7 phase modulation
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Chapter 4
Phase Modulation (PM)
Chapter 4 : Phase Modulation (PM)DEKC 3433 Communication Engineering
Faculty of Electrical Engineering 1
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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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