Question

A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100000ohm.Find the maximum modulated frequency which would be detected
Answer is10.62k Hz
Plz solve the problem in easy method

Answer 1

Diode detector for AM signal: 
     this is a low pass filter, removing the carrier frequency and giving back the envelope.

     In a diode (tunnel diode) detector for amplitude modulation, we use a diode in series with the AM signal.  Then to the output of the diode, a parallel combination of a resistor R and a capacitor (condenser) C  are connected.  The other end of R and C are grounded.
     The voltage or current signal at the R and C is the envelope of the modulated signal, which is the demodulated message (audio) signal.

     ω_c = carrier frequency (angular)  = 2 π f_c
     ω_m = audio signal frequency  (angular) = 2 π f_m

We choose RC time constant such that :
        ω_c > 1/RC  > ω_m
         f_c  >  1/(2πRC)  > f_m
         f_c >  1/(2π*250*10⁻¹² * 10⁵)    >  f_m
         f_c  >  6366.2 Hz > f_m

If the input signal is modulated to 100%  (amplitude of the modulating audio signal divided by carrier amplitude), then the above are the limiting frequencies.

 If the AM signal is modulated by a modulating factor = mf  < 1, then

         f_c >  1/(2πRC)  * 1/mf  > f_m
         f_c > 6, 366.2 *  100/60  > f_m
           f_c  >  10, 610.3 Hz  > f_m

maximum audio frequency detectable = 10.6103 kHz
the carrier frequency must be more than  10.6103 kHz