EE 3323 Section 8.9 Noise Performance of FM Systems

8/6/2019 EE 3323 Section 8.9 Noise Performance of FM Systems

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EE 3323

Principles of CommunicationSystems

Section 8.9Noise Performance of FM Systems

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Noise Performance of FM Systems

A block diagram of an analog communication system receiversystem is shown below.

Transmission

Medium

BPFBR

n(t)

J(t) y(t)J(t) + n(t)

Sin ,Nin Sout ,NoutDetector

LPFB

ReceiverDemodulator

r(t)

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An FM receiver is shown below:

JFM(t)

n(t)

imiter requency

iscriminatoryo(t)

r(t)

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T e si al is

JFM(t) =AC c s

2TfCt+ kfx(t)dt

t ea iti e noiseis

(t)= c(t) cos(2TfCt) s(t)sin(2TfCt)

t erecei e si nalis

r(t)=AC cos

2TfCt+ kfx(t)dt

+ c(t) cos(2TfCt) s(t)sin(2TfCt)

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Thepow

erin t

herece

ived

signal is

Pr= r2(t)

Pr=

ACcos

2TfCt+ kfx(t) dt + nc(t) cos(2TfCt) ns(t) sin(2TfCt)

2

Pr=AC

2

2+

1

2 nc

2(t) +1

2 ns

2(t)

Sin=AC

2

2

Nin=1

2 nc

2(t) +

1

2 ns

2(t)

Nin= nc2(t) = 2N0B=

N0W

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Th limiterprodu es sign l of onst nt mplitude. All ofthe inform tion is in the phase angle of the signal. The

dis riminatorprodu es a signal

JD

(t) =d

dtU(t) 2Tf

C

JD(t) = 2TfC kfx(t) 2TfC

JD(t) = kfx(t)

The output signal po er is

Sout= kf2x2(t)

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Next i the t t ise p werwithan nm late arrier.

r(t) =A s( TfCt) + (t) s( TfCt) s(t) sin( TfCt)

O ser ethe phas r representati n

A nc (t)

ns(t)n(t)

r(t)

E

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The length o the resultant hasor is

| |r(t) [ nc(t)]2 ns

2(t)

and the hase angle is

E(t) tan 1

ns (t)nc(t)

I nc(t) A and ns(t) A the angle E is small and

E(t) $ tan 1 ns (t)A

and or small angles, E(t) $ns (t)

A

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The noise out ut o the discriminator is

n (t)tE(t)

n (t) 1A

ddt

ns (t)

The o er s ectral density o the noise is

Sd([) | |F{nd(t)}2

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Sd([)

F

1

A

d

dtns (t)

2

Sd([) 1A 2 | |j[Ns ([) 2

Sd([)[2

A 2| |Ns ([)

2

Sd([)[2

A 2Sn ([)

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IfSn([)N0

2

[C[C

W W

Sn [)

[

N0

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The discriminator/detector shifts this s ectrum to baseband:

[C[C

2

Sn([)

[

N0

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So S ([)[2A

2N0

[C[C

2W

Sd([)

[

N0ara olic Shape

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and the average o er is

Nout1

2T

g

g

Sd([) d[

Nout1

T

W

N0[

2

A 2d[

NoutN0

TA 21

3[3

0

W

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NoutN0W3

3 TA2

The noise ower at the out ut of the detector goes down with

an increase in carrier ower this is called noise quieting.

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Sout

Nout

3 TA2kf

2 x2(t)

N0W3

3 (2TA2kf

2 x2(t)

2N0W3

The detected signal im roves asA , kfand x2(t) increase.

The detected signal degrades as N0 and W increase.

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Let x(t) Am cos([mt) , x2(t) Am2

2 and

([ Amkf, and F([[m

, W [m so

Sout

Nout

3 TA 2F2

2 N0[m

The in ut signal-to-noise ratio is

SinNin

A 2

2nc

2(t)

A 2

2N0[m

T

TA2

2 N0[m

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so

(S / N)out(S / N)in

3 TA2F2

2N0[m

TA2

2N0[m

3F2

For the detector to im rove the signal-to-noise ratio

3F2u 1or

Fu 13

Fu 0.577

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For conventional AM the out ut signal-to-noise ratio isSout

Nout

A2x

2(t)

nc2(t)

for tone-modulation and wide-band noise owerN0 / 2,

Sout

Nout

A2m2

2N0[m

T

TA2m2

2N0[m

At best, form 1, this is

Sout

Nout

TA2

2N0[m

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So

Sout

NoutFM 3 F

2

Sout

NoutAM

FM signals are better by a factor of 3 F2

. The im rovementis acquired at the ex ense of bandwidth.

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For FM to be better in erformance than AM,

3F2u 1

or

Fu1

3

Fu 0.577

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EE 3323 Section 8.9 Noise Performance of FM Systems

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