Transcript Analog Modulation - Yanshan University

Analog Modulation
(Bilingual Teaching )
Department of Electronics and Communications Engineering
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Chapter 5 Analog Modulation
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INTRODUCTION TO MODULATION
5.1 AMPLITUDE MODULATlON
5.2 NOISE IN AM SYSYEMS
5.3 ANGLE MODULATlON
5.4 NOISE IN FM RECIVERS
5.5 MULTIPLEXING
5.6 FM-RADIO AND TV BOADCASTING
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THE KEY OF THIS CHAPTER
 Characteristic of the Conventional ,
Double-Sideband Suppressed-Carrier,
Single-Sideband and Vestigial-Sideband
Amplitude modulation
 Noise performance of different AM systems
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THE KEY OF THIS CHAPTER

The relationship between FM and PM

Implementation of ANGLE modulators and
demodulators

Noise in FM receivers
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INTRODUCTION 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
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Radio Spectrum
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United States Frequency
Allocation
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INTRODUCTION TO MODULATION

message 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
1 T /2
2
Pm  m (t )  lim 
m(t ) dt
T  T T / 2

m(t) is transmitted through the channel by
impressing it on a carrier signal:
c(t )  Ac cos(2 f c t  c )
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AMPLITUDE 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 characteristics
for the transmitted signal.
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Conventional Amplitude Modulation
s AM (t )
m (t )
Ac
cos 2 f c t
AM modulation model
A conventional AM signal
in the time domain

S AM (t )  [ Ac  m(t )]cos(2 fc t )
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Conventional Amplitude Modulation
m(t) is constrained to satisfy : m(t )  Ac
 If m (t )  Ac the AM signal is overmodulated

Spectrum of the AM Signal
U ( f ) f F [m (t ) cos 2 f c t ] +F [ Ac cos(2 f c t )]
Ac
1
 [ M ( f  fc )  M ( f  fc )]  [ ( f  fc )   ( f  fc )]
2
2
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Conventional Amplitude Modulation
|M( f )|
f
-W
0
W
a) Spectrum of message signal
|U( f )|
low
sideband
Upper
sideband
f
-fc-W -fc -fc+W
fc-W fc fc+W
b) Spectrum of Conventional AM signal
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Conventional Amplitude Modulation
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Example 5.1.1

Modulating signal m(t) is a sinusoid :
m(t )  Am cos 2 f m t
fm
fc
Determine the AM signal, its upper and
lower sidebands, and its spectrum.
 Solution：the AM signal is expressed as
u(t )  [ Ac  Am cos 2 f m t ]cos(2 f c t )
 modulation index:
 AM  Am / Ac
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so that
u(t )  Ac [1   cos 2 f m t ]cos(2 f c t )
 Ac cos 2 f c t 
 Ac
2
cos[2 ( f c  f m )] 
 Ac
2
cos[2 ( f c  f m )]
The lower sideband component is:
ul (t ) 
 Ac
2
cos[2 ( fc  f m )t ]
The upper sideband component is :
uu (t ) 
 Ac
2
cos[2 ( fc  f m )t ]
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
The spectrum of the AM signal
Ac
U( f ) 
[ ( f  f c )   ( f  f c )]
2
 Ac

[ ( f  f c  f m )   ( f  f c  f m )]
4
 Ac

[ ( f  f c  f m )   ( f  f c  f m )]
4
The power of
carrier
component is
Ac2 / 2
U( f )
 Ac 
 
 2 
 Ac  


 4 
 fc  fm
 fc
 Ac  


 4 
 fc  fm
 Ac 
 
 2 
 Ac  


 4 
fc  fm
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fc
 Ac  


 4 
The power of
two sideband
f is
Ac2 β/ 4
fc  fm
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Conventional Amplitude Modulation

The power content of the AM signal is :
1 T /2 2
Pu  lim 
u (t )dt
T  T T / 2
1 T /2
 lim  [ Ac  m (t )]2 cos 2 (2 f c t )dt
T  T T / 2
1
1 T /2
 lim  [ Ac  m (t )]2 [1  cos(4 f c t )]dt
2 T  T T / 2
Ac2 Pm


,
2
2
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Conventional Amplitude Modulation

Since the envelope is slowly varying, the
positive and the negative halves of each
cycle have almost the same amplitude.
integral of
[ Ac  m(t )]2 cos(4 fc t )
is almost zero .
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Conventional Amplitude Modulation

