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# Frequency Modulation

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 Sub Topics To transmit the information bearing signals like audio or video signal or digital data is difficult if it is not so effective.Information bearing signals like sound signals generally will be of low frequency and due to less energy they cannot travel long distance. The modulation process creates the modulated wave that contains the information signal which will be more effective and hence it travels along. There are three types of modulation used in communicationAmplitude modulation (AM)Frequency modulation (FM)Phase modulation (PM)Lets see more about the frequency modulation in this section.

## Definition

The audio or video signal transmitted are not so effective sometimes that may end up with a loss of information. Here is a technique known as frequency modulation that gives the better signal quality even more better than in amplitude modulation even though it's bit expensive. It is a technique where the amplitude of the carrier wave is held constant and its frequency is changed by the modulating signal.

## How Frequency Modulation Works?

In frequency modulation (FM), the information signal modulates the frequency of the carrier signal. As the amplitude of the information signal increases, the frequency of the carrier signal increases. Similarly, as the amplitude of the information signal decreases the frequency of the carrier signal decreases.The Maximum frequency of the modulated signal occurs when the amplitude of the modulating signal reaches its maximum value. When the modulating signal becomes negative, the frequency of the carrier will decrease and will continue to decrease till the modulating signal reaches its negative maximum value.

Frequency modulation

## Equation

The general equation of an unmodulated wave or carrier wave is given by
y = A sin ($\omega$ t + $\phi$)
Where y = instantaneous value of current or voltage
A = maximum amplitude
$\omega$ = Angular velocity in radians per sec
$\phi$ = phase angle in radians
$\omega_t$ = angle in radians

The instantaneous frequency f of the frequency modulated wave is given by
f = fc (1 + k vm cos $\omega_m$ t)
Where fc = unmodulated carrier frequency
k = a constant
Vm cos $\omega_m$ t = instantaneous modulating voltage

The maximum deviation for the signal takes place when cosine term has its maximum value i.e., $\pm$ 1. The instantaneous frequency will be
f = fc (1 $\pm$ kvm)

Hence the maximum deviation $\delta$ will be
$\delta$ = k Vm fc
The instantaneous amplitude of the FM signal is given by
V = A sin[F(\omega_c + \omega_m)] = A sin $\theta$
We have $\theta$ = $\omega_c$ t + $\frac{\delta}{f_m}$ sin $\omega_m$ t

Hence the frequency modulation equation is
V = A sin[$\omega_c$ t + $\frac{\delta}{f_m}$ sin $\omega_m$ t]Hence the equation.

## Spectrum

The frequency modulation spectrum of the FM wave is given by
V = A [ Jo mf sin $\omega_c$ t + J1 mf { sin ( $\omega_c$ + $\omega_m$)t - sin ( $\omega_c$ - $\omega_m$ )t} + J2 mf { sin ( $\omega_c + 2 \omega_m$ )t - sin( $\omega_c - 2\omega_m$ )t} + J3 mf { sin ($\omega_c + 3 \omega_m$)t - sin($\omega_c - 3 \omega_m$)t} + J4 mf { sin ($\omega_c + 4 \omega_m$ )t - sin( $\omega_c - 4 \omega_m)t$} + ........Where Jo, J1, ...... are the bessel functions.

## Circuit

For the frequency modulation. You need to built up the circuit as below:

It consists of resistor, diode, inductor and capacitor. Here input voltage Vin varies as reverse biased junction capacitance value. As the capacitance changes each time, the resonant frequency of the diode capacitance or inductor will change which act as a resonator in an oscillator present in the circuit.

## Spectroscopy

This variation in carrier frequency is known as "deviation". It is expressed in kHz per Volt.The deviation of a carrier in frequency is directly proportional to the audio modulating signal's loudness. The frequency deviation ($\Delta$ f) gives the measure of how much maximum instantaneous difference is there between a frequency modulated signal and the carrier frequency. It is often mistaken with frequency drift, which is entirely a different concept.
Frequency deviation ($\Delta$ f) of an FM waveform is the measure of the amount by which the modulating signal deviates the frequency of the carrier from its rest frequency. It is given as
$\Delta$ f = $f_{\Delta}$ Vm
$f_{\Delta}$ is the frequency deviation constant.