Frequency Modulation Transmission Bandwidth

Ask

A device with input x(t) & output y(t) is characterized by: y(t) = x^2(t). An FM signal with frequency deviation of 90kHz & modulating signal bandwidth of 5kHz is applied to this device. The bandwidth of the output signal is

(a) 370 kHz

(b) 190 kHz

(c) 380 kHz

(d) 95 kHz

Answer is (a)

Concept

To find the transmission bandwidth of an FM signal for non-sinusoidal modulation a factor called DEVIATION RATIO must be considered.

DEVIATION RATIO =  Ratio of maximum frequency deviation to the bandwidth of  message signal . $$D = \frac{\Delta f}{ W}$$

Thus, Transmission Bandwidth is given by : $$B_T = 2(D+1)W$$

This is  the Carson's Rule. There will be a slight modification for single -tone modulated FM Signal case and Sinusoidal FM Signal case.

So, on applying the Above Formula for the given problem:
As the output signal is squared, the frequency deviation is doubled to 180kHz

 DEVIATION RATIO = $\frac{180kHz}{5kHz}$ = 36

Bandwidth , $B_T = 2(36+1)5 = 370KHz$