Ring modulation

Ring modulation is a signal-processing effect in electronics, related to 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.^[1] This circuit is similar to a bridge rectifier, except that instead of the diodes facing "left" or "right", they go "clockwise" or "anti-clockwise".

Examples

These are some audio samples of the ring modulation effect:

Unprocessed original sample

Ring modulation with a 2500 Hz sound

Notice the bell-like sound.

Ring modulation with an exponential sweep from 0 Hz to 9 kHz

On lower modulation frequencies, the ring modulation is perceived as a tremolo effect (as in the first part of the sound)

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Operation

Ring modulators frequency mix or heterodyne two waveforms, and output the sum and difference of the frequencies present in each waveform. This process of ring modulation produces a signal rich in overtones, suitable for producing bell-like or otherwise metallic sounds.

Two oscillators, whose frequencies were harmonically related and ring modulated against each other, produce sounds that still adhered to the overtones 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 $f_{1}=f_{2}=f$ , then $f_{2}-f_{1}=0$ and $f_{2}+f_{1}=2f)$ . 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 mathematically perfect signal output.

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 $f_{1}$ and $f_{2}$ ( $f_{1}<f_{2}$ ) are multiplied, two new sine waves are created, with one at $f_{1}+f_{2}$ and the other at $f_{2}-f_{1}$ . 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 filter the signals prior to ring modulation.

Integrated circuit methods of ring modulation

On the C64 SID chip, ring modulation multiplies a triangle wave with a square wave.

On an ARP Odyssey synthesizer the ring modulator is an XOR function (formed from two NAND gates) fed from the square wave outputs of the two oscillators. Though not equivalent to ring modulation, with square waves the resulting sound is quite similar.

Use in music

Ring modulation was a very commonly used effect in early electronic music, when analog oscillators were only capable of generating waveforms with a predictable series of overtones. One of the best-known applications of the ring modulator was 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.^[2]

In 1963, Don Buchla included an optional ring modulator in his first modular synthesizer, the Model 100. The ring modulator panel unit, Model 111, included two independent passive circuits that each attenuated the input signal by 55 dB.^[3]

Early electronic composers, particularly Stockhausen, used ring-modulator effects. Stockhausen's realization scores for Kontakte (1958–60) and Telemusik (1966) call for it and, 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 from Sonntag aus Licht (2002), which ring-modulates flute and trumpet.^{[citation needed]}

Ring modulators are mostly used in synthesizers and a ring modulator module was a common feature on early modular Moog synthesizers. The ring modulator went out of fashion with the advent of all-in-one synthesizers and sampled-based synthesizers, but has returned as a feature in digital modelling and software synthesizers. Analog ring modulators are also made by Electro-Harmonix and Moog, in the Moogerfooger line of pedals.^{[citation needed]}

In rock music, one of the first uses of a ring modulator was by the United States of America on their self-titled album recorded in late 1967. A ring modulator effect was added to the guitar in the song "That's for the Other One" by The Grateful Dead (1968) and the guitar solo "Paranoid" by Black Sabbath (1972). In a 1990 interview with Guitar Player Magazine, Robbie Robertson (of The Band) revealed that, although he mostly eshews effects in favour of guitar and amp created tones, the one effect he liked to use on his guitar was a ring modulator.^{[citation needed]}

In one of the lineups during the 1970s electric period of Miles Davis, Chick Corea played a piano through a ring modulator. This gave a very different and unusual sound. It can be seen and heard on a DVD release of Davis' performance at the Isle of Wight. Guitarist and fellow former Davis sideman John McLaughlin has also made heavy use of ring modulation on such tunes as "On The Way Home to Earth" from the Mahavishnu Orchestra's Visions of the Emerald Beyond, "Miles Out" from Inner Worlds and "Acid Jazz" from his own John McLaughlin and the Heart of Things: Live in Paris.^{[citation needed]}

Jon Lord from Deep Purple often used the ring modulator with his Hammond organ during live shows (Made in Japan, California Jam), and sometimes even in studio records (Rat Bat Blue).^{[citation needed]}

Luke Vibert showcases the ring modulator sound in the "Fused into music", on his album, Big Soup.^{[citation needed]}

Omar Rodriguez-Lopez, guitarist of The Mars Volta, commonly uses a ring modulator in combination with a number of other effects. A good example occurs in the intro of the song "Roulette Dares."^{[citation needed]}

Mike Einziger of the band Incubus used a ring modulator on the S.C.I.E.N.C.E. album, most notably heard on the intro to the song "Glass".^{[citation needed]}

The band Ex Models uses ring modulation on their guitars throughout their albums Zoo Psychology and Chrome Panthers.^{[citation needed]}

Other applications

Ring modulation has also been extensively used in radio receivers, for example to demodulate an FM stereo signal and to down-convert microwave signals in mobile telephone and wireless networking systems.

References

^ Richard Orton, "Ring Modulator", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publications; New York: Grove's Dictionaries of Music, 2001): "the ring modulator takes its name from the characteristic ring formation of four diodes in its analog circuit."
^ Bentham, Jeremy (1986). Doctor Who: The Early Years. London: W.H. Allen. p. 127. ISBN 0 491 03612 4.
^ Buchla & Associates. Historical. Model 100. 111 Dual Ring Modulator

External links

Harmony Central: Effects Explained: Ring Modulation by Scott Lehman

[1] Richard Orton, "Ring Modulator", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publications; New York: Grove's Dictionaries of Music, 2001): "the ring modulator takes its name from the characteristic ring formation of four diodes in its analog circuit."

[2] Bentham, Jeremy (1986). Doctor Who: The Early Years. London: W.H. Allen. p. 127. ISBN 0 491 03612 4.

[3] Buchla & Associates. Historical. Model 100. 111 Dual Ring Modulator

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