# Ring modulation

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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. 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:

Operation

Ring modulators combine (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 $f_1 = f_2 = f$ , $f_2 - f_1 = 0$ and $f_2 + f_1 = 2f\right)$. 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 $f_2$ ($f_2 > f_1$) 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 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.

It 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".

A ring modulator effect is added to the guitar solo in the song "Paranoid" by Black Sabbath.

In one of the lineups during the 1970s electric period of Miles Davis, Chick Corea played a Rhodes piano through a ring modulator. This gave the distinctive electric piano a very different and unusual sound. It can be seen and heard on a DVD release of Davis' performance at the Isle of Wight.

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 "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.

Other applications

Ring modulation was also extensively used in old radio receivers. Ring modulators were used to demodulate the FM stereo signal. Examples include the HH Scott 310, 335, 345, 370B, and Fisher 500c.

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).

Luke Vibert showcases the ring modulator sound in the "Fused into music", on his album, Big Soup.

Nicholas Briggs (voice of the Daleks and the Cybermen in the BBC science fiction series Doctor Who) uses a ring modulator to alter his voice.

*Heterodyne

* [http://www.harmony-central.com/Effects/Articles/Ring_Modulation/ Harmony Central: Effects Explained: Ring Modulation] by Scott Lehman
* [http://www.turneraudio.com.au/am-fm-radio-tuner-multiplex-decoder.html] A homebuilt stereo FM tuner that uses a ring modulator to decode the FM stereo signal

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