in helping to attain the required electrical performance of sensors, but an increasingly important role is being taken by the packaging. This must be capable of withstanding harsh environments and a resistance to high temperatures, mechanical robustness and resistance to chemicals etc.; and yet the physical outline must also be considered with requirements for a flat package for use in small air gaps, the overall size to be minimal but still be user friendly and yet still afford a reliable assembly method, eg, SMD (surface mount device).

3.8 References [l] Hall, E. H., “On a new action of the magnet on electric current”, Am. . l Math. 2 (1879) 287-292. [2] Thomson, W., “On the effects of magnetisation on the electric conductivity of metals”, Philos. Trans. R. Soc. London A146 (1856) 736-751.

3.8 References

93

[31 Putley, E. H., The Hall Effect and Semiconductor Physics, New York: Dover Publishers, 1960. [41 Beer, A. C., Galvanomagnetic effects in semiconductors, Solid State Phys. Suppl. 4 (1963). [51 Pearson, G. L., “A magnetic Field strength meter employing the Hall effect in germanium”, Rev. Sci. Instrum. 19 (1948) 263-265. [6] Welker, H., “Uber neue Halbleiter-Verbindungen”, Z. Naturforsch. A7 (1952) 744-749. [7] Kuhrt, F., Lippmann, H. J., Hallgeneratoren; Berlin: Springer Verlag, 1968. 181 Weiss, H., Physik und Anwendung galvanomagnetischer Bauelemente, Braunschweig, FRG: F. Vieweg & Sohn, 1969; or: Weiss, H., Structure and Applications of Galvanomagnetic Devices, Oxford: Pergamon Press, 1969. [91 Wieder, H. H., Hall Generators and Magnetoresistors, London: Pion, 1971. 1101 Middelhoek, S., “The sensor lag: a threat to the electronics industry”, in: Solid State Devices 1982, Goetsberger, A., Zerbst, M. (eds.); Weinheim: Physik Verlag, 1983, pp. 73-95. [Ill Middelhoek, S., Hoogerwerf, A. C., “Smart sensors: when and where”, Sens. Actuators 8 (1985) 39-48. [12] Baltes, H. P., PopoviC, R. S., “Integrated semiconductor magnetic field sensors”, Proc. IEEE 74 (1986) 1107-1132. [13] Gallagher, R. C., Corak, W. S., “A metaloxide-semiconductor (MOS) Hall element”, Solid-state Electron. 9 (1966) 571-580. [14] Bosch, G . , “A Hall device in an integrated circuit”, Solid-State Electron. ll (1968) 712-714. [15] Maupin, J. T., Geske, M. L., “The Hall effect in silicon circuits”, in: The Hall Effect and its Applications, Chien, C. L., Westgate, C. R. (eds.); New York: Plenum Press 1980, pp. 421-445. [I61 Randhawa, G. S., “Monolithic integrated Hall devices in silicon circuits”, Microelectron. X 12 (1981) 24-29. [17] Suhl, H., Shockley, W., “Concentrating holes and electrons by magnetic fields”, Phys. Rev. 75 (1949) 1617-1618. [18] Kordic, S., “Integrated silicon magnetic-field sensors”, Sens. Actuators 10 (1986) 347-378. [19] Kireev, P. S., Semiconductor Physics; Moscow, USSR: Visshaia Shkola, 1969, Chap. 4 (in Russian); or: Kirejew, P. S., Physik der Halbleiter, Berlin, DDR: Akademie-Verlag, 1974, Chap. 4. [20] Madelung, O., Introduction to Solid State Theory, Berlin: Springer Verlag, 1978, Chap. 4. [21] Seeger, K., Semiconductor Physics, Berlin: Springer Verlag, 1982, Chaps. 4, 7, and 8. [22] Beer, A. C., “The Hall effect and related phenomena”, Solid-State Electron. 9 (1966) 339-351. [23] Beer, A. C., “Hall effect and beauty and challenges of science”, in: The Hall Effect and its Applications, Chien, C. L., Westgate, C. R. (eds.); New York: Plenum Press, 1980, pp. 229-338. [24] Long, D., Tufte, 0. N., “The Hall effect in heavily doped semiconductors”, in: The Hall Effect and its Applications, Chien, C. L., Westgate, C. R. (eds.); New York: Plenum Press, 1980, pp. 339-354. [25] Allgaier, R. S., “Some general input-output rules governing Hall coefficient behavior”, in: The Hall Effect and its Applications, Chien, C. L., Westgate, C. R. (eds.); New York: Plenum Press, 1980, pp. 375-391. [26] Sze, S. M., Physics of Semiconductor Devices, New York: Wiley, 1981, Chaps. 1 and 2. [27] PopoviC, R. S., HBlg, B., “Nonlinearity in Hall devices and its compensation”, Solid-state Electron. 31 (1988) 1681-1688. [28] Norton, P., Braggins, T., Levinstein, H., “Impurity and lattice scattering parameters as determined from Hall and mobility analysis in n-type silicon”, Phys. Rev. BS (1973) 5632-5653. [29] “Semiconductors” in: Lundolt-Bdrnstein, Numerical Data and Functional Relationship in Science and Technology Vol. 111/17a, Berlin: Springer Verlag, 1982, pp. 380-381, and ref. therein. [30] “Semiconductors” in: Landoft-Bdmstein, Numerical Data and Functional Relationship in Science and Technology Vol. 111/17a, Berlin: Springer Verlag, 1982, pp. 532-535. [31] HSilg, B., “Piezo-Hall coefficients of n-type silicon”, X Appl. Phys. 64 (1988) 276-282. [32] Corbino, 0. M., “Elektromagnetische Effekte, die von der Verzerrung herriihren, welche ein Feld an der Bahn der Ionen in Metallen hervorbringt”, Phys. Z. 12 (1911) 561.

94

3 Magnetogalvanic Sensors

[33] Putley, E.H., The Hall Effect and Semiconductor Physics, New York: Dover Publishers, 1960,p. 49. [34]Wick, R. F., “Solution of the field problem of the germanium gyrator”, J. Appl. Phys. 25 (1954) 741-756. [35]PopoviC, R. S., “The vertical Hall-effect device”, IEEE Electron. Device Lett. EDG5 (1984) 357-358. [36]Hoesler, J., Lippmann, H. J., “Hallgeneratoren mit kleinem Linearisierungsfehler”, Solid-state Electron. ll (1968) 173-182. [37]Lippmann, H. J., Kuhrt, F., “Der GeometrieeinfluB auf den Hall-Effekt bei rechteckigen Halbleiterplatten”, Z. Naturforsch. U a (1958)474-483. [38]Haeusler, J., “Die Geometriefunktion vierelektrodiger Hallgeneratoren”, Arch. Elektrotechn. (Berlin) 52, (1968) 11 - 19. [39]Versnel, W., “Analysis of a circular Hall plate with equal finite contacts”, Solid-state Electron. 24 (1981)63-68. [40]Versnel, W., “Analysis of symmetrical Hall plates with finite contacts”, J. Appl. Phys. 52 (1981) 4659-4666. [41] Versnel, W., “The geometrical correction factor for a rectangular Hall plate”, J. Appl. Phys. 53 (1982)4980-4986. [42]Mey, G. de, “Potential calculations in Hall plates”, in: Advances in Electronics and Electron Physics Vol. 61, P. W. Hawkes (ed.); New York: Academic Press, 1983, pp. 1-61, and ref. therein. [43]Thanailakis, A., Cohen, E., ,,Epitaxial gallium aresenide as Hall element”, Solid-state Electron. U (1969)997-1000. [44]Sugiyama, Y., Taguchi, T., Tacano, M., “Two-dimensional electron gas magnetic field sensor”, Transducers 87 - The 4th. International Conj on Solid-state Sensors and Actuators; Tokyo, Japan, 1987: Digest of Technical Papers, pp. 547-550. [45]Kanayama, T., Oasa, M., Hiroshima, H., Komuro, M., “A quarter-micron Hall sensor fabricated with maskless ion implantation”, Transducers 87 (see ref. 44), pp. 532-535. [46]Maenaka, K., Ohgusu, T., Ishida, M., Nakamura, T., “Novel vertical Hall cells in standard bipolar technology”, Electron. Lett. 23 (1987) 1104-1105. [47]Roumenin, C. S., “Parallel-field triple Hall device”, Dokl. Bolg. Akad. Nauk 39 (1986)65-68. [48]PopoviC, R. S., “Nonlinearity in integrated Hall devices and its compensation”, Transducers87 (see ref. 44), pp. 539-542. [49]Hara, T. T., Mihara, M., Toyoda, N., Zama, M., “Highly linear GaAs Hall devices fabricated by ion implantation”, IEEE Trans. Electron Devices ED-29 (1982)78-82. [50]Kleinpenning, T. G. M., “Design of an ac micro-gauss sensor”, Sens. Actuators 4 (1983)3-9. [51] PopoviC, R. S., “A CMOS Hall effect integrated circuit”, in: 12th Yugoslav ConJ on Microelectronics, MIEL 84; Nis, Yugoslavia, 1984, Vol. 1, 299-307. [52]Kordic, S., Offset reduction and three-dimensionalfield sensing with magnetotransistors, Delft, NL: Delft University of Technology, 1987 (PhD Dissertation). [53]Daniil, P., Cohen, E., “Low field Hall effect magnetometry”, J. Appl. Phys. 53 (1982)8257-8259. [54]“Improved Hall devices find new uses, orthogonal coupling yields sensitive products with reduced voltage offsets and low drift”. Electronics Week, Apr. 29, (1985)59-61. [55]Kordic, S.,Zieren, V., Middelhoek, S . , “A novel method for reducing the offset of magnetic field sensors”, Actuators 4 (1983)55-61. [56]Cristoloveanu, S., “L‘effet magnetodiode et son application aux capteurs magnCtists de haute sensibilite”, Onde Electr. 59 (1979)68-74. 1571 Stafeev, V. I., Karakushan, E. I., Magnetodiodes (in Russian); Moscow, USSR: Science Press, 1975. [58]Lutes, 0.S.,Nussbaum, P. S., Aadland, 0. S., “Sensitivity limits in SOS magnetodiodes”, IEEE Trans. Electron Devices ED-27 (1980)2156-2157. [59]PopoviC, R. S.,Baltes, H. P., Rudolf, F., “An integrated silicon magnetic field sensor using the magnetodiode principle”, IEEE Trans. Electron Devices Ed-31 (1984)286-291.

3.8 References

95

[60] Chovet, A., Cristooveanu, S., Mohaghegh, A,, Dandache, A., “Noise limitations of magnetodiodes”, Sens. Actuators 4 (1983) 147-153. [61] Buehler, M. G., Pensak, L., “Minority carrier Hall mobility”, Solid-state Electron. 7 (1964) 431 -438. [62] Davies, L. W., Wells, M. S., “Magnetotransistor incorporated in a bipolar IC”, in: Proc. ZCMCST Sidney, Australia, 1970, pp. 34-43. [63] PopoviC, R. S., Widmer, R., “Magnetotransistor in CMOS technology”, IEEE Trans. Electron Devices ED-33 (1986) 1334-1340. [64] Ristic, L., Smy, T.,Baltes, H. P., Filanovsky, I., “Suppressed sidewall injection magnetotransistor in CMOS technology”, Transducer 87 (see ref. 44), 543-546. [65] Flynn, J. B., “Silicon depletion layer magnetometer“, 1 Appl. Phys. 41 (1970) 2750-2751. [66] Zieren, V., Duyndam, B. P. M., “Magnetic-field-sensitive multicollector n-p-n transistors”, IEEE Trans. Electron Devices Ed-19 (1982) 83-90. [67] PopoviC R. S., Baltes, H. P., “A CMOS magnetic field sensor”, ZEEE 1 Solid-state Circuits SC-18 (1983) 426-428. [68] PopoviC R. S., Baltes, H. P., “Dual-collector magnetotransistor optimized with respect to injection modulation”, Sens. Actuators 4 (1983) 155- 163. [69] PopoviC, R. S., Widmer, R., “Sensitivity and noise of a lateral bipolar magnetotransistor in CMOS technology”, in: Tech. Dig. Int. Electron Devices Meet., Dec. 1984, pp. 568-571. [70] Gilbert, B., “New planar distributed devices based on a domain principle”, in: IEEE ISSCC Tech. Dig., 1971, p. 166. [71] Persky, G., Bartelink, D. J., “Controlled current filaments in PNIPN structures with application to magnetic-field detection”, Bell Syst. Tech. J. 53 (1974) 467-502. [72] PopoviC, R. S., Baltes, H. P., “A new carrier-domain magnetometer”, Sens. Actuators 4 (1983) 229-236. [73] Goicolea, J. I., Muller, R. S., Smith, J. E., “Highly sensitive silicon carrier domain magnetometer”, Sens. Actuators 5 (1984) 147-167. [74] Gilbert, B., “Novel magnetic-field sensors using carrier-domain rotation: proposed device design”, Electron. Lett. 12 (1976) 608-610. [75] Manley, M. H., Bloodworth, G. G., “Novel magnetic-field sensors using carrier-domain rotation: Operation and practical performance”, Electron. Lett. 12 (1976) 610-611. [76] Weiss, H., Wilhelm, M., “Indiumantimonid mit gerichtet eingebauten elektrisch gut leitenden Einschliissen: System InSb/NiSb”, Z. Phys. 176 (1963) 399-408. [77] Heidenreich, W., Lachmann, D., “Magnetik in der MeRtechnik”, VDI/VDO GMA Bericht l3 (1987) 102- 106. [78] Datenbuch Magne~eldhalbleite~ Siemens, 1982. [79] Borke, U. von, Cuno, H. H., Feldplatten und Hallgeneratoren, Siemens AG Verlag, 1985. [80] Weiss, H., “Feldplatten - magnetisch steuerbare Widerstande”, Elektronische Zeitschriff 17 (1965) 289-293. [81] Hennig, G., Die Feldplatte, Eigenschaften und Anwendung”, Elektronik (Munich) (1965) 225-229. [82] Heywang, W., Sensorik, Halbleiter-Elektronik 17; Heidelberg: Springer Verlag, 1984, pp. 76- 111. [83] Lippmann, H. J., Kuhrt, F., ,,Der GeometrieeinfluR auf den Hall-Effekt bei rechteckigen Halbleiterplatten“, 2. Naturforsch. 13a (1958) 462-474. [84] Wein, H., Welker, H., “Zur transversalen magnetischen Widerstandsanderung von InSb”, 2.Phys. l38 (1954) 322-329. [85] Borcke, U. von, “Feldplatten-Differentialfiihler FP 210”, Siemens Bauteile-Information 10 (1972) 129- 132. [86] Cuno, H., H., “Einfache Berechnung von Feldplattendaten in Abhangigkeit vom Magnetfeld und Temperatur”, Siemens Bauteile-Report 14 (1976) 89-93. [87] Borcke, U. von, “Feldplattenfiihler FP 212 L loo”, Bauelemente der Elektronik 9 (1977) 100-106.

96

3 Magnetogalvanic Sensors

[88] Kuhrt, F., Maaz, K., “Messung hoher Gleichstrdme mit Hallgeneratoren”, Elektrotechn. Z. 77 (1956) 487-490. [89] Heidenreich, W., Kuny, W., “Magnetfeldempfindliche Halbleiter-Positionssensoren; Anwendung, Auswahl und Beispiele, praktische Anwendungsschaltungen”, Elektronik Industrie (1985) 46-52 and 112-118. [go] Teichmann, W., Flossmann, W., “Hallgeneratoren und Feldplatten”, Elektronik (Munich), (1983) 102- 112. [91] Kuhrt, F., “New Hall generator applications”, Solid-State Electron. 9 (1966) 567-570. [92] Cohen, E., “Recent development of Hall-effect devices and applications”, Bulletin of the Electrotechnical Lab. 37, No. 10, (1973) 942-967. [93] Zabler, E.,Hintz, F., “Neue, alternative Lasungen fiir Drehzahlsensoren in Kraftfahrzeugen auf magnetoresistiver Basis”, VDI-Ber. 509 (1984) 263-268. [94] Gutter, F., “Kontaktloses Schalten mit den magnetisch gesteuerten Schaltern SAS 201 und SAS 211 in integrierter Halbleitertechnik”, Siemens Bauteile-Report I2 (1974) 39-41. [95] Lachmann, U., “SAS 231, an integrated Hall effect circuit with analog output”, Siemens Components Report XIV (1979) 225-227. [96] Databook: ICs for Industrial Applications, Siemens (1987). [97] Lachmann, U., “Funktion und Anwendung der Hall-Magnet-Gabelschranke HKZ 101”, Siemens Components 20 (1982) 73-75. [98] Krdger, G . , “Kontaktlose Gleichstrommotoren”, ATM, No. 387, (1968) 79-82. [99] Hanitsch, R., “Electronic control of small DC-machines having a permanent magnetic rotor”, JO Magn. Magn. Muter. 9 (1978) 182-187. [lo01 Huber, W., Neu, H., “Drucksensor nach dem Hall-Prinzip als Lastgeber fur elektronische Zilndanlagen”, Motortechn. Z. 47 (1986) 58-59. [loll Pettenpaul, W., Huber, J., Weidlich, H., Flossmann, W., Borcke, U. von, “GaAs Hall devices produced by local ion implantation”, Solid-State Electron. 24, No. 8, (1981) 781-786. I1021 Pettenpaul, W., Flossmann, W., Heidenreich, W., Huber, J., Borcke, U. von, Weidlich, H., “Implanted GaAs Hall devices family for analog and digital applications”, Siemens Forsch. Entwicklungsber. 11, No. 1, (1982) 22-27. [lo31 Lepkowski, T. R., Shade, G . , Kwok, S. P., Feng, M., Dickens, L. E., Laude, D. L., Schoendube, B., “A GaAs integrated Hall sensorlamplifier”, IEEE Electron Device Lett. EDL-7, No. 4, (1986) 222-224. [lo41 Personal communication with Dr. Marik, Vacuumschmelze GmbH Hanau. [lo51 Wetzel, K., Kuczynski, L., “Leistungsmessung mit Hallgeneratoren an Verbrauchern mit pulsweitenmodulierter Spannung”, Elektronik Information 3 (1986) 132-136. [lo61 Hirschmann, G., “Beriihrungslose Positionsmessung mit Hallsensoren”, Elektronik Information 3 (1986) 66-68. [lo71 ADmus, F., Boll, R., “Messungen an weichmagnetischen Werkstoffen mit dem Hall-Generator”, Elektrotechnische Zeitschrift 77, No. 8, (1956) 234-236.

4

Magnetoelastic Sensors GERHARD HINZ. Vacuumschmelze GmbH. Hanau. FRG HEINZ VOIGT. Daimler Benz AEG.Forschungsinstitut. Frankfurt. FRG

Contents 4.1 4.1.1 4.1.2 4.2 4.2.1 4.2.2 4.3 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 4.5 4.5.1 4.5.2 4.6 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5 4.7

Magnetostriction. Magnetoelastic Interaction . Principles . . . . . . . . . . . . . . . . . Theoretical Considerations . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic and Mechanical Properties of Applicable Magnetic Materials . Alloy Requirements . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Crystalline and Amorphous Alloys for Sensors

. . . . .

. . . . . . . . . . . . . . . . Torque Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . Elementary Considerations . . . . . . . . . . . . . . . . . . . . . Basic Magnetoelastic Sensor Systems

Cross-Qpe and Four-Branch-Type Sensors . . . . . . . . . . . . . . Coaxial-Type Sensors . . . . . . . . . . . . . . . . . . . . . . . Realization of Magnetoelastic Components . . . . . . . . . . . . . . Alternative Torquemeter Systems . . . . . . . . . . . . . . . . . . The Influence and Compensation of Effects Superimposed on the Torque Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . Special Magnetoelastic Sensors . . . . . . . . . . . . . . . . . . . AE Effect and Ultrasonic Wave-Propagation Devices . . . . . . . . . Wiedemann Effect Devices . . . . . . . . . . . . . . . . . . . . . Shock-Stress Sensors . . . . . . . . . . . . . . . . . . . . . . .

98 98 98

102 102 104 105 106 106 108 116 120 123 126

Sensors for Forces and Displacements . . . . . . . . . Magnetoelastic Sensors for Compressive and Tensile Forces Position and Displacement Sensors . . . . . . . . . .

130 130 136

Sensors Combining Magnetostrictive Effect and Other Physical Effects Other Magnetoelastic Sensors . . . . . . . . . . . . . . . . .

141 141 143 144 145 146

References

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

.

. .

147

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

98

4 Magnetoelastic Sensors

4.1 Magnetostriction, Magnetoelastic Interaction 4.1.1 Principles Magnetic materials show a strong interaction between their magnetic and mechanical properties, shape and geometry. Already in the middle of the last century Joule [l] observed that the length of a ferromagnetic specimen changes as a result of magnetization. This phenomenon is known as longitudinal or shape magnetostriction (the so-called volume magnetostriction is not discussed here). About 40 years later Villari [2] described the reverse of this effect, ie, the change in the magnetic properties due to the application of mechanical stress on iron which is also connected with a change in shape. This magnetoelastic effect is the basis for magnetoelastic sensors, excluding special cases. The shape magnetostriction, I , is strongly dependent on the material. It is primarily determined by the composition of the alloy. In crystalline alloys, the direction of the individual crystalline axes varies. For cubic crystals it is customary to refer to the magnetostriction values as I , , , A1,,, I , , , analogous to the denomination of the crystalline axes [3, 41. The longitudinal magnetostriction, I , is dependent on the excitation (field strength or flux density) and attains a saturation value, I , , which is given as a material constant for a particular material; I , can be positive, negative, or close to zero. Amorphous alloys do not have crystals or crystalline axes and, as a consequence, the magnetostriction in these alloys is equal in all directions (isotropic). A quantitive description of magnetostriction and its theoretical derivation from the basic material constants is difficult. However, we wish to point out that the magnetostriction of crystalline alloys is related to the stress dependence of the crystalline anisotropy and to local stresses in amorphous metals [5, 61. A simple dynamic dipole rotation model has been developed for a single domain of a magnetostrictive amorphous metal [7]. From this model, the equation of motion for the coupled magnetization and strain modes was derived. The influence of compressive, tensile and bending stress on the magnetization process and anisotropy energy of amorphous Fe,,Ni,,(P, B)20ribbons has been studied [8] observing also domain structure using the Bitter technique. In this chapter, the magnetostriction and the magnetoelastic interaction are considered mainly from the point of view of phenomena. Depending on the sign of magnetostriction the magnetoelastic effect on the characteristic curve of a soft magnetic alloy varies with the application of compressive or tensile stress. As an example of the effect of tensile stress on materials with positive or negative magnetostriction, the hysteresis loops of crystalline 68% NiFe and pure nickel and of an Co-based amorphous alloy are presented in Figure 4-1. If pressure is applied exactly the opposite behavior is observed.

4.1.2 Theoretical Considerations In the case of magnetoelastic interactions, the conversion of the elastic energy W, into magnetic energy W, is of importance for the efficiency of the sensor [9, 101. Therefore, all

99

4.1 Magnetostriction, Magnetoelastic Interaction

1.2

1.2

T

T

0.8

0.8

1

0.4

6

i

i

0.4

8 0

0

-0.4

-0.4

-0.8

-0.8

a)

-1.2

1

I

-8

0

-4

h)

-1.2

4

Alcm

8

H-

-8

1 0

-4

4

Alcm

8

H-

1.2

T 0.8

t

0.4

B

0

-0.4

-0.8

C)

-1 - 2

-8

-4

0

H-

4

Alcm

a

Figure 4-1. Hysteresis loops under tensile stress 0. (a) Crystalline 68% NiFe, I , = + 25 . (b) crystalline pure Ni, I , = - 35 . (c) amorphous Co-based alloy, I , = - 3 3 . 10-6.

the various types of energy Wi which are significant in a magnetic material should be explained: W,

=

magnetic field energy, which is proportional to the product of field strength and polarization

100

4 Magnetoelastic Sensors

W, = elastic stress energy, which is linked to the magnetostriction I W, = crystalline energy (in crystalline materials), which is heavily dependent on the material; W, does not exist in amorphous materials W, = uniaxial anisotropy energy, which arises, eg, during magnetic field annealing in crystalline and amorphous materials W, = shape anisotropy energy (dependent on the demagnetization factor, N ) .

Let us consider the ratio of stored mechanical energy, W,, to the total stored energy, W i , which determines the magnetomechanical coupling factor K33:

wc7 -K3, = -

c wi

w, w, + w,+ w, + w, +

WN

(4-1)

In order to achieve a large magnetomechanical coupling factor K 3 3 , which should approach to unity, the energy terms W,, W,, W,, and WNmust be small, ie, a soft magnetic material is required with W, and W,, + 0. Moreover, W, should be as small as possible, which is achieved by the selection of the specimen shape. In this case Equation (4-1) is simplified to:

When these conditions are fulfilled, a simple relationship is obtained for an alloy with negative magnetostriction between the mechanical stress 0 applied to a strip and the relative permeability ,ur. Using

and

Equation (4-2) can be transformed after minimizing the total energy into the following relationship [lo]: 0=-.1 PI

Jf 31, * P o

where

J,

=

saturation polarization

,uo = magnetic constant

v, = angle between magnetization and specimen axis

or

(4-5)

4.1 Magnetostriction, Magnetoelastic Interaction

101

where

E = Young’s modulus E = strain. Figure 4-2 shows the magnetization curve of a material in which the above mentioned conditions are completely fulfilled. In this ideal case the permeability, p,, decreases inversely proportional to the tensile stress, 0, and the strain, E . J A

Figure 4-2. Calculated magnetization curves under stress, see Equation (4-6).

I

u=O

material with

As an experimental verification of the calculation with Equation (4-6) Figure 4-3 shows the modification of the magnetization curve of an amorphous alloy strip (composition Co,,Si,,B,,) under tensile load [ll].

r 1.0

-

102

4 Magnetoelastic Sensors

A very high longitudinal magnetomechanical coupling factor K3, of up to 0.95 was reported for amorphous Fe,,(B, Si, C)19 [12], which agrees with a A E effect of 10%. The general relationship is

4.2 Magnetic and Mechanical Properties of Applicable Magnetic Materials As a rule, the magnetic properties of magnetic alloys are of prime importance whereas the mechanical behavior plays a subsidiary role. The exceptions concern applications where hardness, tensile strength and wear resistance are important. Magnetically soft alloys are usually also mechanically soft, soft iron being a typical example. In contrast magnetically hard alloys are mechanically hard, eg, AlNiCo. Magnetoelastic sensors require alloys which combine magnetic softness with mechanical hardness or strength. When considering the known crystalline alloys, for instance the soft magnetic nickel-iron alloys, it soon becomes clear that this combination is possible to only a very limited extent. The tensile strength of nickel-iron alloys is low, and consequently the range of elastic load range is small. On the other hand, a closer look at constructional steels reveals only very moderate magnetic properties in combination with acceptable mechanical properties. Therefore, with classical alloys a compromise always has to be made [lo]. A novel combination of magnetic and mechanical properties is provided by amorphous alloys, which fulfil the above-mentioned specifications in an almost ideal manner, in particular, they are magnetically soft and mechanically hard [13- 161.

4.2.1 Alloy Requirements The requirements on materials for magnetoelastic sensors can be outlined as follows: a) Magnetical. - easily magnetizable, ie, low coercivity H, - high saturation polarization J, - adequate and defined magnetostriction A,. It is important that the ratio dA/dH and dUdB be large, ie, the magnetostriction should vary strongly as a function of the field strength or the induction. b) Mechanical. - high Vickers hardness, HV - high yield strength, R , .

103

4.2 Magnetic and Mechanical Properties of Applicable Magnetic Materials

Table 4-1 gives a survey of the crystalline and amorphous soft magnetic alloys which are suitable for magnetoelastic sensors. The alloys are graded according to the level of magnetostriction [15-171. Table 4-1. Materials for magnetoelastic sensors. Type

A,

Alloy

*

Crystalline

50 Co, 50 Fe 50 Ni, 50Fe 97 Fe, 3 Si 77 Ni, 15 Fe, Mo + Cu 77 Ni, 15 Fe, Mo + Cu +Ti + Nb Spring steel 1.8159 Shaft steel CK 45 Ni

+ 70 + 25 +9 +1

- 0.5 -1 - 35

Hc A/cm

1.4 0.05 0.1 0.01

I .5

-

0.04 0.03 0.003 0.025

Crystalline

+ 2000

50

')

2,

3,

(Tb Dy) Fe,

2,

+8 0.2 -3.5 -8

2.35 1.55 2.0 0.8 0.5 2.1 -2.1 0.6

+ 30

E kN/mm2

200 110 180 100

400 140 350 150

230 140 150 200

220 550

500 1500 450 120

200

T

0.025 15 10 1.5

Amorphous I ) Fe,, B,, Si, Fe,, Ni,, (Mo, Si, B)22 (Co, Fe, Mo)73 (B, Si)27 c075 Sil, B,, Co,, Nil, B,, Si,

R, N/mm2

HV

J,

75

210

0.8 0.55 0.7 0.85 1 .o

460

7003)

30

Examples for trade names of amorphous metals are: METGLAS (Allied Signal Inc.) and VITROVAC (Vacuumschmelze GmbH). New type of rare earth alloy with giant magnetostriction for special sensors and actuators [23]. Compressive strength.

Table 4-1 starts with the crystalline material 50% cobalt-iron, which not only exhibits the highest saturation polarization but also the highest saturation magnetostriction, with I , = +70 however, the magnetic softness is only average. The most commonly used soft magnetic material is silicon-iron with 3 % Si, which also has relatively favorable mechanical properties. Nickel-iron alloys which fall into the category of very soft magnetic materials possess I , with 50% Ni and f 1 values, depending on the Ni content of between +25 for alloys with ca. 77% Ni. However, these alloys are mechanically relatively soft. A pronounced increase in hardness and yield strength of 77% NiFe without a noticeable decrease in the magnetic softness (coercivity and permeability) is attained with precipitation hardening additions such as Ti and Nb. Steels, eg, spring steels or constructional steels, have low magnetostriction values and favorable mechanical properties, but with regard to magnetic softness they are on the boundary between soft magnetic and magnetically semi-hard materials [18]. Pure nickel has a high negative magnetostriction, but as a bulk material it is mechanically very soft. In comparison, sputtered Ni layers are harder. In the family of amorphous alloys which have a n isotropic magnetostriction - a result of their non-crystalline structure - the iron-rich alloys have excellent I , values with good

104

4 Magnetoelastic Sensors

magnetic softness and a high yield strength. In the group of amorphous nickel-iron alloys, depending on the composition, the magnetostriction is average (ca. + 5 10 -6 to +10 . Co-rich alloys with ca. 60 at% Co exhibit lower I , values, in the range k 1 . 10 - 6 . In certain Co-rich alloys the magnetostriction may assume negligibly low values ( I , < 0.1 . 10 -6). A further increase in the Co content leads to negative I , values. All amorphous alloys have hardness values and yield strengths which exceed those of crystalline alloys by several orders of magnitude. It follows that these materials appear to be particularly suitable for magnetoelastic sensors when there are no constructional arguments against their use. However, it should be pointed out that amorphous alloys can only be produced as thin strip (ca. 0.05 mm) and not as solid material or with greater thicknesses. To complete the picture, it should be mentioned that the soft magnetic oxides (ferrites) also exhibit magnetostriction which, in this instance, is also heavily dependent on composition as for for metals and alloys [19, 201. For MnZn ferrites I , is in the range -0.5 to +0.5 NiZn ferrites I , is in the range -1.5 to -10 But there are special ferrites with higher magnetostriction. Giant magnetostrictive alloys are based on rare earth metals such as Tb and Dy [23, 241. They form a new group of materials for special applications.

-

-

4.2.2 Comparison of Crystalline and Amorphous Alloys for Sensors The differences between crystalline and amorphous metals, in particular the mechanical properties, will be discussed in more detail later. The stress-strain curves show extreme dif-

soft magnetic, amorphous ICo based alloy)

/--

spring material, non- magnetic

(Cu Be 2 )

b

7 7 '10 NiFe, hardenable) ........(... .,.................* ***...*.*.*.*

soft magnetic, crystalline --__-__--------------( 7 7 O / 0 NiFe)

-0

I

2 strain .c-

41a

3

Figure 4-4. Stress-strain curves of several materials.

105

4.3 Basic Magnetoelastic Sensor Systems

ferences (Figure 4-4). While amorphous alloys have an almost ideally straight characteristic curve which is even superior to that of (non-magnetic) spring alloys, very slight stress gives rise to plastic flow in crystalline alloys. The tensile strength and yield strength are almost identical in amorphous alloys, and there is no plastic flow. For amorphous alloys elastic strains of up to and over 1% are feasible, for crystalline metals 0.1% is hardly possible. If the coercivity is taken as a measure of magnetic softness versus mechanical hardness, we obtain Figure 4-5. A factor in the range of 5 to 10 separates amorphous and crystalline alloys exhibiting the same coercivity [21, 221.

1oou

-

Fe- alloys Co-a 11oys

amorphous materials 800

1

600

HV

400

200

age-hardenable Fe-77 % N i

-

crystalline materials

-

high purity iron

Fe-77 % ~i

I

Em

Fe-Co

177777771 I

4.3 Basic Magnetoelastic Sensor Systems If we consider the principles of the construction and design of magnetoelastic sensors, three basic systems can be described based on the Villari effect: a. systems with a predefined magnetic flux path where the inductance or permeability is changed by mechanical loading in one direction (“one-dimensional”) b. systems with a flux configuration which changes in two directions but in one plane due to loading (“two-dimensional”) c. systems where the flux configuration is spatially and vectorially changed by the applied load. Figure 4-6 shows sensors of these three types [lo]. For some general information see also [25]. A review on basic principles of amorphous sensor constitutions is represented in [26].

106

4 Magnetoelastic Sensors

IF sensor type

3

1

process variable flux configuration

impresslor tension

bending

I

I

1 - dimensional

5

4

tors ion

compression

1

2- or 3-dimensional

I

Figure 4-6. Principles of magnetoelastic sensors. F Force, T torque.

Simple magnetoelastic force sensors (1) and (2) belong to type (a). They consist either of a single strip or of a pot-core like design. They operate as chokes or coils, their inductance changes being used to indicate the load. Examples of type (b) are circular rings (3) or laminated core packages for load cells (4). In both designs the load can be compressive or tensile stress. The ring (3) is deformed to an ellipse. The core package of an isotropic magnetic material becomes magnetically anisotropic under stress because the core is deformed to a different longitudinal and transversal degree to the load axis. A change in the inductance of the ring or the voltage in the secondary winding of the core indicates the load. Type (c) as a three-dimensional system is realized in torque transducers of shafts (5). The torque changes the permeability of the shaft surface or of a surface layer. The permeability in this instance must be considered as a tensor quantity. Its change can be detected either by cross-type chokes or by cylindrical coils around the shaft.

4.4 Torque Sensors 4.4.1

Elementary Considerations

Measurements of the torque on shafts with the aid of the magnetostrictive effect utilize the dependence, as described in Section 4.1, of the magnetic properties of the shaft material itself or of an additional magnetic coating on the shaft surface on the mechanical stresses arising in the shaft. Therefore we are dealing with indirect measurement of the torque because the effect of the torque on the mechanical stresses arising on the surface of the shaft must be known.

4.4

Torque Sensors

107

In the pure torsion of a cylindrical solid or hollow shaft two principal orthogonal directions of stress arise, ie, compressive and tensile stress. These run in screw-like lines around the shafts, and each forming an angle of f 45 O with the shaft axis [27] (Figure 4-7). The calculation of the principal stresses t at the surface due to a moment of torque T [28] is based on Hooke's law and is expressed as

where t

=

y

= = = = =

G a,

I r

shear stress shear strain shear modulus angle of torsion length radius of shaft

/

,

/

Figure 4-7.

Explanation for calculation of torque on a shaft.

F

In the general case of a hollow shaft with inner and outer diameter d, and do respectively the (radius dependent) torque and shear stress are obtained by the integration of T ( r ) . r . dA (with T = torque, proportional to A = area):

I 'i

'i

Gap - -.-

I

7~

2

(r: - r4)

(4-9)

Gap t d and with -= - and r = - we obtain: I r 2

5 =

32 * T 7~ (d: - d?)

.r.

(4-10)

108

4 Magnetoelastic Sensors

The maximum stress om on the surface of the shaft is (4-11) The relevant maximum strain

E,

defined by (4-12)

(4-13)

where v = Poisson ratio E = Young’s modulus. The complex path of stress and strain on the shaft surface (see Figure 4-8) results, in practice, in equally complicated coil arrangements which can pick up the magnetoelastic interactions. For constructional reasons, it is almost impossible to mount detector coils so that they are capable of directly picking up the changes in amplitude of the permeability in the particularly sensitive principal directions of stress according to Equation (4-6). As described in detail in the following Sections 4.4.2 and 4.4.3 for symmetrical reasons coil arrangements are 45 O to the main directions of selected which permit both the field input and detection in stress. This can be performed successfully with “crossed” yoke coils (Section 4.4.2) or with cylindrical coils (Section 4.4.3) mounted coaxially to the shaft.

*

(T<0

Figure 4-8. Main stresses 5 on the surface of a shaft under torque.

4.4.2 Cross-Qpe and Four-Branch-Qpe Sensors A torque transducer system with a pair of crossed magnetic yokes, named Cross Torductor, was developed by ASEA, Sweden, in 1954 [29, 301. The principle is shown in Figure 4-9. As shown, the yokes are U-shaped magnetic pole pieces facing the shaft surface with a narrow air gap. The ’primary‘ U is positioned in a plane parallel to the shaft axis and carries two excitation coils P 1 and P2. The ’secondary‘ U, positioned in a plane perpendicular to the shaft axis, carries two sensing coils S1 and S2. In the primary circuit, an alternating flux is fed across the air gaps A1 and A 2 into the shaft where it is confined to a shallow depth due to

4.4

Torque Sensors

109

the skin effect. Without a torsional load, the flux pattern is symmetrical and no net flux is sensed in the secondary core via the air gaps A 3 and A4. As soon as the shaft transmits torque, the flux density tends to increase in the direction of tensile stress and to decrease in the direction of compressive stress (assuming positive magnetostriction) so that the flux pattern is distorted as shown in Figure 4-9. In this way, the secondary pole faces are exposed to unbalanced magnetic potentials and a differential flux is picked up which induces a signal voltage in S 1 and S 2 as a function of torque.

-+ u Principal stresses T

torque

P, -P,

S, -S, A,- A,

a)

primary core secondary core air gaps

unloaded shaft

b) loaded shaft N, S primary poles A, B secondary poles

Figure 4-9. Principle of Cross Torductor torque sensor and flux pattern of sensor poles on the surface of a shaft a) without and (b) with torsional load [29].

In Figure 4-10 (from [30]), the magnetic circuit of the cross type torsion sensor is shown. It represents a magnetic bridge circuit with four magnetic impedances. The symbols 1-T and 2-T designate the impedances associated with tensile stress and are linked with P 1, S 1 and P 2 , S 2 referring to Figure 4-9. The impedances associated with compressive stress, linked with P 1, S 2 and P2, S 1, are marked 1-C and 2-C. Further, a shunt impedance is used to represent the leakage flux not connected with the secondary core. In the unloaded state the magnetic bridge is balanced. As soon as the permeability in the shaft experiences magnetoelastic changes by tension or compression due to torque, these changes are detected by the coils S 1 and S 2 in the signal flux branch.

110

I)flux

4 Magnetoelastic Sensors

-

inductive ohmic

Figure 4-10. Equivalent magnetic circuit of cross type torque sensor [30] of Figure 4-9.

A 'degenerated' cross-type torque sensor has been described in [31]: The sensor head consists of a single U-shaped yoke positioned in a plane perpendicular to the shaft axis. One leg of the U carries the excitation coil and the other the detecting winding. The system is designed with a shaft whose surface is upgraded for torque measurement by means of a magnetic layer with good magnetoelastic properties (see Section 4.4.4). A second type of magnetoelastic contact-free torque sensor makes use of the four-branch design [32] illustrated in Figure 4-11. The basic sensor design, the paths of magnetic flux, and the equivalent magnetic circuit are shown in Figure 4-12. The sensor head consists of the center pole with the excitation coil EX and the four corner pole parts carrying the sensing coils 1, 2, 3 and 4.The pole faces of the center and of the branches are placed close to the shaft surface with a clearance of the order of 1 mm. The branches are orientated in the directions of tensile stress and compressive stress. Across the air gaps the coordinated flux components are sensed as shown in the perspective view. In the magnetic circuit diagram, each surface-related path consists of a permeability-dependent reluctance and an ohmic resistance allowing for eddy-current loss. The diagram illustrates the effect of a torque marked by arrow symbols: the impedances 1-T and 3-T decrease owing to tensional stress and 2-C and 4-C increase owing to

Figure 4 4 . Helices of principal tensile and compressive stress on the surface of a shaft subjected to torsion [32]. Correlated changes of permeability are detected by four-branch yoke system with sensing coils 1, 2, 3 and 4 and a common excitation pole.

4.4

Torque Sensors

111

+induct:ive 1 1ohmic

flux

Figure 4-U. Principle of four-branch type torque sensor and equivalent magnetic circuit [30].

compressive stress. This causes the flux portions 1 and 3 to increase and 2 and 4 to decrease since no other physical properties are permitted to vary. The net output signal is obtained by wiring the sensing coils so that the voltage sum from the coils 1 and 3 is deducted from the voltage sum of coils 2 and 4. By this wiring scheme thermal drift of the torque signal voltage is compensated since the individual temperature induced changes of physical properties are cancelled to a great extent. Figure 4-13 illustrates the design of a four-branch sensor head as

Figure 443. Four-branch type torque sensor heads. Pole structures realized by commercial multi-pole ferrites 14 and 18 mm in diameter, (diameter of sensor head 17 and 24 mm, respectively) [33].

112

4

Magnetoelastic Sensors

used for the torque measurements reported in [33]. The required pole structure is rendered by a commercially available pot-shaped 18 or 14 mm multi-pole ferrite core. Considering the application of the sensor principles discussed so far, a number of practical hints might be useful. For a given sensor system the sensitivity, expressed by the signal voltage/torque ratio, is dependent on the dimensions of the shaft and also on its mechanical and magnetic properties. As a rule, steel shafts for industrial application are designed to transmit torsional load under shear stress up to 100 N/mm2 on the shaft surface. Often, the stress is rated at 10-30 N/mm2, eg, in ship propeller shafts where size is controlled by the superposition of torsional and bending loads. For example, Table 4-2 shows the sensitivity of a four-branch type sensor system as evaluated from measurements on 30 mm shafts of five different sorts of steel. Table 4-2. Influence of shaft material on the sensitivity of a four-branch type torque sensor [33], shaft diameter 30 mm. Steel

Shaft material

Sensitivity in mV/Nm

C 15 c 45 C 60 42CrMo4 21CrMoV511

Cementation steel Heat-treatable steel Heat-treatable steel Heat-treatable steel High-temperature construction steel

1.35 4.43 0.60 2.40

1.oo

The figures reveal that magnetoelastic torque sensing requires individual calibration of the sensor system plus shaft. This is true because the magnetoelastic response of a ferromagnetic material of given composition tends to decrease with increasing mechanical hardness. As stated in [30] for automotive applications, shaft hardness can vary from 10% up to 40%, producing a similar variation of the magnetic torque signal sensitivity in a comparable range. The problem of the torque signal dependence on the composition and hardness of the shaft material can in principle be solved either by a sleeve or by a coating of ferromagnetic material with satisfactory magnetoelastic properties on the shaft surface (see Section 4.4.4). The torque sensitivity is also a function of the excitation frequency. By increasing the excitation frequency of the sensor circuit, its response to fast torque transients is improved. On the other hand, the sensitivity of the system might be reduced at higher frequencies, again dependent on the properties of the shaft material. The most favorable frequency must be chosen according to the requirements as to transients, shaft speed, shaft material, oscillator power and output signal. The frequencies used in practice range from 50 or 60 Hz [29] to audio frequencies (400-2000 Hz [30]) and to radiofrequencies, eg, 100 to 200 kHz [33]. Further, the torque signal sensitivity is dependent on the air gap between the pole faces and the shaft surface. Electronic compensation or ring systems are means of overcoming this drawback. Likewise, magnetic inhomogeneities which might impair the torque signal by a periodical superimposed signal can be damped (see Section 4.4.6). Torque signal modulation by radial shaft displacement and circumferential magnetic inhomogeneities in the shaft surface can be avoided to a great extent by ring-type torquemeter designs. Two versions have been developed: one based on the four-branch principle [34], the other based on the cross type design. Figure 4-14 shows the configuration of the latter as utilized in the Ring Torductor developed by ASEA [35-381. In this torque transducer three similar pole rings with coils sur-

*

*

4.4

Torque Sensors

113

round the shaft with a clearance of 2-3 mm in heavy machinery installations. The middle ring carries four AC excited salient poles, marked N-S-N-S in the developed drawing of the shaft surface. The two outer rings carry a set of poles A, B, A, etc., with pick-up coils whose winding directions are reversed alternately. In the winding schemes of the exciting coils and of the pick-up coils the basic bridge circuit of the cross type sensor is preserved. By summing the individual voltages, a net torque signal proportional to the torque is obtained. As indicated in the diagram, the exciting poles are displaced half a pole-pitch relative to the secondary poles and are equidistant from them. Facing the shaft surface each N-S-A-B pole quadruplet senses the magnetic flux pattern which is distorted by tensile and compressive stress due to the torsional load as shown previously for the single cross torductor sensor in Figure 4-9.

x-x

principal stresses

x

-cT

+cT

+a

-0

Figure 4-14. Principle of Ring Torductor torque transducer. (a, b) Physical structure, (c) evolution of the shaft surface under the transducer poles A and B.

Ring Torductors are manufactured in standard units for a wide range of shaft diameters. The number of poles, always a multiple of four, increases with increasing shaft diameter, for example, 4 poles per ring at 60-150 mm, 36 poles per ring at 840-940 mm. The system is operated at a frequency of either 50 or 60 Hz and is dimensioned for a shaft circumferential speed up to ca. 6 m/s. In the axial direction, the triple ring configuration requires an unobstructed space of 250 mm in length. Practical Ring Torductors, eg, o n a propeller shaft on a ship, measure torsional stresses ranging from 60 to 200 N/mm2 on the shaft surface. The accuracy of torque measurement depends on the method of calibration; a n accuracy of 1% (or better) can be obtained. Typical data are: linearity better than 1%, hysteresis error below 1%, and reproducibility better than 0.2%. Figure 4-15 shows a view of a Ring Torductor unit as used for torque measurement on a propeller shaft. For convenience of assembly, the transducer design is divided into two halves (lower part of Figure 4-15). The Ring Torductor system has been used on a trial basis for automatic transmission control in automotive applications [39].

114

4 Magnetoelastic Sensors

Figure 4-15. Ring torductor for measuring torque on ship propeller shafts (shaft diameter ca. 500 mm) (Courtesy ASEA Brown Boveri AG).

The alternative design is the mulitpole four-branch system [40]shown in Figure 4-16.This configuration consists of several, eg, three, individual four-branch type sensors which surround the shaft and are enclosed by a common ring. The excitation poles are located in the center portions and the detecting poles in the two outside portions of the ring-shaped struc-

4.4

Torque Sensors

115

ture. The complete system operates in the same manner as a single four-branch sensor unit shown in Figure 4-12. In the multiple-unit version again the signal voltages from all of the tensile stress sensitive branches and all compressive stress sensitive branches are summed. The difference of the subtotals yields a signal voltage proportional to the torsional stress in the shaft. A

outside portions of sensor center portion of sensor

k A

up coil

Figure 4-16. Multiple four-branch torque sensor design (three excitation coils, centered inside the sensor; twelve pick-up coils, placed o n the outside of the sensor).

A- A

For special applications and improvements of the torductor principle a number of variations have been proposed and realized. For instance, in [41] a transducer has been described, which measures the torque in the outgoing crankshaft of an automotive engine. A Ring Torductor design with four energizing poles and four detecting poles has been reported in [42]. The magnetic system encompasses the shaft which, in the region of torque measurement, carries a rigidly attached cylindrical sleeve or foil of a material with suitable magnetoelastic properties. Each magnetoelastic torque sensor system is necessarily subject to a calibration procedure. In a number of practical applications, calibration can be performed with static torque in the shaft. As a reference, a mechanical load or a strain gage standard might be used. If calibration is required with the shaft rotating, an electric dynamometer generator or a strain gage system operating with slip-rings or a magnetic transducer will be used.

116

4 Magnetoelastic Sensors

4.4.3 Coaxial-Qpe Sensors The cross torque sensor arrangement used to measure a torque as described in Section 4.4.2 may exhibit two distinct disadvantages under certain circumstances: it is sensitive to adjustment and the signal may be superposed by a considerable interference modulation if the shaft surface under detection is magnetically inhomogeneous in the circumferential direction. These negative effects can sometimes be compensated by special measures or by using a ring torque sensor, but these are generally rather complex, see Figure 4-16. A fundamental improvement is obtained by a cylindrical coil arrangement coaxial to the shaft, as proposed in its simplest form by Dokolin et al. in 1979 [43]. In the meantime, the coaxial torque sensor has undergone numerous modifications and improvements [44-491. Table 4-3 shows the different principles and gives the specialities of each measurement technique. The most interesting results are obtained with the designs D and E. In practice, E is currently the best understood solution. A comparison of designs C to E with B shows that the function of the (improved) coaxial torque sensor is essentially based on an anisotropy intentionally introduced in the “magnetic surface” of the shaft, the direction of which coincides with the direction of the torsional main stresses (see Figure 4-17).

c

Figure 4-17. Function of a coaxial torque sensor with a structured foil.

There are various ways of producing these 45” anisotropies:

- by mounting a magnetic foil on the pre-stressed shaft [46]; - by “pre-stressing” a magnetic foil which is then mounted on the shaft in a special ring [45]; - by using “slit” magnetic sleeves (see [48, 50, 51]), mounting magnetic strips at 45” or by using soft magnetic strips with a special structure [49]. In the first two cases we are discussing stress anisotropy (in design D), and in the others a shape anisotropy based on the geometric structure. This additionally introduced anisotropy o n the shaft surface creates a magnetic bias, ie, a preferred direction of the magnetic flux produced by the excitation winding in the direction of the main stresses. When torque occurs in the shaft, this direction changes due to the mechanical stresses arising in the magnetic materials as determined by the magnetoelastic interaction (Section 4.1).

4.4

Torque Sensors

117

Table 4-3. Principal designs of coaxial torque sensors. System variant

Coil design

“Magnetic” surface of shaft

Remarks of measurement effects

Homogeneous

Useful signal superposed with operating current induced voltage. Limited range of linearity. No detection of direction.

Homogeneous

No useful effect.

Grooved structure under 45” - one sided

Limited range of linearity. Principal asymmetry with respect to direction. Useful signal superimposed with operating current induced voltage.

45” structure through “zero point” anisotropy

In principle good symmetry, linearity and zero point suppresion.

Symmetrical grooved structure under f 4 5 ’

As for D.

A

I n

B

C

D

E

Bxm primary

winding

secondary wind i ng

This process is explained in an example in which a 45” structured magnetic foil with negative magnetostriction according to Figure 4-17 is fitted on the surface of a shaft. An AC current in the primary coil N, produces an excitation field in an axial direction which owing to the symmetry of the arrangement in the non-twisted state, causes the same magnetic flux

118

4 Magnetoelastic Sensors

in both secondary coils and consequently the same induced voltage. The two secondary coils are connected in opposition, so that the output voltage in the non-twisted state is zero. If the shaft experiences such torsion that both tensile and compressive stress occur then the flux conduction in the right hand foil part is aided in the direction of the -45 O direction of the strip structure by the compressive stress, while in the left hand part it is opposed by the tensile stress in the +45" direction of the strip structure. The result is an increase in the magnetic flux in the right coil at the expense of the left one, and consequently an increase in the differential voltage U,.When the direction of torsion is reversed this is indicated by the sign of the differential voltage being reversed. Similar processing circuits are used for coaxial torque sensors and those which use strain gage bridges. Figure 4-18 shows a schematic diagram of typical data processing electronics: the generator supplies an excitation current from 10 up to several 100 mA for the primary coil which is generally power-factor compensated to reduce the power consumption. The frequency of the excitation current is between 5 and 50 kHz; the relevant optimum frequency is determined in particular by the electric and magnetic properties of the shaft surface and represents a compromise between the power required and the sensitivity. The response rate plays a minor role here since in most cases it is high enough in comparison with the torque jumps which occur in operation. The secondary differential voltage is amplified symmetrically and is rectified in the correct phase with reference to the oscillator voltage. An interesting type of data processing electronics for a coaxial torque sensor is described in [44].

% *

The principle of the coaxial torque sensor for measuring torque is relatively new and the practical application of these sensor systems is still in the initial stages. Apart from investigations performed in the research departments of industrial concerns and universities, the first experience in the use of this sensor was gained in electric machinery and assembly line drives. In such cases the torque is between 10 and 5000 N m for shaft diameters between 12 and

4.4

119

Torque Sensors

100 mm and leads to typical strains in the range 0.008-0.05%. The coaxial torque sensor which produces a rotational modulation substantially lower than that of crossed torque sensors is particularly effective for small strains. In the medium sensitivity range the interference modulation is less than 2% of the rated signal and a linearity of < 2% (according to data from Vacuumschmelze GmbH, Hanau) is attained. Figure 4-19 shows the construction (schematic) of a sensor system for the drive shaft of an electric motor, and the corresponding characteristic curve using an amorphous soft magnetic structure strip, composition Co,,(SiB),,. A circuit

shaft

Primary secondary coils

a)

V

t'

5 2 3 1

0.1

0,2

%o

E-

D)

Figure 4-19. Sensor system of an electric motor. (a) Construction; (b) characteristics.

120

4 Magnetoelastic Sensors

shown in Figure 4-18 with an excitation frequency of ca. 20 kHz is used for data processing electronics. The coaxial torque sensor is comparatively insensitive to local inhomogeneities of the shaft surface and to radial adjustment deviations, but some critical parameters do exist for this type of sensor. For example, it exhibits a specific sensitivity towards axial displacements of the coil systems with respect to the “sensor-active’’ shaft region. By employing the construction techniques described in Section 4.4.6 the sensitivity can be adequately reduced. Like other magnetic sensors, it also exhibits a certain temperature dependence and an interference field sensitivity. The temperature behavior will be discussed in some detail in Section 4.4.6. If the sensor system is operated in a strong external magnetic field (> 5 A/cm), then an asymmetric shift of the characteristic curves may take place. Here DC fields are far more critical than AC fields. This problem is solved by shielding. Another significant feature is the magnetic behavior of the shaft itself; in critical cases non-magnetic shafts are used which are coated with an appropriate strip. In addition to coaxial measurement systems as in Table 4-3 we should like to point out that recently a rather complex coil arrangement has been proposed by [52], (Figure 4-20); in principle it allows the detection of a torque moment with the correct sign. However, to date there are no data on the working of this system.

I

Figure 4-20. Complex coil arrangement for a torque sensor proposed by [52].

4.4.4 Realization of Magnetoelastic Components Although the measurement of the magnetoelastic effect has been known for over 30 years and has been investigated worldwide, the actual practical applications of this effect have to date been limited to a few special applications. The main reason is that for a long period all

4.4

Torque Sensors

121

efforts were focused on the technically interesting and economically attractive solution of using the twisted shaft itself as the active magnetoelastic component. However, a major prerequisite for this solution is a mechanically suitable shaft which, on the other hand, is also magnetically optimized with regard to the magnetoelastic coupling factor, the permeability, and the hysteresis. In this case the homogeneity of these magnetic terms is subject to stringent requirements over the circumference of the shaft. As a rule, conventional shaft materials d o not meet these requirements. In the case of magnetic steel the magnetic properties can be improved by heat treatment, but this step usually results in a loss of the required mechanical strength (see Figure 4-21).

u

,z

%

U

m

20

-

amorphous f o i l

) b,

i Y

4

stress relieved s t r e n g t h < 700 N/mm*

3

ao 1 0 Figure 4-21. Characteristic curves of torque sensors (cross type) using (a) the shaft as a magnetoelastic component and (b) with a foil [63].

shaft. hardened s t r e n g t h > 1000 0

@,5

1

N/mm2

%o

&-

In some cases, age-hardenable nickel-iron alloys provide a compromise, but their application is limited to special cases owing to the costs involved. Nonmagnetic shaft material is not at all suitable for this application. At the end of the 1960's the use of magnetic sleeves was suggested as a solution, ie, in principle, a magnetically optimized sleeve which is mechanically well bonded with a twisted shaft ([53] and Figure 4-22). The fact that there were no universally suitable alloys for this type of measurement sleeve initially delayed the practial application of this idea o n a large scale, however, the development of special coating technologies and, above all, the emergence of amorphous material (Section 4.2) has recently led to realistic solutions.

Figure 4-22. Principal construction of a torque measurement system with a magnetic sleeve according to [53].

122

4 Magnetoelastic Sensors

A modified, improved version of the earlier possibility [53] was formulated more recently in [54], where a sleeve made of soft magnetic materials with slots at 45 O fulfils the prerequisites for the construction of a coaxial torque sensor (Section 4.3). This design largely eliminates the disturbing rotational modulation due to magnetic homogeneities, while the well-known shortcomings of conventional soft magnetic alloys, ie, mechanical strength and hysteresis remain. According to [55], a further improvement is achieved by using the sleeve merely as an intermediate carrier for an amorphous foil. In this way, the sleeve material can be selected for its mechanical properties and the thermal expansion can be adapted to that of the amorphous foil, while the magnetic properties of the latter can be optimized as required. Different technologies have been proposed in [53-551 as a means of achieving a good mechanical bond between the sleeve and the shaft, including soldering (in particular brazing), welding, and a combination of adhesion and laser welding to attach the amorphous foil to the carrier sleeve. These bonding technologies have been used in preliminary experiments but have yet to be tested on a production scale. This also applies to another group of processes to establish the magnetostrictive components, ie, those which commence with direct coating of the shaft with a material in the form of a layer or foil. Patents [56, 571 cover the use of a magnetostrictive layer on a twisted shaft to improve the measurement accuracy, but only give examples of the coating technology. In contrast, recent papers [58-601 deal with actual investigations of the technologies “plasma jet spraying”, “explosion bonding” and “wire explosion spraying”. Figure 4-23 a shows the arrangement for coating using the “wire explosion spraying” technique. To a certain extent, wire explosion spraying achieves a homogeneous layer and a 45 O structure as required for a coaxial torque sensor. Moreover, within certain limits, it is also possible to subject the coated shaft to heat treatment in order to improve the magnetic or magnetoelastic properties of the “layer”. The results achieved with this direct coating technology are presented in Figure 4-23 b showing an example of a characteristic curve which exhibits good linearity in the investigated (admittedly rather small) range of torque. A typical feature is the relatively low specific output voltage which results from the limited layer thickness and the values of magnetoelastic sensitivity obtained so far with this method. As far as realization is concerned, currently the most highly developed technique is “coating” the shaft directly with a magnetoelastic foil, generally an amorphous foil. However, at present glueing is still the most important bonding technique while other possibilities, such as the use of memory alloys [61] or laser welding are interesting but, to date, have not been sufficiently tested. Instead of amorphous foils surrounding the whole shaft rectangular ribbons have been fixed only over one part of the circumference [62]. It has been shown [63, 641 that with suitable adhesives and thorough preparation of the surfaces, glueing amorphous foils on steel shafts yields load cycles of more than lo7 for a strain of ca. +0.1% (Section 4.4.1). Continuation of this work using the amorphous structure foils described in [63] led to further improved results with regard to reproducibility and to increased experience in the critical behavior of a glueing under a continuous static load. Glueing using an epoxy resin adhesive with a glass transition temperature of about 130°C allows a permanent load at 80°C, and static strain of typically 0.025%;in this case the alterations in the sensitivity after 2000 h of static load are less than 2%. This requires stabilization of both the foil and the adhesive layer.

switch O C: 1

123

Torque Sensors

4.4

R

7

P

/ -

f - .

c ' wire

charge system

0

shaft

L>

T-

Figure 4-23. Schematic diagram of wire explosion spraying and typical results for strip samples with a coaxial coil arrangement [60].(a) Basic circuit for wire explosion spraying; (b) U,,, versus torque characteristics.

--

Fe-Ni Fe-Co-Ni

b)

4.4.5 Alternative Torquemeter Systems In addition to magnetoelastic torque sensor systems, various alternative torque meters have been applied in the field of mechanical engineering (summarized for automotive engineering in [65]). In industrial installations with electric drives, the indirect torque measurement by monitoring the motor current is a preferred and widely used method. In a novel device [66] the secondary current of an induction motor is sensed by means of amorphous microcores near the rotor end-rings. For the direct measurement of torque three groups of sensing techniques have been developed:

- strain gage systems with strain-sensitive resistor elements bonded to the shaft surface (see Volume 3); - reaction force meters in connection with a mechanical brake system or an electric

dynamometer-generator [67]

124

4 Magnetoelastic Sensors

- twist-angle measurement: under torsional load, the twist angle y of the shaft is given by Figure 4-7 and Equation (4-8). For twist-angle torque meters the following principles have been applied (see for instance [68]): a) Mechanical measurement of angular difference by means of a differential gear system; b) measuring the pressure drop in a hydraulic system which translates the relative motion of two flanges subsequent to torsional stress; c) detecting the phase difference between the outputs of two generators coupled with two gears spaced on the shaft; d) sensing the angular displacement via optoelectronic components; e) acoustic torque measurement by determining the resonant frequency of a taut wire between two flanges which control the wire tension due to angular displacement; f) electronic measurement of the phase difference between a pair of toothed wheels or amorphous star-shaped cores on the shaft [69, 701; g) electromagnetic transducer converting shaft twist into an axial component of a magnetic structure surrounding the shaft; h) capacitative meter sensing the torsion-dependent axial clearance between two insulated metallic discs on the shaft; i) measuring the resonant frequency of a microwave cavity which is fixed on the shaft and experiences deformation under torsional load; j ) eddy-current sensor utilizing a pair of concentric metallic sectors or slotted cylindrical shells whose relative angular position varies with torsion so that an electronic circuit produces a torque signal on the base of the eddy-current load varying with the geometry of the system [71, 721. The systems a) to c) operate in mechanical contact with the shaft, and d) to j) operate contact-free. A contact magnetoelastic torque sensor system has been described in [73]: It uses an amorphous magnetic ribbon, fixed on the shaft, in mechanical contact with a sensor head. The torque signal is again obtained by sensing the stress-dependent permeability changes in the ribbon and is fed into a transmitter and picked up by a receiver near the shaft. Table 4-4 presents a synopsis of the various types of torque sensing systems. Regarding installation, handling, space requirement, accuracy, and costs, each sensor system has a preferred field of application. Where contact-free measurement, combined with easy access to the shaft, is demanded and moderate accuracy, say f 10% or better, suffices, magnetoelastic torque sensors will be used in industrial, automotive, and avionic systems. Torque measurements with these sensors can be upgraded to an accuracy of f 2 % by being installed on special shafts of suitable dimensions and material. Advanced performance can be met in test-bed installations where magnetoelastic torque measurement competes with strain-gage or twist-angle devices. In general, these methods are easy to instal and operate. If they cannot be used, eg, because of limited reliability in a heavy-duty industrial environment, the conventional reaction force method in combination with an electric transducer or dynamometer will be used.

Operating temperature of sensor elements possibly higher than with strain gage or magnetoelastic sen-

High-precision alignment of twistangle pickup system at the shaft; rigid structure to hold sensor components

Space at power train for installation Heavy-duty service in industrial of brake or electric dynamometer applications and test beds; no calibration problems

Reaction force Brake system with at lever load cell; electric generator

sors

Same advantages as above; high accuracy; standard calibration for given shaft material and dimensions possible

Strain gage

Sensitivity

Shortcomings

Strain gage elements bonded to shaft surface; for rotating shaft slip-rings or telemetry transducers (power supply, signal pick-up)

Advantages

Strain sensitive resistors in AC bridge Torsion induced twistMechanical, optical or electromagnetic angle of shaft displacement transducer

Requirements

Contact-free measurement; fast transient response; linear characteristic of signal voltage vs. torque feasible; compensation of temperature and air gap influence

Magnetoelastic effect AC magnetic flux bridge circuit

Torque signal obtained by

Unobstructed space at or around shaft; cross section in the order of squared shaft diameter; rigid structure for holding sensor head or coil near shaft surface

Principle

Table 4-4. Comparison of various torque sensor systems.

(signalkorque)

Q .

126

4 Magnetoelastic Sensors

4.4.6 The Influence and Compensation of Effects Superimposed on the Torque Signal As mentioned in the Sections 4.4.2, 4.4.3 the principle of contact-free magnetoelastic torque measurement is subject to several interfering effects. The influence of these effects on the torque signal and means of compensation will be discussed below. a) Influence of the air-gap between the sensor head and the shaft surface As the stress-dependent changes in the permeability in the shaft surface are measured via the reluctances in the magnetic circuit, variations of the air-gaps between the pole faces and the shaft influence the sensitivity of the system. In order to cope with this effect, first a rigid structure for holding the sensor head near the shaft is essential. Remaining radial displacements of the shaft relative to the sensor can be corrected by controlling the excitation power in a constant-current loop. Another means of cancelling air-gap variations has been described in [33], involving a four-branch type sensor with a multi-pole pot-shaped ferrite head (see Figure 4-13). Its excitation coil and pick-up winding array and the electronic circuit is shown in Figure 4-24a. By series-connecting the capacitor C and the excitation coil, a resonant circuit is formed which is tuned to the oscillator frequencyf. The sensor system operates with a frequency f in the range of 100-200 kHz. If the air-gap between the sensor head and the shaft surface increases, the voltage across the excitation coil rises since the attenuation of the resonant circuit is diminished owing to decreasing eddy-current losses in the shaft surface. In contrast, narrowing the clearance increases attenuation and lowers the excitation voltage so that the “net flux supply” decreases as well. The self-adjusting excitation level enables the system to cover a fairly wide air-gap range without significant variation of the sensitivity. By checking the phase angle a, between the oscillator and the output via a phase-sensitive demodulator the characteristic of the signal voltage against torque can be optimized. Figure 4-24 b illustrates the function of the resonant sensor circuit as obtained from measurements on a 28 mm shaft. As outlined in Section 4.4.2, ring-type designs are in principle free of the air-gap effect. However, they require ample unobstructed space for the closed-ring structure to surround the shaft.

b) Inhomogeneities of the shaft surface The torque signal can be impaired by magnetic inhomogeneities of the shaft surface which to a great extent are caused by shaft production and hardening. (For experimental data on inhomogeneity and hysteresis effects as obtained with a cross type magnetoelastic torque sensor, see, eg, [74].) Gross circumferential inhomogeneities due to a residual stress pattern, induced by extrusion, forging and machining of the shaft, should be equalized by heat treatment as recommended, for instance in [75]. Axial inhomogeneity is less relevant as the magnetic sensor usually remains at a fixed position along the shaft. For the rotating shaft, the torque signal experiences a modulation by the above inhomogeneity effects. In many applications a bandpass filter in the signal processor will be adequate for suppressing this modulation. If fast torque transients must be recorded, a compromise in matching the filter and torque signal characteristics must be found. If necessary, the inherent modulation can be picked up from the shaft rotating without load and be put into an electronic storage device. Then, with torque in the shaft, the stored signal is subtracted from the total signal via the signal processor.

Torque Sensors

4.4

127

7 axis shaf

L

phase shift

C II

1

oscillator

I

-+-

a)

+\+ \+'

W - , 'X0

____

w i t h o u t resonant circui t ----x----_x

:

I

I

I

I

I

1

I

0

0.2

O,L

0,6

0.8

1.0

1.2

I.L

air-gap

I

1.6mm

. )

b)

Figure 4-24. Four-branch type torque sensor with resonant excitation circuit for compensation of air-gap influence [33]; ((p: phase angle between oscillator and demodulator). (a) Principal design, (b) characteristics.

c) Influence of shaft speed The torque signal tends to decrease with increasing shaft speed owing to the enhancement of the skin effect. The quantitative deviation depends on the shaft material, the excitation frequency and flux amplitude and on the circumferential velocity. Therefore experimental verification is essential; see, eg, Figure 4-25 [76]. In principle, the influence of the shaft speed can be compensated in the signal processing circuit. The effect is less or not relevant for torque measuring systems which are operated at high frequencies and for shafts equipped with a ferromagnetic amorphous layer on its surface (Section 4.4.4).

128

4 Magnetoelastic Sensors

1200 ’

p‘ /‘

mv

/

100

N m

engine speed -400

-.-

---

3000 r h i n 1800 600

200 Figure 4-25. Example for the performance of a four-branch design torque sensor: signal voltage vs. torque at various speeds 1761; air gap to shaft: 1 mm, sensor size: 21 mm.

d) Influence of an axial displacement in a coaxial torque sensor Coaxial torque sensors operating with a localized structure or any other pre-treatment of the shaft surface (eg, designs C to E in Table 4-3) exhibit a variation in the characteristic curves under axial displacement of the coil system with respect to the “sensor active” shaft region. In principle this effect can be reduced when the active shaft region exhibits larger axial expansion than the coil (or the reverse). A particularly effective constructive measure was proposed in [77] for the push-pull arrangement D and E in Table 4-3: here the primary coil is split and each half applied to the (separately located) secondary coils; moreover the & 45” orientated surface zones are separated by an “inactive” intermediate zone. In this distribution, axial displacement causes opposing variations in the two halves of the system which largely compensate each other (Figure 4-26). e) Temperature behavior The temperature behavior of magnetostrictive torque sensors is dependent on a number of different parameters; apart from the temperature dependence of the magnetic properties of the shaft material, and/or additional sensor foils on the surface of the shaft, the variations in resistance (skin effect), and the thermal expansion and their effect on the geometry and stress conditions also play a major role. Figure 4-27 shows the temperature dependence of a coaxial torque sensor, similar to the design in Figure 4-19, without any special means of com-

4.4

I

I

I

I

1

129

Torque Sensors

I

I

1

0.2

Yo0

0.4

€-

/

-0.8

Figure 4-26. Influence of small axial displacements on sensor characteristics.

25 "C qo 60 80

----

Figure 4-27. Influence of temperature on sensor characteristics without compensation (sensor with amorphous foil).

pensation; in particular apart from a (slight) zero-point drift, the sensitivity decreases under high excitation. By selecting the correct materials, ie, materials that exhibit only small temperature coefficients or combinations of the same magnitude (eg, with respect to thermal expansion) the in-

130

4 Magnetoelastic Sensors

fluence of temperature can be kept adequately low. Moreover, electronic compensation is often effective, eg, by adjusting the excitation frequency if the temperature characteristic is sufficiently reproducible. In some cases compensation can be achieved simply and effectively by utilizing opposing effects. According to [78] in the cross-type sensor the sensitivity decrease at higher temperatures is compensated by a reduction in the air-gap between the poles of the detector yoke and the shaft caused by the thermal expansion of carefully selected materials.

4.5

Sensors for Forces and Displacements

4.5.1

Magnetoelastic Sensors for Compressive and Tensile Forces

As in torque measurement, magnetoelastic sensor systems are widely used for measuring compressive and tensile forces. In practical applications, either an individual load cell is installed or a member of a complex structure under load is used as a magnetoelastic sensing component. The development of magnetoelastic load cells dates back to the 1930’s [79, 80, 811. An early type [82, 831 was built in various sizes for industrial applications. The stress-sensitive component of such load cells is a solid cylinder made of either permalloy [82] or of an ironaluminium alloy [84]. The cylinder has concentric circular slots holding a winding. The length of the cylinder is sufficiently large to ensure an equalized load distribution in the cross section. For measuring compressive forces, the inductance is determined by an AC bridge circuit. Under axial compression the permeability of the cylinder decreases in the direction of compressive stress, causing the inductance of the system to decrease likewise. Load cells of this design yield an output signal of ample power which was considered an outstanding advantage in the pre-transistor age. On the other hand, by the limited penetration of the alternating field into the solid cylinder, the zero balance and the calibration of the signal vs. force response becomes sensitive to drifts in temperature, frequency, and supply voltage. Figure 4-28 shows a photograph of commercial magnetoelastic load cells of the permalloy cylinder type. A magnetoelastic transformer-type sensor, the Pressductor, has proved to be a successful alternative to the choke-type sensor discussed earlier. The Pressductor, developed by ASEA, Sweden (75, 851, has found a wide range of industrial applications, [86-891 because of its excellent performance under harsh environmental conditions, eg, overload, vibrations, electrical interference, moisture, and dirt. The configuration and the function of the Pressductor principle are illustrated in Figure 4-29: The magnetoelastic element (a) consists of a stack of square transformer sheets, each with four holes punched symmetrically on the diagonals. The holes form two pairs of transverse channels in which two windings are placed which cross at right-angles. According to [85] the Pressductor can be understood as a “misdesigned” transformer: no magnetic linkage occurs between the primary and the secondary windings in the stress-free state, as shown in Figure 4-29b. If, according to Figure 4-29c, a compressive force is exerted on the transformer core, the permeability of the sheet material becomes anisotropic and causes the magnetic flux paths to be distorted. Now the “secondary” is magnetically linked with the flux

4.5 Sensors for Forces and Displacements

131

Figure 4-28. Commercial magnetoelastic load cells (stress-sensitive element: permalloy pot-core [82]).

i a1

F

F b)

Figure 4-29. Principle of Pressductor load cell. (a) Design, (b) unloaded configuration of magnetic flux path, (c) loaded configuration of magnetic flux path.

132

4 Magnetoelastic Sensors

produced by the current through the primary winding. Theoretical studies and experiments suggest that the stress-induced magnetic anisotropy causes up to 20% of the total flux to be “shifted” in the Pressductor configuration and be utilized for compressive force measurement.

C)

Figure 4-30. (a) Pressductor element for 25 kN;(b) multiple unit for 12.5 MN; (c) modern Pressductor design [87] (Courtesy ASEA Brown Boveri AG).

4.5 Sensors for Forces and Displacements

133

Pressductor systems operate at conventional power frequency (50 or 60 Hz) and at higher frequencies in the range of 1- 10 kHz. As for the mechanical design, the laminated Pressductor core must have a shape that ensures an even distribution of the force bearing on the region of magnetoelastic flux sensing. Figure 4-30a shows a well-tried configuration. This element has also been used in multiple laminated core designs. An array with 12 elements in parallel, shown in Figure 4-30b, represents a flat heavy-duty load cell, eg, for monitoring the roll-load in a steel mill [85]. Standard multi-purpose Pressductor load cells with a round or rectangular load-bearing area have been developed for compressive forces up to 10 MN. The high technical standard and reliability of these load-cells, combined with modern signal processors, are suitable for control and automation in heavy industry. Typical performance data are: accuracy of calibration 0.1% (0.5% for nominal loads exceeding 5 MN), linearity error 0.1070, hysteresis 0.2070, repeatibility error 0.1%, compression 0.05 mm, temperature compensation for minimal error in the range 20-80°C, and overload 300% of nominal load without influence on signalto-load characteristic. Further development has led to advanced Pressductors, for example a high-precision transducer which meets the specifications of calibration in weighing systems. In this transducer, magnetoelastic signals in the zones of both compressive and tensile stress are processed for enhanced accuracy in force measurement [90]. Another version has been developed for measuring horizontal forces in two directions by means of the configuration shown in Figure 4-31. The main feature of the sensing element is the orientation of the holes in the

s t r i p tension measured component Ft ( c o S / ~- C O S a ) vertical component, abs o r b e d by cell s t r u c t u r e wrapping angles

\

b)

"

I

c)

Figure 4-31. Pressductor applied to the measurement of strip tension in manufacturing of sheet material. (a) Principle, (b) winding, (c) flux pattern without load and with load.

134

4 Magnetoelastic Sensors

laminations: they are turned by an angle of 45" compared with the original design in Figure 4-29. The illustration explains how the magnetic flux linkage between the winding in the horizontal pair of channels and that in the vertical pair of channels becomes effective as soon as the structure is stressed by horizontal forces at its upper and lower face. This load transducer is used for the measurement of strip tension u p to 16 kN at a maximum linearity error of 0.5'7'0,hysteresis effect less than 0.2%, maximum repeatibility error 0.05%. Cross-type and four-branch type sensors can also be used for non-destructive stress analysis. For this, the sensor head is placed on the surface of the structure to be analyzed. When the sensor pole faces are rotated within a plane parallel to the said surface, the stress distribution is detected by the signal voltage being a function of the angle of orientation and indicates the changes in the permeability according to tensile or compressive stress in one or the other direction. Multiple-branch type sensors with four, six, or more even-numbered sensing pole faces afford stress-pattern evaluation without varying the angular position. The signal voltages of the individual pairs of sensing coils are fed into a signal-processing unit which provides an x-y or polar coordinate plot related to the stress-induced orientation of the permeability. The maxima and minima in the plot correspond to the main directions of tensional stress and compressive stress, respectively. It must be pointed out that this method of stress analysis is restricted to a shallow superficial layer, since in steel structures the penetration depth of the alternating magnetic flux is of the order of millimeters or even less, depending on the sensor operating frequency and on the permeability and the electrical conductivity of the material under test. On the other hand, magnetoelastic surface scanning proves to be very helpful in detecting inhomgeneities due to internal and residual stress, in particular caused by machining processes and heat treatment of mechanical parts. Non-destructive magnetoelastic stress analysis has become the basis of well advanced electronic inspection systems, eg, for testing grinding burns on camshafts, crankshafts, bearing races, rollers, pistons, gears etc. [91]. For measuring tensile and compressive stress in part of a loaded structure, a cross-type or four-branch type sensor head (Section 4.4.2) can be applied. If contact-free measurement is not essential, the sensor head can be placed directly, or spaced by a thin non-magnetic nonconducting layer, on the surface of the structural part in question. For high output, the sensing polepieces are aligned with the prevalent direction of force and the sensor coils wired in a scheme which produces the maximum signal. Figure 4-32 gives an example to stress measurement by means of a four-branch magnetoelastic sensor as described in [33]: The sensor head is placed on the surface of a flat rectangular steel bar exposed to tensile load. The signal voltage obtained in the plot increases proportionally to the applied stress and flattens slightly at 220 N/mm2. Investigations such as this can be used for the calibration of magnetoelastic stress-sensitive arrays. Non-contact magnetoelastic measurement of bending stress have been reported in [92]: The stress pattern in a steel sample is measured by means of a magnetic anisotropy sensor which uses the cross-type principle described in Section 4.4.2. The sensor array and the output vs. stress characteristics are shown in Figure 4-33. In the same procedure as for torque detection, foils of amorphous ferromagnetic metal or magnetoelastic active layers can be fixed to the surface of a loaded mechanical component with insufficient magnetoelastic properties (see Section 4.4.4).

135

4.5 Sensors for Forces and Displacements

Y

c-

X

1’ 0

4

=

s= 1.0

220 0

50

100

150

200

250 N/mmz

U-

Figure 4-32. Tensile force signal obtained with four-branch type sensor [33] installed in flat steel bar under stress.

An example for another approach to magnetoelastic stress analysis is the monitoring of pipelines by the measurement of magnetization changes which a steel pipe experiences under stress [93, 941. These changes consist of a major irreversible portion occurring during initial stressing and a minor reversible portion occurring during each stress cycle. For measuring the effects of pipe bending plus internal hydrostatic pressure on the magnetic behavior of steel pipes, a test rig is set up. In this array two pipe sections are magnetized by means of helical windings on each. First, the residual magnetization due to the Earth’s field is removed by AC excitation at a low frequency with the current amplitude being slowly reduced to zero. Then the pipes are magnetized by single unipolar current pulses through the coils, by alignment in the Earth’s field, or by pulling through a permanent magnet “pig” as used in flux leakage detectors. After magnetization, the external radial and axial field profile is measured by a fluxgate magnetometer and compared with the profile of the pipes without stress. To measure the axle load of lorries a construction has been proposed in which the force is transmitted, via a steel ring, to a strip made of magnetostrictive amorphous ribbon fixed across the ring diameter (Figure 4-34). The steel ring converts the compressive load into tensile stress in the amorphous measuring strip, which is surrounded by a coil. This robust measurement set-up is highly sensitive and utilizes the high bending fatigue strength of amorphous metal [95].

136

4 Magnetoelastic Sensors

exciting core detecting core

sample X

a)

b)

Figure 4-33. Magnetic anisotropy sensor for stress analysis [92]. (a) Basic structure ( I = excitation current, UOu, = detecting output voltage, (b) output voltage versus stress characteristic.

(0 approx. 50 mm)

Figure 4-34. Schematic diagram of a force sensor using amorphous material according to [95].

4.5.2 Position and Displacement Sensors Position and displacement sensors can be made up in many diverse designs which detect widely varying measurement ranges and exhibit varying degrees of accuracy, eg, differential transformers, proximity sensors and other inductive systems (Chapter 7).

4.5 Sensors for Forces and Displacements

137

By utilizing the magnetostrictive effect and the favorable elastic properties of amorphous metal, relatively simple sensors can be made up from rings which detect paths and displacements in the range of ca. 0.01 to 10 mm. The principle is explained in Figure 4-35. Single or multiple layer rings of amorphous ribbon with positive magnetostriction and diameters of, eg, 5 to 10 mm can be used as models for simple displacement and position sensors (Figure 4-6). The ring operates both as a core of a transformer and as a spring. If a circular ring is deformed by a force F to an ellipse (deflection by the path As), the initially steep hysteresis (loop 1) flattens rapidly (loop 2). Accordingly, the secondary voltage is reduced from U , to U,. On the removing the load, the ring recovers full elasticity and returns to its original circular shape, and the secondary voltage reacts accordingly [96].

F

U

---

-us

Figure 4-35. Operating principle of a magnetoelastic sensor with a ring of amorphous metal. (a) Deformation by a force F ; (b) change of hysteresis; (c) voltages U,(without load), U, (with load).

The simple model shown in Figure 4-35 was the basis of a series of investigations and considerations on applications which were primarily conducted by Mohri and co-workers [97-991 and Overshott, Meydan and co-workers [loo- 1041. An attempt to calculate the stresses arising in the ring under maximum deflection cmaxhas been described in [98]. A multivibrator circuit with one or two amorphous rings is frequently used as a measurement system. It supplies linear output voltages proportional to the force, or the deflection operating on the ring. Figure 4-36 shows a two-core multivibrator bridge circuit [97], in which a reference core compensates temperature and zero drift.

138

4 Magnetoelastic Sensors

Tr 1

-

active core, 1 0,F

h

L i

T

T

T

T

1 A 1

'

A'"0C

II

reference core, 2

Trz Figure 4-36. Two-core multivibrator circuit with DC output for linear-type transducers [97].

Two transistors, Tr, and Tr, alternate the switching of the cores between remanence and saturation. The increase in differential flux density due to the deformation of one of the cores is converted to DC voltage and appears as an output signal. Compared with strain gages the following advantages can be mentioned: higher temperature stability; higher linearity; and a fivefold higher output voltage. Application of the above as an extensometer has been described in [98]. In this case an amorphous ring core made of an Fe-rich alloy is placed in a fixture as shown in Figure 4-37. The bearings transmit the stress or deflection to the core in a precisely defined manner (Figure 4-37a). The arrangement of the windings (Figure 4-37b) with the division of the primary winding into 1 and 1' and the secondary winding into 2 and 2' compensates magnetic interference fields. The spring prevents the hysteresis effects and resets the spring into exactly the same initial position within the fixture.

.amorphous

core

Figure 4-37. Extensometer. (a) Construction of strain sensing element using amorphous ribbon wound core; (b) configuration of lumped windings.

4.5 Sensors for Forces and Displacements

139

The following data apply to an extensometer with a four-layer core, diameter 10 mm, made eg, for deflections As up to 5 mm: linearity error, 0.18%; temperature of Fe,,Mo,B,,, stability, 0.02%/K; and temperature range, up to 95 "C. The characteristic curve is plotted in Figure 4-38. Detailed investigations of the influence of the arrangement of windings along the circumference of the ring and the position of the bonding point on the ring have been performed in [104]. The four configurations, presented in Figure 4-39, give information o n the influence

Figure 4-38. Characteristics of UOu,versus A s for sensor of Figure 4-37.

F

F

i

pr imar

bonding Point P r imar

a)

bonding point

amorphous core

F

F

t

-amorphous + \

primary

@

L

b)

secondary

core

amorphous core

ssecondary

bondirk point

ondary C)

Figure 4-39. Transducer with different winding configurations a)-d).

d)

140

4 Magnetoelastic Sensors

exerted on linearity, sensitivity, hysteresis, and the reproducibility of the sensors. In connection with this, the distribution of the tensile and compressive strengths within the amorphous cores was more closely examined on a model [103]. By superposing a DC current on the AC current, typically 10 kHz, used to magnetize the core, the linearity of the characteristic curve of the sensor can be improved because bias magnetization has a linearizing effect on the magnetization curve. However, this calls for relatively complex circuitry [102]. Apart from being used to measure displacement, strain and force, rings made of amorphous alloys are also employed as non-contact switches and limiting value selectors. A limiting or threshold selector can be relatively easily realized when, as indicated in Figure 4-35, a defined voltage Us is given as a threshold value. The secondary voltage ratio U,: U, of the undeformed ring-shaped core and the deformed ellipsoidal core can be between 2 : 1 and 9 : 1, giving separation for the definition of the limiting value and to ensure a safe switching distance. It may be advisable to apply pulse magnetization rather than AC magnetization to keep the complexity of the electronic circuitry to a minimum [105]. Figure 4-40 shows the force F for as a single-layer rings, diameter 10 mm, strip width 6 mm, and the secondary voltage U,,,, function of displacement, or of the deflection s for two amorphous alloys with considerably different saturation magnetostriction values 1,.

t0.3

-

I I

LL 0.2

-

N

0.1

-

0-

s-

Figure 4-40. Force F and secondary voltage U,,, as a function of deflection path s on amorphous magnetoelastic rings.

If the arrangement is further refined, then several switching thresholds can be laid down as shown in Figure 4-41. The reproducibility of the switching point for a single-layer ring with a diameter of 10 mm is ca. A s = k0.02 mm [105, 1061. A matrix or line-like arrangement of rings with a switching function leads to a non-contact keyboard. Special shaping of the housing or the use of double rings means that keys with an “action point” can be realized, ie, keys which only trigger the switching function when a minimum operating force is applied [105, 1061.

4.6 Special Magnetoelastic Sensors

141

F

II

I

Figure 4-41. Ring as switch and position indicator for three stages sI-s3.

Figure 4-42 shows a model with a single ring and a double ring. In the first case the “actionpoint effect” is achieved through a depression in the casing and in the second by a change in the configuration of the double rings on depression. key not Pressed

initiation o f action-point

key pressed

operating path

a) ring casing nith depression

Figure 4-42. Keyboard with amorphous rings and action-point effect. (a) Ring casing with depression, (b) . , design using a double ring.

b)

design using a double ring

4.6 Special Magnetoelastic Sensors 4.6.1 AE Effect and Ultrasonic Wave-Propagation Devices Another effect used to measure magnetic fields and to detect field changes is the A E effect. This effect is based on the influence of magnetization on Young’s modulus. The A E effect is well-known from nickel-iron based crystalline constant-modulus alloys and is due to the Invar effect. It also occurs in some amorphous alloys.

142

4 Magnetoelastic Sensors

The field strength and its variations can be determined by delay lines and in tunable surface acoustic wave components. On the basis of the well-known equation for the sound velocity v,

(4-14) where E = Young's modulus; p = density of the material,

it is obvious that a change in E corresponds to a change in sound velocity:

(4-15) As an example of the magnitude of the A E effect, Figure 4-43 shows the Young's modulus of an amorphous alloy Fe,,Ni,,Mo,B,, in the as-quenched state and after annealing [107]. In the annealed state, this means in the softer magnetic state, there is a large difference between the magnetized and the non-magnetized state. The saturation field is ca. 80 A/cm. At room +20%, which corresponds to A v / v = 10%. temperature we derive from Figure 4-43 A E / E J

kN/mm2 160 -

1 2

4

annealed 350 OCI2h

140120.

H- H,

a

U

p

A

1 0 0 - H=O <====----RY H= HS

80 -

H= 0

- A

t Tc

60 -

40

as quenched

-

H, = 80 Alcm

20 -

0-

1

'

"

"

'

1

Figure 4-43. A E effect of an amorphous FeNi-based

A device using the A E effect for magnetic field sensors has been proposed by [108]. It consists of a piezoelectric substrate, a magnetostrictive amorphous film and signal input and output transducers (Figure 4-44). A digitizer with a cordless cursor to input the coordinates of graphics can also be based on delay line principle using Fe-based amorphous ribbons or wires [107].

143

4.6 Special Magnetoelastic Sensors

transducers signal .---/

M O U t D U t

‘iC

magnetostr ict ive amorphous f i l m Figure 4-44. Magnetically tunable delay line.

In addition to the field dependence of the A E effect, the temperature dependence can also be used in temperature sensors, eg, in frost sensors or thermal sensors. These and other sensors based on ultrasonic propagation effects have been surveyed in [log, 1241. In the same way as the change in Young’s modulus E, the change in shear modulus G can be used to detect and measure magnetic fields. This method has been described as “shear-wave magnetometry” [110]. Instead of Equations (4-14) and (4-15) for zero-order shear waves we write

V =

and

&.--

(4-16)

V

where

G = shear modulus. In a practical device, a shear wave is propagated along a strip of amorphous material. The wave is triggered by a piezoelectric transducer bonded to one end and received by a second transducer at the other end of the strip. The change in phase is detected by a phase meter. The phase change is proportional to the field change AH. Fe- and NiFe-based amorphous alloys have been investigated.

4.6.2 Wiedemann Effect Devices The Wiedemann effect, which was discovered in 1858 and falls under the category of magnetoelastic effects, can also be used as a base for force and torque transducers (see Chapter 4.2). A torque sensor for static forces using a lever arm (a) and a force sensor balance with a spring made of magnetic material (b) have been proposed [lll]. Figure 4-45 shows the principle of the design of both transducers. Similar considerations for the application of helical magnetostrictive transducers have been investigated by [112]. Figure 4-46 shows a schematic representation of a transducer operating on the inverse Wiedemann effect (a) compared with an impedance variation (b). In the usual

144

4

Magnetoelastic Sensors

a)

b)

Figure 4-45. Transducers using Wiedemann effect. (a) Torque sensor, (b) force sensor balance.

1

d i s p l a c e m e n t

1

magnetostrictive wire

ion sing a)

b)

Figure 4-46. Schematic representation of helical magnetostrictive spring transducer elements. (a) Inverse Wiedemann effect, (b) impedance variation.

mode of operation Figure 4-46a, alternating current is conducted through a spring made of magnetostrictive wire and an isoperiodic output signal is developed in the solenoidal coil. Axial tension or compression of the spring causes a magnetic anisotropy in the wire having a component coaxial with the solenoid, which results in a change of the output signal. Suitable spring materials are found among the nickel-iron permalloys with special treatment.

4.6.3 Shock-Stress Sensors A new type of transducer using an amorphous ribbon with only a single winding and without electric supply has been reported in [113, 1141. It has been shown that the application

4.6 Special Magnetoelastic Sensors

145

of an impulse force to a ring-shaped transducer causes a localized bending stress which results in a change in the domain wall configuration and in domain wall motions. Figure 4-47 shows a toroid of ca. 14 mm outer diameter, made of an Fe-based amorphous alloy with a single winding over the area where bending stress occurs. The bending causes a n output voltage for a finite time depending on the velocity of application of force F (b). The removal of the force F produces a voltage of opposite polarity (c). The sensitivity can be increased by appropriate annealing of the toroid. These sensors have been suggested for shock-stress, alarm and impulse force sensors.

Figure 4-47. Sensor with an amorphous core [114] operating without power supply.

To detect engine knocking a tuned vibration detector was investigated using a short strip of amorphous ribbon with positive magnetostriction in a resonant system [115]. Similar proposals have been made by several authors [log]. Magnetic sensors utilizing twisted wires or ribbons made of Fe-based amorphous alloys without any windings have been realized for detecting rotational speed, distances or other mechanical quantities [110, 1171. They use the Matteucci effect and the large Barkhausen effect.

4.6.4 Sensors Combining Magnetostrictive Effect and Other Physical Effects An interesting force-sensing device which combines two physical effects, the magnetostrictive effect and Hall-effect, has been proposed by [118] and is shown in Figure 4-48. The magnetic circuit consists of two magnetostrictive rods (1) of 45% NiFe and of two yokes of soft iron with pole pieces in the middle (2) to form a flux return path. A Hall element (4) is fixed in a small air-gap (3) between the pole pieces. The system is magnetized by a constant current through the windings ( 5 ) . If a force F is applied to the system the two rods (1) with positive magnetostriction are stressed and change their flux density. This results in a flux change in the total circuit, including the air-gap. The flux change is detected by the Hall element and corresponds to the force F to be measured. This sensor is specifically applicable to grippers of robots and to force measurement in general.

146

4 Magnetoelastic Sensors

1 2

+

2

F

1

Ia)

b)

Figure 4-48. Force-sensing sensor. (a) Design, (b) characteristic.

