1 lecture 7 am and fm signal demodulation introduction demodulation of am signals demodulation of fm...
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1
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
2
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)
3
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
4
Envelope detection circuit.
Diode
C
R2
R1
R S( t ) Sf ( t ) Operational Amplifier
Low-pass filter Half-wave
rectifier
Sr ( t )
5
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 )
6
Circuit diagram of the low-pass filter.
86 10to10; ggeeout
C
R2
R1
eout
Operational Amplifier ein RΣ eΣ
-g Σ
7
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 out
outin CRR
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
221
2
jH
0e
8
2210
1
210
221
21010
CR1log10R
Rlog20
CR1
1
R
Rlog20)(log20
jH
1
210
101
210
2
R
Rlog20
1log10R
Rlog20log20:
CR
1 jH
dB01.3R
Rlog20
2log10R
Rlog20log20:
CR
1
1
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101
210
2
jH
CRlog20R
Rlog20
CRlog10R
Rlog20log20:
CR
1
2101
210
2210
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210
2
jH
CRtan 21
2)(
4)(
CR
1
CR)(CR
1
2
22
c
9
φ(ω)
ω
(a) Amplitude Bode plot (in decibels)
(b) Phase Bode plot (in radians)
ω
constant time delay
RC
20·log10 | H( jω ) |
plot of 20·log10
R2 R1 20·log10
R2 R1
-20·log10 ( ωR2 C )
ωc = 1 R2 C
ωc = 1 R2 C
- π 2
- π 4
ωgain?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
11
Block diagram of synchronous demodulator.
Sm ( t )
Sc ( t )
S ( t )
Multiplier Low-pass filter
Sdemod( 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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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 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)
ttdt
tdAttA
dt
dccfcf
sin
)(cos
t
mcc dSktfAtS )(2cos)(
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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 nearly rectangular 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
fcfenvm
;
dt
tdAA
dt
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 Controlled Oscillator (VCO)
SVCO ( t ) = AVCO ·sin [ 0 t + 0( t )]
Sf ( t ) = Af ·cos [ c t + ( t )]
SVCO ( t )
Phase Detector
Low-pass filter
18
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 )
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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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.
orig
regBD
1
21
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
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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:
• 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 1log2