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Question

# An angle modulated signal with carrier frequency fc is given by, s(t)=Accos[2πfct+5sin(3000πt)+10sin(2000πt)] The bandwidth (using Carson's rule) of the signal s(t) will be

A
38 kHz
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B
42 kHz
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C
28 kHz
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D
33 kHz
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Solution

## The correct option is A 38 kHz θ(t)=2πfct+5sin(3000πt)+10sin(2000πt) ft=12πdθ(t)dt=fc+7500cos(3000πt)+10000cos(2000πt) So, Δf=7500+10000=17.5 kHz fm(max) = 1500 Hz = 1.5 kHz Deviation ratio, D=Δffm(max)=17.51.5=353 Bandwidth, BW=(1+D)2fm(max)=(1+353)(3) kHz=38 kHz

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