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On Rings and Things

The world of electronic music seems to be rather insular. Take, for instance, the fate of the poor Ring Modulator. If you only read the Wikipedia page on Ring Modulators you might come to conclusion that the only use of ring modulators was in electronic music instruments; indeed, the majority of the references (22 out of 25) refer to documents in the electronic music realm. If you knew better you might think this was just a little blinkered. Which it is. But that's not all.

The Wikipedia page is both factually incorrect, and missing key details which one would think any decent reference document would include, such as who invented it, and when, and for what. Except it doesn't.

Say Hello To Frank

The ring modulator, as we know it today, was invented in 1934 by Frank A. Cowan while at American Telephone & Telegraph Co. (AT&T) for use in telephone systems. It is described in US patent 2,025,158 (filing date June 7 1934, publication date December 24 1935) (local copy). The structure proposed by Cowan is shown below:

It was offered as an improvement on the invention of Clyde R. Keith at Bell Labs (again, for telephone applications), described in US Patent 1,855,576 from 1929. Cowan's approach was both simpler and cheaper: while still using only four diodes Cowan reduced the number of transformers needed from four to two. Thus, from Cowan's patent, the structure that we know today as the Ring Modulator emerged - the combination of an input transformer with split secondary, bridge or "ring" of four diodes, and an output transformer.

One interesting thing to note about Cowan's circuit is its symmetrical elegance: the modulating input and the output terminals can be reversed, thus the same circuit can be used as both a modulator and a demodulator.

A more digestible read on ring modulators can be found in Lt. Reginald Clubb's Masters Thesis "Double balanced bilateral ring modulator" (1953) (local copy).

Theory Of Operation

The Cowan Modulator is a so-called chopping modulator - only the sign of the carrier is important, and an ideal carrier changes sign as quickly as possible, from -1 to +1 and vice versa:

From: R. Clubb, Double balanced bilateral ring modulator, p.7, 1953

The output of the Cowan modulator comprises the sum and difference products following the multiplication of the carrier with the voice signal. Now, as we all know from our school maths lessons:

sin(a)sin(b)  =    1
 (cos(a-b) - cos(a+b))

In technical jargon this is a double-sideband suppressed carrier (DSB-SC) modulator - the output comprises two sidebands (the sum and difference) and no carrier is present. In radio terms this is a nice result since we don't want to waste precious transmitter energy on the carrier, and subsequent filtering can remove one of the sidebands to save yet more spectrum for use in the well-known single-sideband suppressed carrier (SSB-SC) modulation scheme.

But wait - I hear you cry - if the carrier input to the modulator is a square wave with sharp fast edges, won't that have harmonics off into daylight (3f, 5f, 7f, ....)? Well, yes, it will, but remember that we follow the modulator with a filter, so we don't need to worry about them. And since, certainly in radio systems, the carrier frequency is likely to be one of the common IF frequencies (e.g., 10.7MHz) the filtering does not need to be too aggressive as the first harmonic is up around 31MHz.

Now, back to the trig identity above. As you can see, the output is simply the product of the two inputs - it multiplies both inputs together. As it is sign-agnostic -- both inputs can be positive or negative -- if we plot the inputs versus outputs on a piece of graph paper we find we need four quadrants, since the X and Y axes (corresponding to the inputs) can be positive or negative. Thus this circuit is in the class of circuits known as Four Quadrant Multipliers.

There are many examples of IC-based circuits, including the classic Gilbert cell, various types of multiplier chip such as the Motorola MC1495, and various combinations of op-amps and two-quadrant multipliers (e.g., LM13700, SSM2164). Together with the ring modulator they all implement the four-quadrant multiplier function. However, they are not ring modulators in and of themselves, any moreso than "an orange is a type of apple".

When Is A Ring Modulator Not?

Sadly, as demonstrated by the Wikipedia page, a circuit or device is often claimed to be a ring modulator when in fact it most definitely is not, and is in fact most likely some form of IC-based four-quadrant multiplier. To put this into context, looking on ModularGrid there are about twenty ring modulators in production in the Eurorack modular synthesizer format. Of those, only a couple are actual Cowan-type diode ring modulators, the rest are transistor-based four-quadrant product multipliers.

Going By The Books

As the saying goes: "When the going gets weird, the weird turn pro". I've seen several supposedly edited and reviewed books that contradict the Cowan patent.

Newnes Telecommunications Pocket Book by Steve Winder, shows the Cowan modulator as having a single winding input transformer, lots of resistors, diodes not in a suitable ring, and operating in a "shorting" mode. Weird.

Analog, Digital and Multimedia Telecommunications: Basic and Classic Principles by Omar Fakih Hamad, draws the Cowan modulator with three transformers, although now they are simpler non-centre-tapped designs.

Analogue and Digital Communication Techniques by Grahame Smillie, is the weirdest so far, stating that the Cowan modulator is single-balanced only, and in the accompanying diagram goes the furthest by omitting the two transformers completely, as well as getting the diode ring wrong.

If anyone can explain to me how any of these descriptions of the Cowan modulator are related to the patent then please contact me.

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