Question

In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of ______.

Answer 1

Concept:

For a DSB-full carrier wave, the transmitted power is given by:

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

μ = Modulation index.

p_c = Carrier power.

The above expression can be written as:

\({P_t} = {P_c} + \frac{{{P_c}{\mu ^2}}}{2}\)

\(\frac{{{P_c}{\mu ^2}}}{2}\)= Sideband power.

Analysis:

For modulation index ‘μ₁’, the ratio of sideband to carrier power will be:

\(\frac{{{P_s}}}{{{P_c}}} = \frac{{{P_c}\mu _1^2}}{{2 \times {P_c}}} = \frac{{\mu _2^2}}{2}\)   ---(1)

For μ₂ = 2μ₁, the ratio will be:

\(\frac{{{P_s}}}{{{P_c}}} = \frac{{{P_c}\mu _2^2}}{{2 \times {P_c}}} = \frac{{\mu _2^2}}{2} = \frac{{4\mu _1^2}}{2}\)

\(\frac{{{P_s}}}{{{P_c}}} = 2\mu _1^2\)   ---(2)

Comparing Equations (1) and (2), we conclude that the ratio has increased by a factor of 4.