Frequency Modulation (FM)
The frequency modulation (FM) is a type of angle modulation in which the instantaneous frequency fi(t) is varied in linear proportion with the instantaneous magnitude of the message signal x (t).
The mathematical expression for FM is as follows:
In this expression fc denotes the frequency of unmodulated carrier and the constant kf represents the frequency sensitivity of the modulator. Its units are Hz/ volt, assuming the message signal to be a voltage signal.
Since the instantaneous frequency fi(t) of FM is changing continuously with time, we have to take the integration of x (t) over a duration of 0 to t.
Now we can write the expression of θ (t) for FM.
The expression for θ (t) of FM wave is given by:
Mathematical Expression for FM
We can use θ (t) to write the expression for FM in time domain as under:
Relationship between FM and PM
The expressions for the FM and PM waves in the time domain are given by:
Generation of FM Using Phase Modulator
Comparing the above expressions, we can conclude that an FM wave is actually a PM wave having a modulating signal
This means that we can generate FM wave by applying the integrated version of x (t) to a phase modulator as shown in figure 1 below.
Fig. 1: Generation of FM using Phase Modulator
Sharma, Dr Sanjay. Analog Communication Systems (Page 290). . Kindle Edition.