Ring modulation
Encyclopedia
Amplitude modulation
Amplitude modulation is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent...
or frequency mixing
Frequency mixer
In electronics a mixer or frequency mixer is a nonlinear electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies f1 and f2 are applied to a mixer, and it produces new signals at the sum f1 + f2 and difference f1 -...
, 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 diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
s 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
Effects unit
Effects units are electronic devices that alter how a musical instrument or other audio source sounds. Some effects subtly "color" a sound, while others transform it dramatically. Effects are used during live performances or in the studio, typically with electric guitar, keyboard and bass...
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
Transformer
A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...
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.
Examples
These are some audio samples of the ring modulation effect:Operation
Ring modulators frequency mixFrequency mixer
In electronics a mixer or frequency mixer is a nonlinear electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies f1 and f2 are applied to a mixer, and it produces new signals at the sum f1 + f2 and difference f1 -...
or heterodyne
Heterodyne
Heterodyning is a radio signal processing technique invented in 1901 by Canadian inventor-engineer Reginald Fessenden where high frequency signals are converted to lower frequencies by combining two frequencies. Heterodyning is useful for frequency shifting information of interest into a useful...
two waveform
Waveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...
s, and output the sum and difference of the frequencies present in each waveform. This process of ring modulation produces a signal rich in partials, suitable for producing bell-like or otherwise metallic sounds. As well, neither the carrier nor the incoming signal are prominent in the outputs, and ideally, not at all.
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
Digital signal processing
Digital signal processing is concerned with the representation of discrete time signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing...
techniques by simply multiplying the time domain
Time domain
Time domain is a term used to describe the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various...
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
Time domain
Time domain is a term used to describe the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various...
is the same as convolution
Convolution
In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation...
in the frequency domain
Frequency domain
In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....
, 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
Intermodulation
Intermodulation or intermodulation distortion is the amplitude modulation of signals containing two or more different frequencies in a system with nonlinearities...
products can be generated by carefully selecting and changing the frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
of the two input waveform
Waveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...
s. If the signals are processed digitally, the frequency-domain convolution becomes circular convolution
Circular convolution
The circular convolution, also known as cyclic convolution, of two aperiodic functions occurs when one of them is convolved in the normal way with a periodic summation of the other function. That situation arises in the context of the Circular convolution theorem...
. If the signals are wideband
Wideband
In communications, wideband is a relative term used to describe a wide range of frequencies in a spectrum. A system is typically described as wideband if the message bandwidth significantly exceeds the channel's coherence bandwidth....
, this will cause aliasing
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...
distortion, so it is common to oversample
Oversampling
In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled...
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
Inverted spectrum
Inverted spectrum is the apparent possibility of two people sharing their color vocabulary and discriminations, although the colours one sees — their qualia — are systematically different from the colours the other person sees....
—High frequencies become low, and vice versa.
Integrated circuit methods of ring modulation
On the C64Commodore 64
The Commodore 64 is an 8-bit home computer introduced by Commodore International in January 1982.Volume production started in the spring of 1982, with machines being released on to the market in August at a price of US$595...
SID
MOS Technology SID
The MOS Technology 6581/8580 SID is the built-in Programmable Sound Generator chip of Commodore's CBM-II, Commodore 64, Commodore 128 and Commodore MAX Machine home computers...
chip, ring modulation multiplies a triangle wave
Triangle wave
A triangle wave is a non-sinusoidal waveform named for its triangular shape.Like a square wave, the triangle wave contains only odd harmonics...
with a square wave
Square wave
A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels...
.
On an ARP Odyssey
ARP Odyssey
The ARP Odyssey was an analog synthesizer introduced in 1972. Responding to pressure from Moog Music to create a portable, affordable "performance" synthesizer, ARP scaled down its popular 2600 synthesizer and created the Odyssey, which became the best-selling synthesizer they made.The Odyssey is...
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. Use of multplier ICs means that the modulation products are largely confined to sum and difference frequency of inputs (unless the circuit is overdriven), rather than the much more complicated products of the rectifier circuit.
Use in music
One of the first products dedicated for music was the Bode Ring Modulator developed in 1961 by Harald BodeHarald Bode
Harald Bode was a German engineer and pioneer in the development of electronic music instruments.- Biography :...
. Also in 1964 he developed the Bode Frequency Shifter, which produced a clearer sound by eliminating a side band. These devices were designed to be controlled by voltage, for today's modern modular synthesizer architecture also advocated by him, and these modules were licensed to R.A. Moog
Moog Music
Moog Music is an American company based in Asheville, North Carolina which manufactures electronic musical instruments. The current Moog Music is the second company to trade under that name.-R.A. Moog Co. and the original Moog Music:...
for their Moog modular synthesizer
Moog modular synthesizer
Moog modular synthesizer refers to any of a number of monophonic analog modular synthesizers designed by the late electronic instrument pioneer Dr. Robert Moog and manufactured by R.A Moog Co...
s started in 1963-1964. In 1963, Don Buchla
Don Buchla
Don Buchla is a pioneer in the field of sound synthesizers, releasing his first units months after Robert Moog's first synthesizers...
included an optional ring modulator in his first modular synthesizer, the Model 100
Buchla
Buchla & Associates, Inc. is a manufacturer of electronic musical instruments, notably synthesizers and unique MIDI controllers. The 200e Electric Music Box and Lightning III are currently in production.-Buchla Music Box :...
