Angle Modulation

BYMuhammad Uzair

Rasheed2009-CPE-03

UCE&T BZU MULTAN

BYMuhammad Uzair

Rasheed2009-CPE-03

UCE&T BZU MULTAN

Contents

Properties of Angle (exponential) ModulationTypes

Phase Modulation Frequency Modulation

Properties

Angle Modulation: A non-linear process:-– Modulated wave does not look like message wave– Amplitude of an exponentially modulated wave is constant

Therefore, regardless of message signal the average transmitted power is

– It is less sensitive to noise

2

2

1cAP

Basic Concept

First introduced in 1931

A sinusoidal carrier signal is defined as: )]([cos)( ttAtc ccc

For un-modulated carrier signal the total instantaneous angle is:

)()( ttt ccc

Thus one can express c(t) as: ][Re)(cos)( )(tjccc

ceAtAtc

Thus: • Varying the frequency fc Frequency modulation• Varying the phase c Phase modulation

Basic Concept - Cont’d.

In angle modulation: Amplitude is constant, but angle varies (increases linearly) with time

t

Amplitude Ac

Initial phase c

Unmodulated carrier

Slope = c/t

t = 0

t(ms)

Unmodulated carrier

0

c(t) (red)

-/211/223/235/247/2

1 2 3 4

Phase-modulatedangle

Frequency-modulatedangle

20

-1

m(t)

Phase Modulation (PM)

PM is defined If 0180)()( ppc KtmKt

Thus )]([cos)( tmKtAtc pccPM

Where Kp is known as the phase modulation index

Ac

c(t)

c(t)

c(t)

i(t)

Instantaneous frequency

Rotating Phasor diagram

)()(

)( tdt

tdt cc

ci

Instantaneous phase )()( tmKt pi

Frequency Modulation (FM)

The instantaneous frequency is;

Where Kf is known as the frequency modulation index.

Note that )()( tmKt fc

)()( tmKt fci

Integrating )()( tt cci

0)()(0

t

fcc dttmKtt

Substituting c(t) in c(t) results in: ])([cos)(0t

fccFM dttmKtAtc

Instantaneous phase

Bandwidth of Angle modulation

• For FM:-

BmkB pfFM

822

1

BfBFM 22

2pfmkf

pfmk

Frequency deviation=

• Deviation Ratio:-

B

f

• Carson’s Rule:-

12 BBFM

Note : Deviation ratio is also called modulation

index

• For PM:-'pfmk

max' tmmp Where,

Now,

B

mkB ppPM 2

'2

THANKS