3.2 Frequency modulation

1.1 Terminology used in electronic communication system
1.2 Bandwidth of signals
1.3 Bandwidth of transmission medium
1.4 Earth's atmosphere

2.1 Propagation of electromagnetic waves in the atmosphere

3.1 Amplitude modulation
3.2 Frequency modulation
3.3 Necessity of modulation

In frequency modulation, the frequency of the carrier wave varies in accordance with the modulating signal. In frequency modulation, the amplitude of the modulated is same as that of the carrier wave.

The instantaneous frequency of the frequency modulated wave is, $$\upsilon (t) = {\upsilon _c} + k\frac{{{V_m}}}{{2\pi }}\sin {\omega _m}t$$

where, $k$ is the proportionality constant

The maximum and minimum values of the frequency is, $$\begin{equation} \begin{aligned} {\upsilon _{\max }} = {\upsilon _c} + \frac{{k{V_m}}}{{2\pi }} \\ \\ {\upsilon _{\min }} = {\upsilon _c} - \frac{{k{V_m}}}{{2\pi }} \\\end{aligned} \end{equation} $$

Frequency deviation, $$\delta = {\upsilon _{\max }} - {\upsilon _c} = \frac{{k{V_m}}}{{2\pi }}$$ or $$\delta = {\upsilon _c} - {\upsilon _{\min }} = \frac{{k{V_m}}}{{2\pi }}$$

Frequency modulation index $\left( {{\mu _f}} \right)$, $${\mu _f} = \frac{\delta }{{{\upsilon _m}}} = \frac{{k{V_m}}}{{2\pi {\upsilon _m}}}$$