Another proposal combines a magnetostrictive amorphous strip bonded with a piezoelectric transducer (PZT). The strip is magnetized by a bias DC field to be measured. Changes in strip length by the DC field are converted into electrical signals by the PZT element [119]. A schematic diagram of a magnetometer apparatus with a linear response from approximately 1.5 . to 1 A/m is represented in Figure 4-49. A sensitivity of l o v 4 A/m per 1/Hz was reported for an Fe-based alloy.

1

Figure 4-49. Schematic diagram of a magnetometer [119] using two different physical effects.

4.6.5 Other Magnetoelastic Sensors Apart from the above-mentioned sensors and transducers, further proposals have been published on the use of magneto-elastic and stress-magnetic effects. A survey has been published [109]. Zero-magnetostrictive or high-magnetostrictive amorphous alloys are being

4.7 References

147

applied in fields where conventional crystalline materials are difficult to use. T h e following Table 4-5 lists such sensors a n d sensor elements with some notes on performance a n d applications. Table 4-5.

Other magnetoelastic sensors.

Sensor or sensor element

Performance

Application

References

Magnetic strain gage

More sensitive than standard As strain gages in resistance strain gages robotics, robotic wrists

[120, 121, 1251

Tension sensor

Using frequency mode of transverse vibrations of strings

Tensile force sensor

[122, 1261

Current sensor, load and displacement sensor

[123, 1271

Plastically helical-formed Sharp voltage pulse generaamorphous magnetostric- tion tive ribbons

4.7 References [l] Joule, J. P., “On a new class of magnetic forces” Ann. Electr. Magn. Chem. 8 (1842) 219-224. [2] Villari, E., “Change of magnetization by tension and by electric current” Ann. Phys. Chem. 126 (1865) 87- 122. [3] Bozorth, R. M., Ferromagnetism, New York: Van Nostrand, 1955. [4] Kneller, E., Ferromagnetismus, Heidelberg: Springer, 1962. [ 5 ] Tebble, R. S., Craik, D. J., Magnetic materials, New York: Wiley-Interscience, 1969. [6] Furthmiiller, J., Fahnle, M., Herzer, G., “Theory of magnetostriction in amorphous and polycrystalline ferromagnets”, J. Magn. Magn. Mat. 69 (1987) 79-88 and 89-98. [7] Mermelstein, M. D., “Coupled mode analysis for magnetoelastic amorphous metal sensors”, IEEE Trans. Magn. MAG-22 (1986) 442-446. [8] Aroga, C. et al., “Magnetoelastic effects in amorphous FeNiPB alloys”, IEEE Trans. Magn. MAG-17 (1981) 1462-1467. [9] Chin, G. Y., “Processing control of magnetic properties for magnetostrictive transducer applications”, J. of Metals, Jan. (1971) 42-45. [lo] Boll, R., Borek, L., “Magnetic sensors of new materials”, Siemens Forsch.-Entw. Ber. 10 (1981) 83-90. [ll] Glassy metals, magnetic, chemical and structural properties, Hasegawa, R. (ed.); Boca Raton, Florida: CRC Press, 1983. [12] Wun-Fogle, M., Clark, A. E., Hathaway, K. B., “Permeability in ‘frozen’ high magneto-mechanical coupling amorphous ribbons”, J. Magn. Magn. Mat. 54-57 (1986) 893-894. [13] Hilzinger, H. R., Hillmann, H., Mager, A., “Magnetostrictive measurements of Co-base amorphous alloys”, Phys. stat. sol. (a) 55 (1979) 763-769. [14] Warlimont, H., Boll, R., “Applications of amorphous soft magnetic materials”, J. Magn. Magn. Mat. 26 (1982) 97-105.

148

4 Magnetoelastic Sensors

[15] Amorphous Metallic Alloys, Luborsky, F. E. (ed.); London: Butterworth, 1983. [16] Warlimont, H., “New magnetic materials by rapid solidification”, in: Rapidly Quenched Materials Vol 11, Steeb, S . , Warlimont, H. (eds.); Amsterdam: North-Holland, 1984, 1599-1609. [17] Soft Magnetic Materials, Boll, R. (ed.); London: Heyden & Son, 1979. [18] Werkstoffkunde, Stahl Vol. 2, VDE; Heidelberg: Springer, 1985, Abschn. D20. [19] Heck, C., Magnetism and Metallurgy of Soft Magnetic Materials, New York: North-Holland, 1977. [20] Snelling, E. C., Soft Ferrites, London: Butterworth, 1988. [21] Boll, R., Hilzinger, H. R., “Eigenschaften und Anwendungen von amorphen Magnetwerkstoffen”, etz 102, No. 21 (1981) 1096-1100. [22] Davis, L. A., Ramanan, V., R., V., “Metallic glasses as magnetomechanical materials”, in: Metallic and semiconducting glasses 111, Proc. Intern. Con$ Metallic and Semiconducting glasses, Hyderabad/India, Dec. 1986, Bhatnagar, A. K. (ed.); Trans. Tech. Publications, CH. [23] Clark, A. E., “Magnetostrictive rare earth-Fe, compounds”, in: Ferromagnetic Materials Vol. 1, Wolfarth, E. P. (ed.); Amsterdam: North Holland Publishing Company, 1980. [24] “Magnetostriction: the competive edge”, Sensor Review 8 (1988) 41 -43. [25] Norton, H., N., Sensor and analyzer handbook, Englewood Cliffs, N J: Prentice Hall, 1982. [26] Boll, R . , “Magnetoelastische Sensoren mit amorphen Metallen”, Verhandlungen der DPG 6 (1984) 1408- 1416. [27] Dubbel, Taschenbuchf u r Maschinenbau, Beitz, W., Kuttner, K. H. (ed.); Heidelberg: Springer, 1986. [28] Scabo, I., Einfiihrung in die technische Mechanik, Heidelberg: Springer, 1979. [29] Dahle, O., “The Torductor and the Pressductor, - two Magnetic Stress-Gauges of New Type”, ASEA Research l(1958) 45-68. [30] Fleming, W. J., Engine Sensors: State of the Art, SAE Congress, Detroit, MI, I982 Paper 820904, 97-113. [31] Shashi, M., Inomata, K., Kobayashi, T., A torque sensor of the noncontact type, European Patent Application Nr. 0136086, 1984. [32] Beth, R. A,, Meeks, W. M., “Magnetic Measurement of Torque in a Rotating Shaft”, Rev. Sci. Instrum. 25, No. 6, (1954) 603-607. [33] Winterhoff, H., Heidler, E.-A., “Beruhrungslose Drehmomentmessung und Wirbelstrom-Sensoren”, Technisches Messen 50, No. 12 (1983) 461 -466. [34] Hamarak, K., “Schleifringloses Drehmomentmeljverfahren fur die Schwermaschinenindustrie”, Maschinenmarkt 72 (1966) 155-165. [35] Dahle, O., “The Ring Torductor - a Torque-Gauge, without Slip Rings, for Industrial Measurement and Control”, ASEA Journal 33, No. 3, (1960) 23-32. [36] Drakensjo, I., “Torsiometers Based on the Torductor Torque Transducer”, ASEA Journal 43, No. 2, (1970) 23-32. [37] Angheid, E., “Noncontacting Torquemeters Utilizing Magnetoelastic Properties of Steel Shafts”, ASME Paper 69-GT-64, Gas Turbine ConJ, Cleveland, Ohio, March 9, 1969. [38] Torque-meters, Power-meters, Energy-meters for ships in combination with the ASEA TORDUCTOR torque transducer, Catalogue B 07-7700E 1986, ASEA Industry and Electronics, Vasteras, SE. [39] Miller, A. L., “Microcomputer Controlled Automatic Transmission”, in SAE Congress, Detroit, MI, 1982, Paper 820394. [40] Scoppe, F. E., “Magnetostrictive Torque Transducer”, Instrumentation Technology 16 (1969) 95-99. [41] Dahle, O., Torque Transducer, US.Pat. 4135391, 1979. [42] Horter, H.-D., Assembly for Monitoring Torsional Loading of a Drive Shaft, US.Pat. 4364 278 (1982). [43] Yaroslavl, Car, D., Torque in steel shafts magnetic determn. method - uses detection of second harmonic amplitude from combined constant and alternatingfields in torsion section, Russisches Patent A 145-OC/DI SU 657-281, 1979. [44] Iwasaki, S., Torque Sensor, Europ. Patentschrift 0067974, 1982.

4.7 References

149

[45] Harada, K. et al., “A new torque transducer using stress sensitive amorphous ribbons”, ZEEE Trans. Magn. MAG-18 (1984) 1767-1769. [46] Sasada, I. et al., “A new method of assembling a torque transducer”, IEEE Trans. Magn. MAG-19 (1983) 2148-2150. [47] Mohri, K., “Review on recent advances in the field of amorphous-metal sensors and transducers”, IEEE Trans. Magn. MAG-20 (1984) 942-947. [48] Sasada, I. et al., “Torque transducer with stress-sensitive amorphous ribbons of chevron-pattern”, IEEE Trans. Magn. MAG-20 (1984) 951-953. [49] Hilzinger, H. R., Nilius, H. J., Friedrichs, M., Ferromagnetische Foliefiir einen Drehmomentsensor, Deutsche Offenlegungsschrjft DE 35 09552 Al, 1985. [50] Yamasaki, J., “Torque sensors using wire explosion magnetostrictive layers”, IEEE Trans. Magn. MAG-22 (1986) 403-405. [51] Juckenack, D., Molnar, J., “Sensor zur Drehmomentmessung mit amorphen Metallen”, Techn. Messen 53 (1986) 242-248. [52] Himmelstein, S., Wellendrehmomentinesser, Deutsche Offenlegungsschrift DE 35 19 769 A l , 1985. [53] Scoppe, F. E., Electromagnetic torquemeter, U S. Patent 3340729, 1967. [54] Blomkvist, K., Magnetoelastische Drehmomentgeber, Deutsche Offenlegungsschrift DE 33 19449 AI, 1984. [55] Boll, R., Friedrichs, M., Verfahren zur Messung einer mechanischen Spannung in einer Welle, Deutsche Offenlegungsschrjft DE 3407917, 1984. [56] Kawafune, K., Nakazawa, K., Method and device for measuring a stress employing magnetostriction, U S . Patent 3861206, 1975. [57] Maier, W., Horter, H. D., Magnetostriktives MeJverfahren, insbesondere zur Drehmomenterfassung an Wellen, Deutsche Offenlegungsschrjft 2939566 Al, 1981. [58] Sasada, I. et al. “Noncontact torque sensors using magnetic heads and a magnetostrictive layer on the shaft”. ZEEE Trans. Magn. MAG-22 (1986) 406-408. [59] Sasada, I. et al., “Characteristics of chevron-type amorphous torque sensor constructed by explosion bonding”, IEEE Trans. Magn. MAG-23 (1987), 2188-2190. [60] Yamasaki, J., Mohri, K., Ogawa, M., “Preparation of magnetostrictive layers by wire explosion spraying and its application to torque sensors”, IEEE Transl. J , Magn. Jap. (TJMJ) 2 (1987) 767 - 768. [61] Inomata, K. et al., Torque sensor and method for manufacturing the same, Europ. Patent 0107082 Al, 1983. [62] Kobayashi, T. et al., A built-in type amorphous torque sensor for an induction motor. IEEE Trans/. J , Magn. Jap. (TJMJ) 3 (1988) 226-234. [63] Ill, M., Boll, R., Entwicklung eines Drehmomentsensors. AbschluJbericht zum BMFT-Projekt BN 5239, 1984, BMFT, 5300 Bonn, FRG. [64] Boll, R., Hinz, G., “Sensoren aus amorphen Metallen”, Technisches Messen 52, No. 5, (1985) 189198. [65] Fleming, W. J., “Automotive torque measurement: A summary of seven different methods”, IEEE VT-31 (1982) 71-78. [66] Mohri, K., Nakano, M., Mukai, Y., Yoshida, Y., “Detecting of secondary current and torque of induction motors using amorphous microcore field sensors”, ZEEE Trans. Magn. MAG-22 (1986) 397 - 399. [67] Emmerling, A. E., “A torque measurement transducer system”, Electrical Eng. Oct., (1963) 621-625. [68] Ettelmann, D., Hoberman, M., “Torquemeters”, Machine Design, Febr., (1963) 134-139. [69] Mohri, K., Yoshino, K., Okuda, H., Malmhall, R. K., “Highly accurate rotation-angle sensors using amorphous star-shaped cores”, IEEE Trans. Magn. MAG-22, No. 5, (1986) 409-411. [70] Mohri, K., Mukai, Y., Yasuda, K., Takayama, K., “New torque sensors using amorphous starshaped cores”, IEEE Trans. Magn. MAG-23, No. 5 , (1987) 2191-2193.

150

4 Magnetoelastic Sensors

[71] Hachtel, H., Dobler, K., MeJeinrichtung fur einen Drehwinkel und/oder ein Drehmoment, Deutsches Patent DE 2951 148 C2, 1979. [72] Dobler, K. W., Hachtel, H., “Neues Verfahren zur Drehmomentmessung mit Hilfe von Wirbelstromeffekten”, Techn. Rundschau 75, No. 45, (1983) 17- 19. [73] Sahashi, M. et al., “A new contact amorphous torque sensor with wide dynamic range and quick response”, IEEE Trans. Magn. MAG-23, No. 5, (1987) 2194-2196. [74] Jahnig, L., ,,Drehmomentsensoren auf der Basis des magnetostriktiven Effektes“, VDI-Berichte Nr. 509, Diisseldorf: VDI, 1984, 187-191. [75] Torductor Drehmomentgeber l ? ~ pQGTA 101, Katalog YM 221-302 ?: ASEA, Vaster&, Schweden, 1974. [76] Fleming, W. J., Wood, P. W., ,,Non-contact sensor measures engine torque“, Automotive Engineering 90 (1982) 58-62. [77] Erb, O., Koaxialer Drehrnomentsensor, Deutsche Offenlegungsschrjft DE 0s 3 629610, 1986. [78] Hohenberg, R., Means for temperature compensation the response of an electromagnetic torque meter, US Patent 3465581, 1969. [79] Janowski, W., ,,Magnetoelastische Messung von Druck-, Zug- und Torsionskraften,“ ATM V 132-6 (1932). [80] Merz, L., Scharwachter, H., ,,Magnetoelastische Druckmessung“, ATM VU2-15 (1937). [81] Pflier, P. M., Elektrische Messung mechanischer GrOJen, Heidelberg: Springer 1948. [82] Engl, W., ,,Magnetoelastische KraftmeBdosen“, Siemens-Zeitschrjft, No. 5/6, (1955) 219-222. [83] Engl, W., ,,Mechanische Probleme bei elektrischen KraftmeBdosen“, ATM 289 (1960) R 13-R 17. [84] Profos, P., Handbuch der industriellen MeJtechnik, Essen: Vulkan-Verlag, 1974, 474ff. [85] Dahle, O., “The Pressductor - a High-Output Load Cell for Heavy Industry“, ASEA Journal 32, NO. 9, (1959) 9, 115-123. [86] Blickley, G. J., “Microprocessor-based Batch Weighing Using Multiple Magnetoelastic Load Cells”, Control Eng., July, (1984) 86-87. [87] ASEA Pressductor Systems Millmate, Catalogue B 07-7502E, ASEA Industry and Electronics, Vaster& SE, 1986. [88] Checinsky, S. S., Agrawal, A. K., “Magnetoelastic tactile sensor”, SPIE 449, No. 2 (1984) 468-474. [89] ASEA Automation, Pressductor Equipment for Measuring Strip Tension; Reg. 5693, B07-7503E, Vaster& 1987. [go] Nordvall, J. O., “New Magnetoelastic Load Cells for High Precision Force Measurement and Weighing”, 10th IMEKO ConJ TC-3. Kobe, Japan, Sept 1984, 5-9. [91] Rollscan, Information Bulletin R 100s-B, Stresscan SOOC, In$ Bulletin SSOOC-B, Magnetoelastic Sensors, Inj Bulletin S100-C, 1985, American Stress Technologies Inc., Bethel Park, PA 15 102, USA. [92] Yamada, H. et al., “Noncontact measurement of bending stress using a magnetic anisotropy sensor”, IEEE Trans. Magn. MAG-23, No. 5, (1987) 2422-2424. [93] Atherton, D. L., Teitsma, A., “Detection of Anomalous Stress in Gas Pipelines by Magnetometer Survey”, J. Appl. Phy. 53, No. 11, (1982) 8130-8135. [94] Atherton, D. L. et al., “Stress-induced Magnetization Changes of Steel-pipes-Laboratory Tests”. IEEE Trans. Magn. MAG-20, No. 6, (1984) 2129-2136. [95] Kuhn, P. et al., Geber zum Messen mechanischer KrUfte, Europdisches Patent, EPA 0036532, 1981. [96] Boll, R., “Magneto-elastische Sensoren mit amorphen Metallen”, Verhandlungen der Deutschen Physikalischen Gesellschaft. 48. Physikertagung Munster 1984, 1408- 1416. [97] Mohri, K., Korekoda, S. “New force transducers using amorphous ribbon cores”, IEEE Trans. Magn. MAG-14 (1978) 1071-1075. [98] Mohri, K., Sudoh, E., “New extensometers using amorphous magnetostrictive ribbon wound cores”, IEEE Trans. Magn. MAG-17 (1981) 1317-1319. [99] Mohri, K., Sudoh, E., “Sensitive force transducers using a single amorphous core multivibrator bridge”, IEEE Trans. Magn. MAG-I5 (1979) 1806-1808.

4.7 References

151

[loo] Meydan, T., Blundell, M. G., Overshott, K. J., “An improved force transducer using amorphous ribbon cores”, IEEE Trans. Magn. MAG-17 (1981) 3376-3378. [loll Blundell, M. G., Meydan, T., Overshott, K. J., “An A. C. force transducer using amorphous ribbon cores”, J. Magn. Magn. Mat. 26 (1982) 161. [lo21 Meydan, T., Overshott, K. J., “The effect of AC and DC basing on the performance of AC amorphous ribbon transducers”, in: Soft Magnetic materials 7, Blackpool Conj Aug. 1985, 351 -354. [lo31 Meydan, T., Overshott, K. J., “Internal stress distribution model for AC amorphous ribbon transducers”, in: Soft Magnetic Materials 7, Blackpool Conj Aug. 1985, 347-350. [lo41 Meydan, T., Overshott, K. J., “Amorphous force transducers in AC applications”. J. Appl. Phys. 53, NO. 11, (1982) 8383-8385. [lo51 Friedrichs, M., Hinz, G., “Sensoren mit Ringen aus amorphen Werkstoffen als empfindliche Schalter und Positionierelemente”. Paper presented at the Conference “Sensoren - Technologie und Anwendung”, Bad Nauheim, 1984. [lo61 Boll, R., Friedrichs, M., “Sensortaste zur kontaktlosen Erzeugung eines elektrischen Signals bei Tastendruck”, Deutsche Patentschrift DE 3127053 C2, 1983. [lo71 TOrOk, E., Hausch, G., “Search for Invar-like magnetoelastic behaviour in Fe-Ni based metallic glasses“, J. Magn. Magn. Mat. 10 (1979) 303-306. [lo81 Webb, D. C., Forester, D. W., Ganguly, A. K., Vittoria, C., “Applications of amorphous magneticlayers in surface acoustic-wave devices”, IEEE Duns. Magn. MAG-15 (1979) 1410-1414. [log] Mohri, K., “Applications of amorphous alloys for sensors and transducers”, in: Rapidly Quenched Materials Vol. 11, Steeb, S., Warlimont, H. (ed); Amsterdam: North-Holland, 1984, 1687-1690. [110] Squire, P. T., Gibbs, M. R. J., “Shear-wave magnetometry using metallic glass ribbon”, Electronics Letters 23, No. 4, (1987) 147-148. [lll] Ruzek, V. J., ,,Untersuchung des Wiedemann’schen Effektes zur Kraft- und Drehmomentmessung“, Feinwerktechnik & MeJtechnik 92, No. 8, (1984) 415-416. [112] Garshelis, I. J., “Displacement transducer using impedance variations due to core torsions”, IEEE Trans. Magn. MAG-16 (1980) 704-706. [113] Mohri, K., Takeuchi, S., “Stress-magnetic effects in iron-rich amorphous alloys and shock-stress sensors with no power”, IEEE Trans. Magn. MAG-17 (1981) 3379-3381. [114] Overshott, K. J., Meydan, T., ,,Unmagnetized amorphous ribbon transducers”, IEEE Trans. Magn. MAG-20 (1984) 948-950. [115] Anderson 111, P. M. et al., Tuned vibration detector, Europ. Pat. Appl. 0086973A2, Allied Corp. [116] Mohri, K., Takeuchi, S., “Sensitive bistabile magnetic sensors using twisted amorphous magnetostrictive ribbons due to Matteucci-effect”, J. Appl. Phys. 53, No. 2, (1981) 8386-8388. [117] Mohri, K. et al., “Large Barkhausen-effect and Matteucci-effect in amorphous magnetostrictive wire for pulse generator elements”, IEEE Trans. J. Magn. Jap. 1, No. 2, (1925) 231-232. [118] Griffing, B. M., “Force-sensing device”, IBM Technical Disclosure Bulletin 27 (1984) 1199-1200. [119] Partinakis, A., Jackson, D. A., “High sensitivity low-frequency magnetometer using magnetostrictive primary sensing and piezoelectric signal recovery”, Electronics Letters 22, No. 14, (1986) 737-738. [120] Mitchell, E. E., Vranish, J., “Magnetoelastic force feedback sensors for robots and machine tool - an update”, in: Robots 9. C o d Proc. Advancing Applications, Detroit, M: Roboties Int. of SME, 1 (1985), pp. 11-28. [121] Mitchell, E. E. et al., “A new METGLAS sensor”, IEEE Trans. Industr. Electronics IE-33 (1986) 166- 170. [122] Sonoda, T., Veda, R., “Field and force sensors using amorphous ribbons”, IEEE Trans. Magn. MAG-22 (1986) 952-954. [123] Mohri, K., Shirosugi, T., “Pulse-output type magnetic sensors using plastically helical amorphous ribbons”, IEEE Trans. Magn. MAG-l9, No. 5, (1983) 2151-2153. [124] Shirae, K., Honda, A., “Average temperature transducer using amorphous magnetic tape”, IEEE Trans. Magn. MAG-17 (1981) 3151-3153.

152

4 Magnetoelastic Sensors

[125]Wun-Fogle, M., Savage, T., Clark, A. E., “New magnetostrictive strain gauge demonstrates high sensing potentials”, Tech 34, March, (1987)51-54. [126]Woschni, E. G.,,,Moglichkeiten und Grenzen dynamischer Messungen mit dem Saitendehnungsmesser”, Messen, Steuern, Regeln 6 (1963)493-498. [I271 Murakami, A.,Hosaka, K. et al., “An amorphous magnetostrictive delayline cordless digitizer”, IEEE Trans. Magn. MAG-24, No. 2, (1988) 1758-1759;and MAG-25, No. 3 (1989)2139-2744.

5

Magnetic Field Sensors : Flux Gate Sensors WOLFGANG BORNHOFFT. Telefunken Systemtechnik. Hamburg. FRG GERHARD T~ENKLER. Universitat der Bundeswehr. Hamburg. FRG

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1

Introduction

5.2 5.2.1 5.2.1.1 5.2.1.2 5.2.1.3

Flux Gate Sensor Fundamentals . . . . . . . . Theoretical Approaches to the Magnetization Curve Polynominal Approach . . . . . . . . . . . . . Piecewise Linear Function . . . . . . . . . . . . Trigonometric Function . . . . . . . . . . . . .

5.3 5.3.1 5.3.1.1 5.3.1.2 5.3.1.3 5.3.1.4 5.3.1.5 5.3.2 5.3.3 5.3.4 5.3.4.1 5.3.4.2 5.3.4.3 5.3.4.4

Magnetometers . . . . . . . . . . . . . . . . . . . . . . . . Second Harmonic Flux Gate Magnetometer . . . . . . . . . . . Basic Principle of Operation . . . . . . . . . . . . . . . . . . Transfer Function of the Second Harmonic Flux Gate Magnetometer Single-Core Second Harmonic Flux Gate Magnetometer . . . . . . Second Harmonic Flux Gate Magnetometer with Double Core . . . Ring Core Second Harmonic Flux Gate Magnetometer . . . . . . Pulse-Height Sensors . . . . . . . . . . . . . . . . . . . . . Orthogonal Gated Flux Gate Sensors . . . . . . . . . . . . . . Pulse-Position Type Flux Gate Magnetometer . . . . . . . . . . . Basic Principle of Operation . . . . . . . . . . . . . . . . . . Mode of Operation . . . . . . . . . . . . . . . . . . . . . . Transfer Function of the Magnetometer . . . . . . . . . . . . . Design of Microprocessor-Controlled Magnetometer . . . . . . . .

5.4

Conclusion and Outlook

201

5.5

References

202

154

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154 156 156 158 160 161 161 162 163 166 167 177 183 185 187 187 188 190 198

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

154

5 Magnetic Field Sensors: Flux Gate Sensors

5.1 Introduction Flux gate sensors measure the absolute strength of a surrounding magnetic field or the difference in field strength between two different points within a magnetic field. Hence they differ from induction coils, which respond to the time derivative of the magnetic field strength. Flux gate sensors measure weak magnetic fields of approx. 10 - I - lo6 nT. Their measuring range and their resolution are just within the gap between inexpensive sensors such as the magnetoresistive or Hall type sensors with a resolution limit of 10 nT and very expensive magnetometers based on quantum effects such as SQUIDS and others. The basic principle of flux gate sensors has been known since the early 1940s,but it was at the beginning of the 1950s that the development stage of these sensors made their technical introduction possible. The measuring principles of flux gate sensors can be divided into selective and non-selective: - second harmonic principle

- pulse position principle - pulse-height principles.

Despite all the efforts on other measuring principles, flux gate sensors continue to be used in a wide range of applications, because of their high linearity and stability, high direction sensitivity, reliability, ruggedness, relative simplicity, and economical operation. Application areas for flux gate sensors include the following:

-

terrestrial (geomagnetic observations, mineral prospecting) airborne satellite (measurements in outer space) naval (submarine detection, magnetic ship protection) underwater.

Within these areas, major applications are: - magnetic field measuring devices, which measure one, two, or three axes of the magnetic

field or the difference in the magnetic field between two points within these axes - metallographic devices to detect anomalies or gaps within metallic materials or to measure

the coercive field strength of magnetizable materials - compass devices.

5.2 Flux Gate Sensor Fundamentals To convert the flux density B,, in a magnetic field to be measured into an electrical signal, a straightforward method as shown in Figure 5-1 a would be advantageous, but this leads to bad results in weak magnetic fields. Flux gate sensors do not use this straightforward method, and always need a magnetic reference field Bref,as shown in Figure 5-1 b, to compare the

5.2 Flux Gate Sensor Fundamentals

155

magnetic field Be,, to be measured with this reference field by means of a probe with a probe core consisting of magnetizable material.

Figure 5-1. Magnetic field measuring principles. a) Straight foreward method; b) comparision of the flux density to be measured Bet with a reference flux density Bref.

Magnetometer

Output

b)

The reference field is usually an alternating sinusoidal, square-wave, or triangular magnetic field that is superposed on the core by means of a premagnetization winding and periodically saturates the probe core. The comparison result based on the flux density inside the core is evaluated by a pick-up winding that surrounds the core. Hence flux gate probes usually consist of a probe core of magnetizable material with high permeablility and a low coercive field strength which is inserted in a holder and at least two coils, that are wound around this holder, as shown in Figure 5-2.

winding

Figure 5-2. Principle design of a flux gate probe.

‘probe

core

The different measuring principles are based on different shapes of the magnetization curves, which are formed by annealing in accordance with the appropriate principle. Figure 5-3 shows two different types of magnetization curves. Magnetization curve a is of Z characteristic and magnetization curve b of F characteristic (see also Chapter 1, Section 1.5.1).

156

5 Magnetic Field Sensors: Flux Gate Sensors

The main features of the magnetization curves that have to be discussed for the different measuring principles are: - shape - symmetry

- zero-point behavior - saturation behavior. Different mathematical approaches in accordance with the functional principle and the drive current have been made to describe the functional principle of flux gate magnetometers. Currently used approaches are:

- polynominal functions - piecewise linear functions or - trigonometric functions.

The first two are used for magnetization curves of Z characteristic and the second harmonic principle, and a sinusoidal or a square-wave drive current, whereas the third is used for a magnetization curve of F characteristic, a triangular drive current and the pulse-position principle of flux gate magnetometers.

Figure 5-3. Magnetization curve shapes. a) Z characteristic; b) F characteristic.

5.2.1 Theoretical Approaches t o the Magnetization Curve

5.2.1.1 Polynominal Approach To calculate the second harmonic content of the output signal of flux gate probes, which are premagnetized by a sinusoidal drive current, it is good practice to use a polynominal ap-

157

5.2 Flux Gate Sensor Fundamentals

proach, as was first done by Aschenbrenner et al. [3]. This polynominal approach for one branch of the magnetization curve is as follows:

b , ( h ) = U,

+ a , h + u 2 h 2+ u 3 h 3+

* * *

+ u,h".

(5-1)

For reasons of symmetry of the magnetization curve, the other branch is given by

It is useful to make normalized approaches to the magnetization curve [14]. Normalized approaches may be made by dividing the magnetic flux density by B, and the magnetic field strength by H,, thus obtaining

b = B/B, and h = H / H ,

(5-3)

where Bo and H , may be

with B,,, = saturation flux density, and pd = relative differential permeability at B = 0 o n the magnetization curve.

-measured values - - - polynominal approach

Figure 5-4. Mean magnetization curve of a probe core of M 1040 [42]. Dimensions 30 mm x 1 mm x 0.046 mm, measured values, normalized with B, = 0.37 T, H o k , = 0.575 Akm, and polynominal approach with a, = 0.93, a, = 0.05, c, = 1.488, C , = 0.003.

0

2

4

6

8

10

12

h

Figure 5-4 shows the positive branch of the magnetization curve of a 3 cm linear core of a high-permeability NiFe alloy (M 1040) with a constant cross section measured by Trenkler [42] and a mathematical approach described by the polynominal function in accordance with [18]:

b, ( h ) = b2 ( h ) = a, h -

h3

(5-6)

158

5 Magnetic Field Sensors: Flux Gate Sensors

The hysteresis of this curve has been neglected. It can be seen that this approach fits for h < 2.8, ie, for a magnetic field strength below the so-called saturation knee of the magnetization curve with a, = 0.93 and u3 = 0.05. For higher magnetic field strengths, this curve can be described by a linear equation with c, = 1.488 and c1 = 0.003:

b (h) =

cg

+ c, h

(5-7)

As a result, the magnetization curve can be described in its nonlinear part, ie, below the saturation knee, by a simple polynominal function and when the core is saturated, ie, above the saturation knee, by a linear equation.

5.2.1.2 Piecewise Linear Function

In order to simplify the calculation of a flux gate magnetometer using the second harmonic principle and a square-wave drive current, a piecewise linear approach [l] with a linear equation may be used. As shown in Figure 5- 5, the magnetization curve is divided into several sections, which are linearized. Within this approach, the hysteresis is not neglected, as it plays an important role in the functional principle of this type of magnetometer.

t=O

I I

I T

Figure 5-5. Piecewise linear approach of the magnetization curve [l].

The magnetization curve has different slopes. One that can be described by the differential permeability p d , which is the rise of the curve for B = 0 and H = H , , and the saturation permeability p,,,, which is the rise of the curve above the saturation knee for H > H,,, . The 1st section of the hysteresis curve can be expressed as a function of time with respect to the square-wave drive current by 0 Q t
(5-8) 12

5.2 Flux Gate Sensor Fundamentals

159

with

and the second section as t,

< t < t4:

(5-10)

For the third section

t4

(Hmax - Hsat) ( t -

< t <-:T2

H(t)

+)

T

=

+

Hmax

.

(5-11)

The times t, and t4 can be calculated using the equations d Bp A @ -ddt -A-= dt

dH dt

4

=

T @,ax

(5-12)

and (5-13) to give (5-14)

t4 =

TPOPd (Hsat 4Bmax

+ t, .

(5-15)

The fourth and fifth section of the magnetization curve can be expressed in an analogous way. This linear approach to the magnetization curve can be applied with a square-wave drive current and the second harmonic principle; in this case the areas of the resulting waveform and its Fourier coefficients are dependent only on the flux versus time variation, which is linear due to the square-wave drive current (see also Section 5.3.1.1). The effect of a real magnetization curve would be to smooth sharp corners and spikes in the waveform, but their Fourier coefficients would not really be changed. Hence a good firstorder approximation of the magnetization curve can be obtained using this piecewise linear approach.

160

5 Magnetic Field Sensors: Flux Gate Sensors

5.2.1.3 Trigonometric Function To calculate the output signal of a flux gate sensor using the pulse-position principle, it is useful to take a different mathematical approach based on trigonometric functions [14, 421. A suitable trigonometric function to replace the magnetization curve must be symmetrical to zero, have branches nearly parallel to the axis for large positive and negative axis values and must have a point of inflection at zero. A function that fulfills these requirements and is a good approximation for the magnetization curve is the normalized arctan function: B _ - arctan BO

(2-

(5-16)

or b = arctan ( h ) .

(5-17)

The constant values B, and H , can be expressed using the saturation flux density B,,, , and the permeability &, which is the permeability of either the zero point or of the H, point when the hysteresis is not neglected:

It was shown [42] that this approximation fits perfectly for ring cores and linear cores with a reduced cross section in the middle. Figure 5-6 shows the postive branch of a normalized magnetization curve of a 3 cm long linear core of M 1040 with a reduced cross section and the approximation by the arctan function.

-measured values - - - _trigonometrical approach

0

2

4

6

8

10

12

h

Figure 5-6. Mean magnetization curve of a probe core of M 1040 [42]. Dimensions 30 mm x 1 mm x 0.046 mm with reduced cross sectional width of 0.064 mm, measured values, normalized with B, = 0.37 T, H, k, k, = 0.079 A/cm and trigonometrical approach.

5.3 Magnetometers

161

5.3 Magnetometers Many magnetometers have been designed using specific features of the reference field for converting the magnetic field to be measured into an electrical signal. Magnetometers that use a sinusoidal reference field usually evaluate the dissymmetry of the probe output signal caused by the nonlinear magnetization curve of the probe core and the superposed external magnetic field. Two different principles are possible for magnetometers based o n the dissymmetry of the probe output signal: the second harmonic principle and the pulse-height principle. Both are discussed below.

5.3.1 Second Harmonic Flux Gate Magnetometer One of the most popular magnetometers is the second harmonic flux gate magnetometer, which came into use in the 1940s. Many different types of second harmonic flux gate magnetometers have been investigated and developed since then. Second harmonic flux gate magnetometers correspond perfectly to analog electronics design and feature:

-

ruggedness small dimensions great sensitivity adequate stability reliability economy.

Special second harmonic flux gate magnetometers have reached the highest sensitivity and the lowest noise of all flux gate magnetometers. So far, three different types of second harmonic flux gate magnetometer have been developed :

- single probe magnetometer with electrical filtering of the second harmonics - double probe magnetometer with magnetic filtering of the even harmonics

- ring core probe magnetometer with magnetic filtering of the even harmonics. Owing to the relatively large linearity error of the second harmonic flux gate magnetometer, magnetometers with electrical feedback are also used in order to decrease the linearity error. In addition to magnetometers for general purpose, also called magnetoscopes, many magnetometers for special purposes have been built, mostly for use in geophysical and extraterrestrial exploration. Recent developments also use square-wave premagnetization currents instead of sinusoidal currents. These types of magnetometers will also be discussed.

162

5 Magnetic Field Sensors: Flux Gate Sensors

5.3.1.1 Basic Principle of Operation The basic functional principle of this type of magnetometer is as follows. A probe having a probe core of highly saturable material and at least two windings, a premagnetization winding and a pick-up winding, is used to measure an external magnetic DC or low-frequency AC field, Bext. The probe core is driven periodically into saturation by a sinusoidal premagnetization field Bref produced by a sinusoidal current that flows through the premagnetization winding (Figure 5-7). When no external magnetic field is present, the induction in the core, ie, the function arising from mirroring, is no longer sinusoidal and shows a reduction in the amplitude in the maximum regions of the mirrored sinus (Figure 5-7c).

...

premagnetization f i e l d H,,f

-

. . . . . . . . . . . . . . . . . . . ... . . ... . .,. . . .,. .. .. .,. ., . . ..... .. .a

‘....I

f)

Figure 5-7. Basic principle of second harmonic magnetometers [18]. a) Premagnetizing field; b) magnetization curve; c) induction within the core; d) output voltage of the pick-up winding; e) 1st harmonic of the output voltage; f) 2nd harmonic of the output voltage; g) 3rd harmonic of the output voltage.

The output voltage of the probe is proportional to the time derivative of the flux density within the core (Figure 5-7d). It is at first sight a cosine, but it also includes various additional components. A Fourier analysis shows that only odd-frequency coefficients are present, ie, the first and third harmonics. An external magnetic field to be measured is added to the premagnetization field when it is in direction of the probe axis. This external magnetic field causes a further nonlinearity of the magnetic flux density and of the flux inside the core, ie, when a positive external magnetic

5.3 Magnetometers

163

field is applied. The curve in the maximum regions becomes broader and the minimum values will become more sinusoidal, as shown by the dotted lines in Figure 5-7 c and d. A Fourier analysis shows that now odd- and even-frequency components are present (Figure 5-7e, f, and g). As shown later, the second harmonic Fourier component varies with the external magnetic field applied. Hence the amplitude of the second harmonic frequency component will be a measure of the external magnetic field.

5.3.1.2 Transfer Function of the Second Harmonic Flux Gate Magnetometer The transfer function of a flux gate magnetometer evaluating the output voltage of the probe can be calculated by using a polynominal approach [3, 181 and looking for the frequency components that are within the magnetic flux density of the probe core. The use of the polynominal approach simplifies the subdivision into frequency components. When a trigonometrical approach is used [14], a more complicated subdivision into Fourier components has to be performed. Assuming that the probe core is of the linear type, it will be saturated by a sinusoidal premagnetization field:

(5-18) which will be superposed on the external magnetic field Hext.The magnetic field within the probe core will then be (5-19)

where N is the demagnetization factor for a linear probe core [23]: (5-20) To calculate the flux density within the core, it is of advantage to normalize the internal magnetic field strength to H i , which is set to (5-21) Hence the internal magnetic field strength becomes (5-22) The magnetization curve itself will be approximated by a normalized polynominal approach of the third order [18]:

b ( h ) = a , h - a3h3

164

5 Magnetic Field Sensors: Flux Gate Sensors

where b is the normalized flux density: b = B/B,

(5-3)

B, = 2Bsat/n .

(5-4)

with

This approach is used for both the positive and the negative branches of the magnetization curve. The normalized flux density becomes

b = a , hex,+ a , hrefmax sin w t - a3 (hex,+ hrefmax sin w t ) 3

(5-23)

or

3 a3hext * hrefmax 2 b = a , hex, - a3 h %,, -+

(

+ a1 href max

- 3 ~ h32x1 href max

3

-2 a3hex,h :ef

max

cos 2 w t

3

-

1

4a3 h L max

+4 a3h If

)

sin a t -

sin 3 w t

.

(5-24)

It can be seen that the second harmonic component is proportional to the external magnetic field strength. The output voltage of the pick-up winding is proportional to the time derivative of the flux density inside the core: (5-25) where N = is the number of turns of the pick-up winding and A the cross section of the probe core. The output voltage of the pick-up winding will be replaced by the normalized output voltage:

uout

and becomes

=

db uou, dB --- Bo*NA

dt

dt

(5-26)

165

5.3 Magnetometers

The second harmonic component of the output voltage of the pick-up winding is then

U,,,2 h

= - 3 BoN A o a3 he,, h

bfmax sin 2 o t

(5-28)

or

as a linear approximation where K is a constant including the demagnetization factor, the peak value of the premagnetization current, the shape of the core, the polynominal coefficient a 3 , and the saturation flux density of the core. The second harmonic component of the output voltage of the pick-up winding is thus proportional to the magnetic field to be measured and the frequency of the premagnetization current. Using an arc-tan approach to the magnetization curve and calculating the second harmonic Fourier coefficient, it was shown [14] that the output voltage of the pick-up winding is also inversely proportional to the permeability of the core:

(5-30)

=

K-

0

PO p d

He,, sin 2 w t

.

(5-31)

As this output signal is proportional to the premagnetization frequency of the probe and inversely proportional to the permeability of the probe core, these two influence factors must be kept fixed in order not to incur additional measuring errors. The filtering of the second harmonic out of the output voltage of the pick-up winding can be achieved by electrical or magnetic means. With electrical filtering, only a single probe is necessary and the transfer factor K, is constant: K,=-.

uout 2 h

(5-32)

He,, With magnetic filtering two probes are necessary, their pick-up windings have to be connected in anti-series so as to measure a magnetic field difference. In this case the transfer factor Kd is also constant, but depends on the difference in the magnetic field:

(5-33)

When both probes are arranged in such a way that they measure the external magnetic field, double the sensitivity of a single probe core can be achieved.

166

5 Magnetic Field Sensors: Flux Gate Sensors

5.3.1.3

Single-Core Second Harmonic Flux Gate Magnetometer

A simple second harmonic flux gate magnetometer that uses a single core probe is shown in Figure 5-8. A generator produces a sinusoidal premagnetization current that flows through the premagnetization winding of the probe. The probe itself has a linear core; ring-core probes are not applicable for this type of magnetometer as they have a poor directional sensitivity. The output voltage of the pick-up winding contains all frequency components produced by the nonlinear magnetization curve. As only the second harmonic is proportional to the external magnetic field, it has to be filtered out by a resonance amplifier whose pass-wave frequency is tuned to double the frequency of the premagnetization generator.

Generator

c

Probe

-

Resonance Amplifier

-

Display Instrument

Figure 5-8. Single-core second harmonic flux gate magnetometer with reduced performance data.

An improvement in the design of this magnetometer can be achieved by using a phase-sensitive rectifier, as shown in Figure 5-9. This magnetometer consists of a premagnetization generator that produces the sinusoidal premagnetization current, which flows through the premagnetization winding of the probe. The probe also has a linear probe core in order to obtain good directional sensitivity. The output voltage of the pick-up winding of the probe is again filtered by a bandpass filter that is tuned to double the frequency of the generator. It filters the second harmonic contents out of the output voltage.

Generator

1

-

Probe

-

Bandpass

-

Resonance Amplifier

-

Controlled Rectifier

I

Display I n s trurnenl

Frequency Doubler Stage

Figure 5-9. Single-core second harmonic flux gate magnetometer with controlled rectifier for improved performance.

Only the second harmonic contents is amplified and rectified by a controlled rectifier. The output signal of the controlled rectifier is proportional to the magnetic field to be measured. The reference frequency for the controlled rectifier is obtained by doubling the generator frequency. A feedback control of the magnetometer probe may be used to improve the linearity of these two types of magnetometers. Figure 5-10a shows a single linear core magnetometer using a feedback [38].This magnetometer has a special feature in that it does not use a frequency doubler to produce the reference signal for the controlled rectifier, but uses a frequency generator whose output frequency is used directly as the reference frequency for the controlled rectifier and that is halved to obtain the premagnetization frequency for the probe.

5.3 Magnetometers

167

The mean value of the output voltage of the controlled rectifier is amplified by a DC amplifier. The output signal of this DC amplifier is converted by a voltage-controlled current converter to a current that flows through a separate feedback winding of the probe, which produces a magnetic field that is superposed on the external magnetic field to be measured but is of opposite direction. Hence the probe is operating nearly in a zero field in a very small range whose limits are given by the measuring range divided by the gain of the evaluation circuit with respect to the second harmonic. To simplify the probe, the pick-up winding can be used twice, first as a pick-up winding and second as a feedback winding, as shown in Figure 5-lob. In this case the AC output voltage of the pick-up winding is separated from the DC feedback by means of a capacitor.

I

I

c

output

Generator

a)

b)

2nd harmonic

Controlled Rectifier

Voltage controlled Amplifier

Output DC-Amplifier

Output

*

I ,

Figure 5-10. Principle of single-core second harmonic flux gate magnetometer with feed back. a) With separate feed back winding; b) without separate feed back winding.

5.3.1.4 Second Harmonic Flux Gate Magnetometer with Double Core At first sight the second harmonic flux gate magnetometers with a single linear probe core are of very simple construction, so that good efficiency could be expected. Nevertheless, they have a severe disadvantage owing to the electrical filtering of the second harmonic out of the frequency spectrum of the output voltage of the pick-up winding. Imperfect filtering due to imperfect filter circuits or a change in the phase behavior of the probe output signal could cause a false measured value. An improvement can be achieved by using magnetic filtering of the even harmonic out of the output of the pick-up winding. One of the best known second harmonic flux gate magnetometers using magnetic filtering of the even harmonic is that made by Institut Dr. Foerster [9, 36, 371, which uses two linear core probes connected in such a way that they always measure the field difference between two points.

168

5 Magnetic Field Sensors: Flux Gate Sensors

Basic Principle The even harmonics can be filtered out of the output signal with two probes that are connected in a difference circuit, as in this case the sum of all odd-frequency components is zero and the sum of the even components remains [8]. In this case, twice the sensitivity can be obtained compared with a single core magnetometer (Equation (5-33)). 1

Double core Probe

-

2nd harmonic Amplifier

-

Controlled Rectifier Display Instrument

Doubler Stage and Amplifier

Figure 5-11. Principal design of second harmonic flux gate magnetometer with double core [37].

The basic circuit arrangement of this type of magnetometer is shown in Figure 5-11 and consists of - an oscillator

- a probe having two probe cores or two single probes - a measuring amplifier - a controlled rectifier

- a controlled-voltage amplifier with a frequency-doubler stage - a display instrument. The stabilized oscillator with power output stage provides the premagnetization current for the probe. The output voltage of the pick-up winding of the probe is fed into the input of the selective amplifier, whose gain can be set to certain values so as to obtain multiple measuring ranges. In this measuring amplifier the even harmonics are filtered out and amplified. From this amplifier output, the measured voltage passes to the phase-controlled rectifier which will be controlled by a signal of double the frequency of the premagnetization oscillator. This double-frequency signal is obtained by a controlled-voltage amplifier with a frequency-doubler stage. Using a phase-sensitive rectifier makes it possible to indicate the field strength and its direction with respect to the probe.

Probe Design The basic design of general-purpose probes can be divided into two parts:

- one design for field and difference-field measurements - one design for field measurements only. The probe for field and difference-field measurements usually consists of two single elements (Figure 5-12a) that may be on a common or on two separate holders, so as to be able to

169

5.3 Magnetometers

separate both elements from one another for measurement at two different points. Each element consists of:

- the probe core - a ceramic tube - the windings.

The magnetic probe core, which may be made of M 1040 and have a length of 32 mm (standard), a width of 1 mm, and a thickness of 50 pm, is inserted into the ceramic tube and fixed there. Subsequently, the annealing procedure may take place. Thus mechanical stresses due to handling of unprotected probe cores resulting in an increase in probe noise can be eliminated. The premagnetization winding is wound directly around the ceramic tube. In order to prepare a good base for the pick-up winding, only a single layer should be used. The pick-up winding is then wound around the premagnetization winding. This sensitive element is then inserted into a holder, which consists of a hard fiber plate, and connected there with a connection lead. The sensitive element is also adusted magnetically within the holder in order to adjust the sensitive axis of the probe. The probe design for field measurement uses nearly the same sensitive element, but the premagnetization winding is replaced by an external winding.

IIJ ! Figure 5-12, Principal design of double core probes. a) Probe for field or difference field measurement; b) probe for field measurement.

"il

Hext

-ui 2 a)

uil -ui2 bl

As shown in Figure 5-12b the probe includes two sensitive elements that each consist of:

- a probe core - a ceramic tube - the pick-up winding. The probe core and ceramic tube are the same as in the previous mentioned design. The pickup winding is wound directly around the ceramic tube, thus reducing effects due to stray flux to a minimum. The premagnetization winding is placed o n a tube of approx. 1 cm in diameter that is made of a hard fiber plate. Both sensitive elements are inserted in the premagnetization winding tube, adjusted, and fixed there. Additional windings such as test, feedback, and compensation windings can also be placed on the premagnetization tube.

110

5 Magnetic Field Sensors: Flux Gate Sensors

The electrical connections of this probe are such that both pick-up windings are connected in anti-series, so the odd-harmonic components of the output voltage of the pick-up windings are subtracted and only the even-harmonic components remain. This probe design features a higher degree of linearity than the design of Figure 5-12a, and therefore this design is used for triple probes to measure the x-, y - and z-components of the external magnetic field and is also used within gradiometer probes where both sensitive elements are at a certain distance apart, called the base, arranged with parallel sensitive axes or with a common sensitive axis. In gradiometer probes only one sensitive element is placed in each premagnetization winding. As explained earlier, single-core magnetometers have the severe disadvantage that suitable electrical filters are needed to filter the second harmonic out of the probe output signal; probes that filter out the second harmonic magnetically have the problem, however, that both probe elements have to match perfectly. Probes that do not match exactly produce an error signal that limits the performance of the magnetometer. The matching procedure is a well kept secret of the manufacturer of the second harmonic flux gate magnetometer, so that detailed information on the matching procedure is not available. Nevertheless it is likely that the following steps are part of the matching procedure [45]:

- the mechanical dimensions of the probe core must be held within a small tolerance; - all probe cores that are to be matched should be annealed within one annealing procedure to obtain the same magnetic characteristics;

- the probe cores have to be adjusted within the windings; - the output voltage of the pick-up winding of one element has to be tuned with a parallel resistor to the value of the second element; - if the adjustment and tuning procedure is not satisfactory, the probe core has to be

replaced by another one and the matching procedure has to be restarted.

Directional Sensitivity and Transfer Factor The directional sensitivity of every sensitive element is a cosine, ie, the maximum sensitivity is on the longitudinal axis of the element and the minimum sensitivity at an angle of 90" to this axis (Figure 5-13).

a)

bl

Figure 543. Direction sensitivity of the probe. a) Within the probe axis; b) out of the probe axis.

5.3 Magnetometers

171

The transfer factor of second harmonic flux gate magnetometer probes has an accuracy of less than zk 5%. It depends on the magnetization curve of the probe core material, ie, on the permeability, the coercive force, and the accuracy of the windings of the probe. This is why the sensitivity of the magnetometer electronics has to be tuned to the probe transfer factor. A change in the probe makes a new adjustment necessary.

Frequency Range The lower frequency limit of a second harmonic flux gate magnetometer depends o n the long-term stability of the magnetometer and is usually assumed to be zero. The upper frequency limit for the magnetic field to be measured depends on the frequency of the premagnetization current. Commonly used premagnetization currents with a frequency of about 10 kHz allow an upper bandwidth of about 250 Hz, depending on the probe construction and especially o n the probe housing material. When conducting materials such as alloys are used, eddy currents within the housing dampen the field intensity and produce a measurement error. For standard measurement equipment, an upper frequency limit of 10 Hz is commonly used.

Different Probe Dpes For standard measurement equipment of second harmonic fluxgate magnetometers, many different probes with respect to the different measurement tasks are available, and include the following [37] : - Field and Gradient Probe

This probe (Figure 5-14a) consists of two single probe elements with body dimensions of 70 mm x 10 mm x 10 mm, made of a hard fiber plate. This type of probe is used for generalpurpose measurements, as both probes can be placed in a holder parallel for field strength measurement or antiparallel for difference measurements. Moreover, both elements can be separated, so that difference or field measurements between two different points are possible. - Triple Probe

The triple probe (Figure 5-14 b) consists of three single probes that are aligned orthogonally to each other on a common holder, which may be covered by an alloy casing for outdoor measurement. Each probe has to be connected separately to the magnetometer electronics. - Gradient Probe

The gradient probe (Figure 5-14c) consists of a difference-field probe whose sensitive elements are aligned at a certain distance from each other. The sensitive axes of the axial gradient probe are arranged consecutively in the same line, whereas the sensitive axes of the transverse gradient probe are parallel to each other and in the same direction. These probes are mostly used to look for local disturbances in the Earth’s magnetic field. Therefore, the remaining magnetic component of the probe in any direction to the Earth’s magnetic field must be as small as possible. High-performance probes have a remaining magnetic field of ca. 30 nT on turning it at any direction to the Earth’s field. Special probes

172

5 Magnetic Field Sensors: Flux Gate Sensors

s1

52

-53

bl

Figure 5-14. Different probe types for standard

I s1

\52

measurements. a) Field and gradient probe; b) triple probe; c) gradient probe.

reach a remaining magnetic field of 1-2 nT. These gradient probes are usually covered by an alloy casing for outdoor measurement.

- Micro Field Probe The micro field probe (Figure 5-15a) is used for spot measurements of static or slow dynamic magnetic fields. It contains two probes with an effective magnetic core length of 6 mm and diameter 0.2 mm. Arranged at a distance of approx. 6 mm from each other, the sensitive elements of the probe can pick up the magnetic field strength nearly at a point. The previous mentioned field probe, with an effective length of the probe core of 32 mm, integrates the magnetic field to be measured over its length.

- Point Pole Probe The point pole probe (Figure 5-15 b) is used for relative measurements of magnetic fields coming out vertically from the object under test. It measures the difference between two probes that are mounted 20 mm apart with a common axis.

5.3 Magnetometers

173

Plastic body

Probe

0 ist an c e apart

a)

P(

Probe 1

P r o b e I1 Metal plate

b)

51

rotable permanent magnet C)

symmetry adjustment

dl

Probes

Figure 5-15. Different probe types for special measurements. a) Micro field probe; b) point pole probe: c) residual field probe; d) permeability probe.

- Residual Field Probe The residual field probe (Figure 5-15c) measures the magnitude of residual magnetic fields of iron or ferromagnetic components. It is a field probe arrangement consisting of two probes that are within a hard fiber-plate body which also houses a rotatable permanent magnet for compensation of a constant field, eg, the Earth’s magnetic field, which may be superposed onto the field to be measured. - Permeability Probe

The permeability probe (Figure 5-15d) is for exact measurements of the permeability of material in the range p, = 1.01-2. It can also be used for testing non-ferromagnetic materials for inclusions of ferromagnetic material. The permeability probe incorporates a cylindrical permanent magnet of well defined magnetization. Two probes connected in a difference circuit are placed on both sides of the permanent magnet, so that their sensitive axis is aligned orthogonally to the center axis of the permanent magnet. In this case, the two probes do not measure the magnetic field of the permanent magnet. When the cylindrical magnet is placed on a material, whose permeability is greater than 1, a dissymmetry occurs which is proportional to the relative permeability of the material under test. This dissymmetry is measured by the sensitive elements of the probe and

174

5 Magnetic Field Sensors: Flux Gate Sensors

displayed by the magnetometer electronics. Means are provided for adjusting the magnetic center of the permanent magnet accurately.

Design Example of a Second Harmonic Flux Gate Magnetometer As an example of the design of a second harmonic flux gate magnetometer, the design of a battery-powered second harmonic flux gate magnetometer developed in the early 1980s will be discussed [37].

- Oscillator Second to the probe, the oscillator is the most sophisticated functional unit of the second harmonic flux gate magnetometer as it has to avoid all odd and even harmonics. In the example, a two-stage oscillating circuit is used (Figure 5-16), consisting of a transistorized push-pull oscillator with transformer output as the first stage and as the second stage a power output resonance amplifier with additional suppression of harmonics as the second stage. The second stage also has a transformer output, which is used as a matching transformer for the probes. The inductance of both transformers must be tuned in order to reach the predefined system frequency.

*u t

+u/2

t

+u12

t

*u t

\ output t o Premagnetii!ation Winding o f the Probe 4

I

1st Stage Oszillator

I

2nd Stage Output Amplifier

I

Figure 5-16. Principal design of oszillator [ 3 6 ] .

- Frequency Doubler Stage

The frequency doubler stage (Figure 5-17) consists of a n emitter coupled transistor amplifier with an amplification of 1 which produces two sinusoidal signals of the oscillator frequency, one signal being inverted with respect to the other. These two sinusoidal signals are rectified and added together using a diode quartett. The rectified signal, which now has double the frequency of the oscillator, is used to trigger a resonance amplifier with a transformer output stage which is tuned to the double frequency.

- Measuring Amplifier The measuring amplifier (Figure 5-18) consists of a transformer-coupled emitter transistor amplifier whose input circuit is designed as a resonance circuit tuned to double the frequency

175

5.3 Magnetometers *U

i"

t

output to Controlled Rectifier

Figure 5-17.

Principal design of frequency doubler stage [36].

probe~lm

Pick-up Winding

from

Figure 5-18.

Principal design of measuring amplifier [36].

Selector Switch

of the oscillator, ie, the second harmonic. The input transformer of this stage is tuned to the pick-up winding of the flux gate probe. The amplification factor of this amplifier can be changed by selecting different resistors within the emitter of the transistor. Thus it is possible to select different measuring ranges of the magnetometer. The output signal of this stage is then further amplified. - Demodulator and Display Instrument

The demodulator (Figure 5-19) is a four-diode ring demodulator that filters the second harmonic signal contents out of the output signal of the measuring amplifier and rectifies the signal. The demodulated signal is then integrated by an analog instrument and displayed. Additional circuits within the magnetometer are provided for: - Probe compensation

With a compensation circuit that feeds a compensation current into the pick-up winding of the probe, it is possible to compensate DC magnetic fields at the probe location electrically.

- Instrument adjustment An instrument adjustment circuit is provided for adjustment of the magnetometer electronics to the probe transfer factor, which can vary by approx. 5%. With this circuit it is also possible to compensate the influence of different cable lengths between the probe and the electronics.

116

5 Magnetic Field Sensors: Flux Gate Sensors

Measuring Range Selector Switch

I 4 Diode Demodulator

Amolifier

Figure 5-19. Principal design of demodulator

Display Instrument

[361.

- Battery control A battery control circuit switches the instrument to the power supply battery of the second harmonic flux gate magnetometer in order to monitor its supply voltage.

Performance Data The above-described second harmonic flux gate magnetometer possesses the following performance data, which may be typical of such standardized instruments:

-

-

*

+

300 and 100000 nT in several steps; for difference field measurements the respective range lies between +600 and +200000 nT; the accuracy of field strength measurements is approx. +2.5% of full-scale; for a gradient probe the space relationship, which is the maximum measured value when moving the probe in any direction within the Earth’s magnetic field, is smaller than 50 nT; for the permeability probe, the measuring ranges are from 1 to 2 in several steps.

