Question:

Published on: 10 August, 2022

**Explain with proper expression**

**Modulation index****Bandwidth required for transmission of FM**

Answer:

The modulation index in AM wave is defined as the ratio between amplitude of the modulating signal and amplitude of the carrier signal. The mathematical representation is given below

μ = |A_{m} |/|A_{c} |

The modulation index is varied from 0 to 1 for proper communication. Depend on the value of modulation index the signal can be modulated as under modulation (value of μ is less than 1), hundred percent modulation (value of μ is unity) and over modulation (the modulated signal is phase reversal). At the over modulation, the signal will be distorted. Hence the message signal cannot be recovered from the modulated signal at the receiver. So for error less communication the value of modulation index should be bounded by 0 to 1.

The modulation index is defined as for the FM signal

β = (Frequency deviation/Modulating frequency)

The modulation index β is very important in FM because it decides the bandwidth of the FM wave. The modulation index also decides the number of sidebands having significant amplification.

According to the Carson’s thumb formula the bandwidth of the FM signal can be calculated. The FM bandwidth is given as twice the sum of the frequency deviation and the highest modulating frequency. However, it is the approximation rule to calculate FM bandwidth. The formula given below

BW = 2(∆f + f_{m})

Where ∆f if the frequency deviation and f_{m} is the maximum frequency component of the modulating signal.

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