Ring modulation

From Wikipedia, the free encyclopedia

Ring modulation is an effect in electronics, related to amplitude modulation or frequency mixing, performed by multiplying two audio 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 effect 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".

These are some audio samples of the ring modulation effect:

Unprocessed original sample (file info) — play in browser (beta)
Ring modulation with a 2500 Hz sound (file info) — play in browser (beta)
- Notice the bell-like sound.
Ring modulation with an exponential sweep from 0 Hz to 9 kHz (file info) — play in browser (beta)
- On lower modulation frequencies, the ring modulation is perceived as a tremolo effect (as in the first part of the sound)
Problems playing the files? See media help.

Ring modulators are mostly used in synthesizers. They combine or heterodyne two waveforms, and output the sum and difference between the two. This process of ring modulation, which also amplitude modulation, produces a signal rich in overtones, suitable for producing bell-like or otherwise metallic sounds. 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. Some modern ring modulators are implemented using digital signal processing techniques by simply multiplying the time domain signals, producing a mathematically perfect signal output. However, many musicians prefer the sound of germanium diodes and transformers.

The ring modulator 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. Two oscillators whose frequencies were harmonically related, and ring modulated against each other produced sounds that still adhered to the overtones of the notes, but, contained 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 $f 2 + f 1 = 2 f)$ . However, some distortion occurs due to the forward voltage drop of the diodes.

Early electronic composers, particularly Stockhausen, had a love affair with the ring modulator. Stockhausen's realization scores are filled with its utilization, and, indeed, whole compositions are based around it, such as Mikrophonie II (where the sounds of choral voices are modulated against a Hammond Tonewheel organ) and Mantra (where music composed for two pianos is routed through a ring modulator).

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 $f 2 - f 1$ . Two points to note are that firstly the two new waves are unlikely to be harmonically related and secondly that (in a well designed ring modulator) the original signals are not present. It is this that gives the ring modulator its unique tones.

Interesting harmonics can be generated by carefully selecting and changing the frequency of the two input waveforms. If the signals are wideband, it is likely that the circular convolution will cause aliasing distortion, so it is common to oversample the operation or filter the signals prior to ring modulation.

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

On an ARP Odyssey synthesiser 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.

[edit] Other Applications

Ring modulation was also extensively used in old radio receivers. Ring modulators were actually 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).