- the measuring range for field measurements is between

~~~~~~t~~

-

Double Core Probe

-

:----I Voltmeter

2nd harmonic Amplifier

-

Controlled Rectifier

t Stage and Amplifier

Digital Display

---Kevboard

Interfaces

Personal Computer

Figure 5-20. Design of second harmonic flux gate magnetometer with analog to digital converter and standardized interface [37].

5.3 Magnetometers

177

Future Developments Future developments of standardized second harmonic flux gate magnetometers will incorporate a conversion of the analog output signal of the magnetometer into a digital signal that can be understood directly by computers. One system [36] incorporating a commercial digital voltmeter as an analog-to-digital converter can be connected to a personal computer via a standard IEEE 448 interface (Figure 5-20). This system features a measuring range of f 100000 nT for field measurements and f 60000 nT for difference field measurements. The sensitivity is up to 0.1 nT, depending on the measurement time.

5.3.1.5 Ring Core Second Harmonic Flux Gate Magnetometer A basic disadvantage of second harmonic flux gate magnetometers with magnetic filtering of the even harmonics is the necessity to match the two sensitive elements, which should be identical in dimensions, magnetic treatment behavior, and electrical data. As this matching procedure is difficult and does not ensure the performance data required from the probe, a ring core probe can be used, which replaces the two linear probe cores by a single ring and avoids the matching procedure. Unfortunately, the ring core does not possess the directional sensitivity of the linear core, so that other probe core forms such as the race-track type are also in use.

Basic Principle of the Ring Core Flux Gate Magnetometer Figure 5-21 shows the basic principle of the ring core flux gate magnetometer [l] and its origin. Figure 5-21 a shows two linear probe cores that are exposed to an external magnetic field. Both probe cores are excited by a premagnetization winding. Both premagnetization windings are connected in such a way that the internal magnetic field within the left core produced by the positive half-wave of the premagnetization current is antiparallel to the external magnetic field, whereas in the right probe core the internal magnetic field is in the direction of the external magnetic field. The flux density within the cores is measured with two pick-up windings, which are connected so as to suppress the odd harmonics content of the induced voltage. This structure is an open magnetic loop and the magnetic field lines go back through the air. Nevertheless, it could be closed using a magnetic connection between the two probes (dotted lines). In this case the magnetic resistance of the closed loop would be lower than that of the two single cores, so that the excitation current must be reduced to have the same magnetic situation as before. Figure 5-21 b shows the ring core probe which also carries two premagnetization windings and two pick-up windings. They are connected in the same way as the windings in Figure 5-21a. In this case the two premagnetization windings produce an internal magnetic field within the ring core that goes around the whole core. Within the left half of the ring core, this internal magnetic field is opposite to the external magnetic field, whereas in the right section the internal magnetic field is in the same direction, when the positive half-wave of the premagnetization current is looked at. The flux density within the cores is measured with two pick-up windings, which are connected so as to suppress the odd harmonics content of the induced voltage. The pick-up and

118

5 Magnetic Field Sensors: Flux Gate Sensors

III III l e f t care

Oext

I 1 !1 i

I ,

left half core

b)

11 11

Figure 5-21. Basic principle of ring core second harmonic flux gate magnetometer. a) Linear core rot b) ring core probe.

premagnetization windings can also be constructed differently. For example, it is possible to wind the premagnetization winding around the whole ring core and place the pick-up winding as a concentrated winding over the core. Thus the axis of symmetry of the pick-up winding determines the sensitive axis of the probe.

Design of a Ring Core Second Harmonic Flux Gate Magnetometer Ring core second harmonic flux gate magnetometers are used preferentially for extraterrestrial magnetic field measurements. In addition there are some standard magnetoscopes for standard measurement tasks.

5.3 Magnetometers

179

Space-flight magnetometers usually have low detection ranges of f10 to f100 nT with frequency bandpasses of 0 - 1 to 0 - 10 Hz with a resolution of, eg, f1/16 nT [12]. For absolute field measurements, these magnetometers need high long-term stability, low internal instrument noise, and good temperature stability. In order to guarantee a wide measuring range, digital compensation circuits are used to feed compensation currents into the probe. As an example of the design of a ring core magnetometer, an instrument with a square-wave premagnetization current and two orthogonal sensing axes [l] will be described. A block diagram of this two-axis ring core magnetometer is shown in Figure 5-22. It consists of a magnetic multivibrator, a ring core sensor, a frequency-doubling stage and two phase-sensitive detectors and output stages. Controlled Rectifier Magnetic

Ring Core

Controlled

Figure 5-22. Principal design of a ring core magnetometer with square wave premagnetization field.

Doubler Stage

The principle of the probe design is shown in Figure 5-23. On the ring core, with a diameter of 0.5 in and a core width of 0.125 in, made of 4-79 Mo-Permalloy, there are two premagnetization windings, a main winding and a control winding, both cut into two sections. The two pick-up windings are arranged ortogonally to eachother on a plastic winding guide to obtain the necessary orthogonal alignment of the axes within 1'. They have approx. 100 windings and are cut into two sections. Both pick-up windings occupy only a small portion of the periphery in order to minimize cross-coupling effects and to obtain the necessary decoupling of the axes. The functional principle of this magnetometer can be described using a piecewise linear approach (Section 5.2.1.2), neglecting stray effects within the circuit and assuming that the flux x- axis pick- up winding

* , ,

winding main

100 turns

100 turns

Figure 5-23. Principal probe design of a ring core magnetometer.

22 t u r n s

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5 Magnetic Field Sensors: Flux Gate Sensors

density within the core is independent from the external magnetic field. The piecewise linear approach is a good initial approach to describe the functional principle of this magnetometer. It could be shown [l] that the behavior of the Fourier coefficients would not be changed appreciably by a magnetization curve with smoothed-out sharp corners. Figure 5-24 shows the waveforms of the premagnetization voltage, the magnetic flux density, the premagnetizing current, and the output voltages of the right and left parts of the ring core and the total output voltage of the pick-up winding for a n external magnetic field not equal to zero.

a)

et bl iret

cl

ur

dl UI

el

f)

n

t

L

U

-. t

TI 2

Figure 5-24. Functional principle of ring core magnetometer with square wave prernagnetization field. a) Prernagnetization voltage; b) flux within the core; c) prernagnetization current; d) output voltage right half core; e) output voltage left half core; f) total output voltage.

Within the resulting waveform of the output voltage of the pick-up winding, the times t2 and t4 are fixed by the magnetization curve. They d o not include a term that is related to the external magnetic field strength. The times t l , t, , t , , and t 6 , however, include a term related to the external magnetic field strength. For the right half of the core, the times are

(5-34)

5.3 Magnetometers

181

and (5-35)

For the left half of the core, the times are \

/ T

(5-36)

and (5-37)

The resulting waveform is symmetrical about T/2. The amplitudes of the resulting voltages are proportional to (5-38)

and

u,

u , = - pd .

(5-39)

&at

where N is the number of turns of the pick-up winding and A is the cross section of the core. The Fourier coefficients A , are zero, as the integral is an odd function. The Fourier coefficients B, are

(5-40) 0

For the second harmonic signal B, , the function can be integrated piecewise and B, will thus be

271 -

- cos

) +5 T T %)T $ (cos -- ) + .. . 471t2

T

4 x 4 - cos 3 (cos 271 T

271 -

(cos

4xt,

cos

471 t4

T

cos

4714

T

182

5 Magnetic Field Sensors: Flux Gate Sensors

This second harmonic signal B, gives no closed form result, so its value has to be calculated numerically, taking into account the demagnetization factor for the ring core: (5 -42) and the dependence of the permeability of the external magnetic field:

(5-43) where the external magnetic field is

(5-44)

L corresponds to one half circumference of the core and d is the diameter of a rod with an equivalent cross-sectional area to the ring core, p r is the variation of the permeability in accordance to Equation (5-43).

2 -

y - ax is x-axis

1 -

a) Hext

02 0,1 0

- 0,l -0,z

-0,3

- 0,4 -0.5 J b)

Figure 5-25.

Resulting performance of second harmonic flux gate magnetometer with square wave premagnetization field [42]. a) Predicted output voltages of the pick-up winding versus measured values; b) percentage deviation from linear fit versus external magnetic field Hex,.

183

5.3 Magnetometers

Figure 5-25 shows the predicted second harmonic output voltages of the pick-up windings for the x- and y-axes compared with the calculated values. The functional units of this magnetometer are designed as follows (Figure 5-26). The magnetic multivibrator consists of the probe with premagnetization winding (main and control winding) and two switching transistors that drive the probe periodically into saturation. The frequency of this multivibrator is determined by the core characteristics and has a rate of about 100 kHz. Thus the probe performs two functions, one sensing function and one controlling function for the multivibrating frequency.

r i n g core probe

,

d e m o d u l a t o r and output I 1 axis I 0

“out,2 h

Figure 5-26. Functional units of ring core magnetometer with square wave premagnetization field.

frequency doubler

magnetic m u l t i v i b r a t o r

The second harmonic reference signal is obtained by differentiating the square-wave drive voltage and full-wave rectifying the resulting spikes. This second harmonic reference signal is decoupled via an insulation transformer T to make it possible to bias the output at any desired level. The output signal of the pick-up winding of the probe is demodulated with a two-diode rectifier and integration circuit. This demodulator is tuned to the second harmonic of the premagnetization frequency by means of a capacitor in parallel with the pick-up winding. Further, the sensitivity of the magnetometer can be adjusted by a damping resistor parallel to the pick-up winding. The performance data of a standardized flux rate ring core magnetometer for triaxial measurement of the external magnetic field are as follows [35]: the dynamic range is within +lo0 and *100000 nT in four measuring ranges in decade steps for an output signal of *lo V DC and a DC frequency range up to 50 Hz. The zero level stability is less than 0.2 nT/”C and the magnetic noise is less than 0.1 n T / m a t 0-1 Hz bandwidth.

5.3.2 Pulse-Height Sensors As a measure of the magnetic field Ha, to be measured, the pulse-height sensor evaluates the peak value of the induced voltage Ui of a solenoid which surrounds a probe core of high

184

5 Magnetic Field Sensors: Flux Gate Sensors

permeability, but with a magnetization curve of Z-shape and which is driven very high into saturation by a premagnetization current iref(Figure 5-27). Hext

Hext /ref -0

t- t t t

iii 0

winding probe core

Figure 5-27. Functional principle of pulse-height sensor probe.

It can be shown (Figure 5-28) by using a piecewise linear approach to the magnetization curve and a sinusoidal premagnetization current irefthat the flux density within the core and the induced votage Ui are symmetrical about the time axis and the positive and negative peak values Ui, and Ui, are the same (Figure 5-29).

Figure 5-28. Approach of the magnetization curve.

Figure 5-29. Induced voltage versus time.

When an external magnetic field Hex,is superposed on the premagnetization field, the operating point within the magnetization curve is displaced and the time characteristics of the flux density and the voltage Ui lose their symmetry. The peak values of the positive and negative half-waves (Uinand Ui,) are now unequal in their amplitude. The commonly used procedure takes the difference AUi = Ui, - Ui,

(5-45)

as a measure of the magnetic field He,, to be measured. Usually Uipand Ui,are extracted by two peak detectors. This procedure only gives a stable performance with core material with a magnetization curve of Z-shape and with a sinusoidal premagnetization current.

5.3 Magnetometers

185

A modified system was first described by Vacquier et al. [44], consisting of two probes, both carrying only one winding, in series opposition within a bridge (Figure 5-30). A center-tapped transformer Tr, represents the other branch of the bridge. The primary winding of the transformer is fed by an AC current generator. With a further transformer Tr, the unbalanced voltage Ui of the bridge is used as a measure of the external magnetic field after peak detection for the positive and negative half-waves, subtraction from one another, amplification, and indication of the result. Detuning of the bridge by the resistor R stabilizes the arrangement when small magnetic fields are to be measured. A minimum detectable flux density variation of Bmi,= 0.5 nT was reported [44].

Ill 11

Bext

Generator

I r

Peak Detector

-

Amplifier

-@

Figure 5-30. Principal design of pulse height magnetometer [44].

Further magnetometers based on the pulse-height principle were developed [34, 461 and gave very similar data. The described principle is not applied very often because of stability problems with small fields [20].

5.3.3 Orthogonal Gated Flux Gate Sensors Orthogonal gated flux gate sensors differ from the other principles discussed in the directional difference in the polarizing field H p and the magnetic field Hex,to be measured that cross within the magnetizable material at an angle of go", as can be seen in Figure 5-31, which also shows a fundamental example of an orthogonal gated flux gate probe. A pick-up winding in the shape of a solenoid is wound around a long, thin wire of highly permeable material, which at the same time serves to generate the premagnetization field with a sinusoidal premagnetization current (Figure 5-31). The magnetic premagnetization current ire, flows through the wire and generates a circulating polarizing field H , , whose direction lies in the plane of turn of the pick-up winding. Neglecting the field distortion caused by the finite length of the probe, no voltage U, is induced in the pick-up winding when no external magnetic field is present, as there is no field component in the axial direction of the probe. An external magnetic field Hex,in the direction of the probe axis, however, is superimposed on the nonlinear magnetization curve with the polarizing field (Figure 5-32). It generates a

186

5 Magnetic Field Sensors: Flux Gate Sensors

Hext

I

W

Figure 5-31. Principal design of orthogonal sensor probe.

... Hext

Figure 5-32. Magnetic field intensities of orthogonal sensor probes.

flux density component with double the frequency of the magnetic premagnetization current, as a result of the saturation of the core material. The flux density B, (Figure 5-33), lying in the direction of the probe axis, induces in the pick-up winding a voltage Ui , again with double the frequency of the premagnetization current. The amplitude of this double-frequency signal is used as a measure of the magnetic field He,, to be measured. The procedure is dependent on the variation of the permeability of the core material and possesses a cross-sensitivity, which almost corresponds to the size of the demagnetization factor N of the probe core [lo, 261. A close investigation of this probe type [13, 151 showed a conversion factor of 8 V/T . As a variation of this probe type, an area probe with an orthogonal, flat-shaped probe core of high permeability [24] is able to follow flux density variations of Bmi, < 2 nT.

Figure 5-33. Flux density within the core of orthogonal sensor probes.

5.3 Magnetometers

187

A miniaturized probe type was developed [8], the active surface area of which is only 0.64 x 0.76 mm. A probe with extraordinarily small dimensions and which uses a probe core with a weight of 6 vg was developed [ 5 ] and a measure of flux density variations as low as Bmi, I50 nT was demonstrated. A modified probe was reported [25] in which a toroidal core of ferrite in the form of a tube carries the premagnetization windings, while the pick-up winding lies along the longitudinal direction of the tube. A fundamental disadvantage of the orthogonal gated flux gate probe is the measuring error caused by the coercive field strength of the core material, as no probe core is really saturated by the premagnetization current. Therefore, a larger rest magnetization effect has to be considered. Only one probe described [25] saturates the probe core.

5.3.4 Pulse-Position Type Flux Gate Magnetometer One of the most modern flux gate magnetometers is of the pulse-position type. It is a magnetometer with direct time encoding of magnetic fields [42]. This type of magnetometer was developed for series production in recent years. The particular advantage of this magnetometer is an output signal that can be simply converted into a binary signal which can be understood by microprocessors. This measurement principle is directly compatible with requirements for digital signal evaluation. This is why the magnetometer can be described as an intelligent sensor when it is combined with a microprocessor. Further advantages of this flux gate magnetometer are: - high linearity, so no feed back is required

- simplicity of manufacture - ruggedness - small dimensions - great sensitivity with adequate stability

- low cost due to high integration possibility using high integrated digital circuits as gate arrays and microprocessors and may be in the future linear arrays.

5.3.4.1 Basic Principle of Operation

The basic functional principle of this magnetometer can be described by a comparator (Figure 5-34), which compares the magnetic field to be measured with a magnetic reference field, generated by the magnetometer itself. The magnetic reference field has a triangular form, so as to obtain a linear relationship between the output of the magnetometer and the field to be measured.

Figure 5-34. Basic principle of pulse-position type flux gate magnetometer.

Compnrator 'ref

output

188

5 Magnetic Field Sensors: Flux Gate Sensors

Figure 5-35 shows a reference field of triangular form and the external magnetic field. The external magnetic field is of low frequency with respect to the reference field. The comparator switches its output over in the moment the two fields are identical but have opposite directions, so that the difference between the two is zero. Thus a change in the amplitude of the magnetic field to be measured causes a change in the pulse duty factor, as shown in the broken line in Figure 5-35b. The output signal of the comparator is therefore a pulse-length modulated rectangular signal. The comparison element between the external magnetic field and the reference field is a probe having a linear probe core of highly permeable material. Comparison is performed when the flux density inside the core is zero, ie, when the reference field and the field to be measured are identical.

a)

t

output signal

Figure 5-35. Functional principle of magnetometer with direct time encoding of magnetic fields. a) Measured field and reference field (flux density); b) output signal of comparator.

I I

t

b)

5.3.4.2 Mode of Operation The functional units of this flux gate magnetometer are shown in Figure 5-36. They are:

-

a a a a

flux gate probe premagnetization generator differentiating circuit voltage comparator.

The flux gate probe consists of a linear probe core and at least two windings around the core, one premagnetization winding to produce the magnetic reference or premagnetization field and one pick-up winding to pick up the flux density within the probe core.

zat ion

Probe

Output

Figure 5-36. Structure of pulse position type flux gate magnetometer.

5.3 Magnetometers

189

The premagnetization generator produces a premagnetizing current of triangular form. This can be done by a Miller integration circuit or with a square-wave generator and an inductivity, integrating its output signal. This premagnetization current goes through the premagnetization winding of the flux gate probe and periodically saturates the probe core. The output signal of the probe is evaluated with a passive differentiating element and a voltage comparator, which looks for zero transitions of the differentiated signal. The mode of operation of this measurement procedure is shown in Figure 5-37. To simplify the description of the mode of operation, the magnetization curve has been replaced by its middle curve, and hysteresis has been neglected.

b)

a)

Figure 5-37. Operational principle of magnetometer with direct time encoding of magnetic fields. a) Triangular premagnetization field; b) magnetization curve; c) flux density within the probe core; d) output voltage of the pick-up winding; e) differentiated output voltage of the pick-up winding; f) output signal of comparator.

Figure 5-37 a shows the triangular-form premagnetization field. An external DC magnetic field acting in the direction of the sensor axis is added to the premagnetization field and causes a shift of the triangle function along the abscissa. By mirroring the resulting function on the magnetization curve, the flux density within the core is obtained (Figure 5-37c). If no external magnetic field is present, the function arising from mirroring is symmetrical to zero. The voltage induced in the pick-up winding is proportional to the differential quotient of the flux density (Figure 5-37d). The extremes of the induced voltage occur when the flux density is zero. When the voltage induced in the pick-up winding is differentiated again, the

190

5 Magnetic Field Sensors: Flux Gate Sensors

extremes become zero transitions (Figure 5-37 e). If this differentiated voltage U,is evaluated by means of a voltage comparator which changes its output voltage at zero transitions of the input voltage, a rectangular voltage is obtained at the output of the comparator (Figure 5-37 f). The application of an external magnetic field to the flux gate probe causes a shift in the operating point of the curve and in the time position of the zero transitions of the flux density within the core (broken line in Figure 5-37). Hence there is a shift in the extremes of the induced voltage in the pick-up coil, the zero transitions of the differentiated voltage, and the edges of the rectangular voltage at the output of the comparator. The pulse width of the output voltage of the comparator is therefore a measure of the intensity of the external magnetic field applied.

5.3.4.3

Transfer Function of the Magnetometer

The transfer function of this flux gate magnetometer can easily be calculated using an arctan approach for the magnetization curve. It will be calculated for a premagnetization current of triangular shape, by which good linearity of the magnetometer is obtained. Of special interest for this type of magnetometer is a probe core having a reduced cross-section in the middle, which increases the sensitivity of the probe, as shown later.

Magnetic Field Strength Within the Probe Core The magnetic field strength within the probe core depends on the shape of the probe, its cross section, and on the magnetic field where the probe core is applied and which is the sum of the actual values of the external magnetic field Hex, and the reference field Href (Figure 5-38).

1

Hext

Probe core 111

I

Hext

Probe core

bl

Figure 5-38. Internal magnetic field within the probe core. a) Probe core with equal shape; b) probe core with reduced cross section.

5.3 Magnetometers

191

If the probe has an equal cross section over its length, as shown in Figure 5-38 a, the relationship between the field strength Hex,of the external magnetic field where the probe is applied and the internal magnetic field strength Hi,, within the probe core itself is given by H. = Int

Hexi

(1

+ N(pr-

1))

(5-46)

where N is the demagnetization factor, which can be approximated by

::[

N = - In

J

-

(464:

- 11 *

(5-20)

The probe compares the magnetic field to be measured with the reference field and gives an output signal when both are equally large but in opposite directions, ie, when the flux density within the core becomes zero. At this point, the rise of the magnetization curve is given by p d , which replaces pr in Equation (5-46):

for the magnetic field within the probe core which has no reduced cross section. When the probe core has a reduced cross section in its middle (Figure 5-38 b) and assuming that the permeability is high and that there is no stray flux, the magnetic flux within the probe core is constant and the magnetic field lines are according to the outer shape of the probe core. The flux density within the probe core is then proportional to the shape of the cross section and the relationship of the magnetic field strength within the reduced cross section Hredto the field strength of the non-reduced cross section Hnred.Thus: -Hred Hnred

-

Ared Anred

- k,

(5-48)

where k, is a constant. Considering that the reduced cross section is only a small portion of the total probe core and that the non-reduced cross section is constant over a great part of the probe core, the mean value of the field strength within the core can be approximated by Hnred . Thus the internal magnetic field strength within the reduced cross section becomes: (5-49)

In this case the internal magnetic field strength of the probe core is a factor of Anred/!red higher than the internal field strength of a probe core with equal cross section over its whole length. As shown later, this factor increases the sensitivity of the probe. Equation (5-47) can be regarded as a special case of Equation (5-49) with k, = 1. Therefore, in further calculations of the magnetometer characteristics, only probe cores with reduced cross sections will be considered; the respective result for probes having probe cores with equal cross section can then be determined setting k2 to 1.

192

5 Magnetic Field Sensors: Flux Gate Sensors

Normalized Magnetic Field Strength and Magnetic Flux Density The probe compares the external magnetic field to be measured and the reference field produced by the magnetometer electronics and gives an output signal when the two are equally large but of opposite sign. Hence the absolute amplitude of the external magnetic field Hex, must always be smaller than the amplitude of the reference field Href:

IHext I

I HrefI

(5-50)

*

To obtain the normalized magnetic field strength, the internal magnetic field strength Hintis set in relation to the magnetic field strength at the zero crossing of the magnetization curve: (5-51)

To calculate the magnetic flux density within the probe core and the output signal of the probe the trigonometrical approach will be used as this approach possesses a point of inflection at zero. Inserted into the approximation function of the core material, the magnetic flux density B becomes B = B, arctan

Hok2

Hex, + Href + N(pd -

(5-52)

In order to simplify the calculation of the probe output signal, the constant value k , will be introduced:

k, = 1

+ N(pd

-

1).

(5-53)

Hence the magnetic flux density becomes

B = B, arctan Hex, + Href Ho kl k2

(5-54) *

To simplify further, the factors hex,and hrefwill be introduced: (5-55)

and (5-56)

with k2 = 1 in the case of a probe core with equal cross section.

5.3 Magnetometers

193

Probe Output Signal with Triangular Form Reference Field The time behavior of the internal magnetic field strength is given by the time behavior of the reference field and the superposed external magnetic field. To obtain a probe output signal that is linearly related to the magnetic field strength to be measured, a reference field of triangular shape and period Twill be used [42]. The calculation of the probe output signal becomes easy when the origin of coordinates is at the time of the maximum of the triangle. Then the following expressions are obtained:

(5-57)

Range 2: 0


T

Q: href(t) 2

=

hrefmax

4t

(+7 1) + hex,.

(5-58)

In further calculations, only range 1, -T/2 Q t Q 0, will be considered, as the calculation for range 2 is identical. In range 1, the magnetic flux density within the probe core will be:

The magnetic flux density within the probe core cannot be measured directly. Only the flux within the core can be measured by means of a pick-up coil, which picks up the time derivative of the flux. The flux within the probe core will be @ = BA = BOAarctan

t

+ h,,

max

+ hex[)

(5-60)

and the time derivative of the flux, ie, the voltage induced in the pick-up coil, is:

u . = --=Nd@ dt

4hrefmax T

-NAB,.

('+

4hIefmax t + href max + hext) T

2

(5-61)

As explained earlier, the output signal of the probe will be qualified when the flux density within the probe core is zero. There the magnetization curve posesses a point of inflection. Hence it is useful to form the second time derivative of the flux density and to look for its zero transitions.

194

5 Magnetic Field Sensors: Flux Gate Sensors

The second time derivative of the flux will be designated:

dUi U d = d t = -

Nd2@ dt2

( =

4 h r e yt ) 2

. .

-NAB;

(

max

T

t

)

+ href max + hex,

(5-62)

4 href max t + hre, max + hextyy This signal becomes zero for

4 href max t + hrefmax + hex, = 0 T

(5-63)

or, solved with respect to t for ranges 1 and 2:

(5-64)

Range 1:

Range 2:

tz =

href max + hex, 4hrefmax

.

(5-65)

The difference between these two times, ie, the pulse duration time, is

(5-66) Replacing hex,and hrefmax by the values defined in Equations (5-55) and (5-56), the pulse duration time becomes

(5-67) This equation shows that the pulse duration time is linearly related to the external magnetic field which will be measured. The relationship is

A t = a’Hex,+ b’

(5-68)

where b‘ is a constant which describes that the pulse duration time is equal to the half period when no external magnetic field is applied; a‘ is the slope, that is the ratio of the period and the peak value of the reference field Hrerdivided by two. It could be shown that for this type of magnetometer, using a reference field of triangular form, there is a strong linear relationship between the pulse duration time derived from the zero crossings of the differentiated output voltage of the probe and the external magnetic field

5.3 Magnetometers

195

to be measured. This applies both to probes having probe cores with reduced cross sections and to probes having probe cores with identical cross sections.

Sensitivity The sensitivity S is the difference ratio of a change in the output signal to the respective change in the input signal, which is the value to be measured:

S=

A Output A Input

(5-69)

If the differential ratio is used instead, Equation (5-69) has to be derived with respect to the measured value Hext.Thus the sensitivity of this type of magnetometer becomes: (5-70) or, using Equations (5-4), ( 5 - 9 , (5-46), and (5-53) T

(5-71) or (5-72) It is possible to simplify this equation, due to the fact that for common probe core materials and common probe shapes the following two relations may be used: 1

N S Pd

-1

(5-73)

and P d s

(5-74)

Then the sensitivity becomes: (5-75)

This result is very interesting as it shows that the sensitivity of the probe is independent of the relative permeability prn.Thus slight mechanical stresses on the probe core or temperatur changes which could effect a change in the relative permeability do not have any influence on the sensitivity of the probe. Nevertheless, mechanical stresses of the probe core have to be avoided as they result in an increase of the probe noise.

196

5 Magnetic Field Sensors: Flux Gate Sensors

The factor k, = Anred/Ared increases the sensitivity of the probe in a linear manner. Thus probes having probe cores with a reduced cross section in their middle are much more sensitive than other probes. This is of interest for battery-powered systems.

Probe Design Many different probe designs have been investigated in order to find the optimum function of this type of magnetometer [42]. The only probes applicable for this type of magnetometer are those with linear probe cores with or without reduced cross sections in their middle. Ring core probes cannot be used for this type of magnetometer. The probe consists of the probe core, holder, and windings. Figure 5-39 shows two different probe designs, one with a premagnetization winding that is wound around the probe core all along the holder and the other with a premagnetization winding which is split into two parts that are around the non-reduced cross section of a probe core. The advantage of the latter type is that the pick-up winding is as close as possible to the probe core. Hence it can pick up the time derivative of the flux density in the core directly, avoiding as much as possible effects caused by stray flux.

prernagnetization winding 1 and 2

Figure 5-39. Principal probe design. a) Premagnetization winding over all the length of the probe core; b) premagnetization winding devided into two parts.

Probe Core The probe core is a strip of highly permeable material, such as Permalloy or M 1040, with a magnetization curve of F-shape with a smooth point of inflection at zero, a low saturation flux density, and a very low coercive field strength. The dimensions of the strip should be adapted to the design of magnetometer, mainly with respect to its sensitivity, the amplitude of the premagnetization or reference field, and its power consumption. Thus the strip may have a contour as shown in Figure 5-40a and b. The ends of the strips are rounded in order to reduce the rest magnetization compared with probe cores with sharp edges. The strip is usually etched out of a magnetic hard ribbon of the respective material which already has the required final thickness. When the probe core consists of hard magnetic material, it has to be annealed to adjust its magnetic characteristics such as coercive field strength, saturation induction, and shape of

5.3 Magnetometers

197

the magnetization curve. The annealing procedure has to be carried out precisely, depending on the core material used, especially for probe cores with a reduced cross section. After annealing, a tempering procedure can be carried out to adjust the final shape of the magnetization curve at its point of inflection.

Holder The holder may be a ceramic tube or a fiber glass resin tube into which the probe core is inserted and fixed. Figure 5-41 shows a holder made of fiber glass resin. It consits of two half shells. Each shell has the necessary outer contour to form the bobbin frames and a small half chamber for the probe core. The two half shells are clipped together when the probe core has been inserted. The necessary windings may subsequently be wound on the holder. Of special interest is the fixation of the probe core within the holder. The probe core should be fixed without any mechanical stress in order to avoid an increase in the probe performance.

premagnetization winding 1

pick up winding

~

premagnetization winding 2

Figure 5-41. Design of a 4 cm probe.

Windings At least two different windings are necessary, a premagnetization winding, which may be split into two parts, and one pick-up winding in the middle of the core. The pick-up winding

198

5 Magnetic Field Sensors: Flux Gate Sensors

should be as close as possible to the probe core so as to pick up the induced voltage proportional to the time derivative of the flux density in the core and to avoid effects caused by stray flux as much as possible. The premagnetization winding has to be made carefully as it determines the final sensitivity of the probe. The pick-up winding should be of low capacitance in order to obtain a high resonance frequency of this circuit. Additional windings may be placed over the premagnetization winding. These could be test windings, compensation windings, or adjustment windings to set the sensitivity of the probe to a defined value.

Directional Sensitivity The directional sensitivity of the probe is a cosine, ie, the maximum sensitivity is on the longitudinal axis of the probe and the minimum sensitivity is at an angle of 90" to this axis Hence (see Figure 5-13). The ratio of the sensitivities between these two axes is about it is possible to form a triple arrangement consisting of three probes that are aligned orthogonally to one another with excellent mutual decoupling of the sensitivity axes, so that they can sense the magnetic field vector independently of its direction.

5.3.4.4 Design of Microprocessor-Controlled Magnetometer

The particular advantage of the magnetometer with direct time encoding of magnetic fields is its principle of digitizing magnetic fields by means of the evaluation of the point of inflection of the magnetization curve and its digital output signal, which can simply be converted into a binary signal and can be understood by a microprocessor. Hence this type of magnetometer is a n intelligent sensor. By digitizing magnetic fields directly, additional errors that may occur from analog to digital converters are avoided.

Overview of All Functional Units Figure 5-42 shows all the functional units of the magnetic field measuring device [4]:

- magnetometer with magnetic field sensor - code converter

- microprocessor - keyboard - digital display

- digital-to-analog converter - standardized interfaces (IEEE or RS232) - compensation circuit

- calibration circuit. In this arrangement, the magnetometer, magnetic field sensor, and code converter have the task of converting the magnetic field to be measured in a linear manner into a binary figure which can be understood and processed by the microprocessor. The microprocessor itself is

5.3 Magnetometers

Probe -I--

,

r

Magnetometer

I=.

-

4

I

Code

,-

Converter

Compensation Circuit

Calibration

-

199

\

Microprocessor

v

Oigital Display

Ik

O/A Converter

- Analogue*Outputs

-

Figure 5-42. Principal design of microprocessor controlled magnetometer [4].

the heart of this measuring device, which evaluates the input signal and displays it. This signal can also be output by a digital-to-analog converter for external recording. The microprocessor can also compensate constant magnetic fields that may be superposed on the measured value by means of a compensation unit, which feeds a constant current through a compensation winding of the probe. Means for automatic calibration of the system are also provided. A calibration generator that is controlled by the microprocessor automatically feeds a calibration signal through a test winding of the probe and evaluates the result. The mode of operation and the measuring range can be selected via a keyboard. These settings can also be commanded via standardized interfaces such as an IEEE or RS232. The measured values can also be transmitted to an external computer via these interfaces.

Design of Magnetometer One of the main functional units of the microprocessor controlled magnetic field measuring device is the magnetometer, which senses and transforms the measured magnetic field value into an electrical value. The magnetometer consists of three functional units:

- premqgnetization generator - probe - comparator with differentiating circuit.

The premagnetization generator which may be an active generator using an integration circuit produces a premagnetization current of triangular form. The premagnetization winding of the probe is connected via a series resistor to the output of the integration amplifier in order not to shortcut the premagnetization winding magnetically. When the output signal of the triangle generator is not completely symmetrical to zero a bias current will flow through the probe and simulate an offset field. To eliminate this offset

200

5 Magnetic Field Sensors: Flux Gate Sensors

field, all DC components within the premagnetization current can be eliminated by connecting an AC coupling capacitor between the premagnetization generator and the probe. The comparator with differentiating circuit will be connected to the pick-up winding of the probe. It consists of three parts: - a differentiating circuit - a low pass - a voltage comparator.

The differentiating circuit forms the time derivative of the output voltage Ui of the probe and the voltage comparator looks for the zero transitions of the differentiated voltage Ud. The time constant of the differentiating circuit is adapted to the maximum frequency within the induced voltage. In series with the differentiating circuit there should be a low pass in order to reduce electrical noise that may be on the induced voltage and that will be intensified by the differentiating circuit. The voltage comparator should be an operational amplifier with a small slew rate, high speed, high gain, and with hysteresis. The hysteresis does not produce an additional error but a phase shift in the output signal with respect to the premagnetization current. Figure 5-43 shows the induced and the differentiated output voltage of the previously described probe having a probe core with a reduced cross section.

Figure 5-43. Probe output voltages. a) Induced voltage Ui ; b) differentiated voltage

5.4 Conclusion and Outlook

201

Design of Code Converter The pulse length-modulated output signal of the magnetometer is converted to binary code by a code converter so that it can be understood by the microprocessor. The code converter in its simpliest form is a digital counter that counts the pulse duration time by means of time increments that are made by a high-frequency generator. The number of time increments within a period of the reference field is then proportional to the amplitude of the magnetic field to be measured.

Microprocessor and Additional Functional Units The microprocessor incorporates all necessary functions to evaluate the measured values. Its task is also to control all necessary functions, such as calibrating and testing of the complete system before measurement by feeding a test current into a test winding of the probe, compensating constant magnetic fields that may limit the measurement range of the magnetometer by feeding a DC current of the respective polarity into a compensation winding of the probe. The microprocessor can be controlled via a keyboard and standardized interfaces to set specific operating conditions such as the measurement range and filter constants. Measurement results are displayed on a digital display and may be transmitted to an external device via the standardized interfaces. The measurement results can also be output as analog voltage via a digital-to-analog converter for external display or recording.

5.4 Conclusion and Outlook On the basis of two different types of magnetization curves, widely used principles for second harmonic flux gate magnetometers have been described. Since their first appearance in the early 1940s, a long and sometimes rapid development due to space research magnetometers took place before the present performance of these magnetometers with their low magnetic noise of down to 0.01 nT for “second harmonic super-flux gates” was reached. Whereas up to 1980 the main developments were in direction of analog techniques, digital magnetometer principles with direct digital output have since taken over. This type of magnetometer features a n improvement in the dynamics, ie, the relationship between the lowest sensible magnetic field variation with respect to the total measuring range and avoiding errors due to the permeability of the magnetization curve. They also avoid further analogto-digital conversion errors. These magnetometers have become much more important as they fit perfectly to digital signal processing with microprocessors and make possible microprocessor controlled magnetometers and other devices such as magnetic compasses with high performance. Future developments will probably involve further improvements in the dynamic range of these magnetometers, reducing the lowest sensible magnetic field variation. This might be possible by using amorphous core materials, which at the same time improve the handling procedures of the core material.

202

5.5

5 Magnetic Field Sensors: Flux Gate Sensors

References

[l] Acuna, M. H., Pellerin, Ch. J., “A Miniature ~ o - A x i sFlux Gate Magnetometer”, ZEEE Trans. Geosci. Electr. GE-7, No. 4 (1969) 252-260. [2] Acuna, M. H., “Fluxgate magnetometers for outer planets exploration”, ZEEE Trans. Magn. Mag-10 (1974) 519-523. [3] Aschenbrenner, H. et al., “Eine Anordnung zur Registrierung rascher magnetischer Storungen”, Hochfrequenztechnik und Elektroakustik 47, No. 6 (1936) 117-181. [4] Bornhofft, W., “Ein modernes mikroprozessorgesteuertes Magnetometer”, in: NTG-Fachbericht VO~.79, 1982, pp. 271-276. [5] Drosdziok, S., “Magnetometersonden kleinster Abmessungen zur Messung kleiner Magnetfelder”, ATM V 391-12, 1973, pp. 189-190. Dyal, P. et al., “Lunar Surface Magnetometer”, ZEEE Trans. Geosci. Electr. GES, No. 4 (1970) 203-215. Felch, E. P. et al., “Airborne Magnetometers”, Electrical Engineering (1974) 680. Fales, et al., “A Magnetometer Instrumentation Technique Using Miniature Transducer”, Rev. Sci. Instr. 45 (1974) 1009. Forster, F, , “Ein Verfahren zur Messung magnetischer Gleichfelder und Gleichfelddifferenzen und seine Anwendung in der Metallforschung und Technik”, Zeitschrjft fiir Metallkunde 46 (1955) 358-370. Geyger, W. A., “The Ring Core Magnetometer - A New Type of Second Harmonic Flux-Gate Magnetometer”, AZEE Trans. 81 (1962) 65-72. Geyger, W. A., Nonlinear - Magnetic ControlSystem, New York: Mac Craw-Hill, 1964, pp. 328-378. Gordon, D. I., Brown, R. E., “Recent Advances in Fluxgate Magnetrometry”, ZEEE Trans. Magn. MAG-8 (1972) 76-82. Greiner, I., “Feldmessungen nach dem Oberwellenverfahren, Sieb- und Differenzsonden”, Nachrichtentechnik 10, No. 5 (1960) 156-162. Greiner, I., “Feldmessungen nach dem Oberwellenverfahren, methodische Untersuchungen”, Nachrichtentechnik 10, No. 3 (1960) 123-126. Greiner, I., “Feldmessungen nach dem Oberwellenverfahren, Winkelsonden”, Nachrichtentechnik 10, NO. 11 (1960) 495-498. Heinecke, W., Fluxgate Magnetometer with time coded output Signal of the Sensor; ZEEE IM 27, M 4 (1978) 402-405. Heinecke, W., Magnetic Field Measurement with Fluxgate Magnetometers, Rchnisches Messen (tm) 4% NO. 1 (1981), 3-9. Kertz, W., “Einfuhrung in die Geophysik”, in: EZ-Hochschultaschenbiicher, Mannheim: BIWissenschaftsverlag, Vol. 275, 1969, pp. 171 ff. Kuhne, R., “Magnetfeldmessung nach dem Oberwellenverfahren mit dem Eisenkernmagnetometer”, ATM V392-1, August 1952, pp. 175-178. Lawrence, L. G., “Elektronik fur die Geophysik”, Elektronik, No. 11 (1964) 323ff. Lion, S. K., Instrumentation on Scientific Research, New York: MacGraw-Hill 1959, p. 203ff. Ness, N. F., “Magnetometers for space research”, Space Sci. Rev. 11 (1970) 459-554. Osborne, I. A., “Demagnetization Factors of the General Ellipsoid”, Physical Review 67 (1945) 351-357. Palmer, T. M., “A Small Sensitive Magnetometer”, Proc. ZEE II (1953) 545-550. Primdahl, F., “The Fluxgate Magnetometer”, J. Phys. E., Sci. Znstrum. 12 (1979) 241-253. Primdahl, F., “The Fluxgate Mechanism, Part 1: The Gating Curves of Parallel and Orthogonal Fluxgates”, ZEEE Trans. Magn. MAG-6, No. 2 (1970) 376-383.

5.5 References

203

[27] Primdahl, F., “Temperature Compensation of Fluxgate Magnetometers“, ZEEE Pans. Magn. MAG-6, NO. 4, 1970, pp. 819-821. [28] Rose, D. C. et al., “A Saturated Core Recording Magnetometer, Canadian Journal of Research A ”, 28 (1950) 153ff. [29] Scouten, D. C., “Sensor Noise in Low-Level Flux Gate Magnetometers”, ZEEE Trans. Magn. MAG-8, NO, 2, 1972, pp. 223-231. [30] Smith, E. J. et al., “Extraterrestrial Magnetic Fields: Achievements and Opportunities”, ZEEE 7kans. Geosci. Electr. GE14, No. 3 (1976) 154-171. [31] Snare, R. C. et al., “Digital Data Acquisition and Processing from a Remote Magnetic Observatory’’, (1972) pp. 127-134. [32] Striker, S. et al., “A Pulse Position Type Magnetometer”, Trans ZEE (I) SO, No. 55 (1961) pp. 253-258. [33] Stumm, W., “Techniken der Messung magnetischer Felder und ihrer Anwendung”, Messen und PriifedAutomatik, Jan. (1973) 29ff., Febr. (1973) 83 ff. [34] Technical Specification, Static 3 Axis Magnetometer Doc - Re$ 34114, Crouzet. [35] Technical Specification, 3-Axis Fluxgate Magnetometer System, Develco. [36] Technical Specification, Magnetomat C I . 723 11/87, Institut D. F6rster. [37] Technical Specification, Magnetoscop 1.068 3/82, Institut D. Forster. [38] Technical Specification, Magnetometer MF 21, Meerestechnik-Elektronik GmbH, 1988. [39] Technical Specification, Low Noise Variometer Model LNV 01, nano Tesla Inc. [40] Technical Specification, LNS 1-3 Magnetometer, Thorn EM1 Electronics. [41] HR 3 Magnetometer, Publication Nr. 852, Thorn EM1 Electronics. [42] Trenkler, G., “Die Messung schwacher magnetischer Felder mittels Magnetometer mit direkter Zeitverschliisselung”, MeJtechnik 78, No. 10, 205-209. [43] Trenkler, G., “Verfahren zur elektrischen Messung magnetischer Felder”, Messen und Priifen, Sept., (1972) 535ff.; Messen und Priifen, Oct., (1972) 624ff.; Messen und Priifen, Nov. (1972) 705ff. [44] Vacquier, V. et al., “A Magnetic Airborne Detector Employing Magnetically Controlled Gyroscopic Stabilization”, Rev. of Scientific Instruments 18, No. 7 (1947) 483 ff. [45] Wurm, M., ‘‘Beitrage zur Theorie und Praxis des Differenzfeldstarkemessers nach Forster”, Zeitschrift fiir angewandte Physik 11, No. 5 (1950) 210-219. [46] Wyckoff, R. D., “The Gulf Airborne Magnetometer”, Geophysics l3 (1948) 182-208.

6

Magnetic Field Sensors: Induction Coil (Search Coil) Sensors GUNTHER DEHMEL. Technische Universitat Braunschweig. FRG

Contents

6.2 6.2.1 6.2.2 6.2.3

. . . . . . . . . . . . . . . . . . . . . . . . . . . Air-Cored Induction Coil . . . . . . . . . . . . . . . . . . . . . . General Design Considerations . . . . . . . . . . . . . . . . . . . Sensitivity and Internal Noise . . . . . . . . . . . . . . . . . . . Equivalent Circuit Diagram . . . . . . . . . . . . . . . . . . . .

207 207 209 214

6.3 6.3.1 6.3.2 6.3.3 6.3.4

High Permeability Core Induction Coil . . . General Design Considerations . . . . . . . Magnetization of a High Permeability Core . Sensitivity and Internal Noise . . . . . . . Equivalent Circuit Diagram . . . . . . . . .

. . . . .

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

220 220 223 228 234

6.4 6.4.1 6.4.2 6.4.3 6.4.4

Induction Coil Sensors with Electronic Amplifiers . Sensor with Voltage Amplifier . . . . . . . . . . Sensor with Current Amplifier . . . . . . . . . . Sensor with Transformer Coupled Negative Feedback Noise Equivalent Magnetic Field of Sensors . . . .

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

237 237 239 241 243

6.5

Applications

6.6

References

6.1

Introduction

. . . . .

. . . . .

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

206

246 251

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

206

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

6.1 Introduction Induction coil or search coil magnetometers are the simplest type of sensors for precise measurements of magnetic fields. Their operating principle is based upon Faraday’s law of induction:

The voltage induced in closed turns of a coil is proportional to the time rate of change of the flux linked with the coil. Tho fundamentally different kinds of sensors are distinguished: (1) Sensors with stationary coils suitable only for the measurement of magnetic fields, which vary with time or which are AC magnetic fields, and (2) sensors with moving coils with which DC magnetic fields can also be measured. In the general case, a DC field has a local gradient and is superimposed by periodic variations. If it is sensed using a moving coil (which rotates and is additionally shifted in parallel), no technique exists to uniquely and exactly separate or identify the various contributions of the magnetic field to the resulting change of flux linked with the coil [l]. Under certain conditions, this can be achieved approximately [2]. Therefore, only fields constant in time should be measured with moving coils. A treatment of such sensors with rotating, vibrating, or flipping coils, must include a description of their driving mechanisms, which would be extensive. Since they are of rather limited importance, these sensors are deleted here and only a few special types are discussed in the application chapter. The following discussion of fundamentals of sensors with stationary coils is separate for coils with air-cores and with high permeability cores. The many viewcharts and curve representations for both types of induction coils are intended as auxiliary means in an assessment of their achievable performance. The remarks on the various advantages and disadvantages and the construction details, given also in the application chapters, are an aid when designing a sensor. It is thought useful, that the above definition of induction coil sensors be supplemented: They always work passively and if a coil on a high permeability core is used, it is assumed to be magnetized only by the measuring field. An AC or DC premagnetization and all nonlinear behavior of the core are undesired. With induction coil sensors the dynamic range of the coil output voltage may become very large, if both the magnetic field amplitude and the frequency vary greatly. In order to get a field proportional output or registrations of the true shape of magnetic waveforms, the time integral of the output voltage must be formed. For spectral measurements, o n the other hand, the “pre-whitening” effect caused by the differentiating action of the sensor is sometimes advantageous. Both basic types of induction coil sensors can be constructed to be relatively rigid, resistant to hostile environments, and very reliable. The requirements imposed on the connected electronics are few, only low-noise amplifiers are necessary. A general and severe disadvantage, however, is that sensors with a high sensitivity are unavoidably bulky and heavy, an integration together with modern electronics is excluded. A diversified series of industrially produced sensors useful for different measuring purposes does, for all practical purposes, not exist.

6.2 Air-Cored Induction Coil

207

6.2 Air-Cored Induction Coil 6.2.1 General Design Considerations The most fundamental form of an induction coil is the air-cored coil, or loop antenna as it is sometimes called, even if used for picking up induced AC magnetic fields close to the source. Using common materials it can be assembled without any technological difficulties and the finished product, if well designed, may reach a high level of performance. The importance of air-cored coils, a property that has maintained their presence in the ranks over the years, arises from the fact that both their ability to produce magnetic fields from currents, and their capability for sensing fields by measuring the induced voltage, can be precisely precalculated. Thus, they are ideally suited as cheap reference sensors for calibration purposes. Other well-known advantages of air-cored coils will be mentioned here only for reference purposes. Air-cored coils in sensors contain no magnetic materials and thus have no inherent non-linearities and, in principle, an unlimited upper measuring range. In order to maintain all their favorable properties, efforts must be taken to strictly avoid magnetic impurities in the materials. The temperature dependency of the sensitivity can be kept to a minimum and may be calculated. There are no unknown influences which can reduce their excellent short and long term stability. Sensors equipped with air-cored coils are particularly suitable when applying a series connection of two coils (gradiometer configuration) and allow the effect of spatially large-scale ambient magnetic fields (or disturbances) to be compensated for, and small local gradients (or signals) to be detected. One disadvantage is that high sensitivity air-cored coils usually have considerable large dimensions and a great weight. This results in a poor spatial resolution if measurements of non-homogeneous fields are to be made, because the coil gives average values over its geometrical area. This problem can be overcome using the special version of the spherical coil and a mapping of such fields can then be accurately performed [3]. For a sensor coil which must only be magnetically sensitive a carefully designed electrostatic shielding is often necessary. Even though a conducting closed loop in the plane vertical to the magnetic field lines is avoided, eddy-currents in the shielding can reduce the sensitivity. In addition the bandwith can be reduced because of the additional self-capacitance of the winding which is introduced. For a large air-cored coil with a high sensitivity to disturbances, coupled capacitatively to the winding, the shielding can be both important and problematic at the same time. The various construction types used in practice differ greatly in shape. Multilayer solenoids, which have a compact winding and many turns, are used most often and for many diverse purposes. The radial and axial extensions of the winding cross-sectional area range from one to approximately ten centimeters and the diameters from a decimeter up to a few meters. The extremes extend from small coils with mm-diameter for the measurement of high intensity or high frequency fields, up to large loops with several tens of turns, sometimes many kilometers in diameter, which have been laid out for the observation of pulsation phenomena in the earth’s magnetic field. Single layer disk-shaped coils and solenoids are suitable for picking up weak radio frequency fields. Rotating and vibrating air-cored coils are used to measure homogeneous and non-homogeneous DC magnetic fields, respectively. Examples of some applications are briefly discussed in the last section. In contrast, however, shielded small loop

208

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

antennas used as wideband electro-magnetic field probes [4] are out of the scope of this chapter. The following considerations refer to induction coils which are operated at low frequencies. It is important to note that in the discussion of internal noise, it is implicitly assumed that a high utilizable sensitivity is desirable. Normally, such coils are wound as multilayer coils with many turns of enameled wire, and in this regard, two remarks which also apply to coils on a high permeability core are still to be mentioned. When estimating coil resistance and weight the nominal wire ( = conductor) diameter is introduced, thus, the weight of the insulation is neglected. The formulas for calculating inductance and self-capacitance, on the other hand, contain the outer dimensions of the winding cross-sectional area, which includes all spacings between turns and layers. Thus, when calculating the increase of the AC resistance of a coil due to the proximity effect, the lacquer thickness is important and has been taken into account. When constructing a coil the two filling factors defined by Figures 6-1 and 6-2 are of interest. Figure 6-1 shows two possible geometrical winding filling factors, of which an average numerical value may be a, = 0.85. For Figure 6-2 the outer diameter D, and the conductor diameter d of certain types of enameled copper wire have been taken from tables. The resulting lacquer thickness (a) and the copper wire filling factor (b) are plotted versus the nominal wire diameter. Considering both factors, the total cross-sectional area of the winding may be larger than the total copper cross-sectional area by a factor, between 2.1 and 1.2 approximately, for a wire diameter of 50 pm and 5 mm, respectively. In the literature it is often suggested that it may be more advantageous to employ aluminium wire instead of copper wire when the resistance and weight of a coil are the important parameters, as shown in the following comparisons. Two geometrically identical and, therefore, equally sensitive induction coils, one wound with copper wire and the other with aluminium wire, differ in their weights approximately as the material densities ycu = 8.9 and yal = 2.7 g/cm3. If they are brought to the same weight by enlarging the cross-section of the aluminium winding by a factor of ycu/yal their internal noise voltages are proportional to of the respective conductor material with p = resistivity. The numerical the factor = 0.396 and !/= = 0.266 [V g/Am2]”2 and thus, the aluvalues are

fi

v

a,, =

K

T

T

h

h

ll 4

a,? =

Figure 6-1. Winding schemes of multilayer coils with different filling factors total wire cross-sectional area a, =

winding cross-sectional area

T[

2m

6.2 Air-Cored Induction Coil

a)

-E

209

D,-d

2

5

t

0.05

d-

d Figure 6-2. a) Mean lacquer thickness of enameled copper wire versus nominal wire (= copper) diameter d; b) enameled copper wire filling factor a, versus nominal wire (= copper) diameter d a J z copper cross-sectional area a,=

(-

=

wire cross-sectional area

minium coil has only 67% of the noise voltage of the copper coil. When an equal noise voltage for both coils is obtained their weights are proportional to the factor y p , which means that the aluminium coil is only 45% of the weight of the copper coil. Also, the relative mechanical stability of aluminium is better than that of copper. Thus, aluminium wire can be used if it is as readily available as copper wire and has no disadvantages with respect to creating a noncorrosive contact with acceptable thermo-electrical properties. The following estimates, however, all refer to copper wire. +

6.2.2 Sensitivity and Internal Noise In order to demonstrate the possibilities and limitations of air-cored induction coils used as magnetic field sensors, the sensitivity and internal noise for an air-cored coil will be calculated. The results are valid for low frequencies where the effects of the inductance and

210

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

self-capacitance of the coil can be neglected. The coil is threaded by a magnetic flux 0 caused by a time-varying magnetic field H a s shown in Figure 6-3. If the field varies sinusoidally, it can be thought of as consisting of two components of half the amplitude H / 2 , rotating in the same plane but in the opposite direction with an angular velocity o as indicated. The voltage induced in the coil with n turns is ui = -n . dQi/dt, and in the case of a sinusoidal flux variation Qi = Qmax cos (at)is

the open-loop peak output voltage of the coil.

I I

k-W-4

Figure 6-3. Air-cored induction coil in a time-varying magnetic field.

The voltage depends on the coil properties and is proportional to the frequency magneticfield product f . H. The sensitivity of the coil may be defined as

6.2 Air-Cored Induction Coil

21 1

In some specific cases it may be useful to have numerical values for the output voltage with H , say, f . H = 1 nT . Hz. Using a certain product value f

=

a

4 7 [ . 10-7

[-]

v*s A.m

= 10-9

[

" 1

nT Hz m 2

(6-4)

the output voltage becomes

where the coil diameter D is measured in m. Figure 6-4 shows the attainable sensor coil peak output voltage Uo as a function of its diameter D with the number of turns n as parameter.

DFigure 6-4. Air-cored coil output voltage UO at a magnetic field x frequency product 1 nT . Hz versus diameter D with number of turns n as parameter.

212

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

The DC resistance of the coil is RDC = (4 p n D ) / d 2which causes a thermal noise voltage = 1/4 k , T RDc Af as the minimal and unavoidable internal noise that uN= limits the coil’s useful sensitivity. In a practical situation when designing a coil, the allowable weight of the winding

is often more critical than its wire diameter. Thus the noise voltage now becomes

Figure 6-5 shows the noise voltage spectral density U N / m as a function of the coil weight for a copper wire coil. The product nD has been chosen as one of the parameters instead of the wire length x n D, since the number of turns n and the mean coil diameter D are explicit design quantities for a sensor coil. The other parameter is the wire diameter d for which a practical minimum value of 50 bm and maximum value of 5 mm is assumed. The limits given by these wire diameters are indicated in the upper left-hand and lower right-hand corners of the diagram. Finally, the diagram is drawn for numerical values of U N / m between 0.01 and 100 nV/@ ; these are regarded as extreme values since they include the thermal noise of resistors between 0.01 0 and 100 k 0 , as well as the total input noise of today’s bipolar and JFET low noise amplifiers. As an aid in designing very sensitive air-cored induction coil sensors Figures 6-4 and 6-5 can be used in the following way. Firstly, the largest acceptable sensor coil diameter should be selected, and the number of turns required for the measuring task can be taken from Figure 6-4. With the numbers n and D now known, the sensor coil weight for a sufficiently large signal-to-noise ratio and a suitable wire diameter can be determined from Figure 6-5. Since in Figure 6-4 a voltage is given, and in Figure 6-5 a voltage density, the two cannot be compared without an additional restrictive condition being applied. Both signals must be measured within the same bandwidth AA for example by using a spectrum analyzer with Af = 1 Hz. The higher the spectral purity of the signal, the smaller the bandwidth Af of the spectrum analyzer can be made. The signal-to-noise ratio increases as l / A f but at the expense of the building-up time 5 = l/Afof the analyzer output. Using Equations (6-2) and (6-5) the signal-to-noise ratio S / N can be written as

if A f = 1 Hz in Equation (6-5). This ratio is proportional to the diameter of the wire and to the square roots of its specific conductivity a, the number of turns, and the third power of the coil diameter. For a comparison of different sensor coils, often a noise equivalent magnetic field HN is used instead of the S/N ratio. The magnetic field HN generates the noise voltage U, at the output of an ideal coil, ie, one free of internal noise, and denotes the minimum detectable

6.2 Air-Cored Induction Coil

213

'kg

Figure 6-5. Air-cored coil noise output voltage spectral density U N / W versus coil weight W,,, , with wire diameter d and the product number of turns x coil diameter n * D as parameters.

magnetic field; thus it is defined as HN = U N / S o.f. Using Equations (6-3) and (6-5) the noise equivalent magnetic field spectral density of the air-cored coil becomes -HN

w

-

8rn.V;T ~ ~ * p o . d * f i T * f

or when related to the weight of the coil

214

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

For a small and difficult to detect magnetic field, the coil should be large and heavy and preferably wound with a wire of high conductivity. In Figure 6-6 the noise equivalent magnetic field spectral density for an air-cored coil wound with copper wire is shown versus the coil weight at a frequency of 1 Hz. Since only the thermal noise of the induction coil is considered, this magnetic field noise is actually the minimum internal noise of such a sensor but, normally, it also provides the main contribution to the total noise. For frequencies higher than 1 Hz the readings from Figure 6-6 should be multiplied by l / f and thus the noise field may reach remarkably small values. Some limits for the practical design of coils are indicated in the figure. Large loops with diameters between 10 and 100 m which are used as stationary sensors for the observation of earth field variations, cannot have weights of less than 200 g. The indicated number of turns n leads to the weights readable on the scale if wire of 1 mm in diameter is utilized. For transportable coils of 1 and 3 m in diameter with weights less than 28 and 760 g, respectively, and winding cross-section dimensions w = h 5 D the weight of the supporting structure (not taken into account here) will be a multiple of the copper wire weight. Finally, coils of small diameters 0.1 and 0.3 m may not reach weights of 10 and 100 kg, respectively, without violating the assumption w = h 4 D. Therefore, a limit at w = h = 0.3 D is indicated. In the above discussion only the thermal noise of the sensor coil was considered. When an air-cored coil is combined with an electronic amplifier, the noise of the coil normally exceeds that of the amplifier and determines the useful sensitivity of the sensor. In such a case, the above calculations and conclusions are then applicable. Theoretical considerations of this kind have been made in order to maximize the sensitivity of both a relatively small single air-cored coil [51 and of a fairly high number of fabricated large coils a few meters in diameter [6]. If the internal noise of the amplifier is also to be taken into account, the noise equivalent magnetic field representing the noise sources, in both the coil and the amplifier can be calculated in a similar manner. This has been done for the optimization of a medium-sized triaxial sensor with air-cored coils achieving a very high useful sensitivity [7]. This is discussed in Section 6.4.4. In the case of dominant amplifier noise, the absolute signal voltage U, of the coil must be maximized for a given weight which leads to a different conclusion [6]. If the weight of the coil is inserted into Equation (6-2), the output voltage of the coil becomes

Again the diameter of the coil should be made as large as possible but now many turns of thin wire should be used.

6.2.3 Equivalent Circuit Diagram The output voltage U, of an air-cored induction coil can be calculated using Equation (6-2), but only at low frequencies. At higher frequencies the AC impedances of the inductance L , the resistance R,, and the AC conductance of the self-capacitance C,shown in the equivalent circuit diagram of Figure 6-7, must all be taken into account, Even at about a tenth the influence of the resonant circuit may exof the resonant frequency f , = (2 n

m)-'

6.2 Air-Cored Induction Coil

215

Figure 6-6. Air-cored coil noise equivalent magnetic field spectral density H N m versus coil weight W , with coil diameter D as parameter. The weight of indicated number n of turns of large diameters D is for 1 mm wire; practical weight limits for minimum and maximum ratios coil width w (= coil height h) to mean diameter D are marked.

216

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

ceed 1%. A calculation of the frequency response of the sensitivity using the following simple formulas is only approximate, but may be useful for an explanation of a measured response or for an estimation of the possible operating range of a coil to be designed.

c

=:

U Figure 6-7. Equivalent circuit diagram of an air-cored

1

A

The inductance of an air-cored coil depends on the geometry of the winding and the number of turns, is always proportional to the dimension of a length, and is given within a few percent uncertainty by one of the following formulas. Single turn circular loop with D

d:

%

r:

)-

-2+ a

L = 6.28 D In-

[HI,

where a is the skin effect factor; Single-layer solenoid if very long and thin and with negligible insulating gaps between turns:

with w = n . dw ; Single-layer solenoid if shorter (w

L =

D 2 .n 2 + 101 w

[HI;

46 D

Multilayer solenoid if D L =

> 1.6 D ) and compactly wound:

%

w, h :

78.7 D 2 n 2 3D+9w+10h 9

*

[HI

For designation of coil dimensions see Figure 6-3, all to be measured in cm.

6.2 Air-Cored Induction Coil

217

The skin effect factor a in the first formula demonstrates the decrease of inductance with increasing frequency which, in principle, occurs for all kinds of coils. For thin wire with d = 0.3 mm, a = 0.25 at all frequencies of interest. For thicker wire with the diameter d = 1 mm d = 3 mm

a = 0.249/0.244/0.195, and for a = 0.2 /0.12 /0.07 at f = 10/30/100 kHz.

The other formulas refer to low frequency situations. All inductance formulas are taken from [81 and [91. Further details and more complicated formulas of better accuracy can be found in [8, 9, 251. If the effect of changes in coil properties on the inductance has to be estimated, the following two rules are useful: (1) Coils with identical outer dimensions have inductances L proportional to n 2 , and (2) an enlargement of all dimensions of a coil (including wire diameter) by a factor of x causes the inductance to increase linearly by x. The resistance R,, represents the increasing losses in a coil at higher frequencies due to skin and proximity effects, eddy-currents in other parts of the winding and losses in a shielding. Dielectric losses and those caused by radiation may be neglected. For large loops with D % d and not too many turns sufficiently spaced, the increase of the resistance RAc can be assumed to be solely caused by the skin effect and equal to that of a straight wire. In Figure 6-8 the resistance ratio (R,, /RDc) x 100% is shown versus frequency for copper wire of diameters between d = 0.5 and 5 mm. The skin penetration depth for a non-magnetic conductor material is 6 = [2/(wapu,)] f - I ” . Numerical values of 6 can be taken from Figure 6-8 at the level marked d / 6 = 1, where the relative increase in resistance is only about 0.13%. At the critical value d / 6 = 2 the skin effect begins to become noticeable and the additional AC resistance R,, exceeds 2% of the DC value R D c . In order to get a feeling for the increase in resistance that occurs at higher frequencies with an air-cored coil due to both skin and proximity effects the formula

-

RDc

+

R A c = g,

+u

(d/c)’

3

g,

RDC

has been numerically evaluated [lo]. Here the functions g, = f ( d / 6 ) and g, = f ( d / 6 ) separately denote the contributions of the skin and the proximity effect, respectively, both depending on the ratio d/6. They are tabulated in [lo]. For a straight wire or a large singleturn loop g, = 0 and in Figure 6-8 the ratio R,,/RD, = g, - 1 is given. For a singlelayer solenoid with g, > 0 numerical values of u for three different coil geometries (for w / D = 0, 1, and r_ 10 factor u = 3.3, 5.3, and 2 8.9, respectively), and the ratio d/c with c = D, from Figure 6-2 have been inserted. The results are valid if the turns are not too closely spaced (d/c 5 0.6) or, alternatively, as long as g, = 1. Since a densely wound layer is assumed, with a pitch c equal to D, for each wire diameter, the latter condition limits the validity of the results. As can be seen in Figure 6-8, the increase in resistance due to the proximity effect is over ten times larger than that due to the skin effect. Consequently, the numerical values of the factor u given above further multiply the increase. However, it should be noted that here the internal noise of the coil, which depends only on the square root of the resistance, is the main interest. The lumped capacitance C (see Figure 6-7) across the outer terminals of the coil represents the distributed capacitances between adjacent turns and layers. Strictly, this would be true

218

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

100 kHz f-

Figure 6-8. Ratio AC resistance to DC resistance (RAc/R,,) x 100 in percent of a) straight copper wire and b) single-layer solenoids densely wound with copper wire due to skin effect and proximity effect versus frequency. Wire diameter d and length-to-diameter ratio w / D of the coils are parameters. d / 6 is the ratio of wire diameter to skin penetration depth. For details see text.

219

6.2 Air-Cored Induction Coil

only if all the turns were perfectly magnetically coupled. As a result of magnetic stray effects in the winding, the voltage distribution within the coil, and hence the lumped self-capacitance, varies with frequency and increases if the resonant frequency is approached. This effect may not be negligible in single-layer coils with poor magnetic coupling, however in most cases, a constant capacitance C is appropriate for describing the frequency response of the resonant circuit of Figure 6-7. It is difficult to develop general formulas for the self-capacitance C because it depends not only on the dimensions, but also to a great extent, on the internal details of the winding as well as on the workmanship. Normally, the smallest capacitance possible is desired in order to get a wide operating frequency range and a resonant frequency far above this range. By using a low self-capacitance, undesirable restrictions when choosing the parameters for an optimum induction coil sensor are avoided. Besides this, the dielectric losses, which are proportional to the capacitance, are kept to a minimum. After completion of a coil designed according to standards for low-capacitance windings, a measurement of the self-capacitance yields better results than a calculation. An approved method is to measure the resonant frequency of the coil when it is shunted with different additional capacitors C, and to plot 1/cf,)2 versus C,.The result is a straight line which intersects the C,-axis on the negative side at the value C. The following formulas give the dependence of the self-capacitance on the coil geometry and may be useful when designing a low-capacitance coil. For a single-layer solenoid C D, the number and the pitch of the turns and the length of the coil (except for very long coils) have only little influence. The capacitance C versus the ratio w / D is shown in Figure 6-9. Curve 1 in this figure was measured with a coil with one end grounded [ll] and curve 2 was calculated [121.

-

Figure 6-9. Capacitance C of a single-layer coil normalized to its diameter D versus length-to-diameter ratio w/D of the coil (capacitance C in pF and geometrical dimensions w and D in cm).

-W

D

In a multilayer solenoid the self-capacitance is due mainly to the layer-to-layer capacitance. It can be determined using C =

0.37 * E, * w * D [P FI (c - d ) * n,

if the coil is simply wound, ie, twice the layer voltage is between the turns at the one end of two adjacent layers [13]. All dimensions are measured in cm.

220

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

-

Generally, C ( w D ) / h holds, ie, C can be reduced by increasing the height of a coil if its axial length and mean diameter remain constant. Thus, a drastic reduction of the selfcapacitance of a coil can be achieved by dividing the winding into k sections each having a capacitance which is only l/k of the capacitance C of the undivided coil. The series connection of k capacitances C/k, and the taking into account of (k - 1) intersection capacitances Ci yields the total self-capacitance

C +Ci . c,,, = k2 k - 1

-

From this equation it can be concluded that C,,, l/k2 if k is small and C/k > Ci, and C,,, l/k if k is large and C/k < Ci. In either case C,,, can be greatly reduced if the intersection walls of the winding form are appropriately designed. Finally, the self-capacitance of undivided coils with few layers can be decreased by using spacings with a low dielectric constant between the layers, by application of the ,bank winding' scheme, or by the use of wire with double insulation. It is relevant to note that the insertion of all kinds of additional insulation between turns and layers reduces the influence of the proximity effect and the inductance of the coil, whilst leaving the sensitivity unaffected.

-

6.3

High Permeability Core Induction Coil

6.3.1 General Design Considerations The second basic form of a magnetic field sensor or a magnetic antenna, which is used more often than an air-cored coil, is a coil on a long and slender ferromagnetic rod of circular or quadratic cross-section. The magnetic properties of the rod largely determine the characteristics of the sensor. If a high permeability rod is inserted into an originally homogeneous magnetic field (indicated by parallel field lines), the field becomes distorted as shown in Figure 6-10. The figure is taken from [14], where an experimental study of the effective permeability of cylindrical rods by mapping the surrounding magnetic field is described and the displayed field configuration is given. The core concentrates the magnetic flux inside the coil and the ratio of the area of distorted field lines gathered by the core to the cross-sectional area of the core itself enables an estimate of the core's effective low-frequency permeability. Furthermore, it is evident how much the field strength (indicated by the density of the field lines) is reduced at the center of the rod, where the coil is located. Only a vanishing small part of the magnetic field, external to the core, is linked with the coil even if the coil has appreciably radial dimensions. Thus, the voltage induced in the coil by an AC magnetic field depends on the geometry of the core and is, to all intents and purposes, independent of the size of the coil. The change in the field pattern is only minimal if a rod of a slightly smaller diameter is used. Thus, it may be concluded that the effective permeability of the core (if made out of a material of sufficiently high permeability) to a first approximation is inversely proportional to the square of the core diameter.

6.3 High Permeability Core Induction Coil

221

The main advantage, offered by induction coil sensors with a high permeability core, is the increase in sensitivity at a given sensor weight or the significant reduction in size and weight for a given sensitivity. The area of the coil can be reduced by the factor of effective core permeability without reducing the effective induction area or sensitivity. The core permeability is, therefore, a key quality of such induction coils. If the coil is then wrapped tightly around a long and thin core, the reduction of the coil’s radial dimensions means a decrease in the length of wire used and, thus, both a correspondingly lower internal noise and a higher sensor bandwidth. Although high permeability core induction coils are purely magnetically sensitive, it is recommended that they be electrostatically shielded. This is particularly important in the case of very sensitive sensors at higher frequencies, which need an electronic amplifier close to the coil. This can be accomplished more easily with compact coil-rod combinations than with air-cored coils, and the resulting reduction of sensor bandwidth can be kept smaller.

Figure 6-10. Magnetic field pattern around a high permeability core when it is inserted into a homogeneous field. It is valid for low frequencies and if the coil, indicated at the middle of the core, is without current, after [14].

Disadvantages also arise with the use of the high permeability core, and it is this additional component which makes designing a sensor much more difficult. The core permeability depends, in a complex relationship, on the core geometry and on the properties of the ferromagnetic material which are frequency dependent and inherently non-linear. Thus, a complete and self-contained analytical description or optimization of such a sensor is nearly impossible. The material or ring-core permeability is affected by the magnetization of the core, its temperature, and by mechanical stress and shocks acting on the core. In actual cases, a variable premagnetization (eg, when a sensitive, receiving magnetic antenna is rotated in the earth’s magnetic field) can cause an unacceptable modulation of the received signals because of changing sensitivity and a corresponding variation of sensor-internal noise due to

222

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

Barkhausen noise. Non-linear effects caused by small magnetic fields are usually negligible, but an investigation applying a cross modulation technique has been suggested [15] and may be advisable in critical cases. By no means should a saturation of the core due to the measuring or due to an ambient field occur, which also means a strict limitation of the measuring range. If the sensors are to be operated under extreme temperature conditions, the influence of the temperature on the permeability of the core material must be investigated. For example, at low temperatures, high-p ferrites exhibit a severe decrease in permeability which makes all external influences more critical. Since the properties of induction coils with high permeability cores are not precisely predictable, a more careful calibration is important. If mechanical loads may have possibly affected a sensor, the unknown changes in its properties make a more frequent repetition of the calibration necessary. In principle, this calibration should be performed by measuring the frequency response of the output voltage with the sensor exposed to a known AC magnetic field. Since it is difficult to generate a field which is both homogeneous in a large volume and free of disturbances, a purely electrical calibration method has been both theoretically and practically investigated [16, 171, but an absolute calibration of sensors with cylindrical high permeability cores must be performed in a magnetic field of large dimensions, one which may also be of natural origin. In this case then the calibration consists of a comparison with an air-cored coil sensor [18]. There have been some applications of induction coil sensors with high permeability cores where, without the help of usually considerably expensive shieldings, very weak magnetic fields have been observed despite the presence of strong disturbance fields. This was achieved by using two sensors in the gradiometer configuration already discussed for air-cored coils. To take full advantage of this efficient method the sensors must be as near similar as possible for a reasonably long time. This is more difficult to achieve with high permeability cored coils than with air-cored coils. The disadvantages of high permeability cored induction coils cited above are the arguments which are occasionally expressed against the use of such sensors. But all of these negative influences can be kept to a minimum by properly selecting the geometry of the core, ie, essentially a not over-large length-to-diameter ratio. A technical compromise must be reached between the high sensitivity of a sensor and the stabilization of its properties influenced by the ambient environment. In many applications where efficient air-cored coils are too large and difficult to transport, they have been replaced by high permeability core coils. The dimensions of cores utilized in a high kHz-range, range from a few centimeters in length and 1 millimeter in diameter for miniature sensors to some ten centimeters in length and several millimeters in diameter if more space is available and weight is tolerable. At frequencies below 100 Hz, heavy cores up to 2 meters in length and many centimeters in diameter have been used. Overall, the weights of the cores range from a few grams up to more than 50 kilograms and the weights of the coils are of the same order. In large induction coil sensors operated below a few Hertz, eddy-current effects are negligible in both coil and core even if massive cores constructed from highly conductive and permeable alloys are used. At higher frequencies these effects can be kept to a minimum in the coil if a sufficiently thin wire is used (see Figure 6-8), and in addition, a uniform magnetization of the core’s interior can be obtained if the core is laminated and the penetration depth of the magnetic field 6 = [2/(00pu,p0)] is larger than half the lamination thickness t. The penetration depth decreases with the frequency and 6 = t / 2 is reached at the

6.3 High Permeability Core Induction Coil

223

critical frequency f, = 4/(71t z p r p o b ) ,which is the eddy-current limiting frequency; in the case of a Mumetal core it is about f, 6 0 / t For a core with a lamination thickness of t = 0.1 mm, the limit of the ,low frequency range‘, for which the following considerations are valid, is only f, = 6 kHz. A rod made from either a stack of thin tapes glued together or a bundle of straight thin wires can be used. The use of wires may be technologically favorable since it will more readily provide a circular cross-section and a higher critical frequency. The electrical insulation necessary between the laminations or wires will be geometrically neglected in the following discussion. Because of its small electrical conductivity, a ferrite core is suitable for all frequencies of interest. The coil is usually built in the form of a multilayer solenoid. The length of the coil should be about equal to, or somewhat more than, half the length of the core. There is an optimum length and even an optimum shape for the winding cross-sectional area. If the intended area of use is in the audio-frequency range, the coil can have insulation spacers between the layers and/or should be sectorized to reduce the distributed capacitance. J

’.

6.3.2 Magnetization of a High Permeability Core The usual description of the low frequency behaviour of an induction coil with a high permeability core, an example of which is shown in Figure 6-11, is as follows: The induced voltage ui in the coil depends on the number of turns n and the rate of change of the magnetic flux @, in the core,

and in the case of a sinusoidal flux variation

q c=

QCmax

. cos ( a t )

thus the open-loop peak output voltage of the coil is

U,

=

- .

o n

=

o .n p r p o ’ Hi * A , .

Here U, is written as a function of the magnetic field strength Hiinside the core and its material permeability pr. For a sensor description, U, has to be related to the measuring field H far from the core. Let the core be a slender rotation ellipsoid inserted into a homogeneous magnetic field H . Then the field Hi and the magnetization M = 01, - 1) Hiof the core are homogeneous. The magnetized core produces a demagnetizing field Hdm= -N M , with N as the demagnetizing factor. This must be added to the original external field H to get the resulting field inside This equation solved for Hi gives the core, Hi = H + Hdm= H - N 01, - 1) Hi.

H.

’

=

1

1 +N(pr-l)

* H

224

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

and using p1Hi = pCH, the sensor output voltage can now be related to the originally applied external magnetic field H which is to be measured:

where PI

"= 1

+ N (pI -

1)

is the effective permeability of the high permeability core. For a given pI and a calculated numerical value of N,the core permeability pc and the output voltage of the coil may be determined.

Figure 6-11. Induction coil on a cylindrical high permeability core.

The demagnetization factor depends on the length-to-diameter ratio m of the ellipsoid and can be calculated exactly using

where it is more precisely denoted as Ne,im,standing for an ellipsoid with the material permeability pI = 03 and magnetized parallel to the long axis. In cores of any other shape, the internal field Hi and the magnetization M vary in both direction and magnitude throughout the volume. Despite this, the above equations generally hold true and the demagnetization factor N,then valid for the center of the core, must either be determined experimentally or can be approximately calculated. In addition, by evaluating -NCYI, - 2.26 In (1 Neil,

2.15 In (1

+ 0.156 m) + + 0.326 m) +

1 1

which is given in [19], the demagnetization factor for cylindrical cores has been calculated. In Figure 6-12 both Neil,and Ncyi,are shown versus the length-to-diameter ratio m.For rods with a quadratic cross-section, NWlcan be used if the diameter is measured along one side. Furthermore, in Figure 6-12 the influence of a finite material permeability < 03 on Nqi , as it can be taken from Figure 6-13, is shown. For values m < 50, the core permeability pc is almost independent of ,ur but for high values (m > 500) the core permeability pc can be substantially increased by choosing a material of higher permeability pI. A good numerical

6.3 High Permeability Core Induction Coil

+

225

T

/

Ncyl

-

1000

100

mFigure 6-U. Demagnetization factor N of prolate ellipsoids and cylindrical rods (descending curves) and core permeability pc (ascending curves) of cylindrical rods versus the length-to-diameter ratio m of the rod with material permeability pr as parameter.

226

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

approximation for the dependency of p, on m is p, t: 2.1 m3'2 if the length-to-diameter ratio is in the technically important range m = 10 . . . 120 and pr = lo4, see Figure 6-12. The same information can be taken from Figure 6-13, where the core permeability p, is shown as a function of the material permeability pr with m as parameter.

10

*

I

102

I

I

I l l ,

I

lo3

*

I

1

, , , I

I

loL

I

,

/ I , ,

5

I

lo5

'

Pr

I

-

2

5

" ' 1

10

Figure 6-13. Core permeability p, of cylindrical rods versus the material permeability p, with lengthto-diameter ratio rn of the rod as parameter, after [20].

In order to achieve a high sensitivity in the induction coil sensor, the core permeability p, should be made as high as possible which requires a high length-to-diameter ratio m and a high material permeability pr. But it has already been seen in the discussion concerning the disadvantages arising with the use of a ferromagnetic core, that all the instabilities of a high permeability core sensor result ultimately from changes in the material permeability. According to Figures 6-12 and 6-13, the lower the permeability pr the lower the ratio m must be in order to limit the influence of changes in pr.

6.3 High Permeability Core Induction Coil

221

7 f 3.10'

f

/I 1

* 100

1000

m-

Figure 6-14. Influence factor K describing to what extent small relative changes of the material permeability Apr/pr are transferred into relative changes of the core permeability A p C / p c versus the length-to-diameter ratio m of the core with permeability pr as parameter.

228

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

The extent to which relative changes of the material permeability Ap,/p, cause changes in the core permeability Apc/pccan be expressed by the influence factor

The dependency between p, and p,, given for Equation (6-8), differentiated with respect to p, and compared with the differential notation of the above definition of K yields

and if this is then solved for K it yields

K =

1

+

1-N N @ , - 1)

*

In Figure 6-14 the Apr influence factor K is plotted versus the length-to-diameter ratio m of the core for N = Nq,, (m)with the corrections for p, = 3 . lo3 and p, = lo4 taken from Figure 6-12. In Figure 6-14 it can be seen that for m = 100 a small relative change in the material permeability Ap,/p, results in a change of the core permeability Apc/pc(and, thus, of the sensitivity of the sensor) which is negligible (2.5%)at p, = lo5 but possibly unacceptable (50%) at p, = 3000. If a ferromagnetic material has been selected for the core, the permeability and its temperature dependency in the predicted operating range of the sensor are known. From Figure 6-14 the necessary (and maximum) value of m can then be read for an acceptable variation of the sensor sensitivity in the temperature range.

6.3.3 Sensitivity and Internal Noise The open-loop peak output voltage of a coil on a high permeability core is given in Equation (6-8). Inserting the cross-sectional area of the core A, = (n D,2)/4 it can also be written as

-

and the sensitivity defined by Equation (6-3) is then

A comparison of these equations with the respective ones for the air-cored coil shows that, for a single-layer solenoid wound densely around the core (with D = Dc),in the case shown here output voltage and sensitivity are larger by the factor p, than would be expected.

6.3 High Permeability Core Induction Coil

229

With po as expressed in Equation (6-4) the output voltage at 1 nT Hz is

in volts if A , and 0:are measured in square meters. As an auxiliary means of assessing the capabilities of induction coil sensors with high permeability cores, the sensitivity constant So (or induced voltage Uo at 1 nT . Hz) for a coil with n = 10000 turns on a core with material permeability pr = 10000 as a function of its length I and diameter D, is displayed in both Figures 6-15a and b. A scale at the bottom of these figures shows the core volume which can be multiplied by the density to yield its weight. As can be seen, the sensitivity increases sharply with the core length but much less with its diameter. The diagrams in Figures 6-15a and b show the maximum sensitivity that can be obtained at low frequencies with no external load. Furthermore, the coil is assumed to be concentrated at the center of the core. As a result of stray effects, the induced voltage decreases if the coil is shifted towards either end or is spread over a large part of the core [20]. Both dependencies have been verified experimentally for a disk-shaped coil and for solenoids of various lengths on a large ferrite core (length = 1.2 m and diameter D, = 2.2 cm) with a material permeability of p, = 10000. The core was magnetized in a very extended homogeneous AC magnetic field of 1 kHz. The axial length of the disk coil was only 0.6 cm whereas the solenoids had lengths between 12 and 106 cm and were each densely wound with 1000 turns. The results are shown in Figure 6-16, where it has also been verified that integration of curve a leads to curve b. As can be seen, the relative loss of induced voltage for long coils is minimal. However, the diagrams in Figures 6-15a and b do not show whether the sensitivity is utilizable if the thermal noise of the coil is taken into account. In contrast to air-cored coils, the signal voltage Uo and the noise voltage UN depend on the different dimensions of the core and the coil, respectively. To a certain extent, both are independent of each other as long as the necessary condition D, 5 D is fulfilled and w 5 I is chosen. The manner in which the coil weight and the number of turns at both a constant mean coil diameter and core geometry influence the signal-to-noise ratio S/N, can be concluded from the following proportionalities. Given that Uo n and UN it then follows that (1) S/N (with W,,, n and R n at a constant wire diameter d ) , and (2) S/N is independent of n n z at a constant coil weight). (with R As for air-cored coils, the noise equivalent magnetic field spectral density of the coil on a high permeability core is calculated according to the definition HN = UN/So.f. With the thermal noise voltage UN of the coil given by Equation (6-5), and the sensitivity given by Equation (6-lo), it follows for the noise field density

-

-

-

- m,

-m

(6-11)

230

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

I

SO

4 vc

-

Figure 6-15. a) Sensitivity So of an induction coil on a high permeability core versus length I, diameter Dc,and volume Vc of the core (at n = 10000 turns of the coil and permeability p r = loo00 of the core material for Dc = 2-14 mm).

6.3 High Permeability Core Induction Coil

231

Figure 6-15. b) Sensitivity So of an induction coil on a high permeability core versus length I, diameter D,,and volume V, of the core (at n = 10000 turns of the coil and permeability pr = 10000 of the core material for D, = 8-24 mm).

232

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

Figure 6-16. Relative voltage induced a) in a disk-shaped coil versus its location on the core, b) in solenoids versus relative length w/l. (For a coil concentrated at the middle of the core the induced relative voltage = 1).

In comparison to the results for air-cored coils, here the coil diameter D remains in the numerator and the core permeability p, appears in the denominator. For single-layer coils tightly wound around the core, with D D,, the noise magnetic field here is less by the factor p, and as can be seen, H N / W does not depend on the number of turns nor on the wire diameter of the coil if its weight is fixed. However, when noise sources other than the DC resistance of the coil are to be taken into account, it is favorable to operate the induction coil at sufficiently high absolute signal (and noise) output levels by choosing a high number of turns and a thin wire. In order to attain a low value for the noise field, both the resistivity and particularly the average turn length should be kept to a minimum, ie, a coil which is not too short and which is closely wound around a thin core should be used. Furthermore, H N / W decreases with the square root of the coil weight W, and with the product Df . p,, which itself depends on the weight W, of the core. Thus, as with air-cored coils, the total weight of the sensor W, = W, + W, = V, . yw + V, . y, is a crucial quantity if its noise must be kept very small. The question then arises as to how the total weight allotted to a sensor should be distributed between the coil and the core. A numerical calculation of the noise equivalent magnetic field spectral density H N / W as a function of the sensor weight W, has been made in order to show what is theoretically attainable. Several assumptions are made for this calculation however. Firstly, as it is done elsewhere [21, 221, the weights of the coil and the core are assumed to be equal and thus, the relationships W, = W, = V, yw = V, . y, and W, = 2 W, all hold. Secondly, two cores with a material permeability p, = 10000 and length-to-diameter ratios of m = 50 and rn = 100 are adopted which yields fixed values for the core permeability p,. The inserted numerical values for the material densities are yc = 8.6 g/cm3 for the Mumetal core, and yw = ycu . a, a, = 6.2 g/cm3 for the mean density of the coil with ycu = 8.9 g/cm3 and the filling factors a, = 0.85 (taken from Figure 6-1) and a, = 0.82 (taken from Figure 6-2b J

+

233

6.3 High Permeability Core Induction Coil

for 0.2 mm wire). Then for each numerical value of the coil weight inserted in Equation (6-11) the core diameter D,can be calculated using

D, =

17. rc

*

Yc

Furthermore, the mean diameter D of the coil has to be calculated from the core diameter 0,. For equal weights of the winding and the core, the relationship V,,, = r] V, holds for the volumes, where r] = y c / ( y c u . a, u,). Using the dimensions of the coil and the core shown in Figure 6-11 this can be written as

and for a chosen width of the coil w = r] 1/2 = 0.7 . I the mean diameter becomes D = 1.37 D,.Finally, the spreading of the coil over about 70 per cent of the core length causes a 13 per cent reduction of the sensitivity (see curve b in Figure 6-16). The appropriate increase in the noise is to be taken into account. The result is shown in Figure 6-17, where the minimum noise equivalent magnetic field density H N / W resulting from the thermal W[0.83 noise of the coil is plotted versus sensor weight W , . As can be seen, H , / W for both length-to-diameter ratios m of the core, and H N / W l/m at a constant weight. For some applications, where sensors with a very small noise equivalent magnetic field are needed or where tolerable weight and available space are very limited, design considerations have been made with regard to favorable coil dimensions or geometry, the optimum distribu-

-

-

ws

-

Figure 6-17. Minimum noise equivalent magnetic field spectral density H , / W of an induction coil sensor with high permeability core versus sensor weigth W, (at length-to-diameter ratios m = 50 and 100, permeability pr = 10000 of the core material, and f = 1 Hz).

234

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

tion of weight between coil and core, and a minimum total weight. Many parameters are necessary for the description of such sensors, particularly if their frequency response is also taken into consideration and as a result therefore, some practical numerical assumptions are often made to maintain the overall picture and get useful results. For coils of constant length w, the improvement of S/N with an increasing diameter ratio D,/D,has been investigated [23]. Despite a growth of volume with increasing Do,above values of Do = (6 . . . 8) D, the ratio S/N becomes almost constant because of the progressively increasing resistance. An overall optimization of the coil’s geometry results in a parabolic shape for the winding cross-sectional area. Such a coil was constructed but the gain when compared to the simple cylindrical coil was found to be not more than about ten percent. Considering the difficulties encountered in constructing a parabolic coil, it is not recommended as a good solution [24]. Other general theories for optimizing induction coil sensors with a high permeability core have been published. A system of analytical equations describing the combination of a coil on a core and an electronic amplifier, is developed in [26]. Here the dimensions of coil and core, the electrical characteristics of the coil, the demagnetization factor of the core, and the contributions of all components to the frequency response and internal noise of the sensor are considered. The result is a large set of variable parameters, with an optimization procedure in a multi-dimensional indicated with which the minimum deviation of S/N from (S/N)max space can be found. Practically however, a number of restrictions governed by the particular application must be considered and ultimately, the design is determined by the small allowable weight and the required frequency range of the sensor. An optimization theory for inductioncoil magnetometers at higher frequencies [27] introduces these many parameters in a series of equations describing the mechanical and electrical properties of the coil and core, the optimum weight distribution between iron and copper, and the equivalent magnetic field noise. Many pictures show the influence of variables, trends of functional correlations at several steps of the optimization procedure, and an approach to a favorable sensor design. In view of the complexity of the theory, some parameters such as amplifier noise and input impedance, influence of temperature, conductor material, and coil design are assumed to be given or negligible. Variations in these parameters could only be introduced through a multiple repetition of the optimization procedure. A number of sensors, differing in size and weight, have been designed using the relationships discussed above describing the magnetization of a high permeability core in a magnetic field, the non-uniform flux distribution inside the cylindrical core, and the dependency of the sensitivity on the weight of the coil and the core [28, 291. The core dimensions used range in length and diameter from 350 and 5 mm to 2000 and 20 mm, respectively. The coils have numbers of turns between 2 * lo4 and 1.5 lo5 and a weight comparable to that of the respective cores. The sensitivity and the frequency response of all sensors has been measured, and it has been shown that for each of the various applications mentioned, a well suited or even an optimal sensor configuration can be found.

6.3.4 Equivalent Circuit Diagram The electrically equivalent circuit of an induction coil on a high permeability core is shown in Figure 6-18. Compared to that of an air-cored coil, it has two additional elements Re and R, representing the eddy-current and hysteresis losses within the core, respectively. The

235

6.3 High Permeability Core Induction Coil

numerical magnitudes of all elements are typically different from those of the air-cored coil. In order to attain a theoretical predetermination of the frequency response of a sensor, its equivalent circuit elements should be measured [30]. I

coil

I

I

core

I

I

c: :

t

*

v

U

7 0

Figure 6-18. Equivalent circuit diagram of an induction coil on a high permeability core.

The inductance is difficult to calculate because the core is part of an open magnetic circuit and the large air gap has a dominating influence on the flux distribution in the core. Here the inductance is less dependent on the coil geometry than it is with air-cored coils and may be assessed using 10-*[H] , where A , and 1 have to be measured in cm2 and cm, respectively, and the length of the coil is assumed to be approximately equal to that of the core, w t: I [31]. The inductance increases if the coil is shortened and a correction factor /3 > 1 must be applied. Once again using the large ferrite core mentioned above with 1 = 1.2 m and D, = 2.2 cm, the inductance of a diskshaped coil as a function of its location on the core, and the inductance of various single-layer solenoids of 1000 turns each as a function of their relative lengths w/l, was measured. The results shown in Figure 6-19 are arranged in such a way that this figure may be directly compared to Figure 6-16 and the difference becomes immediately apparent. This difference is due to the fact that, in one case the core is magnetized by an external homogeneous field, and in the second case it is magnetized by the current passing through the coil when its inductance is measured. The self-capacitance of a single-layer solenoid on a high permeability core can be taken from Figure 6-9. Since it is very small, the distributed capacitance between the layer and the core must also be considered and it may even be the dominating factor. If the core is electrically conducting, and together with one terminal of the layer, grounded, a cylindrical capacitor is formed with a voltage distribution rising linearly towards the open terminal. In this case, the resulting shunt-capacitance

236

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

