Short note: Envelope detector

An envelope detector is a simple non-coherent demodulator for DSB-FC AM. Its output follows the envelope (peaks) of the AM wave, which is $A_c[1 + k_am(t)]$.

          D
 AM in --|>|---+-------+---- output
               |       |
               C       R
               |       |
 ------------- +-------+---- ground

Working

• On the positive half cycle the diode conducts and the capacitor charges quickly to the peak through the small source resistance ($r_sC \ll 1/f_c$).
• When the input falls below the capacitor voltage, the diode is off and $C$ discharges slowly through $R$.
• The output is a slightly rippled copy of the envelope; a DC-blocking capacitor removes the carrier DC level, giving $m(t)$.

Time constant condition

$$\frac{1}{f_c} \ll RC \ll \frac{1}{W}$$

• If $RC$ is too small: large carrier ripple.
• If $RC$ is too large: diagonal clipping (output cannot follow a falling envelope). To avoid it, $RC \le \dfrac{\sqrt{1-\mu^2}}{\mu\,\omega_m}$.

Advantages: very simple, cheap, no local carrier needed; used in all AM broadcast receivers.

Limitations: works only for DSB-FC with $\mu \le 1$; distortion by diagonal clipping and negative peak clipping; poor at low SNR (threshold effect).