# Circuits for Multiplying two Analogue Signals - AM Modulation

I've recently been learning about various communication topics and modulation schemes. One of the most basic is Amplitude Modulation and DSB-SC. Both of these modulation schemes (in addition to numerous others) require the use of a multiplication block.

What sort of basic physical circuits can be used to multiply two analogue signals? For example in AM modulation.

I know Op-Amps can be used as weighted summers, integrators and differentiators - can op-amps be used to implement an analogue multiplier? If so, are there any particular op-amp parameters which are particularly critical in multiplier design?

• OTAs can be used as a multiplier. LM13700s are cheap and available. – Matt Young Nov 5 '15 at 15:54
• Just like multiplication with slide rules, one option is to change the problem. Take the log of two voltages, sum them, then take the inverse log. Now you just have to figure out how to take the log of a voltage. :) – Nick Johnson Nov 5 '15 at 16:12
• There used to be cheap and cheerful 4-quadrant analog multipliers and modulators, MC1495/1595. Last I looked, they becoming hard to find... LM13700 is good if you don't need 4 quadrant operation, but for DSBSC you do. – Brian Drummond Nov 5 '15 at 16:23

A simple BJT operated in the saturation region is a good start to understanding how a multiplier works: -

I'm not talking about the BJT operated in the normal region (where the collector current remains flat for large changes in VCE) - I'm talking sub 300mV between collector and emitter.

Look at the pretty colored lines between 100mV Vce and 200mV. Notice that they all have different slopes and these different slopes represent a different conductance (collector current divided by Vce). So, by varying the base current you can make a variable resistor. This is how linear BJT multipliers work. A multiplier is a modulator and you can modulate amplitude of (say an audio signal) by using a pot.

Unfortunately most op-amps can't be made to work in this way so they are not very useful for multiplication but I'm sure someone will point out one that is!

However, the simple BJT multiplier is not that great - you have to dc bias the AC signal so that it doesn't get distorted sub 50mV on the graph but it's a start and works pretty well for AM broadcast modulation: -

If you want full double side-band suppressed carrier modulation you need a four quadrant multiplier (double balanced mixer) and these can be fashioned by BJTs like this: -

One design I was looking at recently uses the SA602. It's a double balanced mixer and oscillator (combined) so it's pretty useful: -

When it comes to AM, op-amps aren't really what you should be looking for.

With AM modulation the amplitude of a (carrier) signal is modulated. A possible implementation for this is by using a variable gain amplifier (VGA). A VGA works like the volume knob on a radio but without the knob of course. Instead the volume is determined by the modulating signal.

I'm not saying that it is impossible to make an opamp based analogue multiplier but most designs that contain opamps use these just for amplification. The actual device that provides the multiplication is often a JFET as it can behave as a voltage controlled resistor.

Nowadays with communication transceivers being very digitized, the modulation is mostly done in the digital domain using a DSP type block. So the signal is constructed using formulas in the digital domain, converted to analog with a DAC, mixed up in frequency to the RF carrier frequency and fed to the Antenna.