must be added to the coil’s self-capacitance. In this formula D - D, is the thickness of the dielectricum between the coil and the core and E, its dielectric constant. The self-capacitance of a multi-layer solenoid on a high permeability core can be calculated using the equation given for air-cored coils, and the methods for reducing the capacitance also apply here. Lastly, if a coil is subdivided into many small sections, the shunt-capacitance C, which is to be added becomes a major part of the resulting total self-capacitance. For relatively compact induction coil sensors with high permeability cores, the important electrostatic shielding can easily be attained and the additional capacitance term introduced above should be further taken into account. The uncertainties in these contributions to the total self-capacitance of the sensor make its calculation an impractical proposition. It should instead, be measured in the manner described for air-cored coils. As a result of the much smaller dimensions of high permeability core induction coils, the DC resistance is smaller than that of air-cored coils of a comparable sensitivity, even if a thinner wire is used. This in turn, shifts the onset of an additionally noticeable AC resistance to higher frequencies. Thus, for coils with winding designs which assure small capacitances not only between the layers and sectors, but also between the winding, the core, and the case as well, the DC resistance to a good approximation represents the total resistance in the increased frequency range. At least two other kinds of losses in the core are noteworthy. The eddy-current losses are proportional to f 2 and whilst they can be kept to a minimum by using sufficiently thin laminations of the core, it is at the expense of an increase in Barkhausen noise. The hysteresis losses are proportional to f and are negligible for a well selected core material at small magnetic reversal amplitudes. These losses are represented in the resonant circuit by the additional series resistances Re and R , , respectively. It is questionable whether a numerical calculation of these resistances and of their influence on the frequency response of the sensor is worthwhile. If such a calculation is to be made, the greater influence of the electrostatic

3.4

3 1.0

0.5

W

1.0

Figure 6-19, Relative inductances of a) a disk-shaped coil versus its location on the core b) of solenoids versus relative length w/l. (For a coil distributed over the whole core with w / l = 1 the relative inductance = 1).

6.4 Induction Coil Sensors with Electronic Amplifiers

231

shielding and an artificial damping resistor, which often is shunted to the capacitance, should be considered. This shielding should not form a closed conductor loop around the core and should be subdivided, especially at higher frequencies, into narrow strips towards the ends. The damping resistor is adjusted in order to get an acceptably small resonance step-up in the frequency response of the sensor sensitivity.

6.4 Induction Coil Sensors with Electronic Amplifiers A number of applications for induction coil sensors exist, where the large output signal of the sensor coil can be directly indicated by a panel meter or further processed by an electronic integrator, in order, for example, to yield a signal proportional to the magnetic field strength. Many decades ago, very sensitive induction coil galvanometer set-ups for the observation of the various pulsation phenomena of the earth’s magnetic field came into widespread use. The mechanical time constant of the indicating galvanometers, or of the galvanometer amplifier combinations, is chosen such that true waveforms showing either the time rate of change of the magnetic field or of the field itself are recorded. In both cases the frequency and phase responses and the transient behavior, which is dependent on the properties of the induction coil and its electrical equivalent circuit diagram, have been investigated and the results are extensively discussed in the literature [32, 33, 34, 35, 361. More recently, induction coil sensors have found diverse applications in various other areas including biomagnetics, space exploration, and electromagnetic sounding for scientific or prospecting purposes, all of which also require an extremely high sensitivity. In these cases, the sensors are combinations of induction coils with low-noise preamplifiers designed according to the results of optimization considerations. The various types of sensors now in use will be discussed briefly in the following sections.

6.4.1 Sensor with Voltage Amplifier An induction coil connected to an amplifier with a very high input impedance is most often used and an example is shown in Figure 6-20. Here it is indicated that the amplifier may consist of an operational amplifier operated as a non-inverting voltage amplifier. The operational amplifier itself has either a field-effect transistor input stage or a discrete source follower stage must be inserted before, in order to reach the input impedance of typically Ri> 1 MQ and Ci< 10 pF. Low noise high-frequency JFETs with a high transconductance and a low reverse transfer capacitance are particularly suitable. The operational amplifier is assumed to have sufficient open loop gain and bandwidth, SO that the amplification factor

within the whole frequency range of interest. The frequency response of the sensor = A . Uo (0)F ( w ) with an open-loop voltage Uo of the output voltage is then U, (0)

238

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

I I

I

Figure 6-20. Induction coil connected to a high input impedance (voltage) amplifier.

coil according to Equations (6-2) or (6-8) and the response of the sensor sensitivity S, (0) = A So ( w ) . F (0) using So taken from Equation (6-3) or (6-10). The transfer function F ( w ) of the L R C,,R,,-low-pass filter is given by

F(w) =

K

f\

1 - -)2 + i 2 D 0,

(6-12) w 0,

where K = R,,/(R + R,,) is a voltage divider factor, w , = (KLC,,) angular frequency, and

is the resonant

is the damping of the resonant circuit. The maximum resonance step-up occurs at the frequency w,, = w, (1 - 2D2)1’2.Here it is assumed that the amplifier input resistance Ri, parallel to possibly another resistor for an adjustment of the damping, is represented by R,,. The amplifier input capacitance Ci is included in the capacitance C,,. Typical frequency responses of the sensor output voltage U, for a given constant value of the magnetic field amplitude and of the sensor sensitivity S, are shown in Figure 6-21. Uo and So are the respective quantities that correspond to the coil at low frequencies. A sag in both curves, shown by the dashed lines, is often found with laminated cores of high permeability alloys if the eddy-current losses are not negligible. The large value for the inductance L of a coil on a high permeability core and a small capacitance C,,result in a resonant circuit of extremely high characteristic impedance vz/c and, often, in a high Q-factor also. The corresponding large resonance step-up must normally be reduced by a damping resistor parallel to Ri. The adjustment of this damping resistor, such that a flat-top response with only a small step-up results, is rather critical. In Figure 6-22 the curves for three different values of D between D = 0.4 and D = 0.6 are shown and the

6.4 Induction Coil Sensors with Electronic Amplifiers

239

effects on the step-up and the bandwidth can be seen. In many cases the Equations (6-12) can be simplified. For low noise coils R Q R,, so that K = 1. Then, for an acceptable value D = 0.5 the damping resistance becomes R,, = V ' T and D = 0.4 and 0.6 are obtained with R,,= 1.25 * and 0.83 I/wc,,, respectively.

V q

Figure 6-21. Frequency responses of the sensitivity S, and the output voltage U, of an induction coil sensor with a voltage amplifier at a constant magnetic field amplitude.

Figure 6-22. Resonance step-up of the sensitivity S, at different values of the damping D.

6.4.2 Sensor with Current Amplifier The second possibility for this circuit is with an induction coil connected to a low-impedance amplifier or current-to-voltage converter. This combination, as yet, is still seldom used. A triaxial sensor, however, with air-cored coils and current amplifiers and having a very small internal noise, has been described in [6]. Figure 6-23 shows the circuit with an inverting operational amplifier and negative feedback via R,, which causes the input resistance Ri = R , / A , to be a few ohms. The shunted capacitance C,, can then be neglected and there

240

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

I

Figure 6-23. Induction coil connected to a low input impedance (current) amplifier.

is no longer an upper band limitation from the circuit’s resonant frequency. The ideal behavior for this circuit can only be obtained if a sufficiently large bandwidth of the operational amplifier is employed, which at a high ratio R,/R may be difficult to achieve. The sensor output voltage for a constant magnetic field is

where R, = R + (R,/A,) is the total resistance in series with the inductance L. The frequency response of the sensor output voltage is shown in Figure 6-24. For low frequencies

w

--c

Figure 6-24. Frequency response of the output voltage UA of an induction coil sensor with a current amplifier at a constant magnetic field amplitude. 0 4 w , = RJL the sensor output voltage increases linearly with the frequency, and at frequencies 0 % w I it becomes independent of the frequency. The transition frequency 0,is the corner frequency of a L R low-pass filter, which can be made fairly low, especially for sensors with high permeability cores. Above oI, where the low-pass filter is integrating, the

6.4 Induction Coil Sensors with Electronic Amplifiers

241

main operating frequency range of the sensor begins. Here the sensor output is proportional to the magnetic field strength only and, using Equation (6-2), is given by

for an air-cored coil, and with Equation (6-9)

for a coil on a high permeability core. It is appropriate in this case to redefine the sensitivity S, as the voltage U, related to the magnetic field H. By inspection of the equations above R , / L decreases as the corner frequency w , is reduced. it can be seen that the sensitivity S, If the geometry of an air-cored coil or of the high permeability core of a sensor remains n 2 , then the unchanged, and if R , is kept constant and the inductance is assumed to be L , n/L l / n . This indicates that such sensors can have a high sensor sensitivity becomes S sensitivity-bandwidth product even if coils with not too many turns are used, as is commonly the case in sensors with a voltage amplifier. Small values of R,, which are necessary for a small corner frequency w l , may cause DC stability problems with the operational amplifier. These problems can be avoided by inserting a series capacitance C,, as indicated by dashed lines in Figure 6-23. The series resonant circuit thus formed, causes a lower corner frequency step-up of the output voltage U, and sensitivity S,. This is shown in Figure 6-24 and can be adjusted by varying the resistance R,.

-

-

-

-

6.4.3 Sensor with Transformer Coupled Negative Feedback In the third possible combination of an induction coil and an amplifier, which is possible only with a high permeability core, a negative feedback from the amplifier output to the sensor coil is applied [37, 381. As shown in Figure 6-25, from the sensor output voltage U, a current via R , is fed into the inductance L, which produces a counteracting magnetic field in the core. If, at all frequencies of interest w , the phase condition for negative feedback R , %- w L , is satisfied and a close transformer coupling is assumed, the sensor output voltage is

(6-13)

v m

where A = (1 + R,/R,) is the amplification factor, M = is the coefficient of mutual inductance, Uo( w ) is the induced voltage according to Equations (6-2) or (6-9), and F (0) is the transfer function of the LRC low-pass filter defined by Equation (6-12). The amplifier is assumed to have a high open-loop gain A , and a high input impedance Riparallel to Ci (which are elements included in R,, and C,,, respectively) so that, finally, R,, 4 R.

242

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

Figure 6-25. Induction coil connected to a voltage amplifier with transformer coupled negative feedback to the coil.

If Equation (6-13) is solved for UA,it becomes (6-14)

At low frequencies o Q w I , this is a high-pass filter transfer function and at high frequencies, w % or,it is a low-pass filter transfer function. The corner frequencies are w l = R,/A M for the high-pass filter, and o2= ( A M/RF) of for the low-pass filter. Normally, o1Q o2and therefore Equation (6-14) can be approximated by the bandpass filter transfer function

-

-

Here, the first term is the frequency independent sensor output voltage in the band between w I and w2,which is affected by the second term (= high-pass filter transfer function) for frequencies o Q o1or by the third term (= low-pass filter transfer function) if w % 0 2 . This frequency response is shown in Figure 6-26. The bandwidth Af of the operating frequency range of the sensor, within which the output voltage is directly proportional to the magnetic field strength, can be defined as

v-

lies in the middle and does not limit the Even if the resonant frequency w, = frequency band of operation, it is advantageous to have a small value of C,,in order to achieve a high sensitivity and a large bandwidth. When dividing the coil into sectors, here it

!I OIz

6.4 Induction Coil Sensors with Electronic A m p l ~ e r s

“A

243

20

-200,001

0

1

0.1

1

10

102

lo3

Figure 6-26. Frequency response of the output voltage UA of an induction coil sensor with negative feedback transformer coupled to the coil.

is particularly important to distribute the turns equally over the sectors in order to shift the higher resonances of the coil to the highest possible frequencies.

6.4.4

Noise Equivalent Magnetic Field of Sensors

The total internal noise of an induction coil sensor, ie, of an induction coil-preamplifier combination according to the equivalent circuit diagram of Figure 6-20, can be calculated using the appropriate equivalent noise circuit diagram shown in Figure 6-27. The four noise sources contributing to the internal sensor noise are: The noise voltage (G/Af)1’2 and the noise current ( K / A f ) I ” , both representing the thermal noise of the coil resistance R and of

I I

Figure 6-27. Equivalent noise source circuit diagram of an induction coil sensor.

244

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

the damping resistor R,,, respectively, and then the noise voltage (?/A f ) and the noise current (?/A f )]I2, describing the internal noise of the amplifier related to its input. All noise voltages and currents are written as spectral densities because the amplifier noise is generally dependent on the frequency. Thus far, the thermal noise voltage of the coil resistance R (representing all losses in copper and ferromagnetic material if applicable) has been the only source of noise and has been set equal to U N . Now, the total noise power density U i / A f related to the amplifier input is the sum of squares

z

where = R + iwL. The noise voltage of the coil and the two noise currents (causing a are to be multiplied by the low-pass filter transfer voltage drop across the coil impedance function F (a). If one assumes an ideal sensor, free of internal noise, the above noise voltage at the preamplifier input may be thought to be caused by an induced voltage

a

Using the definition for the sensor sensitivity So = Uo/f H, the appropriate noise equivalent magnetic field power spectral density can be written as

In order to get a realistic idea of the quantitative contributions of the various noise sources to the total noise, this equation has been numerically evaluated for a typical medium sized audio-frequency sensor with a high permeability core. For the low-noise preamplifier with JFET input stage, rather conservative values for the input noise voltage and noise current,

-

(-$)

-

1/2

=

4 n V / a and

($)

1/2

=

4f A / m ,

respectively, are inserted. For the coil n = 20000 turns, a resistance R = 3 k Q a capacitance C,,= 20 pF, and a width w = 112 are assumed. For the core a length I = 350 mm, a diameter D, = 6 mm (giving m = 58), and a permeability pc = 950 are taken. Thus, the sensor has an inductance L = 70 Hz and a sensitivity So = 3.2 pV/nT Hz. The result is shown in Figure 6-28. All noise contributions expressed as magnetic field noise power spectral densities are individually shown, and they can be summed to yield the total noise equivalent magnetic field spectrum. At low frequencies, as can be seen, the thermal noise voltage of the coil determines the total sensor noise. As is indicated, an increase in the sensitivity So whilst leaving the coil resistance unchanged, would reduce the total noise, whereas an enhanced low frequency excess noise of the amplifier might increase it. Below the resonant frequency, the noise voltage of the preamplifier, being about half that of the coil, increases

-

6.4 Induction Coil Sensors with Electronic Amplifiers

245

I HN2 -

Af

t t

total noise

/

damping resistor thermal noise

I \'

1

10-12

I

I

t---t----

lo-'&

lo-&

10-2

-w

U

P

Figure 6-28. The different contributions to the noise equivalent field and the total noise spectral density function of an induction coil sensor with preamplifier.

the total noise by only 20%. Generally, the noise voltages of coil and amplifier should be in the same order of magnitude, which means a coil resistance R t: 100 SZ for the best low-noise voltage amplifiers. Around the resonant frequency, the current noise of the damping resistor R,, determines '/~ the total noise. With the above numerical values inserted K = 1 and R < ( J ~ / C )(see Equation 6-12). Then, for an acceptable resonance step-up D = 0.5 is chosen, and it follows that R,, = ( L / C ) ' l 2t: 1.9 M a , leading to the high current noise. Here, at the expense of a much greater resonance step-up, the total noise could be considerably reduced by increasing RII. Sensors operated in a narrow band centered around the resonant frequency can have a

246

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

particularly small internal noise. Otherwise, full advantage can be taken of an amplifier having a low current-noise only if the characteristic impedance (L/C)1’2 is very high. Above the resonant frequency, the weighted amplifier noise again increases due to the steep decrease in the sensitivity So . F (0) and ultimately, after superseding the white noise of the resistor R,,, the amplifier noise becomes responsible for the total noise. The noise equivalent magnetic field of an induction coil sensor with a low impedance amplifier (the equivalent circuit diagram of which is shown in Figure 6-23) can be calculated in a similar way. Due to the fact that the capacitance C,, is missing, it follows

At lower frequencies w < RJL the noise equivalent magnetic field power spectral density is proportional to f -* and determined by both the noise voltage of the amplifier and the noise voltage of the coil, or by whichever of the two is much larger. At frequencies around w = R,/L, both terms contribute to the total noise. At higher frequencies w > R,/L, the second term causes a frequency independent noise density as shown in Figure 6-28 at (w/w,) = 1. Thus, to make this type of a sensor as quiet as the one with the high impedance amplifier it is a case of matching the induction coil and the amplifier. For the third kind of induction coil sensor, with a transformer coupled negative feedback to the induction coil on a high permeability core, one additional noise source, compared to those shown in Figure 6-28, contributes to the total noise. It is calculated in [38] and the result is shown in principle comparable to that shown in Figure 6-28. Since the frequency response of the sensor output voltage or of the sensitivity does not show a resonance step-up, the damping resistor R,,can be either very large or completely omitted, and the noise equivalent = 1. magnetic field then becomes very low at frequencies (w/w,)

6.5

Applications

There are many different applications of induction coils with air and high permeability cores, and an accordingly large variety of specific designs, described in the literature. Not always the term induction coil sensor is used according to the definition given in the introduction. Sometimes, for example, magnetic field probes are called induction coil sensors when the field to be measured causes a change in the self-inductance of the coil. Among the well-known applications are the control of traffic lights by waiting cars, the magnetic doors in airport buildings, and nondestructive testing of conducting workpieces. These sensors are excluded here by definition. An extension of these sensors, however, leads to forms with two coils, where small changes of the mutual coupling inductance between them is measured. Their functioning principle, in turn, is comparable to the operation of an induction coil sensor (receiving coil) measuring an artificial magnetic field (generated by the transmitting coil). Both types of active measuring devices are widely used in geological prospecting. In the following, a short survey of applications of sensors with stationary induction coils is given, together with some comments on the most typical requirements and properties. In-

6.5 Applications

241

teresting and important applications of sensors with moving coils can be found in the literature cited in review articles [39-411. Several kinds of such sensors have also been applied in geophysics [42, 431, where those with rotating coils are the most significant types. They are suited for measuring very accurately the direction of the earth’s magnetic field and can be advantageously used to determine small inhomogeneities and field gradients. A modern standard application is the precise testing of the quality of multipole magnetic fields in nuclear physics. Since induction coil sensors are preferably used in scientific research, the definition of the measuring task and the necessary development of related sensors with specific properties were often established at the same time (or even in a reversed order) and a broad variety of industrially fabricated sensors is not available in the market. By far the most numerous applications of induction coil sensors can be found in the field of geophysics. With the measurement of waveforms of magnetic field fluctuations and/or of the spectral density functions of magnetic noise, and by recording their variations in time and space, naturally ocurring physical phenomena can be identified. The measuring ranges, if not regarded as unlimited, may be characterized by the amplitude limits and T and the frequencies and lo5 Hz. Since the early beginning of geomagnetic observations micropulsations have been investigated. These are often near harmonic oscillations of the earth’s magnetic field, lasting for many periods and with spectral energy concentrations at certain frequencies between and about 1 Hz. For measurements on ground air-cored coils and two- or three-axis coil systems up to many meters in diameter have been used. Highly sensitive low-frequency induction coil sensors with long high permeability cores are more easily to transport and, therefore, utilized at many geomagnetic observatories. Besides the AC magnetic fields of the comparatively strong micropulsations a background continuum of magnetic noise of many natural sources induces currents in the conducting earth’s surface with the associated secondary magnetic and electric fields. From measurements of related H and E field components the magnetotelluric exploration method determines the electrical conductivity distribution in the subsurface. Preferably, induction coil sensors with high permeability cores are used here. In the last years the audio-frequency magnetotelluric exploration at higher frequencies became more and more important and is now the domain of induction coil sensor applications. Some details of sensors used for the above purposes are given in Table 6-1. Magnetotelluric measurements, using the above mentioned active devices, are also performed on ground, in boreholes, and on the ocean floor. The magnetic fields are sensed during or after their artificial excitement. This does not change the requirements to the sensors drastically. But their response is exactly defined in time and/or frequency, which leads to a considerably higher sensitivity of the measurements. The need for the development of low-noise and highly sensitive sensors with volumes and weights of typically less than 1 dm and 1 kg, respectively, came from their accomodation on many spacecrafts [l]. With these sensors the temporal and/or spatial fine structure of the earth’s outer magnetic field or of the interplanetary magnetic field has been investigated followed by the identification of a large variety of electromagnetic waves in the earth’s magnetosphere and in the solar wind plasma. Some details of such recently used sensors are listed in Table 6-2. Induction coil sensors have also been used for biomagnetic measurements. The magnetic fields of the human heart and brain have been discovered with their aid. The necessary

I

2

. 105 5.6 . 10' 3 .1 0 ~

5 . IOS/AWG36

I

Mumetal

annealed Permalloy

material

150

x 3.5 $

180 x 2.5

length x diameter

Cnre

Metronix 878

-

ferrite

ferrite frame (2 components)

2372/AWG 14

too00

laminated Mumental

45 OOO/AWG 3 1

90 x 2.2 $

36 x 36 x 3.8/1.8

60 x 1.6 $

120 x2.3 $

183 x 2.5 $

I

0.7 mV/(nT.Hz)

Coil sensitivity

I 8.6 pV/(nT.Hz)

23 pV/(nT. Hz)

2.6 mV/(nT. Hz)

transformer output; f, = 1.3 kHz

current amplification

;lf

1

[491

[481

mation source

I I Hz.. .20 kHz

0.2 Hz.. . = l0kHz

0.0006.. .10 Hz

0.001.. . 2 Hz

0.001.. .I0 Hz

feedback

1 quant. step

Remarks

t

0.001...10Hz

Frequency range

A great number of similar applications of induction coil sensors are reported in the more recent literature, but normally the technical details of sensors are missing.

1

Metronix 879

1 1

2~

S

v

U

1

laminated Mumetal

1 ~ ~ laminated ~ 2 2 Moly-permalloy

fi --t

3

3

L'Aquila, Italy

-

3

ponents

I Number of1

Siple, Antarctica

Manufacturer/Type

AudioUniversity of Magnetotellurics California

Magnetotellurics

I

Or

1 Observation

Induction coil sensors with high permeability cores used for micropulsation, magnetotelluric, and audio-magnetotelluric measurements.

Micropulsations

Application

Table 6-1.

I

2

GALILEO Jupiter Atmospheric Probe (Lightning and Radio Emission Detector)

ULYSSES (Radio and Plasma Wave Experiment)

275

3o0x5@

2000/140 pm

1500/60 pm

5 $

...100 kHz

10.. SO0 Hz

D,I

1...50 kHz

10 Hz.. .3.5 kHz

70 Hz.. .2.8 kHz

10kHz.. .2MHz

260 x I I

266

laminated high-p material

~~

20 Hz.. .60 kHz

0,I.. ,400 kHz

1 Hz.. . I kHz

260x l l @

frame 800 x 1250

400

0.18 pV/(nT- Hz)

threshold 5 pT

13 pV/(nT-Hz)

Hz

. .So0

394 x 4.8 $

~~

6 pV/(nT. Hz)

3.5 pV/(nT. Hz)

5 Hz.. .2.2 kHz

Coil sensitivity

...10 kHz

S

Frequency range

410

350(320) x 6

length x diameter [mml

50OOO/70 pm

ferrite

ferrite

Sakigake/MST 5 (Plasma Wave Probe)

GALILEO Jupiter Orbiter (Plasma Wave Investigation)

ferrite

(Plasma Wave Instrument) 105

laminated Mumetal

Core

AMITE

I /aluminiumtube

(Plasma Wave Instrument)

nickle-iron

8OOOO/AWG47 laminated high-p material air-core

Mumetal

bundle of 0.2 $ Mumetal wires

material

loo00

60000/50 pm

Coil (turns/wire)

5oOO/AWG40

I

I

3

Number of measuring :omponents

Dynamic Explorer A

~

ISEE 3 (as above)

ISEE 1 (2) (Plasma Wave Investigation)

HELIOS A and B (AC Magnetometer)

Spacecraft (Experiment)

Table 6-2. Examples of induction coil sensors on spacecraft.

flux feedback

flux feedback

matching transformer

Remarks

Information source

250

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

utilizable sensitivity is still higher than in geophysical applications, but the measuring ranges are less extended in amplitude and frequency and range approximately from 10 - I 4 to 10 T and from 0.1 to 500 Hz, respectively. Here, the superconducting SQUIDS are successful competitors (see Chapter 10). For measurements at such low levels in amplitude, a trade-off between spatial resolution (limited by sensor size) and sensitivity can become a problem and the application of very expensive magnetic shielding is often necessary. Some important applications demonstrate the utility of low-frequency magnetic fields for information transmission, where the applied transmitting loops and receiving antennas are built similar to induction coils. Many railway traffic safety systems depend on the simple and reliable functioning of these devices. Some of them indicate only the passing of a train, others additionally enable a speed measurement and offer a bidirectional communication between train and stations. Moreover, a traffic guidance system for motor-cars on freeways is under investigation, using similar transmission devices. Further examples are the pick-up coils in hearing aids, which directly receive the audio-frequency field generated by loops in the floors of conferencerooms, concert halls, classrooms, churches, etc. The signal-to-noise ratio during operation replaces the amplitude measuring range in these applications. Induction coil sensors are often called magnetic antennas, since they receive the magnetic component of electromagnetic waves. There is no difference in principle as long as they are designed for use at low frequencies. In the increasingly important field of “Electromagnetic Compatibility” the magnetic antennas used for measuring the “radiated” emissions of electronic modules or equipment are actually induction coil sensors picking-up induced magnetic fields. Jaw-type probes, eg, induction coils on slotted ferrite ring cores, d o the same when measuring the “conducted” emissions o n the associated cables. True applications of magnetic antennas include: the long solenoidal induction coils on a high permeability core proposed for reception on submerged submarines, and the low-frequency loop or ferrite antennas for direction finders in navigation systems of for field-intensity meters. The induction coils used as magnetic field sensors or magnetic antennas in the various and very diversified applications described above, have been specially designed for suitable measuring ranges and, if necessary, according to the results of optimization theories. Here the design and realization of the sensors was independent of certain basic technological developments, if one disregards the manufacturing of improved soft magnetic high permeability materials and low noise integrated amplifiers. In relation to induction coil sensors, therefore, a general trend of future development parallel to technological progress on certain areas cannot be seen clearly. But, without doubt, occasionally sensors with a further increased sensitivity and an improved signal-to-noise ratio will be required. A noise reduction by only one order of magnitude without extending volume and weight already seems to be unattainable, but could possibly, at least partly, be realized using 1. further improved soft magnetic materials with a high material permeability, even under premagnetization and in a wide temperature range, 2. materials having a small Barkhausen noise, which so far has often been considered as negligibly small and unneccessary to be investigated, 3. high permeability cores of special geometrical shapes, eg, allowing miniaturized coils with a small thermal noise, and 4. electronic amplifiers having a low input noise voltage as well as a low noise current and, at the same time, a small input capacitance. Recently developed amplifiers have an input noise voltage density of less than 1 nV/I/Hz (if bipolar transistors are used) and a noise cur-

-’

6.6 References

251

rent density of less than 1 f A / m (in case of field effect transistors at the input). A matching of the sensor coils to these extreme values normally causes difficulties. 5 . The use o f correlation techniques in order to extract a signal from the embedding noise is customary. The application of two identical smaller sensors instead of a single bulky one, and a cross-correlation of their output signals, has been proposed for magnetic field measurements on spacecraft [44]. In connection with that, the question can be posed and more generally be investigated, what improvement in both signal-to-noise ratio and bandwidth could be gained, if one bulky sensor would be replaced by an array of smaller sensors with the same total weight. The multiple sensors, of course, must be decoupled from each other and, would thus require much more space.

6.6 References (11 Ness, N. F., “Magnetometers for Space Research”, Space Sci. Rev. 11 (1970) 459-554. 121 Sonett, C. P., “The distant geomagnetic field; 2: modulation of a spinning coil emf by magnetic signals”, J Geophys. Res. 68 (1963) 1229-1232. [3] Brown, F. W., Sweer, J. H., “The flux ball: A test coil for point measurements of inhomogeneous magnetic fields”, Rev. Sci. Instr. 16 (1945) 276-279. [4] Lindsay, J. E., “Wide-band E/H field sensing probes: A discussion of probe interactions and coupling problems. A model for the analysis of the loop antenna”, Report E-19 of the PhysikalischTechnische Bundesanstalt, Braunschweig, Fed. Rep. Germany, 1981. [5] Blackett, P. M. S., “A negative experiment relating to magnetism and the earth’s rotation”, Phil. Trans. Royal Society of London. Series A-Mathem. and Phys. Sciences (App. 3) 245 (1952) 309-370. [6] Campbell, W. H., “Induction loop antennas for geomagnetic field variation measurements”, ESSA Techn. Rep. ERL 123-ESL 6, Envinronmental Science Service Administration Earth Sciences Labs., Boulder, COL., USA, 1969. [7] Macintyre, S. A., “A portable low noise low frequency three-axes search coil magnetometer”, IEEE Trans. on Magnetics MAG-16 (1980) 761-763. [8] Terman, F. E., Radio Engineers’ Handbook, New York: Mc Graw-Hill, 1943, p. 52ff. [9] Welsby, V. G., The Theory and Design of Inductance Coils, London: MacDonald, 1960, p. 42ff. [lo] Terman, F. E., Radio Engineers’ Handbook, New York: Mc Graw-Hill, 1943, p. 77. [Ill Welsby, V. G., The Theory and Design of Inductance Coils, London: MacDonald, 1960, p. 148. [12] Hak, J., Eisenlose Drosselspulen, Leipzig: K. F. Koehler, 1937, p.145. (131 Terman, F. E., Radio Engineers’ Handbook, New York: Mc Graw-Hill, 1943, p. 101. [14] Selzer, E., “Determination experimentale du champ d’un cylindre d’alliage permeable, suppose place dans un champ magnktique uniforme, parall6lement a son axe de revolution”, Ann. Geophys. 12 (1956) 144-146. [15] Ueda, H., Watanabe, T., “Linearity of ferromagnetic core solenoids used as magnetic sensors”, J Geomagn. Geoelectr. 32 (1980) 285-295. [la] Russell, R. D., Watanabe, T., “A Proposal for a Bridge Method for the Calibration of Geomagnetic Sensors”, J. Geomag. Geoelectr. 32 (1980) 155-170. [I71 Zambresky, L. F., et al., “A New Method to Calibrate Induction Magnetometers”, J Geomag. Geoelectr. 32 (1980) 47-56. [18] Hayashi, K., et al., “Absolute Sensitivity of a High-p Metal Core Solenoid as a Magnetic Sensor”, J Geomag. Geoelectr. 30 (1978) 619-630.

252

6 Magnetic Field Sensors: Induction Coil (Search Coil) Sensors

[19] Warmuth, K., “Uber den ballistischen Entmagnetisierungsfaktor zylindrischer Stabe”,. Arch. $ Elektrotechnik 41 (1954) 242-257. [20] Bozorth, R. M., Chapin, D. M., “Demagnetization Factors of Rods”, J. Appl. Phys. 13 (1942) 320-326. [21] Wiese, H., et al., “Geomagnetische Instrumente und M e h e t h o d e n ” , in: Geomagnetismus und Aeronomie, Vol. 2, Fanselau, G. (ed.); Berlin: VEB Deutscher Verlag d. Wissenschaften, 1960, p. 358. [22] Whitham, K., “Measurement of the Geomagnetic Elements”, in: Methods and Techniques in Geophysics, Vol. 1, Runcorn, S. K. (ed.); London: Interscience Publishers, 1966, p. 134. [23] Richter, W., “Induktionsmagnetometer fur biomagnetische Felder”, Experimentelle Technik d. Phpik 27 (1979) 235-243. [24] Hill, L. K., Bostick, F. X., Micropulsation sensors with laminated mumetal cores, Report No. 126, Electr, Engineering Res. Lab., The University of Texas, Austin, TX, USA, 1962. [25] Meinke, H., Gundlach, F, W., Taschenbuch der Hochfreguenztechnik Heidelberg: Springer-Verlag, 1968, pp. 17-32. [26] Cerulli-Irelli, P., Progretto e ottimizzazione di un magnetometro ad induzione, Rep. LPS 71-2, Lab. di Ricerca e Technologica per lo Studio del Plasma nello Spazio, CNDR Roma, Italy, 1971. [27] Lukoschus, D. G., “Optimization theory for induction-coil magnetometers at higher frequencies”, IEEE Trans. Geoscience Electronics GE-17 (1979) 56-63. [28] Onishi, N., Kato, Y.,“Characteristics of the Induction Magnetometer with a High Permeability Cylindrical Metal Core”, in: Proc. Fac. Engineering Tokai University, Tokai, Japan, 1976, No. 1, pp. 171-176. [29] Saito, T., et al., “Development of new time-derivative magnetometers to be installed on spacecraft”, Bull. Inst. Space Aeronaut. Science Llniv. Tokyo, B 16 (1980) 1419-1430. [30] Ueda, H., Watanabe, T., “Comments on the Anti-Resonance Method to Measure the Circuit Constant of a Coil Used as a Sensor of an Induction Magnetometer”, Sci. Rep. Tohoku University, Series 5, Geophysics, 22 (1975) 129-135. [31] Porstendorfer, G., “Magnetotellurische Untersuchungen unter Verwendung hochpermeabler Spulen”, Freiberger Forschungshefte C174 (1965) 91 - 108. [32] Thellier, E., “EnquCte sur les appareils enregistreurs des variations rapides du champ magnktique terrestre” Ann. Intern. Geophys. Year 4 (1957/58) 255-280. [33] Wiese, H., et al., “Geomagnetische Instrumente und M e h e t h o d e n ” , in: Geomagnetismus und Aeronomie, Vol. 2, Fanselau, G. (ed.); Berlin: VEB Deutscher Verlag d. Wissenschaften, 1960, p. 352ff. [341 Whitham, K., “Measurement of the Geomagnetic Elements”, in: Methods and Techniques in Geophysics, Vol. 1, Runcorn, S. K. (ed.); London: Interscience Publishers, 1966, p. 130. [35] Lokken, J. E., “Instrumentation for receiving electromagnetic noise below 3000 cp/s”, in: Natural Electromagnetic Phenomena below 30 kch, Bleil, D. F. (ed.); New York: Plenum Press, 1964, p. 404ff. [36] Schmidt, H., Auster, V., “Neuere M e h e t h o d e n der Geomagnetik”, in: Handbuch der Physik, Vol. 4913, Flugge (ed.); Heidelberg: Springer, 1971, p. 342ff. [37] Clerc, G., Gilbert, D., “La contre-reaction de flux appliquee aux bobines a noyau magnktique utilisee pour l’enregistrement des varations rapides du champ magnetique“, Ann. Gdophys. 20 (1964) 499-502. [381 Micheel, H. J., “Induktionsspulen mit induktiver Gegenkopplung als hochauflosende Magnetfeldsonden”, ntz archiv 9 (1987) 97-102. [39] Gordon, D. I., “Methods for Measuring the Magnetic Field”, IEEE Trans. Magnetics MAG4 (1972) 48-51. [401 Trenkler, G., “Verfahren zur elektrischen Messung magnetischer Felder (Teil 1)”, messen + prufen (1972) 535-538, 797.

6.6 References

253

[41] Germain, C., “Bibliographical Review of the Methods of Measuring Magnetic Fields”, Nuclear Znstr. and Methods 21 (1963) 17-46. [42] Wiese, H., et al., “Geomagnetische Instrumente und Mehethoden”, in: Geomagnetismus und Aeronomie Vol. 2, G. Fanselau (ed.); Berlin: VEB Deutscher Verlag der Wissenschaften, 1960, pp. 308-361. [43] Whitham, K., “Measurement of the Geomagnetic Elements”, in: Methods and Techniques in Geophysics, S. K. Runcorn (ed.); London: Interscience Publishers Inc., 1960, pp. 127-135. [44] Anav, A., et a]., “A Correlation Method for Measurement of Variable Magnetic Fields”, ZEEE Trans. Geoscience Electronics GE-14 (1976) 106- 114. [45] Taylor, W. W. L. et al., “Initial Results from the Search Coil Magnetometer at Siple, Antarctica”, J. Geophys. Res. 80 (1975) 4762-4769. [46] Cantarano, S., et al., “A Facility for Measuring Geomagnetic Micropulsation at CAquila, Italy”, ZI Nuovo Cimento 6C (1983) 40-48. [47] Benderitter, Y., le Donche, L., “Contribution a L’Etude des Capteurs Magnttique a Induction pour la prospection Magneto-Tellurique”, Rev. Physique Appliqut!e 5 (1970) 183- 185. [48] Vozoff, K., “The Magnetotelluric Method in the Exploration of Sedimentary Basins” Geophysics 37 (1972) 98-141. [49] Catalog of Geophysical Instruments and Services, 1987, Metronix and Geometra, Braunschweig, FRG. [50] Labson, V. F., “Geophysical Exploration with Audio-Frequency Natural Magnetic Fields” Geophysics 50 (1985) 656-664. [51] Dehmel, G., et al., “Das Induktionsspulen-Magnetometer-Experiment(E4)”, Raumfahrtforschung l9 (1975) 241-44. [52] Gurnett, D. A., et al., “The ISEE-1 and ISEE-2 Plasma Wave Investigation”, ZEEE Trans. Geoscience Electronics GE-16(1978) 225-230. [53] Scarf, F. L., et al., “The ISEE-C Plasma Wave Investigation”, ZEEE Trans. Geoscience Electronics GE16 (1978) 191-195. [54] Shawhan, S. D., et al., “The Plasma Wave and Quasi-Static Electric Field Instrument (PWI) for Dynamics Explorer-A”, Space Science Instrumentation 5 (1981) 535-550. [55] HBusler, B., et al., “The Plasma Wave Instrument on Board the AMPTE IRM Satellite”, ZEEE Trans. Geoscience and Remote Sensing GE-23 (1985) 267-273. [56] Hirao, K., “The SuiseiBakigake (Planet-A/MS-T5) Missions”, ESA SP-1066 (1986). [57] Yeates, C. M., et al., GALZLEO: Exploration of Jupiters System NASA SP-479, 1985, NASA, Washington, DC, USA. [58] Stone, R. G., et al., The ZSPM Unnifed Radio and Plasma Wave Experiment, ESA SP-1050, 1983, ESA.

7

Inductive and Eddy Current Sensors WALTER DECKER.PETER KOSTKA. VDO Adolf Schindling AG Schwalbach. FRG

Contents 7.1 7.2 7.2.1

. . . . . . . . . . . . . . . . . . . . . . . . . . Sensors Excited by Permanent Magnets . . . . . . . . . . . . . . .

Introduction

257 257

7.2.1.1 7.2.1.2 7.2.1.3 7.2.2 7.2.2.1 7.2.2.2 7.2.3 7.2.3.1 7.2.3.2 7.2.3.3

Variable Reluctance Sensors with Fixed Permanent Magnets (Magnetic Pickups) . . . . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . Variable Reluctance Sensors with Moving Permanent Magnets . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Tachometer Generators with Permanent Magnets . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . .

257 257 260 261 264 264 266 266 266 267 268

7.3 7.3.1 7.3.1.1 7.3.1.2 7.3.1.3 7.3.2 7.3.2.1 7.3.2.2 7.3.2.3 7.3.3 7.3.3.1 7.3.3.2 7.3.3.3

AC-Excited Sensors for Linear Movement . . . . . . . . . . . . . . Linear Variable Differential Transformers . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . Variable Inductance Sensors/Variable Leakage Path (VLP) Sensors . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . Variable Gap Sensors/Differential Cross-Anchor Sensors . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . .

269 269 269 275 277 278 278 280 282 283 283 287 287

7.4 7.4.1 7.4.1.1 7.4.1.2 7.4.2 7.4.2.1

AC-Excited Sensors for Rotary Movements . . . . Synchros . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . Applications and Properties . . . . . . . . . . . Resolvers . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . .

287 287 287 288 293 293

. . . . . . . . . .

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

256

7 Inductive and Eddy Current Sensors

7.4.2.2 7.4.3 7.4.3.1 7.4.3.2 7.4.3.3

Applications and Properties . . . . . . . . . . . . . . . . . . Inductosyns . . . . . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . .

7.5 7.5.1 7.5.1.1 7.5.1.2 7.5.2 7.5.2.1 7.5.2.2 7.6 7.6.1 7.6.2 7.6.3 7.7 7.8 7.9 7.10

.. .. . . . . . . . Eddy Current Sensors . . . . . . . . . . . . . . . . . . . . . . Eddy Current Tachometer . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Proximity Sensors . . . . . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Inductive Flowmeters . . . . . . . . . . . . . . . . . . . . . . . Physical Principle and Construction . . . . . . . . . . . . . . . . Applications and Properties . . . . . . . . . . . . . . . . . . . . Signal Conditioning . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . Noise of Inductive Sensors . . . . . . . . . . . . . . . . . . . . . Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

. .

294 295 295 296 297 297 299 299 300 300 300 304 304 304 306 306 307 308 309 31 1

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

7.2 Sensors Excited by Permanent Magnets

257

7.1 Introduction This chapter describes different types of sensors based on Faraday’s law of induction : inductive sensors, which use the effect of voltage induction, and eddy current sensors, based on the induction of currents due to alternating magnetic fields. These sensors have become very important in industrial measurement for measuring, among other things, displacement, proximity and rotation, force, accelerations, weight and pressure, and torque. Hence there are different principles available and the designer of the sensors can choose the optimum type to meet special demands and to achieve the best performance. This chapter can give only brief descriptions for some main principles since the range of sensor principles and applications is very extensive. The effects used to generate a voltage within the sensors are a varying magnetic flux within a magnetic circuit due to variations of an air gap or changes of the direction of the magnetic polarization, variation of the coupling between coils, or changes of inductance of coils due to the displacement of a soft magnetic core within the coils or relative motions of coils. Eddy current effects are utilized by the displacement of electrically conducting material within the oscillating magnetic field of a multipole permanent magnet or a coil.

7.2 Sensors Excited by Permanent Magnets 7.2.1 Variable Reluctance Sensors with Fixed Permanent Magnets (Magnetic Pickups) 7.2.1.1 Physical Principle a n d Construction

Variable reluctance sensors with permanent magnetic excitation are sensors that do not need any external energy or supply. They are based on the principle of electromagnetic induction, as follows. A permanent magnet produces a magnetic flux within a magnetic circuit of various shape. Owing to changes of the length of an air gap within the circuit, the reluctance of the circuit and hence the magnetic flux will change. This change in flux induces a voltage U in a pickup coil according to Faraday’s law : U(t) = - N *d@/dt

(7-1)

where

N @J

t

= number of coil windings = magnetic flux through the = time.

coil

The output voltage thus depends on the change in flux with respect to time, ie, the quicker the flux changes, the larger is the voltage.

258

7 Inductive and Eddy Current Sensors

The construction of variable reluctance sensors depends on the application. In its simplest form, it consists of a permanent magnet in coil. Here we shall describe a typical, commonly used form. The sensor consists of a cylindrical or rectangular permanent magnet with axial magnetization, attached with an iron pole, which is surrounded by a pickup coil (Figure 7-1).

Figure 7-1. Construction of an inductive sensor (courtesy VDO Adolf Schindling AG). 1) contact socket, 2) terminal package, 3) permanent magnet, 4) cap, 5 ) soft magnetic core, 6) coil, 7) plate, 8)Wade connector.

The pole is positioned in front of a rotating impulse gear, a ferrous milled steel disk or an approaching iron component. The impulse gear or steel disk is carried by the shaft whose speed is to be measured or the moving iron component joined to the body whose displacement is to be measured. Hence the air gap between the gear or iron component and the pole changes when they are approaching or receding from the sensor. In several cases a ferromagnetic yoke is used to close the magnetic circuit in order to increase the flux concentration within the circuit which will result in a higher output voltage [l, 21 (see Figure 7-2). The changes in magnetic flux for a sensor as shown in Figure 1-2 can be seen in Figure 7-3 which shows two computed shapes of the magnetic field for two positions of the gear wheel: with a tooth placed opposite the sensor core at minimum air gap (continuous lines) and the tooth displaced to it with maximum air gap (dashed lines). The shape of the sensor is determined by many parameters. The dimension of the impulse gear and the sensor core diameter must be well tuned. In general, the core has to be slightly smaller than or at most as wide as the teeth width and the distance between the teeth must be larger than the core diameter. Other parameters are the maximum available space for the

7.2 Sensors Excited by Permanent Magnets

259

yoke

Figure 7-2. Sensor with yoke.

impulse gear

coil

magnet

Figure 7-3. Changes in the magnetic flux with varying air gap. Continuous lines: minimum air gap; dashed lines: maximum air gap.

sensor, the maximum coil resistance, and the minimum output voltage at a given minimum speed of the parts to be measured. Hence, for different applications we have many different variations and dimensions of the sensors. Some different forms of sensors are shown in Figures 7-4 (C-shaped sensor) and 7-5 (radially magnetized permanent magnet). Instead of the permanent magnet, some systems use a DC excited coil [3]. The choice of materials for and the shape of such sensors will mainly depend on the constructor’s experience in magnetism, since the mathematical treatment of the magnetic circuit is inaccurate in most cases. As many parameters are unknown or can be predicted only with difficulty, such as the operating points of both the magnet and the yoke on the hysteresis loop, the influence of small air gaps following mechanical mounting and the magnetic and mechanical tolerances of the impulse gear, calculations of the circuit with the reluctance model, for example, will lead to only rough approximations.

260

7 Inductive and Eddy Current Sensors

cores

gear

magnet

coils

Figure 7-4. C-shaped sensor.

coil

magnet yoke

gear

/

core

I

I

Figure 7-5. Sensor with radially magnetized permanent magnet.

In order to achieve improved magnetic pickups, the use of numerical field calculations with finite-element or finite-difference methods with the aid of a computer is necessary [4]. An example for such a computation is given in Figure 7-3, where the exact course of the magnetic flux of a sensor is shown.

7.2.1.2 Applications and Properties The main application of these sensors is the detection of rotary motion and proximity. Most applications involve the measurement of the rotary speed of shafts or wheels. Owing to some advantages which will be described below, they are used, for example, in a large number of automotive control systems to measure

- the rotational speed of position of crankshafts, gearings, etc., and - the rotational speed of car’s wheels to generate a speed signal or for break control (ABS)

P, 31. Another application of this type of sensor is the measurement of proximity or velocities. In this case, the inductive sensor is often used as a switch to recognize the approaching of a ferromagnetic part which will change the flux within the coil like the tooth of a wheel. Since the output voltage of the sensor depends on the varying magnetic flux, only movements above a certain minimum speed can be detected. An example of a variable magnetic reluctance speed

7.2 Sensors Excited by Permanent Magnets

261

sensor which measures cam-shaft rotational frequency was given by Armstrong and Wilkinson [ 5 ] . Furthermore, this type of sensor is used for material testing based on a leakage flux principle [6]. In general, inductive sensors using permanent magnets have major advantages over other types of sensors. They are very robust and have a nearly infinite lifetime because they do not contain mechanically movable parts. Since they can be constructed with fully hermetically sealed housings, they may be used within aggressive media and under rough conditions. The limits of operation depend on the properties of the materials used, such as the plastic sealing material, or the corrosion resistance of metallic capsules and electrical connections. They can be used within an environment of 100% humidity. They are almost insensitive to shock, where levels of up to 30000 g have been reached. The pressure resistance is good and may reach values of 140 x lo6 N/mZ. For these sensors no external supply will be necessary. They can be used over a large temperature range, which will be limited by the mechanical properties of the materials used, the temperature dependence, and the Curie point of the magnets. Typical operating temperatures of these sensors are from -50°C up to more than 200°C. If special materials are used, they also can be used at cryogenic temperatures. Values of output voltage vary from 0.2 up to 80 V. A high resolution (depending on the size of the teeth or parts to be measured) can be obtained. For example, the rotating shaft speed can be measured with an accuracy of less than 0.1% and magnetic transduction of gears can be determined with an accuracy of hundredths of a mechanical degree. The frequency range varies from 1 Hz up to the MHz range. It is limited by eddy current effects, which reduce the effective magnetic cross section and increase the impedance of the pickup coil. Further, the iron core acts like a shortened secondary winding of a transformer. As a result of these effects the output voltage of the sensor is not linear at high frequencies, as expected from Equation (7-1). Some disadvantages of this type of sensors should be mentioned. The dimensions of the sensor must be adjusted to the size of the parts to be measured, eg, the teeth of the gear. Hence, a specifically dimensioned sensor can only be used for a small range of applications. Different applications require different constructions. Slow rotations and small displacements are difficult to measure, since the induced voltage becomes smaller the more slowly the flux changes. To avoid this influence, Forkel [7] proposed a modified sensor with a measuring range from 1 Hz up to 10 kHz with constant output amplitude. However, it requires an external supply and is based on the principle of a flux-gate magnetometer. Another problem is the control of the air gap under production conditions. Small changes to the gap may result in large changes in the amplitude of the output signal [8]. In order to change the reluctance of the magnetic circuit a force is necessary. Although it is very small, it cannot be neglected in some applications, eg, in sensors which measure streaming fluids or gases with an impeller.

7.2.1.3 Signal Conditioning The output signal of DC-excited sensors with permanent magnets consists of one or more voltage peaks, induced within the coil. If there is only one soft magnetic object (eg, a single

262

7 Inductive and Eddy Current Sensors

tooth of an impulse gear) approaching the sensor we have an analog output signal as shown in Figure 7-6. The amplitude of the signal depends on the speed of the approach. U

-U position Figure 7-6. Output voltage U of a DC-excited sensor with permanent magnets, when a single iron object passes by.

If the speed of the gear wheel is to be measured, the signal will be an alternating voltage and depends on the type of wheel used. For example, spur gears generate sinusoidal signals, whereas star wheels will give some sharper pulses, owing to the distribution of the iron in the wheels. With a given sensor and actuator shape, the output signal generally depends on two factors:

- The speed of the approach or removal of the gear wheel or iron part will influence the amplitude of the signal. An example of the output voltage versus speed is given in Figure 7-7 for a typical sensor used in automotive applications. Hence there is a lower limit for the speed to be measured, which is given by the lowest signal-to-noise ratio which can be decoded. - Further, the signal amplitude is to first order inversely proportional to the air gap between sensor core and moving iron objects. This relationship is shown in Figure 7-8 for different speeds. These two parameters mainly have to be taken into account for signal conditioning. Using a gear wheel there are two possible means of evaluation: measurement of the output amplitude or measurement of the frequency which is always proportional to the rotary speed.

Output voltage measurement This sort of evaluation is acceptable only f w simple rotary speed control systems because there are influences that can disturb an exact result. First there is the length of the air gap

7.2 Sensors Excited by Permanent Magnets

38

->

I

-

25

-

20

-

a,

263

a=0.5rnrn

m

4-

P

4-

1s:

P

4-

0

10

-

5

-

/

I

i

0

508

1000

1500

frequency [Hzl

Figure 7-7. Output voltage U versus frequency f. a : distance between impulse gear and sensor.

air gap [mm I

Figure 7-8. Output voltage U versus length of the air gap for different rotary speeds.

which is important. If the air gap is small, the sensor’s output voltage can vary owing to mechanical tolerances of the system such as eccentricities of gear wheels and shafts. If greater distances are realized, this influence becomes less important owing to the smaller slope of the voltage versus air gap characteristic (see Figure 7-8).

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7 Inductive and Eddy Current Sensors

The temperature coefficients of the magnets have to be taken into account when the sensors are used at different temperatures, since they are related directly to the output voltage. Using hard ferrite magnets, for example, the temperature coefficient of the remanence (and with it the magnetic flux) is of the order of -0.2%/K.

Frequency measurement If more exact measurements are required, the frequency of the sensor signal is considered. In most cases, the output voltage is transformed by a Schmitt trigger into rectangular pulses (see Figure 7-9). Hence the signals can be evaluated in digital form.

~

-

To measure small signals, the design of both, the sensor and the electronic unit are important. The noise level of the sensor and the trigger level of the electronics define the minimum speed that can be measured. When the input impedance of the circuit and the ohmic resistance of the sensor match well, optimum power transfer can be realized which is insensitive to disturbances.

7.2.2 Variable Reluctance Sensors with Moving Permanent Magnets 7.2.2.1 Physical Principle and Construction This kind of inductive sensors consists of an iron (in most applications) C-shaped core which is surrounded by a pickup coil. The magnetic flux through the sensor is produced by a rotating or linearly moving multi-pole magnet positioned in front of the sensor. A rotating ring magnet is used to detect rotary movements and a linearly moving magnet is used to

Figure 7-10. Construction of a variable reluctance sensor with moving permanent magnet. 1) magnetic field, 2) magnet, 3) coil, 4) C-shaped soft magnetic core, 5 ) signal terminals.

7.2 Sensors Excited by Permanent Magnets

265

Figure 74. Variable reluctance sensor (courtesy VDO Adolf Schindling AG).

measure displacements. The distance between the ends of the core, which means the length of the sensor, is determined by the distance of the magnetic poles. The construction of such a sensor is shown in Figure 7-10, and Figure 7-11 gives a view of a complete sensor. Owing to the alternating polarity of the magnet, the magnetic flux through the core changes its direction and an AC output voltage is induced according to Equation (7-1). The amplitude and frequency of the induced voltage depend on the speed with which the magnetic poles pass the sensor. The sinusoidal output signal is given in Figure 7-12 for various speeds of motion.

Figure 7-12,Output voltage U of the sensor for different speeds u ( v , < u2),

266

7 Inductive and Eddy Current Sensors

7.2.2.2 Applications and Properties As described above, this type of sensor is used to measure rotary speed or linear displacement. The sensor shown in Figure 7-11, for example, is used in automotive applications as speed pickup to detect the rotary speed of a speedometer magnet. The sensor is attached to the speedometer in such a manner that the magnetic field of the speedometer magnet will give a maximum induction within the sensor coil. As can be seen in Figure 7-12, the output voltage of the sensor is small for low rotary speeds, so the magnet should have a larger number of poles which ensures that a sufficiently high output voltage is reached at the lowest rotary speed. Typical values for automotive applications are, for example, 8 or 12 poles at a minimum rotary speed of about 350 rpm. The induced voltage will then be greater than 300 mV [9].

7.2.3 Tachometer Generators with Permanent Magnets 7.2.3.1 Physical Principle and Construction Tachometer generators are electrical devices based on the AC dynamo principle. They are able to transform rotary motions into electrical signals, such as voltage or an frequency signals, proportional to the rotary speed. There are two types of tachometer in use: DC and AC generators. Both are based on the same physical principle: a multi-pole permanent magnet is mounted tightly on a shaft, the speed of which is to be measured. This rotor is moving inside several stator coil windings as in a synchronous machine (Figure 7-13).

permanent

b L,,

L,,

L,i

stator windings

Figure 7-0. Principle of a construction of tachogenerator.

According to Faraday's law, a voltage will be induced within the coils, which depends on the number of coil windings N , the exciting magnetic flux GE and the rotational speed n [lo]:

7.2 Sensors Excited by Permanent Magnets

267

The frequency f of the voltage induced is proportional to the rotational speed n and the number of magnetic poles p :

f

-n.p.

(7-3)

The signals described above are typical of an AC tachometer. To obtain a DC output, the voltage induced within the stator windings is rectified with a commutator and brushes. This construction is more complicated and has several disadvantages, such as wearing out of brushes and the commutator and influences of dirt, air pressure, and humidity. Also, a DC amplifier is needed for signal conditioning. Owing to these problems, DC tachometers today are used only in applications where it is necessary to prevent errors due to phase shifting. To obtain a DC output signal, today some external electronic units are available, which offer the cheaper and less sensitive means of rectifying the AC tachometer signal [ll].

7.2.3.2 Applications and Properties A typical application of tachometer generators is to count numbers of revolutions. They are built in different forms, depending on the application, and offer some good properties [12-141. With DC tachometers typical speeds of 750-2000 rpm can be measured. The linearity within this range can be limited to less than 1% depending on the respective load resistance (see Section 7.2.3.3). The amplitude of the voltage lies between a few volts and hundreds of volts [lo]. Commercially available DC tachometers have a peak-to-peak ripple of less than 1% [15]. Using AC tachogenerators, the frequency of the output signal can be used for the determination of rotational speed, Typical ranges of speed are 150-3000 rpm. With special devices measurements up to 50000 rpm are possible. Hence the output frequency depends on the number of poles of the permanent magnet. The number of poles has to be adjusted to the rotary speed : small speeds require a large number of poles, high speeds need smaller numbers of poles. Advantages of these sensors are:

- they are very robust; - they do not need external supply advantage; and - they offer a high output voltage. Some of the disadvantages are:

- the linearity depends on the effective load resistance (see Figure 7-14); - the temperature dependence of the stator windings (copper) is of the order of 0.4%/K; - a high armature reaction; and - harmonic oscillations of more than 10% of the output signal.

268

7 Inductive and Eddy Current Sensors

7.2.3.3 Signal Conditioning Tachogenerators can only measure speeds at a certain minimum level. TYpically they are used for the measurement of speeds in the range of a few hundred revolutions per minute. At such speeds, the output voltage has an amplitude of several volts which allows the direct measurement of the signal without the use of additional electronics.

Figure 7-14. Output voltage U versus rotary speed n for different load resistances R.

The linearity of the output signal depends on the specific load resistance. Figure 7-14 shows different output signals with respect to different load resistances. As can be seen, linearity for higher rotary speeds can only be obtained with a good adaptation of the tachometer to the load resistance. The linearity within the typical measuring range can be limited to less than 1% [lo]. Since the output voltage and the changing angular velocity are proportional, tachogenerators offer additional applications for arithmetic operations such as integration or differentiation. A description of such networks was given by LazAroiu and Slaiher [16]. Weschta [17] described an additional electrical circuit for the determination of the angular position of the rotor.

7.3 AC-Excited Sensors for Linear Movement

269

7.3 AC-Excited Sensors for Linear Movement 7.3.1

Linear Variable Differential Transformers

7.3.1.1 Physical Principle and Construction The linear variable differential transformer (LVDT) is based on the principle of a differential transformer with variable coupling between primary and secondary coils. It was pioneered in the 1940s by Schaevitz [18]. Since that time, many different sensor forms and applications have been developed and various new functional ranges have been found. The form of this type of sensor depends largely on the application. Therefore, the following descriptions can only give a general overview of the principles of these sensors and of some of their applications. The LVIYT consists basically of one primary and two secondary coils located on either side of the primary coil. The three windings are situated on a cylindrical bobbin, in which a movable soft magnetic core is located (Figure 7-15). The armature is mounted on a non-

secondary winding 1

I

I

primary winding

secondary winding 2

I

I \ I \

bobbin

core

Figure 7-15. Principle of construction of an LVDT.

magnetic plunger, which is sometimes spring loaded, and placed against the device to be measured. Figure 7-16 shows an example of such a device with very small dimensions. The secondary windings are connected in series circuit (differential coils), so the resulting output signal corresponds to the differential voltage of the two coils. Figure 7-17 shows the electrical circuit of this sensor. The primary coil is excited by an alternating current. The magnetic coupling between the primary and secondary windings and the magnetic flux then will be determined by the position of the core in relation to the coils. The core is displaced by the parts to be measured via the nonmagnetic rod.

270

7 Inductive and Eddy Current Sensors

Figure 7-16. Photograph of a small size LVDT (courtesy Althen Mess- und Datentechnik GmbH). output voltage 0

secondary winding 1

secondary winding 2

core

I

primary winding Figure 7-17. Electrical circuit of an LVDT.

From Faraday’s law, the voltage U induced in one secondary coil can be calculated from

U

=

- N * d@/dt = - M dI/dt ,

where N = number of coil windings @ = magnetic flux M = mutual inductance between the primary and secondary coil I = primary current.

(7-4)

7.3 AC-Excited Sensors for Linear Movement

271

The following holds for differential transformer :

M , and M2 are functions of the position x of the soft magnetic core. Hence M = M2 - M I = M ( x )

or

U 7 M ( x ) .TtI/dt U

M(x) = dI/dt *

(7-7) (7-8)

The amplitude of the secondary voltage is thus proportional to the position of the core and the phase displacement of the primary and secondary signal indicates the position of the core relative to the zero position. As already stated, the output voltage of the sensor corresponds to the differential voltage of the two coils. With the core in the zero position in the center of the two secondary coils, the secondary voltages have the same amplitude and are 180" out of phase. Therefore, the difference will be zero. If the core is now displaced, the magnetic flux within the secondaries changes as shown in Figure 7-18. The voltage induced in one secondary coil will increase, whereas the voltage induced in the other will decrease. The resulting signal gives the dependence of the sensor output voltage on the core position according to Equation (7-7). The output signal of a sensor with a normal uniform winding is shown in Figure 7-15 is linear only for small displacements of the core near the zero position. If the core approaches one end of the coil system, the output voltage decreases owing to the reduction in the magnetic field in this direction. Hence larger displacements produce a nonlinear output voltage as shown in Figure 7-19. In its basic form, the LVDT can be used in many applications for the measurement of short strokes. To measure larger displacements, the relationship between the measured displacement with a linear output signal and the length of the sensor will become disadvantageous. To obtain better relationships between stroke and sensor length, some modified forms of coil windings were used, which were first described by Lipshutz [19]. However, this type of coil winding has the disadvantage that their production is difficult. Some commonly used examples of modified coils are summarized below.

Balanced linear-tapered secondaries Figure 7-20 shows the principle of the construction of a sensor with balanced linear-tapered secondary windings. It can be seen that the arrangement of the coils differs considerably from the basic construction shown in Figure 7-15. The primary winding uniformly covers the whole length of the sensor, whereas the secondaries are wound on the primary tapered from both ends to the middle. This form of sensor coil requires perfect symmetry of the two secondaries to obtain a good balance. Nevertheless, the magnetic field will decrease at the ends of the coils and the stroke will not reach the full length of the sensor.

212

7 Inductive and Eddy Current Sensors

a)

Figure 7-18. Computed magnetic field of the LVDT. a) core in zero position, b) core displaced.

7.3 AC-Excited Sensors for Linear Movement

273

U

Figure 749. Output voltage U versus core displacement 1.

secondary winding 1

- V

bobbin

primary winding

* a : limits of a linear range. secondary winding 2

I

core

Figure 7-20. Balanced linear-tapered secondary windings.

Overwound linear-tapered secondaries A second type of sensor has overwound linear-tapered secondary coils as shown in Figure 7-21. In this case the secondaries are wound tapered over the whole length of the sensor, which will give a good relationship between sensor length and stroke, but it may be show an unbalanced behaviour.

Balanced overwound linear-tapered secondaries Using the balanced overwound linear-tapered form of windings shown in Figure 7-22, the above-described imbalance can be avoided. For this modification the primary winding is split into an inner and outer coil with tapered secondary windings in-between.

214

7 Inductive and Eddy Current Sensors

secondary winding 1

primary winding

bobbin

secondary winding 2

core

Figure 7-21. Overwound linear-tapered secondary windings.

secondary winding 1

primary winding

secondary winding 2

1 1 1 1 1 1 1 1 1

bobbin

core

Figure 7-22. Balanced overwound linear-tapered secondary windings.

Balanced profiled secondaries A sensor with balanced profiled secondary coils (Figure 7-23) is a variation of the first type described above, in which the section profile of the secondaries is adjusted so as to maintain a greater linear range of measurement.

Complementary tapered windings This is another variant with which the linear range can be extended. Here the bobbin is divided into a number of chambers which carry a defined number of windings of the three coils. A schematic view of such a sensor construction is given in Figure 7-24. Another proposal for increasing the linearity range was given by Wouterse [20]. He suggested using a highly permeable metallic tube surrounding the sensor as a magnetic keeper. This construction leads to a transversal-shaped magnetic field within the sensor instead of the more axial form shown in Figure 7-18.

7.3 AC-Excited Sensors for Linear Movement secondary winding 1

bobbin

275

secondary winding 2

primary winding

core

Figure 7-23. Balanced profiled secondary windings. core I

prlmary wlndlng secondary wlndlng 1 secondary wlndlng 2

Figure 7-24. Complementary tapered windings.

A general statement as to which shape of sensor windings is the best cannot be made; the choice depends on the specifications required and the application. Some of the important features for the sensor construction are sensor size, linearity, absolute reproducibility, resolution, hysteresis, temperature dependence, output voltage required, and stroke to be measured.

7.3.1.2

Applications and Properties

Although the sensor principle of the LVDT has been known since the beginning of this century, for decades these sensors were only rarely used. However, within the last 20 years, many new application in automation, process control and measurements have been developed. LVDTs are well known as optimum position and displacement sensors in thousands of applications in research and industry as a result of their excellent characteristics and properties which will now be described.

216

7 Inductive and Eddy Current Sensors

LVDTs have a nearly infinite mechanical life because owing to the absence of contact and friction between core and coil systems there will be no mechanical or electrical wear. In practice, carefully constructed LVDTs can reach an MTBF (Meantime Between Failure) of several million operating hours. The frictionless operation, combined with the induction principle on which the sensor's operation is based, gives a truly infinite resolution. Only the external electronic unit used limits the resolution, not the sensor itself. The minimum measuring range of today's LVDT displacement sensors is from a few micrometers up to a maximum of 1 m, depending on the construction of the sensor. The linearity in general extends from k 0.025% up to k 0.5% of the nominal displacement. It depends mainly on the previously described shape of the secondary windings (Section 7.3.1.1). The designer of an LVDT should check carefully the linearity required to prevent additional costs due the complicated structures of the coil windings. Another accurate feature of this sensor is the null repeatability. In practice, deviations of the order of less than 0.05% are observed. Since the zero position of the sensor is extremely stable and repeatable, the LVDT can be used as a precision zero-position transducer itself as a part of closed-loop control system or servo system [21]. The temperature dependence of LVDTs is determined by several factors which depend on the mechanical behaviour of the materials used such as creep, rupture or softening. A second limitation is given by electrical properties of the materials such as dielectric strength, changes in conductivity of the conductors, reluctance and resistivity of insulating materials and permeability, and reluctance and Curie temperature of the magnetic materials used. Another influence is given by the use of LVDTs within an environment of rapidly changing temperatures. In this case the inertial thermal reaction of the sensor has to be taken into consideration. According to the construction and the materials used, temperature ranges from -50" up to 600°C can be obtained [22, 231. The temperature coefficients of typical LVDTs are given to O.Ol%/K. The sensors show very little response to transverse motions of the core, and the cross-axis rejection is negligible. This property allows measurements in situations where the core is not moving in a perfectly straight line. Since the movable core and the electric parts of the transformer are perfectly separated from each other, the sensor can be hermetically sealed, so that it can be used in aggressive media and under rugged conditions. The resistance to rough environments depends on the materials used as mentioned above. According to this, some extreme properties of the sensors may be achieved, so they can be used

- in corrosive liquids or vapors ; - at cryogenic temperatures (liquid oxygen, nitrogen or helium down to 4 K) ; - in flammable vapors and particles with temperatures up to 600°C; - in nuclear radiation areas with high radiation levels ;

- at high pressure levels of up to 2 . lo7 N/m2; and - at water pressure of 75 m water column.

Some disadvantages of LVDT-type sensors are : - they need an external supply and electronic units for signal generation and processing;

- electrical and magnetical protection against external fields is necessary ; and - when operating at high temperatures, the sensors need some temperature stabilization.

7.3 AC-Excited Sensors f o r Linear Movement

277

LVDTs can be used for the direct measurement of position and displacement, but in many applications these sensors are used as secondary transducers. In this case the quantity to be measured is transformed into a linear movement of the sensor core. There are many different constructions and methods of transforming the quantities to be measured into core motions which cannot be described in this chapter. Therefore, here we shall give an overview of some commonly used applications of such devices. LVDTs are used as secondary transducers - for the measurement of force, weight and pressure (load-cells and weight cells) [24];

- as level meters; - as plummet flow meters [25] ; - as strain-gage heads ; and

- as gage heads [21] and in other measuring applications. The differential transformer principle is also used for the measurement of angles of rotation. In this case it is called a rotary variable differential transformer (RVDT). The stator windings of RVDTs consist of one primary and two secondary coils wound on a bobbin as in the case of LVDTs. The core, in this case acting as a rotor, has a cardiodic or other special shape which can change the coupling between the stator coils [21, 261. RVDTs can detect angular motions within the range of 180°, and linear operation is possible within the range of f40" with an accuracy of less than 0.5%. With an angle of displacement of about f5", the accuracy will reach a level of less than 0.15%FSR (Full Scale Reading). The flexibility of the LVDT construction and the advantages of this type of sensor have made them virtually indispensable in various modern industries such as the aircraft and spacecraft, nuclear power and automotive industries, mechanical engineering, mining, and materials testing.

7.3.1.3 Signal Conditioning Two main principles are used for signal conditioning of the LVDT ; that is either a carrier amplifier/synchronous demodulator system or a passive demodulator/DC amplifier system. Irrespective of the system used, the sensor needs AC excitation, which is realized by a carrier generator. This generator consists mainly of two or three parts, the oscillator, followed by a power amplifier, and an optional feedback amplitude control. The carrier oscillator produces a sinusoidal signal with a small distortion factor. Sometimes a rectangular signal is used, but it produces an unreliable zero voltage so that the sensor cannot be used as a null-position transducer. An overview of carrier amplifiers is given in [27]. The carrier frequencies used vary from less than 50 Hz up to 1 MHz, but the optimum performance is reached within the range 0.5-10 kHz. When measuring dynamic processes, the following rule of thumb can be applied : the frequency to be measured should not be greater than 10% of the carrier frequency. The supply voltage of LVDTs typically are within the range 1 - 10 V (rms), depending on the size of the sensor and its internal resistance. In special applications voltages up to 50 V (rms) are used.

278

7 Inductive and Eddy Current Sensors

The oscillator feeds a power amplifier which provides a buffered output voltage at low impedance. The gain of the amplifier is adjusted for the LVDT. To obtain a stable primary exciting voltage the carrier signal is fed back to the oscillator via an amplitude control circuit. The secondary voltage of the LVDT can be evaluated in several ways. Using a carrier amplifier/synchronous demodulator system (Figure 7-25), the output signal is amplified by a carrier amplifier and then rectified by a synchronous demodulator with full-wave rectification, which very often is followed by a low-pass filter.

power supply

carrler - gen.

auto,

- amp,

- LVDT - carrler - demodulator

amp.

control

3

phase

Figure 7-25. Block diagram of a carrier amplifier system.

The demodulator is triggered synchronously to the primary supply via a phase shifter from the carrier oscillator. This circuit now produces a signal with an amplitude proportional to the sensor core position. The passive demodulator/DC amplifier system uses a passive demodulator, such as a diode discriminator, followed by a low-pass filter and a DC amplifier (Figure 7-26). Together with a DC-to-AC converter within the primary circuit, the LVDT can be used as a complete DC sensor. power supply

passlve

- carrler - LVDT - demod- gen, ulator

DC amp.

3

Figure 7-26. Block diagram of a DC amplifier system.

This type of DC sensor became important in recent decades with the development of semiconductor and integrated circuit technology which allow the integration of the electronics in the sensor housing. Today integrated interface circuits are available, that include the whole DC electronics described above [28, 291. Owing to the miniaturization of the electronics, it is possible to integrate the electrical circuits within the sensors [30].

7.3.2 Variable Inductance Sensors/Variable Leakage Path (VLP) Sensors 7.3.2.1 Principle and Construction This type of sensor is based on the change in the inductance of one or two coils, produced by a diplacement of a core within the coils. In its simplest form the sensor consists of a coil, wound on a cylindrical hollow bobbin, inside which a soft magnetic core is positioned. The

279

7.3 AC-Excited Sensors f o r Linear Movement

core is connected via a nonmagnetic shaft to the object that is to be measured. When the core is displaced, the inductance of the coil changes, which can be signal processed in an electrical bridge circuit. Hence this construction with one sensor coil has the disadvantage of having a nonlinear characteristic; the VLP sensor type with two coils, which will be discussed in detail, has some more benefits. Two coils of the same shape are wound on a cylindrical hollow bobbin, inside which a cylindrical armature is located as described above. Figure 7-27 shows the principle of construction of this sensor. sensor coils

core

Figure 7-27. Principle of construction of the VLP sensor.

In several constructions, a soft magnetic yoke is used that surrounds the coils axially and gives a more closed magnetic circuit. This increases the linearity range of the sensor. The coils of the sensor are connected as a bridge or half-bridge circuit together with variable complex resistances and the amplifier used (see Section 7.3.2.3). Like the sensor based on the transformer principle (LVDT, RVDT), the variable inductance sensors need an external AC supply, which drives the bridge circuit as shown in Figure 7-28. I I

Figure 7-28. Principle of a bridge circuit.

i

I

OR

The inductance of a cylindrical coil is given by (see, eg, [31]) (7-9) where vacuum permeability relative permeability of the core material N = number of turns A = cross-section area of the magnetic flux I = average length of the magnetic flux path.

p,, = pr =

280

7 Inductive and Eddy Current Sensors

With the core in the zero position, both coils have the same inductance: L = L, bridge voltage UAis then zero, since

UA = UB * (iw L,/(iwL,

+ iwL,)

- t/2)

=

L,

. The

(7-11)

and with L , = L,, UA = 0, where o = excitation frequency and U , = excitation voltage. An axial movement of the armature will now increase the inductance of one coil and decrease the other one. This detunes the bridge circuit and a voltage UAcan be seen: UA = UB * (L

U, = UB * ((L

+ AL/((L + AL) + (L - AL))

+ AL)/2L

- 112)

UA = 1 / 2 . UB AL/L

- 1/2)

(7-12) (7-13) (7-14)

where AL = change in inductance. Let us assume that the amount of inductance, dL,with the displacement of the core dl, that is, dL/dl, is known, then the following holds for small changes in 1: AL = dL/dl* A1

(7-15)

Inserting this term into Equation (7-14), we obtain UA/UB = 1/(2L) dL/dl' AI.

(7-16)

This result shows the dependence of the ratio of the bridge voltage to the input voltage, UA/UB,on the core displacement, Al. The change in the coil inductance as a function of the core position is generally difficult to calculate because of the unknown leakage flux distribution. Moreover, it depends on the material used for the core and the overall size and the geometry of the sensor. The relative permeability, p r , of the core material influences the inductance directly and should be chosen to give a good performance of the sensor. The size of the sensor is normally given by the fitting dimensions of the environment, and the geometry depends on the travel and linearity requirements of the sensor.

7.3.2.2 Applications and Properties The range of applications and properties of variable inductance sensors is nearly the same as for variable differential transformers (LVDTs, see Section 7.2.1.2), so only some of the main properties of this type sensor will be discussed here briefly. The sensors offer a simple construction and, owing to the absence of friction between core and coils, a nearly infinite mechanical life. Depending to the materials used for the construction of the sensors, they can operate under severe conditions and within aggressive media.

7.3 AC-Excited Sensors for Linear Movement

281

The linear displacements that can be measured with variable inductance sensors vary between ca. lo-’ and 1 m, depending on the sensor geometry. The linearity range (measuring range) can cover up to 80% of the sensor length with an error in linearity of less than 3% [32]. Smaller displacements will produce smaller errors. The resolution is truly infinite and is limited only by the noise voltage and the electronics. When used for dynamic displacement measurements, the sensors can be applied within a frequency range from 0 Hz up to several kHz, depending on the excitation frequency. They are limited by the inertia of the armature. The maximum frequency to be measured should be smaller than 20-25% of the carrier frequency. Variable inductance sensors such as LVDTs, are able to work with temperatures near absolute zero and up to approximately 150°C. Some special constructions permit their operation at ambient temperatures of up to 600°C [33]. Higher temperatures may be reached with the sensor construction described by Grinrod [23], involving a DC-supplied coil instead of the soft magnetic core. The sensors are insensitive to high nuclear radiation levels and can withstand accelerations up to 1000 g. Some of the disadvantages of variable inductance sensors are: they need external AC supply and electronics for signal generation and processing; there is a temperature-dependent zero drift of sensitivity with temperature coefficients of the order of 0.05-0.2%/K ; the compensation of temperature effects is possible only within certain limits; a shielding against outer electrical and magnetic fields is necessary. The applications of this type of sensor are numerous. In addition to their operation as position or displacement transducers the sensors are used as gage heads, eg, in mechanical Tension Compression

U

G =Housing Z = Tension link W = Displacement transducer type W 1 K = Core U = Overload stop ET = Sensitivity trimmer

Figure 7-29. Principle of a construction of a force transducer (courtesy Hottinger Baldwin Messtechnik GmbH).

282

7 Inductive and Eddy Current Sensors

engineering and for material testing [6]. Another range of applications involves the measurement of the forces such as load, weight, and pressure [34]. An example of a load cell or force transducer is given in Figure 7-29. It can be seen that the force to be measured is transmitted via the tension link Z which is fixed by a diaphragm spring to the core K. The deflection of the springs has to be strictly proportional to the effective force in order to obtain a linear dependence between force and sensor output signal. For the measurement of pressure, the pressure deflects a diaphragm which is coupled with the core by a tension link and produces a linear motion. Today's pressure sensors typically operate with pressures up to 2 x lo7 N/m2 [35]. Vibrations and accelerations can be measured if the core is connected to a seismic mass which is spring actuated (Figure 7-30). The frequency range of such sensors depends on the mass-spring system used and the damping [361. Further applications include the measurement of fluid levels. For this purpose, a float is fixed to the armature of the sensor. Using a circular construction of the coils and the core, the measurement of angles can be reduced to a displacement measurement with this sensor. With such devices the determination of angles within a range of 300" is possible.

setsntc nass sprmg.

houslno colt 1 core

Figure 7-30. Vibration/acceleration sensor.

7.3.2.3 Signal Conditioning As described in Section 7.3.2.1, the variable inductance transducers operate as a part of a bridge circuit. The AC supply and the signal conditioning are typically realized by a carrier amplifier system, consisting of a carrier generator, a resistor half-bridge, an AC amplifier, and a demodulator (Figure 7-31). The carrier oscillator (generator) G produces a highly stable AC voltage U, which supplies the precision resistor/inductor network. The carrier frequencies used are in the range 50 Hz-500 kHz; a typical value is 5 kHz. With the help of the zero balance N, the bridge voltage U, is balanced to zero if the sensor core is in the zero position. If the bridge is now detuned by displacing the core, a voltage U, will appear. The ratio U,/U, at the input of the amplifier represents the standard output of the variable inductance sensor. This signal is now amplified by the amplifier A and then demodulated by the synchronous demodulator D to produce a DC output signal.

7.3 AC-Excited Sensors for Linear Movement

--

I I -

7

I

I

I

283

I

I

I

I

I

D I

I A

I

t

.-.I I . I

I

J

P = Power supply unit, G = Generator, N = Zero balanCe,UB = Transducer output signal,

U&

= Transducer measuring signal, A = Amplifier, D =

Demodulator

Figure 7-31. Schematic electrical diagram of a force transducer connected with an amplifier (courtesy Hottinger Baldwin Messtechnik GmbH).

7.3.3 Variable G a p Sensors/Differential Cross-Anchor Sensors 7.3.3.1 Principle and Construction The physical principle of variable gap sensors is based on the variation of an air gap within a magnetic circuit. These sensors may be realized by winding a coil on a C-shaped ferromagnetic core. If a ferrous part approaches the ends of the C-shaped core, the ratio between air gap and length of the core is reduced (Figure 7-32). The inductance L is given by (7-17) where vacuum permeability number of coil windings cross section of the core length of the magnetic path iron permeability lL = length of the air gap pL = 1 = permeability of the air gap. po = N = A = IF, = pFe=

The maximum inductance is given at l, = 0 for (7-18)

284

7 Inductive and Eddy Current Sensors coil

1

armature

I

core

Figure 7-32. Construction of a variable gap sensor.

There is a hyperbolic dependence of the normalized inductance L/L,,,

to the ratio

LL ' luFe , see Figure 7-33. * PL

LFe

1

0 Figure 7-33. Characteristic of a variable gap sensor.

The sensitivity is constant only for small displacements of the armature. To achieve a better performance with respect to linearity and temperature dependence, the sensors are constructed as differential variable gap transducers. Two variable gap sensors are connected in series within a bridge circuit, as shown in Figure 7-34. The ferromagnetic armature is positioned in the air gap between the two sensor elements and can move in the direction of the magnetic flux lines. Here the inductance of one coil increases, whereas the inductance of the other when - - .decreases, -

7.3 AC-Excited Sensors for Linear Movement

285

c-,

Figure 7-34. Construction of a differential cross-anchor sensor.

the armature is moved. A short analysis of this circuit was given, for example, by Rohrbach [lo]. If the air gap of the sensor is varied, the ratio U,/U, changes accordingly. If the air gap is changed only slightly, the ratio is nearly proportional to dl. The materials used for the construction of the coil systems and the armature are described in Section 7.7. Some consideration should be given to the core material. A high sensitivity depends on a high relative permeability of the core material. Therefore soft magnetic materials as described in Section 7.7 are used. In cores of solid material eddy currents may become an important factor and may reduce the sensitivity and linearity of the sensor. To reduce eddy currents, the core has to be built of laminated material.

Figure 7-35. Output voltage LI versus core position x.

* a : limits of the linear range.

286

7 Inductive and Eddy Current Sensors

8 I

U

6

a Figure 7-36. Applications of differential cross-anchor sensors.

I

f

7.4 AC-Excited Sensors for Rotary Movements

287

7.3.3.2 Applications and Properties Variable gap sensors show some advantages in the measurement of small displacements. They are highly sensitive and have a high resolution of less than 1 nm [37]. The maximum nonlinearity typically is given as 0.5% [38]. They are used for non-contact applications and offer reaction-free operation. The construction for these sensors can be very robust and they can be used within the same environments as variable inductance sensors (Section 7.3.2.2). Nevertheless, these sensors show larger errors in accuracy than sensors with plungers. Some disadvantages for example, are a small range of linearity (see Figure 7-35), the temperature dependence of the sensitivity, and zero drift which causes difficulties with static measurements. Further the measuring forces cannot be neglected. Variable gap sensors are therefore mainly used in applications where it is not possible to use sensors with plungers. These sensors are typically used as strain gages [lo] and to measure torque [39], pressure, force, load, weight, vibrations, and accelerations [27, 401. Some of these applications and principles are shown schematically in Figure 7-36.

7.3.3.3 Signal Conditioning Variable gap sensors are used as parts of an electrical bridge circuit like variable inductance sensors. Hence for the electrical circuit and operation the conditions are the same as for the latter sensors (see Section 7.3.2.3).

7.4 AC-Excited Sensors for Rotary Movements

7.4.1 Synchros 7.4.1.1 Physical Principle and Construction Synchros are AC-excited electromechanical devices that are used to measure rotary motions from a distant point. They are based on the physical principle that the magnetic coupling between coils changes. In its basic construction, a synchro consists of a stator, which contains three windings displaced by 120". Inside the stator an armature with armature windings rotates. This rotor is supplied with an AC voltage with the help of collector rings. Figure 7-37 shows the principle of construction of the synchro. The sensor transforms the rotational angle a = f ( t ) which is to be measured into phase angles of AC voltages p = f ( t ) . At a given position of a rotor, voltages Uxo,Uyo,and Uzo are induced within the stator windings. They are either in-phase or out-of-phase with the

288

7 Inductive and Eddy Current Sensors

0

S t s2, s 3 stator windings

Figure 7-37. Principle of construction of a synchro.

excitation voltage U , , depending on the rotor position. These voltages change with the angle of rotation a according to

U,,

=

K

U , cos a

(7-19)

-

U,, = K . U , cos (a - 120")

(7-20)

U,. cos ( a - 240")

(7-21)

U,, = K

where K is a constant, depending on the synchro construction (eg, ratio of rotorhtator windings). The voltage U , in general is of the form U , = U,, sin ot. For typical applications, the stator windings are joined in star connection. This gives the following output voltages:

-

u,, = u,, -

~ ' .7sin(a -

Uyo = U , K

v

1200)

(7-22)

sin(a - 240")

(7-23)

=

U,, - U,,

=

U, . K

.

U, =

uz0- U,,

=

U, K

. ~7. sin a

U,,

(7-24)

The shape of these voltages is shown in Figure 7-38. They are similar to the voltages of the three-phase network, that is, they are out-of-phase by 120". A detailed analysis of this type of sensor is given in [16].

7.4.1.2 Applications and Properties The measurement of the above voltages by these sensors is used to determine the angular position of the rotor only, but can be used to determine the errors of the synchro. In typical applications, two synchros are connected to transmit the rotor position, one acting as a transmitter and the other as a receiver.

7.4 AC-Excited Sensors for Rotary Movements

289

Figure 7-38. Output voltage of a synchro.

Tho types of synchro circuits, which will be described here, are in use: torque-type synchros and control-type synchros. a. Torque-type synchros These sensors represent a simple device for driving pointers and dials directly without any amplification. The rotors of torque synchros are both connected to the excitation voltage U,, and their similar stator windings are connected as shown in Figure 7-39. transmitter

receiver

stator 1

stator 2

rotor 1

Figure 7-39. Principle of construction of a torque-type synchro.

rotor 2

290

7 Inductive and Eddy Current Sensors

If both rotors are displaced to the same extent, ie, atransmitter

a, = a,

- areceiver

,

then the terminal voltages of transmitter and receiver are the same and no compensation currents flow. If the transmitter rotor is turned around, ie, a,

>

a,,

compensating currents occur. Depending on the rotor position, they produce a torque on the rotor of the receiver synchro, which tries to adjust this receiver to the same angular position as the exciting one. The torque vanishes only if the position of the receiver rotor equals that of the transmitter. With such torque-type synchros, the angular position of the transmitter rotor can be transmitted directly to the receiver rotor and produce a suitable indication of the rotor position. The active torque is approximately sinusoidal of the form (see Figure 7-40) M

- K . sin(a, - a,) .

(7-25)

Hence we have a maximum torque if the angle between the rotors is nearly 90". If the position of the two rotors is similar (a, = q),we have a nearly linear dependence. Some typical properties of such devices are now given. The transmitted torque is typically of the order of 5 10 - 4 - 1 10 - 2 Nm/ 4 Detection errors of torque-type synchros are bet-

M

angular diff.

Figure 7-40. Torque versus angular difference.

7.4 AC-Excited Sensors for Rotary Movements

291

*

ween k0.5' and 1.50. The maximum rotational speed is typically given as 300 rpm. The diameter of synchros is given as 20-90 mm for a length of 40-150 mm [lo]. b. Control-type synchros If the required torques are high o r the transmission errors have to be kept small, controltype synchros are used. The principle of such devices is shown in Figure 7-41. transmitter stator 1

rotor 1

receiver .stator 2

rotor 2

0

0

Figure 7-41. Principle of

The construction of control-type synchros is similar to that one of the torque-type transmitter, with the rotor connected to the excitation voltage U , . The rotor is mechanically turned to the angle that is to be measured. The receiver synchro uses a drum-wound rotor, which should not produce torques, but should induce a voltage depending o n the angle difference of the rotors: U,

- U,

cos(a, - a , ) .

(7-26)

This voltage is supplied to an amplifier which drives, for example, an induction o r a Ferraris motor. The motor turns the receiver rotor until the rotor voltage U,= 0. Then

a,

=

a,

+ 90"

holds for both rotor positions. The control-type synchro now gives a direct representation of the two rotor positions. Figure 7-42 shows the output voltage versus angular difference. In some applications a gear is inserted between the motor and receiver rotor to reduce the setting error of the rotor. The accuracy reached with these synchros is of the order of k 5' to k 15'. Another typical application of synchros is in surveyors' chains. To measure sums or differences of angles, three or more synchros are connected in series. An example of such a device, which is the so-called differential synchro, is shown in Figure 7-43.

292

7 Inductive and Eddy Current Sensors

Figure 7-42. Output voltage versus angular difference.

transmitter

“1

differential

receiver

I

Figure 7-43. Principle of construction of a differential synchro.

A torque-type synchro is used as a transmitter synchro. Its stator is connected to the stator of a synchro differential and produces a field within the stator that has the same direction as the transmitter rotor field. The rotor of the differential synchro is built like a three-phase rotor which results in additional rotation of the rotor within the receiver synchro: a, = a,

+ ad

Some examples of synchro combinations are given in [24]. In practice, synchros show some errors, which are of mechanical, electromagnetical or external origin. Mechanical errors are produced, for example, by friction of brushes and bearings, an imbalance of the rotors, nonuniform air gaps, and the presence of rotor teeth. Electromagnetic errors mainly occur because of the magnetic anisotropy of the electrical sheets,

7.4 AC-Excited Sensors for Rotary Movements

293

different resistances of the windings, or turn-to-turn short circuits. Some of the external influences are changes in the voltage, frequency of the drive voltage, and temperature effects. The above reasons for errors in synchros lead to a decrease in the accuracy of transmission of the angle. Therefore, for high-performance synchro systems there are demands placed upon the construction and the materials used.

7.4.2 Resolvers 7.4.2.1 Physical Principle and Construction Resolvers are a variant of synchros (rotating transformer). These induction-type devices transform a device's angular rotor position into a signal, that varies with the sine and cosine of the rotor position. A typical resolver consists of a rotor which has two windings displaced by 90" from each other. The stator is built with a single winding or two windings displaced by 90" from each other. The resolver offers the possibility of driving the rotor or the stator coils. Here we shall describe the principle of a resolver with only one winding.

Resolver with one stator winding The stator winding is excited by a voltage:

U,

=

U,, . sin ot

.

(7-27)

Within the rotor windings there are then two voltages of the form

U,, and

=

U, . K

. sin a

(7-28)

- . cos a

(7-29)

U,, = U , K

where K = constant, depending on the resolver construction, and a = actual angle of the rotor position (Figure 7-44). This construction gives directly the vector coordinates U,, and U,, of the rotor angle a. stator

rotor

Figure 7-44. Principle of construction of a resolver with one stator winding.

Resolver with two stator windings Using two stator coils, both the rotor and stator can be used as the primary, depending on the application. We shall describe the case of driving the rotor. The supply of the rotor wind-

294

7 Inductive and Eddy Current Sensors

ings can be realized by a commutator and brushes. Another principle is to use an internal rotating transformer within the resolver, as shown in Figure 7-45. As shown in Figure 7-46, the rotor is excited by two sinusoidal voltages, U,, and U,,. The following output voltages occur at the stator windings :

-

U,,

=

K . U , , sin a

+K.

U,,* cos a

(7-30)

U,,

=

K . U , , sin a

+K.

U , , . cos a .

(7-31)

rotor windings

rotating transformer

housing

rotor supply voltages

/ stator windings

I

++

stator output voltages

Figure 7-45. Schematic principle of a brushless resolver. rotor

stator

7

4 1

uzl

Figure 7-46. Principle of construction of a resolver with two stator windings.

7.4.2.2 Applications and Properties The output voltages of a resolver depend on sine and cosine terms of the angle a of the rotor position. This gives a basis for some special applications of resolvers. They are used, for example, for analog arithmetic operations with trigonometric functions. A second application

7.4 AC-Excited Sensors for Rotary Movements

295

is the determination of the vector coordinates of angles, in general the coordinates of the angle of the rotor. Further, they can be used for coordinate transformations such as conversion from rectangular to polar coordinates [24]. Resolvers are combined with resolver-to-digital (RID) converters, which transform the output signal relationships into digital form. These converters can be produced in hybrid technology with a resolution of typically 12 or 14 bits; with special devices up to 23 bits may be reached [41, 421. They offer accurate measurement and signal processing. Some values obtained with these sensors are:

- an accuracy of less than 1% ; - a resolution of a few angular minutes; and

- frequency ranges from 100 Hz up to 10 kHz. Resolvers are very robust and reliable and can be used in many applications. A typical application is the measurement of angles and rotations within closed-loop servo systems of machine tools and robots.

7.4.3 Inductosyns 7.4.3.1 Physical Principle and Construction Based on the principle of inductive coupling between two windings, inductosyns are a sort of multi-pole resolver (see Section 7.4.2). Depending on the construction, they can be built for measurement of rotation or linear movements. An inductosyn consists of two magnetically coupled parts, which are realized by two planar windings on an insulating material. The first winding, called scale, is fixed to a solid body, such as machine-tool bed, and operates as a stator. The scale of an inductosyn for rotary movements consists of a circular fret-type winding (Figure 7-47 a). Typically the winding is designed as a printed circuit track, bonded to a disk. The other part, the slider, operates as the rotor of the transducer. It is positioned opposite to the scale and turns around with the device, the rotation of which is to be measured. It consists of two identically printed separate windings of fret-type waveform, exactly like that of the scale (Figure 7-47b). One track of the

a) scale Figure 7-47. Schematic diagram of a rotary inductosyn.

b) slider

296

7 Inductive and Eddy Current Sensors

slider is shifted one quarter of a cycle against the other track. The scale and slider are separated by a small air gap. For the discussion of the operating principle, we shall consider the linear inductosyn, which can be derived from the rotating one by reeling off the stator and rotor winding circles. Figure 7-48 shows a schematic drawing of such linear windings.

scale

slider

Figure 7-48. Schematic diagram of a linear inductosyn.

T+T/4

If the scale now is excited by a sinusoidal AC voltage U , , this voltage induces a secondary voltage in each of the two slider windings. The voltages obtained depend on the position of the slider windings relative to the scale. If two tracks are positioned opposite to each other, the induced voltage will reach a maximum value; it becomes zero if the displacement x is one quarter of the track periode p and reaches its minimum when the tracks are displaced by half of the cycle. Hence the output voltage of the slider windings depends on sine and cosine terms of the slider position: U , , = U , . sin (2 u 2 2 =

u,

*

cos (2

71

*

7t

*

x/p)

(7-32)

x/p) .

(7-33)

With this, the position of the slider can be determined for each position within the track cycle. The slider signals arise from an average of several spatial cycles; small errors in the track spacing have little effect and the inductosyn offers a high resolution.

7.4.3.2 Applications and Properties Inductosyns show some advantages in the direct measurement of angular and linear movements. They offer a high resolution and sensitivity, contactless sensing and no wear. Operation in industry with dusty and dirty environments and within vacuum or non-conducting fluids is possible [43]. The temperature stability is good if the materials used for scale and slider have the same temperature coefficient. Some typical values for inductosyns are given in Table 7-1.

7.5 Eddy Current Sensors

297

Table 7-1. Properties of inductosyns. Accuracy

Rotary inductosyn

Linear inductosyn

Absolute error Reproducibility Sensitivity

f 5" < 1" < 0.25"

<2.50 pm

<0.25 pm <0.05 prn

The above-mentioned limits depend on the diameter or the specific length of the transducer [16]. The larger the size, the more track cycles can be placed on the carrier. Inductosyn errors

mainly occur from irregular and eccentric movements of the scale and the slider, and when the air gap is dirty, which may influence the magnetic coupling. There are many applications of inductosyns in mechanical engineering and control technology. They are used for the accurate measurement of rotary and linear movements in machine tools and robots, for position control in direct servo-control systems, and for digital control systems and displays.

7.4.3.3 Signal Conditioning Inductosyns are excited by a sinusoidal voltage with a frequency within the range 1-20 kHz; a typical drive frequency is 2 kHz. The output signal of inductosyns are two sinusoidal voltages in the 100 mV range, which can be processed directly. As for resolvers, there are nowadays inductosyn-to-digital converters which take over the generation and control of the drive voltage and the signal processing of the output voltages.

7.5

Eddy Current Sensors

In this section sensors are described which operate on the principle of induction of eddy currents within an electrical conducting medium due to magnetic fields, which vary with time, and the interaction of the fields generated by these eddy currents with the exciting fields. The description of the eddy current phenomenon can be derived from Maxwell's equations. An analysis of the distribution of a time-harmonic magnetic field in a homogeneous conducting half-space is given here. For the calculation the following assumptions are made: 1. the electrical conductivity o is constant ; 2. the permeability p is constant ; and 3. displacement currents are neglected. To describe eddy current phenomena, the required Maxwell's equations are : curl E = -dB/dt

