Question

Question 4:

A modulating signal m(t) = 0.8cos(200π t) is used to modulate a carrier signal givenby:c(t)=10cos(2π fct) fc >>100Hz

(a) Find the peak power of DSB and conventional AM signals

(b) Obtain the average power for DSB and conventional AM signals

Answer 1

Modulating signal (or) message signal

$m(t)=2cos(4000\pi t)+5cos(6000\pi t)$

$Carrier\space signal, c(t)=100cos(2\pi f_c t)$

$Given\space f_c=50k\space Hz$

$Am_1=2 \space Am_2=5 \space Ac=100 \space fm_1=2kHz \space fm_2=3kHz \space f_c=50kHz$

a) Conventional Am

$Message\space signal\space form\space m(t)=Am\space cos(2\pi f_mt)$

$Total\space modulation\space index\space \mu_t=\sqrt{\mu_1^2+\mu_2^2}$

$\mu_1=\frac{Am_1}{Ac}\space \mu_2=\frac{Am_2}{Ac}\space$

$\mu_1=\frac{2}{100} \space \mu_2=\frac{5}{100}$

$\mu_t=\sqrt{(0.02)^2+(0.05)^2}=0.05$