So

Note that
2
c
A Pm
Pu 

2
2
the second component is much
smaller than the first component ( m(t )  Ac ). This
shows that the conventional AM systems are far
less power efficient than the DSB-SC systems
described in next subsection.
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Conventional Amplitude Modulation
rectify the
 Demodulation
of Conventional AM Signals
received signal
lowpass
filter
DC
component
envelope detector
output of the envelope detector
d (t )  g1  g2 m (t )
gain factor due to the
signal demodulator
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Double-Sideband Suppressed-Carrier AM

DSB-SC AM signal is obtained by
m (t )
sDSB-SC (t )
Accos 2 f c t
u(t )  m(t )c(t )  Ac m(t ) cos(2 f c t )
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Double-Sideband Suppressed-Carrier AM
An example of message, carrier,and DSB-SC
modulated signals.
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Double-Sideband Suppressed-Carrier AM
Spectrum of the DSB-SC AM Signal.
U( f ) 
Ac
[ M ( f  fc )  M ( f  fc ]
2
The bandwidth occupancy of the
amplitude-modulated signal is 2W
the channel bandwidth required
Bc=2W.
 And it does not contain
a carrier component
For this reason, u(t) 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.
1 T /2 2
Pu  lim 
u (t )dt
T  T T / 2
1 T /2 2 2
2
 lim 
Ac m (t ) cos (2 f c t )dt

T
/
2
T  T
Ac2
1 T /2 2

lim 
m (t )[1  cos(4 f c t )]dt
2 T  T T / 2
2
c
A

Pm
2
Pm indicates the
power in the
message signal
m(t)
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Double-Sideband Suppressed-Carrier AM

Example 5.1.2
fc
The modulating signal m(t )  a cos 2 f m t f m
DSB-SC signal and its upper and lower sidebands
Solution :
in the time domain
u(t )  m (t )c (t )  Ac a cos(2 f m t ) cos(2 f c t )
Ac a
Ac a

cos[2 ( f c  f m )t ] 
cos[2 ( f c  f m )t ]
2
2
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
Taking the Fourier transform
Ac a
u( f ) 
[ ( f  f c  f m )   ( f  f c  f m )]
4
Ac a

[ ( f  f c  f m )   ( f  f c  f m )]
4
The lower sideband of u(t)
The upper sideband of u(t)
Ac a
ul (t ) 
cos[2 ( fc  f m )t ]
2
Ac a
uu (t )
cos[2 ( fc  f m )t ]
2
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Spectrum
of u(t)
lower
sideband
upper
sideband
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Double-Sideband Suppressed-Carrier AM
Demodulation of DSB-SC AM Signals.
Modulated
signal
u(t )
 suppose the received
(X)
Modulator
v(t)
LPF (low
pass filter)
Accos( 2fct +  )
vo(t)
signal:
r (t )  u(t )  Ac m (t ) cos(2 f c t )
multiplying r(t) by a locally
generated sinusoid:

Local
oscillator
cos(2 f c t   )
r (t ) cos(2 f c t   )  Ac m (t ) cos(2 f c t ) cos(2 f c t   )
1
1
 Ac m (t ) cos   Ac m (t ) cos(4 f c t   )
2
2
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Double-Sideband Suppressed-Carrier AM

Then, we pass the product signal through an ideal
lowpass filter with the bandwidth W:
1
1
Ac m(t ) cos   Ac m(t ) cos(4 f c t   )
2
2
Then:
yl (t ) 
1
Ac m(t )cos( )
2
 Note that m(t)
is multiplied by:
cos( )
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Single-Sideband AM


A DSB-SC AM signal required a channel bandwidth
of Bc=2W for transmission, where W is the bandwidth
of the message signal.
We reduce the bandwidth of the transmitted signal to
that of the baseband message signal m(t).
the Hilbert transform of m(t)
u(t )  Ac m(t )cos 2 fc t
upper sideband
Ac m(t )sin 2 fc t
lower sideband
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Hilbert transform

Hilbert transform may be viewed as a linear filter
with impulse response
h(t )  1/  t
and frequency response
 j,

H ( f )   j,
 0,

With phase shift /2
f 0
f 0
f 0
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Single-Sideband AM
Generation of a lower
single-sideband AM
signal
Generation of a singlesideband AM signal by
filtering one of the
sidebands of a DSBSCAM signal.
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Example 5.1.4

the modulating signal is a sinusoid
m(t )  cos 2 f m t ,
fm
fc
Determine the two possible SSB-AM signals.
 Solution :
The Hilbert transform of m(t) is :
m(t )  sin 2 fm t
Hence,
(-) sign USSB signal
uu (t )  Ac cos[2 ( f c  f m )t ]
u(t )  Ac cos 2 f m t cos 2 f c t
(+) sign LSSB signal
Ac sin 2 f m t sin 2 f c t
ul (t )  Ac cos[2 ( f c  f m )t ]
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Single-Sideband AM

