# Define Modulation Index,Frequency Deviation and Percent Modulation For FM Wave

## Modulation Index of FM Wave

The modulation index of an FM wave is defined as under:

The modulation index (m_{f}) is very important in FM as it decides the bandwidth of the FM wave . The modulation index also decides the number of side bands having significant amplitudes. In AM, the maximum value of the modulation index m is 1. But, for FM, the modulation index can be greater than 1.

## Frequency Deviation (Δf) of FM Wave

For the single tone FM i.e., the modulating signal x(t) be a sinusoidal signal of amplitude E_{m} and frequency f_{m}.

Therefore,

The unmodulated carrier is represented by the expression:

In FM, the frequency f of the FM wave varies in accordance with the modulating voltage. Thus,

Where, Δf = k_{f} E_{m }and it is called as frequency deviation.

Frequency deviation (Δf) represents the maximum departure of the instantaneous frequency f_{i}(t) of the FM wave from the carrier frequency f_{c}.

Since Δf = k_{f} E_{m ,} the frequency deviation is proportional to the amplitude of modulating voltage (E_{m}) and it is independent of the modulating frequency f_{m}.

## Percent Modulation of FM Wave

The percent modulation is defined as the ratio of the actual frequency deviation produced by the modulating signal to the maximum allowable frequency deviation.

Thus,