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Dr. Ahmed El-Mahdy COMM 601: Modulation I

COMM 601: Modulation I

Lecture 6

Angle Modulation: Frequency Modulation (FM)

Phase Modulation (PM)


Remember


Remember: Phase Shift


Angle Modulation


Angle Modulation

Radar


Angle Modulation

Carrier

Modulating

Signal

FM

PM


Angle Modulation The carrier signal is represented by:

tfAtc cc 2cos)(

frequencycarriertheis

amplitudecarriertheiswhere

c

c

f

A

Types of Angle Modulation

Phase Modulation

(PM)

Frequency Modulation

(FM)

Wide band FM Narrow band FM


Angle Modulation


Angle Modulation: Definitions

dt

td

dt

tdt

dt

tdf

dt

tdtf

ci

ci

)()()(:frequencyradian ousinstantaneThe

)(

2

1)(

2

1)(:frequencyousinstantaneThe -

)()(:phaseousinstantaneThe - ttt c

)(2

1)()()(

)(2(t)or)((t)

:bygiven isfrequency ousinstantane

theand phase ousinstantane ebetween th iprelationsh The-

00

tdt

dtfort

dt

dt

dttfdtt

ii

t

i

t

i


Angle Modulation: Definitions

(t)max:deviation phase Maximum

2

1maxΔdeviationfrequency Maximum

dt

(t)df

(t):deviation phase ousinstantane The

2

1 :deviationfrequency ousinstantane The

dt

(t)d


Phase Modulation Phase Modulation (PM): is that form of angle modulation

in which the instantaneous phase is varied linearly

with the message signal m(t) as: )(t

)()( tmktt pc

)](cos[

:bydomain in time described is signal modulated phase The

[volt].in signal modulating theis

[rad/volt]in modulator theof senstivity phase therepresents:where

tmktAs(t)

s(t)

m(t)

k

pcc

p


Phase Modulation Phase Modulation (PM):

)](cos[ tmktAs(t) pcc

The instantaneous phase deviation of the carrier

is proportional to the message amplitude.

)((t):deviation phase ousinstantane The tmkp

)(max(t)max:deviation phase Maximum tmkp


Frequency Modulation Frequency Modulation (FM): is that form of angle modulation in

which the instantaneous frequency is varied linearly with

the message signal m(t) as:

)(tfi

)()( tmkftf fci

])(2cos[

:bydomain in time described is signal modulatedfrequency The

)(2)(

:bygiven is phase ousinstantane theFM,In

[volt].in signal modulating the is

[Hz/volt]in modulator theof senstivityfrequency the represents:where

0

0

dmktAs(t)

s(t)

dmktt

m(t)

k

t

fcc

t

fc

f


Frequency Modulation Frequency Modulation (FM):

])(2cos[0

dmktAs(t)

t

fcc

The instantaneous frequency deviation of the carrier

is proportional to the message amplitude.

tmk

dt

dmkd

dt

td

f

t

f

0

2

2

1

2

1deviationfrequency ousinstantane The


Frequency Modulation

Maximum frequency deviation represents the maximum

of the instantaneous frequency of the FM signal

from the carrier frequency.

max

2

1maxdeviationfrequency Maximum

m(t)k

dt

(t)df

f


Properties of Frequency Modulation

-As the modulating signal amplitude increases, the

carrier frequency increases and vise versa.

-Maximum frequency deviation is the maximum

change in the carrier frequency produced by the

modulating signal.

-The Maximum frequency deviation is proportional

to the amplitude of the modulating signal.


Example:

tfAtm mm 2cos)(

- The PM signal is given by:

]2coscos[

)](cos[

tfAktA

tmktAs(t)

mmpcc

pcc

For a sinusoidal modulating signal defined by:

Find: - The modulated PM signal

- The instantaneous phase and the instantaneous angular

frequency of PM signal

- The instantaneous phase:

tfAktt mmpc 2cos)(

- The instantaneous frequency:

)sin()(

)( tkAdt

tdt mpmmci


FM with Single Tone Modulating Signal

tfff

tfAkftf

mc

mmfci

2cos

2cos)(

Consider a sinusoidal modulating signal defined by:

tfAtm mm 2cos)(

The instantaneous frequency of the FM signal is given by:

where mf Akf is the maximum frequency deviation

The FM signal is given by:

)1(]sincos[

]sincos[

ttA

tf

ftAs(t)

mcc

m

m

cc

t

fcc dmktAt)s0

])(2cos[(



carrier. dunmodulate

theof2 angle thefrom (t) angle theof )(departuredeviation

maximum theis, that signal, FM theofdeviation phase

maximum therepresents parameter the(1), from ,Physically

signal. FM theofindex modulation theis

where

ctf

fβΔff

Δfβ m

m

)1(]sincos[ ttAs(t) mcc


PM with Single Tone Modulating Signal

rad.in measured signal PM ofindex modulation theiswhere

][

]coscos[

]coscos[

:isPMinsignalmodulating

theandsignalPMfor valiedis analysis sameThe

radAk

ttA

tAktAs(t)

mp

mcc

mmpcc



Depending on the value of the modulation index we have

two cases of frequency modulation

Narrowband FM

Wideband FM

1 1

Now, We need to investigate the bandwidth of FM


Narrowband FM (NBFM)


Narrowband FM (NBFM)

Which is similar to the AM signal which is given by:

The difference between the two equations (AM & NBFM) is the –ve

sign in the last term. Thus the NBFM requires the same transmission

bandwidth as AM. The transmission bandwidth of the NBFM

is similar to the AM

mfBT 2

since


Generation of Narrowband FM

tfAtm mm 2cos)(

tf

Adm m

m

m

sin2

)(

)sin(sin2

ttf

kAAcm

m

fmc

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