Transcript Lecture 6

Lecture 7
AM and FM Signal Demodulation
•
•
•
•
Introduction
Demodulation of AM signals
Demodulation of FM Signals
Regeneration of Digital Signals and Bias
Distortion
• Noise and Transmission Line Capacity
• Channel capacity
• Conclusion
1
Introduction
• The goal of demodulation.
• Demodulation
• Regeneration can exactly reproduce the original
digital signal.
• An AM signal preserves the frequency domain
information of the baseband signal in each sideband,
• Two methods for demodulation of an AM signal:
•
Envelope detection (for DSBTC AM signal)
•
Synchronous detection (coherent or homodyne)
2
FM signal demodulation
• It is more resistant to noise than an AM signal.
• filtering and Limiting the transmitted signal.
• Differentiation to obtain the phase information in the
modulated signal.
• There are four ways to implement differentiation:

Phase-Locked Loop

Zero-Crossing Detection

FM-to-AM Conversion

Phase-Shift or Quadrature Detection
3
Envelope detection circuit.
Low-pass
filter
Half-wave
rectifier
C
R2
Diode
R1
S( t )
R
Sr ( t )
Operational
Amplifier
Sf ( t )
4
Half-wave rectification and filtration of DSBTC AM signal.
Baseband signal Sm ( t )
Modulated signal S ( t )
Rectified signal Sr ( t )
Filtered signal Sf ( t )
5
Circuit diagram of the low-pass filter.
C
R2
eout   ge ; g  10 6 to 108
Σ
-g
R1
ein
eΣ
RΣ
Operational
Amplifier
eout
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ein  e e  eout
d ( e  eout ) e  0

 C

R1
R2
dt
R
In the limit as | g |  , the voltage, e  0 otherwise eout = -g e  
ein
e
de
de
R
  out  C  out or  2  ein  eout  R 2 C  out
R1
dt
R1
R2
dt
R2
 R2
F
 ein  
 U in ; F  eout   U out ;
 R1
 R1
de 

F R 2 C  out   R 2 C j  U out ( j )
dt 

R2
U out
1
H  j  


R1 1  j R 2 C
U in
H  j  
R2
1

2
R1
1    R 2C 
 ( )  tan 1    R 2 C 
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20 log10
R
1

2
H ( j )  20  log10

2
 R1


1


R
C
2






R 
2
 20  log10  2   10 log10 1   R 2 C 
 R1 
 
1
:
R 2C
1
 
:
R 2C
 
1
:
R 2C
R 
20  log H  j   20  log 10  2   10  log 10  1 
 R1 
R 
 20  log 10  2 
 R1 
20  log H  j
20  log H  j


R 
 20  log 10  2   10  log 10  2 
 R1 
R 
 20  log 10  2   3.01 dB
 R1 

R 
2
 20  log 10  2   10  log 10   R 2 C 
 R1 
R 
 20  log 10  2   20  log 10   R 2 C 
 R1 


     tan 1    R 2 C 
 
1
R 2C
  c 
1
R 2C
 
 ( )    R 2 C
 ( )  

4
 ( )  

2
8
20·log10 | H( jω ) |
ωc =
20·log10
R2
R1
1
R2 C
plot of 20·log10
R2
-20·log10 ( ωR2 C )
R1
-3 dB
ωgain?1 =
1
R1 C
ω
(a) Amplitude Bode plot (in decibels)
φ(ω)
ωc =
-
-
1
R2 C
ω
π
4
π
2
constant
time delay
RC
(b) Phase Bode plot (in radians)
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Synchronous Demodulation of AM signals
S  t   Ac   Ac  S m t    cos  2 f c t 
Sdemod  t   k1 A2 c   Ac  Sm t    cos  2 f c t   cos  2 f c t 
 k1 A2 c   Ac  Sm t    cos 2  2 f c t 
1
 A c   Ac  Sm t      1  cos  2  2 f c t  
2
Ac3
A2 c
1 2




 Sm t 
A c   Ac  Sm t    cos  4 f c t 
2k
2k
2k
1
k
2
1
cos       1  cos 2 
2
2

A2 c
S demod  t  
 S m t 
2k
10
Block diagram of synchronous demodulator.
Sc ( t )
S(t)
Multiplier
Sdemod( t )
Low-pass
filter
Sm ( t )
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Demodulation of FM Signal
1 - filter the signal in order to eliminate all noise
outside of the signal band. Broadcast FM signals
are filtered by a band-pass filter prior to
transmitting.
2 - Modulated FM signal is to pass it through a
limiter. This will restrict the signal amplitude to
the range -VL to +VL . The output is a series of
nearly rectangular pulses.
3 - low-pass filter eliminates the higher frequency
components from these pulses to obtain a signal
which very closely resembles the transmitted FM
signal:
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S f t  
4

g filter VL cos  c t   t  
gfilter : gain of low-pass filter (ratio of R2 to R1 )
This amplitude variation in the received signal does not appear at the
output of the low-pass filter, but the phase function  ( t ) is preserved.
After the added noise is removed, the demodulator must restore the
original signal Sm ( t ). It is possible to accomplish this by differentiating
the filtered output signal with respect to time:
(Af : amplitude of filter output, Af · gfilter · VL)
t

