Question

Calculate the modulation index of an FM signal in which the modulation frequency is $2kHz$ and maximum deviation is $10kHz$
A) 5
B) 6
C) 7
D) 8

Answer 1

The FM deviation ratio can be defined as: the ratio of the maximum carrier frequency deviation to the highest audio modulating frequency.
And accordingly, Frequency deviation: $f\Delta$ is the maximum difference between nominal carrier frequency and an FM modulated frequency.

Complete step by step answer:
There are two main classifications for frequency modulated signals and these can be related to the modulation index and deviation ratio.
Frequency modulation Index: Frequency modulation index means; the modulation index indicates by how much the modulated variable varies around its unmodulated level. It has relation with the carrier frequency:
FM deviation ration: One of the issues with the modulation index is that it will vary according to the instantaneous values of deviation and modulating frequency.
On typical audio transmissions, both the frequency deviation and modulating frequency will vary. The frequency deviation will vary according to the level of the audio at that moment. Also, the modulating frequency will vary as normal audio consists of a variety of frequencies, which vary to give the speech or music, etc.
For many applications it is more useful to have a figure for the maximum permissible values

m = (Max frequency deviation)/(Max modulation frequency)

Given:
Maximum frequency of deviation: ${f_{\Delta \max }} = 10kHz$
Maximum frequency of modulation: ${f_m} = 2kHz$
Putting given values in above equation:
$m = \dfrac{{{f_{\Delta \max }}}}{{{f_m}}}$
$m = \dfrac{{10}}{2} = 5khz$
Hence, option A is correct.

Note: The bandwidth of the FM signal is particularly important because it needs to be wide enough to carry the information correctly, whilst also not occupying too much spectrum. If the bandwidth is too wide, then it can spread outside the required channel and cause interference with other users on other channels.
The wide bandwidth of wide band FM enables high quality broadcast transmissions to be made, combining a wide frequency response with low noise levels. Once the signal is sufficiently strong, the audio signal to noise ratio is very good.