Demodulation of SSB-AM Signals
for the USSB signal :
r (t ) cos(2 f c t   )  u(t ) cos(2 f c t   )
ˆ (t )sin 2 f c t ] cos(2 f c t   )
 [ Ac m(t ) cos 2 f c t  Ac m
1
1 cos 2 f c t cos   sin 2 f c t sin 
ˆ (t )sin  + double frequency terms
 Ac m(t ) cos   Ac m
2
2
passing the signal through an ideal lowpass filter
1
1
ˆ (t )sin 
yl (t )  Ac m(t )cos   Ac m
2
2
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Vestigial-Sideband AM


Sideband filter in an
SSB-AM system is
stringent
Can be relaxed by
allowing vestige ,
which is a portion of
the unwanted sideband
VDSB  f 
f
VSSB  f 
VVSB  f 
fc
fc
fc
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fc  W
fc  W
fc  W
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f
f
Vestigial-Sideband AM

A DSB-SC AM signal passing through a
sideband filter with the frequency response H(f)
Ac
U ( f )  [ M ( f  fc )  M ( f  f c )]H ( f )
2
u(t )  [ Ac m(t ) cos 2 f c t ]  h(t )
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Vestigial-Sideband AM

Demodulation of the
VSB signal
vV( t()t )
v (t )  u(t ) cos 2 f c t
V( f ) 
Ac
[U ( f  f c )  U ( f  f c )]
2
Ac
U ( f )  [ M ( f  fc )  M ( f  f c )]H ( f )
2
V( f ) 
Ac
A
[ M ( f  2 f c )  M ( f )]H ( f  f c )  c [ M ( f  2 f c )  M ( f )]H ( f  f c )
4
4
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Vestigial-Sideband AM

The lowpass filter frequency range f  W
Ac
Vl ( f ) 
M ( f )[ H ( f  fc )  H ( f  f c )]
4

VSB-filter characteristic must satisfy :
H ( f  fc )  H ( f  fc )  constant
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f W
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Vestigial-Sideband AM
fa
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W
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Implementation of AM Modulators
and demodulatiors
 Power-Law
Modulation
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Block diagram of power-law
AM modulator
generate a product of
the m(t) with the carrier
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
Switching Modulator.
Ac
 v i ( t ), C ( t )  0
vo ( t )  
C (t )  0
 0,
m (t )
passing vo(t) through a bandpass filter with
the center frequency f = fc and the bandwidth
2W

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
Balanced Modulator.
Care must be taken to select modulators with
approximately identical characteristics so that
the carrier component cancels out at the summing
junction.
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
Ring Modulator.
The switching of the diodes is
controlled by a square wave of
frequency fc,
v o ( t )  m ( t )c ( t )
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Demodulation of AM signals

Envelope Detector.
simple lowpass filter
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Demodulation of DSB-SC AM Signals
yl (t ) 
1
Ac m(t )cos( )
2
 Note that m(t)
is multiplied by: cos( )
Requires a synchronous
demodulator
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Demodulation of SSB and VSB Signals
VSB signal: carrier component
that is transmitted along with the
message
SSB signal: insert a small carrier
component that is transmitted
along with the message
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NOISE IN AM SYSYEMS
 Channel and Receiver model


Channel model Additive white Gaussian noise
(AWGN) communication channel .
Receiver model Ideal band-pass filter followed
by an ideal demodulator
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NOISE IN AM SYSYEMS



Signal-to-noise ratios
Let the power spectral density of the noise w(t) be
denoted by n0/2 , n0 is the average noise power per
unit bandwidth measured at the front end of the
receiver
the band-pass filter having a bandwidth equal to the
transmission bandwidth Bc
Conventional-AM
DSB-SC
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SSB
VSB
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 Channel and Receiver model

The filtered noise n(t) as a narrowband noise :
n(t )  nI (t ) cos(2 fc t )  nQ (t ) sin(2 fc t )
the in-phase noise
component

the quadrature
noise component
The filtered signal x(t) available for demodulation
is defined by
x(t )  s(t )  n(t )
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NOISE IN AM SYSYEMS

Average noise power is equal to n0Bc
Sn(f)
n0/2
- fc
0
Bc
fc
(SNR)c = the ratio of the average power of the
modulated signal s(t) to the average power of the
filtered noise n(t).
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