Question #190191

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

Expert's answer

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"

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