As already mentioned,
frequency modulation and phase modulation are very closely
related and may be termed as Angle modulation. However,
there exist some important differences between the two
that warrant this discussion.
The process of phase modulation consists
of varying the phase of the carrier linearly in proportion
to the modulating signal such that maximum phase shift
occurs during positive and negative peaks of the modulating
signal. If ec is taken to represent the instantaneous
value of the carrier, then
Where,
is the initial phase of the wave.
Let the modulating signal be e
= E sin
t.
If the carrier phase varies sinusoidal with the modulating
signal, then the phase modulated wave is represented
by
Assuming that initially
the
Equation representing the phase modulated
wave may be expanded in a way similar to FM. This expansion
gives:
Where (m)
is termed as the modulation index for phase modulation
and equals
.
The PM wave like FM
waves have identical frequency spectrum. In PM,
is given a fixed maximum value so that as the modulating
frequency Fm varies, frequency deviation
also varies and
remain constant. This is different from FM
where
is constant and can be given a large value. As signal
to noise station at the
receiver output depends
upon frequency deviation and not upon
, FM is preferred to PM. However, this gives an indirect
method of producing frequency modulated waves.
Phase Modulation Circuit
It should be remembered that FM and
PM are closely related and may be termed as angle modulation.
Because in both the cases, the changes in phase angle
as well as frequency of the modulated carrier take place.
Thus, consider a phase modulated wave given below:
Phase modulated wave
Where f(t) is the modulating signal.
The term under the bracket represents
the instantaneous phase angle
Instantaneous angular velocity
Equation shows that in a PM wave, the
frequency varies in proportion to the derivative of
the modulating signal.
Now consider a frequency modulated wave
given as,
Instantaneous angular velocity
The instantaneous phase
change
in the FM wave can be computed by integrating
the angular velocity
Where
is a constant of integration.
The instantaneous phase
angle in a frequency modulated wave varies directly
as the integral of the modulating signal.
An important conclusion
can be derived from the preceding discussion. If the
modulating signal f(t) is integrated before using it
to phase modulate a carrier, the result is an FM wave,
similarly, if the modulating signal is differentiated
before allowing it to frequency modulate a carrier,
the result is a PM wave. An important characteristic
of PM is that it does not require additional pre - emphasis
and de - emphasis like FM. Hence it may be considered
as an FM system with perfect pre - emphasis and de -
emphasis.
is the initial phase of the wave.
= E
the 
)
is termed as the modulation index for phase modulation
and equals
. 
also varies and
remain constant. This is different from FM
, FM is preferred to PM. However, this gives an indirect
method of producing frequency modulated waves.
is a constant of integration.