In an AM system, the modulating signal is a sinusoid with frequen
| In an AM system, the modulating signal is a sinusoid with frequency of fm Hz. If 80% modulation is used, then the ratio of total side-band power in the modulated signal, to the total power is:
A. 0.15
B. 0.24
C. 0.31
D. 0.5
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept:
Total power is given by:
\({P_t} = {P_c} + {P_s} = \frac{1}{2}\left( {1 + \frac{{{m^2}}}{2}} \right){A^2}\)
\(\Rightarrow Ratio = \frac{{Sideband\;power}}{{Total\;power}} = \frac{{\frac{1}{4}{A^2}{m^2}}}{{\frac{1}{4}\left( {2 + {m^2}} \right){A^2}}} = \frac{{{m^2}}}{{2 + {m^2}}}\)
Calculation:
Given, m = 0.8
\(So,\;\frac{{{P_s}}}{{{P_t}}} = \frac{{{{\left( {0.8} \right)}^2}}}{{2 + {{\left( {0.8} \right)}^2}}} = \frac{{0.64}}{{2 + 0.64}} = \frac{{0.64}}{{2.64}} = 0.242\)