# FM - Frequency Modulation

Frequency Modulation is the process in which the frequency of the carrier signal is varied by the modulating signal while the amplitude remains constant.

The big advantage of frequency modulation is its noise reduction ability, because most of noise is appeared as additional amplitude and in FM the amplitude of signal is hold fixed.

If the un-modulated carrier signal is represented by A sin2pf t and the modulating signal is represented by B sin2pfa t.

Then the carrier frequency  “f”  will be changed around the resulting frequency  fc thus

f = fc + Df Sin2pfa t.

The voltage of the frequency modulated signal is represented by

V = A sin[2p(fc + Df Sin2pfa t)t]

Df = frequency change (deviation)

Total variation from lowest to the heights is called carrier swing.

So carrier swing = 2 x Df

Making use of calculus, equation for the frequency modulated signal can be written as

V = A Sin [2pfc t + Df/fa) Cos2pfa t]

Df/fa = mf = modulation index

The carrier signal, modulating signal and modulated signal are shown in the below fig.