# Frequency modulation

**Frequency modulation** (**FM**) is an analog modulation scheme where the signal modulates the frequency of the carrier signal by a tiny fraction. It is used in FM radio.

The digital equivalent is frequency shift keying (FSK).

## Mathematical setting

The output voltage of a FM modulator with input voltage <math>u_{in}</math> is described by:

- <math>u_{out} = sin(2 \pi (f_{carrier} + u_{in} \cdot \Delta f))</math>

where <math>\Delta f</math> is the frequency deviation from the center frequency at <math>u_{in} = 1V</math>.

## Acquired bandwidth

Acquired bandwidth can be determined using Carson's bandwidth rule: two times the sum of the peak deviation <math>\Delta f</math> from the highest frequency occurring in the spectrum of the modulating signal <math>(f_m)</math>:

- <math>bandwidth = 2 \ (\Delta f + f_{m})</math>

## Noise immunity

Noise immunity is higher than amplitude modulation because noise does not shift the frequency of a signal, but adds to it with the superposition principle.

## External links

- History of radio at Wikipedia
- Frequency modulation at Wikipedia