Question

$\text{An amplitude modulated signal is given by,}s\left(t\right)=[20+2cos(3000\pi t)+10cos(6000\pi t\left)\right]cos\left(2\pi f_{c}t\right)V\text{The ratio of the power in sidebands to the power in carrier component is}$

• A. $0.26$
• B. $0.52$
• C. $0.13$
• D. $0.065$

Answer 1

The correct option is C $0.13$

${\mu }_1=\frac{2}{20}=\frac{1}{10}\text{and}{\mu }_2=\frac{10}{20}=\frac{1}{2}\mu =\sqrt{{\mu }_1^2+{\mu }_2^2}{\mu }^2={\left(\frac{1}{10}\right)}^2+{\left(\frac{1}{2}\right)}^2=\frac{1}{100}+\frac{1}{4}=\frac{26}{100}=0.26P_{SB}=P_c\frac{{\mu }^2}{2}\frac{P_{SB}}{P_c}=\frac{{\mu }^2}{2}=\frac{0.26}{2}=0.13$