Posted to the Synth-DIY mailing list by Paul Perry
Edited and expanded by Dave Magnuson

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Paul Perry furnished this information to the SDIY mailing list.  It's a comparison of the functions of 1, 2 and 4  quadrant analog multipliers.  I've edited the text a little, but the basic information was provided by Paul.

First, a little basic theory.  An analog multiplier does exactly what it says... multiplies a pair of inputs together, and outputs the resulting voltage.  These are called n-quadrant multipliers depending on how many quadrants of the X-Y coordinate system are accepted as input voltages.   Generally the inputs are also called X and Y, to correspond with this.  Anyone remember graphing coordinates and lines in geometry class?  Hope so!   +/- 10V signals are common in modular synths, so I'm using these voltage ranges for discussion below.

• A one quadrant multiplier operates only on signals from say 0v to 10v for both the X and Y inputs.  This would correspond with only a single quadrant of the X-Y graph. (X>0 and Y>0)
• A two quadrant multiplier works on signals of for example -10 to +10 for X, but 0 to +10 for Y.  This would allow the entire "top half" of the X-Y graph as input signals.  Any value for X, but Y must still be greater than zero.
• A 4 quadrant multiplier accepts inputs from for example -10 to +10  for both   X and Y, meaning the inputs can come from any quadrant on the X-Y graph.

Now, how does this all relate to synthesizer circuits?  Well, X is usually your audio input, and Y is the control voltage.   So a 1 quadrant multiplier accepts only positive audio inputs, so this would actually be much better for processing CV instead of audio.  The 2- and 4-quadrant models allow the standard bipolar audio waves that are common in synths.

The Y input accepts only positive control voltages in the 1- and 2- quadrant models, but accepts bipolar signals in the 4-quadrant multiplier.    To put this in more simple terms:

• A 1-Quadrant multiplier is a VCA with a half-wave rectifier (diode) on the audio input.  It would be perfect for attenuating and modifying a control voltage applied to the X input with the second CV on the Y input.
• A 2-Quadrant multiplier is a standard VCA.   You can use bipolar signals on the X (audio) input, but are limited to a positive control voltage on the Y input.  The larger the Y signal, the louder the output of the X signal will be.
• A 4-Quadrant multiplier is a ring modulator or balanced modulator.  It allows bipolar signals on each input.   When Y is positive, it allows the X signal to pass through... the larger the voltage on the Y input, the "louder" the X signal will be on the output.   When Y is negative, the X signal passes through INVERTED.  The more negative Y becomes, the larger the inverted X signal will be.     If you've ever used very fast amplitude modulation on a VCA, you'd notice it sounds similar to a ring modulator... it's the same except there is no inversion of the X signal.  In the case of a ring modulator, the inputs are often called signal (X) and carrier (Y)