(7-34)

curl H = J

(7-35)

298

7 Inductive and Eddy Current Sensors

where E = electric field B = magnetic flux density H = magnetic field J = current density. The divergence condition on the magnetic flux B is (7-36)

div B = 0 and the constitutive relations

B = p(H) * H

(7-37)

J=a(E)*E

(7-38)

where p (H) = permeability tensor and a ( E ) = electrical conductivity tensor. Introducing the vector potential A we have

B = curl A .

(7-39)

Substitution of Equation (7-39) into Equation (7-34) and integration gives the electric field in terms of the vector potential:

E = -dA/dt.

(7-40)

For the current density we obtain

J = a(-dA/dt)

(7-41)

Substituting H a n d J in Equation (7-35) with help of Equation (7-37), (7-39), and (7-41), we have with scalar curl curl A l p = - adA/dt

.

(7-42)

Assuming a sinusoidal variation of A, Equation (7-42) becomes (1/p) (curl curl A) = - i a o A

.

(7-43)

With the tranformation curl curl A = grad div A - AA and div A = 0 due to Equation (7-36), Equation (7-43) can be written as (l/p) (AA) = i o a A where A = Laplace operator and i =

(7-44)

m.

7.5 Eddy Current Sensors

299

The vector potential A and hence the flux density B can be taken orthogonally to the conductor surface if the eddy currents are assumed to spread plane-parallel to the conductor surface. Equation (7-43) is the two-dimensional diffusion equation which gives a representation of the current density distribution in the conductor. With suitable boundary conditions, Equation (7-43) is also valid for conducting plates. A closed-form solution for this equation can be given only for a few geometric configurations. The equation can be solved by using different variational methods and numerical calculations. A detailed analysis is given, for example, in [44-481. From a given eddy current distribution within the conductor, the reaction field due to this eddy current can be obtained by Ampere’s law. Depending on their operating principle, eddy current sensors can be divided into two types : directly operating eddy current systems, which will be explained by using the principle of the eddy current tachometer, and proximity sensors explained by electronically evaluated eddy current losses.

7.5.1 Eddy Current Tachometer 7.5.1.1 Principle and Construction

The eddy current tachometer is a well known device for the direct transformation of rotary movements into a pointer deflection. In principle, the system consists of a multi-pole permanent magnet fixed to a shaft whose speed is to be measured. It rotates in a soft iron yoke functioning as a case. An eddy current cup carried by a spindle is suspended between the magnet and the case, so that the magnetic flux passes radially through the conducting material of the cup. The speedometer pointer is fixed on top of the spindle (Figure 7-49).

1

2 10

3

9

4

8

5

7

6

Figure 7-49. Construction of a speedometer (courtesy VDO Adolf Schindling AG). 1) spindle, 2) bearing, 3) holding spring, 4) iron yoke, 5 ) eddy current cup, 6 ) shaft of the magnet, 7) support of the magnet, 8) temperature compensation, 9) permanent magnet, 10) torsion spring.

300

7 Inductive and Eddy Current Sensors

The rotating magnet produces an alternating flux density B within the conducting cup. According to Equation (7-40), eddy currents J are induced within the cylindrical shell of the cup. The eddy currents generate a secondary magnetic field with intensity H.Both magnetic fields react on each other, so a torque acts on the eddy current cup, which tends to follow the rotation of the magnet. The magnitude of the torque depends on the rotary speed of the magnet and is proportional to it. The spindle of the eddy current cup is fixed by a torsion spring, so it will rotate to a position in which the magnetic torque is balanced by the torque of the torsion spring. A detailed analysis of eddy current speedometers is very complex as many parameters are difficult to determine, such as air gaps and the magnetic properties of the materials used. Hence with analytical solutions only approximations can be obtained. Exact calculations of the circuit can only be made by use of numerical computer programs.

7.5.1.2 Applications and Properties

The eddy current tachometer is the basic type of hand-held tachometer for industrial applications, but its widest application is as speedometer in vehicles. In this case the magnet is driven by a shaft of the gear or the car wheels via a flexible cable. The indication of the speedometer is linearly related to the rotary speed of the magnet owing to the linear behaviour of the torque and the return spring. One of the problems with the devices is caused by the temperature dependence of the resistivity of the eddy current cup, in general aluminium or copper with a temperature coefficient of about - 0.4%/K. To reduce this nonlinear effect, temperature compensation is necessary. Typically, a thin plate or ring of thermocompensating material, operating as a magnetic shunt, is put on the magnet.

7.5.2 Proximity Sensors On the basis of the different physical principles involved, we distinguish between eddy current sensors and the other inductive devices in this chapter. In the case of inductive sensors, the main effect resulting from an alternating magnetic field is an induced voltage, whereas for eddy current sensors it is a current.

7.5.2.1 Principle and Construction

Eddy current proximity sensors consist basically of a coil which is a part of a high frequency LC resonance circuit. The inductance of the sensor is positioned such that the magnetic field generated by the coil can spread in all directions around the axis of the coil. The circuit oscillates at its resonance frequency at a constant amplitude. If a conductor is introduced into this field, eddy currents are induced within the conductor according to Equation (7-41), the reaction of which on the resonance circuit will damp the oscillation [49]. This damping first reduces the output voltage of the oscillator and finally reduces the oscillation of the LC circuit (blocking oscillator, eddy current killed oscillator).

7.5 Eddy Current Sensors

301

If there is no conducting material within the magnetic field of the sensor, the impedance of the circuit is low and a high current will flow. If a conductor approaches, the impedance increases and the current decreases. These changes in current are evaluated by an applied demodulator and a trigger circuit and give output information at the defined level, which is normally digital high or low. Figure 7-50 shows the principle of construction of a proximity sensor and Figure 7-51 shows the output voltage characteristic. ferrite core

magnetic field

coil

Figure 7-50. Schematic diagram of a proximity sensor.

5

18

15

distance [ mml Figure 7-51. Output current of a proximity switch versus distance.

Oscillator coils can be simple air cored coils, coils with soft ferrite cores, soft ferrite plates behind the coil, or coils with different shapes of soft ferrite cores. The choice of the coil depends on the specific applications and varies with the materials to be measured [50]. Air cored coils (Figure 7-52) generate an omnidirectional field. They detect the approach of metallic targets in all directions, which can be a problem in industrial applications. A better characteristic of the magnetic field covering one hemisphere can be obtained by using a ferrite plate positioned on the rear side of the coil (Figure 7-53).

302

7 Inductive and Eddy Current Sensors

Figure 7-52. Field distribution o f a proximity sensor with air cored coil.

Figure 7-53. Field distribution of a proximity sensor with ferrite plate.

This construction offers a stronger magnetic field and in the axial direction an extended range of operation. The device is sensitive in any direction of the hemisphere and the magnetic field is nearly the same as that with a coil of twice the length. The most common type of proximity sensors used in industrial applications contains a cupor E-shaped ferrite core, which forces the sensing field mainly in one direction (Figure 7-54). Hence the sensor detects approaches of conducting material only in the direction of the coil axis. To prevent the sensor being disturbed by conducting material in the environment (except the measuring direction), it is shielded in the radial direction, and the sensor operates in a metal frame.

7.5 Eddy Current Sensors

303

Figure 7-54. Field distribution of a proximity sensor with pot core.

The use of ferrite or other soft magnetic cores has the disadvantage that together with the exciting field the generation of eddy currents in the conductor will be influenced. An analysis of eddy current probes with the ferrite cores is given in [51]. Since there are several designs available, the choice of a suitable sensor construction for special applications depends on the environment in which the sensor will be used and the properties required. Modern computation methods (finite-element methods) will help in the design of an optimum sensor for special applications by varying the shapes, materials, shieldings etc. An important aspect of the function of proximity sensors is the size and the material of the conductor. The size and the shape of the target have a great influence on the generation of eddy currents. The following rules should be considered when designing the sensors: a. The surface dimensions of the target at the operating distance should be large enough to prevent variations in the sensor position producing changes in the output signal. This can be achieved experimentally by varying the surface diameter or magnetic field computations. b. The thickness of the target should be larger than the skin depth 6, which is defined as (7-45) where

6

=

skin depth

w = angular frequency 1 = absolute permeability of the target

o = electrical conductivity. The resulting skin depth for a typical material such as steel, depending on the frequency, is f(MW 0.01 0.1 1.o

6(mm) 0.5 0.15 0.05

304

7 Inductive and Eddy Current Sensors

Since typical oscillator frequencies are in the range 100 kHz- 1 MHz, proximity sensors need only thin conducting targets for satisfactory operation. The generation of eddy current depends on the parameters o,o and ,n (see Equation 7-44) and hence it depends on the material used for the target. High values of these parameters produce considerable reaction on the sensor. Ferromagnetic targets show the highest damping behavior, which allows large operating distances, whereas nonmagnetic materials such as copper or aluminium have a smaller damping effect. In most applications steel, which has a high conductivity and a high permeability, is used.

7.5.2.2 Applications and Properties The eddy current sensors described are typically used for the measurement of position by non-contact and proximity sensing. Some advantages of these sensors are high reliability, no wear, reaction-free and maintenance-free operation and high reproducibility. They can be built with hermetically sealed housings for operation within rough environments. Commercial types are available for temperature ranges from - 40°C up to more than 125°C. They can withstand pressure of up to 5 107N/mZ. Eddy current proximity sensors can be used for the direct drive of contactors, relays and electronic systems. Proximity sensors can typically operate within stray magnetic fields of 40 mT, and especially shielded devices can work within fields of up to 400 mT. Typical applications of eddy current proximity sensors are in machine tooling, automatic welding technology, production and process engineering and other industrial applications. The great variety of sensors and electronic evaluations cannot be covered in this chapter, hence only description of fundamental properties of eddy current sensors has been given here.

-

7.6 Inductive Flowmeters 7.6.1 Physical Principle and Construction To detect the motion of charged particles, a principle based on Faraday’s law of electromagnetic induction is used. Its most common application is the measurement of the flow of conducting media such as liquids and slurries, which will be described here. An inductive flowmeter consists of a nonmagnetic piece of piping and electrodes positioned diametrically to the pipe. The pipe is penetrated by a magnetic field at a direction orthogonal to electrodes and pipe. The magnetic field may be static, derived from permanent magnets or from DC-excited coils positioned diametrically to the pipe, but most systems use AC-excited coils to produce the fields (Figure 7-55) [52]. The fluid passing through the pipe acts as an electrical conductor moving in a magnetic field. The charge carriers will now be deflected by Lorentz forces according to F = ~ * ( u x B ) ,

(7-46)

7.6 Inductive Flowmeters

305

L1, L21 field coils El, E2, electrodes

Figure 7-55. Principle of an inductive flowmeter.

where q = charge v = velocity of the particle B = magnetic induction. Since in an electrical field we have F = q . E

(7-47)

where E = electrical field strength, we obtain E = v x B

(7-48)

for the electrical field strength [53]. The induced voltage between the two electrodes thus becomes :

U

=

Eds =

(V

x B)ds

U = d * ( vx B)

(7-49) (7-50)

where d = distance between the electrodes. Having v, B and d rectangular against each other we obtain

U

=

K ,d.

V -

B

(7-51)

where K is a constant factor, which depends on among other things, the conductivity of the fluid. Inductive flowmeters operate only with minimum conductivity. Then we have a linear dependence of the output voltage on the mean velocity at constant magnetic field.

306

7 Inductive and Eddy Current Sensors

7.6.2 Applications and Properties Owing to the non-invasive function of inductive flowmeters, flow measurement has been rapidly developed. Inductive flowmeters offer higher accuracy than other flow-measurement devices and have an output signal that does not depend on the density, temperature or viscosity of the medium to be measured. There is no mechanical influence on the fluids and the pressure losses are small. The diameter of the pipe can be fitted to the associated piping to obtain a constant profile of flow. Pipe diameters from 2 up to 2000 mm can be realized. Using suitable wear-resistant materials for the pipe and electrodes, inductive flowmeters can be used to measure aggressive and corrosive fluids. They are able to measure fluids at temperatures up to 180°C. The accuracy is of the order of 0.5% of the measured value. Typical flow velocities which can be measured are 0.3- 10 m/s. The required conductivity of the fluid is greater than 20 @Ycm for pulsed DC fields and greater than 1 VS/cm for AC fields. Since the mounting of the devices is simple and they have many advantages, they are used in a wide range of applications within the chemical industry and food industry and in water and waste-water management. In addition to their applications as flowmeters, they can also be used as level meters [31]. The future development of inductive flowmeters will be influenced by current research aimed at a lower sensitivity to electromagnetic disturbances, a smaller size of the devices and better resistance of the electrodes to corrosion. To obtain flowmeters with larger diameters, modified inhomogeneous magnetic fields are used [54]. Other developments are directed towards measuring systems for the measurement of nonconductive or low-conductivity fluids, particles, or gases [ 5 5 ] . Using a rotating magnetic field, the measurement of flow within open chutes is possible [56]. Theoretical and practical developments in recent years offer some new criteria for the analysis and optimization of magnetic inductive flowmeters [57].

7.6.3 Signal Conditioning The power supplies and electronic processing of inductive flowmeters requires some attention in order to obtain satisfactory performance in operation. Inductive flowmeters can be constructed for DC, AC or DC-pulsed magnetic excitation. The voltages generated are of the order of 0.5- 10 mV ; depending on the construction. Since the induced signal is so small, problems may arise in discriminating the signal voltage from disturbances. The electrical noise of flowmeters can be devided into two major types : internal and external sources. Internal noise is generated by phase shifting (quadrature) and by the electronics which generate the magnetic field. DC-excited devices produce measurement errors due to unbalanced potentials which occur from interactions of charged particles within the fluid and between the fluid and metal electrodes. These errors depend on the materials used for the pipe and electrodes, the electrochemical behavior, pressure, temperature, and conductivity of the fluids and may reach voltages of 5-100 mV [58]. Another reason for errors is the appearance of polarization voltages. The galvanic coupling between electrodes and the inner resistance of the amplifier produce a current which leads to the polarization effects. To reduce these errors, commercially used flowmeters are driven by AC or pulsed (intermittent) DC currents. In the case of an AC-driven current, the magnetic field alternates con-

7.7 Materials

307

tinously at the frequency of the line current. This produces continuous quadrature which has to be rejected by phase-sensitive electrical circuitry. Using intermittent DC excitation, the quadrature effect is eliminated because there are no signals evaluated during the time of magnetic field changes. Flow signals are sampled only if the magnetic field is stable. A DC-driven current offers another operational advantage, viz., automatic flowmeter nulling. In general, flowmeters require a nulling procedure to eliminate spurious voltages. The output voltage can be adjusted to zero manually when the fluid is not moving, but this procedure is not very efficient owing to an unstable zero level during operation. With pulsed DC excitation, automatic flowmeter nulling can be achieved by setting the zero level during the time when the field coils are not energized and there is no magnetic field. Since the induced voltage is small, it needs an electronic circuit for amplification and some other signal processing. Today the supply of the field coils, amplification of the flowmeter signal, noise suppression and other processing methods have been taken over by integrated circuits, which offer the possibility of obtaining a fully conditioned control signal from the flowmeter [54,591.

7.7 Materials The performance of inductive sensors depends very much on the materials used in the construction of the sensor. The function of the devices is mainly influenced by the magnetic properties of these materials. The wide range of inductive sensor principles include permanent magnets, soft magnetic materials, nonmagnetic metals and plastics. A discription of the different hard and soft magnetic materials is given in Chapter 1, Section 1.5 of this volume, so here we shall discuss only some special aspects for the construction of inductive sensors. For the construction of sensors with permanent magnets, the choice of the permanentmagnet material in principle depends on

- the required magnetic field strength within the magnetic circuit which is mainly limited by air gaps and leakage flux;

- the material chosen for the core and the magnetic yoke; and - the available dimensions for the sensor, the size of gear tooth, minimum length of air gaps, etc. Since there are many different constructions and applications, the choice of the materials depends mainly on the properties of the sensors required. Most sensors of this type use permanent magnets of the AlNiCo type, eg, AlNiCo 37/5 with a high remanence (more than 1.1 T) and a coercivity of about 50 kA/m. If a greater coercivity is required owing to stronger demagnetizing field$ the use of higher coercive materials such as AlNiCo 39/12 with a coercivity of more than 110 kA/m is possible. However, this material offers a lower remanence of about 0.85 T [61]. For some applications FeCrCo alloys can be used [61]. Hard ferrites, which are used in some applications, have a remanence which is half of the magnitude of the remanence of AlNiCo magnets. This will lead to a smaller level of magnetic

308

7 Inductive and Eddy Current Sensors

flux within the circuit. One disadvantage of ferrites is the high temperature coefficient of the remanence of -0.2%/K, which leads to a high temperature dependence of the sensor signal. If the size of the sensor has to be kept very small, the use of rare earth-cobalt magnets (eg, SmCo, NdFeB), which have a remanence of 0.85-1.2 T, is possible. With these materials the dimensions of the magnets can be chosen to be much smaller than with other materials [60, 621. Soft magnetic materials are used for the construction of cores, conducting elements for the magnetic flux and electromagnetic shieldings. For use as a sensor core within variable reluctance sensors or LVIyTs, for example, it is important to use soft magnetic materials with high permeability, high saturation polarization, and low coercivity to obtain a high output signal. The high permeability will lead to large amounts of induction B and the induced voltage U for small changes in the field strength H or the reluctance within the circuit, respectively. A high value of the saturation polarisation is necessary in order to avoid saturation effects within the circuit, which would lead to a decrease in the output signal. Hence the best material to use for the core are soft magnetic alloys like FeNi, FeSi and FeCo with a maximum permeability of 10000 up to 150000 and a saturation polarisation between 1.5 and 2.3 T [63]. Since these alloys are more expensive than mild steel, in many cases some iron or steel materials with lower permeability (100-500) are used, which will give a much smaller output voltage for the same dimensions of the sensor than with high-permeability materials. For some applications the use of soft ferrites is possible. The materials described above are also used for flux carrying parts of the magnetic circuits such as yokes and electromagnetic shieldings. Within the last few years, amorphous (rapidly quenched) FeNi and FeCo alloys have attained some importance in applications for shieldings and some types of cores. They offer some advantages such as mechanical hardness and variation of the magnetic properties (saturation polarisation, permeability) within wide ranges by composition and processing [64], see also Chapter 1, Section 1.5. For the bobbins, normally plastic and ceramic materials, epoxy or nonmagnetic metals are used. The housing of sensors, for example, is a cylindrical metal box, which periodes electrical and magnetic screening against outer fields. In most applications some steel sheets are used, whereas in more sensitive applications soft magnetic housings are used. If there are no special demands on the duty of the sensors, housings of plastic or epoxy can be used.

7.8 Noise of Inductive Sensors The noise of the inductive sensors, which means the appearance of random variations of the sensor signal, has its origin within several parts of the devices. It can be generated by the electronic components, by thermal effects within the coils, and by magnetization and temperature effects within ferromagnetic parts. The noise of the electronics, originated within the electronic parts of supply circuits and circuits for signal processing, will not be described here, since it is treated in details in other literature [65-681. Since all of the inductive and eddy current sensors consist of coils as operating parts, we shall consider some noise effects of the coils (see also Chapter 1). The copper windings of a coil act as a resistance which generates noise voltages and currents due to the thermal motion

7.9 Conclusions and Outlook

309

of the electrons within the metal. From thermodynamics we have the Nyquist theorem for the time-averaged square voltage or current within a frequency band df [69] : 1 2 ( t )= 4kBT/R * df = 4kBTG * df

and U 2( t ) = 4kBTR * df where

k , = Boltzmann’s constant T = absolute temperature R = ohmic resistance G = conductance. Hence for a given coil resistance R , the square root of this mean value is proportional to l/df and the temperature T. It should be noted that for metals, R also changes with temperature. Other noise effects of the sensors are connected with the magnetization of ferromagnetic materials such as sensor cores. Three types of noise are seen : Nyquist noise, excess noise and Barkhausen noise (see Chapter 1). Nyquist noise is generated by the elastic motions of Bloch walls, activated by irregular thermal motions of metal electrons, thermally excited spin waves or thermal motion of impurities within the lattice. The spectral noise generated by this effect is proportional to the frequency. Excess noise appears owing to temperature-induced changes of the shape of Weiss domains or thermal stress of the material. The frequency spectrum for low frequencies is proportional 1If. The third source of noise has its origin in a discontinous magnetization process. A steadily increasing magnetic field does not produce steadily increasing magnetization. Sudden local changes of the magnetic polarisation due to the Barkhausen effect generate a noise (Barkhausen noise) within induction coils. This noise depends on irregular irreversible motions (jumps) of domain walls during changes of the magnetization. These jumps produce a noise voltage consisting of single pulses or groups of pulses [70, 711. npically the voltages generated by Barkhausen noise are several orders of magnitude higher than that generated by thermal effects, so they will determine the behavior of the sensor. The Barkhausen noise depends on the ferromagnetic materials used, the frequency of magnetization, and the shape and amplitude of the driving field. It can be minimized by good accommodation of these factors. See also Chapter 1, Section 1.6 on magnetic noise. Since there are so many different principles, shapes, and materials in use for inductive sensors, it is impossible to give detailed values for the noise voltages or currents in this chapter.

7.9 Conclusions and Outlook The range of applications and different constructions of inductive and eddy current sensors is so extensive that in this chapter only the main principles and some of the main applications

3 10

7 Inductive and Eddy Current Sensors

Table 7-2. Properties and applications of inductive and eddy current sensors. Measuring range

Resolution

Linearity

Variable reluctance sensors

1 Hz- 1 MHz

< 1 Hz

1070

-40 to 200°C

Tachogenerators

100 rpm6000 rpm

10 rpm

< 0.1%

-40 to 150°C

LVDTS

10nm-lm

1 nm

0.1%

Variable inductance/ VLP-sensors Variable gap sensors

100 nm- Im

10 nm

< 3%

1 nm-lmm

< 1 nm

<0.5%

< 10 to 900 K <10 to 900 K <10 to 900 K

Position, displacement force, weight, pressure Position, displacement force, weight, pressure Displacement, pressure, force, vibrations, accelerations, torque, angles

Synchros

0-1000 rpm

<0.1 Deg

<0.1%

-40 to 180°C

Resolver

0- 1000 rpm

< 5’

< 0.1%

Inductosyns


1” 1 pn

< 0.1%

<0.5’

<0.5%

-40 to 180°C -40 to 180°C <10 to 900 K

Transmission of angular position and rotations Angular position and arithmetical operations Angular position Linear movements Angular position

Tachometer

20-10000 rpm

<0.5 Deg

< 2%

Proximity sensors

1-50 mm

0.1 mm

<0.1%

Inductive flowmeters

0.3-20 m/s

0.1 m/s

0.5%

Principle

Temperature range

Applications

Permanent magnetic Rotational speed Proximity Linear movements Rotational speed

AC-excited sensors for linear movements

AC-excited sensors for rotary movements

RVDTs Eddy current sensors

-40 to 70°C -40 to 200 “C

-20 to 180°C

Rotational speed Proximity position Flow of conducting media

could be described. In Table 7-2 a summary of the main principles and properties of these sensors is given. Owing to their excellent mechanical properties, their high reliability, operation within rough environments, their accuracy, size, and other advantages, the market for this types of magnetic sensors has grown considerably in recent years. The variety of types and the possibility of measuring many different quantities with these devices has led to numerous applications in

7.10 References

311

automotive control systems, production and process engineering, robotics, diagnostics, and others. The market for inductive and eddy current sensors is expected to increase in the next few years by possibly 10%. In automotive applications, for example, the number of sensors is expected to increase by about 30% from 1990 to 2000 [72]. This number will include many inductive sensors. Today the trends in the development of these types of sensors are a reduction in the sensor size, extension of the ranges of operation (temperature, environment media, etc.), improvement of the magnetic circuits with computer-aided numerical field calculations and the use of new magnetic materials such as amorphous alloys or magnetic fluids. Another aspect of development is the miniaturization of the electronics. Owing to SMD (Surface Mounted Device) and hybrid technology, electrical circuits for supply and signal processing are nowadays increasingly provided as integrated circuits. In this form the sensor electronics can be completely integrated within the sensor housing, which will lead, for example, to less disturbance of the sensor signals and a better signal-to-noise ratio. Microprocessors and highly integrated electronics will be used within automatic control systems and robotics for further signal treatment.

7.10

References

[l] Schiiler, K.,Brinkmann, K . , Dauerrnagnete; Heidelberg: Springer Verlag, 1970. [2] VDO, Lieferprograrnm, Druckschr$t Nr. 340.1, VDO, Schwalbach, FRG. [3]Op den Winkel, F., Elektronik Applikation 24, No. 15, (1986)56-58. [4]Miiller, W., “Numerical Calculation of Magnetic Fields Excitated by Currents and Hard Magnetic Materials”, in : Proc. 9 Znt. Workshop on Rare Earth Magnets and Their Appl., Bad Soden, FRG, Aug. 30-Sept. 03. 1987. [5]Armstrong, L. R., Wilkinson, J. R., Recent Advancements in Non-Contact Diesel Diagnostics, SAE Papers, 830371, 1983. [6]Warnecke, H. J., Dutschke, W., FertigungsrneJtechnik, Heidelberg : Springer Verlag, 1984. [7]Forkel, W., “Magnetfeldmessungen mit Sattigungskernsonden in der Fahrzeugtechnik”, in : Spezial Sensoren, 86/87, Diisseldorf : VDI-Verlag, 1986. [8]Hood, R. B., Sensors, Displays and Signal Conditioning, SAE Papers, 740015, 1984. [9]VDO, Lieferprograrnrn, Druckschr$t Nr. 340.6, VDO, Schwalbach, FRG. [lo]Rohrbach, Ch., Handbuch fiir elektrisches Messen mechanischer GrGJen, Diisseldorf : VDI-Verlag, 1967. [ll]Elektrotechnik 69, No. 11, (1987)32-33. [12]Richer, B., “Drehzahl Messgeneratoren”, Arch. techn. Messen (1950)I 162-6. [13]Oesterlin, W., “Verfahren und Geritte zur Messung der Drehzahl”, Arch. techn. Messen (1961) V 145-7, 8, 9. [14]Gahler, F., “Elektrische Drehzahlmessung mit hochpoligen Wechselstromgebern”, Elektrowelt (1959)87-88. [15]Tomasek, J., “Velocity and Position Feedback in Brushless DC Servo Systems”, Motor-Con Proc, April, (1985)61 -75. [16]Lazaroiu, D. F., Slaiher, S., Elektrische Maschinen kleiner Leistung, Berlin: VEB Verlag Technik, 1976.

312

7 Inductive and Eddy Current Sensors

[17] Weschta, A., “Measuring Rotary Speed and Angular Position with an AC-Tachogenerator”, Regelungstechnische Praxis 26, No. 11, (1984) 492-497. [18] Schaevitz, H., “The Linear Variable Transformer”, Proc. SESA 4, No. 2, (1946). [19] Lipshutz, J., LI S. Patent 3 054 976, September 1962. [20] Wouterse, “Inductive Position Transducer with Transverse Excitation”, Technisches Messen 54, NO. 1, (1987) 15-19. [21] Herceq, E. E., Handbook of Measurement and Control, Pensauken, NJ : Schaevitz Engineering, 1976. [22] Lechner, R., “Induktive Wegaufnehmer”, Der Elektroniker, No. 1, (1986) 56-60. [23] Grinrod, A., “Precision Linear Measurements in A. G. R. Environments”, in: The Transducer Tempcon ConJ Paper 1983, London, GB, June 14-16, 1983, pp. 271-291. [24] Seippel, R. G., Transducers, Sensors and Detectors, Reston, VA : Reston Publishing Company, 1983. [25] V. d. Pol, R., “Beriihrungslose Positionserfassung eines KBrpers durch eine Edelstahlrohrwandung nach dem Prinzip des Differentialtransformators”, in: Symp. Sensoren Messaufnehmer, Esslingen, FRG, 18-20 Sept. 1984, pp. 21.1-21.7. [26] Hencke, H., “Sensoren zur Erfassung von Drehbewegungen”, Der Elektroniker 23, No. 5 , (1984) 46-50. [27] Hederer, A., Dynamisches Messen, Grafenau : Lexika Verlag, 1978. [28] Hadley, L., Herceq, E., “Interface IC for Linear Variable Differential Transformers”, Electronic Components and Applications, 4, No. 3, (1982) 180-184. [29] Blaesner, W., “Integrierte Ansteuerungsschaltung fur induktive Wegaufnehmer”, Elektronik, Munchen, 36, No. 1, (1987) 40-42. [30] Althen, H., “Aufbau und Entwicklungsstand moderner differentialtransformatorischer Wegaufnehmer”, in : Symp. Sensoren Messaufnehmer, Esslingen, FRG, 1986. [31] Haug, A. H., Elektronisches Messen mechanischer GrOJen, Munchen: C. Hanser Verlag, 1969. [32] Profos, Handbuch der industriellen Messtechnik, Essen : Vulkan-Verlag, 1987. [33] Grant, D. E., “Displacement Measurement in Nuclear Power Industry”, The Transducer Tempcon ConJ Papers 1983, London, GB, June 14-16, pp. 296-307. [34] Operating Manual Q 11, Load Cells and Force Transducers, 1988, Hottinger Baldwin Messtechnik, Darmstadt, FRG. [35] Hellwig, R., “Ubersicht iiber verschiedene Aufnehmerprinzipien fur die elektrische Druckmessung”, Messen, Priifen, Automatisieren, No. 6, (1986) 340-351. [36] Miiller, R. K., “Mechanische GrBssen elektrisch gemessen”, in: Kontakt und Studium 45, Grafenau : Expert Verlag, 1980. [37] Kritschker, P., Cast, Th., “Inductive Cross-Anchor Detector with High Resolution”, Technisches Messen 49, No. 2, (1982) 43-49. [38] Bentley, J. P., Principles of Measurement Systems, New York: Longman Inc., 1983. [39] Valayudhan, C., Bundell, J. H., “A Precision Torque Measurement Transducer System”, in : Proc. IECON 84, Tokyo, 4 22-26 Oct. 1984, Vol. 1 pp. 628-632. [40] Gutzmer, P., Helfer, M., “Einsatz induktiver Wegaufnehmer zum Erfassen von Kolbenquerbewegungen und Kurbelwellenverlagerungen an Verbrennungsmotoren wlhrend des Betriebs”, Messtechnische Briefe 20, No. 2, (1984). [41] Karcher, M., ‘‘ResolverIDigital Converter in Comparison with Incremental Transducers and Tachogenerators”, Elektronik Zndustrie 16, No. 12, (1985). [42] Design und Elektronik, No. 14, July 1988. [43] “und-oder-nor Steuerungstechnik”, Elektronik-Information, No. 7-8, (1984). [44] Smythe, W. R., Static and Dynamic Electricity, New York: McGraw-Hill, 1968. [45] Chari, M., D’Angelo, J., Palmo, M., “Three-Component, ?ivo Dimensional Analysis of the Eddy Current Diffusion Problem”, IEEE Trans. Magn. MAG-20, No. 5 , (1984) 1989-1991.

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[45] Chari, M., D’Angelo, J., Palmo, M., “Three-Component, Two Dimensional Analysis of the Eddy Current Diffusion Problem”, IEEE Trans. Magn. MAG-20, No. 5, (1984) 1989-1991. [46] Chari, M., Csendes, Z., “Finite Element Analysis of the Skin Effect in Current Carrying Conductors”, IEEE Trans. Magn. MAG-l3, No. 5, (1977) 1125-1127. [47] Poltz, “On Eddy Current in Thin Plates”, Archiv f u r Elektrotechnik 66 (1983) 225-229. [48] Gahbler, I., “Berechnung quasistationarer Wirbelstromprobleme”, Archiv f u r Elektrotechnik 64 (1981) 27-36. [49] Solaski, R., Anderson, P., Neill, W., A Technic for Non-Contact Position Sensing, SABPapers, 840304, 1984, pp. 93-108. [50] Holloway, L., “No-Touch Sensing”, in: 26th IEEE Machine Tools Ind. ConJ 1983, Milwaukee, USA, 18-20 Oct., pp. 27-35. [51] Sabbagh, H. A., “A Model of Eddy Current Probes with Ferrite Cores”, ZEEE Trans. Magn. MAG-23, NO. 3, (1987) 1888-1904. [52] Baker, R. C., “Electromagnetic Flowmeters”, Development in Flowmeasurement, London: Applied Science Publishers, 1982. [53] Weiss, A., Die elektromagnetischen Felder, Braunschweig : Vieweg Verlag, 1983. [54] Strohmann, G., “ATP-Marktanalyse Durchfluhefltechnik”, Automatisierungstechnische Praxis, atp 28, No. 3, (1986) 122-129. [55] Hofmann, F., Kiirten, R., v. d. Pol, R., Magnetic Inductive Flowmeter for Low Conducting Fluids, BMFT report no. T84-136, 1984, BMFT, 5300 Bonn, FRG. [56] Bonfig, K. W., “Magnetisch induktive DurchfluBmessung in offenen Kaniilen unter Verwendung eines elektromagnetischen Drehfelds”, Messen und Prufen, No. 1/2, (1982) 48-54. [57] Bonfig, K. W., “Optimization Criteria for Magnetic-Inductive Flowmeter”, Coqference proc. Messcomp 1988, Network GmbH, Hagenburg, FRG, 1988, pp. 6B.3.1-6B.3.9. [58] Bonfig, K. W., “Storeffekte bei der magnetisch induktiven Durchfluhessung”, Messen, Prufen, Automatisieren, No. 12, 1987, 712-717. [59] Banta, F, D., “Magnetic Flowmeter Development”, in: Proc. of the ISA Int. ConJ and Exhibit, Philadelphia, USA, Oct 18-21, 1982, pp. 1183-1196. [60] Dauermagnetische Werkstoffe und Bauteile, Drucksache W2.20-51.OdO488, Krupp-Widia, Essen, FRG. [61] Magnetoflex, Crovac, Platin-Kobalt, Vacozet, Datenblatt M-044, Miirz 1984, Vacuumschmelze, 6450 Hanau, FRG. [62] Selten-Erd Dauermagnetwerkstoffe, Datenblatt M-054, April 1988, Vacuumschmelze, 6450 Hanau, FRG. [63] Soft Magnetic Materials, Boll, R. (ed.); London : Heyden, 1979. [64] Erb, O., “Magnetfeld- und Positionssensoren mit amorphen Metallen”, in : NTG-Fachberichte 93, Berlin: VDE-Verlag, 1986, pp. 192-198. [65] Miiller, R., Rauschen, Heidelberg : Springer Verlag, 1979. [66] Davenpoort, W. B., Root, W. L., Random signals and noise, New York: McGraw Hill, 1958. [67] V. d. Ziel, A., Noise: Sources, characterisation, measurement, Englewood Cliffs, NJ : Prentice Hall, 1970. [68] Smullin, L. D., Haus, H. A., Noise in Electron Devices, New York: Wiley, 1959. [69] Kittel, C., Physik der Wijrme, Miinchen: R. Oldenbourg Verlag, 1973. [70] Bittel, H., Storm, L., Rauschen, Heidelberg : Springer Verlag, 1971. [71] Bittel, H., “Noise of Ferromagnetic Materials”, IEEE Trans. Magn. MAG-5, No. 3, (1969) 359-365. [72] Shah, R., et al., Spezial Sensoren 86/87, Diisseldorf: VDI Verlag, 1986.

8

Wiegand and Pulse-Wire Sensors GERD RAUSCHER. CHRISTIAN R A D E ~ F FVacuumschmelze . GmbH. Hanau. FRG

Contents

8.4 8.4.1 8.4.2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Principles . . . . . . . . . . . . . . . . . . . . . . . . . . Wiegand Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . Design and Properties . . . . . . . . . . . . . . . . . . . . . . . . Influence of Drive Conditions . . . . . . . . . . . . . . . . . . . . Pulse Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulse Wires with High Pulse Voltage . . . . . . . . . . . . . . . . . . Pulse Wires with Low Pulse Voltage for Small Drive Fields . . . . . . . . .

8.5

Amorphous Wires

8.6 8.6.1 8.6.1.1 8.6.1.2 8.6.2 8.6.3

Applications . . . . . . . . . . . . . . . . . . Rotational Frequency Sensors . . . . . . . . . . Simple Revolution Counters . . . . . . . . . . . Incremental Rotary Encoders . . . . . . . . . . . Code Cards and Special Applications . . . . . . Jitter . . . . . . . . . . . . . . . . . . . . .

8.7

References

8.1

8.2 8.3 8.3.1 8.3.2

Introduction

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

..........

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316 316 319 319 321 324 324 328 330 331 331 331 334 336 337 339

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

316

8

Wiegand and Pulse-Wire Sensors

8.1 Introduction Wiegand and pulse-wire sensors are magnetic switching elements which induce pulse voltages in a sensor coil up to 3 V in 1000 turns when a defined field strength threshold is exceeded during remagnetization. In this case the voltage amplitude is largely independent of the rate of field change dH/dt of the applied magnetic field, in contrast to the well-known passive flux density sensors whose output signal decreases to zero with dH/dt. These sensors are particularly suited to detecting magnetic fields, movements, and positions as well as for safety systems due to their high, frequency independent pulse voltages. Another advantage is the wide operating temperature range and, where required, the operation may be independent of power supplies. This magnetic switching effect is based on large reproducible Barkhausen jumps in ferromagnetic wires under tensile stress whose behavior and principles have been investigated by Preisach [l], Sixtus and Tonks [2, 31, and Doring [4].This effect was first realized technically by Wiegand [S] on twisted wires made of Vicalloy (in wt. %: Co 52, V 10, balance Fe). Under optimum drive conditions these so-called Wiegand wires supply high, reproducible pulse-voltages. When remagnetizing these sensors in the usual way with permanent magnets more complex systems may be neccessary to attain optimum drive conditions [6]. In the meantime pulse wires have been developed made from carefully balanced combinations of soft and hard magnetic materials, allowing a wide non-critical range of drive conditions [7, 8, 91. Moreover, the field strength threshold in the pulse wires, ie, the field strength which triggers the pulse, referred to as the switching field strength H , , can be reduced by a factor of ten and set as required.

8.2 Physical Principles Remagnetization in ferromagnetic materials is achieved by domain wall displacements and rotational processes where the flux generally changes continuously with the external magnetic field. In contrast, the magnetic switching effect is characterized by rapid, discontinuous change of flux which, under ideal conditions, causes the entire volume to reverse its direction of magnetization in one large Barkhausen jump. This behavior is attained when the entire volume contains only one magnetic domain whose magnetization, as a result of an inherent anisotropy, can only be parallel or anti-parallel to this preferred direction. Well defined anisotropies can be introduced through mechanical stresses, shaping (demagnetization factor) or by tempering in a magnetic field providing the other energy terms like crystalline anisotropy or arbitrary internal stresses are negligible [lo, 111. In wires there is already a preferred direction of magnetization along the main axis because of the geometry; this form of anisotropy can be enhanced considerably by applying external tensile stresses. The energy density E, of this stress anisotropy is given by

8.2 Physical Principles

317

where I , is the saturation magnetostriction and CJ the tensile stress. Materials with positive magnetostriction exhibit an increase I , in length in the direction of magnetization and, in turn, an increase in magnetization in this direction when tensile stress is applied externally. High values for E, can be achieved according to Equation (8-1) by using materials with high tensile strength and magnetostriction. Both criteria are particularly well fulfilled by CoFe alloys; while NiFe alloys with a medium Ni content can also be used. The following discusses the principles of remagnetization behavior of wires under stress whose hysteresis loops and pulse characteristics are presented schematically together with the measurement set-up in Figure 8-1. After applying a magnetic field sufficient for saturation and

Field coil Wire

!

y

L

Sensor coil

't

Figure 8-1. Measuring device for the hysteresis loop J ( H ) and the induced pulse voltage U ( t ) of wires under tensile stress. u tensile stress, T, switching time, sensor coil 1000 turns.

provided E, is adequately high, the wire remains uniformly magnetized, ie, it consists of only one domain whose magnetization is in the axis of the wire. On reversing the field, a reverse magnetized nucleus must initially be generated with the surface energy of the domain wall

A = lo-'' J/m is the constant of the exchange energy [lo]. This requires a defined field strength H, above the coercivity H , . Remagnetization then takes place at high speed determined exclusively by the net switching field H , - H, and in the quasi static case is no longer dependent on the rate of field change dH/dt. According to [4] we have

318

8

Wiegand and Pulse-Wire Sensors

with d as diameter of an ellipsoid shaped reverse magnetized nucleus which is approximately the same as the grain diameter; J, is the saturation polarization. To achieve high values for the net switching field H , - H, a fine grained microstructure and high tensile strength are required. According to [7] the pulse amplitude increases roughly proportional to the net switching field so that

O - H, - Hc -

fi

(8-4)

results. For the switching time T, in Figure 8-1 we have

where D is the diameter of the wire and p the specific resistivity. These correlations were examined in detail on wires made of VACOFLUX 50 (in wt. To: Co 49, V2, balance Fe). Table 8-1 gives the typical properties of this alloy which features a particularly high magnetostriction and saturation polarization. Table 8-1. Typical properties of the alloy VACOFLUX 50 (in wt. Vo C050, V2, balance Fe). Saturation polarization Saturation magnetostriction Coercivity l) Specific resistivity Tensile strength Young's modulus I)

JS

4 HC P Rm

E

2.35 T +70 . 0.2-20 A/cm 0.4 . Bm 600-2000 N/mm2 230 kN/mm *

depending on the annealing conditions

Figure 8-2 presents the pulse amplitude as a function of tensile stress for wires with a diameter of 0.2 mm after optimum heat treatment. The curve confirms the increase in the pulse amplitude as being proportional to fiaccording to Equation (8-4). The correspond16 V

t

l:

li

4

0 0

100

200 6-

300 Nhm'400

Figure 8-2. Pulse amplitude against tensile stress; sinusoidal field H = 30 A/cm, f = 1 Hz.

8.3 Wiegand Sensors

319

ing pulse curve for three tensile stresses is presented in Figure 8-3. According to this a good reproducible pulse of 6 V is achieved at 60 N/mm2 in 1000 turns, while the net switching field H, - H, is 3.4 A/cm [7]. In this case the pulse characteristic and switching time T, are essentially determined by the eddy current damping. Using Equation (8-5) and the data given by Table 8-1, for ~7= 60 N/mm2 we obtain a switching time of 76 ps which is in good agreement with the result of the measurement in Figure 8-3. A more detailed description of the remagnetization process in these wires is given in [7]. 16 r--

Figure 8-3. Pulse voltage for three values of tensile stress.

t-

8.3 Wiegand Sensors 8.3.1 Design and Properties Wiegand wires are manufactured from Vicalloy wire (Co52, V10, balance Fe) with a diameter of 0.25 to 0.30 mm by a special method of twisting [ 5 ] . This process of cold working performed under tension causes plastic deformation in the outer shell of the wire and sets a coercivity of approx. 30 A/cm in the shell whilst the inner core is subjected to elastic stress at a coercivity of 10 to 20 A/cm. It follows that Wiegand wire primarily consists of a magnetically hardened shell which subjects the magnetically softer core to tensile stresses (Figure 8-4). Consequently the requirements for a magnetic switching effect according to Section 8.2 are fulfilled. The typical range of length for sensor applications is between 8 to 32 mm.

Figure 8-4. Schematic design of Wiegand wire with soft magnetic core and hard magnetic shell, dimensions in mm.

-------8 -32

320

8

Wiegand and Pulse-Wire Sensors

Table 8-2. Typical properties of the Wiegand wire under optimal drive conditions. 5 p e PN 30020, Echlin Sensor Co, Branford CT, USA. Length: 32 mm, diameter: 0.3 mm, sensor coil: 1000 turns on 28 mm, R, = 34 n.

cl,

Pulse amplitude (no load) Pulse width at half amplitude Optimum reset field Setting field, min. Switching field-strength Source resistance Peak power') Pulse energy Temperature range I)

6/2

H R

Hs Ri

PL EL

2.5 v 18 ps -18 A/cm +SO A/cm 19 A/cm 200 n 8 mW 170 nWs -200 +180"C

...

with power matching

The following describes the typical pulse properties of a Wiegand wire, 32 mm long and with 1000 turns. Table 8-2 gives an initial survey of the most important characteristic terms for optimum excitation. Figure 8-5 shows the corresponding pulse characteristic. To measure these data, the wire was remagnetized with an asymmetric field of - 18 to + 100 A/cm parallel 4.0

v

1 1::

U

1.0

0.0

0

60 ps 80

40

20

t6 V 5 -

Figure 8-5. 5 p i c a l pulse voltage of a Wiegand sensor with 1000 turns under optimum asymmetric drive field. 5 p e : PN 30020; Echlin Sensor Co, Branford CT, USA.

4,

2 1 -

Usual Wire 0

lo-'

loo

f-

10'

102Hz ld

Figure 8-6. Pulse amplitude against field frequency for the Wiegand wire and usual wire with comparable coercivity.

321

Wiegand Sensors

8.3

to the axis of the wire. This sensor is characterized by its high pulse voltage at field frequencies below 100 Hz (Figure 8-6). As opposed to this, a wire with similar geometry and coercivity but without a switching effect supplies a strong frequency dependent signal which approaches zero with decreasing frequency. Another advantage of the Wiegand sensor is its wide operating temperature range from -200 to + 180°C. The pulse voltage is not only dependent on the number of turns of the sensor coil but also on the length of the Wiegand wire (Figure 8-7). The reduction of o,, with decreasing wire length is caused by demagnetization effects which increase rapidly the shorter the wire. This is described by the demagnetization field [13]. As a result the net switching field H, - H, which is a decisive factor for the switching effect and pulse amplitude decreases and reduces the pulse voltage, see Section 8.2.

Figure 8-7. Pulse amplitude of the Wiegand sensor in dependence of the wire length; after [12].

I

I

0

10

1

20

Wire Length

1

30

1

I

40

mm

50

8.3.2 Influence of Drive Conditions The previous section described the properties of the Wiegand sensor under optimum, asymmetric excitation. However, the special production process used for Wiegand wires results in a complex dependence of the pulse behavior on the drive conditions. Figure 8-8 shows the

4 V

3

6t.

2 1

l.otA

n n

0

Figure 8-8. Pulse curve (a) and pulse amplitude (b) of a Wiegand sensor in dependence of the reset field - HR; set field 100 A/cm.

322

8

Wiegand and Pulse-Wire Sensors

strong dependence of the pulse voltage on the reset field. If the reset field deviates from the optimum range of -16 to -20 A/cm, the pulse voltage decreases rapidly and at - H R 2 25 A/cm the pulse is irregular and its amplitude unstable (Figure M a ) . Figure 8-9 presents the hysteresis loops for different reset fields. As a rule, the pulse only arises on the setting field side of the hysteresis loop (dashed line) after resetting, ie, the pulse is unipolar. On resetting, only a small, strongly frequency dependent signal is obtained. Furthermore Figure 8-9 shows that the switching field strength H, at which the pulse is triggered, also changes with the reset field. The relationship between the pulse amplitude, the switching field strength and the reset field is presented in Figure 8-10. Good reproducible pulses are only attained in the range HR = -10 to -20 A/cm, the pulses are irregular for -HR > 25 A/cm. The switching effect is very weak with symmetric excitation, eg, at 100 A/cm. According to Figure 8-11 a at 50 Hz a pulse voltage of only 0.4 V is obtained in 1000 turns, at 1 Hz this value falls to approx. 0.1 V. The corresponding hysteresis loop in Figure 8-11 b does not exhibit a pronounced polarization jump but merely two steeper sections which result from the core and the magnetically harder shell, and lead to the two pulses in Figure 8-11 a.

T

1

1,o 0.5

'0

p I!!

- 0,s

-40

- 1.0

'-40 -20

0

20

40

Figure 8-9. Hysteresis loops of a Wiegand wire for different reset fields.

60 Alcm 100

H-

4 V

3

li, t

-

2 1

HR=-15

-

0

5

10 Hs

I

I

15

A/cm

25

Figure 8-10. Pulse amplitude of a Wiegand wire in dependence of the switching field strength H, and the reset field H R .

323

8.3 Wiegand Sensors tO.8

I

v

-

tO.6

-

,

,

,

,

,

,

,

I

,

,

,

,

k = 100 A/cm

Magnetic Field

f

-

50Hz

t0.2

U

-0.8

a)

0

4

12

8

ms

16

t-

Figure 8 4 .

Pulse voltage in 1000 turns (a) and hysteresis loop (b) of a Wiegand wire under symmetric drive field; f = 50 Hz.

b) H-

The strong dependence of the switching behavior on the reset field is based on the interaction between the soft magnetic core and the magnetically harder shell. Magnetic closure domains are nucleated at the ends of the wire due to the demagnetizing field and disturb the required single domain characteristic. It follows that on applying an external field, remagnetization would be initiated in these domains and would be almost continuous without switching effects. However, in the optimum reset state the closure domains are reduced and magnetically stabilized by the stray field of the outer shell previously magnetized by the setting

324

8

Wiegand and Pulse-Wire Sensors

field (Figure 8-4). This guarantees the switching effect providing the reset field only remagnetizes the core, and the shell zone remains magnetized. However, the low coercivity of approx. 30 A/cm in the shell zone means that the reset field range is very limited. A setting field of at least 80 A/cm ensures that the shell is always fully magnetized. The drive conditions would be less critical in a wire where the coercivity of the hard magnetic part is at least one order of magnitude above the coercivity of the soft magnetic switching core. This would practically exclude demagnetization of the hard magnetic part during operation. However, these conditions cannot be realized with the production process used for Wiegand wires.

8.4 Pulse Wires In addition to torsion as used in the Wiegand wire, mechanical stresses can be introduced by other means. Composite wires made of two different alloys are particularly suitable for a process where the shell places the switching core under tensile stress, and in some combinations it also takes over the required permanent magnet function according to Figure 8-3. One possibility is to use alloys with different coefficients of thermal expansion. In a different process the switching core is placed under tensile stress by straining the wire once over the elasticity limit of the shell, whilst the core remains within the elasticity range. Permanentmagnetic material is not normally used as a shell for this variant because of its extreme brittleness and mechanical strength. This particular case requires an additional permanent magnet wire. Carefully selected combinations of materials result in pulse wires with properties which can be adapted to a wide range of technical requirements. As a rule, pulse wires fall into two major categories depending on pulse amplitude and switching field strength.

8.4.1

Pulse Wires with High Pulse Voltage

These wires consist of a composite wire with a switching core made of VACOFLUX which according to Section 8.2 exhibits a particularly pronounced switching effect and a shell of the composition Ni 28, Co 18, balance Fe (in wt 070, VACON 10). The wire diameter is in the range 0.12 to 0.2 mm, the usual wire lengths range from 8 to 20 mm. The tensile strength required for the switching core is introduced by stressing. Since the shell made of VACON cannot act as a permanent magnet, a permanent-magnetic wire is fixed parallel to the composite wire (Figure 8-12). Table 8-3 gives the typical characteristic terms of a pulse wire. Permanent magnetic wire

Figure 83-12. Composite wire

Schematic design of a pulse wire and typical dimensions in mm.

325

8.4 Pulse Wires

Table 8-3. 'Ijrpical properties of the pulse wire MSE 590/003, produced by Vacuumschmelze GmbH, Hanau, FRG. Length: 16 mm, sensor coil: 1000 turns on 12 mm, R , = 40 a. Pulse amplitude (no load) Pulse width at half amplitude Drive field Switching field-strength Source resistance Peak power') Pulse energy I) Temperature range

00

2.5 V

T :,2

10 ps

f30 ... +300 A/cm 20 A/cm 300 a 4 mW 70 nWs

Hs Ri

4 EL

-200

... +180"C

with power matching

U 1

0 10

0

0)

30

20

40

ps

50

tI

Figure 8-W. Pulse voltage in 1000 turns (a) and hysteresis loop (b) of a pulse wire. Type: MSE 590/003 Vacuumschmelze GmbH, Hanau, FRG.

t1.6

-

T

-

tO.8

-

-0.e

-

-1.6

I

bl

-40

-30

I

I

-20

I

I

,

I

-10

0

t10

I

I

I

I

+20 A/cm

t40

H-

Figure 8-13 shows the pulse characteristic and hysteresis loop. As in the Wiegand wire, the pulse only arises on one side of the hysteresis loop (dashed-line) due to the premagnetization

326

8

Wiegand and Pulse-Wire Sensors

of the permanent magnet wire. In contrast to the Wiegand wire, the pulse wire can be driven symmetrically and requires a field strength of only 30 A/cm. Furthermore, the pulse characteristics remain constant over a wide range of field strengths. The upper limit is approx. 300 A/cm and is determined by the coercivity of the permanent-magnetic wire of 450 A/cm. The decisive characteristic of the pulse wire is the frequency-independent pulse amplitude below 100 Hz (Figure 8-14).

lo-'

loo

10;

lo2

HZ

lo3

fFigure 8-14. Amplitude-frequency-response of a pulse-wire sensor; sinusoidal field H = 30 Akm.

The data given so far on pulse voltages refer to no-load conditions, ie, the measurements were performed with an unloaded sensor coil. However, some applications require an appropriate load resistance so that the signal can be transmitted along longer leads without interference. In the following we investigate the dependence of the pulse voltage on the resistive load and the winding parameters. Under no-load conditions the pulse amplitude of a wound pulse wire, with defined material parameters, increases with the number of turns n of the sensor coil:

oo= n K ( H , - H , ) . The constant K i n Qm is determined by the eddy current damping, H , and H , are the switching field strength, and the coercivity respectively. With experimentally determined values for ooand H , - H, = 6 A/cm we obtain K = 3.2 * 10 - 6 Qm. Under load, the current f produces an opposing field of the amplitude

H, =

nf 7

(8-7)

in a sensor coil with the length I by which the net switching field (H, - H , ) is reduced. Consequently, for the pulse amplitude at the load resistance R , we receive

oL

8.4 Pulse Wires

oL= n K ( H , - H, - H , ) - f R c = oo- 1

327

(8-8)

with R, as the winding resistance of the sensor coil (Figure 8-15). The source resistance Ri of the sensor is then

n2 Ri=-K I +R,.

(8-9)

Figure 8-15. Equivalent circuit diagram.

-

As for example with K = 3.2 a m , n = 1000, 1 = 12 mm and a winding resistance R, = 40 SZ we calculate a source resistance of 307 a. With the same load resistance optimum power transfer is also achieved. Figures 8-16 and 8-17 show the dependence of the pulse amplitude and the power (peak value) on the load resistance for three different numbers of turns. In case of power transfer a maximum value of 3.5 mW is attained here. The pulse width at half amplitude increases with decreasing load resistance. The basis for the calculation of the load dependence is the relationship

r&2

- T, - (H, - H,)-'

(8-10)

A

v 3

0 101

102 Rt

-

1 o3

R

lo4

Figure 8-16. Pulse amplitude against resistive load for a pulse wire sensor MSE 590/003 for different numbers of turns (n).

328

8 Wiegand and Pulse-Wire Sensors A

mW

3

!

2

4

0 1 o1

1O2 RL

-

1o3

104

R

Figure 8-17. Peak power against resistive load for a pulse-wire sensor. n = number of turns.

with T, as the total pulse duration, see Section 8-2. If the opposing field fiI from Equation (8-7) is then taken into account in a similar way for the pulse width at half amplitude under load we obtain (8-11) For R L + 0, T ; , ~ attains its maximum value 5Y12 . Ri/R,. For the above example with = 10 ps we obtain the value 5\/2 = 77 ps for RL 0.

5Yl2

+

8.4.2 Pulse Wires with Low Pulse Voltage for Small Drive Fields These wires consist of a soft magnetic NiFe switching core and a permanent magnetic shell, eg, of CROVAC 10 (in wt. To: Cr28, ColO, balance Fe). In this case, the tensile stresses o n the switching core are caused by the two materials having different coefficients of thermal expansion. The diameter of the wire is between 0.12 and 0.2 mm, the wire lengths vary depending on the field of application from 12 to 100 mm. Table 8-4 gives the most important characteristic terms of this type of pulse wire. Table 8-4. Typical properties of pulse wire MSE 590/007, produced by Vacuumschmelze GmbH, Hanau,

FRG. Length: 25 mm, diameter: 0.15 mm, sensor coil: 1000 turns on 12 mm. Pulse amplitude (no load) Pulse width at half amplitude Drive field Switching field-strength Temperature range

4

0.5 V

e l 2

40 ps

Hs

+ 3 ... 100 A/cm 1.8 A/cm - 80 ... +150"C

8.4 Pulse Wires

329

Figure 8-18 shows the typical pulse characteristic and the corresponding hysteresis loop for a pulse wire 25 mm long under 3 A/cm excitation. The actual switching pulse is again found in the dashed-line section of the hysteresis loop. In this type of pulse wire the pulse amplitude is also only slightly dependent on the frequency of the drive field (Figure 8-19). In comparison to the pulse wire with high pulse voltage described in Section 8.4.1, the required excitation fields are lower by one order of magnitude, ie, when used as a sensor the distance to the switching magnet can be substantially larger.

V

F-----------l Magnetic Field

= 100 A h f = 50Hz

-

a1 0

8

4

ms

12

t-

bl

Figure 8-18. Pulse voltage in 1000 turns (a) and hysteresis loop (b) for a pulse wire with low switching field-strength. Qpe: MSE 590/007; Vacuumschmelze GmbH, Hanau, FRG.

330

8 Wiegand and Pulse-Wire Sensors 1.0

1 li,

v

-

0.8

-

0.6

/ex

xx ---',

0.4

-

0.2

I

0

I

I

I

I

fFigure 8-19. Amplitude-frequency-response of a pulse wire sensor MSE 590/007;H = 3 A/cm.

8.5

Amorphous Wires

Amorphous soft magnetic metals produced directly from the melt using rapid solidification have gained in importance in the last few years [14]. These materials are primarily produced as thin ribbons, 20 to 30 pm thick, and they are used, eg, in toroidal strip-wound cores. Moreover, by using rapid solidification technology amorphous wires with a diameter of approx. 130 pm can be produced. As a result of the rapid cooling, mechanical stresses are caused

0.8

I

fiQ

o.6

0.4

0.2

0 100

lo2

10'

Hz

1o3

fFigure 8-20. Amplitude-frequency-response of amorphous wire for different lengths; H = 3 A/cm; composition Fe,,,, Si,,, B,,; diameter 0.13 mm, manufactured by Unitika Co, Uji 611, Japan.

8.6 Applications

331

between the surface zone of the wire and the core which give rise to certain switching effects in high magnetostrictive iron-rich alloys [15]. Figure 8-20 presents the frequency dependence of pulse voltage for amorphous Fe-Si-B wire made by UNITIKA at an excitation of 3 A/cm. The diagram shows a weak switching effect of approx. 0.05 V/lOOO turns below 100 Hz at a wire length of 100 mm. As a result of demagnetization effects this value is only obtained in wires longer than 50 mm. However, the low static coercivity of 0.05 A/cm and the slight jitter, ie, good reproducibility of the pulse, are advantageous. This material is suitable for anti-theft devices since it already emits signals with characteristic higher harmonics at low excitation and low frequencies.

8.6 Applications The following discusses several possibilities of applications for pulse and Wiegand wires and gives information on designs for excitation with permanent magnets. In this particular case, when used as magnetic threshold switches these sensors have an advantage over Hall elements, since they produce a high pulse voltage without power supply. This can be transmitted free of interference because of the high signal-to-noise ratio, and used directly to trigger electronic circuits. Pulse wires offer bounce-free and wear-free switching and produce voltage pulses which, in contrast to passive flux density sensors, supply a constant high signal even at low rotational frequencies. Another advantage is the wide temperature range up to +200°C for continuous operation. The above mentioned properties are particularly effective in rotational frequency sensors, code cards and anti-theft devices. A few of the examples are described in more detail in the following sections.

8.6.1 Rotational Frequency Sensors The construction of rotational frequency sensors with pulse and Wiegand wires is governed by the technical requirements and design specifications as well as the requirements on accuracy and pulse amplitude. The main designs can be classified as follows:

- A rotor with magnets drives a fixed sensor. - A ferrous vane rotor periodically interrupts the stray flux in a fixed arrangement consisting of magnets and a sensor.

- A rotor with wires is scanned by a read-head consisting of two magnets and a sensor coil. 8.6.1.1 Simple Revolution Counters Figure 8-21 shows a simple revolution counter with two rod shaped permanent magnets on a rotor where one magnet resets the sensor and the other triggers the pulse; this results in one pulse per revolution. As a rule, the pulse voltage depends o n the dimensions of the magnet.

332

8 Wiegand and Pulse-Wire Sensors

In all the previous descriptions of the properties of the sensors as given in Tables 8-2 to 8-4, the drive conditions assumed a homogenous magnetic field. However, in practice we are dealing with the inhomogenous fields of permanent magnets whose design influences the swit-

Figure 8-21. Schematic design of a simple revolution counter.

ching behavior of sensors. Figure 8-22 shows the influence of the dimensions of rod shaped magnets on the pulse amplitude and on the pulse initiation distance for a pulse wire MSE 590/003 from Table 8-3. The sensor was triggered by rod shaped magnets made of CROVAC" after resetting. To obtain full pulse amplitude the switching magnet must be slightly longer than the pulse wire, ie, in this case approx. 20 mm when the pulse wire is 16 mm long. With a magnet length of 12 mm, the pulse amplitude falls to approx. 60% because the field is then more inhomogeneous and only part of the sensor is remagnetized. In the examples presented here, the pulse initiation distance between the magnet and the wire increases almost linearly with the diameter of magnet and is in the range of 2 to 10 mm. Figure 8-23 shows sketches of two other very compact designs of revolution counters. In one, the sensor is driven in the axial direction by two magnets whereas the other has only one diametrally magnetized magnet. The revolution counters described so far produce a signal independent of rotational direction. However, in many cases the direction of rotation must be detected and, moreover, it may be specified that upon reversing direction no pulse is lost (dead angle due to hysteresis). In order to determine the direction, the pulse sequence of at least three sensors is required in contrast to Hall elements or field sensitive resistors where information on the direction is already supplied by two sensors with signals shifted by a phase angle of 90". Figure 8-24 shows a revolution counter which detects the direction using three pulse wires displaced by 120". Here, a reset magnet is placed on either side of the triggering magnet at an angle of 60". This ensures that on reversing the direction no pulse is lost through a pulse wire which is not reset. Such rotational actuators are, eg, used together with electro-mechanical resolvers to register the revolutions of an axle and, where necessary, independent of power supply, to ensure that the absolute position is always known. The pulses are registered by battery buffered evaluation electronics. The main field of application is in drive-motors for robots and tooling machines. A rotary actuator with several pulses per revolution as described above can be realized with two fixed magnets and a vane rotor which periodically shields the stray flux of the switching magnet (Figure 8-25). The sensor is reset in this position. When the vane rotor is set in motion again, the field of the reset magnet is released and the pulse triggered. This arrangement is characterized by its particularly simple and cost-effective construction.

8.6 Applications

1

333

1.2 1.0

I

I

I

-0 u

. I

a

f 0.8 n

O

5

'\

I

I I I

L

3u 0.6 n

I

u

f 0.1

I

d

u oz

0.5

1.5

1.0

Magnet diameter

2.0

mm

2.5

12 m mt .,...,,

- I,

/ I

T

6

1

Figure 8-22. Relative pulse amplitude and distance d, of pulse initiation vs. diameter and length I of the approaching set magnet; pulse-wire sensor MSE 5901003.

Figure 8-23. Two examples of a compact revolution counter.

2

0 ' 0.5

1.0

1.5 Magnet diameter

2.0

I

mm

2.5

334

8 Wiegand and Pulse-Wire Sensors

Switching magnet Reset magnet

Figure 8-24. Revolution counter detecting the direction of rotation.

Ferrous vane

Sensor

N

S

Figure 8-25. Tachometer using a ferrous vane rotor.

8.6.1.2 Incremental Rotary Encoders The following describes two types of rotary encoders with higher pulse frequency per revolution, ie, higher positional resolution. The two encoders have different constructions. In one, Wiegand wires are fixed to the circumference of the rotor with evenly spaced slots. The signal is produced and read by a fixed read-head containing a sensor coil as well as a triggering magnet and a reset magnet (Figure 8-26). This type DD 39 100 R 64 100 made by DODUCO,

Slot

05

Rotor

Figure 8-26. Incremental rotary encoder with Wiegand wires attached to the rotor.

8.6 Applications

335

Pforzheim, FRG, incorporates 100 Wiegand wires, each 20 mm long, on an aluminium rotor with a circumference of 200 mm, ie, in this case the positional resolution is 2 mm. The maximum resolution possible for this system is 1 mm. Amplified by a soft magnet core, the sensor coil detects part of the change in flux in the wires caused by remagnetization through the magnets. Appropriate design of the magnets and positioning of the sensor coil results in bidirectional read-heads supplying signals of opposing polarity for the two directions of rotation and unidirectional heads which only emit pulses in one direction of rotation. The latter require a second read-head to detect direction. Figure 8-27 shows a typical pulse sequence of this rotary encoder. The fluctuations in the distance between the pulses have a maximum of 30%, equivalent to 0.6 mm error of graduation on the circumference. This can be attributed to the jitter and the actual scattering of the wires, see Section 8.6.3.

tFigure 8-27. Typical pulse sequence of the Wiegand encoder sketched in Figure 8-26.

Another constructional possibility for incremental rotary encoders is to fit switching and reset magnets to the rotor which drives a cassette with several pulse wires (Figure 8-28). The example shows the construction of a rotary encoder with 120 pulses per revolution. Here 40 alternately poled magnets produce an AC field along the circumference with a period of 18", which is divided by six pulse wires each at an angle of 3". This type of pulse multiplication using several wires is required to achieve higher resolutions, because due to mutual attenuation the magnets must maintain a certain minimum distance. In case of longer leads to the evaluation electronics, the addition of the signals of the individual coils onto one lead is advised, eg, via diodes. Together with the directional detection, only three other leads are required apart from ground. In contrast to the system using a read-head and rotor with Wiegand wires, the pulse amplitude and the pulse energy are used to the full, due to the perfect coupling of pulse wire with sensor coil. In this way an appreciably higher degree of reliability against interference is achieved which is expressed in the source resistance. For read-heads this is, for example, 2 kn for a minimum signal of 0.5 V, as opposed to this wound pulse wires only achieve about 100 SZ. Since the pulse wire systems presented in Figure 8-28 only require a few sensor wires, their actual scattering can be satisfactorily limited resulting in higher accuracy. The limit for positional resolution is roughly 2 mm due to the specified windings. The fluctuation in the distances between the pulses is then maximum 20070, equivalent to 0.4 mm error of graduation on the circumference.

336

8

Wiegand and Pulse-Wire Sensors

Cassette with pulse wires

Coupling by diodes

i

u 1 4

n

1 1 2 3

Direction o f rotation

u

44

i t

1 6 5 6 3 2

AAAAAA

t

Figure 8-28. Incremental rotary encoder using pulse wires; set and reset magnets are mounted on the rotor.

8.6.2 Code Cards and Special Applications Wiegand wires can be used to store binary coded digits on a code card by arranging wires in two parallel grids in a plastic card [12]. A wire in the first grid represents for example logic “0” for this bit, and correspondingly in the second grid logic “1”. The card is read by feeding it past a read-head consisting of magnets and a sensor coil, this differentiates between the pulses reading “0” and “1”. These cards are used in check-in control systems as passes. They cannot be forged and are insensitive to magnetic interference fields. The number of bits corresponds to the number of grid places and is for example 65536 combinations for 16 bits.

331

8.6 Applications

Certain anti-theft security systems use thin, soft magnetic strips and wires which emit a detectable signal on passing through a security gate with an AC field, and trigger an alarm. TO avoid false alarms being triggered by other magnetic objects, the security tag must emit a characteristic signal. Materials with an extreme rectangular hysteresis loop whose signal contains a specific amount of higher harmonics are particularly suitable for this purpose. At the same time, the application calls for low coercivity so that the “gate” can be operated with a minimum of field. Amorphous strips and wires (Section 8.5) and the pulse wires with low switching field strengths described in Section 8.4.2 are ideally suited to this application. The prime advantage of using pulse wires is that the tags which are usually 80 mm long can be shortened to ca. 15 mm. Moreover, the permanent-magnetic component allows the security tag to be deactivated. Another interesting method for providing interference-free transmission of signals from Wiegand and pulse-wire sensors is to trigger an infrared diode directly (Figure 8-29) and then guide the signal via a light wave conductor. When the sensor winding is ideally matched to the diode (power matching) distances of at least 10 m can be bridged.

?Or

Figure 8-29. Signal transmission by light wave conductor LWC; T phototransistor.

H-

I

IR- Diode

1

8.6.3 Jitter Some technical applications, like incremental rotary encoders (Section 8.6.1.2), require a reproducible, stable switching field strength H , at which the pulse is triggered. Due to physical phenomena, individual examples also exhibit fluctuations AH, in the switching field strength and pulse amplitude during different remagnetization cycles, these are referred to as jitter. During AC-field magnetization, jitter is apparent as fluctuations in the time-span between the pulses. In this case for AH, and the fluctuation Ats in the point of switching time the following applies (Figure 8-30): AH5 =

(z)

(8-12)

At5

1s

with H = H sin(w . t ) we obtain

-1

AH, = w

*

At,

.

(8-13)

In practice permanent magnets are mostly used for excitation. Here we are concerned with the positional deviation Ad, of the switching point d, which is obtained from the jitter AH5

338

8 Wiegand and Pulse-Wire Sensors

and the field gradient dH/dx of the drive magnet according to (8-14)

Figure 8-30. Jitter AH, of the switching fieldstrength H, and related time jitter Ats in a sinusoidal drive field.

Figures 8-31 and 8-32 show the typical statistical variation AH,, ie, twice the standard deviation of the switching field H, for one example of a Wiegand sensor and one pulse wire sensor as a function of reset field H R and the field amplitude H , respectively. With reset fields up to 18 A/cm the jitter of the Wiegand wire only is approx. 0.15 A/cm, but with increasing reset field it passes through a steep maximum with values up to 3 A/cm. The statistical variation of the pulse amplitude exhibits similar characteristics. Both the pulse wire types presented in Figure 8-32 reveal that the course of the jitter AH, is almost independent of excitation, and that the level for the pulse-wire type with higher pulse voltage is approximately four fold.

0

10

20 -HR

30

40 Alcm 50

Figure 8-31. Jitter AH, of a Wiegand wire against reset field H R ; set field 120 A/cm.

8.7 References

339

0.8 A/cm

I

0.6 0.L

t

7

tt

MSE 590l003

AH,

0.2

0

-I

MSE 590l007 2o

Lo

6o

4-

A’cm

loo

Figure 8-32. Jitter AH, for the two types of pulse wires against field amplitude H ;f = 50 Hz.

8.7 References [l] Preisach, F., “Permeabilitat und Hysterese bei Magnetisierung in der energetischen Vorzugsrichtung”, Phys. Z. 33 (1932) 913-923. [2] Sixtus, K. J., Tonks, L., “Propagation of large Barkhausen discontinuities I”, Phys. Rev. 37 (1931) 930-958. [3] Sixtus, K. J., Tonks, L., “Propagation of large Barkhausen discontinuities 11”, Phys. Rev. 42 (1932) 419-435. [4] Doring, W., “Uber das Anwachsen der Ummagnetisierungskeime bei grol3en Barkhausen-Sprungen”, 2. Phys. 108 (1938) 137-152. [5] Wiegand, J. R., “Switchable magnetic device”, US Patent 4247 601, 1981. [6] Gevatter, H. J., Kuers, G., “Wiegand-Sensoren fur Weg- und Geschwindigkeitsmessungen”, Tech. Mess. 51 (1984) 123-129. [7] Rauscher, G., “Sixtus-Tonks experiments on strand annealed 49Co-2V-Fe wires”, IEEE nuns. MAG-21 (1985) 1930-1932. [8] Radeloff, C., Rauscher, G., “Pulse generation with short composite wires”, IEEE nuns. MAG-21 (1985) 1933-1935. [9] Rauscher, G . , Radeloff, C . , “Impulsdr~hteals magnetische Geber fur Bewegungs- und Feldsensoren”, Siemens Forsch. EntwicklungsbeK 15, No. 3 (1986) 135-144. [lo] Kneller, E., Ferrornagnetismus, Berlin: Springer-Verlag, 1962. [ll] Chikazumi, S., Physics of Magnetism, New York: Krieger, 1978. [I21 Kuers, G., “Theorie und Praxis der Wiegandsensoren”, Der Konstrukteur 1 (1983). [13] Bozorth, R. M., Ferromagnetism, Princeton: van Nostrand, 1951. 1141 Warlimont, H., Proc. 6th Int. C o d Rapidly Quenched Metals (RQ6), Montreal 1987, in press. [15] Mohri, K., Humphrey, F, B., Yamasaki, J., Okamura, K., “Jitter-less pulse generator elements using amorphous bistable wires”, IEEE Trans. MAG-20 (1984) 1409-1411.

9

Magnetoresistive Sensors UWE DIBBERN. Philips Forschungslaboratorium. Hamburg. FRG

Contents 9.1 9.2 9.2.1 9.2.2 9.2.3 9.2.4 9.3 9.3.1 9.3.2 9.4 9.4.1 9.4.2 9.4.2.1 9.4.2.2 9.4.2.3 9.4.3 9.4.3.1 9.4.3.2 9.4.3.3 9.4.4 9.4.5 9.4.6 9.5 9.6 9.7

. . . . . . . . . . . . . . . . . . . . . . . . . . . Sensor Fundamentals . . . . . . . . . . . . . . . . . . . . . . . The Anisotropic Magnetoresistive Effect . . . . . . . . . . . . . . . Magnetization of Ferromagnetic Thin Layers . . . . . . . . . . . . . Magnetization under External Fields . . . . . . . . . . . . . . . . Stabilization of the Characteristic . . . . . . . . . . . . . . . . . . The Magnetoresistive Sensor . . . . . . . . . . . . . . . . . . . . Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensitivity and Measuring Range . . . . . . . . . . . . . . . . . . Sensor Fabrication . . . . . . . . . . . . . . . . . . . . . . . . Magnetoresistive Materials . . . . . . . . . . . . . . . . . . . . . Fabrication Techniques . . . . . . . . . . . . . . . . . . . . . . Magnetoresistive Layers . . . . . . . . . . . . . . . . . . . . . . Contact and Passivation Layers . . . . . . . . . . . . . . . . . . . Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . Sensor Layout . . . . . . . . . . . . . . . . . . . . . . . . . . General Considerations . . . . . . . . . . . . . . . . . . . . . . Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . Layout of Special-Purpose Sensors . . . . . . . . . . . . . . . . . Generation of Auxiliary Fields . . . . . . . . . . . . . . . . . . . Data on Magnetoresistive Sensors . . . . . . . . . . . . . . . . . . Comparison with Other Magnetic Sensors . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction

342 342 342 344 344 348 350 352 354 356 356 360 360 361 362 363 363 367 369 370 373 375 376 378 378

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

342

9 Magnetoresistive Sensors

9.1 Introduction Magnetoresistive sensors are made from thin films of ferromagnetic transition metals. They belong to a family of sensors which show a high degree of sensitivity through the exploitation of the high internal field inherent in ferromagnetics. Since the parameter influenced by the fields is electrical resistance, signal evaluation is achieved through simple electronic means. These sensors apply an effect discovered more than 130 years ago [l]. However, over 100 years elapsed after its initial discovery before it could be put into practical use. Modern microelectronic technology, especially thin-film techniques, gave the breakthrough which enabled application of the magnetoresistive effect whilst at the same time an increased demand for miniaturized solid-state elements able to convert digital information stored in magnetic bubbles or disks appeared [2-71. Although a sensor giving an analog, field proportional signal had been described very early in [8],it was many years later before sensors intended for industrial use entered the market [9, 101. In recent years, a lot of literature has appeared expanding on the fundamental details and technological advances in the field (as far as possible only papers in English will be cited) [ 11 -201. The net result of this is that magnetoresistive sensors available now are low priced and well suited for the mass market; they will work properly even under severe environmental conditions, eg, in motor cars, yet they can also be used in many applications which require high sensitivity and low-power consumption.

9.2 Sensor Fundamentals The theory of the magnetoresistor seems at a first glance to be laborious as it must take into account complex ferromagnetic behavior. There are, however, a number of facts which can simplify the description of their behavior: Firstly, the magnetization M in ferromagnetics always has the value of saturation magnetization M, - only its direction may be altered; secondly, it is possible to divide the problem into two simpler ones, namely the relation between resistance and magnetization direction and the relation between external fields and the magnetization direction.

9.2.1 The Anisotropic Magnetoresistive Effect The electrical resistivity of solid-state conductors is influenced by magnetic fields in several ways [21]. Firstly, there is a contribution connected with the (ordinary) Hall effect and hence caused by the Lorentz force. It is dependent on geometry (disappearing in a long slab and achieving a maximum, for example, in the Corbino disk). This resistance change is proportional to 01 . B ) * where p is the electron mobility and B is the flux density. It may be disregarded in metals due to their low electron mobility.

9.2 Sensor Fundamentals

343

The second contribution is caused by special band bending at the Fermi surface and is also proportional to B 2 . It is found in nonferromagnetic metals and semimetals; the highest effects have been measured with bismuth. The third effect, the anisotropic magnetoresistance - or magnetoresistive effect - is found in ferromagnetic transition metals and must be explained in more detail as it is the effect utilized by the magnetoresistive sensors covered in this chapter [5, 71. The specific resistivity p is dependent on the angle 6 = q - v/ (see Figure 9-5) between the internal magnetization M and the direction of current I. With p = pIlfor 0 = 0" and p = pl for 6 = 90" it holds that: p (6) = pl

+ (011 - p,)

COS'

6 = pl

+ Ap

*

COS'

6.

(9-1)

The quotient Ap/p, is called the magnetoresistive effect; it is positive in most cases and may amount to several percent [6]. The physical origin of this effect can be traced to the different shifts of energy levels for electrons with positive and negative spins under the influence of magnetic fields. This alters the density of states at the Fermi level [5, 71. Theorists have not succeeded in calculating the effect to better than an order of magnitude, so all data must be determined empirically. Another effect connected with the anisotropic magnetoresistance should be noted here. As the specific resistance p is not a scalar quantity, it gives rise to an electrical field Ey perpendicular to the external electrical field Ex causing the current density j x ;Ey is perpendicular to j but in thej-M-plane (which is normally the plane of the ferromagnetic layer), thus:

Ey = j,

- Ap . sin0 . cos0.

(9-2)

This effect is called the planar (or pseudo or extraordinary) Hall effect as it resembles the normal Hall effect. These two Hall effects should not be confused as they differ totally in terms of spatial relations, suitable materials, and physical origin. It is common practice to consider the quotient A p / p when dealing with the magnetoresistive effect. However, it may be advantageous to consider the terms Ap and p individually when looking for influence of external factors on Ap/p. This will be explained below. Instead of using the specific resistance p, the resistance R shall be considered. In a bar of length I, width w,and thickness t with a current I flowing in the direction I, it may be deduced from Equation (9-1) that: C O S = ~ R ~

+ AR

*

C O S ~ ~

(9-3)

and the voltage drop Ux becomes:

ux

=

PI

.

(9-4)

This drop, especially its field-dependent part, may be compared with the planar Hall voltage Uy calculated from Equation (9-2): 1

U y =A p . I - - s i n O . c o s O . t

(9-5)

344

9 Magnetoresistive Sensors

Comparison of Equations (9-4) and (9-5) shows two main differences between the terms depending on 8: - The magnetoresistive voltage drop Ux does not depend on the sign of '6 (the term is squared), whereas the Hall voltage Uy does. - The ratio of their signal swings is I/w; the magnetoresistive signal will be higher as the designer normally makes I %- w. The planar Hall effect therefore will be employed in sensors with small dimensions only and used for measurements requiring high spatial resolution, eg, with the fields of magnetic disks [22].

9.2.2 Magnetization of Ferromagnetic Thin Layers All ferromagnetic materials have a high internal magnetization due to quantum mechanical exchange coupling which orientates the electron magnetic moments in parallel. However, without external fields, this parallelism is only preserved in small areas, known as domains. Domains with different directions of magnetization are separated by walls with gradually rotated spins. In bulk material, the directions of magnetization may point in all space directions, whereas single crystals have preferred magnetization directions along specific crystal orientations (eg, parallel (111 ) in nickel). Ferromagnetic thin films differ from bulk materials in that their thickness is small compared to usual domain lengths. In soft ferromagnetic metal films, the films which are of interest here, this restricts the magnetization such that it lies in the film plane. This is true even for the magnetic moments in the walls between domains, leading to the creation of alternative wall types to those found in bulk materials [3, 231. The simple theory, given first, describes the magnetic behavior of a single domain. It will be explained thereafter, why a real layer is more complex and conditions discussed that will force the single domain state necessary in most sensors.

9.2.3 Magnetization under External Fields Besides the confinement of the magnetization into the film plane in soft ferromagnetic films, there are further preferred directions due to a number of anisotropies. The first term is the magnetization anisotropy or more correctly, crystal anisotropy. In a similar manner to bulk material, where M has lowest energy along certain orientations, there is one axis of lowest energy, called the easy axis (e.a.). A second term is form anisotropy caused by different demagnetizing fields in different axes. A third contribution caused by mechanical stress can be disregarded here; it disappears if the magnetostriction coefficient h of the layer is zero which happens to be the case in most sensor materials (Section 9.4.1). The rotation of M under influence of an external field H may be calculated by the wellknown Stoner-Wohlfarth theory [24], modified for finite films. The basic idea is to calculate the energy density u as a function of the angle a,, which is the angle between M and e. a.; the equilibrium value of a, is that with lowest u [3, 251. Figure 9-1 gives the geometry: the film has an elliptical shape with the e.a. along one of its axes. Three contributions to u will be taken into account.

9.2 Sensor Fundamentals

345

Figure 9-1. Geometry of a thin film of elliptic shape; the easy axis (e.a.) is supposed to be the major axis (= x-axis).

1. The field energy:

2. The anisotropy energy given by:

uk = k . sin2 a, which only contains one term as there is only one e.a.; k is a material constant.

3. The demagnetizing energy due to creation of free poles at the edges. These poles are described by the demagnetizing field Hd which is homogeneous in ellipsoids and is given by: Hd,, = -N,

*

M, = -N,

*

M * cos

Hdy = -Ny. My = -Ny. M

*

V,

sin a,

N,, Ny and N, (not used here) are the demagnetization factors; they are dependent on the three axes and N, + Ny +NZ= 1. Both fields contribute to the demagnetization energy ud and with Ny - N, = N i t holds that:

ud

=

112 . N,

=

1/2 . N . M . sin2 a,

M 2 . cos2 a,

+ 1/2 Ny . M 2 . sin2 a,

+ 1/2 N,

M2.

(9-10)

It should be noted that demagnetization will not be angle dependent with circular shapes, as then N, = Ny. The total energy density u is the sum: u = k

. sin2 a,

+ 1/2

N M 2 . sin2 a,

+ 1/2 . N, . M 2 - Ha M a cos ( y

- a,).

(9-11) Instead of using k , the anisotropy is usually given by the anisotropy field Hk, which is, of course, also material dependent: Hk = 2

*

k/M.

(9-12)

346

9 Magnetoresistive Sensors

Furthermore, Hk may be combined with Hd = -N

. M to give the characteristic field H,:

Substituting (9-12) and (9-13) in (9-11) results in the sum:

-

u = 112 . H, . M

sin2 a, - H M

. cos ( y -

a,)

+ 1/2 . N,

M.

(9-14)

This equation differs from the known theory-derived version only in the replacement of Hk by H , and in the third constant term - the conclusions of the Stoner-Wohlfarth theory still remain valid. M takes that angle a, with the lowest energy u, calculated by differentiating u with respect to a, and setting the derivative to zero, giving: sin a, =

-

H . sin y

H,

+H

*

cos

This equation is valid for - 1

HY

H,

Y/COS V,

< sin a, <

+ H,/COS

(9-15) '

1, otherwise sin a, = f l .

The most simple case occurs when H, = 0 : M will be rotated fully into the hard direction (a, = f 9 0 " ) when IHyI ZH,, but smaller fields will rotate M less than 90", as given by

(9-15). The result when H, # 0 seems to be more complicated, but since I a, I < 30" in practice, it appears worse than it actually is. The factor l/cos a, may be taken as 1 in most cases so that H, adds to the characteristic field Ho. Otherwise, if the sensor is driven by high fields such that H, s H,, Equation (9-15) simplifies to tan a, = H y / H , = tan y

(H,

S

Hk).

(9-16)

The magnetization and external fields are in parallel but the sensor measures the direction y of the field only, and not its magnitude.

The total permissible rotation of the magnetization is restricted to less than 90" if ambiguity cannot be tolerated. This fact follows on from Equation (9-1) or (9-2) (which have dependencies of cos 28 or sin 213) by replacing I3 with p - iy (w is the angle of current direction and has a fixed value). Usually a, is varied as +30". So far it is not proven that the extremum found by differentiating (9-14) is really a minimum; this can be tested, however, by taking the second derivative of u with respect to a,. In following the idea used by Stoner and Wohlfarth looking where this second derivative disappears, one can separate areas where u is minimum from those where it is maximum. Setting both derivatives to zero and eliminating a, gives: IH,I

2/3

+

IHyI 'I3 = H02/3.

(9-17)

Equation (9-17) describes the Stoner-Wohlfarth astroid, shown in Figure 9-2. This astroid may be used for construction of the permitted solution for a,: the external field vector H is drawn and (dashed) a tangent taken from its tip to the astroid - the angle of this tangent is the angle a, of M. There are two tangents possible if H lies inside the astroid, called a,1 and

9.2 Sensor Fundamentals

347

p2 (see H in the first quadrant), but only one solution p' for fields H' outside the astroid (drawn in the fourth quadrant for distinction).

Figure 9-2. Field relations in the Stoner-Wohlfarth astroid. The (dashed) tangent from the field vector H to the astroid gives the direction of magnetization M . A vector inside the astroid gives two solutions (with angles rp, and qZ), but a vector H' outside has only one: p'.

The two solutions of M have different signs for their x-component M,; M has to switch if H goes outside the astroid and the former sign of M, is then no longer valid. This theory may also be used to calculate the magnetization or hysteresis curves (the MH-diagram), a feature often used to characterize magnetic materials. Figure 9-3 shows the two most important examples (although others are found, eg, in [25]). M is measured parallel to H along the easy axis or the hard axis, respectively. Along the e. a. (Figure 9-3 a) M has only two stable values M = k M,. Theory forecasts switching for H = f Ho (or f Hk for probes with circular shape) shown as the dashed line in the figure; however, experiments show that the switching occurs at a lower field H,, the coercivity (the better the layer quality, the lower the ratio HJH,,). In contrast, Figure 9-3 b shows H and M in the hard direction: the relation is linear for I HI < Ho (or Hk),but otherwise M = M,; this is confirmed by experiment and thus allows measurement of Hk.

Figure 9-3. Magnetization curves parallel to the easy axis (a) and to the hard axis (b); directions of the hysteretic curve in a) are given. The dashed lines in a) are the theoretical curves, the solid ones are the experimental curves.

Up to now it has been assumed that the e.a. was the main axis of the ellipsoid. It is necessary now to discuss what happens if there is an angle E between the e.a. and the main ellipsoid axis. It has been shown [26] that this problem can be handled using new coordinates

348

9 Magnetoresistive Sensors

5 from x and y. This will restore Equation 9-14 (with the addition of an irrelevant constant) such that:

x' and y', rotated an angle

tan 26 = Hk * Sin 2&/(Hd+ Hk *

COS

2&)

(9-18)

with a characteristic field (9-19) All conclusions drawn then from (9-14) remain valid. There are three cases of interest to be discussed: 1.

E

e

1:

tan 25

< tan 2 ~ H;, = Hd

+ Hk.

(9-20)

Small variations of the e. a. (for example, due to misalignment during processing) may be disregarded. 2.

E

= 90": tan (90' -

E)

P tan (90" - 0; Ho = IHd - H k l .

(9-21)

An e. a. along the minor ellipsoid axis reduces the characteristic field, however, small variations in the angle may give rise to larger variations in the coordinate system if Hk = H d . 3.

&

= 45": (9-22)

This last case is of special interest as will be shown later. The rest magnetization M,, ie, M without external fields, can be rotated by slanting the ellipsoid axes against the e.a., a technique that is used in sensor construction. Other angles which are of additional interest, must be calculated using Equations (9-18) and (9-19).

9.2.4 Stabilization of the Characteristic The demands imposed by proper functioning of magnetoresistive sensors lead to restrictions on the external field. These will be explained initially with the aid of the theory given, however, the rationalization must be modified afterwards to account for deviations from the single domain state. Most sensors require that M always exists in only one of its two states, say M, 3 0 or -90" < < 90". It follows from Figure 9-2 and the explanations given in the text that

9.2 Sensor Fundamentals

349

M, 0 for H outside the right wing of the astroid, and that this state is maintained as long as H does not touch the left wing. A correct start may be forced, for example, by a short field pulse with H, > Ho. Unfortunately, these conditions are insufficient: The restrictions on external fields must be tightened in order to create a stable characteristic. It has been shown by experiment that the magnetization may divide into several domains [27]. This situation is caused by the high field energy of a single domain and by unavoidable imperfections in the layer which favour the creation of domain walls. The effects are twofold: For energetic reasons, adjacent domains may have different signs of M,, so destroying the sensor signal. Secondly, domain walls can move and domains may even switch under external fields, thus the signal is impaired by “Barkhausen” noise. The theory surrounding these effects [28, 291 is commonly known as the ripple theory [3]. The magnetization is said to have a ripple, that is a more or less periodic variation of its direction: The local direction varies around the mean value a, calculated above. The angles a,, or a,,, which include 90% or 50% of M around a, respectively, are determined experimentally. Thus by simple conclusion, the mean value of a, must be lower than 90” - ago,in order that the rotation remains below 90” even locally. The ripples are ascribed to local variations of Hk and of the e.a. Theoretical treatments [28, 291 have successfully introduced internal stray fields which may “block” the magnetization. These stray fields are calculated taking into account exchange coupling which causes magnetization dispersion, and different orientation of crystallites. Blocking by stray fields hinders free rotation of M which is then registered by hysteresis in the characteristic. The field relations are explained best by the blocking curve shown in Figure 9-4: the dashed curve (a) is the left wing of the astroid and the single domain theory “allows” all H-vectors to the right of (a). The ripple theory restricts the permissible area to the right of the blocking curve, eg, (b). M will be blocked if the tip of H touches the blocking curve and cannot be rotated back until H i s to the far right of the blocking curve. It can be seen that blocking can occur for certain values of Hy even with positive H,.

Ah,

Figure 9-4. Restrictions for field vectors given by the blocking curve. The dashed curve (a) is the Stoner-Wohlfarth astroid, the solid curves (b) and (c) are two different blocking curves. Only field vectors to the right have a reversible field-magnetization-behavior. Magnetization becomes blocked if the vector tip touches the blocking h ;x curve. The fields given are normalized to Hk:eg, h, = H x / H k ;demagnetization has not been taken into consideration (taken from [28]).

I

00

-9

-1.0

-0.6 ha&)-1

-0.2 0 0.2 0.4 ha(k1-l

350

9 Magnetoresistive Sensors

In using a magnetoresistive sensor then, the operator must guarantee that H is always to the right of the blocking curve (or at the left of its mirror image if M, < 0), otherwise the characteristic may become unstable. It is sufficient, but not always necessary, to have H, higher than a certain minimum. Data must be determined by experiment or checked from the data sheet. An example of sensor characteristics, showing the effect of a stabilizing field, is given in Figure 9-11. The actual position of the blocking curve depends on film quality: a good one would be that described by curve (b) in Figure 9-4, not too far from the astroid, whereas the curve described by (c) belongs to a film unsuitable for sensing applications. Film quality is essentially determined by deposition parameters (especially crystallite diameter, oxygen content, and surface smoothness). Most of these parameters can be summarized in the structure constant S [29] (not to be confused with the sensitivity).

9.3 The Magnetoresistive Sensor The basic element of all sensors is a film (thickness: t ) f a magneto :sistive alloy etched into a rectangular shape (length: 1, width: w) as shown in Figure 9-5a. Electrodes are attached at both ends in this example causing the current Z flowing parallel to the easy axis. Usually the geometry is chosen to make I > w & r.

- I-

C)

I

x

e.a.

Figure 9-5. Geometries of magnetoresistive sensors. White rectangles (length: I, width: w, thickness: t ) are the magnetoresistive layers, hatched parts are electrodes of much better conductivity. a) is the simplest geometry: the current I flows parallel to the e. a., resulting in the square characteristic. b) and c) show linearized sensors due to inclined elements or to barber poles; the current is rotated out of the e.a.

351

9.3 The Magnetoresistive Sensor

The material is characterized by the anisotropy field Hk and the geometry must be described by the demagnetizing field H d . The long, flat rectangle is a good enough approximation of an ellipsoid to allow calculation of the demagnetizing factor: N = t/w

(9-23)

with sufficient accuracy. N may be chosen within a wide range simply by varying width and thickness, as long as N 6 1. Demagnetizing fields perpendicular to the layer plane (N, = 1 -N,-N, = 1) are very large, to the extent that normal field strengths will not elevate M out of the layer plane, a fact that was made use of earlier. As the ellipsoid shape is only an approximation, there are deviations from the assumed homogeneous demagnetizing field. M is rotated less in the upper and lower edges than in the middle of the stripe; the sensor signal is given by a mean value of q. This heterogeneous rotation is the reason for differences between the calculated and measured sensor characteristic at higher fields (see Figure 9-13). The sensor resistance R can be calculated using Equations (9-3) and (9-15). Furthermore, with 0 = q, (ty = 0), having H, = 0 and abbreviating R , + A R = Rb, then:

R ( H ) = Rb - A R (H,/HO)’.

(9-24)

In the same manner, it is possible to calculate the signal of the planar Hall effect starting with Equations (9-5) and (9-15):

U,

=

A p * Z * (l/t)

*

H,/Ho

*

1/1- (H,/H0)’

.

(9-25)

H, must be replaced in both equations by H, + H,/cos p if H, # 0. Both curves are drawn in Figure 9-6: the (dashed) parabola of the magnetoresistive effect and the solid curve with a linear center, representing Equation (9-25), which describes both the barber-pole sensor as well as the planar Hall effect.

Figure 9-6. Calculated characteristics of the simple magnetoresistive sensor in Figure 9-5 a (dashed) and the barber-pole sensor (solid) in Figure 9-5c. The solid curve also represents the characteristic of the planar Hall effect, only the ordinate caption needs to be altered.

I

-1

I

-0,s

I

I

I

0

0.5

1

L

352

9 Magnetoresistive Sensors

Equation (9-24) establishes a square relationship between magnetic field and resistance, whereas (9-25) contrastingly describes a symmetrical S-shaped curve with a linear center part; the linearity error may be made small when only small fields are involved since there is a point of inflection at Hy = 0. It is necessary to remark upon the two possible states of magnetization that can exist, discussed for H, = 0. The calculation of the magnetoresistive signal (9-24) was straightforward - both solutions, pl c 90" and pz = 180" - p,, give the same resistance (depending on the sine and the squared cosine). The signal of the simple magnetoresistor does not depend on the state of magnetization. This does not hold for the planar Hall effect - the calculation of Uyrequires sine and cosine, but the sign of the cosine is different in both solutions. The planar Hall effect transducer thus alters the sign of its signal if the magnetization switches from one state into the other. Correct operation requires that only one of the states is maintained. It has been discussed above that domain splitting and wall movement may occur unless precautions (certain fields with H, > 0) are taken to ensure the desired state of magnetization. The simple magnetoresistor does not require these precautionary measures to secure a correct characteristic - but it will suffer from magnetic noise if these fields are not applied. It is important now to consider what possibilities for linearization of the parabolic fieldresistance relationship exist, and it will then further be discussed whether it is possible to obtain linearized relationships, with positive and negative slopes, for the field dependence of R. A procedure that can yield both signs is advantageous as it allows cancellation of the constant (but temperature dependent) part by combining four, or at least two, elements with different slopes in a Wheatstone bridge. If necessary, a distinction will be made between the single resistor, called a sensor element, and the sensor circuit or sensor bridge consisting of four or two elements.

9.3.1

Linearization

It can be said generally that the square characteristic is caused by the parallelism of magnetization M and current Z without external fields. Linearization can be achieved by either rotating M or by rotating I in this rest state. The simplest way is to rotate M by addition of a constant bias field HB in the y-direction [ll]. Replacing Hy in (9-24) by Hy + HB yields: R ( H ) = Rb

- 2 * A R * Hy * H B / H i - AR (H:

+ H;)/Hi,

(9-26)

which is linear for Hy 4 H,. Unfortunately, this method demands a stable bias field as each variation of H , appears as a variation in the signal H y ; moreover, different slopes require different signs of H s imposing additional difficulties. Methods for introducing additional fields will be discussed later. A bias-linearized sensor will still work well in both magnetization states, although magnetic noise may be present. An alternative way to achieve linearization is by rotation of the current Z through an angle v/ against the e.a. Figure 9-5b gives one of the two solutions known.

9.3 The Magnetoresistive Sensor

353

The rectangular resistive element is inclined at an angle v/ to the e. a. with the current still flowing along the stripe axis [8, 91. The figure shows both of the two possible inclinations. The rest magnetization M, is partly rotated from the easy axis to the stripe axis (see Equation (9-22)) as drawn. It is necessary to force one of the magnetization states by a stabilizing field having the easy direction and this field will, of course, further influence M,. The signal can be calculated by setting 0 = a, - v/ and using Equations (9-3), (9-15), and (9-22). The result is more complex than other cases unless the angle a,, - v/ between M, and I is chosen to be 45 ". This will simply create a term sin (a, - a,,) cos (a, - a,,) as seen in the discussion of the planar Hall effect. The slope of the R-H-dependence can be adjusted by the sign of the inclination - see the two examples in Figure 9-5 b. A Wheatstone bridge can then be realized without any problems. The designer must pay for this advantage however, as the linearized sensor must always be driven in the same state of magnetization stabilized by a field with H, > 0. The inclination angle v/ is chosen by most designers to be +45" [8,91, but steeper inclinations have been reported, too [30]. Different slopes of characteristics can be attained not only by different inclination, but also by the application of positive and negative stabilizing fields to elements with equal current directions [31, 321. This more complicated technique reduces the sensor's sensitivity to asymmetries caused by misalignment, lithographic errors, and to strain gauge effects (which are even present in nonmagnetostrictive materials) since the current flows in the same direction anywhere in the sensor. The second means for rotation of current is the application of slanted stripes of good conductivity as shown in Figure 9-5c [12]. This arrangement is usually termed barber poles because it looks like the well-known sign for barber shops. The barber poles represent a short circuit - the current flowing in the gaps between them will therefore take the shortest path, i. e. perpendicular to the barber poles. If the current inclination is v/, the barber poles will be inclined v/ +90" (this will be modified when edge effects are considered later on); normally I// = +45" will be chosen. The field-resistance relationship can be calculated; with v/ = *45" it yields:

*

R (H) = R, f AR

*

(Hy/H,)

1/1

- (H,/Ho)~

.

(9-27)

This is represented by the solid characteristic in Figure 9-6 which shows good linearity for Hy < 0.5 H, (error 5 5 % ) . Calculation is much simpler than for the inclined element because the ferromagnetic rectangle exhibits the same magnetic behavior as the rectangle in Figure 9-5 a, discussed in detail above. The barber-pole sensor will, like most of the linearized sensors, only function properly in one magnetization state. Switching of M results in the adaption of the other sign of the slope. There is one disadvantage to the barber-pole sensor: its resistivity per unit area is smaller since firstly, its area is partly short-circuited and secondly, the current path is broader, although it is shorter in the gaps between. A Wheatstone bridge can be built of elements with positively and negatively inclined barber poles, and it should be noted that the method utilizing positive and negative stabilizing fields is also applicable.

354

9 Magnetoresistive Sensors

9.3.2 Sensitivity and Measuring Range The quantity actually measured by the magnetoresistive sensor is the magnetic field strength H - in contrast to normal Hall sensors which respond to the flux density B. In a vacuum (and to a good approximation in all non-ferromagnetic materials as well), H a n d B are related by B = po . H with the magnetic field constant p0 = 4 n 10 V s/A m. The sensitive axis is, with few exceptions, the hard axis or y-direction. Sensitivity in the easy or x-direction is lower, sensitivity to fields H, perpendicular to the film plane is negligible due to the large demagnetizing field. The sensitivity So can be defined as the variation of the output voltage Uswith the field variation related to the operating voltage Uo,thus:

