# 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 car

95 views
in General
closed
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 ______.

by (41.0k points)
selected

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.

pc = 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.