department of electronics and communicationsengineeringyansahan university department of electronics...

Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY

Analog Modulation

(Bilingual Teaching )


Chapter 5 Analog ModulationChapter 5 Analog Modulation

INTRODUCTION TO MODULATION 5.1 AMPLITUDE MODULATlON 5.2 NOISE IN AM SYSYEMS5.2 NOISE IN AM SYSYEMS 5.3 ANGLE MODULATlON 5.3 ANGLE MODULATlON 5.4 NOISE IN FM RECIVERS5.4 NOISE IN FM RECIVERS 5.5 MULTIPLEXING5.5 MULTIPLEXING 5.6 FM-RADIO AND TV BOADCASTING5.6 FM-RADIO AND TV BOADCASTING


THE KEY OF THIS CHAPTER

Characteristic of the ConventionalConventional , Double-Sideband Suppressed-CarrierDouble-Sideband Suppressed-Carrier, Single-SidebandSingle-Sideband and VVestigial-Sidebandestigial-Sideband Amplitude modulation

Noise performance of different AM systems


THE KEY OF THIS CHAPTER

The relationship between FMFM and PM PM

Implementation of ANGLE modulators and demodulators

Noise in FM receivers


INTRODUCTION TO MODULATIONINTRODUCTION TO MODULATION

Why Modulation is Used?

Using carrier to shape and shift the frequency spectrum enable modulation by which several advantages are obtained:

different radio bands can be used for communications wireless communications (smaller antennas ) multiplexing techniques become applicable


Radio SpectrumRadio Spectrum


Un

ited S

tates Freq

uen

cy U

nited

States F

requ

ency

Allo

cation

Allo

cation


INTRODUCTION TO MODULATIONINTRODUCTION TO MODULATION message signalmessage signal: The analog signal to be

transmitted is denote by m(t): A lowpass signal of bandwidth W , The power content of this signal is:

2/ 22

/ 2

1( ) lim ( )

T

m TTP m t m t dt

T

m(t) is transmitted through the channel by impressing it on a carrier signal:carrier signal:

( ) cos(2 )c c cc t A f t


AMPLITUDE MODULATlONAMPLITUDE MODULATlON Several different ways of amplitude modulating

the carrier signal by m(t) :

(a) conventional double-sideband AM, (b) double sideband suppressed-carrier AM, (c) single-sideband AM, (d) vestigial-sideband AM.

each way results in different spectral characteristicsspectral characteristics for the transmitted signal.


Conventional Amplitude Modulation Conventional Amplitude Modulation

( )AMs t( )m t

cos2 cf tcA

AM modulation modelAM modulation model

( ) [ ( )]cos(2 )AM c cS t A m t f t

A conventional AM signal A conventional AM signal in the time domainin the time domain


Conventional Amplitude ModulationConventional Amplitude Modulation

m(t) is constrained to satisfy : If the AM signal is overmodulatedovermodulated

( ) cm t A

( ) cm t A

Spectrum of the AM SignalSpectrum of the AM Signal

( )U f f [ ( ) cos 2 ]cm t f t

+ [ cos(2 )]c cA f t

1[ ( ) ( )] [ ( ) ( )]

2 2c

c c c c

AM f f M f f f f f f



-W 0 W f

|M( f )|

-fc-W -fc -fc+W

f

fc-W fc fc+W

|U( f )|

a) Spectrum of message signal

b) Spectrum of Conventional AM signal

Upper sideband low

sideband


Example 5.1.1 Example 5.1.1

Modulating signal m(t) is a sinusoid :

Determine the AM signal, its upper and lower sidebands, and its spectrum.

