Question

A DSB modulated signal x(t)=Am(t)cos(2$\pi f_{c}t$) is mixed (multiplied) with a local carrier $x_L\left(t\right)=cos(2\pi f_{c}t+\frac{\pi }{4})$and the output is passed through a LPF with a bandwidth equal to bandwidth of the message m(t). if the power of the signal at the output of the low pass filter is $P_{out}$ and the power of the modulated signal by $P_{\mu },the\frac{P_{out}}{P_{\mu }}isequalto$____.

• A. 0.25

Answer 1

The correct option is A 0.25
The out put with phase distoration is equal to
$y_o\left(t\right)=\frac{A}{2}m\left(t\right)cos\theta P_{out}=\frac{A^2{P}_m}{2}co{s}^2\theta andpowerofmodulatedsignal,P_m=\frac{A^2}{2}{P}_m\frac{P_{out}}{P_{\mu }}=\frac{\frac{A^2{P}_m}{4}co{s}^2\theta }{\frac{A^2}{2}{P}_m}=\frac{co{s}^2\theta }{2}Now,\theta =\frac{1}{4},\frac{P_{out}}{P_{\mu }}=\frac{1}{4}=0.25$