Demodulation of DSB-FC AM

DSB-FC (conventional AM) can be demodulated by the square law detector or the envelope detector. The envelope detector is the most widely used method and is described here.

Envelope detector

An envelope detector is a diode–RC circuit whose output follows the envelope $A_c[1 + k_am(t)]$ of the AM wave.

            D
 AM in o---|>|----+--------+-------||----o  m(t)
   s(t)           |        |      Cc
                  C        R     (DC block)
                  |        |
       o----------+--------+-------------o

Input: $s(t) = A_c[1 + k_am(t)]\cos\omega_ct$, with $|k_am(t)| \le 1$.

Working

1. Charging: During each positive half cycle, when the input exceeds the capacitor voltage, the diode conducts and $C$ charges rapidly to the peak value. The charging time constant $r_fC$ ($r_f$ = diode + source resistance) is very small compared to the carrier period.
2. Discharging: When the input falls below the capacitor voltage, the diode is reverse biased; $C$ discharges slowly through $R$ until the next positive peak.
3. The capacitor voltage thus follows the positive peaks (envelope) with a small carrier-frequency ripple.
4. A coupling capacitor $C_c$ removes the DC term $A_c$, leaving $A_ck_am(t)$, i.e. the message.

 AM input            Detector output
  /\  /\/\/\  /\        ___
 /  \/      \/  \     _/   \_    _/   (follows envelope,
 \  /\      /\  /             \__/     small ripple)
  \/  \/\/\/  \/

Choice of time constant

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

• $RC \gg 1/f_c$: the capacitor does not discharge much between carrier peaks (low ripple).
• $RC \ll 1/W$: the voltage can follow the fastest change of the envelope.

Distortions

• Diagonal clipping: if $RC$ is too large, the output cannot follow a fast-falling envelope. Avoid by

$$RC \le \frac{\sqrt{1 - \mu^2}}{\mu\,\omega_m}$$

• Negative peak clipping: caused when the AC load (after $C_c$) is much smaller than the DC load $R$; keep $\mu \le R_{ac}/R_{dc}$.
• Over-modulation ($\mu > 1$): envelope no longer equals $m(t)$, so the output is distorted.

Advantages and limitations

• Very simple, cheap, no local oscillator or synchronisation needed: used in all broadcast AM receivers.
• Works only for DSB-FC with $\mu \le 1$; cannot demodulate DSB-SC or SSB; shows a threshold effect at low input SNR.

Example design: for $f_c = 1$ MHz and $W = 5$ kHz, $1\ \mu s \ll RC \ll 200\ \mu s$; choose $RC \approx 20\ \mu s$ (e.g. $R = 10$ kΩ, $C = 2$ nF).