Ring modulation is a signal-processing effect in electronics, an implementation of amplitude modulation or frequency mixing, performed by multiplying two signals, where one is typically a sine-wave or another simple waveform. It is referred to as "ring" modulation because the analog circuit of diodes originally used to implement this technique took the shape of a ring. This circuit is similar to a bridge rectifier, except that instead of the diodes facing "left" or "right", they go "clockwise" or "anti-clockwise". A ring modulator is an effects unit dedicated to producing this sound.
The carrier, which is AC, at a given time, makes one pair of diodes conduct, and reverse-biases the other pair. The conducting pair carry the signal from the left transformer secondary to the primary of the transformer at the right. If the left carrier terminal is positive, the top and bottom diodes conduct. If that terminal is negative, then the "side" diodes conduct, but create a polarity inversion between the transformers. This action is much like that of a DPDT switch wired for reversing connections.
Two oscillators, whose frequencies were harmonically related and ring modulated against each other, produce sounds that still adhere to the harmonic partials of the notes, but contain a very different spectral make up.
If the same signal is sent to both inputs of a ring modulator, the resultant harmonic spectrum is the original frequency domain doubled (if f1 = f2 = f, then f2 - f1 = 0 and f2 + f1 = 2f). Regarded as multiplication, this operation amounts to squaring. However, some distortion occurs due to the forward voltage drop of the diodes.
Some modern ring modulators are implemented using digital signal processing techniques by simply multiplying the time domain signals, producing a nearly-perfect signal output. Before digital music synthesizers became common, at least some analog synthesizers (such as the ARP 2600) used analog multipliers for this purpose; they were closely related to those used in electronic analog computers. (The "ring modulator" in the ARP 2600 could multiply control voltages; it could work at DC.)
Multiplication in the time domain is the same as convolution in the frequency domain, so the output waveform contains the sum and difference of the input frequencies. Thus, in the basic case where two sine waves of frequencies f1 and f2 (f1 < f2) are multiplied, two new sine waves are created, with one at f1 + f2 and the other at f2 - f1. The two new waves are unlikely to be harmonically related and (in a well designed ring modulator) the original signals are not present. It is this that gives the ring modulator its unique tones.
Intermodulation products can be generated by carefully selecting and changing the frequency of the two input waveforms. If the signals are processed digitally, the frequency-domain convolution becomes circular convolution. If the signals are wideband, this will cause aliasing distortion, so it is common to oversample the operation or low-pass filter the signals prior to ring modulation.
One application is spectral inversion, typically of speech; a carrier frequency is chosen to be above the highest speech frequencies (which are low-pass filtered at, say, 3 kHz, for a carrier of perhaps 3.3 kHz), and the sum frequencies from the modulator are removed by more low-pass filtering. The remaining difference frequencies have an inverted spectrum—High frequencies become low, and vice versa.
On an ARP Odyssey synthesizer (and a few others from that era as well) the ring modulator is an XOR function (formed from two NAND gates) fed from the square wave outputs of the two oscillators. For the limited case of square or pulse wave signals, this is identical to true ring modulation.
Analog multiplier ICs (such as those made by Analog Devices) would work quite nicely as ring modulators, of course with regard to such matters as their operating limits and scale factors.
Early electronic composers, particularly Stockhausen, used ring-modulator effects. Stockhausen used ring modulation as early as 1956 for some sounds in Gesang der Jünglinge and his realization score for Telemusik (1966) also calls for it. Indeed, whole compositions are based around it, such as Mixtur (1964), one of the first compositions for orchestra and live electronics, Mikrophonie II (1965, where the sounds of choral voices are modulated with a Hammond organ), Mantra (1970, where the sounds from two pianos are routed through ring modulators), and Licht-Bilder (2002) from Sonntag aus Licht, which ring-modulates flute and trumpet.
One of the best-known applications of the ring modulator may be its use by Brian Hodgson of the BBC Radiophonic Workshop to produce the distinctive voice of the Daleks in the television series Doctor Who, starting in 1963.
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