ELEC250 Introduction to Telecommunications

ELEC250 Lecture 3

ELEC250 Introduction to Telecommunications Lecture 3 Modulation • Overview of modulation • Amplitude modulation

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Why is modulation needed?

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ELEC250 Lecture 3

Modulation • Signals propagate much better at frequencies suited to the transmission medium: – radio waves • v = f ? ( speed of propagation = frequency * wavelength) • efficient conversion of energy to/from electromagnetic plane wave needs antenna dimension roughly ? /4 • 1 MHz carrier: ? /4 = 75m, 1 GHz carrier: ? /4 = 7.5cm

– optical fibres • use frequencies of light best suited to fibre

– plain old telephone service (POTS) • originally engineered to provide voice service • but now we want high-speed digital data transmission • modem = modulator-demodulator Lecture 3

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Modulation • Modulation: – “the process by which some characteristic of a carrier is varied in accordance with a modulating wave” - IEEE Standard Dictionary of Electrical and Electronics Terms

• Alternatively… – modulation involves “piggybacking” information (message) signal onto a carrier wave

• Need three components for modulation: – carrier wave – message signal – modulation technique Lecture 3

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ELEC250 Lecture 3

Modulation • All carrier waves have the same basic form – they are all sinusoidal electromagnetic signals – carrier wave for AM is the same as carrier for FM is the same as optical carrier… – only the frequency changes

• Use common descriptions for various “bands” - ranges of carrier frequencies • Carrier bands often associated with particular modulation schemes

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Frequency bands

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Carrier Frequency Range

Common Description

3 - 30 kHz

Very Low Frequency (VLF)

30 - 300 kHz

Low Frequency (LF)

300 - 3000 kHz

Medium Frequency (MF)

3 - 30 MHz

High Frequency (HF)

30 - 300 MHz

Very High Frequency (VHF)

300 - 3000 MHz

Ultra High Frequency (UHF)

3 - 30 GHz

Super High Frequency (SHF)

30 - 300 GHz

Extremely High Frequency (EHF)

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ELEC250 Lecture 3

Carrier frequencies and applications

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Application

Carrier Frequencies

AM radio

526.5 - 1606.5 kHz

FM radio

88 - 108 MHz

HF CB and marine radio

26.965 - 27.980 MHz

Remote garage door openers

304 MHz

VHF television

45 - 230 MHz

UHF television

520 - 820 MHz

Mobile telephones

820 - 915 MHz

Microwave links

3 - 30 GHz

Satellite links

Various between 137 MHz - 275 GHz

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Electromagnetic spectrum for telecommunications

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ELEC250 Lecture 3

Amplitude modulation (AM) • Vary the amplitude of the carrier wave to reflect the information to be sent • Carrier frequency is usually much higher than frequency of information (modulating) signal – e.g. radio 2NC has carrier frequency 1233 kHz, but frequency of message (voice/music) is less than 5 kHz – “interesting” messages are not sinusoids, so what is meant by maximum frequency in message? Answer involves Fourier analysis of messages, but basically: “interesting signals are sums of sinusoids” – for this lecture: messages are themselves sinusoids Lecture 3

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Amplitude modulation envelope contains the message

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ELEC250 Lecture 3

AM waveforms - various messages

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Representing AM waveforms • Carrier: ec(t) = Vc sin ? ct • Vc = amplitude of carrier, or “peak value”

• ? c = carrier frequency = 2? fc, e.g. radio 2NC uses fc = 1233 kHz • Message: em(t) = Vm sin ? mt • Vm = amplitude of message • ? m = message frequency (assumed sinusoidal here)

• AM waveform:

eAM(t) = Vc(1 + m sin ? mt) sin ? ct • m = Vm/Vc is the modulation index - discussed shortly Lecture 3

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ELEC250 Lecture 3

Representing AM waveforms • Using trigonometric identities sin? sin? = [cos(? -? )-cos(? +? )]/2 and cos(-? ) = cos? can show that eAM(t) = Vcsin ? ct + mVC/2 cos(? c - ? m)t - mVC/2 cos(? c + ? m)t • carrier frequency fc • lower sideband (LSB) frequency fc - fm • upper sideband (USB) frequency fc + fm Lecture 3

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figure contains error for LSB: should be ? c - ? m Lecture 3

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ELEC250 Lecture 3

Modulation index

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50% modulation

1 kHz carrier, 100 Hz message Lecture 3

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ELEC250 Lecture 3

20% modulation

1 kHz carrier, 100 Hz message Lecture 3

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100% modulation

1 kHz carrier, 100 Hz message Lecture 3

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ELEC250 Lecture 3

120% modulation

1 kHz carrier, 100 Hz message Lecture 3

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