chapter 3b pm

8/3/2019 Chapter 3b PM

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CHAPTER 3: PHASE MODULATION (PM)


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Chapter 3/PM Prepared By: Pn.Norliza Mohamed 2

Phase Modulation (PM) is also an angle modulation and very similar to

FM in lots of ways.

PM can be obtained by altering the phase constant of a constant-

amplitude carrier directly proportional to the amplitude of the basebandsignal.

The basic principle of frequency modulation is that a base band voltage

(Vm) changes the phase angle of the carrier linearly by a small amount.

We know that the carrier and the modulating signal is given by:

INTRODUCTION

J[[

!

!

tEtv

tEtv

ccc

mmm

cos)(:signalCarrier

cos)(:signalModulating


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Therefore,

Hence, the phase modulated signal becomes,

GENERAL CONCEPT

[rad/V]

PMforysensitivitmodulationwhere,)(

)(

m

cp

pmpc

mc

E

K

KtvK

tv

J

HJ

HJ

!@

!!

w

ttE

tEKtE

tvKtEtEv

mpcc

mmpcc

mpcc

ccPM

[F[

[[

[HJ[

coscos

coscos

)(coscos

!

!

!!


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The modulation index for PM is given by:

We know that,

MODULATION INDEX

indexmodulationWhere, !

!

p

mpp EK

F

F

rad/VinPMforysensitivitmodulation

HzinsignalmodulatingtheoffrequencyradianindeviationphasemaximumWhere,

)(

!

!!

!!@

w

p

m

pmp

mp

K

f

EK

tvK

J

J

HJ


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From the expression of PM, it now can be expanded as:

This expression can be analyzed to give the phase spectrum fora PM signal.

There are two ways of doing this: Narrow-band phase modulation (NBPM)

Wide-band phase modulation (WBPM)

PM EXPRESSION

? A

? A)cossin(sin)coscos(cossinsincoscos)cos(

coscos

ttttEvBABABA

ttEv

mcmccPM

mpccPM

[F[[F[

[F[

!@!

!


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Here, a simplifying is made that F is small in fact that it makes Fsin[mtalso small, allowing the following further assumptions to be made:

Now the expression for PM can be written in a much simplified form as:

NBPM

tt

t

mm

m

[F[F

[F

cos)cossin(

1)coscos(

!

!

? A

? A

tE

tE

tE

ttEtEtttE

ttttEv

mc

cp

mc

cp

cc

mccpcc

mpccc

mpcmpccNBPM

)sin(2

)sin(2

cos

cossincos)cos(sin1cos

)cossin(sin)coscos(cos

[[F

[[F

[

[[F[[F[[

[F[[F[

!

!y!

!


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General expression for NBPM is superficially similar to the expression for

NBFM. However, further analysis shows the difference which is:

NBPM

-

-

!

!

-

-

!

-

-

!

!

!

!

2)(cos

2)(cos

2cos

2cossin

2)(cos

2)(cos

2cos

)(2

cos)(2

cos2

cos

2cos

2cossin

)sin(2

)sin(2

cos

T[[

T[[

F[

TUU

T[[

T[[

F[

[[T

[[TF

[

TUU

TU

[[F

[[F

[

ttE

tEv

ttE

tE

ttE

tEv

tE

tE

tEv

mcmc

cp

ccNBPM

mcmc

cp

cc

mcmc

cp

ccNBPM

mc

cp

mc

cp

ccNBPM


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This is of course, just a carrier and a single sideband pair whose amplitude spectrum is

exactly the same as for AM and NBFM with bandwidth of2fm.

Obviously the phase spectrum is different and this is where the uniqueness of NBPM.

The useful phase changes must lie between +T and -T. The amplitude and phasespectrum for NBPM can be shown below.

NBPM


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These two methods are closely related and in some respects, very similar.

They both have the effect of changing carrier phase as a function of

baseband voltage.

General expression for both methods are:

RELATION ON PM AND FM

? A

? A

? A

? A

tEtv

ttEtvKtEv

ttE

dttvKtEv

mmm

mpcc

mpccPM

mcc

mfccFM

[

[F[[

[F[

[

cos)(Where

coscos)(cos

sincos

)(cos

!

!!

!

!


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USING PHASE MODULATOR

)(sin

cos)(

cos)(

tvtE

dttEdttv

tEtv

mm

m

m

mmm

mmm

!!

!@

!

[

[

[

[ ? A

? A

? A

pf

m

p

FMmcc

m

m

p

cc

m

m

mp

cc

m

m

mpcc

mpcc

mpccPM

KK

vttE

ttE

tEK

tE

tE

KtE

tvKtE

tvKtEv

!!

!!

-

!

-

!

-

!

!

!

andWhere

sincos

sincos

sincos

sincos

)(cos

)(cos

[

FF

[F[

[[

F[

[[

[

[[

[

[

[


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USING FREQUENCY MODULATOR

)(sin

cos)(

cos)(

tvtE

tEdt

dtv

dt

dtEtv

mmmm

mmm

mmm

!!

!@!

[[

[[

? A

? A

? A

? A

? A

pf

m

p

PMmpcc

mmfcc

m

mmmfcc

mmmfcc

mfcc

mfccFM

KK

vttE

tEKtE

tEKtE

dttEKtE

dttvKtEdttvKtEv

!!

!!

!

-

!

!

!!

andWhere

coscos

coscos

coscos

sincos

)(cos)(cos

[

FF

[F[

[[

[[

[[

[[[

[[


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PM FM

COMPARISON OF PM AND FM

? A

? A

[rad]deviationphasemax.

rad/V

)(cos

)(

!!

!

!

!

w

J

F

J

[

HJ

EK

E

K

tvKtEv

tv

mpp

m

p

mpccPM

mc

? A

? A

? A

[Hz]deviationfrequencymax.

Hz/V2

rad/s/V

)(cos

)(

!

!!

!

!

!

w

f

ff

E

f

E

K

dttvKtEv

tv

mm

m

m

f

mfccFM

mc

[F

T

[

H[


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COMPARISON OF PM AND FM

Square wave baseband signal

Unmodulated carrier signal

PM signal

FM signal

chapter 3b pm

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