Q.An FM signal has a deviation of 10 kHz and a modulating frequency of 5kHz, calculate the modulation index.

These quantities describe how far and how deeply an FM carrier is pushed by the message.

The frequency deviation $\Delta f$ (also written $\delta$) is the maximum change of the carrier frequency from its centre value:

Crucially, the deviation is proportional to the amplitude of the modulating signal and is independent of the modulating frequency. The carrier swing (CS) is the total excursion from lowest to highest frequency:

The FM modulation index is the ratio of the frequency deviation to the modulating frequency:

It is a pure number (no unit) and, unlike the AM index, can be much greater than 1. For a fixed deviation, $m_f$ falls as the modulating frequency rises. …