# Calculation of Modulation index and Maximum frequency deviation in FM wave

## For a FM signal v(t) = 25 cos ( 15* 10^{8}t + 10 sin 1550t), calculate

Modulation index

Maximum frequency deviation

**Options:**

a) 10, 3000.1Hz

b) 20, 1550.9Hz

c) 10, 2465.9Hz

d) 10, 2000.0Hz

Correct Answer: c) 10, 2465.9Hz

**Explanation:**

Standard expression for FM signal is given by

v(t) = A cos ( ω_{c}t + mf sin ω_{m}t)

Comparing with the given equation,

Modulation index m_{f} = 10

Maximum frequency deviation is given by

m_{f} = Δf/f_{m}

Δf = m_{f} * f_{m}

Here f_{m} = 1550/2Π = 246.59 Hz

Δf = 10* 246.59

= 2465.9Hz