# Carson’s rule, Frequency Modulation

## According to Carson’s rule, Bandwidth B and modulating frequency f_{m} are related as

**Options:**

B=2(Δf +f_{m}) Hz

B= f_{m} Hz

B< 2f_{m} Hz

B> 2f_{m} Hz

Correct Answer: B=2(Δf +f_{m}) Hz

**Explanation: **

According to Carson’s rule, the bandwidth required to transmit an angle modulated wave is twice the sum of the maximum frequency deviation and the maximum modulating signal frequency. Or,

B=2(Δf +f_{m}) Hz.

## What is the change in the bandwidth of the signal in FM when the modulating frequency increases from 12 KHz to 24KHz?

**Options:**

40 Hz

58 Hz

24Hz

Bandwidth remains unaffected

Correct Answer: 24Hz

**Explanation: **

According to Carson’s rule, the bandwidth required is twice the sum of the maximum frequency deviation and the maximum modulating signal frequency. Or,

B=2(Δf +f_{m}) Hz

B= 2(Δf +12) Hz = 2 Δf + 24 Hz……(1)

Assuming Δf to be constant,

B’= 2 Δf + 48 Hz……… (2)

(2)-(1),

= 24Hz

Therefore the bandwidth changes by 24Hz.