If the modulation index of an AM wave is changed from 0 to 1, the

SOLUTION

Concept:

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

Analysis:

When μ = 0, the transmitted power will be:

\({P_t} = {P_c}\left( {1 + \frac{{{0^2}}}{2}} \right)=P_c\)

When μ = 1, the transmitted power will be:

\({P_t} = {P_c}\left( {1 + \frac{{{1^2}}}{2}} \right)=\frac{3}{2}P_c\)

The % increase in the modulated signal power is given by:

\(=\rm \frac{{\frac{3}{2}{P_C} - {P_C}}}{{{P_C}}} \times 100\%\)

\(\rm = \frac{{\frac{1}{2}{P_C}}}{{{P_C}}} \times 100 = 50\%\)