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Chapter 4

Phase Modulation (PM)

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Introduction Phase Modulation is a system in which the phase of the carrier signal is

varied by the information signal

The amplitude of the carrier signal is kept constant

The phase (Φ) in the equation V = A cos (wct + Φ) is varied so that its

magnitude is proportional to instantaneous amplitude of the modulating

signal.

Phase differences between two waves are expressed in degrees. In

describing a wave, one full cycle equals 360 degrees.

Thus, if the two waves with the same amplitude and frequency whose

phase varies by 90 degrees are as shown in figure:

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The phase (Φ

) in the equation V = A cos (wct +Φ

) is varied so that itsmagnitude is proportional to instantaneous amplitude of the modulating

signal.

With PM, the maximum frequency deviation occurs during the zero

crossings of the modulating signal

That is, the f is proportional to the slope or first derivative of the

modulating signal.

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PM equation:

If the carrier signal is, vc(t) = Vc cos wc(t)

and Information signal vm(t) = Vm cos wm(t)

The expression for a PM wave is:

Vpm(t) = Vc cos (wct + Φ)

where

Φ  α  Vm(t)= k Vm cos wmt

giving, vpm(t) = Vc cos (wct + kVm cos wmt)

where kVm = ∆Φ  = mp

= is the maximum value of the phase

change introduced by this particular modulation signal and its

proportional to the maximum amplitude of the modulating signal.

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PM equation

The range for Φ is: -π < ∆Φ ≤ π

This value of ∆Φ is called the modulation index for PM, whichis denoted by mp.

So, the general equation for PM is,

Vpm (t) = Vc cos (wct + mp cos wmt)

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Comparison between PM and FM

The modulation index – is defined differently in each system.

In FM, its modulation index, mf = ∆f / f m

In PM, its modulation index, mp = ∆Φ = kVm

Note that Φ is a function of the amplitude of the modulating

signal (Vm

) only and is not a function of frequency of the

modulating signal (f m).

In PM, the phase deviation is proportional to the amplitude of

the modulating signal and is dependent of its frequency.

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In FM, the frequency is proportional to the amplitude

of the modulating signal, Vm, as well as its

frequency, fm.

When the frequency of the modulating signal, f m, is

change, the PM modulation index will remainconstant, whereas the FM modulation index will

change.

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