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 <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.

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