Question

An envelope detector with ideal diode is used to detect an AM wave, whose carrier frequency is 1 MHz and the message signal is band limited to 5 kHz. Which set of the following values of R and C is best suitable to design this envelope detector?

• A. $R=20M\Omega andC=20pF$
• B. $R=20M\Omega andC=10pF$
• C. $R=1M\Omega andC=20pF$
• D. $R=100k\Omega andC=10pF$

Answer 1

The correct option is C

$R=1M\Omega andC=20pF$

For a distortion free detection, the time constant (RC) of an envelope detector should satisfy the following condition:

$\frac{1}{f_c}<<RC<<\frac{1}{f_{m(max)}}$
Given

$f_c=1MHzand{f}_{m(max)}=5kHz$

So, $1\mu s<<RC<<200\mu s$

For option "a"$\Rightarrow RC=100\times {10}^3\times 10\times {10}^{-12}=1\mu s$

For option "b"$\Rightarrow RC=20\times {10}^6\times 10\times {10}^{-12}=200\mu s$

For option "c"$\Rightarrow RC=20\times {10}^6\times 20\times {10}^{-12}=400\mu s$

For option "d"$\Rightarrow RC=1\times {10}^6\times 20\times {10}^{-12}=20\mu s$

So, the values given in option "d" are best suitable.