-’

So = (AUs/AHy) * l / U , ,

(9-28)

to be measured in (mV/V)/(kA/m). Some authors define a different sensitivity S, = So . Urn,,, where U,,, is the highest permissible operating voltage. So is of significance in linear sensors only, ie, if So is not dependent on the field. For the purposes of example here, the sensitivity for barber-pole sensors will be derived; they are linear and their magnetic behavior is easily calculated. The sensitivity of sensors with inclined elements does not differ markedly, but they may have a lower linearity range. It will be assumed further that the sensor is a full-bridge circuit; half bridges have only half the sensitivity. The calculation begins with Equation (9-27) which gives the field-resistance relationship of a single barber-pole element. The full bridge is a combination of four elements, each adjacent one having a different sign. This full bridge sensor has the signal:

Us= Uo * Ap/p * (H,/(HO

+ H,))

*

fl

- (Hy/(Ho + H,))’

(9-29)

and for Hy 4 Ho + H, the sensitivity becomes

Equation (9-30) shows the importance of the characteristic field H,: the sensitivity So is reciprocal to Ho for H, = 0. A field H, > 0 will decrease So, and So is proportional to the magnetoresistive effect Ap/p. A second quantity describing the sensor is the measuring range H, - which can be defined as that field range within which the linearity error will not exceed a certain limit. Taking barber-pole sensors (or planar Hall-effect devices) and a limit of 5% it holds that: HG

0.5 (Ho

+ H,)

(9-31)

Other sensor types, eg, those with inclined elements may have narrower linearity ranges depending on the bias field, H,, and the angle of inclination. Combining Equations (9-30) and (9-31) results in the term:

9.3 The Magnetoresistive Sensor

So HG = 0.5 Ap/p

.

355 (9-32)

With the magnetoresistive effect Ap/p given as constant, the sensitivity can thus only be increased by decreasing the linearity range o r vice versa. The linearity range HG and the sensitivity So are primarily fixed by the designer of the sensor in their choice of thickness t and width w of sensor stripe. Taking t / w = 1/1000 . . . 1/10 and M, = 800 kA/m, this gives Hd = 0.8 . . . 80 kA/m; and with Hk = 0.25 kA/m (Permalloy) it follows that HG = 0.5 . . . 20 kA/m is given essentially by the demagnetizing field. The user may only increase HGby applying a field H, - and normally the designer demands and takes into account a certain H, in order to stabilize the characteristic. A high sensitivity can be achieved with a low characteristic field. One way is to induce the e.a. perpendicular to the long stripe axis (usually the hard direction) and ensure that Ho = IHd - Hkl , according to Equation (9-21). Ho may be made very small if Hd = Hk, but then the relative error in Ho becomes much higher than that in H k , which itself depends considerably on process conditions. A better way is to use a system which depends only on Hkby ensuring Hd Q H k , which can be achieved by making I = w, using the given formulas. However, sensors such as this would have a very low resistance and so be unsuited for most applications. A high-resistance sensor with low demagnetization can be realized by putting a number of stripes parallel with respect to their geometry (but connected electrically in series), ensuring the width of the gaps between them is of the order of their thickness [30]. The signal voltage Usof the sensor can be increased by increasing the operating voltage U, until its maximum value U,,, is reached. The limits of Urn,, are given by the power dissipation maximum Po (or a tolerable temperature rise AT which is related to the thermal resistance R,,and power dissipation maximum Po by Po Rth = AT) or by the tolerable current density j,,, . The lowest detectable field Hmi,is given by the lowest detectable signal voltage which itself must be higher than the noise level. There are a number of sources of noise, and these are thermal noise (the same formula as for normal resistors applies), magnetic o r Barkhausen noise [27], and offset drift, eg, due to thermal gradients or thermal mismatch of the bridge circuit. Thermal noise will be small, whilst Barkhausen noise will be suppressed by a stabilizing field (see Section 9.2.4). Drift effects are minimized by operating the sensor at constant temperature and low power; these are, of course, low frequency signals. The electronic amplifiers necessary with low signals will usually generate more noise than the magnetoresistive sensors themselves. The frequency range of magnetoresistive sensors extends from DC-fields to at least 65 MHz [8].Theoretically, the upper limit should be about 1 GHz, although experimental verification failed due to inductively coupled signals.

356

9 Magnetoresistive Sensors

9.4 Sensor Fabrication 9.4.1 Magnetoresistive Materials From the point of view of the developer in this field the most important properties for a magnetoresistive material are: a large magnetoresistive effect A p / p to ensure a high ratio of signal to operating voltage, a large specific resistance p to realize a certain resistance in a small area, low variation of p and Ap with temperature, low anisotropy field Hk, low ripple or coercivity H,, zero magnetostriction, otherwise mechanical stress will impair sensor data, long term stability of all properties. Most established materials are (crystalline) binary and ternary alloys of Ni, Fe, and Co

- the most preferred one being Permalloy (NiFe 81/19) [2-4,6-14, 16-19,27, 33-39]. Amorphous films, however, have provoked a degree of interest in the last few years [19, 381. Comparisons of measurements done by different authors should be treated with caution; properties like p, Ap/p, Hk,and H, depend not only on thickness, but also on deposition and processing conditions, which are not always reported. The anisotropy field Hkis plotted in Figure 9-7. The lowest values are found with binary NiFe alloys having high nickel content. Amongst these is the Permalloy, already mentioned, with zero magnetostriction. It is seen that even small additions of Co will increase Hkconsiderably; they may at the same time otherwise improve the layer. Hkdepends to a great extent on processing conditions. Data on the magnetoresistive effect A p / p - the most important figure of merit - are reproduced in Figure 9-8. Here the NiCo alloys are favourable showing a peak value of

Ni

Figure 9-7. Anisotropy field Hkas a function of film composition for the Ni-Fe-Co system, deposited at 250°C. Compositions with zero magnetostriction are indicated by the dashed line. The field strength is given in Oersted (1 Oe P 1000/4x A h ) (taken from [33]).

9.4 Sensor Fabrication

351

L.0

r.\

NiCo A NiFe

3.0

I

i I

-"as 2.0

I

a

Q

1.0

Figure 9-8. The magnetoresistive effect A p / p of binary NiFe and NiCo alloys as a function of Ni content. Evaporated films of 30 nm thickness, deposited at 2 0 0 T (taken from [34]).

50

"0

100

% Ni IN FILMS

Ap/p = 3.7% with the composition NiCo 70/30. Unfortunately, this alloy suffers from magnetostriction. NiFe alloys show a much lower Ap/p, but the maximum is found at 85% Ni, a composition in the region of Permalloy. Data on the less common CoFe alloys are given in 1391. If the search is restricted to alloys free of magnetostriction the best alloys are NiFe 81/19 and NiCo 50/50, both with Ap/p = 2.2%. There have been attempts to find alloys which show a higher magnetoresistive effect. In particular, many efforts have been made to improve the NiCo 70130 alloy through addition of a third element [36, 381, but these have so far proved unsuccessful. The magnetoresistive effect of amorphous films is one to two orders of magnitude lower than that of crystalline ones [19, 381. An improvement in this figure could be expected however, because the search was only started a few years ago.

38-

\

\

Figure 9-9. Specific resistivity p of Permalloy as a function of layer thickness t. The dashed curve shows data after cathode sputtering the solid one after annealing in vacuum at 450°C , 2 h (adapted from [51]).

I

40

120

200

I

I

-

280 t / n m

358

9 Magnetoresistive Sensors

The specific resistance p of these alloys is comparable to that of other alloys; generally, it is found that p is increased by Co addition. p shows a marked thickness dependence, an example of which is seen in Figure 9-9 for Permalloy. It increases with decreasing thickness for t < 100 nm. In addition, p depends on deposition or annealing conditions [4, 37, 39-41]. Deposition at T t: 250°C is said to yield the lowest resistivity - but annealing effects will be less pronounced. Since, as a rule of thumb, Ap is not dependent on thickness or processing, all variations in p will introduce inverse variations into Ap/p. The temperature coefficient (TCR) of p, 8 p / a T . l / p , is akin to that of normal metals and to 4 is in the order of 3 . K-I. A positive correlation between Ap/p and the TCR is reported [38], but replacing Fe in the Ni-Fe-Co system by Ge or Zr reduces the TCR much more than it does Ap/p. The dependence of the TCR on thickness and processing is similar to that seen for Ap/p. The variations of Ap with temperature are smaller than those of p ; values between -0.5 and -1.5 K-I are found, the lower figures applying to NiCo alloys. The upper temperature limit - in theory the Curie temperature (= 550°C for permalloy) - is determined in practice by restrictions imposed by the technology used. Magnetoresistive data may - according to the author’s experiments - be extrapolated linearly at least up to 250°C. The magnetic quality of materials is specified best by the coercivity H, which is easily measured (see Figure 9-3) or by the ratio H,/Hk; both should be low. Data for H , in the NiFe-Co system are found in Figure 9-10 [42]. Again, the lowest values are found near the Permalloy composition; the datum of 80 A/m varies, of course, with process conditions. Whilst NiCo alloys have higher H,-values, the ratio H,/Hk may be lower than for Permalloy [18, 35, 361, so producing less magnetic noise. The lowest H , data reported are measured with amorphous layers [19], probably due to absence of grain boundaries - a fact which compensates for the low magnetoresistive effect. H , decreases with increasing temperature; low temperatures are therefore the most critical. The anisotropy Hk may be reduced by annealing but, as has been learnt from experience, this is not true of the coercivity H , [37, 431. The effect of a reduction in Hk would be to shift the blocking curve to lower field strengths. The coercivity has been decreased successfully by using a multilayer structure: several NiFe layers were separated by thin (nm range) nonferromagnetic layers (SO, SO,, Si, Au, Ti) [44]. The improved quality must be paid for, however, by a reduced Ap/p = 1.6 . . . 1.8%. It has been found that H , increases with a decrease in the width of the sensor stripe [26, 361 - the magnitude, however, cannot be explained by demagnetization only. The long-term stability of magnetoresistive layers is excellent [45], even at temperatures above 200°C - results which are much better than with the equivalent semiconductors. (An exception to this are the amorphous layers which may recrystallize at T > 150°C.) These layers, however, need to be covered with good passivation layers, since the nonnoble NiFeCo alloys suffer from corrosion. Corrosion of the alloy is enhanced by it being in contact with more noble metals, like gold conductors or barber poles. Addition of several percent of Cr or Rh reduces susceptibility to corrosion [46, 471, but at the same time this diminishes the magnetoresistive effect. In summary, the most important data are assembled in Table 9-1. Tho compositions stand out as the most promising for application in magnetoresistive sensors. There is, on the one hand, the well proven permalloy, which has zero magnetostriction and low anisotropy, but only moderate magnetoresistive signal. It is a good candidate for sensors intended for the

9.4 Sensor Fabrication

359

Fe

Figure 9-10. (Wall) coercive field H, as a function of composition for the Ni-Fe-Co system; coercive field strength is given in Oe (taken from [42]).

Table 9-1. Comparison of some important magnetoresistive thin-film materials. Parameters shown are specific resistivity p, magnetoresistive effect Ap/p, anisotropy field Hk, coercivity H , , magnetostriction coefficient A, and saturation magnetization M,. Values apply to films of about 100 nm thickness at room temperature. Some of the data, especially H , and Hk, may vary considerably as a result of process variations. Material NiFe NiFe NiCo NiCo NiFeCo CoFeB ') ')

81:19 86:14 50:50

70:30 60 : 10 : 30 72 :8 : 20

amorphous

22 15 24 26 20 86

2.2 3.0 2.2 3.7 2.5 0.07

250 200 2500 2500 2000 2000

80 100 1000 1500 250 15

=O - 12 -0 -20 -5

=O

1.1 0.95 1.25 1 .o 1.3 1.3

360

9 Magnetoresistive Sensors

detection of low fields and for operation in a wide temperature range. There are, on the other hand, the alloys containing about 30% cobalt which show a much better Ap/p but worse magnetostriction behavior; Hk is high, but H,/Hk may be lower than for NiFe, and these cobalt-containing alloys show a lower temperature dependence for Ap. Their best field of application seems to be in bubble memories and reading heads.

9.4.2 Fabrication Techniques 9.4.2.1 Magnetoresistive Layers Magnetoresistive layers are deposited by vacuum evaporation or cathode sputtering (electroplating has decreased in popularity) [3, 251. Deposition conditions have to be controlled carefully as the layers are very sensitive to contamination or composition variation. Oxygen partial pressure has to be low ( < 10 - 4 Pa) [48], since magnetic properties of NiFe films will be degraded with only a 2% oxygen content [49]. Most papers recommend - though this is in contrast to the author's experience - substrate temperatures between 200 and 300°C [18, 29, 34, 351. There are doubts whether this temperature effect is really due to crystallite growth or is, in fact, caused by incorporation of residual gas atoms at grain boundaries [SO]. The deposition - at least if done at low temperatures - should be followed by an annealing process (see below). The easy direction may be induced by deposition in a homogeneous magnetic field of at least 1 kA/m. The requisitions for homogeneity (deviation < 1 " in industrial production) poses problems, particularly in the vicinity of a ferromagnetic target. Substrates used must have extremely smooth surfaces; different glasses (quartz or hard glass), or oxidized silicon are a good choice, whilst ceramic substrates are not so good. Single crystal substrates may produce unwanted anisotropy. Different thermal expansions of substrate and layer are tolerable, at least with zero magnetostriction layers. Vacuum evaporation as a technique has been used very successfully for quite a few years now [34-36, 39, 41, 45, 48, SO]. The (temperature dependent) deviation of composition between source and layer has to be kept in mind; an advantage of evaporation is the simplicity of composition variation. Medium deposition rates (about 5 m/min) are approved. Cathode sputtering is quite well established too, be it normal RF sputtering [19, 20, 49, 51, 521 or magnetron sputtering [37]. Worse results have been achieved with ion-beam sputtering

WI. Targets must be pure, especially free of oxygen, and should be vacuum melted. Bias sputtering reduces oxygen contamination but will also influence the composition [52], and bad experience with bias may be caused by the latter effect. The real deposition process has to be preceded by a careful preclean of the target. Cathode sputtering gives good reproducibility and well adhering layers and is thus favored in industrial production. It has been reported that permalloy films may be improved (better Ap/p and lower H , ) by H;-ion implantation [54]. Annealing of magnetoresistive films is recommended, especially for films deposited at low temperatures [19, 20, 35, 37, 41, 42, 45, 54-56]. Annealing has to be done under low oxygen pressure in vacuum or hydrogen [56]. It reduces p (and thus increases Ap/p) and H k , but may have no or even negative influence on H, [29, 421. Annealing should last several hours

9.4 Sensor Fabrication

361

at T 300°C; this temperature is relevant since crystal growth may impair magnetic properties at T > 350°C. Annealing should occur in a homogeneous field of several kA/m, since this field will rearrange crystal orientation to induce the easy direction - if this has not already been achieved during deposition. Lowest H,-values have been attained by rotating the easy direction into the former hard direction or by annealing in a field rotating with a frequency of one to several Hz [19, 56, 571. ;5:

9.4.2.2 Contact and Passivation Layers Magnetoresistive sensors consist not only of the ferromagnetic layer already discussed in detail but also - like other components made in thin-film technology - of layers for contact and passivation purposes. These will be dealt with only briefly here as they are produced by well-known technologies. Experience has shown that magnetoresistive alloys adhere very well, so special adhesion layers would be superfluous. Contact layers are necessary not only for external connections, but also for realizing the barber poles which rotate the current paths. The most well established materials for this purpose are gold and aluminium, and both may be contacted by bond wires. Au has the lower resistivity and better stability, but NiFeCo layers are less noble and so may corrode under humidity when in contact with the gold. This problem can be solved by using Al, but only at lower temperatures. A1 is less stable, only permits lower current density, and develops intermetallic compounds when in contact with Au (bond wires!) at T > 150°C; this last effect is known as “purple plague”. Contact layers can, in addition, diffuse into the NiFeCo alloys. Although magnetic degradation has not been observed [45], considerable interdiffusion or even formation of intermetallic compounds must be considered as a potential problem with respect to long-term stability [ 5 8 ] . Thus, barrier (and sometimes adhesion) layers of Mo, Ta or WTi are recommended as countermeasures. The demand for long-term stability can only be completely fulfilled with proper passivation layers. The necessary prerequisites are an impermeability to oxygen or water and deposition by low temperature processes. Best approved are SiO, and Si,N, layers laid down by plasmachemical processes or sputtering, a standard technique employed in the semiconductor industry. These layers were unsatisfactory, however, for sensors with the barber-pole structure [51]: it was found that covering of the steep slopes was incomplete. As an alternative, organic passivation layers of polyimide were found to give good results. The careful structuring of magnetoresistive, contact, and passivation layers is achieved with well established techniques [51] that need not be mentioned here. It is worth noting, however, that pemalloy can be wet chemically etched with an etch consisting of H,SO,, H,O,, HF and H,O [51]. Restrictions o n dimensional tolerances for magnetoresistive sensors are much more severe than for other microelectronic devices since the sensitivity and resistance depend o n the width of the stripe. But more critical, perhaps, is the fact that most sensors are bridge circuits containing resistors whose structures are perpendicular to each other (inclined stripes or barber poles). The author noted the experience that lengths perpendicular to one another may differ

362

9 Magnetoresistive Sensors

by an amount in the order of 0.1 to 0.2 pm due to errors in the photolithographic processes. Although this is only a fraction of a wavelength, it amounts to several percent of, eg, a barber-pole gap of 4 pm and appears as a bridge unbalance of the same magnitude. Nowadays, high-precision electron-beam masks and well adjusted exposure equipment help to minimize these deviations.

9.4.2.3 Measurement Techniques Production processes are monitored closely by measurements during processing in a similar manner to the completed sensors. Only techniques specific to magnetoresistive sensors will be dealt with here, however. All magnetic fields are weak enough to be generated by air coils like Helmholtz coils or cylindrical coils; their field is homogeneous, easily calculated and (contrary to coils with ferromagnetic cores) absolutely proportional to the current. It may be necessary to shield (or compensate for) the earth’s field and other stray fields. The parameters which are measured during processing (the layer data) are H k , H,, Ap/p, p, and the position of the easy axis. Hkand H, are determined by creating an M-H- (or BH-)diagram (magnetization curve), a circular shape (silicon wafer) is appropriate. Figure 9-3 gives the curves to be expected though other examples are drawn in [25]. The positions of the easy and hard axis are found by rotating the sample. The characteristic field Hois obtained in the same way with the structurized layer, whilst p and Ap/p may be measured using the well established four-point probe; the four probes should be arranged in a square or rectangular manner - formulae can be found in [59]. It is possible to buy specialized commercial apparatus which has been especially adapted for thin-film evaluation. Sensitivity and linearity range can be taken from the characteristic of a complete sensor (ie, the output signal Usis taken as a function of the external field H,, with a bias or stabilizing field as parameter). The direction of the external field, however, must be aligned precisely with the sensor’s sensitive axis (hard axis or y-direction), especially when no stabilizing field is being applied. If the alignment is not precise, small components H, are induced which will switch the magnetization and thus, indirectly the characteristic also, resulting in what is known as the “butterfly-curve”. An example of characteristics showing the influence of a stabilizing field in the x-direction is given in Figure 9-11. The minimum stabilizing field H, necessary (hysteresis should be lower than even that shown in Figure 9-11c) is an indication of layer quality - this H, depends on the maximum applied field H,,. A better form of quality estimation is a plot of Usagainst H, with a constant (but preferably not vanishing) H,,. Since this is a horizontal line in the Stoner-Wohlfarth astroid Since switching (Figures 9-2 and 9-4), the magnetization switches and changes the sign of Us. should occur without transition when crossing the astroid, smaller switching fields and broad transitions are thus an indication of lower quality. max to The magnetoresistive effect Ap/p should be the ratio of maximum signal swing Us, operating voltage Uo.This is true only in the first approximation due to the effects of incomplete current rotation and inhomogeneous demagnetization (see Section 9.4.3.1). The former effect can be corrected for by also measuring the square terms (Figure 9-13), but the

9.4 Sensor Fabrication

/

363

1

Figure 9 4 . Influence of stabilizing field H, on the sensor output signal Us; for clearness shown on a bad sample with high H,; t t: 60 nm, w = 40 pm, H, = 1.5 kA/m. a) H, = 0, M is blocked and will not be deblocked totally, and there is severe hysteresis; even the offset differs from b) and c). b) H, = 0.19 kA/m, hysteresis max. 12%, the s-shaped curve is recognized. c) H , = 0.38 kA/m, hysteresis reduced to 2%, maximum signal higher than in b) and occurring at higher H,,.

latter cannot. The magnetoresistive effect measured with complete sensors is smaller than that measured with the circular shaped layer.

9.4.3 Sensor Layout 9.4.3.1 General Considerations The layout is determined primarily by the type of sensor required (biased, slanted stripes or barber poles), sensitivity So, and resistance R . The simple stripe arrangement like that drawn in Figure 9-5 is used only when the field to be detected is restricted to small volumes (eg, magnetic disks). Industrial general-purpose sensors are designed to have greater resistance in the order of 1 kQ or higher, in order to ensure a high signal voltage in spite of low power dissipation and so be comparable with other sensors, like pressure sensors. Several technological restrictions must be needed, however. Firstly, the thickness t has a lower limit; otherwise the magnetoresistive effect becomes too low and the resistivity shows too much scatter. This limit is between 30 and 40 nm, although layers of only 20 nm have been reported. Secondly, the current density j has an upper limit j,,, may be high compared to usual conductors if the magnetoresistive alloy has been passivated (j,,, = 10" A/m2 for

364

9 Magnetoresistive Sensors

Permalloy [45]). Nevertheless, the current I may itself be limited as t is sometimes very low. (Further restrictions with barper-pole sensors are discussed below.) In addition, power dissipation must be small in order not to exceed certain temperature limits and to ensure low temperature gradients. Even a layer of t = 30 nm and p = 30 l o - * SZ m has a sheet resistance of R, = 10 sZ/O. Thus, a resistance of 1 kSZ requires a length-width ratio of I/w = 100, usually only ever realized in a meander structure. The design starts with material selection which will determine Ap/p, p, and Hk : thickness effects should always be borne in mind. Sensitivity So or linearity range HG (the two are interrelated, see Equation (9-32)) must be given in order to determine & and the thickness to width ratio t / w = p (Equations (9-13), (9-22), and (9-23), respectively); the demagnetization may be reduced by ensuring small gaps between the stripes, thereby introducing mutual magnetic coupling. Additional quantities to be fixed are resistance R,, power Po,or operating voltage U,. Design of a sensor linearized by a bias field is the most simple task; a similar treatment may also be used for sensors with inclined stripes, however, barber-pole sensors require a different approach. Assuming normal resistor geometry, R = p . I/(t w), one gets:

-

-

(9-33) Both, t and w must be increased if t happens to be below its lower limit (30 to 40 nm). The designer should also bear in mind that current density j achieves its highest value at the point of current reversal in the meander. Length I and area A are easily calculated when R,, p, t, and w are known. Normally, the designer tries to minimize A by utilizing the permissible values of t or j . The area decreases with increasing linearity range HG , so high-sensitivity sensors need larger areas. This simple, straight forward procedure can, however, be improved; the general idea is to reduce demagnetizing effects, to increase HG and optimize the bias field [16, 18, 30, 32, 601. Lower area or higher sensitivity are obtained by reducing demagnetization with tight coupling between the stripes; separation between stripes must be of the order of their thickness. The effects of mutual coupling and of heterogeneous (ie, nonhomogeneous) demagnetization have been analyzed quantitatively with great success [32, 601. Further optimization can be achieved through the choice of the best inclination angle p of the elements (normally taken to be 45"). The difference between p and (p, (angle of rest magnetization M,, ie, without unknown fields but with bias) should amount to 45". (po depends on anisotropy Hk and demagnetization H d , but also on the bias field and even on p itself. There are no simple formulas or recipes available to help determine the right solution - optimization must be performed using computer simulation. A lot of relevant information for this can be found in [60]. The description of barber-pole sensors is different from the others as barber-pole sensors have a simpler magnetic behavior. All stripes are in the e. a., and the distances between them must be increased (barber poles extend the stripes and must have a clearance) so that no coupling effects are present. Understanding the electrical behavior of barber-pole sensors on the other hand is more difficult, although simple calculations will lead to an optimum design [51, 611; a more detailed computer simulation, however, will be found in [62].

9.4 Sensor Fabrication

365

The geometry of the barber poles is shown in Figure 9-12. Disregarding edge effects, it is seen that each gap has length a and width w fl, and that the fraction s/(s + a) is shortened by the barber poles. The resistance therefore is:

R,

=

1/2

. a/(s + a) . p . l/(w - t) .f .

(9-34)

/b-P\

T

Figure 9-12. Geometry of the barber-pole structure; current paths are drawn. Rotation of current is f45' in the middle, but much less at the edges; the rotation averaged over the gap is thus 45" -5. The current paths in the barber poles are longer and denser than in the gaps.

W

The correction factor f accounts for edge effects and the resistivity of the barber poles; experience shows that f = 1.2. The resistance in this type of sensor is 2 to 4 times smaller than that in any other sensor having the same area. The important parameters to be considered are voltage drop U, and current density j , (all barber-pole parameters will be denoted by the index B). U, and j , are calculated in relation to U and j in the magnetoresistive layer, since the expressions can be split up into material parameters and factors dependent on geometry only:

j,/j = t/t,

q

.

(9-36)

The geometric factors 0 and q depend only on the ratio a/s of barber-pole gap to barberpole width, and both are drawn in Figure 9-13. A good design would have U,/U d 1, and usually U B / U = 0.1. If 1 < a/s < 2 with 0 < 5 and taking good conductors (Ag, Cu, Au, Al) with p B / p 0.1, the barber-pole thickness t, must be at least five times the thickness of the magnetoresistive layer t, so that the quotient of the current densities j,/j will be in the region of 0.3 to 0.5. However, the lower j , may restrict the maximum current since j,,, of good conductors ( j < lo9 A/m2 for Al) may be much lower than that of, for example, Permalloy. Furthermore, barber poles impose a number of geometrical restrictions: J

- t,

- 1

2 5.t

< a/s < 2

- w 2 2.a - s 2 2 . tB

(as discussed), (as discussed), (otherwise edge effects will influence sensitivity), (otherwise the current will not flow in the whole layer).

Combining these four inequalities gives t/w < 1/20 . s/a from which it is possible to deduce that HG < 25 kA/m * a/s. The linearity range HG of barber-pole sensors is more

9 Magnetoresistive Sensors

366 L

14 -

12 10 -

8-

64 2 -

0,l

0,2

0,5

1

2

5

10

a/S

Figure 9-13. Variation of current density ratio q and voltage drop ratio Q in the barber poles with geometry a/s.

constricted than that of other sensors, though H G can, of course, be increased by applying a field in the easy direction (H, > 0). To the designer, the choice of barber-pole width is a compromise. The barber-pole width s should be small to create small stripe widths w and thus ensure that high HG values are feasible (small area!), whilst large barber-pole widths ensure that only small errors are incurred due to width variations caused by the lithographic processes, as mentioned above. A good compromise, in the author's experience, is to have s = 4 pm. The current flowing in the barber poles generates a magnetic field in the magnetoresistor which can be used as a stabilizing field [63]. The x-component of this field is:

H, = U(2 * w) * a/(a

+ s) ,

(9-37)

where I is the current. Normally this field should have the same direction in all stripes; this prohibits some of the possible combinations of current direction and barber-pole inclinations [15] and instigates the need for normal conductors for current reversal in meanders. It has been shown that the linearization created by barber poles is not perfect [61]. The reasons for this are edge effects (the current flows parallel to the stripe axis, see Figure 9-12) and the voltage drop U, (a part of the current remains in the magnetoresistor). The mean current is thus inclined at an angle less than 45" to the x-axis, say 45" - 5. This effect can be described (in place of Equation (9-27)) by the term: R(H) = R ,

*a

H , / H , . 1/1 - (H,/Ho)2

- p a(H,/Ho)2,

(9-38)

where a and p may be interpreted as A R . c o s 2 5 and A R s i n 2 5 respectively. The total resistance variation can be defined as A R = (a2+ p2)'". These equations are also valid for sensors with inclined elements.

9.4 Sensor Fabrication

367

When elements with different slopes are combined in a bridge, the bridge signal Usonly contains the linear part, whilst the square part influences the total resistance; in other words, the bridge resistance is field dependent. Both terms can be measured separately as shown in Figure 9-14. Small square terms have a negligible effect on the linear signal; any nonlinearities can be completely removed by driving the bridge with constant current. The relative square part P/(a2 + p2)”2may be approximated by a simple formula [61]: /?/(a2+ P2)1’2= U B / U + a/l/Z- . w. The first term represents the voltage drop ( ~ 0 . 1 ) and the second the geometry of the gap between two barber poles (see Figure 9-12); it is simply the ratio of the areas of the triangles at the edges (area: a2/2 each) and the total stripe area

(w

a.

l/Z-).

I I

1%

Figure 9-14. Measured linear and quadratic terms of a barber-pole sensor with HG = 2 kA/m. The maximum voltage swings of the linear part (a) and the square part @?) are indicated. The deviations from the theoretical curves (the bell shaped curve, for example, should be the parabola of Figure 9-6) are due to the heterogeneous (ie, nonhomogeneous) demagnetizing field present at higher field strengths.

kAlm

9.4.3.2 Examples These explanations can now be ameliorated by demonstrating the layout of a number of genuine sensors. The full-bridge circuit in Figure 9-15 is the first modern example of a magnetoresistive sensor known to the author. Linearization is achieved using inclined elements, with the long resistor folded into a meander; the arrowlike outline indicates its (horizontal) sensitive axis. The layer is constructed from NiFeCo 73 : 16: 11 alloy, thickness 100 to 200 nm, and the easy axis is vertical, but in the paper plane. Figure 9-16 is a schematic layout of the first commercial general-purpose sensor: the Sony DM 101A, described in [9]. Linearization is achieved using perpendicular current paths, which is similar to the inclined elements arrangement. The half bridge is made from NiCo 76 :24

368

9 Magnetoresistive Sensors

Figure 9-15. Full-bridge sensor linearized by inclined elements; white areas represent the NiFeCo alloy. Each of the four horizontal fish-bone structures is one of meandered resistors. The resistors are connected; outside contacts have to be made at the crosses. The sensitive axis is horizontal. Dimensions are not reported, but are supposed to be in the mm-range; the resistance is estimated to be 300 i2 (taken from [S]).

Figure 9-16. Scheme of the layout of an industrial halfbridge sensor with perpendicular elements. (The real sensor has two meanders of 23 stripes each, width = 27 pm, length = 1.1 mm, gap = 20 pm.) Chip size = 3.0 x 2.5 mm2, total resistance 1.5 ki2 (taken from Sony data sheet DM 101 A).

Figure 9-17. Commercial barber-pole sensor with median sensitivity (KMZ 10 B). The left photo shows the complete device with four resistors in the four quadrants and bond pads beneath; between the pads are two "digital" resistor networks for laser trimming. The right photo is an enlarged view of the center, where bright aluminium conductors are discerned from the grey Permalloy stripes. The resistors differ in the inclination of the barber poles. Chip size is 1.6 mm x 1.6 mm, resistance 1.7 kQ, w = 10 pm, t = 44 pm, a = s = 4 pm.

369

9.4 Sensor Fabrication

alloy of 100 nm thickness. It is designed to measure fields above 5 kA/m, the signal being dependent on the direction of the field only (as seen in Equation (9-16)). Field intensity can be measured by adding a known bias field. A commercial barber-pole sensor, designed by the author, is shown in Figure 9-17. The four resistors of the full bridge are located in the four quadrants. The magnetoresistive layer is constructed from Permalloy, at a thickness of 44 nm, and conductors are made from aluminium. Each resistor consists of 13 Permalloy stripes, between which are the A1 conductors carrying the reverse current. The unavoidable offset can be cancelled out by laser cutting the shorting bars of trimming resistors located between the bond pads. This sensor was not designed to have the lowest area, and a more sophisticated example is shown in [20].

9.4.3.3 Layout of Special-Purpose Sensors Special sensors have been designed, which by virtue of a special layout will measure only fields which show spatial variation; these fields may be generated, for example, by permanent magnets with multipole magnetization or by soft iron gear wheels plus a single-pole magnet. The first of these layouts, shown in Figure 9-18, utilizes the fact that the resistors of a bridge are (usually) located apart, separated by Ax and Ay [17, 641. The field is described by a linear approximation over the sensor’s dimensions, which is permissible for low and medium spatial variance: H ( x , y ) = H , + aH/& . Ax + aH/ay Ay. A straight forward calculation shows that a sensor can not only be sensitized to H , (as for the usual sensors), but also to aH/& or aH/ay, resulting in sensors which respond to the gradient of the field only. These sensors are suited for large gradients, the output being given by aH/ay . Ay; the field at each resistor should not exceed H,. The gradient sensor may be (and has been) realized using the general arrangement shown in Figure 9-17 (but not with the layout in Figure 9-15) which was originally made for a linear sensor. Gradient sensors are produced by changing the inclination of the barber poles as indicated in Figure 9-18. They can, of course, also be constructed from elements linearized by inclined current paths.

Figure 9 - 1 Spatial arrangement and electrical connection of magnetoresistors to build full-bridge circuits. The resistors are denoted by the squares, the sign in the square gives the sign of the characteristic. The sensitive axis is the y-axis - the output of each element is a linear function of the field at its center. The normal arrangement is shown in Figure 9-18a with signal proportional to the field at the center of the whole bridge. The arrangements in Figure 9-18b and 9-18c cancel constant fields and respond to field differences at the resistor center only, ie, the gradients.

S - Hy

a)

aHY S- aY

bl

S-- aHY ax C)

310

9 Magnetoresistive Sensors

The magnetoresistor can also be made sensitive to fields which show only a periodic spatial variation [19, 651. Figure 9-19 gives an example layout. The magnetic field has the wavelength I , say H (s) = H , . sin (s . 2 x / I ) , where s is a spatial coordinate. The resistors shown are simple stripes with no linearization; their square characteristic produces a signal with spatial period I / 2 . Stripes located at even and odd multiples of I / 4 respectively, produce a signal with 180” phase shift and are connected in a bridge. The sensor layout must match the field period; it is a system well suited for sensing fields of short wavelengths, where other sensors have failed.

Figure 9-19. Measurement of periodic fields. This fullbridge sensor has resistors with square characteristics, R , , , R , , , . ., R4,. They are located at even or odd multiples of 114, producing thus a signal during mutual displacement of sensor and field; the period is 1/2 (taken from [65]).

.

9.4.4 Generation of Auxiliary Fields It has been emphasized that a bias or a stabilizing field should be applied during sensor operation. The magnitude of this auxiliary field is in the order of 1 kA/m, and the direction can as well be the easy direction (stabilizing field) as the hard direction (bias field). There are three modes of field generation that are generally known: by a current conducting coil, by a permanent magnet, or by exchange coupling with an antiferromagnetic film. The simplest way, applicable in the first two cases, involves the use of an external coil or magnet. This will not be discussed here, since the details of its use are subject to the preferences of the user. Rather, this section concentrates on “integrated” solutions, i. e., the means of field generation - namely the deposited and structured layers - are prepared during sensor processing and are inseparable from the sensors themselves. Most arrangements described are used in magnetoresistive recording heads, the sensors working in an environment without high fields. Industrial general-purpose sensors, however,

9.4 Sensor Fabrication

371

have to be stable after (not during) incidental magnetic pulses of at least 10 kA/m, imposing severe demands on the coercivity, for example, of hard magnetic layers. All additional layers must preserve the smoothness of the magnetoresistive layer, which prohibits making multiturn coils around the magnetoresistor. Fields can be generated by singleturn conductors, but the current will flow along the long stripe axis due to the geometry. The field thus points in the y-direction and, whilst being suited for linearization by bias fields, it is not suited for stabilization which requires an x-field. Several biasing schemes are discussed in [13, 66-68] and are depicted in Figure 9-20. The arrangement shown in Figure 9-20a consists of a nonmagnetic conductor and the magnetoresistor; the two may be separated by an insulating layer, the advantage being there is no partial shorting of the magnetoresistor signal. However, the disadvantage is the thickness and that a more complicated process is required. The current I can be approximated to: I z t . M, which is rather high (30 to 100 mA). The sandwich shown in Figure 9-20b is more complicated, but has two magnetoresistors with opposite bias, thus enabling a bridge circuit. The bias current can be described by I = t . M, d / w (where d is the total thickness of the sandwich) which is much lower than the former example. The sensing current itself can also be used for creating a bias field, as shown in Figure 9-2Oc. The ferromagnetic shunt can additionally act as a second magnetoresistor allowing for a similar arrangement as that in Figure 9-20b, but without the separate conductor. The layers should be isolated electrically. Figure 9-20. Bias field generation. The outline gives cross sections along the hard axis and shows conductor C, magnetoresistor MR and ferromagnetic shunt Sh. Current direction and field lines are indicated. a) Single magnetoresistor and conductor, b) dual magnetoresistor with separate conductor, c) magnetoresistor with ferromagnetic shunt.

MR

Sh

a)

In barber-pole sensors, a field with an x-component is generated automatically, as already discussed in Section 9.4.3.1 and Equation (9-37), its magnitude being in the region of 0.05 to 0.5 kA/m during normal operation. This value is too small for stabilization in general-purpose applications but suffices, for example, when measuring the earth’s field. In addition, this field can be used for forcing the correct magnetization state by applying a short (- 1 ps) high (10 times normal) current pulse. It is also possible to generate auxiliary fields using permanent-magnetic films [68, 70-731. Generally, permanent magnets will produce a field with local inhomogeneities [70] - an effect which may be overcome by increasing the distance between the layers via a spacer layer (which has an additional role as an insulator). The field H , generated by a layer of thickness t,, length I, and remanent flux density B, (demagnetization is negligible for I 2 tp) is given by:

H,

=

t,

*

BJ(1. fig) .

(9-39)

372

9 Magnetoresistive Sensors

t, may be small for biasing purposes, t, = 0.5 . t (B, = 0.8 T as in ferromagnets), but it becomes rather large for generating stabilizing fields; t, amounts to several vm for I = 0.3 to 1 mm. This is inconvenient for thin-film technology, but t, can be reduced by splitting the layer with a number of small gaps in the field direction and increasing the demagnetizing field. Most hard magnetic layers have their preferred direction perpendicular to the plane and are thus not suited to this application unless they have been deposited by oblique incidence. In-plane fields may be generated by CoCr [72], Copt [73], SmCo, and similar materials [74, 751. These layers are sputter-deposited at high substrate temperatures and in a high field, yielding a coercivity which can be higher than 100 kA/m. In addition to these ferromagnetic films, other ferrimagnetic films such as Fe,O, and Fe,O, have been used successfully [70, 711, although the thickness t, of these layers needs to be about three times those described above. This type of layer may be sputter-deposited from an Fe target, either by reactive deposition with 0, addition or by subsequent oxidation of the Fe film. An alternative method of deposition is by screen-printing 'of an SmCo, or ferrite powder, preferably onto the rear of the substrate [51]. An example of the characteristic of such a sensor is shown in Figure 9-21. The Curie temperature Tc of all these layers is much higher than the usual operating temperatures of the sensors, so irreversible demagnetization due to temperature effects can be disregarded. The generated field Hp has a negative temperature coefficient (that of Br); in certain circumstances this may even be advantageous since not only does it compensate for the negative TC of the sensitivity So, but also the required stabilizing field is lower at higher temperatures.

Figure 9-21. Characteristic of a barber-pole sensor (see Figure 9-17 for layout) stabilized by hard magnetic ferrite powder, screenprinted to the rear of the substrate. The sensor was overcharged twice to demonstrate stability without further stabilizing means.

9.4 Sensor Fabrication

373

Sensors that possess a hard magnetic layer should be magnetized only once, since remagnetizing will alter the offset of a full bridge when the field direction is altered by this process. The third method used to stabilize the magnetoresistive layer is exchange coupling with an antiferromagnetic film [76, 771. This induces a unidirectional anisotropy in contrast to the uniaxial situation described so far. Best results are reported with an FeMn film, possibly deposited on a Cu film to stabilize the antiferromagnetic y-phase [77]. The direction of anisotropy can be induced by deposition in a field or by subsequent annealing in a field above the Nee1 temperature. One advantage of this method of stabilization over permanent-magnetic layers is that the system is restored even after periods of high magnetic noise, but it can tolerate only small fields in the x-direction (opposing the “unidirection”). To date, exchange coupling like this can only be used at low temperatures, the upper limit being 100 to 150°C [77]. It seems to be a good alternative solution for reading heads, but is less suited for the industrial sensors.

9.4.5 Data on Magnetoresistive Sensors Having dealt with the theoretical description, some data on actual magnetoresistive sensors are given below. The information is representative for the different types of sensors, although preference has been given to sensors which are commercially available. The first example is the Sony family, the design of which is shown in Figure 9-16 and described in [9]. These sensors are made from NiCo 76:24 alloy which has both a high magnetoresistive effect, but also a high H k . There is obviously no easy direction induced into the layer, this would be superfluous since the sensor is built to measure high fields. The direction u, of magnetization is thus parallel to the field direction (see Equation (9-16)), the angledependent part of the signal being described by a term cos (2 . q). The external field H has to be higher than a field HI ( H I 4 kA/m) to avoid blocking and thus hysteresis, but a maximum signal is attained only for H 2 H , ( H , = 8 kA/m), where magnetization is saturated. The magnitude of an external field H may be measured by applying a fixed bias field HB whose magnitude should be at least H I , but better H,. Some data has been collected in Table 9-2. Although the sensitivity is not very high, the signal swing can be rather large. The company also offers sensors with fixed bias magnets (not

Table 9-2. Some examples of Sony magnetoresistive sensors. The first two are half bridges, the DM-208 is a full bridge. The sensitivity has been calculated (assuming a bias field H , = H , ) so they are comparable to other sensors. The maximum signal swing is also quoted as this is relevant to proposed applications. Type

DM-106B

DM-110

DM-208

Dimension

Resistance R , Sensitivity So at HB = H , Signal swing Max. oper. voltage

2.3 1.8 8 16 10

280

0.65 3.5 8 38 13

kC2 (mV/V)/(kA/m) kA/m mV/V V

1.7

8 15 50

374

9 Magnetoresistive Sensors

integrated). Another special sensor (DM-211) is of the type described in Figure 9-19, intended for gear-wheel measurements, etc. All these sensors have a low temperature coefficient of ~p = -0.5 10-3 K - 1 . A second example of commercial magnetoresistive sensors are the Philips barber-pole sensors of the type shown in Figure 9-17. Having a Permalloy layer and aluminium barber poles, the sensitivity can be varied using different thicknesses and widths. The most important data are given in Table 9-3 - not only information relevant for application, but design data also, and this sensor line shows that the sensitivity may be adjusted by varying the geometry, but not the material. Their characteristic is the s-shaped curve drawn in Figure 9-6, which is measured in Figure 9-21 (only the center part - 2 kA/m Q Hy Q 2 kA/m may be used). These sensors require - except at very low fields - a stabilizing field, whose magnitude (max 3 kA/m) depends o n the amount of magnetic noise present. Table 9-3. Data on Philips barber-pole sensors. All three are full bridges with equal chip sizes of 1.6 mm x 1.6 mm; see Figure 9-17 for layout of KMZ 10B. The sensors should be operated with a stabilizing field whose magnitude depends on the sensor type and on the amplitude of magnetic noise present. Type KMZ 10 Layer thickness Stripe width Number of stripes Barber-pole width Barber-pole gap Characteristic field Measuring range Sensitivity at stabil. field TC of So (U = const.) TC of S, ( I = const.) Bridge resistance TC of Ro Max. oper. voltage

A

t W

n S

a

33 30 14 4 10

HO

1.2

HG

f0.5 14 0.5 -0.4 -0.15 1.3 + 0.25 9

SO Hx

RO

UO

B

44 10 13 4 4 3.8 f2.0 4.0

3 -0.4 -0.1 1.7 + 0.35 12

C

130 6 30 4 4 17.6 f7.5 1.5 3 -0.5

-0.15 1.4 + 0.35 10

Dimension nm Pm

Pm Pm kA/m kA/m (mV/V)/(kA/m) kA/m "70 . K - I To ' K - I kC2 % .K-' V

All these sensors are mounted in plastic housings similar to plastic transistors (especially the Philips sensors), but flattened to allow tight contact with the magnets and iron parts modifying the field lines. Another commercial magnetoresistive sensor available is the MRE-104 made by Nippondenso; although only a small amount of information is supplied, the sensor appears to be very similar to the Sony DM-106B described above. The contribution from Honeywell should also be noted, who have completed their line of magnetic sensors with a magnetoresistive sensor based on Permalloy, called SS2. This sensor is integrated with an electronic switch and switches between 1.2 and 0.9 kA/m irrespective of field polarity, although unfortunately no further information is available. For comparison, data from noncommercial sensors with optimized sensitivity [16, 30, 321 will also be given. These sensors are linearized by inclined elements, similar in layout to the

375

9.4 Sensor Fabrication

arrangement in Figure 9-15. Sensitivity has been optimized by reducing demagnetizing effects and adapting inclination angle and bias field. These sensors are made for low-field measurements, such as the determination of earth's field and its variations. The signal swing, when a field 8 A/m is applied, varies between 400 and 950 pV/V (optimum bias) which may be converted to a value of So = 30 ... 60 (mV/V)/(kA/m) [30]. The best of these full bridges have resistances of 50 kSZ or even more; smaller resistances tend to increase the noise level. The authors have also given the detection limits, which are determined by the sensor and amplifier noise levels [16]. The equivalent magnetic noise level is, in the best case, reported A/(m . to be 3.7 The operating range of different arrangements of magnetoresistive sensors has been drawn in Figure 9-22 on a logarithmic scale of the field strength H (and for comparison on a scale of the flux density B, too). The normal operation covers the range from some 10 A/m to some 10 kA/m, but this measuring range may be extended up to eleven decades by variations of the measuring arrangement and/or improved signal evaluation.

*

-

m).

a: b:

I

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I

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I

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I

I

I

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I

I _____ -_-

I

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I

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I

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I

-.

L.

d:

H I

'

1

'

1

'

l

'

i

'

lo2

loo

I

'

I

lo6 Alm

loL

B I

'

I

'

I

10-l2 10-lo

'

I

'

I

'

I

lo-'

'

I

10'

T

Figure 9-22. Operating range of magnetoresistive sensors. a) Normal operation as described throughout this chapter. b) Measurement of field direction only (see Equation 9-16) or sensitivity reduced by a high x-field (see Equation 9-30). c) Drift reduced by switched magnetization as discussed in Section 9.5 and [82, 831. d) Noise and drift minimized by switched magnetization and bandwidth reduction [16].

9.4.6

Comparison with Other Magnetic Sensors

Magnetoresistive sensors are adapted to medium field strengths from a few amperedmeter to several 10 kA/m. They are further characterized by having an analog output with a frequency-independent signal, and they are produced by a mass-fabrication technique resulting in low prices. When compared to other sensor types, the best match is found with (normal) Hall sensors. These have mostly similar properties except that they need to be operated at higher fields

376

9 Magnetoresistive Sensors

(from 1 kA/m to 1000 kA/m); they also suffer from larger temperature effects unless GaAs is used, since they are made from semiconductors. Both types of sensors can be integrated with on-chip signal conditioning electronics. The sensitivity of Hall elements is about 0.2 to 0.3 (mV/V)/(kA/m) (converted data) and consequently lower than that of the magnetoresistives (see Chapter 3). Field plates, which are sometimes called magnetoresistive sensors as well, use the same physical effect as Hall sensors (the Lorentz force in semiconductors), but they are made to vary their resistance. They have a square resistance-field relation, so the resistance can increase more than 10 times, but they also need high fields of about 1 T ( P 800 kA/m). Linearization, if needed, has to be achieved using a bias field. Field plates are made from InSb (high electron mobility!) which limits the upper temperature at which they can function accurately to 100 to 120°C. The sensitive axis of Hall sensors and of field plates is perpendicular to the plane of the element, enabling arrangements with smaller airgaps. When considering the best sensor type for the important application of incremental position sensing, two more competitors appear in induction coils and pulse wires; however, whilst the first of these can withstand rather high temperatures, it is unsuitable at low frequencies, and neither type can be produced by batch processing because of the coils used. They do, however, have the advantage of being active sensors which do not need a power source. In addition to this group of sensors, used mainly in mass applications, there is a second group intended for the measurement of low fields or low gradients. All these, like flux gates or even squids, are more expensive as they need more electronic equipment. There is only a minimal chance that a sensor of one group could replace one of the other, and this holds true even for the magnetoresistive sensor which is the most sensitive of the first group.

9.5

Applications

Applications will be discussed only briefly here, since they are the topic of Chapter 11. Nevertheless, there are certain points specific to magnetoresistive sensors which need to be mentioned. It should be remembered, however, that producers of magnetoresistive sensors do offer information about applications for their products. Magnetoresistive reading heads had been proposed as early as 1971 [7, 11 - 131, but they have been used only in special applications for control purposes. Solid-state devices, especially magnetoresistive ones, are superior compared to inductive heads and may replace them in high density recording [78]. The most important application for general-purpose sensors, however, is contactless position sensing. This is done with the aid of a permanent magnet in utilizing its position-dependent field or by evaluating the field distortions created by soft-iron moving parts [lo, 19, 20, 65, 79, 801. The arrangement is similar to that used by other magnetic sensors, especially Hall sensors, but magnetoresistive sensors can and should be driven with lower fields; indeed, ferrite magnets will suffice in many cases (although they have a higher temperature effect). The arrangement for incremental position measurement (eg, by counting the teeth of a gear wheel) shown in Figure 9-23, differs from that used successfully by other sensors: The field

377

9.5 Applications

Figure 9-23. Position sensing via field distortion caused, for example, by a soft-iron gear wheel. The drawing shows the sensor (with its sensitive axis) fixed to the magnet (marked with its poles); only one gear cog (hatched) is indicated. a) Symmetric position: no field component in the sensitive axis; b) asymmetric position: considerable field distortion produces a component in the sensitive direction; c) arrangement perpendicular to a) and b): the sensor is mounted off-center to use the magnet’s stray field for stabilization.

@$jlB N S

a)

bl

C)

distortions (which have a higher relative variation than the main field) are sufficient to use the full linearity range of the sensitive magnetoresistive sensor. This method works quite well as long as the cog dimensions are larger than the sensor chip. Smaller cogs, giving better resolution, are measured using the special sensors discussed in Section 9.4.3.3; the mounting is that depicted in Figure 9-23. Other applications cover measurement of currents or electric power [lo, 18, 79-81]. The use of magnetoresistive sensors as magnetometers, ie, for inspecting the magnetic field of the earth (also a compass), has been described by several authors [8, 16, 18, 30, 321. A special operating mode can be used when it is only these small fields that are to be measured: The magnetization is switched between the two stable states, thus switching between two characteristics of different slope but equal offset. A phase-sensitive detector or even a lock-in amplifier eliminates offset and offset drift of sensor and amplifier and decreases the noise level. Magnetization switching can be effected with a square wave bias (with amplitudes > H , to guarantee stable states, see Figure 9-2) [82] or with short pulses only [83]. The measurement can be done without any stabilizing field in the latter case, although this method will only work for small fields (<250 A/m), otherwise blocking will occur. A further advantage brought by magnetization switching is the cancellation of fields perpendicular to the sensitive axis. Last but not least, it should be noted that the sensor is a good zero-field detector because of its high sensitivity. It can be employed with field compensation and enables a higher accuracy than is usually possible with standard methods. It is recommended to use a stabilizing field in the x-direction in the order of 1 to 3 kA/m for many applications, provided that sensors with an internal biasing means are not available. Practically, this field can be generated by small permanent magnets or even by the magnet necessary for position sensing itself. The electronic circuitry of magnetoresistive sensors is not specific [lo, 79, 801. The usual sensors are full or half bridges (single magnetoresistors are suitable for AC-fields only) and these can be evaluated using known circuits from other bridge-type sensors , eg, pressure sensors. The temperature-dependent bridge resistance has been used as a temperature indicator, the temperature dependence of the sensitivity being reduced by driving with a constant current [9] or with a negative impedance converter (NIC) [lo].

378

9 Magnetoresistive Sensors

9.6 Conclusions and Outlook More than two decades of research and development have established the magnetoresistive principle. Different practical realizations confirmed the high sensitivity and stability of magnetoresistive sensors, and the manufacturing techniques that accompanied the microelectronic technology revolution ensure that their size is ever smaller and their cost remains low - the two prerequisites for mass-market acceptance. Sensitivity and measuring range can be adjusted by manipulating geometry and bias fields, and whilst the sensors are suited best for medium field strengths and may well determine strength and direction of the earth’s field, for example, in navigation systems, they can also be designed to read the information off magnetic disks or to measure positions by the aid of a permanent magnet in industrial applications. The necessity for a bias or a stabilizing field can be a drawback, and this problem may repel potential users, although simple solutions with external magnets are known. An important task for the near future, therefore, must be the development of a reliable and cost-effective technology for “integrated” bias field generation; a hard job, especially for the industrial sensors which are used in a wide temperature range. Another area ripe for development is the combination of sensors and electronics on a single chip. This, of course, is no technological problem, but rather is retarded by the lack of standardization on sensor interfaces. It is doubtful, however, whether magnetoresistive layers themselves will be improved considerably in the coming years.

9.7 References [l] Thomson, W., Proc. R. SOC.London, A 8 (1857) 546-550. [2] Mitchell, E. N., Haukaas, H. B., Bale, H. D., Streeper, J. B., X Appl. Phys. 35 (1964) 2604-2608. [3] Cohen, M. S., in: Handbook of Thin Film Technology, Maissel, L. I., Glang, R. (eds.); New York: McGraw Hill, 1970, pp. 17-1- 17-88. [4] Krongelb, S., X Electron. Muter. 2 (1973) 227-238. [5] McGuire, T. R., Potter, R. I., IEEE Trans. Magn. MAG-11 (1975) 1018-1038. [6] Thompson, D. A,, Romankiw, L. T., Mayadas, A. F., IEEE Trans. Magn. MAG-ll(l975) 1039-1050. [7] Gestel, W. J. van, Gorter, F. W., Kuijk, K. E., Philips Tech. Rev. 37 (1977) 42-50. [8] Hebbert, R. S., Schwee, L. J., Rev. Sci. Instrum. 37 (1966) 1321-1323. [9] Makino, Y., X Electron. Eng. 105 (1975) 34-38. [lo] Dibbern, U., Petersen, A . , Electron. Comp. Appl. 5 (1983) 148-153. [ l l ] Hunt, R. P., IEEE Trans. Magn. MAG-7 (1971) 150-154. [12] Kuijk, K. E., Gestel, W. J. van, Gorter, F. W., IEEE Trans. Magn. MAG-11 (1975) 1215-1217. [13] Shelledy, F. B., Brock, G. W., IEEE Trans. Magn. MAG-11 (1975) 1206-1208. [14] Gebhardt, O., Richter, W., Phys. Status Solidi A 60 (1980) 467-473. [ 151 Druyvesteyn, W. F., in: Vaste Stof Sensoren, Middelhoek, S., Broese van Groenau, A., Verwey, J. F. (eds.); Deventer: Kluwer, 1981, pp. 87-94. [16] Hoffmann, G. R., Birtwistle, J. K., X Appl. Phys. 53 (1982) 8266-8268. [17] Dibbern, U., Sens. Actuators 4 (1983) 221-227. [18] Kwiatkowski, W., Tumanski, S., X Phys. E 19 (1986) 502-515.

9.7 References

319

[19] Kersten, P., Volz, H., NTG-Fuchber. 93 (1986) 186-191. [20] Dibbern, U., Sens. Actuators 10 (1986) 127-140. [21] Jan, J. P., in: Solid State Physics, Vol. 5, Seitz, F., Turnbull, D. (eds.); New York: Academic Press, 1957, pp. 1-96. [22] Fluitman, J. H., J. Appl. Phys. 52 (1981) 2468-2470. [23] Middelhoek, S., J. Appl. Phys. 34 (1963) 1054-1059. [24] Stoner, E. C., Wohlfarth, E. P., Philos. Trans. R. SOC. London A 240 (1948) 599-642. [25] Prutton, M., Thin Ferromagnetic Films, London: Butterworths, 1964. [26] Fluitman, J. H. J., Thin Solid Films 16 (1973) 269-276. [27] Tsang, C., Decker, S. K., J. Appl. Phys. 53 (1982) 2602-2604. [28] Hoffmann, H., IEEE Trans. Mugn. MAG-2 (1966) 566-570. [29] Hoffmann, H., Thin Solid Films 58 (1979) 223-233. [30] Hoffman, G. R., Hill, E. W., Birtwistle, J. K., IEEE Trans. Magn. MAG-20 (1984) 957-959. [31] Paul, M. C., Sauter, G. F., Oberg, P. E., US Patent 3 546 579, 1970. [32] Hoffman, G. R., Birtwistle, J. K., Hill, E. W., IEEE Trans. Mugn. MAG-19 (1983) 2139-2141. [33] Wilts, C. H., Humphrey, F. B., J. Appl. Phys. 39 (1968) 1191-1196. [34] Asama, K., Takahashi, K., Hirano, M., AIP Con$ Proc. 18 (1973) 110-114. [35] Collins, A. J., Sanders, I. L., Thin Solid Films 48 (1978) 247-255. [36] Sanders, I. L., IEEE Duns. Mugn. MAG-19 (1983) 104-110. [37] Solt, K., Thin Solid Films 125 (1985) 251-256. [38] Inagaki, M., Suzuki, M., Iwama, Y., Mizutani, U., Jpn. J. Appl. Phys. Part I 2 5 (1986) 1514-1517. [39] Freitas, P. P., Berger, L., Silvain, J. F., J. Appl. Phys. 61 (1987) 4385-4387. [40] Mayadas, A. F., Janak, J. F., Gangulee, A., J. Appl. Phys. 45 (1974) 2780-2781. [41] Krongelb, S., Gangulee, A., Das, G., IEEE Puns. Magn. MAG-9 (1973) 568-570. [42] Hoffmann, H., Miyazaki, T., IEEE Trans. Mugn. MAG-10 (1974) 556-559. [43] Hoffmann, H., J. Appl. Phys. 57 (1985) 3831 and unpublished work. [44] Herd, S. R., Ahn, K. Y., J; Appl. Phys. 50 (1979) 2384-2386. [45] Gangulee, A., Bajorek, C. H., d’Heurle, F. M., Mayadas, A. F., IEEE Trans. Mugn. MAG-10 (1974) 848-851. [46] Rice, D. W., Suits, J. C., Lewis, S. J., J. Appl. Phys. 47 (1976) 1158-1163. [47] Rice, D. W., Suits, J. C., J. Appl. Phys. 50 (1979) 5899-5901. (481 Chapman, V. B., Mawaha, A. S., Collins, A. J., Thin Solid Films 58 (1979) 247-251. [49] Hammer, W. N., Ahn, K. Y., J. Vuc. Sci. Technol. 17 (1980) 804-807. [50] Chapman, V. B., Collins, A. J., Garwood, R. D., Thin Solid Films 89 (1982) 243-248. [51] Sauermann, H., Dibbern, U., Report BMFT-FB-T 85-021, 1985, Bundesminsterium fur Forschung und Technologie, 5300 Bonn 2, FRG. [52] Reith, T. M., Davis. R. E., Leavitt, J. A., J. Appl. Phys. 57 (1985) 4195-4197. [53] Nagai, Y.,Toshima, T., J; Vuc. Sci. Technol. A 4 (1986) 2364-2368. [54] Imura, R., Sugita, Y., Appl. Phys. Lett. 42 (1983) 302-304. [55] Takahashi, M., J. Appl. Phys. 33, Suppl., (1962) 1101-1106. [56] Iwata, T., Hagedorn, F. B., J. Appl. Phys. 40 (1969) 2258-2266. [57] Makino, Y., Aso, K., Uedaira, S., Hayakawa, M., Ochiai, Y., Hotai, H., J. Appl. Phys. 52 (1981) 2477-2479. [58] Kitada, M., Yamamoto, H., Tsuchiya, H., Thin Solid Films 122 (1984) 173-182. [59] Norton, R. H., IEEE 7huns. Magn. MAG49 (1983) 1579-1580. [60] Tumanski, S., Stabrowski, M. M., IEEE Trans. Magn. MAG-20 (1984) 963-965. [61] Dibbern, U., IEEE Duns. Mugn. MAG-20 (1984) 954-956. [62] Tumanski, S., Stabrowski, M., Sens. Actuators 7 (1985) 285-295. [63] Feng, J. S. Y., Romankiw, L. T., Thompson, D. A., IEEE Trans. Mugn. MAG-l3 (1977) 1466-1468. [64] Dibbern, U., Ger. Put. Appl. D E 33 I7 594 A I, 1983.

380 [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83]

9 Magnetoresistive Sensors Sekizawa, S., Seki, T., Takahashi, T., US Patent 4 639 807, 1983, and Japanese Patents cited there. Jeffers, F. J., IEEE Trans. Magn. MAG-15 (1979) 1628-1630. Tsang, C., J. Appl. Phys. 55 (1984) 2226-2231. Bhattacharyya, M. K., Davidson, R. J., Gill, H. S., J. Appl. Phys. 61 (1987) 4167-4169. Smith, N., IEEE Trans. Magn. MAG-23 (1987) 259-272. Bajorek, C. H., Krongelb, S., Romankiw, L. T., Thompson, D. A., AIP Con$ Proc. 24 (1974) 548-549. Bajorek, C. H., Thompson, D. A., IEEE Trans. Magn. MAG-ll (1975) 1209-1211. Bajorek, C. H., Hempstead, R. D., IBM Tech. Disclos. Bull. 21 (1979) 4239-4240. Kitada, M., Kamo, Y., Tanabe, H., Tsuchiya, H., Momata, K., J. Appl. Phys. 58 (1985) 1667-1670. Munakata, M., Goto, K., Shimada, Y., Jpn. J. Appl. Phys. 23 (1984) L749-L751. Cadieu, E J., Cheung, T. D., Wickramasekara, L., J. Appl. Phys. 57 (1985) 4161-4163. Hempstead, R. D., Krongelb, S., Thompson, D. A., IEEE Trans. Magn. MAG-14 (1978) 521-523. Tsang, C., Lee, K., J. Appl. Phys. 53 (1982) 2605-2607. Vinal, A. W., IEEE Trans. Magn. MAG-20 (1984) 681-686. Petersen, A., Proc. 4th Int. Con$ Automotive Electronics; IEE, London, 1983, pp. 8-13. Petersen, A,, Proc. Transducer Tempcon ConJ 84, Harrogate, Tavistock, Devon, UK: Trident Int. Exhibitions, 1984, pp. 275-289. Kwiatkowski, W., Baranowski, B., Tumanski, S., IEEE 7 h s . Magn. Mag-20 (1984) 966-968. Tumanski, S., IEEE 7kans. Magn. MAG-20 (1984) 1720-1722. Petersen, A., NTG-Fachber. 93 (1986) 200-205.

10

SQUID Sensors HANS KOCH. Physikalisch-Technische

Bundesanstalt. Berlin

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.1

Introduction

10.2 10.2.1 10.2.1.1 10.2.1.2 10.2.2

Fundamental Principles . . . . . . Josephson Junctions . . . . . . . Josephson Effects . . . . . . . . . RSJ Model . . . . . . . . . . . . Flux Quantization . . . . . . . .

10.3 10.3.1 10.3.1.1 10.3.1.2 10.3.2 10.3.2.1 10.3.2.2 10.3.2.3 10.3.3 10.3.3.1 10.3.3.2 10.3.3.3 10.4 10.4.1 10.4.1.1 10.4.1.2 10.4.1.3 10.4.1.4 10.4.2 10.4.2.1 10.4.2.2 10.4.3 10.4.3.1 10.4.3.2 10.4.4 10.4.4.1 10.4.4.2

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

. . . . . . . . . . . . . . . . . . . . . . . . SQUID Basics . . . . . . . . . . . . . . . . . . RF SQUID . . . . . . . . . . . . . . . . . . . Magnetic Flux Relations . . . . . . . . . . . . . . RF SQUID Characteristics . . . . . . . . . . . . . DC SQUID . . . . . . . . . . . . . . . . . . . Magnetic Flux Relations . . . . . DC SQUID Characteristics . . . . Flux Modulation of a DC SQUID Complete SQUID System . . . . . Signal Input Coupling . . . . . . Read-out Schemes . . . . . . . SQUID Sensor Periphery . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

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

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

. . . . .

. . . . .

. . . . . . . ....... Practical Devices . . . . . . . . . . . . . . . Josephson Tunnel Junction . . . . . . . . . . . Lithography and Thin-Film Techniques . . . . Junction Fabrication . . . . . . . . . . . . . Junction Characteristics . . . . . . . . . . . .

. . . . . . .

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

Alternative Configurations ........... -0-Hole RF SQUID . . . . . . . . . . . . . . RF SQUID Fabrication . . . . . . . . . . . . . RF SQUID Electronics . . . . . . . . . . . . . Integrated DC SQUID Magnetometer . . . . . . Fabrication . . . . . . . . . . . . . . . . . . . DC SQUID Electronics . . . . . . . . . . . . . Alternative SQUID Configurations . . . . . . . Bulk SQUIDs . . . . . . . . . . . . . . . . . Non-planar Thin-Film SQUIDs . . . . . . . . .

.........

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

383 384 384 384 386 387 389 390 390 392 395 395 397 400 401 401 403 406 408 408 408 411 413 416 418 418 420 422 422 426 429 429 429

382

10

SQUID Sensors

10.4.4.3 Hybrid SQUIDs . . . . 10.4.4.4 Planar Thin-Film SQUIDs

............... ............... Sensitivity Limits .................. Noise . . . . . . . . . . . . . . . . . . . . . . . .

10.5 10.5.1 Energy Sensitivity . . 10.5.2 10.5.2.1 White Noise Regime 10.5.2.2 l/f Noise . . . . . High-T, SQUIDs . . 10.5.3 10.6

Conclusion

10.7

References

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. .

430 430

.

430 430 432 432 434 436

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438 438

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

10.1 Introduction

383

10.1 Introduction A SQUID (Superconducting Quantum Interference Device) is the most sensitive magnetic sensor to date, achieving a magnetic field resolution in the order of several fT.The operation of SQUID sensors is based on two effects, observable only in the presence of superconductivity: flux quantization and Josephson effects. Superconductivity is a unique thermodynamic state characterized by the condensation of the conduction electrons into pairs featuring opposite momentum and spin (“Copper pairs”). In the theoretical temperature limit of T = 0 K all conduction electrons of the superconducting material are condensed into these pairs. At elevated temperatures an increasing number of excitations occur (“pair breaking”), leading to a number of “quasi-particles” (electrons with a missing counterpart) in addition to the pair condensate. At a critical temperature T,, all pairs break and superconductivity ceases. T, values for some important materials are given in Table 10-1. The last three examples are representatives of the very recently discovered ,,high-T, superconductors”. Some materials, eg, Cu, Ag, and Au, seem to stay non-superconducting at all temperatures, except when brought into contact with a superconductor (“proximity effect”). lhble 10-1. Important superconducting materials. Material

Critical temperature, T, (K)

A1 In Hg Pb Nb

1.18 3.4 4.15 7.2 9.25

Critical temperature, Tc (K)

Material NbTi alloy NbN Y1Ba2Cu30(7

-x)

Bi,Sr,Ca,Cu,O, T1,Ca,Ba,Cu30,

9.5 17 90 110 120

The superconducting electron pairs are able to carry an electric current through the conductor without any loss, ie, “superconductivity” (only at very high frequencies do losses develop). The superconductive state is not only characterized by perfect conduction, but also by many other phenomena occurring simultaneously below T,, such as the ability of the superconducting material to expel magnetic flux (perfect diamagnetism or “Meissner effect”), the occurrence of an energy gap, etc. The condensed electron pairs of the superconducting state are usually described by the socalled order parameter (Ginzburg-Landau theory [l]), which is mathematically similar to a many-body wave function with a well-defined amplitude I w (r)I and phase angle 0 ( r ) :

Although the order parameter itself is not an observable physical propertiy, its amplitude can be related to the electron pair density n, (r), and the phase angle to the classical canonical momentum p (r) = mu + q A of the electron pairs of mass m = 2m, and charge

384

10 SQUID Sensors

q = 2 e in the presence of a magnetic field ( B = V x A , where A = magnetic vector poten-

tial) :

n, (4

=

I w (4I

p ( r ) = 2m,v

+ 2eA

(10-2) =

hVB

(10-3)

(V and V x represent the vector operations grad and curl, respectively). Thus it is obvious that an understanding of superconductivity requires a certain insight into quantum mechanics. The scope of this chapter on SQUID sensors is restricted to their electric and magnetic characteristics. Superconductive phenomena such as flux quantization and Josephson effects are therefore treated with the aim of discussing the electric and magnetic effects that they produce rather than presenting an in-depth physical picture. Readers interested in the physical aspects fo superconductivity are referred to standard textbooks [2-51. SQUID sensors and systems are commercially available, but their variety is extremely limited when compared with the amount of material published on them within the last 20 years. The reasons for this discrepancy may be that the market segment for SQUID sales is still narrow and that SQUIDs are the most sensitive devices available for many applications, so in order to obtain an optimal performance special configurations matched to the experimental requirements are often necessary. In this chapter, we shall describe not only how a commercial SQUID functions, but also give some insight into the fabrication of SQUIDs. Limitations of space, however, will allow only representative descriptions, ie, one Josephson junction fabrication scheme, one practical rf and one DC SQUID, and one read-out electronic circuit in order to expound the principles. The huge number of alternative configurations will be dealt with in the form of tables with references to the literature available. A very valuable and up-to-date review on SQUIDs, that is aimed at specialists in the field has been published very recently [6].

10.2 Fundamental Principles 10.2.1

Josephson Junctions

10.2.1.1 Josephson Effects The classical Josephson junction consists of an insulating barrier between two superconductors thin enough to couple “weakly” the two order parameters representing the superconducting states of both sides: (10-4)

where I ty,I , I iyzl and B,, 0, are the amplitudes and phase angles, respectively.

10.2 Fundamental Principles

385

The coupling between the two superconductive states via the barrier is maintained by electron pair tunneling. In addition to this so-called Josephson tunnel junction (or SIS junction, superconductor insulator superconductor), various other configurations also allow a weak coupling between two superconductors and exhibit a behavior similar to that of tunnel junctions. Thin normal conducting layers (SNS junctions), thin superconducting constrictions (microbridges) and combinations of these (eg, point contacts) are examples of such “weak links”. All weak links show distinct relations between the difference of the phases of the two order - 8, and the current density j = i/A (of the current i passing through the parameters 6 = weak link of cross-sectional area A ) and the voltage drop v at the weak link (Note: throughout the text lower-case letters denote AC quantities and capital letters DC quantities). In the case of the classical Josephson tunnel junction (the weak link best understood in theory), the so-called Josephson relations [7] are j = J, sin 6

(10-6)

and

u = i ~ 2 swat e

.

(10-7)

To a first approximation, these relations are also true for all other types of weak links. In the first Josephson relation (10-6), J, denotes the critical current density of the junction: if a Josephson junction is biased by a constant current source and the current is increased from I = 0, no voltage drop occurs (“zero voltage state”) until the critical value of the current density is reached. Once the critical current is passed, a voltage drop that depends on the time evolution of the phase difference 6 (second Josephson relation, Equation (10-7)) takes place. The value of J, is dependent on material, geometry, and temperature. The thicker the barrier, ie, the weaker the coupling, the lower is J,. Integration of the second Josephson relation results in

6

=

6, + 2 e / h v t .

(10-8)

If 6 in Equation (10-6) is substituted by this expression, one obtains j = J,

sin (w,t

+ do).

(10-9)

Thus, when a voltage drop occurs at a weak link, an AC current flows with a voltage-dependent frequency (Josephson frequency) f J = wJ/2rt = ( 2 e / h ) . v ( 2 e / h = 484 x 10” Hz/V is called the Josephson frequency-voltage ratio). A relationship between voltage u and current i of a junction is obtained by combining Equations (10-6) and (10-7): u = (h/2e sec6/Ic) di/dt = L(6) di/dt

.

(10-10)

Thus a Josephson junction has an effective inductance L dependent on the phase difference 6 across the junction.

386

10 SQUID Sensors

10.2.1.2 RSJ Model

In a practical Josephson junction, in addition to the supercurrent is = I, sin 6 , a normal current in due to a leakage current and due to tunneling quasi-particles (single electrons lacking a counterpart to form a Copper pair) and a displacement current id due to the unavoidable capacitance of tunnel junctions are also present. They are considered in the very commonly used RSJ model (resistively shunted junction model) [8,9] depicted in Figure 10-1. This model describes most of the problems in Josephson device electronics sufficiently well. Only in very few extreme cases is an approach such as that introduced by Werthamer [lo] necessary.

I

Figure 10-1. RSJ (resistively shunted junction) model.

The RSJ model involves an ideal Josephson element obeying the Josephson relations, shunted in parallel by a resistor R and a capacitor C. Thus a bias current Z is subdivided according to Figure 10-1 into

Z = v/R

+ I, sin 6 + C dv/dt .

(10-11)

In order to understand the essential behavior of a Josephson junction (or subsequently a SQUID), even the capacitance can be omitted in the model (C = 0). It should be noted that also in practice the tunnel junctions, when applied to SQUIDS, are shunted with resistors in order to reduce the often adverse role of the capacitance (cf, Section 10.4.1). Then v / R + C dv/dt. By using the second Josephson relation (10-7):

u = A/2e a6/at we obtain

Z/Z, = h/(2eRZC) ad/&

+ sin 6.

This may be directly integrated and for the average voltage V = ( v ) (capital letters for DC or average values) we have:

v=o for Z c I, v = RZ, v ' m for z > z, .

(10-12) =

h/2e (86/at>

(10-13)

Figure 10-2a shows the I - Vcharacteristics for such a simple model junction (with C = 0).

381

10.2 Fundamental Principles

Although this characteristic should be displayed as a V-Z characteristic since the bias current is the independent and the voltage is the dependent variable, this choice of display has become common practice in the literature on superconducting electronics. Figure 10-2b illustrates the time evolution of the supercurrent is for two certain (average) voltage values ( W R I , = 0.1 and 1.5) indicated in Figure 10-2a. If a constant bias current I is applied, the average value of the normal current ( i n )through the resistive shunt and the average value of the supercurrent (is) through the ideal junction add up to I. Note the strong nonsinusoidal time evolution of is for low voltages, giving rise to a large contribution to the average value of is. At higher voltages the average of is approaches ( i s ) = 0. The strong change in frequency is also obvious from Figure 10-2b (f(l.5 mV) = 0.73 x 10” Hz).

<>

< >

-2 a)

-1

-

0

2

1

V/RI,

b)

o

-

1

2

t/r,

Figure 10-2. (a) I-Vcharacteristic for a simplified RSJ model (C = 0). (b) Time evolution of the supercurrent is for two different values of the average junction voltage V ( V / R I , = 1.5, upper trace; V R I , = 0.1, lower trace; T, = 2 . R I , s/V, period of the lower trace).

10.2.2 Flux Quantization As has been mentioned in the Introduction, the classical canonical momentum p = rnv + q A of the electron pairs of mass m = 2 me and charge q = 2 e in the presence of a magnetic field is related to the phase 0 (r) of the order parameter w (r) describing the superconducting state:

p = A V O = 2me v

+ 2eA

(10-14)

where A = magnetic vector potential. The wave-like character of the superconducting state is evident from the quantization of trapped magnetic flux in multiple-connected superconducting regions as in rings or cylinders: along a closed path inside the superconductor but surrounding a non-superconducting region (see Figure 10-3),the phase of the “wave function” is required to differ by 2 R n, where n = 0,

388

10 SQUID Sensors

'-'

$ Bext

Figure 10-3. Superconducting ring with externally applied magnetic induction Be,, , circulating shielding current and path integral $ used.

1, 2, 3, . . ., in order to avoid destructive interference (or, in other words, in order to fulfil the requirement of a unique value of w (r) at every point inside the superconductor). Hence if a path integral (path as indicated in Figure 10-3) is applied to the above equation:

Ape-

dl =

8 (2m, u + 2eA)

(10-15 )

dl

the integrad of the left-hand side should equal 2 x n (compare the similarity to the rather simplified BohddeBroglie picture of an electron represented by its wave function, circling an atom and requiring a phase difference of 2 n n for a closed path, thus leading to the quantization rules for electron momenta). Since the pair current density given by j = n, 2 eu is negligibly small inside a superconductor (except within the so-called penetration depth), the first term on the right may be cancelled, and A 2nx = 2 e $ A . dl

(10-16)

remains. If we apply the Stokes theorem and the definitions of the magnetic induction B = V x A and of the magnetic flux @ = ## B d S through a surface S, then the flux quantization s rule is evolved:

-

nh/2 e

=

$A dl

=

I# (V s

@

=

nh/2e

=

x A ) . d S = jj B * d S s

n @o.

(10-17 )

The quantity @o = h / 2 e = 2.07 x Wb is termed the flux quantum. This can be experimentally verified by applying a magnetic induction B,, parallel to the axis of a superconducting ring or cylinder (cf, Figure 10-3). The flux quantization rule is then fulfilled for the total magnetic flux Gi within the non-superconducting cross section of area S. The externally applied flux , @ , duced flux:

=

##

B,,

d S is compensated in units of @o by an appropriate self-in-

s

(10-18) due to the circulating shielding current Zcirc ( L = self-inductance of the ring).

389

10.3 SQUID Basics

It should be mentioned that the number of flux quanta inside the ring is determined by the value of the externally applied induction Be,, at the incident of the transition from the normal to the superconducting state during cool-down. After passing the transition temperature (the so-called critical temperature T,)a variation of B,, does not induce a flux jump as might be inferred from Figure 10-4a. Instead, via the self-induced flux & = LI,,,, an everincreasing shielding current Z,,, keeps the total flux inside the ring & constant until a critical current density J, is reached that forces the superconductor to become normal conducting. The thick solid lines in Figures 10-4a and 10-4b thus represent the states reached after cooldown in a constant freezing field proportional to the & values of the x-axis, and the thin dashed lines represent the possible states when the externally applied flux is varied after cool-down below T,. Important note: Flux trapping is an annoying incident which frequently occurs during SQUID applications, spoiling the signal detection. Its occurrence depends on the materials used, the geometries, and electromagnetic interference. Thermal cycling in a magnetically well shielded environment helps to remove this phenomenon.

r

3

A-

0

-1 -1

a)

0

1

1

I\

r

\

\

-0.5u -1

2 Qext/Qo

3

-1

b)

0

1

__1c

2

3

Qext/@o

Figure 10-4. (a) Resulting total magnetic flux inside a superconducting ring @,” vs. the externally applied flux &, while passing the transition temperature Tcduring cool-down (b) Self-induced flux & due to the circulating shielding current I,,,, .

10.3 SQUID Basics A SQUID consists of a superconducting ring (in practice the “ring” may be of any shape, provided that the superconducting material completely surrounds a void) interrupted at one or two positions by a Josephson junction. SQUIDs with one junction are rf SQUIDs and those with two junctions are DC SQUIDs, because of the different types of electronic read-out commonly used for them. Both types will be discussed separately in the following sections.

390

I0 SQUID Sensors

10.3.1 RF SQUID

10.3.1.1 Magnetic Flux Relations When a superconductor is placed inside a magnetic field which is not too strong (in order not to destroy superconductivity), the field is completely expelled from the interior of the superconductor due to the Meissner effect, except for a very thin layer at its boundary. The so-called London penetration depth I , is a material- and temperature-dependent measure of the thickness of this layer (eg, I , (Nb) = 40 nm). At a distance I , from the vacuum/superconductor interface, the magnetic field strength falls to l/e of its value at the interface. Inside this layer, shielding currents flow and prevent the magnetic field from penetrating into the superconductor. When the flux quantization rule was derived in the preceding section (Section 10.2.2), the path integral was chosen so that at no point does it enter the boundary layer. Hence the term in the path integral containing the current densityj could be neglected (cf, Equation (10-15)). If a superconducting ring contains a weak link, it is not possible to find a path with negligible current density close to the weak link (Figure 10-5). Then the following expression remains:

(10-19) with A = 2 m,/(n,(2 e)2) . The whole integral on the right-hand side of Equation (10-19) is called a fluxoid, and therefore the more generally valid rule is that of fluxoid quantization:

n@,, = Gi

+ A $ j *d l .

(10-20)

When a path integral of the above type crosses a weak link that interrupts a superconducting ring, then a considerable current density j exists in this region of the path, and this must be taken into account. The whole phase difference for one circular path (as indicated in Figure 10-5) must therefore again be 2 x n and is made up of the contribution from the magnetic flux threading the ring and the remaining phase difference across the weak link: a

2 x n = 2n1p~/@,+ 2 x A / @ 0 S j . d l

(10-21)

-a

where 2 a = length of the region with considerable current density, and

(10-22) Note that this configuration is in principle the heart of an rf SQUID sensor. Again, the relation between a magnetic flux inside the ring @i and the externally applied flux is given by the relation: @i

=

+ Li.

(10-23)

10.3 SQUID Basics

391

2a

Figure 10-5. Superconducting ring containing one weak link (included: path of integral f).

In this case i obeys the first Josephson relation i = Z, sin 6. In Equation (10-22) it has been shown that 6 is related to gi, thus 6 may be replaced accordingly (the term 2 n n can be disregarded in an argument of a sine function):

The corresponding characteristics are shown in Figure 10-6 for three different values of the parameter nPL @, = 2LZc/@0).The choice of this parameter is obvious from nPL = 1; it is the limiting case between the non-hysteretic (eg, nPL = 0.5) and the hysteretic mode (eg, nPL = 5).

The hysteretic mode is characterized by the occurrence of negative slopes in the characteristics. If the externally applied magnetic flux is increased, the internal flux follows the characteristics only up to the point where the slope becomes infinite, and then, as following the subsequent negative slope would be unfavorable as regards energy, a flux jump as indicated in Figure 10-6 occurs. The situation is similar when the externally applied flux is decreased, but as the flux jumps for decreasing external flux occur at different values @at than for increasing external flux, a hysteretic behavior of the rf SQUID configuration is the result. The case PL = 0 is similar to the behavior of a normal conducting ring. In order to illustrate the role of the self-induced flux &, Figure 10-7 shows an example of increasing (thick lines) externally applied flux for nPL = 3. Both figures should be compared with Figure 10-4, showing a superconductive ring without a weak link, in order to assess the influence of this. 3

f2 1

Figure 10-6 Relation between the magnetic flux inside a superconducting ring with one weak link dinand an externally applied flux dextfor n& = 0.5, 1, and 5 .

a 0

1

2

3 gsxt

/!&

392

10 SQUID Sensors

1 -1

0

1

2

3

@ext /go

a)

-1

b)

0

1

2 % 5

3 /Po

Figure 10-7. Relation between the internal flux Qin, the externally applied flux Omt (a), and self-induced flux @$ (b) for increasing flux Oat (n& = 3).

10.3.1.2 RF SQUID Characteristics

The relationships between the input and output signals of an rf SQUID may be obtained with the electronic circuit shown in Figure 10-8 as a block diagram. The SQUID ring is coupled inductively to an L C tank circuit that is tuned to the frequency of an rf signal provided by an rf oscillator.

Q-r

input

QGSOUID

tank circuit

Figure 10-8. Electronic circuit for obtaining the rf SQUID characteristics.

10.3 SQUID Basics

393

The peak value of the voltage drop urf across the tank circuit is measured by an rf amplifier together with a detector. This serves as the output signal to be investigated in the following section in relation to the rf signal power Prfapplied to the tank circuit. In addition, the value of uIf is dependent on the low-frequency input signal: the flux @ext applied to the SQUID ring via the inductively coupled input coil. The whole scheme resembles those well-established parametric amplification schemes known from other fields of electronic engineering: a very weak low-frequency input signal is mixed with a relatively strong rf pump signal via a device with a pronounced nonlinear characteristic. Owing to the parametric up-conversion, the detected signal appears amplified as a sideband signal adjacent to the rf bias signal at the output of the device. Next the interplay between the signals will be analysed in more detail. By applying a certain magntic DC bias field to the SQUID ring via the input coil, a working point may be chosen corresponding to @ext = rz& (cf, Figure 10-6 and the points in the inserts at the top of Figure 10-9a). If the rf pump signal is applied to the tank circuit, an additional rf flux @rf is coupled to the SQUID loop, providing a modulation of the flux threading the SQUID ring. The amplitude of this rf modulation for different power levels of the rf oscillator signal is indicated in the inserts of Figure 10-9a by thick lines. When the rf power is increased, first the amplitude of the output voltage vrf increases proportionally until a Grf amplitude is reached, where an excursion around one hysteresis loop takes place as indicated in the left insert of Figure 10-9a. This has far-reaching consequences, since such an excursion is dissipative. The energy thus absorbed is extracted from the tank circuit, resulting in an instantly decreased It takes several cycles (depending on the quality factor of the tank circuit) before the original value of @ r f is regained. Thus vIf is now modulated accordingly as illustrated in trace 1 in Figure 10-9b, and its peak value remains the

a)

o

A

B-

c 4

b)

0

10

20

30

40

t/T

vs. rf pump Figure 10-9. (a) Development of the staircase pattern: output voltage peak value signal power Prffor the two extreme DC bias cases, geXt= n o o (thick line) and gat = (n - 1/2) go (thin line). The inserts at the top indicate the respective section of the flux relation characteristic (cf, Figure 10-6) covered by the rf modulation for the first and second part of the staircase plateau. A, B, and C are the bias levels from which the triangle patterns in Figure 10-10 were derived. (b) Schematic diagram of the urf traces, illustrating the output voltage modulation at different instances marked 1 and 2 in the staircase pattern.

394

10 SQUID Sensors

same even if the power level of the pump signal is further increased, leading to a plateau in characteristics. the u,f,max/Prf The only consequence of an increase in rf power is a quicker build-up of the oscillation amplitude equivalent to an increase in the modulation frequency (see trace 2 in Figure 10-9b). amplitude to This continues until the PI level becomes strong enough for the regained reach its former value within one cycle. There is then sufficient energy to force the SQUID through a second dissipative hysteresis as indicated in the right insert. Again, is instantly depressed and must be built up, leading to a uIf signal similar to trace 1. A further increase in rf power PIfincreases the modulation frequency again (trace 2), until enough energy is provided within one cycle to overcome the energy dissipation of two hysteretic excursions at once. Only then is the amplitude of urf able to increase again, until the next hysteresis is reached. In this way, the so-called “staircase pattern” develops. If the working point (set by the magnetic DC bias flux) is changed to GeXt = (n - 112) do,the thin line staircase pattern in Figure 10-9a results. To summarize, uIf is not modulated while at the staircase slopes. The plateaux result from the need for a replacement of the amount of energy absorbed by one hysteric excursion, leading to a modulation of uIf. The description of the rf SQUID operation given above is illustrative (cf, [ll]) but incomplete. In particular, it cannot explain the development of a staircase characteristic for a non-hysteretic rf SQUID. A more rigorous theoretical treatment yields the staircase characteristic for this non-hysteretic case, too [12]. As the inductance L of the SQUID ring is nonlinearly dependent on the magnetic flux (Figure 10-6), it influences the quality factor of the tank circuit accordingly, leading to the parametric up-conversion mentioned at the beginning of this section. In another mode of operation, the rf power level PIfis kept constant (ie, the dashed vertical lines indicated by A, B, and C in Figure 10-9a) and the magnetic flux @ext is varied. This , ~ ~ ~ is the normal mode of operation of an rf SQUID. In this case the peak value of u , ~varies between the two extreme examples shown in Figure 10-9a, and the so-called “triangle pattern” is then obtained (Figure 10-10). This triangle pattern represents the commonly used rf SQUID output/input signal dependence ( u , ~ , , = , ~f(#ext))r and is exploited in the rf SQUID readout electronics introduced in Section 10.3.3.2.

0

1

2

3 Qext/go

4

Figure 10-10.

Triangle pattern: output vs. input signal for three different bias values indicated in Figure 10-9a.

10.3 SQUID Basics

10.3.2

395

DC SQUID

10.3.2.1 Magnetic Flux Relations A configuration consisting of a superconductive ring containing two weak links forms the main part of a DC SQUID. If the same procedure is used for the path integral h $ V B dl as for the rf SQUID (cf, Equation 10-22),

2nn

=

2~@~/@ - ,6,,

+ 6,

(10-25)

is obtained, 6, and 6, being the phase differences A 0 at both weak links. For DC SQUID applications a constant bias current I b would be fed to the configuration (shown in Figure 10-11). This bias current is divided between the two branches as follows:

Ib= i,

+ i,

=

I,,

sin 6,

+ Ic2

sin 6,

(10-26)

(in order to show the essential relationships, only ideal Josephson junctions are considered in this context, and not the more realistic RSJ model). 6, may be replaced with the help of Equation (10-25) (disregarding 2 n n in the sine argument), thus

Ib= I , , Again,

@i

sin 6,

+ I,,

sin (6, - 2 n @i/@o).

is the sum of the externally applied flux

@ext

(10-27) and the self-induced flux:

icircmay be replaced by

(10-29)

icirc= (i, - i , ) / 2 . The currents in the branches i, and i, may be regarded as the superposition of:

i. the branch currents in the case of a symmetrical device (no applied flux present, hence i,,o= 1b/2 and i2,0 = I&); and ii. the circular current iCi, due to the flux. The relations between Ib,i , , i, and icircare illustrated in Figure 10-12 for the top feeding point. Hence, @s =

(10-30a)

L (i, - i J / 2

and @in = @ext

+ L / 2 (Icz sin 6, - I,,

sin 6,).

(10-30b)

396

10 SQUID Sensors

1 Figure 1 0 4 . Superconductive ring with two weak links fed by a constant bias current Ib, respresenting the basic configuration of a DC SQUID.

vA\

Figure 10-12. Relation between the currents at the top feeding point of the DC SQUID.

'circ

1

3,1%

t

OS5

0

-0.5

-1 -1 a)

0

1

2

-1

3

L t 190

b)

0

1

2 4 x t

3

1%

and the externally applied flux @ext and (b) the Figure 1043. Relation between (a) the internal flux self-induced flux GSand Gat for a superconductive ring with two weak links.

must be calculated numerically [13]. Figure 10-13 presents The relation between qjinand the results for the parameters pL = 2LIc/@, = 1, z b = 1.0 Z, (and pL = 1, z b = 2.1 Z, for the less modulated curves) and should be compared with Figures 10-4 and 10-7. If both junctions are still superconducting (in this example for pL = 1, z b = 0.8 zc), the circulating current IciX is a DC quantity. Otherwise (eg, for BL = 1, z b = 2.1 I,), iciXand therefore & are AC quantities, hence the less modulated curves in Figure 10-13 represent time averages of @s and &. The role of the self-induced flux 9,is shown in Figure 10-13b.

391

10.3 SQUID Basics

10.3.2.2 DC SQUID Characteristics In designing a DC SQUID, a numerical evaluation of a lumped circuit model using the RSJ model for the junctions and taking noise into account by placing Johnson noise sources at the junction shunt resistors provides useful orientation as to how a practical SQUID would behave. In Figure 10-14 such a lumped circuit model is displayed (cf, [14]). For clarity, only symmetric branches (ie, I,, = I,, = I , , R , = R , = R , etc.) will be discussed here. The time-dependent voltage drop across the whole SQUID, v (t), is given by either u = u1

- L / 2 di,,/dt

(10-31)

v = v2

+ L / 2 diCi,/dt.

(10-32)

or

Hence v (t) = ( v ,

+ u,)/2.

Figure 10-14. Lumped circuit model of a DC SQUID with symmetrical branches.

(10-33)

'noise

/noise

The constant bias current Ibis divided into two branch currents, i, and iz: Ib

= i,

+ i, .

(10-34)

At the junctions, each branch current is split into three components:

i,

=

I, sin 6,

i, = 1, sin 6,

+ ( v , + uN,)/R + C d v , / d t + (0, + v N , ) / R + c dv,/dt.

(10-35) (10-36)

398

10 SQUID Sensors

In order to show the principal relationships, in another simplification the noise ( v N , , ,= 0) and the role of the capacitance (C = 0) are omitted. i, and i2 may be replaced by the bias current Zb and the circulating current icirccaused by the applied magnetic flux (cf, Equation (10-29)):

i,

=

Zb/2 - icirc

(10-37)

i,

=

zb/2

+ icirc

(10-38)

and u , , by ~ the second Josephson relation (10-7): v,,, = h / 2 e

as,,,/at.

(10-39)

Together with the relation between the circulating current icirc and the externally applied flux @ext (cf, previous section), a system of four coupled equations is constructed that can be solved numerically:

(10-40)

36, _ - (1b/2

at

- iCir,

as _ , -- (I& + iCi, at

- I, sin 6,) 2 e / h R

- Z, sin 6,) 2e/AR

(10-42)

.

(10-43)

Figure 10-15 illustrates a representative time evolution of the phase differences of both junctions 6, and 6,,the resulting circulating current icirc and the voltage v ( t ) = v1 + u2 for an arbitrary choice of the initial conditions (6, (t = 0), 6,(t = 0)). Note the transients at the beginning and the evolution to a steady state that represents the “real” situation. The voltage and the circulating current oscillate even when the applied flux is constant. The term “interference” in the acronym SQUID results from the “interference” of the phase difference 6, and 6,, which is manifest in icirc cc (6, - 6,). The oscillations of u (t) are very fast (Josephson relation), thus the amplifiers used for voltage read-out register the average voltage ( u ( t ) ) only. Figure 10-16 shows a representative DC SQUID I - ( v ( t ) > characteristic obtained by solving the equations given above for various applied flux values and /IL= 1. The key features of the characteristics are: i. I,, the zero voltage current, is modulated periodically by the applied flux with a period Go (“critical current modulation”). ii. Consequently, a part of the voltage carrying regime is also flux modulated (“voltage modulation”). The magnitude of the voltage modulation decreases with increasing bias current.

399

10.3 SQUID Basics

a)

50 4,2

40 130 20 10

I

0 0

20

40

-1 60

o

80

t/0,/2nIcR

I

40

20

60

a0

t / P O / 2 n I,R

c

0

-

20

40

60

80

t/P0/2n

I,R

Figure 10-15.Time evolution of (a) the phase differences 6, and 6, at both junctions, (b) of the circulating current iCi,,, and (c) of the voltage v for PL = 1, an applied flux of QeXt = 0.25 Go, and a bias current of Ib = 2.1 I , . 5

I/&

I: 2 1

Figure 10-16. I-LJcharacteristics of a DC SQUID for various applied flux values = O@,, 0.25@,, 0.5@,, 0.75 @, and 1 @, and PL = 1.

, @,

0 0

0.5

1

1.5

2

2.5

/ I , R

400

10 SQUID Sensors

10.3.2.3 Flux Modulation of a DC SQUID

When the DC SQUID characteristics are calculated with the model introduced above, two important parameters can be recognized ([15]). The hysteresis parameter

PC = 2 n Z , R 2 C / @ o

(10-44)

determines whether the characteristics show switching or whether they are smooth. The latter is the case for Pc < 1. This is the regime exploited in practical SQUID devices. The modulation parameter PL =

2LZ,/@,

(10-45)

determines the depth of modulation AZ, = (Z,,,,= as demonstrated in Figure 10-17. It has been shown [14] that a value of PL = 1 leads to an optimum signal-to-noise ratio. In Figure 10-17, in addition to the zero voltage currents for the whole device I,, the zero voltage currents through the individual junctions I,,,, Zo,2 have been included for DL = 1, 2.5

,

101L 1

2 -

1

.

10

5

-

-

1 -

0

0.5

r

-

1.5

1

gext

1.5

w

2

/go I

I

0 0

. 0

Figure 10-17. Zero voltage currents I,, of a DC SQUID modulated by the applied flux

0.5

5 1 A

m 1.5

gext/go

Figure 10-18. Modulation of the average output voltage ( v ) of a DC SQUID by the applied magnetic flux @ext (parameter: bias current Ib).

10.3 SQUID Basics

401

showing the effect of switching the orientation (sign) of I,,, at each value of @ = ( 2 n - 1) @0/2 (cf, Figure 10-13). Another way of illustrating the effect of the modulation of the I-Vcharacteristics is shown in Figure 10-18, which illustrates the dependence of the average voltage ( v ) versus the applied magnetic flux for different bias currents Ib (cf, Figure 10-16). This characteristic reflects practically the most important relation, since it displays the voltage as measure of the magnetic flux applied to the DC SQUID. This voltage-flux relation resembles the “triangle pattern” of an rf SQUID (Figure 10-10). Both characteristics show the flux periodicity in units of @o and, when properly biased, sharp minima that can be exploited by the read-out electronics introduced in Section 10.3.3.2.

10.3.3 Complete SQUID System 10.3.3.1 Signal Input Coupling Commercial SQUID sensor devices are generally available in a small cylindrical package containing the SQUID sensor itself mounted together with an input coupling coil and either an rf tank circuit (rf SQUID) or a matching transformer (DC SQUID). The magnetic field detection must then be maintained with a pickup coil connected to the input coil via two superconducting screw contacts on the sensor device package. A so-called flux transformer [16] is thus formed (cf, Figure 10-19), consisting of two connected superconducting coils, one for signal pickup and one for coupling the signal to the SQUID loop via / z between the input coil inductance L, and the the mutual inductance Mi,sQ= /qSQv SQUID loop inductance LsQ (ki,sQ= coupling constant). As the whole flux transformer configuration is superconducting (including the screw connections), the principle of flux quantization also applies to it. A magnetic flux caught by the large pickup loop drives a circulating current, which in turn produces a flux in the input coil coupling it to the SQUID loop. Optimum signal transfer is achieved if the inductances of the pickup coil L, and the input coil Liare matched (ie, equal). SQUID inductances are usually small in order to obtain an optimum signal-to-noise ratio, but then it is difficult to couple the magnetic flux into the SQUID ring efficiently without a flux transformer. An example of a proper flux transformer design will be given in Section 10.4.3. Another advantage of using a flux transformer is that it is possible to reduce the bandwidth of the SQUID input according to experimental requirements with the help of damping filters. High-frequency noise may easily deteriorate the signal-to-noise ratio owing to downmixing at the nonlinear characteristics of the Josephson junctions [17]. Further, the pickup loop configuration may be individually tailored to extract the optimum signal level from the individual type of signal source investigated (size, shape of samples, etc.). Very frequently, pickup loops are configured to detect a magnetic field gradient [16]. These are coil configurations with two or more connected coils of opposite windings arranged at certain distances (“baseline”) from each other (see Figure 10-20b). As distant sources produce spatially very homogeneous fields, these configurations very efficiently reduce many of the unwanted signals (noise sources) and chiefly detect the wanted

402

10 SQUID Sensors

a)

A 1

SQUID-package flux transformer

Figure 10-19. Flux transformer coupled to a SQUID loop: (a) schematic; (b) real device.

signals from the adjacent sample that produces spatially very inhomogeneous fields at the “gradiometer” coils. A distant noise source might still produce a considerable field gradient at the measurement site owing to field distortions generated, for instance, by the steel structures of the building. In this event, so-called second-order gradiometers may also compensate this gradient for signal discrimination. In addition to this, the geometry of the gradiometer may be optimized to localize a magnetic source or to discriminate between different types of sources, eg, current dipole vs. quadrupole (important in biomagnetic applications). Figure 10-20 shows different types of gradiometers: the three-dimensional ones (a-d) are usually wire-wound whereas the planar configurations (e-f) are well-suited to thin-film technology and are thus an appropriate choice for an integration with thin film SQUIDS (cf, Section 10.4.3).

10.3 SQUID Basics

Figure 10-20. Various pickup coil configurations: (a) magnetometer coil; (b-f) gradiometers: (b) 1st order, (c) 2nd order, (d) asymmetric 1st order, (e) planar 1st order, (f) planar 2nd order.

e)

403

f)

The gradiometer’s performance is largely dependent on the quality of the “balancing”, ie, the achievment of zero response to spatially homogeneous fields and/or field gradients. Further limitations are imposed on the design of gradiometers when several SQUID sensors are combined to work as a multi-sensor configuration. Such a system may be implemented for parallel read-out for an instantaneous magnetic field mapping. This in turn allows a magnetic source to be localized without changing the sensor’s position relative to it, and to evaluate source propagation effects and nonperiodic events (biomagnetism). The requirements on the design of gradiometers for multi-sensor systems are sometimes conflicting: high sensitivity, good localizability of sources, avoidance of cross-talk between channels, and added to this the whole configuration must fit into the Dewar (cf, Section 10.3.3.3) and balancing must be possible independently for each channel. Such multi-channel systems have been the subject of recent research [18, 191.

