Fundamental of Communication Systems ELCT332 Fall2011 1

C H A P T E R 5

ANGLE MODULATION AND DEMODULATION

Fundamental of Communication Systems ELCT332 Fall2011 2

Concept of instantaneous frequency.

Nonlinear Modulation

Frequency Modulation (FM)Phase Modulation (PM)

Instantaneous Angular Frequency

Angle Modulation Exponential Modulation

Phase Modulation

Frequency Modulation

Fundamental of Communication Systems ELCT332 Fall2011 3

Phase and frequency modulation are equivalent and interchangeable.

Nonlinear Modulator

Fundamental of Communication Systems ELCT332 Fall2011 4

Generalized phase modulation by means of the filter H(s) and recovery of the messagefrom the modulated phase through the inverse filter 1/H(s).

Modulation and Demodulation

Fundamental of Communication Systems ELCT332 Fall2011 5

FM and PM waveforms.

Example

Sketch FM and PM waves for the modulating signal m(t), The constants k f and kp are 2π×105 and 10π, respectively, and the carrier frequency fc is 100MHz.

Fundamental of Communication Systems ELCT332 Fall2011 6

Example

Sketch FM and PM waves for the modulating signal m(t), The constants k f and kp are 2π×105 and π/2, respectively, and the carrier frequency fc is 100MHz.

Frequency shift keying:modulating by a digital signal

Phase shift keying

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Bandwidth of Angle Modulated Waves

Narrowband FM (NBFM)

Narrowband PM (NBPM)

Fundamental of Communication Systems ELCT332 Fall2011 8

Bandwidth of Angle Modulated Waves: Wideband FM (WBFM)

Peak Frequency Deviation

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Spectral Analysis of Frequency Modulation

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Example: Estimate BFM and BPM for the modulating signal m(t) for kf and kp are 2π×105 and 5π, respectively. Assume the essential bandwidth of the periodic m(t) as the frequency of its third harmonic.

What will be the bandwidth if the amplitudde of m(t) is doubled?

Fundamental of Communication Systems ELCT332 Fall2011 11

Narrowband PM generator. (b) Narrowband FM signal generator.

Generating FM Waves: NBFB Generation

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(a) Hard limiter and bandpass filter used to remove amplitude variations in FM wave. (b) Hard limiter input-output characteristic.

(c) Hard limiter input and the corresponding output. (d) Hard limiter output as a function of θ.

Bandpass Limiter

Eliminate the amplitude variations of an angle-modulated carrier

𝑣𝑜ሾ𝜃ሺ𝑡ሻሿ= 𝑣𝑜ቈ𝜔𝑐ሺ𝑡ሻ+ 𝑘𝑓න 𝑚ሺ𝛼ሻ𝑑𝛼𝑡−∞

= 4𝜋ቊcosቈ𝜔𝑐ሺ𝑡ሻ+ 𝑘𝑓න 𝑚ሺ𝛼ሻ𝑑𝛼𝑡−∞ − 13cos3ቈ𝜔𝑐ሺ𝑡ሻ+ 𝑘𝑓න 𝑚ሺ𝛼ሻ𝑑𝛼𝑡

−∞ + ⋯ቋ

Fundamentals of Communication Systems ELCT332 Fall2011 13

Block diagram of the Armstrong indirect FM transmitter.

Indirect Method of Armstrong: WBFM Generation

Generating NBFM first and then converted to WBFM by using additional frequency multipliers.Frequency multiplier can be realized by a nonlinear device followed by a bandpass filter.𝑦ሺ𝑡ሻ= 𝑎2𝑐𝑜𝑠2 𝜔𝑐𝑡+ 𝑘𝑓න𝑚ሺ𝛼ሻ𝑑𝛼൨= 0.5𝑎2 + 0.5𝑎2cos[2𝜔𝑐𝑡+ 2𝑘𝑓න𝑚ሺ𝛼ሻ𝑑𝛼]

𝑦ሺ𝑡ሻ= 𝑐0 + 𝑐1 cos𝜔𝑐𝑡+ 𝑘𝑓න𝑚ሺ𝛼ሻ𝑑𝛼൨+ 𝑐2 cos2𝜔𝑐𝑡+ 𝑘𝑓න𝑚ሺ𝛼ሻ𝑑𝛼൨+ ⋯+ 𝑐𝑛 cosn𝜔𝑐𝑡+ 𝑘𝑓න𝑚ሺ𝛼ሻ𝑑𝛼൨

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Designing an Armstrong indirect modulator.

Example: Design an Armstrong indirect FM modulator to generate an FM signal with carrier frequency 97.3 MHz and Δf=10.24kHz. A NBFM generator of fc1=20 kHz and Δf=5Hz is available. Only frequency doublers can be used as multipliers. Additionally, a local oscillator with adjustable frequency 400 and 500

kHz is readily available for frequency mixing.

97.3𝑀𝐻𝑧= 2𝑛2ሺ2𝑛1𝑓𝑐1 − 𝑓𝐿𝑂ሻ𝑓𝐿𝑂 = 2−𝑛2ሺ4.096× 107 − 9.73× 107ሻ< 0 97.3𝑀𝐻𝑧= 2𝑛2ሺ2𝑛1𝑓𝑐1 + 𝑓𝐿𝑂ሻ, 𝑓𝐿𝑂 = 2−𝑛2ሺ5.634× 107ሻ,𝑛2 = 7,𝑓𝐿𝑂 = 440𝑘𝐻𝑧 𝑀1 = 16, 𝑀2 = 128

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(a) FM demodulator frequency response. (b) Output of a differentiator to the input FM wave.(c) FM demodulation by direct differentiation.

Demodulation of FM Signals

𝐻ሺ𝑓ሻ= 𝑗2𝜋𝑓𝑅𝐶1+ 𝑗2𝜋𝑓𝑅𝐶≈ 𝑗2𝜋𝑓𝑅𝐶𝑖𝑓2𝜋𝑓𝑅𝐶≪1

Slope Detection

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Effects of Nonlinear Distortion and Interference

Immunity of Angle Modulation to Nonlinearities

Amplitude Modulation

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Effect of interference in PM, FM, and FM with preemphasis-deemphasis (PDE).

Interference Effect

Angle modulation is also less vulnerable than AM to small signal interference from adjacent channels

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure 5.15 Preemphasis-deemphasis in an FM system.

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure 5.16 (a) Preemphasis filter and (b) its frequency response. (c) Deemphasis filter and (d) its frequency response.

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure 5.17 Superheterodyne receiver.

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure 5.18 (a) FM stereo transmitter. (b) Spectrum of a baseband stereo signal. (c) FM stereo receiver.

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure 5.19

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure 5.19 FM and PM signals in the time and frequency domains.

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure 5.20 Signals at the demodulator: (a) after differentiator; (b) after rectifier.

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure 5.21 FM modulation and demodulation: (a) original message; (b) recovered signal.

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure P.5.1-1

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Figure P.5.1-2

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Figure P.5.1-3

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Figure P.5.1-5

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Figure P.5.4-1

Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc.

Figure P.5.4-2