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7/30/2019 lecture6b
1/22
1
Lecture 7AM 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
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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)
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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
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Envelope detection circuit.
Diode
C
R2
R1
RS(t) Sf(t)Operational
Amplifier
Low-pass
filterHalf-wave
rectifier
Sr(t)
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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)
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Circuit diagram of the low-pass filter.
86 10to10; ggeeout
C
R2
R1
eout
Operational
Amplifierein Re
-g
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R
0)(C
RR 21
e
dt
eedeeee outoutin
In the limit as |g| , the voltage, otherwise eout = -g e
dt
deee outoutin CRR 21 dt
deee outoutin CR
R
R2
1
2or
)(CRCR
;;
R
R
R
R
22
1
2
1
2
jUjdt
deF
UeFUeF
outout
outoutinin
CR1
1
R
R
21
2
jU
UjH
in
out
CRtan)(
CR1
1
R
R
21
2
21
2
jH
0e
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2
2101
2
10
2
21
21010
CR1log10R
R
log20
CR1
1
R
Rlog20)(log20
jH
1
210
10
1
210
2
RRlog20
1log10R
Rlog20log20:
CR
1 jH
dB01.3R
Rlog20
2log10R
Rlog20log20:
CR
1
1
210
10
1
210
2
jH
CRlog20R
Rlog20
CRlog10R
Rlog20log20:
CR
1
210
1
210
2
210
1
210
2
jH
CRtan 21
2)(
4)(CR
1
CR)(CR
1
2
2
2
c
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()
(a) Amplitude Bode plot (in decibels)
(b) Phase Bode plot (in radians)
constant
time delay
RC
20log10 |H(j)|
plot of20log10
R2R1 20log10
R2R1
-20log10 (R2 C)
c =1
R2 C
c =1
R2 C
-
2
-
4
gain?1 =1
R1 C
-3 dB
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Synchronous Demodulation of AM signals
tftSAAtS cmcc 2cos
tftSAAk
tSk
A
k
A
tftSAA
tftSAA
tftftSAAtS
cmccm
cc
cmcck
cmcck
ccmcckdemod
4cos2
1
22
22cos12
1
2cos
2cos2cos
223
21
221
21
2cos12
1cos2
tSk
AtS m
c
demod 2
2
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Block diagram of synchronous demodulator.
Sm(t)
Sc(t)
S(t) MultiplierLow-pass
filter
Sdemod(t)
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Demodulation of FM Signal
1 - filter the signal in order to eliminate all noiseoutside of the signal band. Broadcast FM signals
are filtered by a band-pass filter prior totransmitting.
2 - Modulated FM signal is to pass it through a
limiter. This will restrict the signal amplitude tothe range -VL to +VL . The output is a series ofnearly rectangular pulses.
3 - low-pass filter eliminates the higher frequencycomponents from these pulses to obtain a signalwhich very closely resembles the transmitted FMsignal:
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ttVgtS cLfilterf
cos4
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 theoriginal 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)
ttdttd
AttAdt
d
ccfcf
sin
)(
cos
t
mcc dSktfAtS )(2cos)(
D
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Data
Transmission Medium
1. Rectangular pulses are generated.Pulse
Generator
Low Pass
Filter
FM
Modulator
2. High-frequency components are
removed and the wave is given a
more suitable shape for modulation.
Sine Wave
Generator
Band Pass
Filter
3. Frequency of sine wave carrier is
varied by the data signal.
4. Sidebands with low data content
are removed.
Noise
Transmitter
1. Components and noise outside the
transmitted signal bandwidth are
removed.
Band Pass
Filter
Limiter
FM
Demodulator
2. Signal is converted into a nearlyrectangular wave so that amplitude
distortions can be ignored
Sine Wave
Generator
Regenerator
3. Demodulation recovers the data
signal.
4. Data signal converted to
rectangular pulses.
Receiver
Data
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Received signal S(t)
Limited signal SL (t)
Filtered signal Sf(t)
+VL
+VL
+VL
+VL
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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:
tSK
AAtStSK
dt
dm
f
cfenvm
;
dttd
AAdt
tdAtS fcfcfenv
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:
There are four ways to implement a differentiator:A. Phase-Locked Loop (PLL)
B. Zero-Crossing DetectionC. FM-to-AM Conversion (also called a slope detector)
D. 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)
Sout(t)Sf(t)Sphase(t)
Voltage ControlledOscillator (VCO)
SVCO(t) = AVCOsin[0t+
0(
t)]
Sf(t) = A fcos[ ct+ (t)]
SVCO(t)
Phase
Detector
Low-pass
filter
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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 (andFM-to-AM conversion) is that no source of thecarrier frequency is required to demodulate thesignal. A digital signal can easily be recoveredfrom a FM signal in this manner.
Decoding an analog signal may be difficult by thismethod, since the signal at the low-pass filteroutput does not closely resemble the basebandsignal.
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Received signal S(t)
Zero Crossing Detection
Fully rectified signal
Pulse Generator
Low Pass Filter
Regenerator Threshold
Regenerated baseband
signal Sm(t)
Limited and filtered
signal Sf(t)
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Demodulated signal
Original digital signal
mark space mark space mark space
Regenerator threshold
is too high
Regenerated signal with
positive bias distortion
mark space mark space mark space
Regenerated signal with
negative bias distortion
Regenerator threshold
is too low
mark space mark space mark space
Noise is any signal that interferes with a transmitted signal It can be
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Noise is any signal that interferes with a transmitted signal. It can beanother message signal, a random fluctuation in the amount ofsignal attenuation, environmental noise, or additional voltagesintroduced by the transmitting or receiving equipment.
N= k T W
k: the Boltzmann constant = 1.3710 10-23 Joules per degree KelvinT: temperature degrees Kelvin;W: bandwidth in Hertz
The channel capacity is the maximum rate at which data can beaccurately 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 atransmission line perturbed by AWGN of powerN, the upper limitto the channel capacity in bits per second is:
W: bandwidth of the channel in Hertz
S: power of the signal in the transmission bandwidth
N: power of the noise in the transmission bandwidth
N
SWC 1log 2