10.3.3.2 Read-out Schemes

Both the DC SQUID and the rf SQUID can be electronically read-out by taking advantage of the periodic V ( @ )responses described in the respective sections (Figures 10-10 and 10-18). The dynamic range would be small if a direct read-out were employed. Counting the flux periods would not be accurate enough for most applications. Better resolution and a large dynamic range can be obtained with a linearization scheme termed the “flux locked loop” (FLL) [20]. In this scheme, an AC flux (usually at 100 kHz) is applied to the SQUID in addition to the input signal to be detected. Modulation techniques such as this one are often used in dedicated measurements to detect small changes of noisy low-frequency signals (lock-in detection). Figure 10-21 shows schematically the resulting output voltage waveform for three different choices of DC flux bias. If the modulated flux is DC biased at a minimum (or maximum) of the “triangle” pattern, a frequency-doubled voltage develops (Figure 10-21a). If the DC component of the flux deviates from this working point, a voltage component with the fundamental frequency develops which is in-phase or out-of-phase with the modulating flux, depending on the sign of the flux change (Figures 10-21b and c).

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10 SQUID Sensors

Figure 10-21. The three basic output voltage (0)waveforms obtained for the respective DC bias values of the modulated flux 6.

A circuit exploiting this property may be used for both types of SQUIDs, as indicated in a block diagram in Figure 10-22. The circuit employs an oscillator with two purposes: i. via a modulation coil it modulates the flux threading the SQUID loop (in the case of an rf SQUID the tank circuit inductance may be used as a modulation coil); and ii. it provides the reference for the phase sensitive detector (PSD). The latter detects and amplifies the signal output from the modulation amplifier. A highgain integrating amplifier connected to the phase-sensitive detector provides the DC feedback to the SQUID circuit and thus a linearized output voltage drop across the feedback resistor R . This voltage is a direct measure of the magnetic flux applied to the SQUID. Instead of feeding back the modulation signal to the SQUID loop itself, it may be advantageous to couple the signal to a section of the flux transformer circuit in order to null the current [21]. This operation mode reduces cross-talk problems in multi-channel SQUID applications [22]. In addition to this most popular read-out scheme, several others have been proposed, eg, i. a relaxation oscillator read-out suitable for hysteretic SQUIDs ([23] and references cited therein);

10.3 SQUID Basics

405

F

I

detector

41

\I

rnodulatioA feedback input

input

SQUID

I\

tank circuit

-

bias current source

" out

matching circuit

integrator

I -

7 modulation feedback Input

I I

m o d u lotion

input

SQUID

Figure 10-22. Flux-locked loop read-out scheme. Right of dashed line, central part of the circuit; left of dashed line, two different interface circuits for rf SQUID (top) and DC SQUID operation (bottom).

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10 SQUID Sensors

ii. a digital read-out consisting of a comparator, an up-down counter and a digital-to-analog converter in a feedback loop. This concept appears to be very promising for future “onchip” integration to provide an “intelligent sensor” [24]. An alternative design of a digital read-out requires only two leads per SQUID [25] - a considerable advantage for multisensor systems with their need for minimized heat loss per channel.

10.3.3.3 SQUID Sensor Periphery More than with any other type of magnetic sensors, the performance of SQUIDs depends very much on the quality of a specially adapted periphery. SQUIDs need to be cooled to an operating temperature Toppreferably below half the value of the critical temperature T, of the superconductive material of which they are made. Fluctuations of the operating temperature then have a minute effect on the critical electrical parameters (eg, I,) and thus contribute little to the overall noise. The sensors are normally immersed in liquid helium (Top = 4.2 K). With the advent of high - T, superconductors, it is hoped that liquid nitrogen (Top = 77 K) might also become feasible as a coolant. Although some SQUID applications might be performed inside a liquid helium storage can by using a dip-stick set-up, most applications require specially designed Dewars, a kind of thermos flask. The essential points in the design of SQUID Dewars are: i. closest proximity of the source of the magnetic induction to the pickup coils of the SQUID sensor; depending on the type of source and pickup coil, l/r - l / r 4 laws for signal detectability exist; ii. materials employed next to the sensor coil should be virtually free from magnetic or magnetizable impurities and should suppress eddy currents in order to keep the noise level low (eg, the use of rf shields should be avoided near the sensor). The quality of the Dewar design may be judged from its contribution to the overall noise of the SQUID system. The minimum wall thickness in the proximity of the SQUID pickup coil must be achieved without violating the safety margins of mechanical stability. The helium evaporation rate due to heat leaks should also be kept as low as possible to reduce the number of helium refills necessary. GFRP (glass fiber-reinforced plastic) Dewars are predominantly employed for most SQUID applications [26, 271. Figure 10-23 is a schematic representation of such a Dewar’s cross section. The inner and outer walls are made of GFRP. Between both walls a vacuum is maintained as in a thermos and supported by a getter. Heat radiation losses are minimized by “super-insulation” (several layers of thin metallized plastic foils with a high reflection coefficient). The detector coil and the SQUID sensor set-up are immersed in the liquid helium stored within the inner container. They are fixed to a rod through which the electric leads are fed to the preamplifier unit positioned at the top of the,dip-stick at room temperature. The first preamplifier is rarely cooled in order to reduce the amplifier noise, because this would considerably increase the helium evaporation rate.

401

10.3 SQUID Basics

preamp unit shroud baffle outer dewar wall inner

Figure 10-23. Schematic cross section of a glass fiber-reinforced plastic Dewar equipped with a SQUID insert.

superinsulation liquid He SQUIDsensor

~

tail section

pick- u p coil

The evaporating helium is forced by baffles to flow along the wall of the Dewar neck, thus cooling the neck and a metal shroud attached to it, which in turn cools the super-insulation via metal strings connected to the shroud and various points of the metallized layers. The baffles also act as thermal radiation shields. The critical region is that next to the detection coils. Here, the super-insulation should consist of only a few layers in order to keep its noise contribution low. The double wall should be thin and shaped according to the sample: various solutions have been found for different applications, eg, horizontal room-temperature access for geophysical (rock) samples via a cylindrical double-wall channel straight through the Dewar [28], or a tail section with a spherical bottom for biomagnetic brain research [19]. For many years, investigations have been carried out into the possibility of using closedcycle cryocoolers for SQUID applications in order to be independent of the liquid helium supply. Noise levels which are too high (eg, pressure waves in the working gas), intolerable temperature fluctuations and the poor long-term performance are still unattractive features of such systems [29]. Another important point concerning the SQUID periphery concerns environmental noise reduction techniques. Owing to their extremely high sensitivity, SQUID sensors are not only susceptible to the sample signal but also to all extraneous noise sources, ranging over the whole bandwidth from DC to several hundred GHz (thermal noise, building vibrations, solar activity, interference from radio, RADAR, subway, etc.). The SQUID sensor output signal is periodic in Go, and its dynamic range is relatively small. Owing to its extreme broadband response, already noise spikes producing a flux of @ > @0/2may unlock the read-out electronics, thus leading to false results. SQUIDS of normal sensitivity would not show any voltage modulation in the usual laboratory environment: the ever-present electromagnetic noise impairs its electrical characteristics (“noise rounding”) and leaves the device incapable of signal detection. A combination of different methods is necessary to obtain useful measurement conditions: electrical and magnetic shielding (Section 1.8), specially designed gradiometer coils (Section 10.3.3.1), and advanced electronic filtering techniques (analog and digital filtering [30, 311).

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Shielding is recommended at different levels. The SQUID sensor itself may either be placed inside a superconductive cylinder and connected to the outside world via a “flux transformer” (Section 10.3.3.1) or it may be designed to be “self-shielding” (eg, the two-hole rf SQUID, see Section 10.4.2). In addition, the measurements should be performed in shielded rooms [32] employing either eddy-current shielding or magnetic-field damping, with wall materials of high permeability (Mumetal). More details are given in Chapter 1, Section 1.8. To summarize, a SQUID sensor is only as good as its environment. Only careful shielding, cooling, and implementation of noise reduction techniques make it a useful tool.

10.4 Practical Devices 10.4.1 Josephson Tunnel Junction 10.4.1.1 Lithography and Thin-Film Techniques Josephson tunnel juction fabrication is nowadays based on methods the same as or similar to those employed in semiconductor device fabrication, namely lithography and thin-film techniques (valuable overviews have been given [33, 341). The thin-film technique is used to produce a whole electronic circuit, ie, devices (eg, Josephson junctions), and leads (eg, superconductive interconnections in the form of thin-film strip lines) on a substrate. Commonly a silicon wafer is used as a substrate. Numerous methods of thin-film deposition exist and have been used for superconductive thin films: thermal evaporation, electron-beam evaporation, plasma sputtering, ion-beam sputtering, molecular-beam epitaxy, etc. In recent years with the trend to “all-refractory” (ie, hard) materials, sputtering has become the method of choice. Sputtering is a process that takes place in discharges when ions created in the plasma are accelerated to an electrode surface (target) and “kick off” atoms from the target material. This creates a vapor of target material that forms a deposit on the substrate placed opposite the target, thus forming the thin film. Deposition rates are dependent on the electric energy deposited in the plasma, on the cathode fall voltage, the type of gas (normally argon) and the total gas pressure, the partial pressure of impurities (they sometimes have a considerable effect on the plasma parameters), the use of specially shaped magnetic fields (magnetron sputter sources), the value of a bias voltage at the substrate, the location of the substrate relative to the target, and the target condition (surface topography, implanted impurities, etc.). Cleanliness is important, as even small impurities may drastically degrade the superconductivity. Nevertheless, the vacuum system does not need to be of UHV (ultra-high vacuum) quality when niobium technology is involved, because niobium is an excellent getter material (ie, it reacts with the residual gas). The trick is first to sputter the niobium target for several minutes (sometimes up to 30 min) while covering the substrate, and only then to expose the substrate for deposition.

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409

A few more important points to be observed in order to obtain a high-quality superconductive film are: cleaning the substrate prior to deposition by rf sputtering (sputter cleaning) high deposition rates additional substrate bias substrate temperature control no other processes in the system than the standard process optimized sputter parameters. It should be emphasized that each sputter plant has its own individual properties, and a careful process optimization procedure should be maintained individually for each plant. The parameters given in Table 10-2 may be used as guidelines for producing a thin niobium film with a DC magnetron sputter source. lilble 10-2. Sputter parameters for Nb thin-film fabrication. Parameter

Value

Parameter

Value

Nb target diameter Target-substrate distance Ar pressure

10 cm I cm 1.0 Pa

Discharge power Deposition rate Nb film thickness

1000 w 270 nm/min 300 nm

The best quality criteria for superconducting films are the T, values and the superconducting transition width of the resistivity vs. temperature curve. The so-called residue resistivity ratio (RRR) (resistivity at 293 K relative to the resistivity just above T,) is a more ambiguous measure of the quality with reference to superconductivity. Lithographic techniques are usually used to structure a thin film into leads or electrode layers for devices. The two most popular methods of structuring a thin film (for instance, into a strip line) are illustrated in Figure 10-24. In the left column the “lift-off” process is shown, and on the right an etching process: The steps are as follows:

a. Photoresist is applied to either the substrate (lift-off method, left) or to a substrate that is already covered with the thin film to be structured (etching method, right). b. The photoresist is exposed by contact printing with chromium masks as shown. The contrast of the chromium masks must be in reverse for the two structuring methods (if socalled positive photoresists are used, the contrast must be inverse for both methods). c. Development (ie, removal) of the exposed resist. The remaining resist has very different tasks to fulfil, as follow. d. The lift-off method (left) is continued by the deposition of the thin-film material. In the etching method, the photoresist acts as an etch mask, that is, it protects the underlying thin film from the subsequent etching process. This etching process may be either an etching bath which dissolves the thin-film material (wet etching) or a plasma o r ion-beam process where the thin film is removed by a sputtering process in an inert or reactive gas atmosphere, ie, “dry etching”, more specifically, “plasma etching”, “reactive ion etching” (RIE), “reactive ion-beam etching” (RIBE).

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Figure 10-24. Main fabrication steps of the "lift-off" process (left) and an etching process (right). The cross sections of the substrate are white, those of the thin film are black and those of the photoresist are either hatched or cross-hatched, depending on whether it is exposed or unexposed. In (b) contact printing with chromium masks is indicated.

e. The final step in both methods is the removal of the remaining photoresist in an ultrasonic acetone bath that reveals the desired thin-film structure. The lift-off process obtained its name from this step, as here the thin film on top of the photoresist is also washed away. Both methods have their advantages and drawbacks. The major disadvantage of the lift-off process is the necessary restriction of the process temperature during thin-film deposition, as the photoresist cannot withstand a temperature above 120°C, cross linking of the resist occurs, and lift-off becomes impossible. On the other hand, etching methods require a complicated end-point detection that becomes increasingly difficult if multi-layer thin-film circuits are to be fabricated. In addition, the etching may harm the superconducting properties by implants if not performed with great care. It is also very difficult to maintain smooth-edged surfaces after etching. With both processes special care is necessary to obtain good edges. Superconducting thin films in particular require well-defined edges, otherwise the edge regions may vary in their critical temperature T, , ie, at different temperatures the superconducting cross-section will be different. Edges of bad quality may result with the lift-off process because during thin-film deposition the edge of the photoresist is partially covered, leading to a connection between the thin film on the substrate and the thin film on the resist. After lift-off, the resulting rupture at the thinnest part of the connection leaves very rough edges (ears) as shown in Figure 10-25a. These are sources of trouble, particularly in multi-layer circuits (bad step coverage in subsequent insulation layer deposition, sources of electric breakthroughs followed by shorts, etc.). One way to avoid this is to bathe the resist prior to development in chlorobenzene, which hardens the top layer of the resist [35]. The subsequent development produces an overhang that leads to much better edges (cf, Figure 10-25b).

41 1

10.4 Practical Devices

4

b)

4

Figure 10-25. Edge quality obtained with three different processes: (a) lift-off; (b) chlorobenzene; and (c) dry etching.

The dry etching process, also often leads to edges of bad quality: the increased sputtering rate at the edges due to the spatially higher ion density, due in turn to reflected ions, results in trenching pitches. The redeposition of sputtered material at the photoresist edges also results in ears (cf, Figure 10-25c). An added disadvantage is that etched edges often have a very rough surface and the properties of the surface layer are often degraded.

10.4.1.2 Junction Fabrication A sample fabrication scheme for a complete tunnel junction including a resistive shunt is introduced next (the parameters given are only guidelines). The process is a modification [36] of the very common SNAP process developed at Sperry [37] (cf, Figure 10-26). First a trilayer consisting of the base electrode, the barrier, and the counter electrode layer of all the tunnel junctions to be made is deposited: Nb layers 300 and 30 nm thick are deposited with a DC magnetron sputter source with the data given in the previous section. The Si,N,, barrier is formed as follows: a 2 nm thick layer of a-Si is deposited from an rf magnetron sputter source in an Ar plasma (pressure, 1.0 Pa; deposition rate, 1.1 nmlmin; power density, 0.5 W/cmZ). Nitridation is then performed in an N, rf plasma for 1 min (pressure, 1.5 Pa; power density, 0.06 W/cmZ; voltage, 80 V). This considerably improves the barrier properties of the tunnel junction (reduction of leakage currents, etc.). Next, patterns for the individual circuits are structured either by lift-off or etching methods. The windows for the junctions and the contact pads are now defined by covering these parts with photoresist. The whole wafer is then placed in an anodization cell filled with a solution of ammonium pentaborate and ethylene glycol in water and equipped with a platinum electrode (cathode). The other electrode is connected to the thin film (anode). The application of a monotonously increasing voltage to the cell leads to anodization (oxidation) of the top Nb layer, except where it is protected by the resist. A minimum in a simultaneously recorded Z ( t ) trace indicates that the anodization depth has reached the Si barrier and the process is stopped. This step has given the process its name, (selective niobium anodization process, SNAP). Next, an interconnection thin-film lead is deposited on top of the counter electrode, and the tunnel junction itself is complete (including the electric connections).

412

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a)

resist Nb

Trilayer deposition, patterning

Anodization

Strip- line connection delsosition

Pd

Shunt deposition

d Figure 10-26. (a) Nb- Si&-Nb junction fabrication steps (thin-film thicknesses not to scale); (b) circuit diagrams equivalent to the fabricated junction (last cross-section in (a)).

Finally, a strip line of Pd (2-20 nm thick) is deposited to act as an ohmic shunt. The specific resistivity of such a Pd strip is p = 7 p a cm at 4.2 K. The relevance of a shunt for a tunnel junction will be explained in the next section. In Figure 10-26b an equivalent circuit of the fabricated microstructure is shown. In practice, the second (large) junction can be disregarded because its active area is chosen to be much larger than that of the relevant (small) junction. The critical current for the large-area junction is much larger than that of the small junction and it acts as a superconducting connection. In Figure 10-27 a scanning electron microscope image of such an Nb-Si,N,-Nb junction with a Pd shunt is shown. Table 10-3 summarizes typical junction parameters.

Table 10-3. Nb-Six N,,-Nb junction parameters. Parameter

Value

Parameter

Value

Nb penetration depth, I , Specific capacitance, C / A Dielectric constant, E Window area

75 nm 4 pF/cm2 -8 16 pm2

Pd shunt resistivity, p Critical current, Z, Current density, Jc Product, Ic R,

7 pC2 cm at 4.2 K 1-25 pA 6-150 A/cm2 10-100 p v

10.4 Practical Devices

413

Figure 10-27. Scanning electron microscope image of a Nb - S i p y- Nb tunnel junction. The scale bar at the bottom represents 10 pm. (Courtesy of U. Gernert, Zentralinstitut fur Elektronenmikroskopie, TU Berlin).

10.4.1.3 Junction Characteristics Figure 10-28 illustrates the I-V characteristic of a Josephson tunnel junction fabricated according to the description given in the preceding section but without a shunt. The characteristic evolves as follows: a bias current fed from a constant-current source is increased but, owing to the Josephson effect (electron-pair tunneling), no voltage drop occurs at the junction (zero voltage state) until the critical current Z, is reached. A switch then occurs to the so-called quasi-particle characteristic, and the working point remains on this characteristic whether the bias current is increased or decreased until another critical value is reached, where a switch-back (capture) to the zero-voltage state occurs. Reversing the polarity results in symmetrical behavior. Note the completely different shape compared with the Z-V characteristic presented in the introductory section (Figure 10-2a). The model characteristic there is roughly matched if a tunnel junction is shunted. This is generally done if tunnel junctions are applied to SQUIDS, as SQUID operation usually requires single-valued junction characteristics. There are two reasons for the strong deviation of the characteristic in Figure 10-28 from that in Figure 10-2a which can be explained by means of the RSJ model introduced in Section

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3 1

-2 -3

L 0

-3

-6

3

V( mv)

Figure 10-28. I-; characteristic of an unshunted Josephson tunnel junction.

10.2.1.2: the non-negligible capacitance of tunnel junctions and the occurrence of an additional effect, the “quasi-particle tunneling”. Both reasons will be explained in more detail. The capacitance of the RSJ model shown in Figure 10-1 was neglected in the calculation of the characteristic in Figure 10-2a. In the case of a tunnel junction, l/w C is no longer small with respect to R. Taking in account the capacitance, results in hysteretic characteristics (cf, Figure 10-29), if the so-called hysteresis parameter satisfies the inequality

Pc

=

271 Z, R ZC/&

>

1

.

(10-46)

Thus, in turn, non-hysteretic characteristics are obtained if a shunt R,, is added that yields Pc < 1. The characteristics in Figure 10-29 still do not resemble those in Figure 10-28. The remaining deviation exists because two different tunneling effects are present simultaneously: the

0

0.5

1

1.5

2

/ b R

Figure 10-29. I-v characteristics for an RSJ model with different capacitance values (p, = 2 x I , R Z C / @ , ) .

415

10.4 Practical Devices

“Josephson effect” (electron-pair tunneling, also called Cooper pair tunneling [7], and the “Giaever effect” (quasi-particle tunneling) [38]. The influence of the Giaever effect alone can be shown experimentally, as Cooper pairs (the carriers of the supercurrent) cannot tunnel through thicker barriers ( z 5 nm) where quasi-particles still possess an appreciable tunneling yield. (Quasi-particles, the carriers of the normal current in a superconductor, are, roughly speaking, electrons lacking a counterpart to form a Cooper pair, or such a counterpart lacking an electron to form a Cooper pair. The latter is often termed a “hole”, but this is not equivalent to “holes” in semiconductor physics. For a more detailed description see, eg, [4].) In Figure 10-30 the I-V characteristic of a tunneling contact with a suppressed Josephson current is shown, exhibiting the pure quasi-particle characteristic. With quasi-particle tunneling, the resistance R (with reference to the picture of the RSJ model) becomes strongly nonlinear, R = R ( V ) . A voltage-dependent conductivity G = 1/R ( V ) with such a nonlinear characteristic must be substituted for R in the RSJ model in order to reproduce the measured characteristic shown in Figur 10-28. 6

/(mA)

I :I 0 -2 -4 -

-6

Figure 10-30. I-V characteristic of a Giaever tunnel junction.

1

-6

-3

I

1

0 3 6 +V(mV)

I, Modified Figure 10-31. RSJ model taking into account the nonlinear quasi-particle conductance G = 1/R ( V ) and an added shunt resistance R,, .

: i f R s h 7-F

The hysteresis can be eliminated by the resistive shunt added in the fabrication process described, ie, in the picture of the RSJ model, the nonlinear quasi-particle conductance l / R ( V ) is shunted by an ohmic resistor Rsh, damping the role of the capacitance C and linearizing the Giaever characteristic (cf, Figure 10-31).

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Figure 10-32 shows the Z-V characteristic of the fabricated Nb-Si,N,-Nb junction for different shunt values close to the hysteretic limit. Other types of weak links, such as point contacts, microbridges or SNS junctions, exhibit non-hysteretic Z-V characteristics similar to the characteristic of the non-hysteretic regime in Figure 10-32 without the necessity for adding a shunt.

1

0.00

-0.2

-0.1

0

0.1

0.2

+v(mv)

Figure 10-32. Variation of the I-V characteristics due to different shunt resistances Rsh: 1, 4.051; 2, 4.451; 3, 5.351; 4, 7.251; 5, 11.451.

Common quality criteria for unshunted tunnel junctions are (cf, Figure 10-28): a. the “ZcRNproduct”, ie, the product of the value of the critical current I, and the normal resistance RN (the asymptote of the quasi-particle curve above the gap voltage V,); b. the gap voltage V, reflecting the sum of the energy gaps of the two electrode materials; c. the “V, value”, the product of the quasi-particle resistance at 2 mV, R q P , and the critical current I, (a valuable criterion for the magnitude of leakage currents through point defects of the barrier, for instance). All three criteria should be as large as possible. Good values are ZcR, > 1 mV, Vg > 3 mV for all-Nb junctions and V, > 20 mV. For SQUID applications, the ZcRN product of the shunted, non-hysteric junction is of major importance because it determines the sensitivity which can be achieved. Another obvious quality criterion for junction fabrication is the standard deviation of the parameter variation within one wafer and from wafer to wafer.

10.4.1.4 Alternative Configurations Innumerable different types of Josephson junctions have been invented, fabricated, and implemented in cryoelectronic circuits. Details of fabrication techniques for junctions, their physical characterization and theories explaining their operation have been published in thousands of scientific papers. Only the most successful junction configurations will be mentioned here.

10.4 Practical Devices

417

There are two main classes: tunnel junctions consisting of two superconduction electrodes separated by a thin barrier layer (one example has been described in detail in the previous sections) and microbridges, which are very small superconducting constrictions separating (or, rather, weakly connecting) two superconducting banks. The still popular point contact (see Section 10.4.2.1) may be maintained either as a very small tunnel junction, as a microbridge, or as an array of tunnel junctions, microbridges (pin-holes) and ohmic and capacitive shunts (this more or less undefined array seems to be the most common). Tunnel junction configurations may be divided into subclasses according to the combinations of materials used or to special geometries. Starting with material combinations, again a subdivision into different materials used for the superconducting electrodes and for the barrier is possible, but here only the most popular fabrication lines will be introduced.

Lead/(lead alloy)-oxide barrier junctions Lead as an electrode material has excellent superconducting properties. It is a type I superconductor, and therefore few problems with trapped flux occur in devices with lead electrodes. Lead allows a very reliable oxide barrier formation process to be used, the so-called “Greiner process” [39]. A major drawback is its poor resistance to aging in a humid atmosphere and its mechanical instability during thermal cycling between room temperature and liquid helium temperature (poor cyclability). The introduction of lead alloys (PbIn, PbInAu, PbBi) improved the storage and cycling reliability, but junctions made of the so-called refractory materials (Nb and NbN) have proved a major step forward in this respect and lead alloy techniques are now almost completely outdated. However, the lead alloy process developed at IBM for the Josephson computer project remains one of the most sophisticated and mature techniques ever perfected in cryoelectronics [40].

Refractory-artificial barrier junctions It was several years before the higher mechanical and thermal ruggedness of Nb or NbN junctions could be matched with satisfactory electrical characteristics and a sufficiently high production yield (reproducibility) comparable to the standard set by lead alloy techniques. Natural oxides of Nb or NbN tended to produce barriers with a dielectric constant that was too large and had detrimental effects at the interface between the barrier and the superconducting electrodes. Especially during the deposition of the counter electrode, when the highly reactive Nb is hot and the mobility of impurities is high, degradation of the superconducting properties in close proximity to the barrier is unavoidable (reduction of T, in the proximity layer). So-called artificial barriers were an improvement [41]. Nb-a- Si-Nb, NbN-MgO-NbN and Nb-A1, 0,-Nb became the most widely accepted material combinations [37, 42, 431. NbN junctions have the advantage of a high critical temperature (T, (NbN) = 15 K vs. T, (Nb) = 9 K), but the disadvantage of a large penetration depth compared with Nb junctions. At present, the Nb-Al, 0,-Nb process developed at Bell [44] and refined at Fujitsu [43, 451 is considered to represent the state of the art. Most tunnel junction techniques that meet the requirements for mass production involve a planar thin-film process. The junctions consist of a trilayer (base electrode-barrier-counter electrode), and the junction size is defined by a window in an insulating layer (cf, Section 10.4.1.2).

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For high-performance SQUID applications, extremely small junction contact areas seem to be an advantage in order to obtain optimum SQUID parameters [46] and to reduce l/f noise contributions [47] (cf, Section 10.5.2.2). Great effort is therefore being made to decrease the junction size either by improving the lithographic techniques (ie, e-beam lithography) or with special geometries. Varieties of overlap and edge junctions are some examples of the latter [48-521. In addition to insulators as barrier materials, normal conducting or semiconducting material may also be utilized, producing so-called SNS junctions. Whereas normal conducting barriers lead to junctions with a resistance too low to compete with shunted SIS tunnel junctions in SQUID applications, the use of semi-metals or highly doped (ion-implanted) semiconductors seems to be promising [53-561. Microbridges used as Josephson weak links in SQUIDS provide a sufficiently high resistivity only if they are extremely small (widths of less than 100 nm). This can be achieved either by sophisticated lithographic methods [57-591 or by micro-channels in an insulating barrier that is otherwise too thick for tunneling [60]. For a long time, point contacts were the weak links of choice for SQUID applications and they are still in use because of their simplicity (see the following section). Detailed reviews have been given 161, 621. A valuable review on non-tunnel-type weak links is given in [63].

10.4.2 Two-Hole RF SQUID 10.4.2.1 R F SQUID Fabrication This section describes a fabrication scheme for an rf SQUID from a very successful design introduced by Zimmermann [64]. This so-called two-hole SQUID gives a remarkably good performance and is easily fabricated even in workshops without sophisticated equipment. It consists of a rigid body turned out of bulk niobium with a geometry as specified in Figure 10-33. The main features are two holes for flux penetration, a connecting slit, and a point contact made out of two Nb screws, one with a blunt end and the other with a sharp tip. For mechanical rigidity, both screws have lock-nuts attached. Stable contacts may be obtained if the tip of the sharp screw is oxidized by heating in air until the tip turns to a bluish color. The art of establishing a good point contact is to tighten the screw carefully so that only at one spot on the tip is the oxide layer ruptured in such a way that a Josephson junction results [65]. The setting of the contact may, with some experience, be controlled at room temperature by measuring the contact resistance. A more systematic method is to cool the SQUID to liquid helium temperature and watch the evolution of the staircase pattern described in Section 10.3.1.2 (Figure 10-9a). If this is well done, the oxide surrounding this microcontact stabilizes the arrangement efficiently against mechanical shock, vibrations, and thermal cycling between room temperature and liquid helium temperature. This is in contrast to the very sharp and clean screw tips which might be thought of to be a better choice. The chief attraction of the two-hole design is its inherent insensitivity to external noise fields because, in contrast to the simple superconducting ring described in the introductory section, no current flows through the junction for spatially homogeneous fields if the design is truly symmetrical (the shielding currents around both holes cancel at the point contact).

10.4 Practical Devices

1.

* f i 5 T * 2

J

419

"

25

Figure 10-33. Rvo-hole rf SQUID layout (in mm); slot not to scale.

Figure 10-34. Two-hole rf SQUID (demounted): (a) with input coil (left), rf coil (right), and the point contact Nb screws (plus lock nuts); (b) side view of the SQUID body.

420

10 SQUID Sensors

An external signal may be introduced to the device with a wire-wound signal coil by placing it in one hole and generating a flux modulation from one hole to the other, detectable via the point contact. This signal coil is usually the counterpart of a pickup loop of a flux transformer (Section 10.3.3.1). The electronic read-out may be maintained with an rf coil placed in the other hole of the device. A practical two-hole rf SQUID with an input and rf coil assembly and point contact screws is shown in Figure 10-34a. Figure 10-34b is a side view of the SQUID body showing the two holes.

10.4.2.2 RF SQUID Electronics

A block diagram of an rf SQUID read-out scheme is shown in Figure 10-22, featuring the flux locked loop (FLL) concept. In this section, a detailed practical circuit is discussed [66], representing the symbols “rf amp”, “rf detector” and “mod amp” in Figure 10-22. Commercially available instruments may be used to complete the FLL circuit: a lock-in amplifier and a function generator. The circuit in Figure 10-35 is mounted in a shielded housing at the top of the dip-stick assembly shown schematically in Figure 10-23. The connection to the cooled tank circuit at the SQUID sensor is maintained with a miniature coaxial cable through the dip-stick pipe. The distributed capacitance and inductance of this cable are unavoidably parallel with the tank circuit elements and must be taken into account when designing the tank circuit. Typical values for the elements of the rf SQUID sensor used in connection with this circuit are given in Table 10-4.

Table 10-4. Practical rf SQUID parameters. Parameter SQUID inductance, L,, Flux transformer: Pickup loop inductance, L , Input coil inductance, Li

Value 1 nH 10 pH 10 pH

Parameter

Value

Tank circuit (20 MHz): RF coil inductance, L,, Capacitance, C,, Quality factor, Q Cable inductance, L,,, Cable capacitance, C,,,

160 nH 400 pF 100 200 nH/m 80 pF/m

The circuit shown in Figure 10-35 consists of five parts. From left to right, it begins with an interface stage connecting the SQUID tank circuit and providing a resonance tuning with the tuning diode BB 109. It also contains connections to the 20-MHz oscillator and to the modulated feedback from the lock-in amplifier. Behind the interface is a cascode-type preamplifier circuit and a second rf amplifier stage. The demodulator in conjunction with a low-pass filter extracts the modulation signal changed characteristically by the triangle pattern (cf, Figure 10-21). This signal is then amplified by the modulation amplifier.

10.4 Practical Devices

I

l

l

421

422

10

SQUID Sensors

A common modulation frequency is 20 kHz and a typical signal bandwidth 1 kHz. With the sensor and circuit data given above, one of the most sensitive biomagnetic experiments has [67] (for an exbeen performed with a system signal resolution of better than 5 planation of the unit fT/m, see Section 10.5.2).

fT/m

10.4.3 Integrated DC SQUID Magnetometer 10.4.3.1 Fabrication The most popular DC SQUID design to date is the thin-film washer SQUID introduced and refined by a team at IBM [68, 691 and partly based on the work of Dettmann et al. [70]. The idea behind this design is to take advantage of the fact that the inductance of a thin-film strip line is greatly reduced when a ground plane is added to it [71, 721. SQUIDS have therefore been developed which have a thin-film SQUID “ring” shaped like a square washer and acting as a ground plane to the secondary coil of the flux transformer. This results in easier and improved coupling between the input coil and the SQUID ring. In the following, the fabrication of an integrated DC SQUID magnetometer consisting of such a washer SQUID and a thin-film flux transformer is described. Such a design has been introduced in [73]. The set-up is displayed in Figure 10-36, both as a circuit diagram and as a schematic layout of the thin-film device. The washer SQUID is indicated by the hatched pattern. It is electrically insulated by dielectric layers from the flux transformer, which is made up of the pickup loop and the spiral input coil (insulation layers are not sketched). The basic design aspects of a DC SQUID are summarized below (cf, [15, 741).

spiral input coil :V>

‘SQUID

spiral input coil (counter electrode)

I

(a)

LSQ

loop

Figure 10-36. DC SQUID with integrated flux transformer: (a) circuit diagram; (b) schematic layout of the thin-film device.

10.4 Practical Devices

423

Non-hysteric DC SQUID operation requires the hysteresis parameter pC to be less than unity. The modulation parameter Pr should be approximately unity in order to obtain the best performance of the signal-to-noise ratio:

pC = ~xZ,R’C/@, < 1

(10-47)

Assuming that these conditions are met, the intrinsic energy sensitivity of a DC SQUID is approximately given (for the white noise region [15]; cf, Section 10.5.1) by a thermal and quantum contribution as follows:

where y I is of the order of 3-5, y 2 of the order of 0.1-0.2, h = Planck’s constant, and kB = Boltzmann’s constant. Thus the I, R product of the junctions should be optimized. This in turn requires low junction capacitance and low SQUID inductance values, leading to small junction areas and high junction current densities. Another important objective in designing a SQUID is to have good signal coupling to the SQUID. The signal input coil (usually the secondary of a flux transformer) with an inductance Li generally greater than 100 nH must be coupled tightly to the SQUID loop inductance LsQ, which is usually less than 100 pH, via the mutual inductance Mi,sQ: (10-50)

where ki,sQ = coupling constant. More important in practice than the intrinsic energy sensitivity En is the “coupled energy sensitivity” with reference to the current passing through the input coil E,. It is given by E, = E,,/ktsQ

(10-51)

demonstrating the necessity for good coupling (ki, sQ + l), which is difficult to achieve for inductances of such different values. One way to achieve it is to make use of thin-film techniques where both inductances can sQ > 0.9 has been achieved with a layout in be placed in close proximity. A coupling with ki, which the SQUID loop is fabricated in the shape of a square washer (cf, Figure 10-36) and the signal input coil is placed on top of it as a spiral coil separated by a thin insulating layer (the latter is not shown). The need for a return line for the spiral coil requires a multilayer thin-film technique with reliable insulation between the layers. It has been shown [75] that the inductance of a thin-film square washer is given approximately by LSQ= 1.2poa

(10-52)

where a is the width of the square hole, as long as the overall size of the washer is more than three times that of the hole. The washer acts as a superconducting ground plane for the spiral input coil. Ground planes considerably reduce the inductances of strip lines and guide the flux through the hole [75] (flux focusing).

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10 SQUID Sensors

For this design, the mutual inductance Mi,sQ and the input coil inductance L, scale approximately as Mi, S Q = ~ L S Q

(10-53)

Li

(10-54)

and =

n2Lsq

where n = number of turns. As a consequence, the design can be carried out as follows: a. According to the maximum achievable I, R product for non-hysteretic operation (result of a junction fabrication process optimization), a SQUID loop inductance L,, is chosen to fulfil pL = 1. b. The size of the washer must then be adapted to the size of the required signal input coil inductance Li,which has to be matched to the signal pickup circuit (in the case of a magnetometer flux transformer L, = L , , where L, = inductance of the pickup loop). Figure 10-37 shows practical integrated DC SQUID magnetometers in the all-Nb, thin-film technique [76] (cf, Figure 10-36). Figure 10-37a presents an overall view of one magnetometer showing the large pickup loop (18 mm in diameter) on top, and the spiral input coil-washer configuration at the bottom. Figure 10-37b is a blow-up of the latter. The spiral coil, its return line, the washer, and the two junctions (bottom) can now be easily recognized. Figure 10-37c shows the junctions and the shunt configuration enlarged. A detailed view of one junction was given in Figure 10-27. The electrical characteristics of the device are shown in Figure 10-38. The I-V characteristics (Figure 10-38a) and the V-B characteristics (Figure 10-38b) compare relatively well with the corresponding theoretical curves (Equations (10-16) and (10-18)). (The “noise” seen in Figure 10-38b is due to the preamplifier used and is not intrinsic to the SQUID.) Characteristic data of the magnetometer are listed in Table 10-5. Deviations from ideal behavior are often seen in characteristics published for other SQUIDs, and are due to the fact that real devices differ from the simple lumped circuit models. Complicated interactions of the Josephson frequency with the strong nonlinearities, distributed stray capacitances and inductances lead to resonances and irregularities in the I-V and V-B characteristics. With a sophisticated design process including (analog) computer simulations and more realistic models, many artifacts can be eliminated, for instance by using damping resistors and/or other filter elements [77]. Optimization for specific applications is therefore possible, often leading to considerably better results than those achievable with commercially available SQUIDS. With the SQUID magnetometer shown in Figure 10-37, a white noise level of better than 5 fT/I/Hz can be obtained when operated without matching transformer with a conventional flux-locked loop circuit in a magnetically shielded room. In addition to the direct flux transformer coupling scheme presented here, another scheme has gained some popularity, viz, the double transformer concept introduced in [78] and for instance adopted in [79] for an integration of planar gradiometers.

10.4 Practical Devices

Figure 10-37. (a) Integrated DC SQUID magnetometers (diameter of pickup loop, 18 mm); (b) scanning electron micrograph of the DC SQUID with the spiral input coil of the thin film flux transformer; (c) enlarged view of the junction-shunt configuration. (b and c: Courtesy of U. Gernert, Zentralinstitut fur Elektronenmikroskopie, TU Berlin)

(a)

425

426

10 SQUID Sensors

> 6o

3 0

3 - 30

P

fo -30

-200 -100 (a)

0

- 60 100

voltage/pV

I

-0.3 -0.15

200

(b)

I

I

i

0

0.15

0.3

magn. induction/nT

Figure 10-38. Electrical characteristics obtained with the magnetometer shown in Figure 10-37. (a) I-V characteristic; (b) V-B characteristic.

Table 10-5. Magnetometer parameters. Parameter

Value

Parameter

Value

SQUID inductance, L,,

620 pH 19 60 nH 110 nH 6 nH 0.7 pF

Critical current, 2Z, Shunt resistance, R / 2 Sensitivity, /3/& White noise cf > 1 Hz):

15 pA 3.6 i2 0.25 nT/@,

Input coil turns, n Pickup loop inductance, L , Input coil inductance, Li Mutual inductance, Mi,,, Junction capacitance, C

10.4.3.2 DC SQUID Electronics In principle, the read-out electronics presented in Sections 10.4.2.2 and 10.3.3.2 could also be used for a DC SQUID, provided that some minor changes are made in the bias and preamplifier stage. For general interest, another circuit will also be introduced that has been very successful commercially and is particularly interesting because of its noise reduction technique (double modulation scheme). This circuit is described in a patent [80], but will be explained here in outline, stressing the main features. As will be shown in Section 10.5, one of the main sensitivity limitations in practice is due to the low-frequency l/f noise. The circuit considerably reduces this noise contribution, mainly by means of an alternating bias current and an adapted read-out scheme instead of the conventional DC biasing. The basic idea is to exploit the different symmetries involved when the bias current polarity is reversed: (i) for the flux fluctuations of the real signal itself and (ii) for the flux fluctuations derived from effective resistance fluctuations in one of the DC SQUID branches.

421

10.4 Practical Devices

This is illustrated in Figure 10-39 for the two bias current polarities ( + I b and -Ib).As the I-V characteristics of DC SQUIDS are symmetrical with reference to the origin, a polarity reversal of the bias current, + I b -+ -Ib, is followed by a polarity reversal of the average output voltage value, + V, - V , , also. +

b'

+AV

Figure 10-39. Relations of the output voltage change A V and magnetic flux change A @ for a fictitious small operating resistance drop in the left branch of a DC SQUID for two inverse bias currents (a signal flux change + A @ is taken into account in the lower figure).

Vh

tE 9

-6

-

_ _

-

+AV

-Av

case 1 : flux change due t o c u r r e n t change

+ A @ + I,= - A@-I, CaSe

+ A v + Ib=+Av-

r

AI:

I,

2: signal f l u x change:

+A@+ I,= +A@-

lb

+ A V + IT-AV-

I,

Assuming that the fluctuations responsible for the l/f noise result in a fluctuation of the effective operating resistance, this can be modelled as a change in the bias current partitioning between the two SQUID branches. In other words, at one instant the current in one branch is increased by the amount A I and because I b is constant, the current in the other branch must decrease by - AZ simultaneously. In effect, a circulating current Zci, with an amplitude of A I is generated causing a flux change A 9 = L A I. This flux change is superimposed on the signal to be measured and thus impairs the measurement. The situation for a reversed bias current is such that the current partitioning the left and the right SQUID branches is the same as before, provided that the state of the

428

10 SQUID Sensors

effective operating resistances remains the same. However, now the sign of the effective circulating current Zcirc is reversed, which means that the flux change is also reversed, +A@+,, = The related V = V ( @ )characteristics show that owing to the double phase reversal, in both cases +zb and -&, a positive voltage change occurs, + A V,,, = + A V- Ib. The situation is different for a flux change of the measurement signal itself, A @ : in both cases + z b and -zb the resulting circulating current has the same sign. Thus + A @ + , b + A@-lbleads to a reversal of the voltage change polarity: + A V,,, = - A V-,b. To summarize: a bias current Zbpolarity reversal is followed by an output voltage change A V polarity reversal if the voltage change A V$ is due to a signal flux change A @. This is not the case if the output voltage change A V, is caused by effective resistance fluctuations in one of the SQUID branches. Thus the latter signal A V, will not be mixed or heterodyned by a bias current modulation and demodulation scheme, contrary to the signal A Vo. The central part of the read-out electronics consits of a bridge as shown in Figure 10-40 driven by a square-wave oscillator (typical frequency 0.5 MHz) that provides the switching bias current to the DC SQUID.

~

,

~ Gelectr.Z q 1000

BW‘’’ 1

Input coil

SQUID m o d u l a t i o n loop coil

Figure 10-40. Block diagram of a DC SQUID double modulator read-out scheme.

The circuit elements, termed “balance modulator” and “bias modulator”, function as adjustable impedances to balance the bridge in a way that the large bias switching + V, + - V, is nulled, so that the rf amplifier in the diagonal of the bridge senses only the variations A V around I V, I. The balance modulator in conjunction with the reference voltage V,, sets the actual value of I V, I. The bias modulator in the other bridge branch in conjunction with the feedback circuit (diagonal transformer, rf amplifier, bias demodulator, integrator) nulls any changes A V around 1 Val caused by variations in the flux signal detected by the SQUID. The different output for noise-generated flux change and real signal flux change is obvious from the timing diagram (Figure 10-41). This circuit is also usually operated in a flux-locked loop (FLL) mode (typically at 125 kHz) superimposed on the signal processing described above.

10.4 Practical Devices

I

1 I "noise" I, Figure 10-41. Timing diagram.

429

I I 1 signal I

n~

Alternative double noise reduction techniques have been introduced [81, 821, claiming even better results.

10.4.4

Alternative SQUID Configurations

For both categories, rf and DC SQUIDs numerous types have been invented over the years. A collection of references for most of these types is given in Section 10.7. First a short introduction to the classification will be given. 10.4.4.1 Bulk SQUIDs

The early practical SQUID sensors were fabricated from bulk material (usually niobium) and employed point contact junctions. Even nowadays they are still very popular because they can be made without sophisticated fabrication equipment and easily altered to an experimentalist's needs. The two-hole SQUID introduced in detail in Section 10.4.2 is one representative of this category. Even more successful commercially has been the toroidal SQUID. An extension of the two-hole SQUID concept, the multi-hole SQUID design, performs at a comparable signal-to-noise ratio but with an increased magnetic field sensitivity. The idea behind this fractional turn loop concept was later adopted for planar thin-film devices also. DC SQUIDs have also been fabricated as point contact bulk devices, but the requirement of the reproducible and reliable operation of two point contacts simultaneously is so difficult that rf SQUIDs have been favored for years.

10.4.4.2 Non-planar Thin-Film SQUIDs These devices have been fabricated most frequently by applying a superconducting thin film to a cylindrical substrate (quartz rod). Both rf and DC SQUIDs have been made with this technique, which has been made outdated by planar technology.

430

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SQUID

Sensors

10.4.4.3 Hybrid SQUIDs For hybrid SQUIDs, a planar thin-film technique is employed for junction and SQUID loop fabrication, but the input and output coils are wire-wound and coupled to the SQUID via specially shaped superconducting bulk material housings. Nowadays, most SQUID sensors commercially available are hybrids, but this may change soon in favor of all-thin-film SQUIDs.

10.4.4.4 Planar Thin-Film SQUIDs The planar thin-film technique allows planar input/output/modulation coils or flux transformers and even the read-out electronics to be integrated, leading to so-called “intelligent” sensors. In addition, higher sensitivities, better coupling, and more accurately balanced gradiometers can be achieved with integrated devices made with the thin-film technique. Thin-film SQUIDs in published reports fall into three categories: i. simple, often extremely small superconducting loops containing one or two junctions made in order to demonstrate the feasability of quantum interference with novel materials (eg, high-T, superconductors), junctions, or designs or in order to achieve maximum “intrinsic” sensitivity; these are not suitable for practical application but are of some value for research; ii. practical SQUIDs with integrated input coupling and modulation coils (cf, Section 10.4.3); iii. designs with special features (alternative coupling schemes, integrated read-out, etc.).

10.5

Sensitivity Limits

10.5.1

Noise

The reader may not be familiar with the correct treatment of quantities that are subjected to noise. The different definitions will therefore be explained in detail on the example of a fluctuating magnetic induction signal B ( t ) as shown in Figure 10-42. Its linear mean value is +T

f

( B ) = lim 1/(2T) T+ m

B(t)dt

(10-5 5 )

-T

and the fluctuation of this value is described by

B(t) = B(t) -

(B)

.

(10-56)

The mean square value or variance o 2 is defined as +T

o2 =

( B ( t ) 2 )= lim 1/(2T) j ( B ( t ) ) 2 d t = ( B 2 ) - ( B ) 2 T+m

-T

(10-57)

431

10.5 Sensitivity Limits

Figure 10-42. Fluctuating magnetic induction signal with different mean values indicated.

-

47-7--

time/a.u

where ( B 2 ) is a measure of the total power of the B field, ( B ) 2a measure of the constant fraction and ( B 2 )a measure of the fluctuating fraction of the total power. The rms (root mean square) value 0 of the fluctuation is given by (10-58) The noise of a system is commonly represented as a frequency spectrum of the “spectral power the spectral power density S , (J) being the noise power within a bandwidth density” S , 0, of 1 Hz centered around the frequencyf. Thus the total noise power over the whole frequency range is given by (10-59)

0is a useful quantity when comparing different noise sources with different bandwidths. A typical noise spectrum seen by a SQUID may look like that in Figure 10-43. At low frequencies it contains a region of decreasing power density with increasing frequency (l/fnoise), followed at intermediate frequencies by a “white” noise regime superimposed with signals S,

100 ,1

Figure 10-43. Qiical frequency spectrum of the magnetic field noise of a DC SQUID in a flux-locked loop circuit.

1

‘

I

0.001

I

I

01

I

1

I

to

I

to2

--+- f / H z

I

to3

1

toL

432

10 SQUID Sensors

from line sources. Above a cut-off frequency resulting from the read-out electronics (not from the SQUID), the power density drops again. For white noise, the spectral power density S,w has only to be multiplied by the particular bandwidth of the detection instrument to give the total noise power. In practice, the spectral power density is measured within a certain narrow bandwidth A j The value of S, (f) often remains constant within this bandwidth, and the noise signal can then be represented by an rms value B :

B(t) =

B expj(ot

+ cp)

=

v

m

expj(wt

+ cp) .

(10-60)

The so-called “field noise” I/s,y> with the unit T/I/HZ (tesla per square root Hz) is therefore a very popular quantity when a sensor performance is compared with the rms values of the signals to be detected, and is often cited in the literature. In order to obtain a rough measure of the detected noise power, one should always remember to square this value and to multiply it by the bandwidth of the particular measurement device used. An integration over the relevant frequency spectrum would be more correct. Similarly, the detected rms value of the magnetic induction may be obtained in the case of white noise if I/s,y> is multiplied by the square root of the appropriate bandwidth. The spectral densities for other quantities are defined in the same way. As an example, the sensitivity limits of a DC SQUID due to intrinsic noise sources will be discussed below.

10.5.2 Energy Sensitivity 10.5.2.1 White Noise Regime It is assumed that the noise sources responsible for the white noise of a DC SQUID are the two shunt resistors R generating Johnson current noise. The spectral density is given by:

S,(f)

= 4kBT/R

(10-61)

where k, = 1.38 x 10 -23 J K - I = the Boltzmann constant and T = temperature. These noise sources produce a current noise around the SQUID loop with the spectral density S,(f) and a voltage noise across the SQUID with a spectral density S, (f). The current noise around the SQUID loop generates a flux noise. This in turn means that only an applied signal flux change A @ that is greater than the order of the flux noise level will be detectable. The relations between energy, current, and flux ( E = 1/2 LZ2 and Z = @/L) allow an equivalent flux noise per unit bandwidth En to be defined (in J/Hz) that characterizes the detection sensitivity of a SQUID. is thus the energy per 1 Hz bandwidth coupled The minimum detectable flux energy Emin into the SQUID that matches the level of the flux noise energy:

433

10.5 Sensitivity Limits

Typical values for the flux noise in a SQUID are of the order of &/l/HZ and for field noise = = The energy sensitivities of commercial SQUIDs are as follows: for rf SQUIDs: En < for DC SQUIDs: En <

J/Hz J/Hz

=

T/I/HZ

=

.

.

In research laboratories, energy sensitivities of the order of En < 10 -33 J/Hz have been reached with DC SQUIDs [ 8 3 ] , but these SQUIDs are of academic interest only and are not suitable for practical use, as their loop area is far too small to couple flux into it effectively with an input coil. The need for such small loop areas in order to obtain these extreme energy sensitivities results from the following considerations. It has been shown by numerical calculations [14, 841, that for a low-noise DC SQUID at T = 4.2 K (parameters Pc = 1 and pL = 1; cf, Section 10.3.2), the spectral density for the voltage noise is (10-63)

S,(f) = 16 kB T R

and the voltage-flux transfer function is

(8v/8@), = R / L

.

(10-64)

Hence, E/AE

=

S,(f)/(A

AE = (A@)2/2L

E = S, ( f ) / [ 2 L(8 v / 8 @ ) 2 ]= 8kB T L / R ,

(10-65)

or, with Pc = 1 and PL = 1,

E = 16kBTI/LC.

(10-66)

Hence the SQUID loop inductance LSQand the junction capacitance C should be as small as possible to obtain the best flux noise energy value, sometimes also called “intrinsic energy sensitivity”. More relevant for devices for practical use is the so-called coupled energy sensitivity:

E, = E/k&,

(10-67)

where is the coupling constant between the input coil inductance Li and the SQUID loop inductance LSQ: (10-68)

SQUID systems with a coupled energy sensitivity below En = 100 h ( h = Planck’s constant) have been reported [85-871, demonstrating the extraordinary sensitivity of SQUID devices.

434

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SQUID Sensors

The superior energy sensitivities obtained in recent years with DC SQUIDs have triggered a renaissance of this SQUID family and a decline in the popularity of rf SQUIDs achieved in the previous decade.

10.5.2.2 l / f Noise

In many applications, not only the thermal noise contribution is an important limit. At low frequencies, the l/fnoise contribution becomes dominant and it is one of the goals in SQUID design and fabrication to push the lower frequency limit (where the transition from white noise to l/fnoise dominance occurs) to values below 1 Hz or even lower. The actual causes of l/f noise in SQUID sensors are still controversial [88-901, but experiments with very small contact area junctions (edge junctions) [91, 921 indicate the strong role played by traps within the junction barrier that catch and release individual tunneling electrons at random. This produces local variations of the barrier height, thus leading to resistive fluctuations. A single trap causes a “random telegraph signal” which has a Lorentzian power spectrum: S,y) a [I

+ ( 2 x f ~ ) ~ ] .- ’

(10-69)

A superposition the telegraph signals of several traps results in a l/f power spectrum. DC SQUIDs with high-quality edge junctions exhibiting extremely low l/f noise have been fabricated [93]. Prior to this performance demonstration it was believed that a l/fnoise level Hz) &/HZwas a limit intrinsic to all DC SQUIDs [88]. of the order of lO-’O/(f/l There are some ways of reducing the l/f noise contribution of SQUID sensors. To explain this, the “in-phase” and the “out-of-phase” fractions of the noise will be dealt with separately (cf, Figure 10-44) [94]. In- phase

Out - of- p ha se

Figure 10-44. In-phase (left) and out-of-phase (right) mode of the critical current fluctuations in a DC SQUID and their contribution to the noise power spectrum.

10.5 Sensitivity Limits

435

For the in-phase mode (+), the critical current fluctuations of both junctions Arc, and AZ,, add to the zero voltage current fluctuation of the SQUID AI: : A I J = Arc,

+ Arc,.

(10-70)

Thus the voltage fluctuation of the SQUID is A

v = 112 (a war,) hi:.

(10-71)

The spectral density of the voltage noise is then

For the out-of-phase mode (-), a fluctuating circulating current and thus a flux fluctuation result: A I L = Arc, - A I C 2 .

(10-73)

Hence A @ = L/2 (Arc, - AZJ

.

(10-74)

The spectral density of the flux noise is then given by So (f) = L2/4 (SIC,u, +

Sic, 0 )= L2/2 SICu, .

(10-75)

The spectral density of the resulting voltage noise is S,u,

=

L2/2

(av/a@)’ S l c u , .

(10-76)’

Hence the total noise power spectrum for a constant-current biased DC SQUID is given by

S, v) = 112

[a v/arJ2+ L2 (a v/a@)2] SICu,

(10-77)

where the first term is caused by the in-phase fraction and the second term by the out-of-phase fraction. The in-phase term can be removed when the SQUID is read out with the standard fluxlocked loop technique (Section 10.3.3.2). A slow change in voltage (slow compared with the modulation frequency) results only in a vertical shift of the triangle pattern (cf, Figure 10-21), but not in a n alteration of the amplitude of the signal component with the modulation frequency. The out-of-phase term can be removed with a SQUID read-out according to the double modulation scheme described in detail in Section 10.4.3.2. Another cause of l/fnoise is moving flux trapped in the thin-film or bulk material of the SQUID. This flux motion is probably thermally activated. Little is known about this phenomenon and there is no modulation scheme for reducing this noise component.

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10 SQUID Sensors

Intensive research aimed at a better understanding of the causes of Vfnoise is under way, particularly the investigation of SQUIDs at ultra-low temperatures (< 100 mK) [95], as many high-performance applications of SQUIDs will be maintained at frequencies around and below 1 Hz.

10.5.3

High-T, SQUIDs

The recent availability of superconducting materials with a high critical temperature T, (high-T, superconductors) will open up new perspectives for SQUID development, but it is not by chance that this topic has been included in this section dealing with noise. It is obvious from the preceding discussion that thermally generated noise determines the sensitivity limit in the white-noise regime. An elevated operating temperature raised from 4.2 to 77 K increases this level by the factor 1/77/4.2. The temperature 77 K is the boiling point of liquid nitrogen, which is the appropriate choice of coolant for operating high-T, devices; 77 K is close to the critical temperature T, of the new materials (90-120 K). Hence temperature fluctuations still have a pronounced effect on the electrical characteristics, making materials with an even higher T, very attractive. Other drawbacks of the bulk material or the polycrystalline films of ceramic superconductors with their granular structure seem to be their strong tendency to trap flux, to experience flux creep and to have low critical current densities (of the order of 100 A/cm2). The thermally activated flux motion seems to be the likely cause of a pronounced l/fnoise in the highT, SQUIDs so far produced. The polycrystalline high-T, material may be regarded as composed of many superconducting grains connected with each other via weak links across the grain boundaries. This threedimensional net of innumerable weak links is an interesting aspect of these novel materials in itself, and has been exploited for SQUID operation [96, 971. Single crystals and single crystalline thin films grown epitaxially on an appropriate substrate (eg, SffiO, or MgO) exhibit much higher current densities (> lo6 A/cm2) and less l/f noise [98]. Such thin films might be better suited for SQUID fabrication. Two of the technical difficulties to be overcome are the very small coherence lengths, of the order of 0.5-2 nm, and the high process temperature needed to obtain the correct oxygen stoichiometry. The coherence length is a measure of how much the superconductive state extends across an interface between a superconductor and an insulator, and is thus a measure of a useful tunnel barrier thickness. This aggravates the structuring of weak links or the formation of tunnel junctions, because the geometric dimensions of microbridges or the quality of the superconducting electrodes in the proximity of the tunneling barrier must extend over such lengths. The high process temperatures required are a disadvantage in standard lithographic techniques and are responsible for the detrimental thin-filmhbstrate interdiffusion. Multi-layer techniques will therefore be very difficult to establish, and this in turn means that an acceptable signal input coupling into the SQUID loop will be difficult to achieve, in particular as sensitivity requirements call for even smaller SQUID inductances than are necessary for 4.2 K SQUIDs. Up to now, most reports on SQUIDs fabricated from high-T, material have chiefly been aimed at demonstrating that these SQUIDs work.

431

10.5 Sensitivity Limits

2 Y

2t

T= 77 K

00

40

‘ 80

120

160

200

f [Hzl

Figure 10-45. (a) Cross section of a two-hole rf SQUID made from high-T, material (YBa,Cu,Oo_,,); (b) noise spectrum; (c) triangle pattern [loll.

2LO

438

10 SQUID Sensors

The previously mentioned intrinsic weak links at the grain boundaries have often been exploited [99]. Other devices employ bulky point contacts or break junctions [loo]. In Figure 10-45, the performance at 77 K of a two-hole rf SQUID made from YBCO (YBa,Cu,OaJ is demonstrated [loll. The data should be compared with those in Figures 10-10 and 10-43. A selected collection of references to particularly interesting high-T, SQUID designs is presented in Section 10.7. The great research activity in this field will rapidly produce a vast number of additional publications and, it is to be hoped, improved versions of reasonably sensitive high-T, SQUIDs of practical value. However, the extreme sensitivity demanded in many applications will still be the domain of SQUIDs operated at 4.2 K.

10.6 Conclusion SQUID sensors are the most sensitive and precise magnetic field detectors available, particularly for low-frequency signals. Their periodic response to magnetic flux acts as a built-in calibration with a fundamental constant, the flux quantum (Go = h/2e = 2.07 x lo-'' Wb). Other physical quantities may also be measured with SQUID sensors with high precision, such as voltage, current, magnetization, susceptibility, temperature (SQUID noise thermometer), and displacement (SQUID detector in gravitational wave antennas). SQUIDs may also be employed as low-noise amplifiers, particle (neutrino !) or magnetic monopole detectors, and for other seemingly exotic applications. A drawback of SQUID sensors is their low operating temperature and their sensitivity to interference from extraneous noise sources, making a sophisticated infrastructure necessary. However, several areas of applications have achieved growing acceptance in recent years. Biomagnetic diagnostic systems in particular are now being manufactured in growing numbers by several companies. The boom in high-T, superconductor research has also boosted sales of SQUID susceptometers used to characterize the high-T, samples. High-T, superconductors themselves may be used to fabricate SQUIDs, allowing operating temperatures Top> 77 K, easily achievable with liquid nitrogen. Although these SQUIDs will not be as sensitive as those operated at 4.2 K, they will probably enjoy a wider distribution among potential users in the near future.

10.7 References [l] Ginzburg, V. L., Landau, L. G., Zh. Eksp. Teor. Fiz. 20 (1950) 1064. [2] Tinkham, M., Introduction to Superconductivity; New York: McGraw-Hill, 1975. [3] Buckel, W., Supraleitung, Weinheim: Physik-Verlag, 1977. [4] Van Duzer, T., Turner, C. W., Principles of Superconductive Devices and Circuits, New York: Elsevier North-Holland, 1981.

10.7 References

439

[5] Barone, A., Paterno, G . , Physics and Application of the Josephson Effect, New York: Wiley, 1982. [6] RyhBnen, T. et al., J. Low Temp. Phys. 76 (1989) 287-386. [7] Josephson, B. D., Phys. Lett. 1 (1962) 251-253. [8] Stewart, W. C., Appl. Phys. Lett. U (1968) 277-280. [9] McCumber, D. E., J. Appl. Phys. 39 (1968) 3113-3118. [lo] Werthamer, N. R., Phys. Rev. 147 (1966) 255-263. [Ill Lounasmaa, 0. V., Experimental Principles of Methods Below I K, London: Academic Press, 1974, pp. 140-188. [12] Erne, S. N. et al., J, Appl. Phys. 47 (1976) 5440-5442. [13] De Bruyn Ouboter, R., De Waele, A. T., in: Progress in Low Rmperature Physics, Gorter, C . J. (ed.); Amsterdam: North-Holland, 1970, pp. 243-290. [14] Tesche, C. D., Clarke, J., J. Low Temp. Phys. 29 (1977) 301-331. [15] Ketchen, M. B., IEEE Trans. Magn. MAG-17 (1981) 387-394. [16] Silver, A. H., Zimmerman, J. E., in: Applied Superconductivity Vol. 1, Newhouse, V. L. (ed.); New York: Academic Press, 1975, pp. 1-112. [17] Ambegaokar, V., Halperin, B. I., Phys. Rev. Lett. 22 (1969) 1364-1366. [18] Koch, H., in: Superconducting Quantum Electronics, Kose, V. (ed.); Berlin: Springer, 1989, pp. 128-150. [19] Ilmoniemi, R. et al., in: Progress in Low Temperature Physics Vol. XII, Brewer, D. F. (ed.); Amsterdam: Elsevier, 1989, in press. [20] Clarke, J. et al., J. Low Gmp. Phys. 25 (1976) 99-144. [21] Claassen, J. H., J. Appl. Phys. 46 (1975) 2268-2275. [22] ter Brake, H. J. M. et al., Cryogenics 26 (1986) 667-670. [23] Muck, M. et al., Appl. Phys. A47 (1988) 285-289. [24] Drung, D., Cryogenics 26 (1986) 623-627. [25] Fujimaki, N. et al., IEEE 7kans. Electron Devices 35 (1988) 2412-2417. [26] Goree, W. S., in: SQUID Applications to Geophysics Weinstock, H. (ed.); Tulsa, OK, USA: Society of Exploration Geophysicists, 1981, pp. 85-92. [27] Crum, D., in: Biomagnetism: Applications and Theory, Weinberg, H., Stroink, G . , Katila, T. (eds.); New York: Pergamon Press, 1985, pp. 21-28. [28] ter Brake, H. J. M. et al., J. Phys. E. 17 (1984) 1024-1030. [29] Heiden, C., in: SQUID '85 - Superconducting Quantum Interference Devices and their Applications, Hahlbohm, H. D., Lubbig, H. (eds); Berlin: Walter de Gruyter, 1985, pp. 701-715. [30] Erne, S . N., in: Biomagnetism - an Interdisciplinary Approach, Williamson, S . J., Romani, G. L., Kaufman, L., Modena, I. (eds.); New York: Plenum Press, 1983, pp. 579-589. [31] Lehmann, H., in: Biomagnetism - an Interdisciplinary Approach, Williamson, S. J., Romani, G . L., Kaufman, L., Modena, I. (eds.); New York: Plenum Press, 1983, pp. 591-624. [32] Erne, S. N., in: Biomagnetism - an Interdisciplinary Approach, Williamson, S . J., Romani, G. L., Kaufman, L., Modena, I. (eds.); New York: Plenum Press, 1983, pp. 569-578. [33] Williams, R. E., Gallium Arsenide Processing Techniques; Dedham, MA: Artech House, 1984. [34] Glaser, A. B., Subak-Sharpe, G. E., Integrated Circuit Engineering; Reading, MA: Addison-Wesley, 1977. [35] Havemann, R. H. et al., J. Vac,, Sci. Techno/. 15 (1978) 292. [36] Cantor, R. et al., submitted for publication in J. Appl. Phys. [37] Kroger, H. et al., Appl. Phys. Lett. 39 (1981) 280-282. [38] Giaever, I., Phys. Rev. Lett. 5 (1960) 147-148. [39] Greiner, J. H. et al., IBM J. Res. Dev. 24 (1980) 195-205. [40] Sandstrom, R. L. et al., ZEEE Trans. Magn. MAG-23 (1987) 1484-1488. [41] Braginsky, A. I. et al., in: SQUID '85 - Superconducting Quantum Interference Devices and their Applications, Hahlbohm, H. D., Lubbig, H. (eds); Berlin: Walter de Gruyter, 1985, pp. 591 -629.

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[42] Shoji, A., in: SQUID '85 - Superconducting Quantum Interference Devices and their Applications, Hahlbohm, H. D., Liibbig, H. (eds); Berlin: Walter de Gruyter, 1985, pp. 631-657. [43] Morohashi, S. et al., Appl. Phys. Lett. 48 (1986) 254-256. [44] Gurvitch, M. et al., Appl. Phys. Lett. 42 (1983) 472-474. [45] Kotani, S. et al., ZEEE Trans. Magn. MAG-23 (1987) 869-874; Morohashi, S., Hasuo, S., J. Appl. Php. 61 (1987) 4835-4849. [46] Buhrmann, R. A., Physica 126 B + C (1984) 62-69. [47] Rogers, C. T. et al., IEEE Trans. Magn. MAG-23 (1987) 1658-1661. [48] Niemeyer, J., Kose, V., in: SQUID, Superconducting Quantum Interference Devices and their Applications, Hahlbohm, H. D., Liibbig, H. (eds.); Berlin: Walter de Gruyter, 1976, pp. 179-191. [49] Daalmans, G. M., in: SQUID '80, Hahlbohm, H. D., Liibbig, H. (eds.); Berlin: Walter de Gruyter, 1980, pp. 399-415. [50] Broom, R. F. et al., Appl. Phys. Lett. 37 (1980) 237-240. [51] Raider, S. I., Drake, R. E . , IEEE Trans. Magn. MAG-17 (1981) 299-303. [52] Koch, H., in: Extended Abstracts of 1987 International Superconductivity Electronics Conference, Tokyo; 1987, pp. 281-284. [53] Seto, J., van Duzer, T., Appl. Phys. Lett. 19 (1971) 488-490. [54] van Dover, R. B. et al., J. Appl. Phys. 52 (1981) 7327-7343. [55] Serfaty, A. et al., J. Low Temp. Phys. 63 (1986) 22-34. [56] Houwman, E. et al., IEEE Trans. Magn. 25 (1989) 1147-1150. [57] Laibowitz, R. B. et al., in: SQUID '80, Hahlbohm, H. D., Liibbig, H. (eds.); Berlin: Walter de Gruyter, 1980, pp. 353-363. [58] Rogalla, H. et al., in: SQUID '85 - Superconducting Quantum Interference Devices and their Applications, Hahlbohm, H. D., Liibbig, H. (eds); Berlin: Walter de Gruyter, 1985, pp. 671-683. [59] Ohta, H., IEEE Trans. Magn. MAG-23 (1987) 1072-1075. [60] Yanson, I. K., Zh. Eksp. Teor. Fiz. 66 (1974) 1035-1050 (Sov. Phys.-JETP 39 (1974) 506-520). [61] Zimmerman, J. E., in: Proceedings of the Applied Superconductor Conference, IEEE Pub. No. 72-CHO682-TABSC; New York: IEEE, 1972, pp. 544-561. [62] Weitz, D. A. et al., J. Appl. Phys. 49 (1978) 4873-4880. [63] Likharev, K. K., Rev. Mod. Phys. 51 (1979) 101-159. [64] Zimmerman, J. E. et al., J. Appl. Phys. 41 (1970) 1572-1580. [65] Buhrman, R. A. et al., 1 Appl. Phys. 45 (1974) 4045-4048. [66] Scheer, H., personal communications. [67] Erne, S. N. et al., Int. J. Neurosci. 37 (1987) 115-125. [68] Jaycox, J. M., Ketchen, M. B., IEEE Duns. Magn. MAG-17 (1981) 400-403. [69] Tesche, C. D. et al., IEEE Trans. Magn. MAG-21 (1985) 1032-1035. [70] Dettmann, F. et al., Phys. Status Solidi A 51 (1979) K 185-K 188. [71] Young, D. R., in: Progress in Cryogenics Vol. 1, Mendelson, K. (ed.); New York: Academic Press, 1959, pp. 1-33. [72] Chang, W. H., J. Appl. Phys. 50 (1979) 8129-8134. [73] Wellstood, F. et al., Rev. Sci. Instrum 55 (1984) 952-957. [74] Ketchen, M. B., IEEE Trans. Magn. MAG-23 (1987) 1650-1657. [75] Ketchen, M. B. et al., in: SQUID '85 - Superconducting Quantum Interference Devices and their Applications, Hahlbohm, H. D., Lubbig, E. (eds); Berlin: Walter de Gtuyter, 1985, pp. 865-871. 1761 Cantor, R. et al.Extended A bstracts of I989 International Superconductivity Electronics Conference, Tokyo; 1989, pp. 63-65. [77] Knuutila, J. et al., J. Low Temp. Phys., 68 (1987) 269-284. [78] Muehlfelder, B. et al., IEEE Truns. Magn. MAG-19 (1983) 303-307. [79] Knuutila, J. et al., Rev. Sci. Instrum 58 (1987) 2145-2156. [80] Simmonds, M. B., Giffard, R. P., US Pat. 4 389 612, 1983.

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441

Foglietti, V. et al., ZEEE Trans. Magn. MAG-23 (1987) 1150-1153. Drung, D. et al., ZEEE Trans. Magn. 25 (1989) 1034-1037. Wakai, R. T., van Harlingen, D. J., Appl. Phys. Lett. 52 (1988) 1182-1184. Clarke, J., Physica l26B (1984) 441-448. Martinis, J. M., Clarke, J., ZEEE Trans. Magn. MAG-19 (1983) 446-448. Knuutila, J. et al., J. Low Temp. Phys. 71 (1988) 369-392. Drung, D. et al., in: Extended Abstracts of 1987 International Superconductivity Electronics Conference, Tokyo; 1987, pp. 21-24. [88] Koch, R. H. et al., J. Low Temp. Phys. 51 (1983) 207-224. [89] Wellstood, F. C. et al., ZEEE Trans. Magn. MAG-23 (1987) 1662-1665. [go] Weissman, M. B., Rev. Mod. Phys. 60 (1988) 537-571. [91] Rogers, C. T., Buhrman, R. A., in: Advances in Cryogenic Engineering - Materials 32, Reed, R. P., Clark, A. F. (eds.); New York: Plenum Press, 1986, pp. 489-498. [92] Rogers, C. T., Buhrman, R. A., Phys. Rev. Lett. 55 (1985) 859-862. [93] Tesche, C. D., in: SQUZD '85 - Superconducting Quantum Interference Devices and Their Applications, Hahlbohm, H. D., Liibbig, H. (eds.); Berlin: Walter de Gruyter, 1985, pp. 797-806. [94] Clarke, J., in: Superconducting Electronics NATO ASI Series, Vol. F 59, Nisenoff, M., Weinstock, H. (eds.); Berlin: Springer, 1989, pp. 87-148. [95] Wellstood, F. C. et al., Appl. Phys. Lett. 50 (1987) 772-774. [96] Pegrum, C. M. et al., Appl. Phys. Lett. 51 (1987) 1364-1366. 1971 Robbes, D. et al., Nature (London) 331 (1988) 151-153. [98] Ferrari, M. J. et al., IEEE Trans. Magn. 25 (1989) 806-809. [99] Koch, R. H. et al., Physica ClS3-155 (1988) 1685-1689. [loo] Zimmerman, J. E. et al., Jpn. 1 Appl. Phys. 26 (1987) 2125-2126. [loll Zhang, Y. et al., IEEE Trans. Magn. 25 (1989) 869-871. [81] [82] [83] [84] [85] [86] [87]

Additional References to Section 10.4.4 (Alternative SQUID Configurations) Bulk SQUIDS rf, single-hole, point contact Zimmerman, J. E., Silver, A. H., J. Appl. Phys. 39 (1968) 2679. rf, two-hole, point contact Zimmerman, J. E. et al. [64]. Giffard, R. P. et al., J. Low Temp. Phys. 6 (1972) 533-611. rf, multi-hole, point contact Zimmerman, J. E., 1 Appl. Phys. 42 (1971) 4483-4487. rf, toroidal, point contact Goodman, W. L. et al., Proc. IEEE 61 (1973) 20-27. Rifkin, R. et al., J. Appl. Phys. 47 (1976) 2645-2650. Fujita, T., in: SQUID '80; Hahlbohm, H. D., Liibbig, H. (eds.); Berlin: Walter de Gruyter, 1980, pp. 561-568. microwave SQUID Hollenhorst, J. N., Giffard, R. P., IEEE Trans. Magn. MAG-15 (1979) 474-477. Long, A. P. et al., Rev. Sci. Znstrum. 51 (1980) 8-13. Ahola, H. et al., J. Low Temp. Phys. 35 (1979) 313-328.

442

10 SQUZD Sensors

Kuzmin, L. S. et al., in: SQUID '85 - Superconducting Quantum Interference Devices and Their Applications: Hahlbohm, H. D., Lubbig, H. (eds.); Berlin: Walter de Gruyter, 1985, pp. 1027-1034. Smith, A. D. et al., ZEEE Trans. Magn. MAG-23 (1987) 1079-1082. rf, toroidal, resistive, noise thermometer Kamper, R. A., Zimmerman, J. E., J. Appl. Phys. 42 (1971) 132-136. DC, point contact Paik, H. J. et al., ZEEE Trans. Magn. MAG-17 (1981) 404-407. Silver, A. H., Zimmerman, J. E., Phys. Rev. 157 (1967) 317-341. DC, magnetometer Forgacs, R. L., Warnick, A., Rev. Sci. Instrum. 38 (1967) 214-220. DC, SLUG device Clarke, J., Philos. Mag. 13 (1966) 115.

Thin-film non-planar rf, cylindrical, microbridge Mercerau, J. E., Rev. Phys. Appl. 5 (1970) 13-20. Nisenoff, M., Rev. Phys. Appl. 5 (1970) 21-24. Falco, C. M., Parker, W. H., 1 Appl. Phys. 46 (1975) 3238-3243. Duret, D. et al., Rev. Sci. Instrum. 46 (1975) 474-480. Pierce, J. M. et al., ZEEE Trans. Magn. MAG-10 (1974) 599-602. DC, cylindrical, shunted tunnel junction Clarke, J. et al., J. Low Temp. Phys. 25 (1976) 99-144.

Hybrid SQUIDS rf, hybrid, commercial Fagaly, R. L., Sci. Prog. (Oxford) 7 l (1987) 181-201. DC, hybrid, commercial Fleming, D. L. et al., ZEEE Trans. Magn. MAG-21 (1985).

Thin-film planar DC, small loop area, tunnel junction Jaklevic, R. C. et al., Phys. Rev. A140 (1965) 1628-1637. Hu, E. L. et al., ZEEE Trans. Magn. MAG-15 (1978) 585-588. Ketchen, M. B., Voss, R. F., Appl. Phys. Lett. 35 (1979) 812-815. Voss, R. F. et al., J. Appl. Phys. 51 (1980) 2306-2309. Wakai, R. T., van Harlingen, D. J., Appl. Phys. Lett. 49 (1986) 593-595. DC, small loop area, microbridge Decker, S. K., Mercereau, J. E., Appl. Phys. Lett. 23 (1973) 347-349. Richter, W., Albrecht, G., Cryogenics 15 (1975) 148-149. Voss, R. F. et al., Appl. Phys. Lett. 37 (1980) 656-658. Voss, R. F. et al., in: SQUID '80; Hahlbohm, H. D., Labbig, H. (eds.); Berlin: Walter de Gruyter, 1980, pp. 365-380. Ohta, H. [59]. DC, microbridges, burn-in technique Hamasaki, K. et al., in: Proc. 11 th Znt. Cryogen. Eng. Con$ Berlin (West) 1986; Klipping, G., Klipping, I. (eds.); Guildford: Butterworths, 1986, pp. 508-511. Lam Chok Sing, M. A. L., Thesis; Universitt de Caen, 1989.

10.7 References

443

DC, thin-film point contacts Uehara, G. et al., in: Extended Abstracts of 1987 International Superconductivity Electronics Conference, Tokyo; 1987, pp. 273-276. DC, SNS junctions Kuriki, S., Mizuno, K., in: Extended Abstracts of 1987 International Superconductivity Electronics Conference, Tokyo; 1987, pp. 269-272. Houwman, E. P. et al. [56]. rf, two-hole Ehnholm, G. J. et al., in: Proceedings of the 14th International Coderence on Low Temperature Physics, 4: Krusius, M., Vuorio, M. (eds.); Amsterdam: North-Holland, 1975, pp. 234-237. Fujioka, K. et al., in: Proc. IIfhZnt. Cryogen. Eng. C o d Berlin (West) 1986; Klipping, G., Klipping, I. (eds.); Guildford: Butterworth, 1986, pp. 512-516. DC, multi-loop Cromar, M. W., Carelli, P., Appl. Phys. Lett. 38 (1981) 723-725. Carelli, P., Foglietti, V., J. Appl. Phys. 53 (1982) 7592-7598. Sweeny, M. F., ZEEE Duns. Magn. MAG-21 (1985) 656-657. DC, double-loop, resistive shunt Koch, H., in: SQUZD '85 - Superconducting Quantum Interference Devices and Their Applications: Hahlbohm, H. D., Liibbig, H. (eds.); Berlin: Walter de Gruyter, 1985, pp. 773-777. Ohkawa, N. et al., Jpn. J. Appl. Phys. 24 (1985) L798-L800. DC,relaxation oscillator Maslennikov, Y. V. et al., in: Extended Abstracts of 1987 International Superconductivity Electronics Conference, Tokyo; 1987, pp. 144- 146. Muck, M. et al. [23]. DC/rf, NbN Fujita, T.et al., ZEEE Trans. Magn. MAG-11 (1974) 739-742. Claassen, J. H. et al., in: SQUZD '80: Hahlbohm, H. D., Lubbig, H. (eds.); Berlin: Walter de Gruyter, 1980, pp. 334-344. Kuriki, S. et al., ZEEE Trans. Magn. MAG-23 (1987) 1064-1087. DC, Nb3Ge, microbridges Rogalla, H. et al., J. Appl. Phys. 55 (1984) 3441-3443. Rogalla, H. et al. [58]. DC, Nb3Ge, SNS junctions Dilorio, M. S., Beasley, M. R., ZEEE Trans. Magn. MAG-21 (1985) 532-535. DC, integrated input coupling coil Dettmann, F. et al. [70] Ketchen, M. B. et al. [15, 74, 751. Jaycox, J. M. et al. [68]. Ketchen, M. B., Jaycox, J. M., Appl. Phys. Lett. 40 (1982) 736-738. Tesche, C. D. et al. [69, 931. Clarke, J. [84]. deWaal, V. J. et al., Appl. Phys. Lett. 42 (1983) 389-391. Pegrum, C. M. et al., ZEEE Duns. Magn. MAG-21 (1985) 1036-1039. Noguchi, T. et al., in: SQUZD '85 - Superconducting Quantum Interference Devices and Their Applications: Hahlbohm, H. D., Lubbig, H (eds.); Berlin: Walter de Gruyter, 1985, pp. 761-766. Katoh, Y. et al., in: Extended Abstracts of 1987 International Superconductivity Electronics Conference, Tokyo; 1987, pp. 277-280. Bondarenko, S. I. et al., Cryogenics 23 (1983) 263-264.

444

10 SQUID Sensors

DC, double transformer Muehlfelder, B. et al. [78]. Muehlfelder, B. et al., ZEEE nuns. Magn. MAG-21 (1985) 427-429. Muehlfelder, B. et al., Appl. Phys. Lett. 49 (1986) 1118-1120. Knuutila, J. et al. [77, 79, 861. Ryhlnen, T. et al. [6]. DC, integrated magnetometer Wellstood, F. C. et al. [73]. Koyanagi, M. et al., in: Extended Abstracts of 1987 International Superconductivity Electronics Corlference, Tokyo; 1987, pp. 33-36. Nakanishi, M. et al., in: Extended Abstracts of 1987 International Superconductivity Electronics Corlference, Tokyo; 1987, pp. 265-268. DC, integrated planar gradiometer Ketchen, M. B. et al., J. Appl. Phys. 49 (1978) 4111-4116. deWaal, V. J. et al., J. Low 2 m p . Phys. 53 (1983) 287-312. Drung, D. et al. [87]. Fujimaki, N. et al. [25].

Additional References to Section 10.5.3 (High T, SQUIDS) rf, intrinsic junctions of the bulk material Pegrum, C. M. et al., Appl. Phys. Lett. 51 (1987) 1364. Colglough, M. S. et al., Nature 328 (1987) 47. Tichy, R., et al., J. Low Temp. Phys. 70 (1988) 187-190. Gallop, J. et al., Phys. Lett. A128 (1988) 222-224. rf, break junction Zimmerman, J. E. et al., Appl. Phys. Lett. 51 (1987) 617-618. Harvey, I. K. et al., Appl. Phys. Lett. 52 (1988) 1634-1635. rf, toroidal Zhang, Y. et al., [loll. rf, two-hole Harrop, S. et al., ZEEE Trans. Magn. MAG-25 (1989) 876-877. rf, point contact Ryhlnen, T. SeppB, H., IEEE Duns. Magn. MAG-25 (1989) 881-884. DC, point contact de Waele, A. T. A. M. et al., Phys. Rev. B35 (1987) 8858-8860. DC, current pulse trimmed intrinsic junctions Robbes, D. et al., Nature 331 (1988) 151-153. Lam Chok Sing et al., ZEEE Trans. Magn. MAG-25 (1989) 889-892. DC, small loop area, intrinsic junctions Koch, R. H.et al., Appl. Phys. Lett. 51 (1987) 200-202. Hauser, B. et al., Appl. Phys. Lett. 52 (1988) 844-846. Nakane, H. et al., Jpn. J. Appl. Phys. 26 (1987) 11925. DC, thick film Lin, A. Z. et al., ZEEE nuns. Magn. MAG-25 (1989) 885-888.

10.7 References

DC, small loop area, grain boundary junction on bicrystal substrate Chaudhari, P. et al., Phys. Rev. Lett. 60 (1988) 1653. DC, small loop area, epitaxial film Koch, R. H. et al., Physicu (2153-155 (1988) 1685-1688. Sandstrom, R. L. et al., Appl. Phys. Lett. 53 (1988) 444-446.

445

11

Applications MICHAEL R . J . GIBBS.PATRICK T. SQUIRE. University of Bath. Bath. UK

Contents 11.1 11.2 11.2.1 11.2.2 11.3 11.4 11.4.1 11.4.2 11.4.2.1 11.4.2.2 11.4.2.3 11.5 11.5.1 11.5.2 11.5.3 11.5.4 11.5.5 11.6 11.7

. . . . . . . . . . . . . . . . . . . . . . . . . . . Sensor Classification . . . . . . . . . . . . . . . . . . . . . . . Classification by Measurand . . . . . . . . . . . . . . . . . . . . Introduction

448

Other Factors Affecting the Choice of Sensors

448 448 450

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

. . . . . . . . . . . . . . . . . . . . . . . . Magnetic Field Measurement . . . . . . . . . . . . . . . . . . . . Comparative Survey . . . . . . . . . . . . . . . . . . . . . . . . Applications of Magnetic Field Measurement . . . . . . . . . . . . Biomagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . Geomagnetism and Space Research . . . . . . . . . . . . . . . . Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid Mechanical Transducers . . . . . . . . . . . . . . . . . . Basic Material Requirements . . . . . . . . . . . . . . . . . . . . Displacement Transducers . . . . . . . . . . . . . . . . . . . . . Velocity Transducers . . . . . . . . . . . . . . . . . . . . . . . Strain Transducers . . . . . . . . . . . . . . . . . . . . . . . . Force and Torque Transducers . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application Areas

450

.

.

.

.

451 451 457 457 460 462 465 465 466 471 472 473 475 475

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

448

11 Applications

11.1 Introduction In order to discuss applications of magnetic sensors, it is first necessary to define what is meant by an application. This is not a straightforward matter, because there can be a hierarchy of applications. For example, consider a Hall effect sensor : the primary quantity measured is the component of magnetic induction perpendicular to the plane of the sensor, averaged over the active area. An example of a primary application of this would be a Hall effect Gaussmeter. At the secondary level a Hall effect sensor can be used in a proximity switch, where it is acting as a position sensor by virtue of the spatial variation of magnetic induction near a permanent magnet. The switch itself will be used as a component in a system or instrument, such as a computer keyboard. This in its turn may be part of a yet larger system, such as a process controller in a chemical plant. It becomes more and more difficult to predict and classify the possible applications, the further removed they become from the primary application. In this chapter we shall therefore restrict the discussion to primary and secondary applications. In some cases only primary applications will be discussed. In a chapter of this length it is not possible to give comprehensive cover of all applications, nor to give much detail of individual applications. We have tried to include most of the important primary applications, and to give enough detail to make useful comparisons between rival technologies. Some of the preceding chapters give more detailed accounts of selected applications.

11.2 Sensor Classification 11.2.1 Classification by Measurand Sensors can be classified under a number of headings. Perhaps the most fundamental factor is the primary quantity to be measured, or measurand. These are conveniently placed into families, such as mechanical or electromagnetic. The list in Table 11-1 [l] includes most quantities. The group labelled “Other” has been abbreviated, because magnetic sensors have not yet made a significant impact in measuring these quantities. Although a magnetic sensor might be devised for temperature, it is unlikely to be competitive with alternative technologies. It is even more unlikely that magnetic sensors will be useful as primary or secondary sensors for other quantities in this group. It is also unlikely that magnetic sensors will be useful for some of the quantities in the fluidmechanical group, such as density, humidity, and viscosity. These quantities will therefore not be considered further in this chapter. This leaves the solid-mechanical and electromagnetic quantities as the major field of application for magnetic sensors, with limited applications, such as liquid level and pressure in the fluid-mechanical group. The extent to which magnetic sensors have been used, or are currently under consideration, for various measurands, is indicated in Table 11-2. Some aspects for definition and classification of magnetic sensors have been stated in Chapter 1, Section 1.2.

449

11.2 Sensor Classification

Table 11-1. Selected list of measurands for sensors. Solid-mechanical Displacement Position Strain Speed and velocity Acceleration Mass Force Stress Torque

1

linear and angular

Fluid-mechanical Density Flow rate Humidity Liquid level Pressure Viscosity

Sensor Type x

Hall effect Magnetoelastic Fluxgate Induction coil Inductive Wiegand Magnetoresistive SQUID

Ax/x

Current Voltage Power Electric field strength Magnetic induction Electric flux Magnetic flux

Other

Temperature Heat flux Light intensity Color Nuclear radiation Chemical

Solid mechanical &/df 0 dO/dt m,Ra S

S

P

Electromagnetic

P S

s

S S

P

P P

P S

S

T

Fluid mechanical Level p Flow

P

S

Electromagnetic I I, U k?, H @

P

P

S

S

S

P

P

S

s s

s s

s s

S

P S

S

P

S S

S

s

S

s

P P P P P

P P

P P P

P

450

11 Applications

11.2.2 Other Factors Affecting the Choice of Sensor In addition to the classification of sensors by measurand, it is necessary to consider other attributes, such as range and accuracy. It may also be important to consider factors such as the cost and size. Table 11-3 lists various attributes in two categories: the primary category includes those factors that are related directly to the measurand ; the secondary category includes other factors. Table ll-3. Sensor attributes to be considered for applications. Primary

Secondary

Range Bandwidth Accuracy Resolution Linearity

Size Operating temperature Immunity to chemicals Immunity to radiation Invasiveness Impedance Interfacing capability Reliability Power required cost

11.3 Application Areas Sensors are used in applications covering almost every area of human activity. It is helpful to classify these areas, because the priorities vary widely from one to another. Table 11-4 gives a possible scheme of classification. Table 11-4. Areas of application for sensors. Aerospace Automotive Biomedical Consumer/domestic Industrial : Chemical Construction Electrical Mechanical Scientific research Surveying and prospecting

Few comprehensive surveys of sensor application by area have been published. TWOrecent reviews help to put magnetic sensors into perspective. The first [2] relates to automotive powertrain sensors. Table 11-5, reproduced from this review, lists many of the quantities that may

11.4 Magnetic Field Measurement

451

need to be sensed in a fully controlled automotive environment, together with the critical attributes, and proposed sensor types. It is interesting to note the small but significant contribution to the sensing technology offered by magnetic sensors. It should also be noted that, in addition to the quantities shown in Table 11-5, it is sometimes desirable to measure torque. As described in Chapter 4 (see especially Table 4-4), magnetoelastic torque sensors offer a number of useful features for this application. Sensors used in automotive applications must be cheap. As pointed out in [21, sensors and actuators make up about 60% of the cost of powertrain control systems, so the trend to more highly automated vehicles provides a strong incentive for developing new sensors that are optimized in terms of both performance and cost. It should also be pointed out that integration is an important trend in automotive instrumentation, and this favors silicon-based sensors [3]. It is likely, nevertheless, that magnetic sensors will continue to play a part in automotive applications. The second recent review of sensor application areas [4]is in consumer electronics and home appliances in Japan. Table 11-6, reproduced from this review, shows the relatively minor impact of magnetic sensors in this area. However, two remarks should be made here. The first is that where they are used, magnetic sensors are uniquely important, most notably in magnetic recording. The second point to be made is that in this application area low cost is a consideration of paramount importance. It is normally the case that magnetic sensors tend to be more expensive than alternatives, where they exist, with the result that in extremely costsensitive applications they are not normally chosen. It is also true in consumer applications that integration is an important consideration, and this often reduces the attraction of magnetic sensors. Perhaps their most likely use outside magnetic recording will be in the relatively humble task of motor revolution control, where inductive sensors are strongly favored (see Chapter 7).

11.4 Magnetic Field Measurement 11.4.1

Comparative Survey

As indicated in Table 11-2, seven of the types of sensors treated in earlier chapters of this book can be used as primary sensors of magnetic field. Of these, five may be regarded as of significance for present applications, namely Hall sensors, fluxgates, induction coils, magnetoresistive sensors, and SQUIDS. Magnetoelastic sensors are currently under investigation as field sensors, but as yet are still at the laboratory stage. Wiegand and pulse-wire sensors are not suitable for normal field measurement. For the sake of completeness, one should also note the importance in geophysical and space measurements of resonance magnetometers, which lie outside the scope of this book; details of these can be found in [ 5 ] . A more general review of magnetometry, but at a more superficial level, can be found in [6]. The choice of sensor for field measurement will depend on many factors, which may be interrelated. It is not possible, therefore, to give a simple prescription for selecting the optimum sensor for a particular application. What we have done here is first to give a general comparison of the sensor types, and then to give additional information to assist the user in making a final choice.

Piezoresistive silicon strain gaged diaphragm or capacitive diaphragm

As above

As above

Differential transformer +diaphragm or capacitive diaphragm

Metal film or semiconductor film

Thermistor

Thermistor

Cr/AI thermocouple

Thermistor

Hall effect or optical digitizer or eddy current

Inlet manifold absolute

Inlet and exhaust manifold pressure sensor (diesel engines)

Barometric absolute pressure sensor

Transmission oil pressure sensor

Inlet manifold air temperature sensor

Coolant temperature sensor

Diesel fuel temperature sensor

Diesel exhaust temperature sensor

Ambient air temperature sensor

Distributor mounted timing/ triggedspeed sensods

sensor (petrol engines)

or differential pressure

Proposed sensing method

Sensor/type

zero to maximum engine speed

-40°C to +100"C

to +75OoC

- 40 "C

to +200"C

- 40 "C

- 40°C to +200°C

-40°C to 150 "C

f 1%

As above

As above

As above

k 2%

+2% or k 5%

f 1%

k3%

50- I05 kPa 0-2000 kPa

k 3%

klqo at 25 "C

0- 105 kPa

20-200 kPa

Accuracy

Range

Table 11-5. Optimized specifications for automotive powertrain sensors [2]

to

+ 125 "C

-40°C to

-40°C to +10O0C

-40°C to + 750°C

-40°C to +200"C

As above

-40°C to 150°C

+160°C

- 40 "C

As above

As above

- 40°C to + 125 "C

Temperature operating range

N/A

As above

As above

As above

10 s

20 ms

10 ms

10 ms

10 ms

1 ms

Response time

h)

e

-40°C to

&I% k 3%

0-5 kQ from min. to max. pedal travel 0-4 kQ from closed to open throttle 8-position selection 0-5 kQ

Potentiometer

Potentiometer

Cam operated switch or potentiometer

Optical encoder

Linear displacement potentiometer Microswitches

Piezoelectric accelerometer

Accelertor pedal position sensor

Throttle position sensor

Gear selector position sensor

Gear selector hydraulic valve position sensor

EGR valve position sensor

Engine knock sensor

Closed throttle/wide open throttle sensors

-40°C to +125"C

f 2%

f 200 kg/h

Ultrasonic or corona discharge or ion flow

-40°C to + 125"C -40°C to + 125"C -40°C to +125"C

f 2%

N/A

0-10 mm

'g' range TBE

5 to 10 kHz

N/A

-40°C to +lOO"C

f 2%

As above

N/A

-40°C to +150°C

+ 125"C

As above

-40°C to + 125"C

N/A or k 1%

Or

(two ranges)

* 2%

+ 125"C

- 40°C

to

Inlet manifold air mass flow (bidirectional)

10 to 200 kg/h or 20 to 400 kg/h

f 5%

Vane meter or hot wire

As above

-40°C

Inlet manifold air mass flow (unidirectional)

Temperature operating range

Optical digitizer with fiber optic linkage or eddy current Optical digitizer or reed switch or Hall effect

Accuracy

Crankshaft mainted timing/ triggerhpeed sensors Road speed sensor (speed0 cable fitting)

Range

Proposed sensing method

Sensor/type

Table ll-5. Continued.

Depends on resonant frequency

N/A

N/A

N/A

N/A

N/A

N/A

1 ms

but target is 1 ms

35 ms for vane only others TBE

N/A

N/A

Response time

3dS 'hotodiode 'hototransistor 3CD image sensor blOS image sensor

Si pressure sensor bletal diaphragm 3ellow

C pressure sensor 'otentiometer

t

4umidity sensor 3as sensor on sensor iall sensor blR device {all IC

t;

rhermistor TC

f t

3imetal

-k

t

rhermocouple rhermoferrite Shape memory alloy nfrared sensor Si transistor C temDerature sensor

PSP

11.4 Magnetic Field Measurement

455

The most fundamental points to be considered are the range of field strength to be measured and the operating frequency. As shown in Figure 1-2 (see Chapter 1) the range for flux densities of potential interest are from about 1 f T to 100 T, some 17 orders of magnitude. The frequency range for practical applications is also very wide; at one extreme are geophysical and space measurements lasting for some years, for which the lowest frequency components may need to extend to lo-* Hz; at the other extreme, some data transfer operations may require measurements at 1 GHz. We have limited the frequency range considered Hz to lo6 Hz. The general picture is shown in here to 12 orders of magnitude from Figure 11-1.

Figure 11-1. Operating regions for magnetic field sensors. F: Fluxgate; H : Hall effect; I : Induction coil; M : Magnetoresistive ; S : SQUID.

r

-'$j

-4

-2

0

2

L

E

Log,o f / Hz

Figures like this need some explanation if they are not to be misleading. The first point to make is that it is not possible to draw definite boundaries around the operating region for any sensor type. In some cases the information is not available; in other cases conflicting information is given in different sources; in yet further cases the boundary is purely notional, in the sense that a particular sensor could be used in a region, but in practice no one would do so because alternatives are clearly preferred. Those parts of the boundaries that are uncertain in any of these ways are indicated by broken lines. Even where a solid line is shown, it should

456

I1 Applications

not be regarded as an absolute limit, but rather as an estimate of the current status, based on the authors' judgement of the available sources. In order to permit further comparison of the available sensors, we present in Table 11-7 additional information on the various sensor types. Again, caution is needed in taking this information too rigidly; it is intended to allow initial comparison to be made between the sensor types. When considering a sensor on the basis of the information in Figure 11-1 and Table 11-7 it must be noted that the ranges of operation apply to the whole class of sensor: a particular device will usually be designed to operate in a limited part of the range. For instance, an induction coil designed to measure terrestrial magnetic fields can be a meter or more in diameter, and weigh some tens of kilograms. The associated electronics will be optimized for low-frequency operation, and the magnetic induction range of interest will be from about 1 pT to 60 pT (see Chapter 6,Section 6.5). The earlier specialist chapters expand on some of these details, and in the case of commercially available devices the manufacturers' data will of course need to be consulted.

Table ll-7. Additional factors for choosing sensors for magnetometry. Where upper and lower figures are given they define a range. Sensor type

Size/mm(a)

T/T

Hall effect

0.1 10

- 210

Power/W Cost(b) Other comments

0.001 150 (200)(') 1

+

Magnetoresistive 0.1 10 Fluxgate 10 100

- 40 150

0.001 1

+

- 40

0.001 10

+

200

Induction coil

5 1000

- 213 >300(d)

0 (e) 10(O

+

Inductive

10

- 213

1000

> 300

1 1000(h)

- 273 50(h)

SQUID

+ (B)

+++

Notes : (a) Typical linear dimension (b) Relative indication only (') Upper limit in brackets for GaAs (d) Upper limit set by insulation of windings (e) Sensor power only: signal processing not included (0 Only for rotating coil type (g) Sensor requires milliwatts. Refrigerator power not included (h) Only with or including dewar

Good linearity. Sensitive to radiation. InSb most sensitive. GaAs best for high temp. Si less sensitive but good for integration More sensitive than Hall effect, but less linear High linearity, possible direct digital measurement with pulseposition-type Absolute. Self generating in alternating fields. Inherently linear. Very radiation tolerant. Operation under rugged conditions, long duration of life Only considered where the need to measure very weak fields justifies cost

457

11.4 Magnetic Field Measurement

11.4.2 Applications of Magnetic Field Measurement Numerous examples of applications are mentioned in the text of earlier chapters. The major areas of primary application are:

-

Biomagnetism Geomagnetism Identification Laboratory field measurement - Nondestructive testing - Planetary and space research - Submarine communication and detection The sensors in common use in these areas are shown in Table 11-8. Note that it has been necessary to include resonance field sensors in order to give a realistic comparison between available types. We now discuss in more detail applications within selected areas. Table 11-8. Sensors used in various application areas of magnetic field measurements. Application area

Hall effect

Flux-Gate

Induction coil

Inductive

++

+ ++ ++

+ +++ +

+

+++

+

++

++

Nondestructive testing

++

++

++

Planetary and space research

+++

+++

+++

++

Biomagnetism Geomagnetism Identification Laboratory field measurement

Submarine communication and navel warfare and detection I)

+

Magnetoresistive

+ +++

SQUID Resonance ')

+++ +

+++ ++

+

+ ++

+

++

Only for the sake of completeness

11.4.2.1 Biomagnetism

Biomagnetism is the study of the magnetic effects produced in or near living matter by (a) ion currents, (b) magnetic contaminants, or (c) paramagnetic or diamagnetic material in an applied magnetic field. The main attraction of biomagnetism as a diagnostic technique is its noninvasiveness; except for the third type, it is totally noninvasive. The goal of biomagnetic measurements is to diagnose, or help to diagnose, malfunction in organs, or other

458

11 Applications

pathological conditions giving rise to magnetic effects outside the body. Ideally the equipment for this purpose should be cheap enough for widespread use. The main characteristics of biomagnetic activity are the strength, frequency spectrum, and spatial distribution, of the resulting external field. The first two characteristics are shown in Figure 11-2 [7] for several sources.

1

,

I

I

I

I

(

Maqnetized lunq cmlarninanls

Abdominol currents v

Cardioqram

I

I-

Owlopram piomgnelic nwmal tissue in 0.1 mT field

--

Fetal cardioaom Encaphologram ( 8 ) Enceqhologrorn ( a I

,-.-

Hts Purkinle HipOocamprs Scnsarimotor cater

.

.._...._

Evaked ccdical activily

10 lo-'

I

10'

10'

FREQUENCY ( Hz 1

lo3

Figure ll-2. vpical amplitude and frequency ranges of biomagnetic effects [7].

It is clear from Figure 11-2 that biomagnetic fields are very weak. Reference to Figure 11-1 shows that, for most of the sources, only induction coils and SQUIDS are sufficiently sensitive. If the sole purpose of a measurement is to detect activity, induction coils offer a cheaper alternative to SQUIDS. However, the high sensitivity of induction coils at the low frequencies typical of biomagnetic effects is only achieved with large coils (Chapter 6 ) . This makes the spatial resolution very poor, and so most measurements of biomagnetic fields reported until now have been obtained with SQUID magnetometers. A further complication is that in normal environments the ambient magnetic noise greatly exceeds all but the strongest biomagnetic fields. Elaborately screened low-noise chambers have been constructed [8], in which the weakest signals can be observed directly (see also Chapter 1, Section 1.8). For routine applications these are often far too large and costly; it is therefore necessary to use gradiometric coil configurations (see Chapter 10, especially Figure 10-20). Until recently, only single sets of coils were used, and in order to obtain spatial information the coils had to be scanned around the subject. This was time-consuming, and often the signal did not remain stable for long enough. Now it is possible to obtain spatial information in a much shorter time, by using multiple-coil arrangements ; typical of the current art is the seven-channel system described by Knuutila et al. [9]. Examples of the results obtained using the system are shown in Figure 11-3.

459

11.4 Magnetic Field Measurement

n v)

01

0

1

I

I

1

20

LO

60

80

Frequency ( H z )

Figure 11-3. Examples of magnetic brain signals made using a multichannel SQUID magnetometer. a) Spectral density of brain noise over left occipital lobe; b) Auditory evoked response to sound in ear, recorded over auditory cortex; c) Isocontour field map recorded over auditory cortex [9].

1

460

I 1 Applications

