lecture6b

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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


Regenerated signal with

negative bias distortion

Regenerator threshold

is too low


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

lecture6b

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