# AM demodulation with AD633 as Square Law Detector

AM demodulation is the process of extracting message signal from the AM modulated wave received by AM receiver. The AM modulated wave is generated using AM modulator circuit at the AM transmitter. The AM signal can be either standard AM(also called conventional AM), DSB-SC AM or SSB-SC AM. In literature there are two methods of AM demodulation-(1) using Square Law Detector (2) using Envelope Detector. A square law detector is one that uses non-linear device such as transistor, diode or any device that is capable of squaring the input to get squared output. The output signal from the square law detector is then low pass filtered to recover the message signal. Envelope detector uses diode which also performs essentially squaring function and so both are basically equivalent. Here it is presented how the AD633 multiplier IC can be used as a square law detector and perform AM demodulation.

The following shows a circuit diagram wherein at the transmitter, the AD633 IC is used for generating standard AM signal which is then amplified using a BJT amplifier. Then at the receiver, another AD633 integrated circuit is used as a square law detector which square the input AM signal and then the output is low pass filtered using 2nd order RC low pass filter circuit.

The following shows the AM modulator circuit diagram at the transmitter.

The message tone signal Vtxm of 1KHz frequency, 1.2V amplitude and the carrier signal Vc of 100KHz frequency, 320mV are applied to the X1 and Y1 pins of the AD633 IC while the X2 and  Y2 pins are grounded. Resistor R3 and R7 are used to adjust the scaling voltage to unity. The output of the modulator is defined as,

$$W = \frac{(X1-X2)(Y1-Y2)}{10V} \frac{R3+R7}{R3}+S$$

where, S is the summing input which can either be connected to add signal to the output or grounded.

With R3=1kOhm and R7=9Kohm the output reduces to,

$$W = (X1-X2)(Y1-Y2)+S$$

with $$X1= A_m cos(2Ï€f_mt)$$ and $$Y1 = A_c cos(2Ï€f_ct)$$ we have,

$$W = (A_m cos(2Ï€f_mt))(A_c cos(2Ï€f_ct))+A_c cos(2Ï€f_ct)$$

$$W = (1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct)$$

which is the equation of standard AM signal wave

The standard AM signal wave generated by AD633 modulator circuit is of small amplitude and hence an amplifier is connected to the output. This bipolar junction transistor amplifier is shown below.

This bipolar junction transistor(BJT) amplifier can be quickly designed with the online BJT amplifier design calculator. The BJT amplifier is biased using voltage divider biasing method.

Next in the circuit above, the received AM signal is demodulated using the AD633 IC based square law detector. This demodulator circuit along with the 2nd order RC filter is shown below.

The AM signal is applied to both the X and Y inputs and so the output is as follows,

$$W = \frac{(1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct) (1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct)}{10}+Z$$

or, $$W = \frac{(1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct) (1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct)}{10}+Z$$

or, $$W = \frac{(1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct) (1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct)}{10}+0$$

or, $$W = \frac{(1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct) (1 + A_m cos(2Ï€f_mt))A_c cos(2Ï€f_ct)}{10}$$

or,  $$W = \frac{(1 + A_m cos(w_mt))A_c cos(w_ct) (1 + A_m cos(w_mt))A_c cos(w_ct)}{10}$$

or, $$W = \frac{(1 + A_m cos(w_mt))^2 (A_c cos(w_ct))^2}{10}$$

or, $$W = \frac{1}{10}[1+2 A_m cos(w_m t)+A_m^2 cos^2(w_mt)][A_c^2 cos^2(w_c t)]$$

or,  $$W = \frac{1}{10}[A_c^2 cos^2(w_c t)+2 A_m cos(w_m t) A_c^2 cos^2(w_c t)+A_m^2 cos^2(w_mt) A_c^2 cos^2(w_c t)]$$

using the trigonometric identity, $$cos^2x=\frac{1+cos2x}{2}$$ for $$cos^2(w_c t)$$ we have,

or,  $$W = \frac{1}{10}[A_c^2 \frac{1+cos2(w_c t)}{2}+2 A_m cos(w_m t) A_c^2 \frac{1+cos2(w_c t)}{2}+A_m^2 cos^2(w_mt) A_c^2 \frac{1+cos2(w_c t)}{2}]$$

or, $$W = [A_c^2 \frac{1+cos2(w_c t)}{20}+A_m cos(w_m t) A_c^2 \frac{1+cos2(w_c t)}{10}+ \frac{A_m^2 A_c^2}{20} cos^2(w_mt) + \frac{A_m^2 A_c^2}{20} cos^2(w_mt) cos2(w_c t)]$$

In the above equation, the 3rd term is the required message signal which can recovered using low pass filter. In the above circuit diagram low pass filter of 2nd order(two cascaded LPF) is used to filter out the high frequency component of the demodulated signal and allow the message signal frequency to pass through. The RC filter has resistor value of 750Ohm and capacitor value of 10nF which gives cutoff frequency of 22KHz approximately.

The following shows the transmitted message signal(1KHz, 1.2V), the carrier signal(100KHz,320mV), the AM signal, and the recovered message signal(or demodulated AM signal).

The following video demonstrates AM demodulation with AD633 multiplier IC(Integrated Circuit) as square law detector.