Calculation of bandwidth in FM using Carson’s rule

Q.  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.
- Published on 14 Oct 15

a. 1 KHz
b. 50 KHz
c. 102 KHz
d. 150 KHz

ANSWER: 102 KHz
 
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

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