Solution： the AM signal is expressed as

( ) cos 2 m m m cm t A f t f f

cos 2( ) [ ]cos(2 )mc cmu f tt fAA t

modulation index:modulation index: / AM m cA A


so that

The lower sidebandlower sideband component is:

The upper sideband component is :

( ) [1 cos 2 ]cos(2 )

cos 2 cos[2 ( )] cos[2 ( )]2 2

c m c

c cc c c m c m

u t A f t f t

A AA f t f f f f

( ) cos[2 ( ) ]2

c

l c m

Au t f f t

( ) cos[2 ( ) ]2

c

u c m

Au t f f t


The spectrum of the AM signal

( ) [ ( ) ( )]2

[ ( ) ( )]4

[ ( ) ( )]4

cc c

cc m c m

cc m c m

AU f f f f f

Af f f f f f

Af f f f f f

( )U f

4cA

2cA

4cA

4

cA 4

cA

2cA

cfc mf f c mf f c mf f cf

c mf f

f

The power of The power of carrier carrier

component is component is AAcc

22 / / 22

The power of twThe power of two sideband is o sideband is AAcc

22

ββ/ / 44


The power content of the AM signal is :

/ 2 2

/ 2

/ 2 2 2

/ 2

/ 2 2

/ 2

1lim ( )

1lim [ ( )] cos (2 )

1 1lim [ ( )] [1 ]

2cos(4 )

T

u TT

T

c cTT

T c

T

cT

P u t dtT

A m t f t dtT

A m t dtT

f t

2

,2 2

c mA P



Conventional Amplitude ModulationConventional Amplitude Modulation Since the envelope is slowly varying, the

positive and the negative halves of each cycle have almost the same amplitude.

integral of

is almost zero .

2[ ( )] cos(4 )c cA m t f t



Note thatNote that the second component is much smaller than the first component ( ). This shows that the conventional AM systems are far less power efficient than the DSB-SC systemsDSB-SC systems described in next subsection.

2

2 2c m

u

A PP

( ) cm t A

SoSo


Conventional Amplitude ModulationConventional Amplitude Modulation Demodulation of Conventional AM Signals

rectify the rectify the received signalreceived signal

lowpass filtelowpass filterr

envelope detector output of the envelope detector output of the envelope detector

1 2( ) ( )d t g g m t

DC DC componentcomponent

gain factorgain factor due to the signal demodulator


Double-Sideband Suppressed-Carrier AM

DSB-SC AM signal is obtained by

DSB-SC ( )s t( )m t

cos2 cf tcA

( ) ( ) ( ) ( ) cos(2 )c cu t m t c t A m t f t


Double-Sideband Suppressed-Carrier AMA

n exam

ple o

f messag

e, carrier,and

DS

B-S

C

An

examp

le of m

essage, carrier,an

d D

SB

-SC

m

od

ulated

sign

als. m

od

ulated

sign

als.



Spectrum of the DSB-SC AM Signal.

The bandwidthThe bandwidth occupancy of the

amplitude-modulated signal is 22WW the channel bandwidth required

( ) [ ( ) ( ]2

cc c

AU f M f f M f f

Bc=2W.

And it does not contain a carrier componenta carrier component

For this reason, uu((tt)) is called a suppressed-carrier signal.



Power Content of DSB-SC Signals. / 2 2

/ 2

/ 2 2 2 2

/ 2

2/ 2 2

/ 2

1lim ( )

1lim ( )cos (2 )

1lim ( )[1 cos(4 )]

2

T

u TT

T

c cTT

Tc

cTT

P u t dtT

A m t f t dtT

Am t f t dt

T2

2c

m

AP

PPmm indicates the power in the message signal mm

((tt))



Example 5.1.2The modulating signal

DSB-SC signalDSB-SC signal and its upperupper and lower lower sidebands

( ) cos 2 mm t a f t m cf f

SolutionSolution : : in the time domain

( ) ( ) ( ) cos(2 )cos(2 )

cos[2 ( ) ] cos[2 ( ) ]2 2

c m c

c cc m c m

u t m t c t A a f t f t

A a A af f t f f t


Taking the Fourier transform

( ) [ ( ) ( )]4

[ ( ) ( )]4

cc m c m

cc m c m

A au f f f f f f f

A af f f f f f

The lower sideband of u(t)

( ) cos[2 ( ) ]2c

l c m

A au t f f t

The upper sideband of u(t)

( ) cos[2 ( ) ]2c

u c m

A au t f f t


Spectrum of u(t)

lower sideband

upper sideband


Demodulation of DSB-SC AM Signals.

