Chapter 5

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Communication Systems

Instructor: Engr. Dr. Sarmad Ullah Khan

Assistant ProfessorAssistant ProfessorElectrical Engineering Department

CECOS University of IT and Emerging [email protected]

Chapter 5

Dr. Sarmad Ullah Khan

Angle Modulation and Demodulation

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Outlines

• Non Linear Modulation

B d idth f A l M d l t d W


• Bandwidth of Angle‐Modulated Waves

• Generating FMWaves

• Demodulation of FM Signals

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Outlines







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Non Linear Modulation

• Modulation of carrier signal can be achieved byamplitude phase and frequency


amplitude, phase and frequency• Modulating amplitude results in amplitude

modulation• Modulating frequency results in frequency

modulation• Modulating phase results in phase modulationg p p• Frequency modulation and phase modulation

collectively called angle modulation

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• Noise power reduction• Reduce bandwidth by using modulation schemes


• Reduce bandwidth by using modulation schemes• Bandwidth reduction means more users• FM varies frequency of carrier w.r.t. signal m(t)

w(t) = wc(t) + km(t)• If mp is peak amplitude of m(t)

M d i l f i f ld b• Max. and min. value of carrier frequency would bewc + kmp , wc - kmp

• Spectral component remains with the band of 2kmp

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• Means k control the bandwidth• In practice it was not true


• In practice, it was not true• FM bandwidth is greater than AM bandwidth

• AM varies the amplitude of carrier signal while FMvaries the instantaneous frequency of carrier signal

• Means carrier frequency change continuously• Means carrier frequency change continuously• Consider a sinusoidal signal

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)(cos)( tAt


• (t) = instantaneous phase (radians)• Hypothetical case of (t)


Hypothetical case of (t)• Acos(wct + 0)• (t) tangent to (wct + 0) at ‘t’• When ∆t→0

Acos(wct + 0) = Acos(t)

• Angular frequency of is wc

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)cos()( 0 tAt c 21 ttt

)(t

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• (t) = instantaneous phase (radians)• (w t + ) is slop to (t)


• (wct + 0) is slop to (t)• Instantaneous frequency wi at

any instant is a slop to (t)

dt

dtwi

)(

• Angle of carrier vary with m(t)

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dwtt

ii )()(


• In PM, angle (t) vary linearly with m(t):


• kp is constant and wc is carrier frequency• When 0 = 0

PM )(cos tmktwA pc dtktdd )()()(

• The wi varies linearly with the derivative of modulatingsignal

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)(twi

dt

tdmkwc

dt

tmktwd

dt

tdp

pci )()()(

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• As wi varies linearly with modulating signal, wehave FM


have FM

)(twi )(tmkw fc

)(ti dmktwdwt

fc

t

i )()(

FM

t

fc dmktwA )(cos

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)(ti )(tmktw pc PM

PM

)(twi

)(cos tmktwA pc

dt

tdmkwc

dt

tmktwd

dt

tdp

pci )()()(

FM)(twi )(tmkw fc

12TASK: Make block diagrams of PM and FM modulators

f

)(ti dmktwdwt

fc

t

i )()(

FM

t

fc dmktwA )(cos

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)( ti

PM

)( tmktw pc

)(cos tmktwA pc

PM

PM

)( tw i

)(pc

dt

tdmkwc

dt

tmktwd

dt

tdp

pci )()()(

DirectPhase

modulator PM waveModulating

signal source

twAcos

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twA ccos

IndirectModulating

signal source

DifferentiatorFrequency modulator

PM wave

twA ccos



FM )(twi )(tmkw fc

)(ti dmktwdwt

fc

t

i )()(

DirectModulating signal source

Frequency modulator FM wave

twAcos

fci

FM

t

fc dmktwA )(cos

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Indirect

twA ccos

IntegratorPhase

modulatorFM wave

Modulating signal source

twA ccos

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Example 5.1


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Example 5.1


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Outlines







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Bandwidth of Angle‐Modulated Waves

