Question

What is the modulation factor on FM transmission?

Answer 1

The modulation index for AM is equivalent to the frequency modulation index but obviously related to FM. The difference between the two forms of modulation, the FM modulation index, is measured in a different way. The ratio of the amplitude of the line-to-neutral inverter output voltage to one-half of the available DC bus voltage as defined by the Modulation Index.

Complete step-by-step solution:
Frequency Modulation:
The frequency of the carrier signal is varied proportional to the Amplitude of the input modulating signal that is called the frequency of modulation and the input is a single tone sine wave.
Frequency Modulation Equation:
$v = A{\text{ }}sin\left[ {wct + \left( {\dfrac{{\Delta f}}{{fm}}} \right){\text{ }}sin{\text{ }}wmt} \right]$
$= A{\text{ }}sin{\text{ }}\left[ {{\text{ }}wct{\text{ }} + {\text{ }}mf{\text{ }}sin{\text{ }}wmt{\text{ }}} \right]$
Where,
A$$$$ = The amplitude of the FM signal
\Delta f$$$$ = Frequency deviation
mf$$$$ = Modulation Index of FM
$mf = \dfrac{{\Delta f}}{{fm}}$
$wm = 2\pi {\text{ }}fm{\text{ }}wc = 2\pi {\text{ }}fc$
The Modulation Index of Frequency Modulation:
The ratio of the frequency deviation of the carrier to the frequency of the modulating signal is defined as the modulation index of FM.
mf$$$$ = Modulation Index of FM$=$ $\dfrac{{\Delta f}}{{fm}}$
From the above formula and definition of the modulation index, it can be seen that there is no term that includes the carrier frequency and this means that it is totally independent of the carrier frequency.

Note: The FM transmitters use a maximum modulation index of about$5.0$, so the resulting bandwidth is $180kHz$.
The ratio of the amplitude to the frequency of the modulating signal because the strength of the sidebands depends on the modulation index.
The amplitude of the modulating signal equals the maximum frequency deviation $\Delta f$ of the resulting wave.