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An audio signal by e_(S)=15 sin 2pi (2000t) modulates a carrier wave given by e_(C)=60sin 2pi(100,000)t. Calculate (a)the percentage modulation (b) frequency spectrum of the modulated wave. |
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Answer» Solution :a)Signla Amplitude ,B=15,Carrier amplitude, A=60 `m=(B)/(A)=(15)/(10)=0.25` `therefore ` PERCENTAGE modulation =`0.25xx100=25%` b)By comparing the given EQUATIONS of signal and carrier with their standard FORM `e_(S)=E_(s)sin omega_(s)t=E_(S)sin2pi f_(S)t` and `e_(C)=E_(C)sin omega_(C)t=E_(C)sin 2pif_(c)t` We have signal frequency `f_(s)`=2000 Hz and carrier frequency `f_(C)`=100,00 Hz The frequencies present in modulated wave i) `f_(c)`=100,000 Hz=100kHz ii) `f_(c)-f_(s)`=100,000-2000 =98 kHz iii)`f_(c)+f_(s)`=100 kHz+2kHz=102 kHz Therefore,frequency spectrum of modulated wave extends from 98 kHz to 102 kHz (This is CALLED band width.) |
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