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
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 new 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).
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
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 more digestible read on ring modulators can be found in Lt. Reginald Clubb's Masters Thesis
"Double balanced bilateral ring modulator" (1953).
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:
| (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
there are fourteen ring modulators in production in the Eurorack modular synthesizer
Of those, only three are actual Cowan-type diode ring modulators, the other eleven
(almost 80%) are four-quadrant 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