# Numerical - Depth of Modulation/ Modulation Index

## Calculate the depth of modulation when a transmitter radiates a signal of 9.8KW after modulation and 8KW without modulation of the signal.

a.) 80%

b.) 67%

c.) 50%

d.) 100%

Correct Answer: 67%

**Explanation:**

P_{total }= 9.8KW

P_{c} = 8KW

Power of the signal (P_{total}) transmitted by a transmitter after modulation is given by

P_{total} = P_{c} (1+ m^{2}/2)

Where P_{c }is the power of carrier i.e., without modulation

M is the modulation index

Therefore,

9.8= 8(1+ m^{2}/2)

9.8/8=1+ m^{2}/2

m=0.67 = 67%