S ( t )  Ac  cos  2 f c t  k  S m (  ) d








d
d (t ) 

A f cos   c t    t     A f   c 
 sin   c t    t  
dt
dt 



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Data
Transmitter
Sine Wave
Generator
Noise
Pulse
Generator
1.
Rectangular pulses are generated.
Low Pass
Filter
2.
High-frequency components are
removed and the wave is given a
more suitable shape for modulation.
FM
Modulator
3.
Frequency of sine wave carrier is
varied by the data signal.
Band Pass
Filter
4.
Sidebands with low data content
are removed.
Transmission Medium
Receiver
Band Pass
Filter
Limiter
Sine Wave
Generator
Data
FM
Demodulator
1.
Components and noise outside the
transmitted signal bandwidth are
removed.
2.
Signal is converted into a nearly
rectangular wave so that amplitude
distortions can be ignored
3.
Demodulation recovers the data
signal.
Regenerator 4.
Data signal converted to
rectangular pulses.
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+VL
Received signal S ( t )
+VL
+VL
Limited signal SL ( t )
+VL
Filtered signal Sf ( t )
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• The DC offset can be removed with a capacitor placed in
series to the differentiator. The varying portion of the
signal is proportional to the original signal:
• By passing the differentiated signal through an ideal envelope
detector and low-pass filter, we can recover the original signal.
The carrier frequency determines the DC offset of this signal,
which will be much larger than the varying portion of the signal:
d  t  
d  t 

S env  t    A f  c 

A


A

f
c
f
dt
dt


Af
d
 K  S m  t  ; Senv  t   A f  c 
Sm  t 
dt
K
•
A.
B.
C.
D.
There are four ways to implement a differentiator:
Phase-Locked Loop (PLL)
Zero-Crossing Detection
FM-to-AM Conversion (also called a slope detector)
Phase Shift or Quadrature Detection
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Phase-Locked Loop (PLL) - negative feedback.
The PLL consists of three basic components:
A. Phase detector (PD)
B. Low-pass filter (LPF)
C. Voltage controlled oscillator (VCO)
Sf ( t )
Phase
Detector
Sphase( t )
Low-pass
filter
Sout ( t )
SVCO ( t )
Voltage Controlled
Oscillator (VCO)
Sf ( t ) = Af ·cos [ c t +  ( t )]
SVCO ( t ) = AVCO ·sin [ 0 t +  0( t )]
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Demodulation by Zero Crossing Detection
•
•
•
•
•
•
Zero crossing detector
Positive voltage.
Negative voltage.
Pulse generator.
low-pass filter.
The advantage of zero crossing detection (and
FM-to-AM conversion) is that no source of the
carrier frequency is required to demodulate the
signal. A digital signal can easily be recovered
from a FM signal in this manner.
• Decoding an analog signal may be difficult by this
method, since the signal at the low-pass filter
output does not closely resemble the baseband
signal.
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Received signal S ( t )
Limited and filtered
signal Sf ( t )
Zero Crossing Detection
Fully rectified signal
Pulse Generator
Low Pass Filter
Regenerator Threshold
Regenerated baseband
signal Sm ( t )
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Regeneration of Digital Signals and Bias
Distortion
• To produce rectangular pulses, we send the demodulated signal
to a regenerator, which detects whether the signal level is above
a certain threshold.
• A poorly adjusted regenerator threshold can cause “bias
distortion”, where the digital signal produced is not identical to
the original signal.
 reg
BD  1 
 orig
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mark
space
mark
space
mark
space
Original digital signal
Demodulated signal
Regenerator threshold
is too high
Regenerated signal with
positive bias distortion
mark
space
mark space
mark
space
mark
space
Regenerator threshold
is too low
Regenerated signal with
negative bias distortion
mark space
mark
space
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Noise is any signal that interferes with a transmitted signal. It can be
another message signal, a random fluctuation in the amount of
signal attenuation, environmental noise, or additional voltages
introduced by the transmitting or receiving equipment.
N = k·T·W
k: the Boltzmann constant = 1.3710  10-23 Joules per degree Kelvin
T: temperature degrees Kelvin;
W: bandwidth in Hertz
• The channel capacity is the maximum rate at which data can be
accurately transmitted over a given communication link
(transmission line or radio link) under a given set of conditions.
• Shannon proved that if signals are sent with power S over a
transmission line perturbed by AWGN of power N, the upper limit
to the channel capacity in bits per second is:
S 

C  W  log 2  1  
N 

•
•
•
W:
S:
N:
bandwidth of the channel in Hertz
power of the signal in the transmission bandwidth
power of the noise in the transmission bandwidth
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