# Frequency modulation

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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 $u_{in}$ is described by:

$u_{out} = sin(2 \pi (f_{carrier} + u_{in} \cdot \Delta f))$

where $\Delta f$ is the frequency deviation from the center frequency at $u_{in} = 1V$.

## Acquired bandwidth

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

$bandwidth = 2 \ (\Delta f + f_{m})$

## 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.