# Frequency Modulation

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## Frequency Modulation

In Frequency Modulation PDF the frequency of the carrier is varied in accordance with the instantaneous value of modulating signal. Here amplitude and phase are kept constant. The frequency modulation index is mostly over 1, and it usually requires a high bandwidth at a range of 200 kHz. FM operates in a very high-frequency range, normally between 88 to 108 Megahertz.

To generate a frequency-modulated (FM) signal, the frequency of the radio carrier is changed in line with the amplitude of the incoming audio signal. The frequency of the carrier is made to increase as the voltage in the information signal increases and to decrease in frequency as it reduces.

### Frequency Modulation Formula

The FM modulated signal is given by: y ( t ) = A cos ( 2 π f c t + k f ∫ t x ( α ) d α + φ 0 ) where A is the carrier amplitude, kf is the frequency deviation constant, and ϕ0 is the initial phase offset.

### Frequency Modulation Equations

It can be represented mathematically as;

m(t) = Am cos (ωmt + Ɵ) ……………… 1

m(t) → modulating signal

Where,

Am → Amplitude of the modulating signal.

ωm → Angular frequency of the modulating signal.

Ɵ → It is the phase of the modulating signal.

Same as amplitude modulation, when we try to modulate an input signal (information), we need a carrier wave, and we will experience

C(t) = Ac cos (ωct + Ɵ) ………….. 2

Angular modulation, which means ωc (or) Ɵ of the carrier wave, starts varying linearly with respect to the modulating signal, like amplitude modulation.