te311 lecture08 dsb sc modulation
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8/10/2019 TE311 Lecture08 DSB SC Modulation
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TE311: Introduction toAnalogue Telecommunications
PART II
Lecture #8Linear Continuous Wave Modulation-II
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IntroductionPoints to be discussed in this lecture
Double Side-band Suppressed Carrier (DSB-SC) Modulation
Generation of DSB-SC Signals
Demodulation of DSB-SC Signals
Quadrature Amplitude Modulation (QAM)
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Double-Sideband Suppressed Carrier(DSB-SC) Modulation
A double-sideband modulated (DSB-SS) signal
( )s t is
defined as follows
( ) ( ) ( )cos 2 cs t m t f t =
( )m t is baseband message signal with bandwidth HzB
cf is the carrier frequency in Hz.
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DSB-SC ModulationFourier transform of a DSB-SC signal is obtainedfrom its time domain description as follows
( ) ( ) ( )1
2 c c
S f M f f M f f = + +
( ) ( )F
m t M f Transmission bandwidth for a DSB-SC signal is
related to the bandwidthT
B
B of the message signal by
2T
B B=
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DSB-SC Modulation
The spectrum of the DSB-SC signal is similar to thatof the AM signal except for the spectral peaks at
cf .
( )m t ( )s t
BB
( )M f
f
cf cf
( )S f
f
cf B+ cf B cf B cf B+
Uppersideband
Lowersideband
( )0M ( )0.5 0M
DSB-SC
modulator
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Generation of DSB-SC SignalsGeneration of a DSB-SC signal is derived from the
time-domain expression i.e. ( ) ( ) ( )cos 2 cs t m t f t = .
( )s t ( )m t
( )cos 2 cf t
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Generation of DSB-SC SignalsBalanced modulator
A DSB-SC signal is generated using two AM signalgenerators in a balanced configuration.
+
AMmodulator
AMmodulator
( )m t
( )2s t
-
( )cos 2 cf t
( )s t ( )m t
( )1s t
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Generation of DSB-SC SignalsShunt-Bridge Diode Modulator
During the positive half cycles of ( )cos 2 cf t all
diodes are forward biased and ( )0 0v t = .During the negative half cycles of ( )cos 2 cf t all
diodes are reverse biased and ( ) ( )0v t m t = .
( )s t
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Generation of DSB-SC SignalsThus
( ) ( )( ) ( )
( ) ( )
0
0 cos 2 0
cos 2 0
c
c
f tv t
m t f t
m t x t
>=
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Generation of DSB-SC Signals( ) ( ) ( )
( ) ( ) ( ) ( )
0
3
sin / 21 2 cos 22 / 2
c
n
v t m t x t
nm t m t nf t n
=
=
= +
Taking the Fourier transform on both sided gives
( ) ( ) ( ) ( )
( ) ( )23 2
sin1
2
nF
c cnn
Mm t x t M n M n
=
+ + +
where ( ) ( )F
m t M f
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Generation of DSB-SC SignalsPassing through a bandpass fil ter centered at( )0v t c with bandwidth 2Bwhere B is the bandwidth of ( )m t gives
( ) ( ) ( )
2cos 2
c
s t m t f t
=
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Generation of DSB-SC SignalsRing (or Double-Balanced) Modulator
( )s t
During the positive half cycles of ( )cos 2 cf t diodesand are forward biased whereas and are
reverse biased and
1D
3D 2D 4D
( ) ( )0v t m t = .
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Generation of DSB-SC SignalsDuring the negative half cycles of ( )cos 2 cf t diodes
and are reverse biased whereas and are
forward biased and1D 3D 2D 4D
( ) ( )0v t m t = . Thus
( ) ( ) ( )
( ) ( )
( ) ( )
0
cos 2 0
cos 2 0
c
c
m t f t
v t m t f t
m t x t
>=
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Generation of DSB-SC SignalsTaking the Fourier series of ( )x t it follows that
( ) ( ) ( )
( )( ) ( )
0
3
sin / 24 cos 2
/ 2 c
n
v t m t x t
nm t nf t
n
=
=
=
Taking the Fourier transform on both sided gives
( ) ( )
( )
( ) ( )3
sin / 22
/ 2
F
c cn
n
m t x t M n M nn
= + + where ( ) ( )
F
m t M .
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Generation of DSB-SC SignalsPassing through a bandpass fil ter centered at( )0v t c with bandwidth 2B where B is the bandwidth of
( )m t gives
( ) ( ) ( )
4cos 2
c
s t m t f t
=
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Demodulation of DSB-SC SignalsSynchronous Demodulator
Lowpass
filter
( )m t ( )s t ( )s t
( )cos 2
cf t
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Demodulation of DSB-SC SignalsLowpass filter input signal ( )s t
( ) ( ) ( )
( ) ( )
( ) ( ) [ ]
2
cos 2
cos 2
1 1 cos 2 (2 )2 2
c
c
c
s t s t f t
m t f t
m t m t f t
=
=
= +
Lowpass filter output signal
Bandpass signalBaseband signal
( ) ( )1
2
m t m t =
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Quadrature Amplitude Modulation(QAM)
Transmitted signal ( )s t for DSB-SC modulationoccupies twice the bandwidth of the baseband signal
( )m t .
To improve bandwidth utilization efficiency, two DSB-SC signals can be transmitted over the samebandwidth using two phase-quadrature carriers.
Two baseband signals can be separated at thereceiver by synchronous demodulation using twophase-quadrature carriers.
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Quadrature Amplitude Modulation(QAM)
Such a system is called quadrature amplitude
modulation (QAM) or quadrature multiplexing.
/ 2
( )1m t
( )2m t
( )cos 2 cf t
( )sin 2 cf t
2( )sin(2 )cm t f t
1( )cos(2 )cm t f t
signal
QAM
/ 2
LPF
LPF
( )cos 2 cf t
( )sin 2 cf t
( )2m t
( )1m t
Channel
1( )x t
2( )x t
( )s t
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Quadrature Amplitude Modulation(QAM)
Transmitted QAM signal ( )s t ( ) ( ) ( ) ( ) ( )1 2cos 2 sin 2c cs t m t f t m t f t = +
Demodulated signals
( ) ( ) ( )( ) ( ) ( ) ( ) ( )
1
1 1 2
2 cos 2
cos 4 sin 4
c
c c
x t s t f t
m t m t f t m t f t
=
= + +
( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
2
2 2 1
2 sin 2
sin 4 sin 4
c
c c
x t s t f t
m t m t f t m t f t
=
= +
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Quadrature Amplitude Modulation(QAM)
Applying and( )1x t ( )2x t to a lowpass filter withbandwidth equal to the bandwidth of the baseband
signal ( )m t yields ( )and1m t ( ).2m t
Example: Show that a slight error in the phase of thequadrature carriers will result in loss of signals andinterference between channels (co-channel interference).
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Reading Assignments1. B.P. Lathi, Modern Digital and Analog
Communication Systems , Chap. 4, Part 1.
2. Extra reading:
W. Tomasi, Electronic Communications
Systems, Chaps. 4 & 5.
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