Correct Answer - Option 1 : 7.4%
Concept:
The generalized AM expression is represented as:
s(t) = Ac [1 + μa mn (t)] cos ωc t
The total transmitted power for an AM system is given by:
\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)
Pc = Carrier Power
μ = Modulation Index
The above expression can be expanded to get:
\({P_t} = {P_c} + P_c\frac{{{μ^2}}}{2}\)
The total power is the sum of the carrier power and the sideband power, i.e.
\({P_s} = P_c\frac{{{μ^2}}}{2}\)
Analysis:
Total sideband power is calculated as:
\({P_s} = P_c\frac{{{μ^2}}}{2}\)
% of sideband power is given as:
⇒ \( \frac{P_c \frac{μ^2}{2}}{{P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)}\)
⇒ \( \frac{μ^2}{μ^2+2}\)
putting μ = 0.4, we get
⇒ \( \frac{0.4^2}{0.4^2\;+\;2} \times 100 = 0.074 \times 100\)
= 7.4 %
