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