11.4.2.2 Geomagnetism and Space Research Geomagnetic measurements are among the oldest in science. For instance, measurements of the magnetic declination in London are available from 1570 to the present [lo]. Nowadays, measurements of the magnetic field at or near the earth’s surface can be used for a wide range of scientific and technical purposes. At the fundamental level, they can give information on the composition of the earth’s mantle, and about the dynamic processes in the earth’s core. At the more applied level, geomagnetic measurements are invaluable in mineral exploration and the location of buried objects. The magnitude of the earth’s field is typically about 50 pT at the surface; this sets the range of interest towards the lower end of the scale in Figure 11-1. Taken in conjunction with the need for rugged operation, often unattended for long periods, this indicates that the most suitable sensor types are fluxgates and induction coils. With these, once again, the resonance magnetometers are commonly used. Longterm measurements of the geomagnetic field are normally carried out at fixed observatories, which are located in most parts of the world [ll]. Standard equipment at such stations includes either fluxgates or induction coils to measure the vector components of the field, and a proton precession magnetometer to measure the total field. (Note that all the sensors considered in this book are vector types, which measure a particular component of the field.) Some information on induction coils and their applications to geomagnetic measurements are given in Chapter 6. Here we give an account of some of the other geomagnetic measurements that have been carried out. Many of the interesting features of the geomagnetic field occur on a long timescale (at low Hz and frequencies). Figure 11-4 shows a power spectrum of the field between about 10 - 2 Hz. It will be seen that there are a number of small peaks in the spectrum, corresponding to various terrestrial and cosmic phenomena. The 11-year peak corresponds to the solar cycle, the 27-day peaks to the solar rotation period, and the 1-day peaks to the earth’s rotation. Examples of raw data from fluxgate magnetometers are shown in Figure 11-5. Such data are of the utmost importance to geophysicists involved in modelling the behavior of the earth and sun [ll]. In recent years, geomagnetic measurements have been extended into the atmosphere and space, by magnetometers carried in aircraft, rockets, satellites and spacecraft. Magnetometry on the earliest spacecraft was dominated by helium resonance instruments, modified to permit

Log,,frequency / Hz

Figure 11-4. Power spectrum of the geomagnetic field at low frequencies, showing features of geophysical interest (after [ll]).

461

11.4 Magnetic Field Measurement

---I

t-

z

100 nT

43700 nT 0

6

3

-50

9

12

2‘1

15

i4

t :

-700t

0

100

200

300

Days

Figure ll-5. Typical time records of the earth’s field a) 24-hour record of vertical component at Hartland, U.K., 12th February 1989; b) Daily mean of the vertical component at Chambon-la-Forst, France, in 1986 [Ill.

vector measurements to be made. These reached their final form in the Pioneer 10 and 11 missions to Jupiter and Saturn [12]. Typical data for the combined sensor and signal processing , 3.4 kg, volume were as follows: Ranges + 4 nT to +140 pT, noise power 10 ~ T / H z ” ~mass 6000 cm3, power 4.4 W. The wide range required for these missions, set by the strong magnetic field around Jupiter should be noted. A detailed account of these measurements is given in [13]. At about the time of these flights, fluxgate magnetometers where achieving performance adequate for the purpose, and were extensively deployed in subsequent missions. In 1977 the International Magnetospheric Study was launched, to study the dynamic plasma and field environment of the earth. Instrumentation included two indentical triaxial fluxgates o n separate, closely orbiting spacecraft [14]. The highly elliptical orbit exposed the magnetometers to a wide range of fields, requiring a correspondingly wide range for the sensors. The instruments used had ranges of f 2 5 6 nT and f 8 1 9 2 nT, accurate to 0.025%, or 1 in 213. The noise level was about 3 pT/Hz”* at 1 Hz. The total mass was 2.4 kg, volume 4500 cm3, power 3.9 W. In 1984 the Active Magnetospheric Particle Tracer Explorers project, a collaborative venture between the USA, the FRG, and the UK, used three satellites equipped with triaxial fluxgates to map the field 550 km above the earth’s surface, as part of a study of ion transport through the magnetosphere. The instruments aboard the U. S. spacecraft [15] were similar to those used in Voyager, Viking and GIOTTO missions, with ranges from k 16 nT to + 65 536 nT and 13-bit

462

I 1 Applications

resolution, requiring only 1 W of power. The European version [16] was similar to that used in the HELIOS mission. It had ranges of *4 pT and +60 pT, with 16-bit resolution. The . results from this instrument are shown in noise level was less than 25 ~ T / H Z ’ ’ ~Typical Figure 11-6.

c

t 100

&

-

&

50 0 100 50

G O

- 50

- 150

c

f.100 Q

50

n

w

30 32 34 36 38 40 42 44 4 6 48 50 52 14 1984 SEE 4 DAY=248

54 56 58

0

2

4

6

8

10 12

min

15 h

Figure ll-6. Typical record from the IRM fluxgate magnetometers, showing multiple crossings of magnetic boundary layers during a magnetic storm [16].B, BX, BY, BZ: flux density and its components.

11.4.2.3 Identification By identification we mean applications such as card reading, coin validation and security systems. Taken together, these probably account for the most widespread application of magnetic sensors. The basic principle of magnetically encoded cards is shown in Figure 11-7. Alternately magnetized regions indicate a “0” or a “1” in a binary sequence. In practice, the regions are usually between 0.1 and 0.5 mm apart, which limits the distance over which the stray field extends to a similar range. The magnitude of the stray field amounts to 0.1-1 mT. The sensor requirement is thus for sensitivity in the range 10 -4- 10 -3 T, spatial resolution of 0.1 mm, combined with extreme cheapness and reliability. Figure 11-1 and Table 11-7 suggest that either Hall effect or magnetoresistive sensors might be suitable ; in practice, magnetoresistive sensors are preferred for their higher output for the necessarily small size. Coin validation, like card reading, is an extremely common operation worldwide. Various systems are in operation, among which the system based on magnetoresistive sensing, illustrated in Figure 11-8, is a competitive choice [18]. The principle is that the alternating field between the two coils is disturbed by the coin as it passes through. The phase of the magnetic field close to the coin with respect to the far field varies in a characteristic fashion for a particular type of coin, as shown in Figure 11-9. This phase signature is sent to a microprocessor to identify the type.

-

11.4 Magnetic Field Measurement

--VISA

463

MAGNETIC -.#STRIPE

-CARD

L

/i

Figure 11-7.Schematic diagram of magnetically encoded card and card reading sensor [17].

COIL D R I V E

co"'t

r *

MAQNETO RESISTOR

I

MICROPROCESSOR

ACCEPT

Figure 11-8. Schematic diagram of a coin validation system [18].

I

-.

464

11 Applications

40 OA

W Ill

w

35

g

30

LL L3

x

- COMMON POUND SLUG - POUND

COIN

8 25 z

g 20 W

15 O

w vl

10

2 a

5 0

I

-5 -15 -lo

i 0

0

5

5

10

10

15

15

20 25 30 35 POSITION OF COIN l m m )

20 25 30 35 POSITION OF COIN l m m )

40

40

45

45

50

50

Figure 11-9. Signatures of various coins measured with a magnetoresistive validation system [18].

Security systems for checking the movement of items are in widespread use in shops, offices and other public buildings. Perhaps the most familiar are those in use in shops to detect when an attempt is made to remove goods without paying. The item is “tagged” with a magnetic element, which responds to an interrogating signal at the exit. A similar system is used in libraries, to detect the unauthorised removal of books. A discussion of the use of Wiegand and pulse-wires for this purpose is given in Chapter 8, Section 8.6.2.

11.5 Solid Mechanical Transducers

465

11.5 Solid Mechanical Transducers 11.5.1

Basic Material Requirements

For transducers involving the conversion of mechanical information to magnetic or electric signals, the prime consideration must be the magnetic properties of the material. However, many mechanical transducers have to work in environments which are mechanically, thermally or chemically hostile. It is these extra constraints which must either be overcome by engineering design, or by careful choice of magnetic material. Designs can be produced which involve no direct contact between transducer and the input mechanism (eg, in a rotary encoder), but for many force or torque transducers there is a direct mechanical linkage. The following sections review the material-related issues in applications of magnetic sensors (see also Chapter 1, Section 1.5). With crystalline magnetic materials the general rule is that magnetic and mechanical softness go together, as do mechanical and magnetic hardness. This is a direct consequence of the link between macroscopic metallurgical properties of the material and the magnetic properties ~91. For transduction of force (linear and rotational) or displacement, where there may be mechanical contact with the magnetic material, the transduction element must be rugged. This would, in general, involve high hardness, a high tensile strength, and a high shear modulus. In choosing crystalline materials there must always be a trade-off between the magnetic and mechanical requirements. Soft materials such as the NiFe alloys can be mechanically hardened by alloying with Ti or Nb, without serious degradation of certain magnetic properties. However, this causes the material brittleness to increase. Magnetically hard materials, such as TbDyFe alloys, are mechanically hard and also mechanically brittle, which can lead to severe handling problems. As pointed out in the specialist chapters (eg, Chapter 4), the advent of metallic glasses over the last twenty years has overcome much of the incompatibility between mechanical and magnetic properties. Good magnetic softness is combined with high hardness and high yield strength. Metallic glasses also offer other advantages. Many form a passive layer giving a measurement of corrosion resistance. Their wear resistance is very high (laminations of metallic glases are being used in tape recorder heads for metallic tapes), and their coefficient of sliding friction is very low, typically ~ 0 . 2 - 0 . 3 [20]. Also, the wide compositional ranges available (non-commercially as yet) allow fine tuning of both magnetic and mechanical properties (see, for example, [21]). To obtain the maximum material response in any given transducer arrangement, the relative orientation and coupling between input mechanism (force, displacement etc.) and magnetic properties must be optimized. Optimization of the response of the magnetic properties is primarily achieved by control of the magnetic anisotropy. In crystalline materials the magnetocrystalline anisotropy dominates. This is related to, and often has the same symmetry as, the crystal structure. The NiFe materials are capable of supporting an induced uniaxial anisotropy produced by field annealing. Anisotropy can also be introduced via strainmagnetostriction coupling in any material with a non-zero saturation magnetostriction. In metallic glasses there is no macroscopic magnetocrystalline anisotropy as a consequence of the topological disorder, and the easy direction can be controlled by thermo-mechanical treatment (see, for example, [21]). The anisotropies introduced are stable up to continuous service

466

I1 Applications

temperatures of = 120°C. A drawback with metallic glasses is that for many compositions the ductility is severely degraded by the heat treatments necessary to optimize the magnetic response. This problem can sometimes be circumvented by heat treatment after the device has been configured. Magnetic elements in transducers come in a wide range of forms : toroids, wires, rods, films on substrates. Some transducer elements are free-standing, others form part of a more complex structure. Careful matching of thermal expansion coefficients may often be needed in order to avoid unnecessary straining of material. Constraints imposed by bonding between magnetic material and other elements of the system must also be considered. Mechanical strain can couple with the magnetic properties to degrade the overall device response. Crystalline magnetic materials are available in all bulk forms, and compositions have been optimized for transducer applications. Commercially available metallic glasses come in the form of thin sheet (20-40 pm thick by up to 25 cm wide), or wire (initial diameter 125 pm). The commercial compositions have not been optimized for transducer applications, but special alloys are available. Both crystalline and noncrystalline materials can be deposited by sputtering or evaporation.

11.5.2 Displacement Transducers Garratt [22] has reviewed the whole field of displacement transducers, and Table 11-9 shows his classification scheme. Figure 11-10 illustrates the possible ranges of linear displacement which may be sensed using the sensor categories listed in Table 11-2. The boundaries defined should be taken as order of magnitude figures only. It is clear that there is considerable overlap between the sensor categories, and other factors than available range must be taken into account in choosing a given technology. Magnetoresistive Inductive (LVDTI Inductive variable

1 Magnetoelastic 1

gap

I P

-9

I

-0

-1

Hall Effect

1

I

-6

-5 -4 -3 -2 Log,,, displacement (m)

-1

0

I

1

Figure ll-10. An indication of the useful ranges for various linear displacement transducer technologies.

Hall effect and magnetoresistive sensors for displacement rely on the same basic principle (see Chapter 3). The stray field from a permanent magnet is measured by the sensor. In a basic system of a single sensor element and magnet, the detected signal is a nonlinear function of distance from the permanent magnet. Linearization of the output signal requires further signal processing and/or multi-element sensors. The need for post-detection processing has brought about the development of “smart” sensors. Here the Hall element or magnetoresistor is integrated with the processing and drive circuitry onto a single “chip”. The only require-

Strain :

Indirect Position :

Temporal metrology :

Surface metrology:

Direct Dimensional metrology :

Force, velocity Acceleration Displacement, velocity Acceleration, force

Length, height, width Diameter Thickness (thin films) Position Angle Level Texture Roundness Straightness Flatness Contours and surface deformations Thermal expansion Vibrations Creep Tilt

lo4

5 x lo5

1 x 106 1 x lo5

1 x lo5

5 x 10’ 5 x 10’ 1 x 105 5 x 106 2 x lo4 1 x lo3 4 x lo4 2 x lo4 2 x 104 1 x lo4 2 x lo4 1 x 106

Maximum rangeto-resolution ratio

Table 11-9. Classification scheme for displacement transducers (after [22]).

5 mstrain

50

1 1 0.1

20 1

1

50 2 to 50 0.1 50 2 0.5 0.2 0.5 2

Range (mm)

0.5 pstrain

10 - 1

1 to 10-1 10 - 1 10 - 3 10 -2 10 - 1 5 x 10-1 5 x 10-~ 2.5 x 10 - 1 10 --I 1 10 - 3 10 -2 10 - 3 10 - 3

Resolution (vm)

102 to 106

102 to 106

10 10 10 <1 102 to 106 <1 10

50

100 to 300

<1


Frequency response (Hz)

B

3.

4

2r

0 n

%

0,

$

bl

4

LI.

468

I1 Applications

ment then is a power supply and an output channel, once the device is calibrated. The major advantages of Hall and magnetoresistive sensors are reliability, high noise immunity, the possibility of packaging to reduce environmental sensitivity, and no contact between the transducer and the system to be detected. Several of the features of these devices shown in Table 11-7 are relevant here: they can be physically small, and require few interconnections or high power. Intrinsically a magnetoresistive sensor element will generate a larger signal than the Hall element, which may be a determining factor in package design. Hall elements have an intrinsically linear output, whilst magnetoresistive require a biasing magnetic field for linearization. Both technologies suffer from an upper temperature limit of around 180"C which arises from the limitations of the materials used, either semiconducting or magnetic. Also, neither technology is intrinsically radiation hard. Given the range available with Hall effect devices or magnetoresistors, the applications are limited to proximity detection o r the detection of small lateral motion. This can lead on to use in such areas as keyboards and keypads. The ability to mass produce Hall effect or magnetoresistive elements means that the unit cost of the sensor based on these principles is low. In industries where the unit cost is part of the final product cost (eg, the automotive industry) these technologies offer a significant advantage. Inductive and induction coil sensors together offer the greatest range of linear displacement transduction. They are robust with a long lifetime. As there is no requirement for direct contact between system and sensor they can be environmentally and shock insensitive. The range of operating temperatures is also wider than for magnetoresistive or Hall effect devices. Induction coil sensors offer a range from - 50°C to 500°C, and inductive sensors a range from - 50°C to 600°C. The most widely used inductive transducer for linear displacement is the LVDT (linear variable differential transformer), which was discussed in some detail in Chapter 7, Section 7.3.1. LVDT's are frictionless devices allowing measurements of systems where loading must be kept to a minimum, and also giving very long mechanical life. The resolution is truly infinite, only limited by the associated electronic circuitry. The symmetrical construction of the LVDT gives null repeatability, and good cross-axis rejection. Given that LVDT's can be sealed units, they are ideally suited to work in hostile environments including areas of high neutron flux. Linearity is typically 0.1-0.2% of the full range of the transducer. The construction cost of an LVDT is high, as there are a number of precision engineered components. This makes the overall unit cost higher than for a Hall effect or a magnetoresistive sensor. Table 11-10, taken from Table 5 of [22], gives an overview of inductive displacement transducer specification. An interesting, and novel, use of an inductive technique for linear displacement has recently been proposed [23, 241. The device is illustrated in Figure 11-11. A permanent magnet on the moving member reverses the direction of magnetization in a certain length of a semi-hard magnetic core. The sensing is achieved by measuring the inductance of a solenoid wound around the core. By variation of the winding pitch a high degree of linearity can be achieved. Conversely, for systems with an inherent nonlinearity (eg, car fuel tank depth gage), the win-

M T H OF MAGNET

**

:: I

CJ

1

f

SLENDER FERROMAGNETIC ELEMENT

Figure ll-ll. Schematic diagram of linear transducer (after [23]).

-

0.2

5

2 0.4

Variable-reluctance 5 type in proximity to ferromagnetic component Eddy-current type in 50 proximity to ferro- 1.8 magnetic component

0.2

-20 to 90

-40 to 150

0.2

0.2

-20 to 60

- 5 to 55

-40 to 80

0.01

0.005

0.005

0.1

-

0.005

0.1

1

0.3

(0.1)

4

0.2

<0.5

100

LVDT with internal 50 oscillator and demodulator; springloaded plunger

Spring-loaded beam

plunger

Variable reluctance or LVDT+ Spring-loaded

Inductive:

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bm)

coupling

scale)

Repeat- Temperature Temperaability coefficient ture range

Mechanical coupling and conversion S p e of conversion Range Linearity and mechanical (mm) (%full

074 07

012

025

025

06

019

(mm)

Size

Table ll-10. Examples of typical transducers with respect to performance.

None None

None

0.5

0.001

0.3

I

(N)

Static force

2 1.2

4.5

2.4

10

1.4

2

13 13

22.5

-

100

20

20

500

2

lo4 lo4

-

-

5 0.2

500

500

0.1 0.005

500

response (Hz)

2

(pm)

Whole system Relative Relative Resolu- Electrical cost cost tion frequency

2 x lo3 2 x lo3

2.5 X lo3

-

2 x lo4

2 x lo4

2 x lo4

ratio given by output section

Oscillator, demodulator, 3 1/2-digit read-out

Oscillator, demodulator, range switching, 3 1/2-digit read-out

Oscillator, demodulator, range switching, gearbox, chart recorder Requires stabilized power supply and digital or analog read-out

Oscillator. demodulator, range switching, 3 1/2-digit read-out

Rangea p e of processing and to-resolution output

a

0 (D

$

2

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0

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2 2 $

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470

I1 Applications

ding pitch of the solenoid can be adjusted to linearize the output. The system is intrinsically cheap and rugged. Magnetoelastic displacement transducers primarily rely on the stress dependence of the permeability of a magnetic material. As described in Chapter 4, toroids of metallic glass offer the best mechanical as well as magnetic properties. Devices based on this principle have not, as yet, gone beyond the demonstrator stage. Mitra and Ghatak [25] have reported a system with a resolution of a few pm. There is no clear advantage on available range, repeatability or sensitivity. The unit cost is high, as the present cost of metallic glasses as a raw material is high. But this is not prohibitive in general for applications requiring small quantities, such as sensors. Digital encoders for linear displacement offer resolutions down to 0.1 mm. The digital signal can be generated by a Hall or magnetoresistive element reading a pre-recorded track, and a pulse count being taken. A linear displacement transducer based on magnetostriction has been reported [26]. A tube of magnetostrictive material is in the field of a movable permanent magnet. A current pulse in the tube causes a torsional pulse in the tube at the position of the permanent magnet. A time-of-flight measurement of the pulse gives the distance from the datum point of the permanent magnet. The system resolution is infinite, and long distances can be used (say up to several meters). The drawback is the bulky electronics that is required. A number of essentially similar sytems have been proposed to produce a linear transducer for machine tool applications. One commercially available type is based on the inductosyn principle, explained in Chapter 7, Section 7.4.3.2. A schematic of the basic system, taken from [27] is shown in Figure 11-12. A combination of digitally recorded track and at least two multielement read heads can give resolutions down 0.05 mm over a track length of up to 2 m. The resolution is achieved from a combination of signal processing and appropriate spacing of the read heads. The traversing speed is high, typically several hundred meters per second, with permissible accelerations up to 200 m/s2. The operating temperature range is limited to O-5O0C, but there is a high degree of protection from environmental dust or fluid. The units are made costly by the head technology needed to achieve the stated resolution, but offer easy interfacing to automated machine systems. The sensing of rotary displacement is primarily achieved with Wiegand wire sensors (see Chapter 8). The newly available wire-form metallic glasses will bring mechanical advantages in this area. The tensile strength of approximately 3.3 GPa, Young’s modulus of 162 GPa and Vickers hardness of 940 DPN are very suitable for applications requiring load toleration.

II

w -/

Figure U-U. Schematic diagram of a linear displacement transducer [27]. 1) Magnetic scale; 2, 3) read heads; 4) carrier generator; 5) divider; 6) phase shifter ; 7) mixer; 8) filter ; 9) pulse former ; 10) flip-flop ; 11) filter ; 12) indicator ; 13) variable phase shifter; 14, 16, 17, 18) windings; m : recorded elements at wavelength A.

11.5 Solid Mechanical E-ansducers

471

11.5.3 Velocity Transducers Linear and angular velocity sensors can be divided into two categories depending on whether the output signal should be analog or digital. For analog output an inductive technique is best, the output voltage being directly proportional to velocity by Faraday's law. There is, however, a signal-to-noise problem at low speeds. Digital output using magnetoresistive sensors can give lo6 pulses per revolution. Using digital technology removes the noise problem even at low rational speeds. Linear velocity transducers are obtained by differentiation of the output from linear displacement transducers. It is necessary to choose a linear transducer which can withstand high velocities, such as the hybrid device described in Section 11.5.2. The most basic angular velocity transducer is the tachometer, which is an analog device (Chapter 7, Section 7.2.3). A coil is fixed to the rotating shaft with a fixed permanent magnet close by, or permanent magnets are fixed to the shaft and the coil is held stationary. As the shaft rotates, the flux cutting the coil changes, and the induced voltage is directly proportional to the rotational velocity. Using slip rings a DC voltage output is possible. Typical sensitivity is 5 V/lOOO rpm, with maximum speed of 6000 rpm, linearity 0.01% and temperature stability 0.01%/ "C. The proportionality between output voltage and speed limits the low rotation speeds that can be measured to about 100 rpm. Magnetoresistive units can be used to provide digital output, and are suitable for use in motor control. They are very compact, low cost and easily interfaceable to control electronics. The main application area is in the control circuitry of brushless motors. A second digital method of detecting angular velocity is the variable reluctance technique. A schematic illustration of such a device is shown in Figure 11-13. The sensitivity depends on the gap between the pole piece and the rotating wheel, and the number of magnetic inserts. A frequency response up to 10 kHz has been achieved over a temperature range of -40°C to 160°C.

Figure 11-l3. Schematic diagram of a variable reluctance velocity transducer.

412

I 1 Applications

An adaptation of velocity or acceleration transducers is in seismic surveying. An inductive pick up arrangement is mounted on a seismic mass which is free to vibrate. By Faraday’s law, and a suitable arrangement of coils and excitation signal, there is an output signal which can be made to give information on the acceleration magnitude and direction. A typical device will have a range of +20 g, a linearity of better than 0.1070,and a threshold of lod6 g. The excitation would be of the order of 20 V at 20 kHz.

11.5.4 Strain Transducers Semiconductor strain gages have been widely available for a number of years. Their figure of merit (FOM) is defined to be FOM = R

(z)

where R is the electrical resistance and E is the strain. Typical FOM are 2 for a metallic element and 250 for a semiconductor type. Recently Wun-Fogle et al. I281 have proposed a strain gage using metallic glasses. The FOM is now defined in terms of the strain dependence of the material permeability, p1, as FOM =

PI

($)

n

ALUMINUM BENOING BEAMS

/ METGLAS RIBBON ON

\

MU METAL SWELO

\

PICKUP COILS

I

SIGNAL GENERATOR LOCK IN AMPLIFIER

4 Figure 11-14. A strain gage sensor using magnetoelastic metallic glass [28]. Diagram of the experimental bending beam apparatus showing the two aluminium bending members with a metallic glass ribbon bonded to the top of one and a metallic glass ribbon bonded to the bottom of the other.

11.5 Solid Mechanical Transducers

473

Their proposed arrangement is shown in Figure 11-14. The FOM is measured as being in excess of 2 x 10’. The dynamic range is as great as lo4, extending from 0.01 Hz to 100 Hz.The authors claim that the range could be further extended. The temperature dependence of the FOM is very low, which offers a significant advantage over semiconducting devices. Problems of mechanical loading degrading the magnetic response of the metallic glass are overcome by using a high viscosity bond rather than a rigid adhesive bond. It is this viscous bond which will ultimately determine the frequency response, and the noise floor. With the bond used the strain is relieved in around 10 minutes, and so integration times to overcome noise must be much shorter than this for a true reading. This application of the magnetic material to a strain gage is a prime example of choosing a material where the magnetic and mechanical properties are suitable, as discussed in Section 11.5.1.

11.5.5

Force and Torque Transducers

Magnetic force transducers are usually based on linear displacement transducers coupled to appropriate sensing elements. The elastic deformation of the sensing element is transformed into a measure of applied force via the appropriate stresslstrain relationship. Some examples of sensing elements are shown in Figure 11-15 (see also Chapter 4, Sec-

(b) flat (proving frame)

(a) proof ring

(d) solid cylinder

Figure 11-15. Sensing elements for force transducers.

(c) flat with stress concentration holes (dumbell-cut proving frame)

(e) rectangular with stressconcentration hole

414

I 1 Applications

tion 4.3). Figure 11-16 shows how a proof-ring coupled with an LVDT (see Section 5.2) can be used as a force transducer for tensile or compressive loads. The device sensitivity will be limited by the mechanical properties of the sensing element rather than the properties of the LVDT.

*

force (compressive or tensile)

Figure 11-16. Proof-ring based force transducer including an LVDT.

Figure 11-17. Schematic diagram of an inductance bridge transducer.

The metallic glass force transducers described in Chapter 4, Section 4.5.1 are able to combine the sensing element and transducer. This is again a result of the combination of soft magnetic and hard mechanical properties in metallic glasses. The saving in simplicity of design is masked by the high raw material cost already highlighted above. Meydan et al. [29] have demonstrated a sensitivity of 35 pT/g and acceptable linearity up to a load of 350 g for such a 10 mm diameter transducer. The excitation was at 15 kHz with the primary field of 14.3 A/m. A no-power shock sensor based on a similar design has been proposed by Mohri

11.7 References

475

and Takeuchi [30].For maximum sensitivity the metallic glass has been devitrified to give a fine crystal structure. A shock as small as that produced by a 6 g mass dropping from 5 mm can be detected. They believe that this sensitivity is adequate for such systems as knock sensors in cars. For the measurement of compressive forces or pressure an inductance-bridge transducer can be used. Figure 11-17 is a schematic diagram of one such device. As the central diaphragm is displaced, the reluctance in each arm of the bridge will change, and the signal output is a measure of the direction of force and the magnitude. A typical design can be used in ranges from 0-3.5 MPa over a temperature range of 0-100°C. The resolution is essentially infinite. Standard torque sensors bond semiconductor strain gages onto the shaft. As discussed in Section 5.4, it is now possible to use magnetic detection by depositing or gluing magnetic material onto the shaft.

11.6 Conclusions Any review of applications is likely to become out of date in a short time, as new applications are discovered and existing ones are abandoned. In the case of magnetic sensors, some applications are already mature, with a large commercial base. An example of this is the LVDT for displacement measurement. Other applications are likely to remain because they are intrinsically magnetic; Hall probes for laboratory magnetic field measurement are an example of these. It is always possible that a new field measuring technology will emerge, particularly at very low fields, where the operational problems of the SQUID encourage the development of alternatives. Some newer applications have already become widespread ; card readers are an example of an application in which magnetic sensors excel. New applications in the mass markets of consumer goods and automotive engineering offer the greatest financial reward, but are the hardest to gain because of the combined requirements of low cost and ability to operate in rugged environments, together with a trend towards integration, which favors semiconductor sensors. In the areas of industrial instrumentation, fiber-optic sensors are posing a serious challenge to many existing technologies [31].In some specialist applications it is possible that the combined magnetidfiber-optic sensor may prove successful, although this is unlikely on a wide scale. In conclusion, one may assert that magnetic sensors have an important but limited part to play among the whole range of sensor technologies, and that there are no obvious developments in progress that are likely to change this situation drastically over the next ten years.

11.7 References [I] Norton, H. N., Sensor and Analyzer Handbook, Englewood Cliffs, NJ: Prentice Hall, 1982. [2] Westbrook, M. H.,“Sensors for automotive application”, J. Phys. E: Sci. Instrum. 18 (1985) 751 - 758.

[3] Brignell, J. E . , “Interfacing solid state sensors with digital systems”, J. Phys. E : Sci. Instrum. 18 (1985) 559-565.

416

11 Applications

[4] Kobayashi, T., “Solid-state sensors and their applications in consumer electronics and home appliances in Japan”, Sens. Actuators 9 (1986) 235-248. [5] Hartmann, F., “Resonance magnetometers”, ZEEE Trans. Magn. MAG4 (1972) 66-75. [6] Foner, S., “Review of magnetometry”, ZEEE Trans. Magn. MAG-17 (1981) 3358-3363. [7] Romani, G.R., Williamson, S. J., Kaufman, L., “Biomagnetic instrumentation”, Rev. Sci. Znstrum. 53 (1982) 1815-1845. [8] Cohen, D., “Large-volume conventional magnetic shields”, Revue de Physique Appl. 5 (1970) 53-58. [9] Knuutila, J., Ahlfors, S., Ahonen, A., Hiillstrc)m, J., Kajola, M., Lounasmaa, 0. V., Vilkman, V., Tesche, C., “Large-area low-noise seven-channel dc SQUID magnetometer for brain research”, Rev. Sci. Znstrum. 58 (1987) 2145-2156. [lo] Malin, S. R. C., Bullard, E., “The direction of the earth’s magnetic field at London 1570-1975”, Philos. Trans. Roy. SOC.London. Ser. A 299 (1981) 357-423. [ll] Courtillot, V., Le Mouel, J. L., “Time variation of the earth’s magnetic field”, Ann. Rev. Earth Planet. Sci. 16 (1988) 389-476. [12] Smith, E. J., Connor, B. V., Foster, G. T., “Measuring the magnetic fields of Jupiter and the outer solar system”, ZEEE Trans. Magn. MAG-11 (1975) 962-980. [13] Smith, E. J., Gulkis, S., “The magnetic field of Jupiter: a comparison of radio and spacecraft observations”, Ann. Rev. Earth Planet. Sci. 7 (1979) 385-415. [14] Russell, C. T., “The ISEE 1 and 2 fluxgate magnetometers” ZEEE Trans. Geosci. Electron. GE-16 (1978) 239-242. [15] Potemra, T. A,, Zanetti, L. J., Acuna, M. H., “The AMPTE CCE magnetic field experiment”, ZEEE Trans. Geosci. Remote Sens. GE-23 (1985) 246-249. [16] Liihr, H., Klbcker, N., Oelschliigel, W., Hausler, B., Acuna, M., “The IRM fluxgate magnetometer”, ZEEE Duns. Geosci. Remote Sens. GE23 (1985) 259-261. [17] Data Sheet on Ferromagnetic Magnetoresistive Sensors and their Applications, MR Sensors Ltd., St. Mellons, Cardiff, UK. [18] Data-Sheet - Coin Validation, MR Sensors Ltd., St. Mellons, Cardiff, UK. [19] Chen, C-W., Magnetism and Metallurgy of Soft Magnetic Materials, New York: Dover, 1977. [20] Lee, D. H., Evetts, J. E., “Sliding friction and structural relaxation in metallic glasses”, Acta. Metall. 32 (1984) 1035-1040. [21] Luborsky, F, E., Amorphous Metallic Alloys, London: Butterworth, 1983. [22] Garratt, J. D., “Survey of displacement transducers below 50 mm”, JO Phys. E. :Sci. Znstrum. 12 (1979) 563-573. [23] Garshelis, I. J., Fiegel, W. S., “A magnetic position sensor”, J, Appl. Phys. 64 (1988) 5699-5701. [24] Garshelis, I. J., Fiegel, W. S., “An improved magnetic position sensor”, (to appear in) ZEEE Trans. Magn. MAG-25 (1989). [25] Mitra, A., Ghatak, S. K., “An AC transducer system to detect small displacement and current using amorphous magnetic material”, JO Magn. Magn. Muter. 66 (1987) 361-365. [26] New, R. E., “A non-contacting transducer for use in hydraulic or pneumatic cylinders”, Transd. Techn. 12 (1989) 11-13. [27] Uemura, S., Kanagawa-ken, Magnetic heads utilized as a displacement measuring instrument, US Patent 3597749, 1969. [28] Wun-Fogle, M., Savage, H. T., Clark, A. E., “Sensitive, wide frequency range magnetostrictive strain gage”, Sens. Actuators 12 (1987) 323-331. [29] Meydan, T., Blundell, M. G.,Overshott, K. J., “An improvement force transducer using amorphous ribbon cores”, ZEEE Trans. Magn. MAG-17 (1981) 3376-3378. [30] Mohri, K., Takeuchi, S., “Stress-magnetic effects in iron-rich amorphous alloys and shock-stress sensors with no power”, ZEEE Trans. Magn. MAG-17 (1981) 3379-3381. [31] Grattan, K. T. V., “Recent advances in fibre optic sensors”, Measurement 5 (1987) 122-134.

12

Trends RICHARDBOLL. Vacuumschmelze GmbH. Hanau. FRG

Contents 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10

. . . . . . . . . . . . . . . . . . Magnetogalvanic Sensors . . . . . . . . . . . . Magnetoelastic Sensors . . . . . . . . . . . . . Flux Gate Magnetometers . . . . . . . . . . . . Inductive Coil and Search Coil Sensors . . . . . Inductive and Eddy Current Sensors . . . . . . Wiegand and Pulse-Wire Sensors . . . . . . . . Magnetoresistive Sensors . . . . . . . . . . . . . SQUID Sensors . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . Introduction

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

478 478 479 479 480 481 481 482 482 483

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

418

12

Trends

12.1 Introduction Sensors are the key element to the further advancement of microelectronics in diverse fields of application. In combination with the growing integration of electronics and the continuous development of precision and high-precision mechanics, sensors contribute to increasing the safety of many products. This applies to automation technology, measurement and processing, automotive, biomedical, and environmental technologies [l -31. These general trends are also valid for magnetic sensors, eg, rotational frequency and torque sensors. On the other hand, sensors are being used increasingly to obtain access to data banks. The natural consequence is an ever widening field of application [4]including the fact that sensors are arousing interest in the areas of CAD and CIM. In addition, more and more national and international companies are entering the market to coordinate and develop new sensor technologies. The number of established specialist symposia and conferences underlines the promising future attributed to sensors. The key role of sensors is based on the following general aspects.

- product innovations are often possible only as a result of suitable sensors; - low cost, intelligent, high accuracy sensors frequently set the pace for developments in

automation technology and in the fields of manufacturing and processing;

- sensor techniques also promote information and communication technology; - in the field of automotive technology sensors play a significant role in safety, environmen-

tal problems, and ease of handling (instruments, etc). The magnetic sensors discussed in Volume 5 - categorized according to individual sensor groups and principles - exhibit the following trends outlined below. The authors’ contributions are included in the relevant chapters.

12.2 Magnetogalvanic Sensors In the current development of semiconductor magnetic field sensors, two approaches can be distinguished. In the first, workers try to build better devices based on the conventional Hall and magnetoresistive effects. Innovations come through the better understanding of the details of the operating principle and secondary effects, and trough the application of everimproving microelectronics technology. In the second approach, one hopes to build better sensors by combining the conventional galvanomagnetic effects with other phenomena taking place in semiconductor devices. The results are modified conventional semiconductor devices, such as bipolar transistors, diodes, and FETs, which are referred to as magnetotransistors, magnetodiodes, and mag-FETs, respectively. Many interesting magnetic field sensors of this kind have been proposed during the last 30 years. However, none of them has (yet) become a competitor to the Hall-effect devices and magnetoresistors. A still larger application potential of Hall devices may be expected if their performance can be improved. To this end, means should be found to decrease offset dramatically, improve stability, and reduce cross-sensitivity [ 5 ] .

12.4 Flux Gate Magnetometers

479

The microelectronic revolution has strongly influenced and stimulated the further development of new galvanomagnetic sensors because, in general, sensors that have as high a performance-to-price ratio as the microelectronic circuits themselves are highly desirable. This also applies, of course to magnetic field sensors and similarly determines trends in their development. An obvious way to achieve the goal is to make use of available mainstream technology. Accordingly, most new developments in the field of galvanomagnetic sensors take advantage of the availability of high-quality materials and the well established sophisticated methods of fabrication that are used in integrated circuit production. Such a trend has been further motivated by the possibility of being able to integrate a magnetic field sensor and some signalprocessing circuitry on the same chip. These integrated sensors, with “one-chip” signal processing, are called “smart” sensors [6]. It is interesting, however, that only the semiconductor magnetic-field sensors have the potential to be fully compatible with contemporary integrated circuits [7], and hence they are the natural choice for the realization of smart magnetic sensors.

12.3 Magnetoelastic Sensors To date the Villari effect is the most commonly used magnetoelastic effect, the main applications being in torque sensors and load cells. Following their use in the ship propeller shafts and heavy machinery shafts, the next target for torque sensors will probably be automotive gear boxes and electric motors, fields which may well involve the use of new technologies (see Chapter 4). Numerous other application possibilities for magnetoelastic effects are being researched in laboratories or are under trial, eg, utilizing the elastic deformation of circular rings for simple path and power actuators and for switching, and utilization of the Wiedemann effect for torque registration or weighing purposes (Chapter 4). The AE effect should also be mentioned together with its use for delay lines and in digitizing graphic systems. Sensors combining the magnetostrictive effect and other pyhsical effects are also at the experimental stage (see, eg, Chapter 4, Section 4.6). The further development of magnetic materials will certainly aid the progress of magnetoelastic sensors. Here we can refer to soft magnetic amorphous alloys featuring excellent mechanical properties and new high-magnetostriction alloys on the basis of rare earths (see Chapter 4, Section 4.2 and Table 4-2).

12.4 Flux Gate Magnetometers For flux gate magnetometers, new and promising developments in the range of the probes, which are the converters of magnetic fields into electrical signals, are essentially only to be expected in the pulse-position systems. In contrast to the analog operating harmonic and pulse-amplitude method, the developments in digital semiconductor technology can be

480

12

Trends

utilized for these systems in order to attain distinct improvements in the signal-to-noise ratio and the signal conversion rate, as novel and hitherto unpublished papers demonstrate. The application of magnetizable, amorphous metals as probe cores makes a further contribution in this direction. The advantages of these materials, as there are low losses at high frequencies, small coercive field strength, and insensitivity of the magnetic properties towards mechanical stress in operation, promise considerable developments in the lower effective range limit, the long-term stability, the synchronism, and the conversion rate of the probes. Of special importance is the fact that by selective heat and magnetic field treatment of the probe cores the properties of the magnetometers can be optimized. A future focus in the development of flux gate magnetometers will be the application of digital signal methods, as used in the pulse-position procedure, in connection with downstream digital signal processing modules. By the application of multiple probes, either as double probes or as spatial probe arrays, in addition to the diminution of the signal-to-noise ratio an increase in the directional sensitivity and, further, direct determination of the field structures are to be expected. Looking at the limit values achievable with the flux gate magnetometers and taking the above-mentioned future developments into consideration, a lower limit of the effective range of 1-10 pT within the frequency range 0 up to more than 100 Hz can be foreseen, where with pulse-position procedures and digital after-processing a direct effective range of 5-6 orders of magnitude is possible. For magnetic field detection with portable devices or with long mission durations, there does not exist an alternative to the flux gate magnetometers.

12.5 Inductive Coil and Search Coil Sensors Inductive coils (or search coils) are strictly passively operating magnetic field sensors, which are suitable only for the measurement of AC magnetic fields. They show an increase in sensitivity and resolution proportional to the frequency up to their frequency limit, owing to their functioning principle, the law of induction. They are of a relatively simple mechanical and electronic design, contain air-cored coils or coils on high permeability soft iron or ferrite cores, and may show outstanding performance. Sensors of very different sizes and shapes are applied for various tasks in science and technology. Normally, they are specially designed and optimally adapted to the intended application. In the market, there is no variety of industrially produced inductive coil sensors with the exception of a small series of sensors designed for the scientific geophysical or geological prospecting applications. They are available with operating frequency ranges between 10 - 4 and lo4 Hz, in the form of single sensor components or two- or three-axis systems, and typical features are their high sensitivity, bulkiness, and weight. Inductive coil sensors represent a basic class of magnetic field sensors, that are not very dependent on special technological developments in the fields of materials, manufacturing processes, or components. Merely the general improvements in the properties of ferromagnetic materials and low-noise, low-frequency integrated semiconductor amplifiers have led to more sensitive sensors of reduced weight and size. Ferrites and amorphous metals of very high permeability are increasingly used as high-permeability cores. Finally, from the increasing per-

12.7 Wiegand and Pulse-Wire Sensors

481

formance of these sensors some further applications may result, but other than this no special trend in development and appliations seem likely.

12.6 Inductive and Eddy Current Sensors Owing to their mechanical properties, high reliability, ability to operate within rough environments, accuracy, size, and other advantages the market for inductive and eddy current sensors has grown considerably in recent years. The variety of types and the possibility of measuring different quantities with these devices have led to applications in many industrial areas and in research [8-lo]. The sensors are used in increasing numbers mainly in automotive applications. Other ranges of operation are in production engineering, process engineering, robotics, diagnosis, and others. A new range of applications has arisen with the developments in CAM. Some current trends in sensor development are:

- reduction of the size - extension of the range of operation (temperature etc)

- improvements in the magnetic circuits with the help of computer-aided numerical field calculations

- use of new magnetic materials such as amorphous alloys or magnetic fluids. Another development is the miniaturization of the electronics. Owing to SMD and hybrid techniques electrical circuits for supply and signal processing are nowadays increasingly provided as integrated circuits. In this form, electronics can be completely integrated within the sensors, which leads to many advantages, eg, less disturbance of signals. Microprocessors and highly integrated electronics are used within automatic control systems and robotics for further signal treatment. The market for inductive and eddy current sensors will increase further owing to expanding automation within the next few years possibly by ca. 10%. In automotive applications the number of sensors is expected to increase by about 30% from 1990 to 2000. This increase will include a large number of inductive sensors. Other ranges of applications are expected to show similar expansion [ll].

12.7 Wiegand and Pulse-Wire Sensors The development of Wiegand and pulse-wire sensors has opened up a series of new possibilities, for building up rotational frequency sensors and magnetic switching elements with high signal-to-noise ratios. For example, pulse-wire sensors are now integrated in highprecision photoelectric rotary encoders, acting as a revolution counter independent of the mains. Moreover, a growing field of application is offered by the wide range of operating temperature, eg, rotational frequency actuators mounted directly on the shaft of electric

482

12 Trends

motors. With respect to security or anti-theft devices composite wires with low switching field strengths are of interest. These wires with extremely low jitter, are also expected to enter the field of sensor applications in competition with cobalt-based amorphous wires with negative magnetostriction [12]. Further improvements of their switching properties, especially the pulse amplitude, will be subject to future developments.

12.8 Magnetoresistive Sensors The main efforts in improving magnetoresistive sensors are seen in two different fields. The first concerns the quality of the ferromagnetic thin layer and is of interest especially for very sensitive sensors used, eg, as magnetometers or for magnetoresistive reading heads. The coercive field strength, H , , which is the measure of the magnetic quality (see Chapter 9, Section 9.2.3) is successfully decreased by double or multiple ferromagnetic layers, seperated by non ferromagnetic thin layers as mentioned in Chapter 9, Section 9.4.1. This system, originally developed for other applications (inductive reading heads), is now also utilized in magnetoresistive sensors too [13, 141. Another approach for improving magnetic quality, reported some years ago [15], is suppression of layer texture by addition of a small amount of nitrogen ; this technique is becoming more popular now [16]. The magnetoresistive effect of these improved layers is now comparable to that of normal ones. Other efforts are aimed at the adaptation of magnetoresistive sensors to special applications, eg, in the automotive industry. This includes position sensors with a special layout adjusted in geometry to given gear wheels (see Chapter 9, Section 9.4.3). However, there are also demands for sensors withstanding severe environmental conditions like higher operating temperatures, corrosive atmospheres, or high voltage spikes. The magnetoresistive principle seems to be better qualified than, eg, semiconducting sensors, but the devices have to be manufactured with improved and thus more expensive technologies.

12.9 SQUID Sensors The strength of SQUID sensors is their extremely high sensitivity, particularly at low frequencies. However, their inconveniently low operational temperatures and their high sensitivity to electromagnetic interference require a sophisticated infrastructure (liquid helium supply, glass-fiber-reinforced epoxy Dewar vessels, electromagnetic shielding, and advanced know-how), thus limiting their application mainly to a few research laboratories in the past. In addition, SQUID sensor systems are relative expensive. This situation changed only recently, when SQUID systems became a commercial success and experienced a much wider distribution with the discovery of high-T, superconductors. Research activities in this field spurred an urgent need for SQUID magnetometers and susceptometers.

12.10 References

483

Other applications on the brink of a commercial success are SQUID multisensor systems for biomagnetism (eg, magnetocardiography and magnetoencephalography). Here the real innovation is taking place : several development laboratories in industry have produced the first prototypes of highly complex multisensor systems. Almost entirely the thin-film DC-SQUID concept is favoured over rf SQUID design and the trend is towards higher levels of integration so as to include planar thin-film gradiometers, preamplifiers and/or digital read-out circuits. With these developments, SQUID sensors should become much more versatile and cheaper. This should trigger additional applications such as particle and radiation detection, nondestructive testing of pipelines, welds and electronic circuits, etc. The impact of high-T, -superconductor SQUIDs will be moderate in the short term as the advantage of SQUIDs over other magnetic field sensors lies in the ability to perform very low noise measurements with utmost sensitivity. It will be a difficult competition for high-T, SQUIDs either with other types of magnetic field sensors or with the sophisticated and reliable low-temperature SQUIDs.

12.10 References [l] “Sensortechnik 2000”, Sensor Magazin, No. 5 (1988) 22-25. [2] McCelland, S., “Searching for trends in Japanese sensor technology”, Sensor Review 8, No. 1 (1988) 33-35. [3] Kistler, J., “Entwicklungstendenzen der Sensortechnik”, Technika, No. 15/16 (1987) 9- 16. [4] Schneider, E., “Online Datenbanken iiber Sensoren”, Sensor Magazin, No. 3 (1987) 26-27 and NO. 4 (1987) 25-26. [5] PopoviC, R. S., “Hall-effect devices”. Sens. Actuators, (1989) (in press). [6] Middlehoek, S., Hoogerwerf, A. C., “Smart sensors, when and where”, Sens. Actuators 8 (1985) 39-48. [7] Baltes, H. P., PopoviC, R. S., “Integrated semiconductor magnetic field sensors”, Proc. ZEEE 74 (1986) 1107-1132. [8] Mohri, K. et al., “New torque sensors using amorphous star-shaped cores”, ZEEE Trans. Magn. MAG-23 (1987) 2191-2193. [9] Mohri, K., “Review on recent advantages in the field of amorphous metal sensors and transducers”, IEEE Trans. Magn. MAG-20 (1984) 942-947. [lo] Kanamaru, Y. et al., “Characteristics of level and two axis attitude detectors using magnetic fluid”, ZEEE Ttans. Magn. MAG-23 (1987) 2203-2205. [ll] Spezial Sensoren 86/87, Diisseldorf : VDI-Verlag, 1986. [12] Yamasaki, J. et al., “Large Barkhausen discontinuities in Co-based amorphous wires with negative magnetostriction”, J. Appl. Phys. 63, No. 8 (1988) 3949-3951. [13] Hur, J. H., Comstock, C. S., Pohm, A. V., Peary, L. A . , “Magnetoresistivity in NiFeCo multilayer films”, J. Appl. Phys. 63 (1988) 3149-3150. [14] Kitada, M., Shimizu, N., “Magnetic and magnetoresistive properties of multilayered thin films”, Thin Solid Films 158 (1988) 167- 174. [15] PCitzelberger, H. W., “Magnetron sputtering of permalloy for thin-film heads”, ZEEE Trans. Magn. MAG-20 (1984) 851-853. [16] Lo, J., Hwang, C., Huang, T.C., Campbell, R., “Magnetic and structural properties of high rate dual ion-beam sputtered NiFe films”, J. Appl. Phys. 61 (1987) 3520-3525.

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

Index

ABS 260 AC dyamo principle 266 AC tachometers 266f. AC-excited sensors 269-297 - rotary movements 287-297 see also linear variable differential transformers; variable inductance sensors; variable gap sensors; synchros; resolvers; inductosyns acceleration sensors 282 action point effect 140f. aerospace applications 450 agressive fluids measurements 306 air-cored coils, proximity sensors 301 f, air-cored inductions coils 207-22Off. - amplifier noise 214 - capacitance 219f. - design 207ff. - equivalent circuit diagram 214-220 - filling factors 208 - inductance 216 - internal noise 212ff. - noise equivalent magnetic field 213 ff. - output voltage 210ff. - proximity effects 217ff. - resistance 208 - sensitivity 207-220 - skin effect 217ff. - weight of the winding 212 alloys, amorphous 103ff., 308 - crystalline 104f. - magnetic 15, 100-106, 142, 307ff., 317 - magnetoresistive 350ff. - magnetization curve 1OOf. AlNiCo alloys 307

AlNiCo magnets 15 aluminium coils 209 amorphous alloys 103ff., 308 amorphous films 356ff. amorphous materials, force sensors 136 - non-contact switches 140f. - position and displacement sensors 138f. amorphous metals 15 amorphous ring-core sensors 137-141 amorphous wires 330f., 337 amplifier noise, air-cored induction coils 214 amplifiers, carrier 278 - current 239ff. - DC 278 - induction coil sensors 237-246, 250 - measuring 174f. - voltage 237ff. analog arithmetic operations, resolvers 294 analog position sensors 85 angle, Hall 61 ff. - rotation 277 see also twist-angle angle measurements 295 angle sensors 286 anisotropy magnetization 344-350 annealing, magnetoresistive layers 360 anti-theft devices 331, 336 audio-magnetotelluric measurements 246 automotive applications 450ff. - magnetogalvanic sensors 88f., 91, 113 - torductors 113 automotive powertrain sensors 452f. auxiliary fields, magnetoresistive sensors 370ff. axle load of lorries, measurement 135

486

Index

balanced linear-tapered secondaries 271 ff. bandwidth, induction coil sensors 242 barber pole sensors 368, 372, 374 barber poles 364ff. Barkhausen jumps 40, 316 Barkhausen noise 19f., 236, 309, 349 battery control, flux gate magnetometers 176 bias fields, magnetoresistive sensors 370ff. biasing of magnetoresistors, magnetic 68 ff. biomagnetic fields 8 biomagnetism 457 ff. biomedical applications 450 bipolar integrated circuit process, Hall sensors 56 Bitter coils 24 blocking curve, magnetization 349f. brain signals, magnetic 459 brushless DC motors 89f. bulk SQUIDS 429 c-shaped sensors 260 CAD 478 calibration, high permeability core inductions coils 222 camshafts, rotational frequency measurements 261 capacitance, air-cored induction coils 219f. car wheels, rotational speed measurements 260 card reading sensors 462 ff. carrier amplifier 278 carrier concentration, low 53 carrier velocity 45 carrier-domain magnetic sensors 74f. ceramic materials, sensor housings 308 ceramic superconductors 436ff., 483 CGS electromagnetic units 6 charge-carrier transport phenomena 45 f. check-in control systems 336 chemical industry, applications of inductive flowmeters 306 chemical sensors 454 chips, Hall-effect 92 CIM 478 circuit diagram, equivilant 16, 214-220, 234ff., 327 circuits, magnetic see magnetic circuits CMOS 73 Co-based alloys loof., 317 coaxial torque sensors 128

coaxial-type sensors 116-120 - complex coil arrangement 119 - data processing electronics 117 - electric motors 118 - principal designs 120 - sensitivity 119 Cobalt 70, loof., 317 code cards 336f. code converter, pulse-position type flux gate magnetometers 201 coefficient of magnetoresistance 51 coercitivity 11f. CoFe alloys 317 coil systems 20-24 coils, aluminium 209 - Bitter 24 - Helmholtz 21 - moving 39 - stationary 38 see also air-cored (induction) coils; induction coil sensors coin validation sensors 462ff. combined-effects magnetoeleastic sensors 145f. compass 2 complementary tapered windings 274 f. composite materials 15 composite wires 324 compressive strength 15 compressive-force sensors 130-135 consumer applications 450ff. consumer equipment sensors 454 contact layers, magnetoresistive 361 control-type synchros 291 ff. Cooper pairs 383 coordinate transformation, resolvers 295 copper wire 209 Corbino disk 51 f. core materials 307 cores, soft magnetic 303 see also air-cored; double-core; high permeability core; ring core correction factor, geometrical 53 correlation techniques 251 corrosive fluids measurements 306 coupling factor, magnetomechanical 100 crankshafts, rotational speed measurements 260 critical current 434f. critical temperature, superconductivity 383 ff. cross-sensitivity, Hall sensors 59 cross-type force sensors 108-115, 134f.

Index cross-type sensors, magnetic circuits 109ff. Crovac 328, 332 cryogenics 406ff. crystalline alloys 104f. Curie temperature 13 - magnetoresistive films 372 current, amplifier 239ff. - critical 434f. - density 298 - measurements 76ff., 79 - noise 16f. - shielding 388f. cylindrical coils 22 f. damping, induction coil sensors 238 data banks 478 DC amplifier 278 DC SQUIDS 395-401 - electronics 426ff. - energy sensitivity 423 - integrated 422-429 - noise 424ff. see also SQUIDS DC tachometers 266f. DC-excited sensors see permanent-magnet excited sensors ; reluctance sensors definition of magnetic sensors 3 ff. demagnetization factor, high permeability cores 224f. demodulator, flux gate magnetometers 175f. design, air-cored induction coils 207ff. - coaxial-type sensors 120 - double-core flux gate magnetometers 168ff., 174ff. - flux gate magnetometers 168ff., 174ff. - flux gate sensors 155f. - magnetic circuits 84 - magnetoresistive sensors 363-370 - orthogonal gated flux gate sensors 186 - pulse height sensors 185 - pulse position type flux gate magnetometers 196ff., 199ff. - ring core flux gate magnetometers 178-183 - SQUIDS 392ff., 397ff., 418ff. - Wiegand sensors 319ff. dewars, SQUIDS 406ff. diagram, electrical, force sensors 283 - - reluctance sensors 264 - - variable inductance sensors 283

481

- equivilant circuit 16, 214-220, 234ff., 327 differential cross-anchor sensors see variable gap differential magnetoresistors 68 ff., 87 f. differential synchros 291 f. differentiating circuit 200 digital position sensors 81 f. direct drives 304 displacement measurements 466-470 - linear 266, 281 - rotary 470 displacement sensors 136-141, 275f., 286 domain walls 316f. domains 348ff. - boundaries 39ff. double-core flux gate magnetometers 167-177 - design 168ff., 174ff. - frequency range 171 - probe types 171ff. - sensitivity 170f. - transfer factor 170f. see also flux gate magnetometers AE effect 36 - magnetoeleastic sensors 141ff. earth’s magnetic field 6f., 377, 460ff. eddy current effects 261 - high permeability core induction coils 222f., 236 eddy current sensors 124, 297-304, 469 - applications and properties 310f. - direct operating 299f. - proximity 299-304 - trends 481 eddy current tachometers 299f. - applications and properties 300 eddy currents 39 - pulse wires 326 effects, action point 140f. - AE 36, 141ff. - eddy current see eddy current - galvanomagnetic 35f., 45-52, 72 - Hall see Hall effect - Josephson see Josephson - Joule 36 - magnetic resonance 5 - magnetoelastic 36ff. - magnetoelectric 37 - magnetoresistive 35, 51, 62ff., 342ff., 362f. - magnetostriction 36ff.

488

Index

- Matteucci 37 - Meissner 42, 383ff., 390 - physical, magnetic sensors 34f. - proximity 217ff. - short-circuiting 56 - skin, air-cored induction coils 217ff. - Villari 37 - Wiedemann see Wiedemann - Zeemann 5 electric motors, coaxial-type sensors 118 - magnetic field 8 electric resistivity, specific 13 electrical diagram, force sensors 283 - reluctance sensors 264 - variable inductance sensors 283 electromagnetic systems 38 f. electromagnetic units 6 electromagnets 23 f. electronic amplifiers, induction coil sensors 237-246, 250 encoder, rotary 334ff. energy sensitivity, SQUIDS 423, 432 ff. energy spectrum of Barkhausen noise 20 epoxy metals, sensor housings 308 equivalent circuit diagram 16 - air-cored induction coils 214-220 - high permeability core induction coils 234ff. - pulse wires 327 etching 410 excess noise 19, 309 exchange energy 317 extensometers 138 l/f noise 434ff. Faraday’s law 2, 38, 206, 257, 266 FeCo alloys 308 FeCrCo alloys 307 feedback, negative, induction coil sensors 241 ff. feedback control of flux gate magnetometers 166f. FeNi alloys 308 ferrimagnetic films 372 ferrite plates, proximity sensors 301 f. ferrites, hard 15 - soft 15 ferromagnetic films 372 ferromagnetic materials 316ff. ferromagnetic targets 304

ferromagnetic thin layers, magnetization 344 ff. FeSi alloys 308 Fe-Si-B wires 331 field plates 376 field probe, flux gate magnetometers 171 field strength, noise 18 figure of merrit (FOM), strain gages 472 filling factors, air-cored induction coils 208 films, amorphous 356ff. ferrimagnetic 372 - ferromagnetic 372 - magnetoresistive 370ff. - permanent magnetic 370ff. thin 408ff., 429f. see also layers flow measurements 306 flowmeters 277 see also inductive flowmeters fluids 261, 306 flux changes 316 flux densities, orthogonal gated flux gate sensors 186f. - pulse position type flux gate magnetometers 192 - scales 9 flux gate magnetometers 461 f. basic principles of operation 162f. battery control 176 demodulator 175f. - design 168ff., 174ff. double-core see double-core - feedback control 166f. - field probe 171 Fourier coefficients 165 frequency doubler stage 174 gradient probe 171f. - instrument adjustment 175 magnetization curve 163 ff. matching procedure 170 - measuring amplifier 174 f. - performance data 176 point pole probe 172f. probe compensation 175 - pulse-position type see pulse-postion type flux gate sensors 153-203 - application areas 154 - fundamentals 154-160 magnetization curve, theoretical approaches 156-160 - measuring principles 154

-

-

-

-

-

-

Index

-

orthogonal gated 185ff. - principle design 155f. - pulse height 183ff. flux linking 38f. flux modulation, SQUIDS 400f. flux noise 432f. flux patterns, cross-type sensors 109 flux quantization 384, 387ff., 390ff., 401 f. flux relations, SQUID sensors 390ff., 395 ff. flux transformers 422f. - SQUID sensor systems 401f. flux-locked loops, SQUIDS 404f. FOM see figure of merrit food industry, inductive flowmeters 306 force, compressive 130-135 - Lorentz 304ff. - reaction 123ff. - tensile 130-135 force measurements 277 force sensors 123ff., 130-136, 146, 281f., 473ff. - amorphous materials 136 - cross-type 134f. - electrical diagram 283 - four-branch-type 134f. four-branch-type sensors 110-115, 127f. - force 134f. - magnetic circuits 111 - multiple 115 - sensitivity 112 Fourier coefficients, flux gate magnetometers 165 - ring core flux gate magnetometers 181 f. frequency doubler stage, flux gate magnetometers 174 frequency measurements, rotational 261 frequency range, double-core flux gate magnetometers 171 - reluctance sensors 261 frequency response, pulse wires 326, 330 full-bridge magnetoresistive sensors 367 ff. GaAs 92 gage heads 281 galvanomagnetic components, position sensing 83 galvanomagnetic effects 35 f., 45-52 - combined 72 galvanomagnetic semiconductor sensors 86

489

Gauss 2 gear wheel 262f. gear wheel sensors 87 gearings, rotational speed measurements 260 generators, tachometer 266ff. geomagnetism 460ff. gradient magnetoresistive sensors 369f. gradient probe, flux gate magnetometers 171 f, gradient sensors 401 ff. gradiometer configuration, high permeability core induction coils 222 gradiometers, SQUIDS 401 ff. gridded magnetoresistors 65 half-bridge magnetoresistive sensors 368 Hall angle 61 ff. Hall coefficient 47-50 Hall effect 35, 46ff. - extraordinary (planar) 342, 351 - ordinary 342 Hall-effect chips 92 Hall-effect IC 56f., 88f. Hall field 46 Hall mobility 46 Hall plates 52-60 Hall scattering factor 46, 49ff. Hall sensors 52-60, 82, 88ff., 375f. - carrier concentration 53 cross-sensitivity 59 - electron densities 57 geometrical correction factor 53 geometry 54ff. - noise 58f. - nonlinearity 60 offset 59f. performances 57-60 sensitivity 57ff. short-circuiting effect 56 structures 56f. - technology 56f. Hall voltage 36, 47, 53 hard ferrites 15, 307f. hard magnetic layers 372 hard magnetic materials 13ff. helical magnetostrictive spring sensor 144 Helmholtz coils 21 high magnetic fields 23 f. high permeability core induction coils 220-237 calibration 222 - eddy current effects 222f., 236

-

-

-

490

Index

-

equivalent circuit diagram 234ff. gradiometer configuration 222 hysteresis losses 236 inductance 236 internal noise 232ff. magnetization 223-228 magnetic field patterns 221 noise equivalent magnetic field 232ff. sensitivity 228ff. sensors 222, 238 thermal noise 229 high-mobility semiconductors 49 high-pass filter 242 high-T, SQUIDS 436ff. high-T, superconductors 436ff., 483 homogeneous DC fields 21 ff. Hooke’s law 107 hybrid SQUIDS 430 hysteresis loop 19 - magnetostriction 99 - soft magnetic materials 10f. hysteresis losses, high permeability core induction coils 236 IC see integrated circuit identification, magnetic sensor application 462 ff. InAs 49 induced voltage, pulse height sensors 184 inductance, air-cored induction coils 216 - high permeability core induction coils 236 - mutual 241, 423ff. inductance sensors, variable see variable inductance sensors induction coil sensors 4, 205-253, 468ff. - applications 246-251 bandwidth 242 definition 206 electronic amplifiers 237-246, 250 high permeability core 238 noise equivalent magnetic field 243 ff. output voltage 240f. - transformer coupled negative feedback 241 ff. trends 480f. induction coils see air-cored induction coils; high permeability core induction coils inductive flowmeters 304-307 applications and properties 306 signal conditioning 306 f.

-

-

-

inductive sensors 4, 255-313, 468ff. - AC-excited see AC-excited sensors - applications and properties 310f. - materials 307f. - noise 308f. - trends 481 see also permanent-magnet excited sensors; eddy current sensors; reluctance sensors; DC-excited sensors inductosyns 295 ff. - applications and properties 296f. - signal conditioning 297 injection-modulation mechanism 74 InSb 49, 64f., 91f. instrument adjustment, flux gate magnetometers 175 integrated DC SQUIDS 422-429 integrated-circuit (IC) technology, Hall sensors 56f., 88f. interference effects, SQUIDS 398 interfering effects on the torque signal 126-130 interrupter for automotive use, noncontact 88f. jitter, remagnetization 337 ff. Josephson effects 42, 383 ff. Josephson relations 385 Josephson tunnel junctions 408-418 - characteristics 412 ff. - fabrication 411 f. - special configurations 416ff. - techniques 408ff. Joule effect 36 junctions, barrier 417 - resistively shunted 386f., 414ff. - Josephson see Josephson layers, ferromagnetic 344ff. - hard-magnetic 372 - magnetoresistive 360ff. - multi- 208f., 436 - soft-magnetic 373 - thin 344ff., 362f. see also films lead-oxide barrier junctions 417 length-to-with ratios of magnetoresistors 62ff. level measurements 282, 306 level meters 277 light wave conductor (LWC) 337 linear displacement measurements 266, 281 linear movement measurements 269-287

Index linear position sensors 81 f. linear variable differential transformers (LVDT) 269-278 - applications and properties 275 ff. - balanced linear-tapered secondaries 271 ff. - balanced profiled secondaries 274 - complementary tapered windings 274 f. - computed magnetic field 272 - electrical circuit 270 - measuring range 276 - overwound linear-tapered secondaries 273 f. - signal conditioning 277 f. - temperature dependence 276 linear-tapered secondaries 271 ff. linearization, magnetoresistive sensors 352f. liquid-helium storage 406ff. lithography 408 ff. load cells 277, 282 - magnetoelastic 130f. loops, flux-locked 404f. Lorentz force 304ff. low-pass filter 241 f. lumped circuit model, SQUIDS 397 LVDT see linear variable differential transformers LWC see light wave conductor

M 1040, magnetization curve 160

- probe core 169 machine tooling 304, 470 MagFETs 73 magnetic alloys 15, 100-106, 142, 307ff., 317 magnetic biasing of magnetoresistors 68 ff. magnetic circuits 89 - closed 81f. - cross-type sensors 109ff. - design 84 - four-branch-type sensors 111 magnetic effects for sensors 2 magnetic field gradient sensors, SQUIDS 401 ff. magnetic field intensities, orthogonal gated flux gate sensors 186 magnetic field measurements 451 -464 magnetic field measuring principles 155 magnetic field patterns, high permeability core induction coils 221 magnetic field sensors 4, 205-253 see also magnetometers magnetic field strength, pulse-position type flux gate magnetometers 190ff.

magnetic fields, AC, shielding 26 f. bio- 8 conventional coils 9 DC 21 ff., 24f. earth’s 6f., 377, 460ff. energy 18 fluctuating 16 high 23f. linear variable differential transformers 272 natural 6ff. noise 8 noise equivalent 213 ff., 232 ff., 243 ff. - outer space If. - permanent magnets 8f. - proximity sensors 302 f. - scales 9 - standard 20-24 - superconducting coils 9 - technical 8f. - time-varying, air-cored induction coils 210 magnetic flux, reluctance sensors 259 magnetic flux linking 38f. magnetic foils 116f. magnetic heads 4 magnetic induction, fluctuating 430ff. magnetic materials 9-16, 102ff. - coercivity 105 - hard 13 ff., 307f., 372 - mechanical properties 15 - permanent 14 - shielding 24-29 - soft 10-13, 303 - stress-strain curves 104f. magnetic measurements 76ff. magnetic noise 8, 16-20 see also noise magnetic pickups 257-264 see also permanent magnets magnetic resonance effects 5 magnetic sensors, applications 447-476 - carrier-domain 74f. - classification 4, 34, 448ff., 456 - definition 3ff. - historical background 2f. - physical effects 34f. - physical principles 33-42 - trends 477-483 magnetic shielding 250 - closed 27

491

492

-

Index

materials 24-29, 250 openings 27 magnetic sleeve 121 magnetic strain gages 147 magnetic switching elements 316 magnetic terms and units 5f. magnetic vane switch 89 magnetic yoke materials 307 magnetically conducting materials 83 f. magnetically tunable delay line 143 magnetization, anisotropy 344-350 - ferromagnetic materials 316ff. - ferromagnetic thin layers 344ff. - high permeability cores 223-228 - stabilized 348ff. magnetization curve, alloys 100f. - blocking curve 349f. - flux gate magnetometers 163ff. - flux gate sensors 156-160 - piecewise linear function 158f. - polynomial approach 156ff. - pulse height sensors 184 - theoretical approaches 156-160 - trigonometric function 160 magnetocardiography 483 magnetodiodes 72 magnetoelastic components, realization 120ff. magnetoelastic effects 36ff. magnetoelastic interaction 98 ff. magnetoelastic load cells 130f. magnetoelastic sensor systems 105 f. magnetoelastic sensors 4, 97- 151, 470 - combined-effects 145 f. - special types 146f. - trends 479 - ultrasonic-wave-propagation 143 magnetoelectric effects 37 magnetoencephalography 459, 483 magnetogalvanic sensors 4, 43-96 - applications 75-92, 113 - history 44f., 91f. - trends 478f. magnetomechanical coupling factor 100, 102 magnetometers 146, 161-201, 377, 451-464 - DC SQUIDS 422-430 see also flux gate; magnetic field sensors magneto-optical sensors 4 magnetoresistance 51 f. magnetoresistive alloys 350ff.

magnetoresistive effect 35, 51, 62ff., 342ff. - thin layers 362f. magnetoresistive films 370ff. magnetoresistive layers 360 ff. - properties and characteristics 362f. magnetoresistive materials 356-363 magnetoresistive sensors 4, 341-380, 466 f, - applications 376f. - auxiliary fields 370ff. - characteristics 351 ff., 373 ff. - design 363-370 - fabrication 356-376 - full-bridge 367ff. - geometries 350f. - gradient 369f. - half-bridge 368 - linearization 352 f. - sensitivity 354f. - trends 482 magnetoresistors (MR) 61-71, 82 - differential 68ff., 87f. - geometry(-dependent) factor 61 ff. - gridded 65 - length-to-with ratios 62ff. - magnetic biasing 68ff. - materials 63f. - NiSb needles 65ff. - properties 67f. - resistance 62ff., 70 - sensitivity 70 - technology 64ff. - temperature compensation 71 magnetostriction 98 ff. - effects 36ff. - types of energy 99f. magnetostrictive ribbons 147 magnetostrictive spring sensor 144 magnetotelluric measurements 246 magnetotransistors 73 f. magnets, AlNiCo 15 - electro- 23f. - permanent see permanent magnets - Rare earth/Cobalt 70 malleable alloys 15 matching procedure for flux gate magnetometers 170 materials, amorphous see amorphous - ceramic 436ff. - composite 15

Index

-

core 307 - ferromagnetic 316ff. - high-T, 436ff. - inductive sensors 307f. - magnetic see magnetic materials - magnetically conducting 83 f. - magnetoelastic 121 - magnetoresistive 356-363 - magnetoresistors 63 f. - nonmagnetic 304, 308 - powder composite 15 - reluctance sensors 259 - shielding see magnetic materials; magnetic shielding materials testing 261 Matteucci effect 37 Maxwell’s laws 2 measurands, classification of magnetic sensors 448 ff. measurements, agressive fluids 306 - angle 295 - audio-magnetotelluric 246 - corrosive fluids 306 - current 76ff. - displacement 266, 281, 466-470 - flow 306 - force 277 - frequency 261 - level 282, 306 - linear displacement 266, 281 - linear movement 269-287 - magnetic 76ff. - magnetic field 451-464 - mechanical 465-475 - micropulsation 246 - nonconductive fluids 306 - periodic field 369 - position 304, 376f. - power 79ff. - pressure 271, 282 - proximity 260 - revolution 266 - rotary displacement 470 - rotary movement 287-297 - rotation angles 277 - rotational frequency 261 - rotational speed 260 - speed 260, 265f. - streaming fluid 261 - strip tension 133

493

-

velocity 260 277, 282 measuring amplifier, flux gate magnetometers 174 f. mechanical measurements 465-475 mechanical properties of magnetic materials 15 mechanical sensors 454 Meissner effect 42, 383 ff., 390 metals, amorphous 15 crystalline 15 micro field probe, flux gate magnetometers 172 micropack packages 67, 91 microprocessor control, pulse-position type flux gate magnetometers 198ff. micropulsation measurements 246 miniature sensors, high permeability core induction coils 222 MKSA system 5 Mo Permalloy 179 MOS transistors 73 motors, brushless DC 89f. movement measurements, linear 269-287 rotary 287-297 moving permanent magnets, reluctance sensors 264ff. MR see magnetoresistors multi-coil arrangements 22 multilayer air-cored induction coils 208 f. multilayer techniques 436 multivibrator circuit, two-core 138 mutual inductance 241, 423 ff.

- weight

-

-

natural magnetic fields 6ff. nickel-iron based alloys 103, 142, 317 NiSb 65ff., 91 noise, air-cored induction coils 212ff. Barkhausen see Barkhausen current 16f. excess 19, 309 - l/f 434ff. field strength 18 - flux 432f. - Hall sensors 58f. - high permeability core induction coils 232ff. - inductive sensors 308f. - magnetic 8, 16-20 - - energy calculation 18 - Nyquist 16f., 309 - resistance 16 - SQUIDS 424ff., 430-438

-

494

Index

-

thermal see thermal noise - voltage 16 noise equivalent magnetic field, air-cored induction coils 213ff. - high permeability core induction coils 232ff. - induction coil sensors 243 ff. noise power spectra 434f. nonconductive fluids measurements 306 noncontact interrupter for automotive use 88 f. noncontact position sensors 81 ff. noncontact switches 140f. nondestructive stress analysis 134ff. nonlinearity, Hall sensors 60 nonmagnetic materials 304, 308 Nyquist noise 16f., 309 Oersted 2 offset, Hall sensors 59f. orthogonal gated flux gate sensors 185ff. - design 186 oscillator, flux gate magnetometers 174 oscillator coils, proximity sensors 301 outer space magnetic fields 7f. output signals, pulse-position type flux gate magnetometers 193ff. - SQUIDS 403ff. output voltage, air-cored induction coils 210ff. - induction coil sensors 240f. - reluctance sensors 261 ff. - ring core flux gate magnetometers 18Of. overwound linear-tapered secondaries 273 f. packages, micropack 67, 91 passivation layers, magnetoresistive 361 performance, ring core flux gate magnetometers 182 periodic field measurements 369 Permalloy 179, 356ff. permanent magnetic films 370ff. permanent magnetic materials 14 permanent magnetic wires 324 permanent magnets 307f., 331 f., 369 - fixed 257-264 - moving 264ff. permanent-magnet excited sensors 257-268 see also inductive sensors; reluctance sensors permeability, initial 12f. see also high permeability permeability probe, flux gate magnetometers 173f.

permeability tensor 298 pickup coils, SQUID sensor systems 401 f. pickup winding, flux gate magnetometers 164 piecewise linear function, magnetization curve 158f. pipeline monitoring 135 plastic materials, sensor housings 308 point pole probe, flux gate magnetometers 172f. Poisson ratio 108 polarization, saturation 11f. polynomial approach to the magnetization curve 156ff. position measurements 304, 376f. position sensors 81 ff., 136-141, 275f. - amorphous materials 138f. - analog 85 - digital 81f. pot core, proximity sensors 303 powder composite materials 15 power measurements 79ff. power spectra, noise 434f. premagnetization field, pulse-position type flux gate magnetometers 189 - square wave 179ff. premagnetization generator, pulse-position type flux gate magnetometers 199 Pressductor 130ff. - measurement of strip tension 133 pressure cans 90f. pressure measurements 277, 282 pressure sensors 286, 475 probe compensation, flux gate magnetometers 175 probe types of double-core flux gate magnetometers 171ff. process and production engineering 304 prospecting 450 proximity effects, air-cored induction coils 217ff. proximity measurements 260 proximity sensors 299-304 - applications and properties 304 - magnetic field distribution 302f. pulse characteristics, ferromagnetic materials 317ff. - Wiegand sensors 320ff. pulse height sensors 183ff. - induced voltage 184 - magnetiation curve 184 - principal design 185

Index pulse-position type flux gate magnetometers 187-201 - code converter 201 - design 196ff., 199ff. - differentiating circuit 200 - magnetic flux density 192 - microprocessor-controlled 198ff. - operation 188ff. - output signal 193ff. - premagnetization field 189 - premagnetization generator 199 - sensitivity 195f., 198 - transfer function 190-198 see also flux gate pulse-wire sensors 4, 41, 315-339, 464 - trends 481 f. pulse wires 324-330 - applications 331-339 - eddy currents 326 - equivalent circuit diagram 327 - frequency response 326, 330 - high pulse voltages 324-328 - low pulse voltages 328ff. - properties 325 ff., 328 ff. - remagnetization jitter 337 ff. see also pulse-wire sensors radiation sensors 454 rare earth-cobalt alloys 308 rare earth-cobalt magnets 15, 70 reaction-force meters 123ff. reading heads, magnetoresistive sensors 376 recording heads, magnetoresistive 370 refractory-artificial barrier junctions 417 reluctance sensors 257-266, 469-471 - applications 260f. - c-shaped 260 - construction 258 - electrical diagram 264 - frequency range 261 - materials 259 - moving permanent magnets 264ff. - output voltage 261ff. - properties 260f. - signal conditioning 261 ff. remagnetization, ferromagnetic materials 316ff. - jitter 337ff. residual field probe, flux gate magnetometers 173 residue resistivity ratio (RRR) 409

495

resistance, air-cored induction coils 208 - magnetoresistors 62 ff., 70 resistance noise 16 resistively shunted junction (RSJ) model 386f,, 414 ff. resistivity, specific electric 13 resolvers 293 ff. - applications and properties 294f. - brushless 294 resonance effects, magnetic 5 revolution counters 87f., 331 ff. revolution measurements 266 RF SQUIDS 390-394 - design 418ff. - electronics 420ff. - staircase pattern 393 f. - two-hole 418-422 ring core flux gate magnetometers 177-183 - design 178-183 - Fourier coefficients 181f. - functional units 183 - output voltage 18Of. - performance 182 - square wave premagnetization field 179ff. see also flux gate ring core sensors, amorphous 137-141 ring cores, slotted ferrite 250 ring torductors see torductors robots, drive motors 332 rotary displacement measurements 470 rotary encoder, incremental 334 ff. rotary movement measurements 287-297 rotation angles measurements 277 rotational frequency measurements 261 rotational frequency sensors 331-335 rotational speed measurements 260, 262 f. RRR see residue resistivity ratio RSJ see resistively shunted junction saturation polarization 11 f. scattering factor, Hall 46, 49ff. Schmitt trigger 263 scientific applications 450 screen printing, ferrimagnetic films 372 search coil sensors 205-253 - trends 480f. second harmonic flux gate magnetometers 161-183 secondaries, balanced profiled 274 - linear-tapered 271 ff.

496

Index

security systems, magnetic sensor application 462 ff. semiconductor sensors, galvanomagnetic 86 semiconductors 61 ff., 71 ff. - high-mobility 49 - physical properties 64 sensitivity - air-cored induction coils 209-214 - coaxial-type sensors 119 - double-core flux gate magnetometers 170f. - four-branch-type sensors 112 - Hall sensors 57ff. - high permeability core induction coils 228ff. - magnetodiodes 72 - magnetoresistive sensors 354 f. - magnetoresistors 70 - pulse-position type flux gate magnetometers 195f., 198 - SQUIDS 423, 430-438 - variable gap sensors 284 sensor systems, magnetoelastic 105 f. sensors, AC-excited see AC-excited - acceleration 282 - angle 286 - barber pole 368, 372, 374 - c-shaped 260 - carrier-domain magnetic 74 f. - chemical 454 - choice 85f. - coaxial-type see coaxial-type - cross-type see cross-type - DC-excited see permanent-magnet excited sensors; reluctance sensors - differential cross-anchor see variable gap - displacement 136-141, 275 f., 286 - eddy current see eddy current - flux gate see flux gate - force see force - four-branch-type see four-branch-type - galvanomagnetic 86 - gradient see gradiometers - Hall see Hall - high permeability core induction coils see high permeability - induction coil see induction coil - inductive see inductive - magnetic see magnetic - magnetic effects 2 - magnetic-field 4, 205-253 - magnetoelastic see magnetoelastic

- magnetogalvanic see magnetogalvanic - magneto-optical 4 - magnetoresistive see magnetoresistive - magnetoresistor see magnetoresistors - mechanical 454 - orthogonal gated flux gate 185ff. - permanent-magnet excited 257-268 - position see position - pressure 286, 475 - proximity see proximity - pulse height see pulse height - pulse-wire see pulse-wire - radiation 454 - reluctance see reluctance - ring-core see ring-core - search coil see search coil - shock-stress 144f. - smart 92, 479 - SQUID see SQUID - strain 286, 472f. - temperature 454 - tension 147 - torque see torque - variable gap see variable gap - variable inductance see variable inductance - velocity 471f. - vibration 282 - Wiedemann-effect 144 f. - Wiegand see Wiegand shaft-swinging sensor 286 shafts, coatings 122 - material 112 - torque measurements 107f. shear modulus 107, 143 shear stress 107 shear wave magnetometry 143 shielded room 28f. shielding, magnetic 24-29, 250 - SQUIDS 407f., 420 shielding current, superconductors 388 f. shielding factor 26, 28 ship propellers 114 shock-stress sensors 144f. short-circuit straps 64f. short-circuiting effect, Hall sensors 56 signal conditioning, inductive flowmeters 306f. - inductosyns 297 - linear variable differential transformers 277 f. - reluctance sensors 261 ff. - tachometer generators 268

Index

- variable gap sensors 287 - variable inductance sensors

282f. signal input coupling, SQUID sensor systems 401 ff. silicon Hall-effect IC 88 f. single-core flux gate magnetometers 166f. Sixtus-Tonks experiment 39f., 316 skin depth 303 skin effect, air-cored induction coils 217ff. skin penetration depth, air-cored induction coils 217 smart sensors 92, 479 soft ferrites 15 soft magnetic alloys 308 soft magnetic cores 303 soft magnetic materials 10-13, 303 soft-magnetic layers 373 solenoids 236 solid mechanical transducers 465-475 sound velocity, measurement 142 space flight flux gate magnetometers 179 space research 460ff. spacecraft applications, induction coil sensors 249 speed control, rotary 262f. speed measurements 260, 265 f. see also velocity sputtering, Josephson tunnel junctions 409 magnetoresistive layers 360 square wave premagnetization field, ring core flux gate magnetometers 179ff. SQUID sensor systems 401 -408 signal input coupling 401 ff. SQUID sensors 4, 42, 381-445 characteristics 392ff,, 397ff. magnetic flux relations 390ff., 395ff. periphery 406ff. - practical devices 408-430 - special configurations 429 f. - trends 482 SQUIDS, bulk 429 DC see DC SQUIDS - design 392ff., 397ff., 418ff. - flux modulation 400f. flux-locked loops 404f. - gradiometers 401 ff. - high-T, 436ff. - hybrid 430 - interference effects 398 lumped circuit model 397

-

-

-

-

-

497

-

magnetic field gradient sensors 401 ff. magnetometers 422-430 noise 430-438 output signals 403ff. - RF see RF SQUIDS - sensitivity 430-438 - shielding 407f., 420 - thin-film 429f. stabilized magnetization 348 ff. staircase pattern, RF SQUIDS 393 f. standard magnetic fields 20-24 steels 103 Stokes theorem 388 Stoner-Wohlfarth theory 344 ff. strain gage heads 277 strain gage torquemeters 123ff. strain gages, magnetic 147 - figure of merrit (FOM) 472 strain sensors 286, 472f. streaming fluid measurements 261 stress analysis, nondestructive 134ff. stress anisotropy 316f. stress sensor 286 strip tension, measurement 133 substrates, magnetoresistive layers 360 superconducting coils 24 - magnetic fields 9 superconductivity 383 ff., 436ff., 483 superconductors, ceramic (high-T,) 436 ff., 483 - shielding current 388 f. surface energy 317 surveying 450 switching time, remagnetization 317 f. synchros 287ff. - applications and properties 288-293 - control-type 291 ff. - differential 291 f. - torque-type 289ff. tachometer generators 266ff. -, signal conditioning 268 tachometers 334, 471 f. - eddy current 299f. targets, magnetoresistive layers 360 technical magnetic fields 8f. temperature, critical 383ff. - Curie 13, 371 temperature compensation, magnetoresistors 71 temperature dependence, linear variable differential transformers 276

498

Index

temperature sensors 454 tensile-force sensors 130- 135 tension measurements 133 tension sensors 147 terms, magnetic 5f. testing, materials 261 thermal energy 18 thermal noise 16-19 - air-cored induction coils 214 - high permeability core induction coils 229 thermomagnetic noise 16-19 thin films, techniques 356ff., 370ff., 408ff. see also films thin-film SQUIDS 429f. thin layers, ferromagnetic 344ff. - magnetoresistive effect 362 f. see also layers tooling, machine 304, 332 torductors 112ff. - automotive applications 113 torque measurements, shafts 107f. torque sensors 106-130, 473ff. - coaxial 128 - complex coil arrangement 119 - data processing electronics 117 - reaction force meters 123 - strain gage 123ff. - twist-angle 124 torque signal, interfering effects 126-130 torque-type synchros 289ff. transducers, solid mechanical 465-475 transfer factor, double-core flux gate magnetometers 170f. transfer function, flux gate magnetometers 163ff. - induction coil sensors 238 - low-pass filter 241 f. - pulse-position type flux gate magnetometers 190-198 - flux gate magnetometers 163ff. transformer coupled negative feedback, induction coil sensors 241 ff. transformers, linear variable differential see linear variable differential - magnetic field 8 triple probe, flux gate magnetometers 171 tunnel junctions see Josephson twist-angle torquemeters 124f. two-core multivibrator circuit 138

ultrasonic-wave-propagation, magnetoelastic sensors 143 units, electromagnetic 5 f. Vacoflux 318, 324 Vacon 324 vacuum evaporation, magnetoresistive layers 3 60 vane switch, magnetic 89 variable gap sensors 283 -287 - applications and properties 286f. - construction 284f. - sensitivity 284 - signal conditioning 287 variable inductance sensors 278-283 - applications and properties 280ff. - construction 279f. - electrical diagram 283 - signal conditioning 282 f. variable leakage path (VLP) sensors see variable inductance sensors vector potential 298 velocity, carrier 45 - sound 142 velocity measurements 260, 265 f. velocity sensors 471 f. vibration sensors 282 Vickers hardness 15 Villari effect 37 voltage, air-cored induction coils 210ff. - Hall 36, 47, 53 - induction coil sensors 240f. - noise 16 - pulse height sensors 184 - pulse wires 324ff. - reluctance sensors 261 ff. - ring core flux gate magnetometers 180f. voltage amplifiers, induction coil sensors 237 ff. waste-water managements, applications of inductive flowmeters 306 weight measurements 277, 282 weight of the winding, air-cored induction coils 212 welding, automatic 304 Wiedemann effect 37 Wiedemann-effect sensors 144f. Wiegand sensors 4, 41, 315-339, 464 - design and properties 319ff. - drive conditions 321 ff.

Index

-

switching behavior 322ff. - trends 481f. Wiegand wires, applications 331 -339 - remagnetization jitter 337ff. windings, complementary tapered 274 f. wire explosion spraying 122f. wires, amorphous 330f., 337 - composite 324 - permanent magnetic 324

- pulse see pulse wires - Wiegand see Wiegand yield strength 15 yoke materials, magnetic 307 Young’s modulus 15, 36, 108 Zeemann effect 5 zero-field detectors 377

499

Sensors

Edited by, W.Gopel, J. Hesse ,J. N. Zemel Copyright OVCH Verlagsgesellschaft mbH,1989

List of Symbols and Abbreviations The following list contains the symbols most frequently used in this book. To avoid redundancy, subscripts are only noted in exceptional cases. References to chapters (where the quantities are explained in more detail) are only given for symbols with special meanings or in cases of uncommon use.

Symbol

Designation

ll

edge length of a cube gap between barber poles half axis of ellipsoid representing probe core side length of the quadratic pole face of a permanent magnet copper filling factor of enameled copper wire shielding attenuation filling factor of coil winding polynominal coefficients amplification factor area, core cross section area average loop area of a coil coefficient, dependent on the carriers' effective masses and the energy bands' structure coil area constant of exchange energy vector potential cross section area of a high permeability core Fourier coefficients not reduced cross section open loop gain of an amplifier reduced cross section iron core cross section

0, 0,

a, a.

.. .a,

A

A A, A" Anred

A, Ared

b

half axis of ellipsoid representing probe core normalized magnetic induction ratio of the electron mobility and the hole mobility normalized branches of the magnetization curve magnetic induction (flux density) magnetic induction at a biasing magnetic field external magnetic induction maximum value of magnetic induction minimum detectable flux density variation Fourier coefficients

Chapter 1

9 5 3 6 1

6 5 6 6

3 2 8

6 5 5 6 5

1

502

Symbol

List of Symbols

Designation noise induction offset magnetic induction remanence ; remanent induction reference magnetic induction saturation induction circular component of induction induction in direction of the probe axis induction value, used to normalize peak flux density magnetic induction in the axis perpendicular to the pole face of a permanent magnet, flux density in z-direction magnetic induction in an iron core magnetic induction in an air gap magnetic induction at the detection limit of a sensor maximum energy density

cot

C

cd

Ci

d

Dc DO

c1

half axis of ellipsoid representing probe core length of a permanent magnet pitch of turns System constant of a power measurement circuit polynominal coefficients capacity coefficient, dependent on the recombination process collector current contact differentiating capacity input capacitance of an amplifier integration capacity intersection capacitance of a divided coil shunt capacitance total self-capacitance of a coil geometry-dependent constants of a magnetoresistive plate total circuit parallel capacitance diameter, distance thickness of layer system (general) wall thickness inner diameter outer diameter distance of pulse initiation damping of resonant circuit diameter diameter of winding (coil) diameter of wires diffusion coefficient of charge carriers diameter of high permeability core outer diameter of winding

Chapter 1

3 1, 9 5 5 5 5 5

2, 3 2, 3 3 3 3 1 5 3 6 3 5 3 3 3 6 6 6 6 6 6 3 6

503

List of Symbols

Symbol

Designation

Chapter

outer diameter of wire

6

carrier charge elementary charge electric field strength energy Young’s modulus demagnetized Young’s modulus external electric field band gap energy magnetic field energy intrinsic energy sensitivity saturation Young’s modulus thermal energy of a material Hall electric field pulse energy in a resistive load energy of stress induced anisotropy

3

frequency correction factor bandwidth critical frequency (eddy current limiting frequency) Josephson frequency resonant frequency reference frequency force low-pass filter function, transfer function strip tension

10 10

2, 4, 8 2 3 3 1 10

2 1

3 8 8

9 6 6 10

6 5

6 4

function of the Hall-device geometry proximity effect function skin effect function conductance geometrical correction factor shear modulus geometrical correction factor for B = 0

3 6 6

height (radial extension) of winding area cross section normalized magnetic field strength Planck constant normalized external magnetic field strength normalized internal magnetic field strength normalized magnetic reference field strength maximum value of normalized magnetic reference field strength coefficient of magnetoresistance magnetic field strength field amplitude (of sinusoidal fields) magnetic field strength

6 5 10 5 5 5 5 3

I 3 4 3

8 5

504

Symbol

i i iin

iref

List of Symbols

Designation

Chapter

Vickers hardness coercitive field strength, coercitivity coercitivity of polarization circular magnetic field strength critical magnetic field strength demagnetizing field field strength of demagnetizing field external magnetic field (interference field) external magnetic field strength internal magnetic field (inside a magnetic shield) magnetic field strength in a high permeability core internal magnetic field strength anisotropy field longitudinal magnetic field strength mean value of Hex,, averaged over sensor area maximum value of magnetic field strength lowest detectable field noise field strength magnetic field strength within the non-reduced cross section polarizing field field generated by permanent magnetic layer remanent magnetic field strength magnetic field strength within the reduced cross section magnetic reference field strength maximum value of reference field strength saturation field strength switching field strength saturation field strength circular component of magnetic field strength components of magnetic field strength in a Helmholtz coil bias field (in y-direction) magnetic field in an iron core linearity limit of sensor field amplitude in the sensor coil of a pulse wire under load magnetic field in an air gap coefficient of magnetoresistance in a long strip of conducting material noise equivalent magnetic field strength reset field for Wiegand wires field strength, used to normalize characteristic field horizontal, vertical component of Earth field coefficient of magnetoresistance in an infinite sample

4 1

2 3

9 6 1 5, 9 1

6 5 9 2 9 5

9 1 5 5

9 9 5 5 5

8 8 5 5 1 9 3

9 8 3 3 6 8 5

9 1

3

(-1)”Z

(AC)current AC input current premagnetization current

3 5

505

List of Symbols

Symbol

Designation

Chapter

iL

AC load current spectral density of noise current spectral density of amplifier input noise current spectral density of thermal noise current of resistance R,, (DC) current

3

i ,2

( i 2 / Af ) i / 2 ( i i , , / Af ) i / 2 I

i Iin

In

4 I, IC IE

current amplitude (in the sensor coil of a pulse wire under load) DC input current noise current collector saturation current current in x-direction collector current emitter current

Js

current density maximum tolerable value of j current density in the barber poles current density magnetic polarization critical current density saturation polarization

k, kB

Boltzmann constant

j, j Jmax

jB

J J Jc

ki,j K

I IF,

L Li LF LH

rn

constant value number of sections of a divided coil coupling constant coefficient constant damping constant of the pulse-wire sensor crystalline anisotropy constant influence factor (how changes in pr are transferred into changes in p c ) voltage divider factor transfer factor of difference signal transfer factor of field signal constant value magneto-elastic coupling factor length mean path length of an iron core inductance length of ring probe core integration inductivity feedback inductance length of air gap length-to-diameter ratio of a cylindrical core mass

1

6 6 1, 4, 7, 9, 10, 11

8 3 1 3 2 3 3

9 9

1, 3, 6 , 7 , 10 5

6 10

3 5, 7

8 9

6 6 5 5 5 4

1, 3, 1

6

506

Symbol

List of Symbols

Designation

Chapter

magnetization middle symmetry mutual inductance torque saturation magnetization rest magnetization (He,, = 0)

3 6, I , 10 4, 7 9 9

carrier (electron) concentration number of domain walls number of turns number of windings speed of rotation total number of turns intrinsic carrier concentration particle density number of time increments number of layers, number of turns per layer demagnitization factor number of turns, number of coil windings relevant demagnetizing factor relative non linearity in the Hall voltage rate of flux linkage demagnetization factor of a cylindrical rod at pr = 03 donor density demagnetization factor of a rotational ellipsoid at ,ur = primary coil secondary coil demagnetizing factors along the three axes

PL PO

momentum hole concentration number of magnetic poles track period pressure thickness to width ratio parameter (ie, temperature) peak power in a resistive load power dissipation

4

(electron) charge

r

position vector radius coordinates of coils Hall scattering factor (ohmic) resistance reset of digital circuit resistance at biasing magnetic field

P

r, r’ rn

R Rb

3 2 6, 8 3

I 6 3 10 5 6 5, 6 1, 2, 5, 7

03

9 3 2 6 3 6 4 4 9

3 I I 3, 11 9 3 3, 8

9

2, 10 1 3

5 3

501

List of Symbols

Symbol

Designation

Chapter

compensating resistance DC resistance of the sensor coil resistance representing eddy-current losses resistance representing hysteresis losses internal resistance source resistance of a pulse-wire sensor tensile strength yield strength sheet resistance (ie, a layer of square shape) (total) series resistance thermal resistance AC resistance resistance at magnetic induction B DC resistance feedback resistor Hall coefficient intrinsic Hall coefficient load resistance resistance at magnetic induction B = 0 resistors in a negative feedback network total circuit

3 8

AC shielding factor deflection path displacement of a sensor to a target surface recombination velocity width of barber poles width of sense contact stages sensitivity static shielding factor surface, area sensitivity with Uo = Urnax supply-voltage related sensitivity prime sensitivity (ie, Sx = S,) spectral density secondary sensitivity (P: parameter, eg, temperature) absolute sensitivity sensitivity of an induction coil sensor referred to preamplifier output supply-current related sensitivity equivalent input magnetic field noise spectral density noise voltage spectral density l/f-noise-voltage spectral density thermal noise spectral density sensitivity of an induction coil (at low frequencies) sensitivity with Uo = 1 V shielding factor perpendicular to a shield axis (cylinder)

6 6 3 8 8 4 9 5, 6 9 6 3 6 6 3 3 8 3, 9 6 6 1

4, 6 3 3

9 3 4 5

1 3, 10 9 3 3 10

3 3 6 3 3 3 3 3 6 9 1

508

List of Symbols

Symbol

Designation

Chapter

SII SIN

shielding factor parallel to a shield axis (cylinder) signal-to-noise ratio

6

t

lamination thickness thickness of Hall plate thickness of magnetoresistive layer time pulse duration time time increment thickness of permanent layer thickness of barber poles time jitter of the pulse voltage (absolute) temperature time constant torque critical temperature switching time (pulse duration) Curie temperature

6 3 9

coil geometry factor energy density Hall voltage voltage energy density, demagnetization part instantaneous value of induced voltage energy density, anisotropy part AC offset voltage normalized output voltage spectral density of noise voltage AC Hall voltage energy density, field part AC load voltage instantaneous value of random noise voltage voltage amplitude of voltage second time derivation of voltage induced voltage input voltage negative induced voltage positive induced voltage second harmonic component of induced voltage maximum tolerable value of Uo noise voltage induced voltage (open loop peak value, at low frequencies) operating voltage of sensor, differential voltage output voltage second harmonic component of output voltage

6 9 3

TC U

1

5

4 10 8 1, 9

9 6 9 3 5 1 3 9 3 6 8 5 5

3 5 5 5

9 1 6 9 3, 4, 5 5

509

List of Symbols

Symbol

Designation receiver voltage premagnetization voltage sensor output voltage, threshold voltage voltage between x and y positions of rotors planar Hall voltage bridge voltage sensor amplifier output voltage excitation voltage voltage drop in barber poles DC output voltage Hall voltage Hall voltage in a long plate best linear fit to the measured Hall voltage values AC load peak voltage pulse amplitude under load noise voltage supply voltage voltage amplitude pulse amplitude without load open-circuit output voltage

Chapter

I 5 9

I 9

I 6 7 9

4 2 3 3 3 8 6 3 I

8

velocity voltage voltage volume volume of high permeability core volume of winding (copper) core volume

6 6 1

length (axial extension) of winding area cross section plate or strip width weight of the core energy in magnetic materials sensor weight induced uniaxial anisotropy energy weight of the winding of a coil magnetic field energy crystalline energy shape anisotropy energy, demagnetizing energy elastic stress energy

6 3, 9 6 4 6 4 6 4 4 4 4

factor of geometrical enlargement of a core intercenter separation of a differential sensor long axis spatial coordinates, position, displacement mechanical stress

6 3

short axis

9

10 10

9

3

510

List of Symbols

Symbol

Designation

Chapter

Z

axis perpendicular to layer plane spatial coordinate perpendicular to the pole face of a permanent magnet impedance

2, 9 3 1, 6

angle of rotation Hooke's 1/ f-noise parameter material nonlinearity coefficient skin effect factor temperature coefficient of resistance wrapping angle local variation of q against its mean value correction factor for the inductance of a coil on a high permeability core geometry nonlinearity coefficient temperature coefficient of Hall sensitivity wrapping angle hysteresis parameter modulation parameter angle of external magnetic field density of conductor material twist angle shear strain average density of winding surface energy of a domain wall density of aluminium density of copper difference of phase angles penetration depth of magnetic field due to skin effect width of an air gap Laplace operator angle of easy axis (e,a.) strain dielectric constant of a material permittivity (dielectric constant) of vacuum reduction of current rotation geometrical factor of barber-pole sensors ratio of volumes angle Celsius temperature angle angle between magnetization and current phase angle Hall angle coefficient of magnetostriction ratio of the contacts' length and the circumference of a Hall plate shape magnetostriction tooth period of a gear-wheel elastic strain

1 3 3

Z a

a50?

P

PC P2

Y

YW

YAI

YC"

6

A &

8, &O

r

rl

ff

e 0 0( r ) @H

I

6 3 4 9 6 3 3 4 10 10 9 6 4 4 6 8 6 6 10 1, 6, 7 3

9 4, 11

9

9 6 3

9 10

3 9 3 4 3 2

511

List of Symbols

Symbol

Designation longitudinal magnetostriction constant magnetoelastic strain saturation magnetostriction transversal magnetostriction constant London penetration depth magnetostriction in the crystallographic directions of cubic crystals absolute permeability carrier (electron) mobility complex permeability permeability tensor core permeability relative differential permeability at B = 0 initial permeability relative permeability relative permeability relative saturation permeability relative permeability of iron Hall mobility relative permeability of air (pL = 1) permeability of vacuum (magnetic constant) Poisson's ratio coherence length density of the material specific resistivity specific resistivity of aluminium specific resistivity at magnetic induction B specific resistivity of barber poles specific resistivity of copper specific resistivity at B = 0 specific resistivity perpendicular to M specific resistivity parallel to M electrical conductivity geometrical factor of barber-pole sensors specific conductivity standard deviation stress electrical conductivity tensor variance building-up time carrier relaxation time shear stress at the surface of the shaft pulse width at half amplitude under load pulse width at half amplitude without load angle angle between oscillator and demodulator angle between magnetization and specimen axis angle of magnetization M

Chapter 2 2 4, 8 2 10 4

3, 9 1 7 6 5 1 5 5 7 3 7 4 10 4

6 3

9 6 3

9 9 7 9 3, 6 10 2,4,8,11 7 10 6

3 4 8 8 4 4 9

512

Symbol

List of Symbols

Designation

Chapter

phase angle rotation angle, angle of torsion value of v, for Hex, = 0 magnetic flux magnetic flux in a high permeability core external magnetic flux instantaneous value of magnetic flux instantaneous value of magnetic flux in a high permeability core flux inside a ring maximum value of magnetic flux resulting magnetic flux exciting magnetic flux magnetic flux quantum angle of current I wave function angular (circular) frequency angular frequency of a frequency reponse maximum angular resonant frequency angular corner frequencies (of a frequency reponse)

I

Abbreviation Explanation ABS AC ASEA

automatic break system alternating current Allmaenna Svenska Electriska Aktiebolaget

CAD CAM CIM CMOS

computer aided design computer aided manufacturing current contact computer integrated manufacturing complementary-symmetric metal oxide semiconductor

DC D.L.

direct current discrete layer

e. a. emf emu ECG EX FET FLL FOM

easy axis electromotive force electromagnetic units electrocardiogram exitation coil field effect transistor flux locked loop figure of merit

GFRP

glas fiber-reinforced plastic

HiFi

high-fidelity

cc

3 9

6 5 6 6 10 5, 6 5

I 10

9 10

List of Symbols

Abbreviation Explanation

IC IEC IEEE

integrated circuit International Electrotechnical Commission Institute of Electrical and Electronics Engineers

JFET

junction field effect transistor

LVDT

linear variable differential transformer

MagFET MKSA MOS MR MTBF

magnetic field effect transistor Meter, Kilogram, Second, Ampere (-System) metal oxide semiconductor magnetoresistor meantime between failures

NIC

negative impedance converter

PCB PSD PZT

printed circuit board phase sensitive detector piezoelectric element

rf, RF rms RIBE RIE RRR RSJ RS 232 RVDT

radio frequency root mean square reactive ion-beam etching reactive ion etching residue resistivity ratio resistively shunted junction (model) standard interface rotary variable differential transformer

sc SMD SNAP SNR SQUID, SQ

sense contact Systkme Internationale (International System of Units) superconductor-insulator-superconductor surface mounted device selective niobium anodization process signal-to-noise ratio superconducting quantum interference device

TC TRC Tr

temperature coefficient temperature coefficient of resistance transformer

UHV

ultra-high vacuum

VLP

variable leakages path (sensors)

SI SIS

513