An audio signal is modulated by a carrier wave of 20 MHz such that the bandwidth required for modulation is 3 kHz. Could this wave be demodulated by a diode detector which has the values of R and C as (i) `R = 1 k Omega, C = 0.01 mu F (ii) R = 10 k Omega, C = 0.01 muF (iii) R = 10k Omega , C = 1 mu muF`.

Options

A. `R=1kOmega,C=0.01muE`
B. `R=10kOmega,C=0.01muF`
C. `R=10kOmega,C=0.1pF`
D. None of these

Answer

A

Explanation

`v_(c)=20MHz=20xx10^(6)Hz`
`(1)/(v_(c))=(1)/(20)xx10^(-6)=0.05xx10^(-6)=0.5xx10^(-7)s`
Band width =`20_(m)=3kHz=3xx10^(3)Hz`
`v_(m)=1.5xx10^(3)Hz`
`(1)/(v_(m))=(1)/(1.5)xx10^(-3)=0.7xx10^(-3)s`.
Diode detector can demodulate when
`(1)/(v_(c))ltltRCltlt(1)/(v_(m))`
(i)RC=`1kOmegaxx0.01muF=10^(3)xx(0.01xx10^(-6))=10^(-5)s`. it can be demodulated.
(ii) RC=`10kOmegaxx1xx10^(-8)=10^(-4)s` It can be demodulated
(iii) RC`=10kOmegaxx1pF=10^(4)xx10^(-12)=10^(-8)s`
It cannot be demodulated.