(X)Modulator

v(t)

Modulated signal

u(t )

Accos( 2fct + )

Localoscillator

LPF (lowpass filter)

vo(t)

suppose the received sig

nal:

( ) ( ) ( ) cos(2 )c cr t u t A m t f t

multiplying r(t) by a locally generated sinusoid:

cos(2 )cf t

( ) cos(2 ) ( )cos(2 )cos(2 )

1 1( )cos ( )cos(4 )

2 2

c c c c

c c c

r t f t A m t f t f t

A m t A m t f t




Then, we pass the product signal through an ideal lowpass filter with the bandwidth WW: :

1 1( )cos ( )cos(4 )

2 2c c cA m t A m t f t

Then:1

( ) ( ) cos( )2

l cy t A m t

Note that m(t) is multiplied by:

cos( )


Single-Sideband AM Single-Sideband AM

A DSB-SC DSB-SC AM signal required a channel bandwidth of BBcc=2=2WW for transmission, where WW is the bandwidth of the message signal.

We reduce the bandwidth of the transmitted signal to that of the baseband message signal m(t).

( ) ( ) cos 2 ( )sin 2c c c cu t A m t f t A m t f t

the Hilbert transform of m(t)

lower sideband

upper sideband


Hilbert transformHilbert transform

Hilbert transform may be viewed as a linear filterlinear filter with impulse response

( ) 1/h t t

and frequency responsefrequency response

, 0

( ) , 0

0, 0

j f

H f j f

f

With phase shift


Single-Sideband AMSingle-Sideband AM

Generation of a lower Generation of a lower single-sideband AM single-sideband AM signal signal

Generation of a single-Generation of a single-sideband AM signal by sideband AM signal by filtering one of the filtering one of the sidebands of a DSB-sidebands of a DSB-SCAM signal. SCAM signal.


Example 5.1.4 the modulating signal is a sinusoid

Determine the two possible SSB-AM signals. Solution :

The Hilbert transform of m(t) is :

( ) cos 2 , m m cm t f t f f

( ) sin 2 mm t f tHence,

( ) cos 2 cos 2 sin 2 sin 2c m c c m cu t A f t f t A f t f t

(-) sign USSB signal ( ) cos[2 ( ) ]u c c mu t A f f t

(+) sign LSSB signal ( ) cos[2 ( ) ]l c c mu t A f f t


Single-Sideband AMSingle-Sideband AM

Demodulation of SSB-AM Signals for the USSB signal :for the USSB signal :

( ) cos(2 ) ( ) cos(2 ) c cr t f t u t f t

ˆ c[ ( ) cos 2 ( )sin 2 ] os(2 ) cc c c cA m t f t A m t f tf t

1 1ˆ( )cos ( )sin double frequency ter s+ m

2 2 c cA m t A m tcos 2 cos sin 2 sin c cf t f t

passing the signal through an ideal lowpass filter passing the signal through an ideal lowpass filter

1 1ˆ( ) ( ) cos ( )sin

2 2l c cy t A m t A m t


Vestigial-Sideband AMVestigial-Sideband AM Sideband filter in an

SSB-AM system is stringentstringent

Can be relaxed by allowing vestige , which is a portion of the unwanted sideband

f

f

f

cf

cf

cf

cf W

cf W

cf W

DSBV f

SSBV f

VSBV f


Vestigial-Sideband AMVestigial-Sideband AM A DSB-SC AM signal passing through a sideban

d filter with the frequency response H(f)

( ) [ ( ) cos 2 ] ( )c cu t A m t f t h t

( ) [ ( ) ( )] ( )2

cc c

AU f M f f M f f H f


Vestigial-Sideband AMVestigial-Sideband AM Demodulation of the Demodulation of the

