WINSEM2014-15_CP3050_12-Feb-2015_RM01_angleModulation (1)

7/23/2019 WINSEM2014-15_CP3050_12-Feb-2015_RM01_angleModulation (1)

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Angle Modulation

Phase and frequency modulation together is called Angle Modulation

c t+ ( t)

()x ( t)=Acos

(t)=c t+ (t)

Also represented as exponential modulation

x ( t)={a e(j c t+ (t)) }

Where,

( t)= Instantaneous phase of the carrier signal

d(t)dt

= Instantaneous frequency of the carrier signal

(t)= Instantaneous phase deviation

d(t)dt = Instantaneous frequency deviation

Phase Modulation

( t)m ( t)

(t)=kp m (t)

kp=phase sensitivity (radians

volt )

c t+kp m (t)()

xpm (t)=Acos

=kpAm=Modulation Index

Frequency Modulation


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d (t)dt

m (t)

d (t)dt

=kfm (t)

( t)=kf

t

m ( s )ds

kf=frequency sensitivity (radians

volt )

c t+kf

t

m ( s) ds

()x fm ( t)=Acos

m(s )=kf

t

Amcos wm t dt

( t)=kfAm

m

sinm (t)

c t+ sinm ( t)()

x fm(t)=Acos

=kfAm

m=Modulation Index

Taking Fourier series of periodic part of the signal

x ( t)=Ae {e (j c t) ! e(j sin m ) }

e(jsin m )="eriodic #i$nal (%iscrete&ime 'ourier #eries)

f( t)=e (jsinm )=

n=

(n ! ejnm t

(n=m2 )

)/m

)/m

ejn

mt! e

(j sinm ) dt


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&=2 )

m

!et m=x

(n= 1

2 ))

)

ejnx

! e(j sinx ) dx

1

2 ))

)

ej ( sinxnx)

dx

This is the standard equation of "essel function of order n

(n=*n()

x ( t)=A{e(j c t)!n=

(n ! ejnm t}

A{n=

*n( ) ! e(j ct) ! e

jnm t}

A{n=

*n( ) ! ej ( ct+n m t) }

xfm( t)=An=

*n( ) !cos (c t+n m t)

A series expansion of FM spectral #and$idth gives #and$idth of

+andwidth=

FM %eneration

Indirect method

a& %enerate '"FM#& Frequency multiplication

%enerate '"FM

x ( t)=A cos(c t+(t))

A cosc tcos ( t)A sinc tsin (t)


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'o$ (ince (t),2) -cos (t) ,1 - sin (t) , (t)

x.+'M(t)=Acosc t

Inphase

A(t)sinc t

/uadrature phase

Frequency multiplier

x ( t)=A cos(c t+(t))

e ( t)=A cos(n c t+n sinmt)

After passing through "PF $ith centre frequency as fc=n fc

e i ( t)=Acos(c t+ sinmt)

)irect method

a& *artley +scillator

#& "alanced FM discriminator

*artley oscillator


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o= 1

0(

(=(okm ( t)

= 1

0 (o(1km (t)

(o)

1

0 (o1

1km ( t)

(o

=o(1+ km ( t)(o)

o(1kf1

m ( t) )

okfm (t)

Where,kf=kf

1okf

1= km

2(o

"alanced FM discriminator


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(lope )etector

omplex envelope representation of 21 ( f) (#lope(ircuit)

~21( f)={j4 )a ( f++ t/2 )|f|


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d ~s ( t)dt =

d

dt[A c e(j2) kf

t

m (3) d3)]

j 2) kfm (t)A c e(j2) kf

t

m (3) d3

)

~s1 (t)=j) + tA c a[1+ 2kfm ( t)+ t ]e(j2) kf

t

m (3) d3)

~s( t)

|~s1(t)|=) +ta A c[1+ 2kfm ( t)+t ](econd slope circuit

~

22 ( f)=~

21(f)=j)a (f++t/2 )

|~s2(t)|=) +ta A c[12kfm ( t)+t ]|~s1(t)||~s2( t)|=4 ) kfa A c m ( t)

|~s1(t)||~s2(t)|=4 ) kfa A c m ( t)

"alanced FM

)iscriminator

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WINSEM2014-15_CP3050_12-Feb-2015_RM01_angleModulation (1)