Envelope detector circuit and waveforms

An envelope detector is a simple non-coherent demodulator that recovers the message from a DSB-FC (standard AM) wave by following its envelope $A_c[1+\mu m(t)]$. It needs no local carrier, so it is used in almost all AM broadcast receivers.

Circuit

        D
 o----->|-----+--------+-----o
 AM    diode  |        |
 input       === C     > RL   v_o(t)
 s(t)         |        >     (envelope)
 o------------+--------+-----o

Working

1. Positive half cycle (charging): when the input is higher than the capacitor voltage, the diode conducts. The capacitor charges quickly through the small source resistance $R_s$ to the peak of the carrier cycle. The charging time constant $R_sC$ is very small.
2. Between peaks (discharging): when the input falls below the capacitor voltage, the diode is reverse biased. The capacitor discharges slowly through $R_L$ with time constant $R_LC$.
3. At the next carrier peak the diode conducts again and tops up the capacitor. So the output is the envelope with a small RF ripple at $f_c$.
4. A following RC low-pass filter removes the ripple and a coupling capacitor blocks the DC term, leaving $m(t)$.

Choice of time constant

$$\frac{1}{f_c} \ll R_L C \ll \frac{1}{W}$$

where $W$ is the message bandwidth.

• If $R_LC$ is too small, the capacitor discharges too fast and the output has large RF ripple.
• If $R_LC$ is too large, the capacitor cannot follow a falling envelope, giving diagonal clipping.

Also $\mu \le 1$ is needed; with over-modulation the envelope no longer matches $m(t)$ and the output is distorted.

Waveforms

AM input:
   /\    /\/\/\    /\
 /\/\/\/\/    \/\/\/\/\
 \/\/\/\/\    /\/\/\/\/
   \/    \/\/\/    \/

Detector output (before filter):
    __/\/\__        __
  _/        \_    _/
 /            \__/
 (envelope + small ripple)

After LPF: smooth copy of m(t)