VSB signal VSB signal ( )V t

( ) [ ( ) ( )]2

cc c

AV f U f f U f f

( ) ( ) cos 2 cv t u t f t

( ) [ ( ) ( )] ( )2

cc c

AU f M f f M f f H f

( ) [ ( 2 ) ( )] ( ) [ ( 2 ) ( )] ( )4 4

c cc c c c

A AV f M f f M f H f f M f f M f H f f

( )v t


Vestigial-Sideband AMVestigial-Sideband AM The lowpass filter frequency rangeThe lowpass filter frequency range

f W

( ) ( )[ ( ) ( )]4

cl c c

AV f M f H f f H f f

VSB-filter characteristic must satisfy :VSB-filter characteristic must satisfy :

constant( ) ( ) c cH f f H f f f W


Vestigial-Sideband AMVestigial-Sideband AM

af W


Implementation of AM Modulators anImplementation of AM Modulators and demodulatiors d demodulatiors

Blo

ck d

iag

ram

of p

ow

er-law

B

lock

dia

gra

m o

f po

wer-la

w

AM

mo

du

lato

r A

M m

od

ula

tor

Power-Law Modulation

generate a product of the m(t) with the carrier


Switching Modulator.

( )cA m t

( ), ( ) 0( )

0, ( ) 0i

o

v t C tv t

C t

passing passing vvoo((tt)) through a bandpass filter with through a bandpass filter with

the center frequency the center frequency ff = = ffcc and the bandwidth and the bandwidth

22WW


Balanced Modulator. Balanced Modulator.

Care must be taken to select modulatorsmodulators with approximately identical characteristicsapproximately identical characteristics so that the carrier component cancels out at the summing junction.


Ring Modulator.Ring Modulator.

TheThe switching of the diodes switching of the diodes is cis controlledontrolled byby a square wave a square wave of freof frequencyquency ffcc, ,

( ) ( ) ( )ov t m t c t


Demodulation of AM signals Demodulation of AM signals Envelope Detector.

simple lowpass filter simple lowpass filter


Demodulation of DSB-SC AM Signals Demodulation of DSB-SC AM Signals

Requires a Requires a synchronous synchronous demodulatordemodulator

Note that m(t) is multiplied by: cos( )

1( ) ( ) cos( )

2l cy t A m t


Demodulation of SSB and VSBDemodulation of SSB and VSB Signals Signals

SSB signal: insert a SSB signal: insert a small carrier small carrier componentcomponent that is transmitted that is transmitted along with the message along with the message

VSB signal: VSB signal: carrier componentcarrier component that is transmitted along with the that is transmitted along with the message message


Channel modelChannel model Additive white Gaussian noise (AWGN) communication

channel .

Receiver modelReceiver model Ideal band-pass filter followed by an ideal demodulator

NOISE IN AM SYSYEMSNOISE IN AM SYSYEMS

Channel and Receiver model


NOISE IN AM SYSYEMSNOISE IN AM SYSYEMS Signal-to-noise ratios Let the power spectral densitypower spectral density of the noise ww((tt)) be den

oted by n0/2 , nn00 is the average noise power per unit bandwidth measured at the front end of the receiverthe front end of the receiver

the band-pass filter having a bandwidth equal to the transmission bandwidth BBcc

ConventionalConventional-AM

DSB-SC

SSB

VSB


Channel and Receiver model

The filtered noise nn((tt)) as a narrowband noisenarrowband noise :

cos(( ) 2 ) sin 2 )) (( ) (cI Q cf tn t n f tt n t

the in-phase noise component

the quadrature noise component

The filtered signal xx((tt)) available for demodulation is defined by

( ) ( ) ( )x t s t n t


NOISE IN AM SYSYEMSNOISE IN AM SYSYEMS Average noise power is equal to nn00BBcc

Sn(f)

n0/2Bc

- fc fc0

(SNR)(SNR)cc = the ratio of the average power of the modulated signal ss((tt)) to the average power of the filtered noise nn((tt)).

department of electronics and communicationsengineeringyansahan university department of electronics...

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