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An audio signal given by e_(s)=15sin 2pi(2000t) modulates a carrier wave given by e_(s)=60sin 2pi (100,000t). If calculate (a) Percentage modulation (b) Frequency spectrum of the modulated wave. |
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Answer» Solution :(a) Signal AMPLITUDE, `B=15` Carrier amplitude, `A=60""m=B/A=(15)/(60)=0.25` `:.` 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)sin 2pif_(s)t` and `e_(C)=E_(c)sin omega_(c)t=E_(c)sin2pi f_(c)t` we have signal frequency `f_(s)=2000Hz` and carrier frequency `f_(c)=100,000` Hz The frequencies present in modulated wave (i) `f_(c)=100,000` Hz = 100 kHz (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 98kHz to 102 kHz is called band width. |
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