Q.Determine the modulation index of an FM carrier having a frequency deviation of 25 kHz and a modulating signal of 5 kHz. Also determine the carrier swing.

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. …