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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

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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

R S( t ) Sf ( t ) Operational Amplifier

Low-pass filter Half-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 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

210

101

210

2

jH

CRlog20R

Rlog20

CRlog10R

Rlog20log20:

CR

1

2101

210

2210

1

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

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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

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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 )

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

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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

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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