• Angle modulation is non linear• Bandwidth analysis cannot be done directly by


• Bandwidth analysis cannot be done directly byFourier transform

• For bandwidth of FM, let

a(t) =

t

dm )(

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tjwtajktaktwjFM

cffc eAeAet )()]([)(

)](Re[)( tt FMFM

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• And


• Modulated wave consists of unmodulated carrierplus various amplitude modulated terms

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• The signal a(t) is the integral of m(t)• If M(f) is band limited to B then A(f) is also band


• If M(f) is band limited to B, then A(f) is also bandlimited to B

• Spectrum of a2(t) is simply A(f)*A(f) and is bandlimited to 2B

• an(t) is band limited to nB• Hence modulated wave has unmodulated carrierHence modulated wave has unmodulated carrier

and spectrum of a(t), a2(t),….., an(t) centered wc

• Modulated wave is not band limted• However, in practice bandwidth of FM is finite

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• Because n! increases much faster than |kfa(t)|n


Narrow Band Angle Modulation• When kf is very small such that

|k (t)| << 1

0!

)(

n

tak nnf

|kfa(t)| << 1then

• This approximation is linear like AM expression

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]sin)([cos)( ttaktAt cfcFM


• Bandwidth of a(t) is B, bandwidth of is 2B• Narrow band PM signal is approximated as


)(tFM

• Narrow band PM signal is approximated as

• NBPM has approximate bandwidth of 2B

]sin)([cos)( ttmktAt cPcPM

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Wideband FM bandwidth Analysis• FM signal is meaningful if frequency deviation is


• FM signal is meaningful if frequency deviation islarge enough

• Practically, kf is large such that |kfa(t)| << 1 notsatisfied

• Hence, we have wideband FM signal (WBFM)• Consider m(t) and its stair case )(tm

Consider m(t) and its stair case• Each pulse is called cell

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)(tm


Wideband FM bandwidth Analysis


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Wideband FM bandwidth Analysis• FM signal correspond to single cell has frequency


• FM signal correspond to single cell has frequencywc+kfm(tk) and duration 1/2B

• Fourier transform of sinusoidal pulses correspondto a cell is a sinc function

• Minimum and maximum frequencies are wc-kfmpand wc+kfmpc f p

• Peak frequency deviation and estimate FMbandwidth is

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Wideband FM bandwidth Analysis• In NBFM


• In NBFM

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Example


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Outlines







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Generating FM Waves

• Two ways of generating FM waves– Direct


– Direct– Indirect

• NBFM Generation

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Generating FM Waves

• Indirect method (Armstrong)– NBFM is converted to WBFM using frequency


– NBFM is converted to WBFM using frequencymultiplier

– Frequency multiplier is realized by a non linear devicefollowed by bandpass filter

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Generating FM Waves

• Indirect method (Armstrong)


– Output spectra will be at wc, 2wc, ….., nwc

– Device having nonlinearity and bandpass filter calledfrequency multiplierfrequency multiplier

– Such multiplier increase carrier freq. and freq. deviation– This is basis of Armstrong freq. modulators

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Generating FM Waves

• Indirect method (Armstrong)– Generally freq deviation is increase by factor ‘n’ which


– Generally, freq. deviation is increase by factor n whichalso increase carrier freq.

– Freq. mixing is applied to reduce carrier freq. to desirevalue

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Generating FM Waves

• Direct method


– IN Hartley or Colpitt oscillators, frequency is given by

– If C varies by m(t) as

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Generating FM Waves

• Direct method– Then


– Then

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Generating FM Waves

• Direct method


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Problem 5.3‐2


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Outlines







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Demodulation of FM Signals


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Problem 5.4‐2


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Problem 5.4‐2


Solution:

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Chapter 5

Engineering

Transcript of Chapter 5