What is the frequency deviation formula?

Hint:Frequency deviation is a concept in frequency modulation (FM) to describe the difference between the two frequency extremes of the frequency modulated signal and the carrier signal. Frequency Modulation (FM) of a signal is a methodology of signal transmission where the information signal is encoded on the carrier wave. The frequency of the carrier wave is modified in accordance with the amplitude of the information signal while the amplitude is kept constant.

Complete step by step solution:
The carrier wave is like a vehicle for the transport of information signals from sender to receiver. The information signal is converted to electrical and then modulated to the carrier wave. This frequency modulated signal’s instantaneous frequency changes with time around the carrier frequency. This indicates that the FM signal’s immediate frequency varies depending on the modulating signal.

Frequency deviation is the maximum change in instantaneous frequency from the average frequency. The frequency deviation of radio is of particular importance in relation to bandwidth because less deviation means that more channels can fit into the same amount of frequency spectrum.

Standard expression for baseband FM signal is given by:
\[x\left( t \right){\rm{ }} = {\rm{ }}A{\rm{ }}cos{\rm{ }}({\rm{ }}{\omega _c}t{\rm{ }} + {\rm{ }}{m_f}{\rm{ }}sin{\rm{ }}{\omega _m}t)\]----- (1)
Where \[{\omega _c}\]= carrier frequency, \[{\omega _m}\]= modulating signal frequency, \[{m_f}\]= modulation index and A = amplitude
The frequency deviation,\[\Delta f\] is related as,
\[\Delta f = {m_f}x(t)\]----- (2)
Maximum frequency deviation is,
\[\Delta f = {m_f}{f_m}\]
where \[{f_m} = {\omega _m}/2\pi \]----- (3)
For the case of tone (single frequency) modulation, frequency deviation is:
\[\Delta f = {m_f}{A_m}\]------- (4)
where \[{A_m}\]= amplitude of the modulating signal

Note: Tone modulation is a special case of frequency modulation in which modulation is carried out by a single frequency (tone) signal. In that case, there is some minor change in the standard expression of the baseband signal combining the information and the carrier wave.