What is Phase Modulation

Phase Modulation (PM)

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Phase modulation is a type of angle modulation in which the angular argument θ(t) is changed in linear proportion with the instantaneous magnitude of the message signal x(t).

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Mathematically, For PM, 

Here, it may be noted that the first term in the above expression i.e., 2πfct represents the angular argument of the unmodulated carrier (i.e., when x (t) = 0).

Whereas the second term kp x (t) represents the proportional phase change, because kp is the phase sensitivity in radians per volt.

x (t) is the message signal which is assumed to be a voltage signal.

The value of fc i.e., θ(t) at t = 0 has been assumed to be equal to zero for the sake of convenience.

Mathematical Expression for PM

A phase modulated can be mathematically expressed in time domain as follows:

Substituting the expression for θ(t), we get,

PM Wave :

This expression shows that the PM wave has a constant amplitude equal to that of the carrier but the phase shift is a function of x (t).

We can also note that there is a proportional change in frequency associated with the phase change.