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EE 3323
Principles of CommunicationSystems
Section 8.9Noise Performance of FM Systems
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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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