A carrier is modulated to a depth of 40%. The percentage increase in the transmitted power is

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 the carrier is not modulated, i.e. modulation index = 0, the transmitted power is the carrier power only, i.e.

P_t = P_C

When modulated with a modulation index of 40%, the total power is calculated as:

\({P_t} = {P_c}\left( {1 + \frac{{{0.4^2}}}{2}} \right)\)

The percentage increase in power will be:

\(=\frac{{P_c}\left( {1 + \frac{{{0.4^2}}}{2}} \right)-P_c}{P_c}\times 100\)

\(=\frac{0.4^2}{2}\times 100~\%\)

 = 8 %