# Frequency Modulation

Frequency Modulation is a Modulation Scheme where the incoming signal modulates the frequency of the Carrier Signal by a tiny fraction. Used e.g. in FM Radio.

A variation of Frequency Modulation is sometimes also used for digital Transmissions, this is then called Frequency Shift Keying or FSK-Modulation.

## Visualisation

it would be nice to have a gnuplot picture here, is it possible to upload the gnuplot script for toying, too?

## 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 $u_{in} = 1V$.

## Aquired Bandwidth

...can be determined using Carson's Bandwidth Rule: two times sum of the peak deviation $\Delta f$ from the highest frequency occuring in the spectrum of the modulating signal $(f_m)$:

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

## Noise Immunity

is higher than the one of Amplitude Modulation Schemes since athmospheric disturbances and noise usually don't shift the frequency of a signal but add their contribution to the amplitude of the transmitted signal. Amplitude variations don't affect FM much.