. Also Tom Oberheim built a ring modulator unit for his musician friend
The United States of America (band)
The United States of America was an American experimental rock and psychedelic band whose works are an example of early electronic music in rock and roll.-History:...
in the late 1960s, and it became an origin of Maestro Ring Modulator, one of the earliest ring modulator effect
Effects unit
Effects units are electronic devices that alter how a musical instrument or other audio source sounds. Some effects subtly "color" a sound, while others transform it dramatically. Effects are used during live performances or in the studio, typically with electric guitar, keyboard and bass...
products for guitarists.
Early electronic composers, particularly Stockhausen
Karlheinz Stockhausen
Karlheinz Stockhausen was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. Another critic calls him "one of the great visionaries of 20th-century music"...
, used ring-modulator effects. Stockhausen used ring modulation as early as 1956 for some sounds in Gesang der Jünglinge
Gesang der Jünglinge
Gesang der Jünglinge is a noted electronic music work by Karlheinz Stockhausen. It was realized in 1955–56 at the Westdeutscher Rundfunk studio in Cologne and is Work Number 8 in the composer's catalog of works...
and his realization score for Telemusik
Telemusik
Telemusik is an electronic composition by Karlheinz Stockhausen, and is number 20 in his catalog of works.-History:Through his composition student, Makoto Shinohara, Stockhausen was invited by the Japan Broadcasting Corporation NHK to visit Tokyo, and to carry out two commissions in their...
(1966) also calls for it. Indeed, whole compositions are based around it, such as Mixtur
Mixtur
Mixtur, for orchestra, 4 sine-wave generators, and 4 ring modulators, is an orchestral composition by the German composer Karlheinz Stockhausen, written in 1964, and is Nr. 16 in his catalogue of works...
(1964), one of the first compositions for orchestra and live electronics, Mikrophonie II
Mikrophonie (Stockhausen)
Mikrophonie is the title given by Karlheinz Stockhausen to two of his compositions, written in 1964 and 1965, in which “normally inaudible vibrations . ....
(1965, where the sounds of choral voices are modulated with a Hammond organ
Hammond organ
The Hammond organ is an electric organ invented by Laurens Hammond in 1934 and manufactured by the Hammond Organ Company. While the Hammond organ was originally sold to churches as a lower-cost alternative to the wind-driven pipe organ, in the 1960s and 1970s it became a standard keyboard...
), Mantra
Mantra (Stockhausen)
Mantra is a composition by the German composer Karlheinz Stockhausen. It was composed in 1970 and premiered in autumn of the same year in Donaueschingen...
(1970, where the sounds from two pianos are routed through ring modulators), and Licht-Bilder (2002) from Sonntag aus Licht
Sonntag aus Licht
Sonntag aus Licht is an opera by Karlheinz Stockhausen in five scenes and a farewell, to a libretto written and compiled by the composer. It is the last-composed of seven operas that comprise the cycle Licht...
, which ring-modulates flute and trumpet.
Also ring-modulator was the major component used in Louis and Bebe Barron
Louis and Bebe Barron
Bebe Barron and Louis Barron were two American pioneers in the field of electronic music...
's music for the 1956 film Forbidden Planet
Forbidden Planet
Forbidden Planet is a 1956 science fiction film directed by Fred M. Wilcox, with a screenplay by Cyril Hume. It stars Leslie Nielsen, Walter Pidgeon, and Anne Francis. The characters and its setting have been compared to those in William Shakespeare's The Tempest, and its plot contains certain...
.
One of the best-known applications of the ring modulator may be its use by Brian Hodgson
Brian Hodgson
Brian Hodgson is a British television composer and sound technician. Born in Liverpool in 1938, Hodgson joined the BBC Radiophonic Workshop in 1962 where he became the original sound effects creator for the science fiction programme Doctor Who...
of the BBC Radiophonic Workshop
BBC Radiophonic Workshop
The BBC Radiophonic Workshop, one of the sound effects units of the BBC, was created in 1958 to produce effects and new music for radio, and was closed in March 1998, although much of its traditional work had already been outsourced by 1995. It was based in the BBC's Maida Vale Studios in Delaware...
to produce the distinctive voice of the Dalek
Dalek
The Daleks are a fictional extraterrestrial race of mutants from the British science fiction television series Doctor Who. Within the series, Daleks are cyborgs from the planet Skaro, created by the scientist Davros during the final years of a thousand-year war against the Thals...
s and the Cybermen
Cyberman
The Cybermen are a fictional race of cyborgs who are amongst the most persistent enemies of the Doctor in the British science fiction television series, Doctor Who. Cybermen were originally a wholly organic species of humanoids originating on Earth's twin planet Mondas that began to implant more...
in the television series Doctor Who
Doctor Who
Doctor Who is a British science fiction television programme produced by the BBC. The programme depicts the adventures of a time-travelling humanoid alien known as the Doctor who explores the universe in a sentient time machine called the TARDIS that flies through time and space, whose exterior...
, starting in 1963.