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Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
Analog Modulation
(Bilingual Teaching )
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
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
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
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
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
THE KEY OF THIS CHAPTER
The relationship between FMFM and PM PM
Implementation of ANGLE modulators and demodulators
Noise in FM receivers
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
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
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
Radio SpectrumRadio Spectrum
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
Un
ited S
tates Freq
uen
cy U
nited
States F
requ
ency
Allo
cation
Allo
cation
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
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
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
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.
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
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
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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
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
Conventional Amplitude ModulationConventional Amplitude Modulation
-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
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
Conventional Amplitude ModulationConventional Amplitude Modulation
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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
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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
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
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
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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
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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
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Conventional Amplitude ModulationConventional Amplitude Modulation
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
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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
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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
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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.
Department of Electronics and CommunicationsDepartment of Electronics and Communications EngineeringEngineering YANSAHAN UNIVERSITYYANSAHAN UNIVERSITY
Double-Sideband Suppressed-Carrier AM
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.
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Double-Sideband Suppressed-Carrier AM
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Double-Sideband Suppressed-Carrier AM
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))
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Double-Sideband Suppressed-Carrier AM
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
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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
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Spectrum of u(t)
lower sideband
upper sideband
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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
Double-Sideband Suppressed-Carrier AM
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Double-Sideband Suppressed-Carrier AM
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( )
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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Vestigial-Sideband AMVestigial-Sideband AM
af W
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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
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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
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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.
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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
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Demodulation of AM signals Demodulation of AM signals Envelope Detector.
simple lowpass filter simple lowpass filter
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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
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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
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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
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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
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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
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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)).