Audio Engineering Myths: “Ring Modulation”

If you look at contemporary synths, they often advertise frequency modulation (where you modulate the frequency of something with something else), and then something they call “ring modulation”.

This is not limited to buzzword/hipness design studios – even Waldorf in their description of the fantastic Blofeld do this.

It’s still wrong.

Excursion: The Ring Modulator

The ring modulator is an ancient design from HF electronics. Consisting bascially of two transformers and a four-diode bridge, it gets its name from the very diode bridge.

Looking at the diodes in the circuit above, we see that their “arrows” (and that’s the direction the current flows) all point in a circular fashion. That is, from every point on that bridge, the current can (for ideal diodes, and superconductivity) flow clockwise ad infinitum.

This sets it apart from the more well-known rectifier bridge, often used in AC/DC converters shown below:

Here, the arrows all point in one direction (from top to bottom).

And with that, it becomes clear:

The ring modulator gets its name from the fact that in its diode bridge, the diodes are aligned in an unusual fashion that allows the current to move in a circle or ring from any point.

So what does the Ring Modulator do?

On a top-level view, let’s first look at the signs of our input signals Uy and Ux from the diagram above, and let’s furthermore assume Uy is a square wave with an amplitude higher than that of Ux. The thing also works with other signals, but this makes the explanation easier.

In this context, Ux is our audio signal, and Uy is the signal used for modulation.

Now, if Ux is positive, then V1 and V2 conduct, thus the top side of transformer T1/2 is connected to the top side of transformer T3/4 and the bottom is connected to the bottom.

For negative Ux, the opposite happens: the top of T1/2 is connected to the bottom of T3/4 and vice versa.

That means that the signs of our input signals get multiplied.

In that very simple case with the square Ux and Ux>>Uy, that is all there is – and that means for the output simply

Ua = UxUy

If we look at that in the frequency domain, we may remember that multiplication in one domain leads to faltung in the other domain.

Assuming that Ux is a simple sine with frequency fx and the frequency of Uy is fy (and not sweating the details that Uy is a square, not a sine), we get with that multiplication/faltung shifts of one frequency by the other: The output signal contains the frequencies fy+fx and fy-fx. There’s neither fx nor fy in the output, though.

And this is what the ring modulator does: it multiplies two signals (i.e. modulates the amplitde of one with the amplitude of the other), and as the end result, we get both so-called sidebands, but none of the original signals itself.

There you have it:

A ring modulator performs dual sideband amplitude modulation with suppressed carrier (DSB SC AM). It’s called that. Not “ring modulation”.

Annex: The Ring Modulator today

From the implementation, you might think it’s odd to use two transformers, a diode bridge and maybe a lot of support circuitry to simply perform a multiplication, and you’d be right: around the 60s, ASICs doing just analogue multiplication had become widely available (and were used, among other applications, for just hte DSB SC AM in place of a ring modulator). And in your DSP or uC, it’s just a basic command.

The ring modulator as a name of a component in synthesizers or as a stand-alone effects device seems to be as much alive as ever, if not more. And that’s a good thing entirely. Frequency shifting, frequency inversion – all those are things that can greatly expand the sonic palette of your synth, guitar, or whatever you choose to apply it to.

References

Thanks to MovGP0 and Wykis for releasing the drawings used in this article to the public domain.