Explain the working principle of envelope detector with waveform. For the same, calculate the charging and discharging time for source resistance rs=5ks2, the rc filters values are 10kc2 and 1 onf respectively.
Answers
The formula is derived from practical experiences and not from mathematical 1st principles. It is unprovable other than by being practical and thinking what a diode detector has to achieve.
Firstly, the formula states that RC has to be equal to or greater than 1ωc.
If the RC time constant were too short there would be significant levels (ripple) of the carrier frequency on the output - this is not what is wanted from a diode detector (or an AC rectifier in a power supply) BUT, it's never going to be a perfect brick wall filter and so carrier ripple has to be acceptable (to some degree).
Personally, I would like to see the RC time constant 5 times greater than 1ωc
At the other end of the scale, RC cannot be too big or it will start to significantly attenuate high frequencies in the "detected" analogue waveform that is represented by 1ωm.