Calculation of bandwidth in FM using Carson’s rule

What is the required bandwidth according to the Carson’s rule, when a 100 MHz carrier is modulated with a sinusoidal signal at 1KHz, the maximum frequency deviation being 50 KHz.

Options:

(a) 1 KHz
(b) 50 KHz
(c) 102 KHz
(d) 150 KHz

Correct Answer: 102 KHz

Explanation:

According to Carson’s rule, bandwidth of FM is given by 2(Δf+ fm) where Δf is the deviation in frequency and fm is the frequency of sinusoidal signal. The required bandwidth is therefore calculated as
2* (50KHz + 1KHz)
= 2 * 51 KHz
= 102 KHz