In
electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, ring modulation is a
signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
function, an implementation of
frequency mixing, in which two
signals
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
are combined to yield an output signal. One signal, called the carrier, is typically a
sine wave or another simple
waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...
; the other signal is typically more complicated and is called the input or the
modulator
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
signal. A ring modulator is an electronic device for ring modulation. A ring modulator may be used in music
synthesizers and as an
effects unit
An effects unit or effects pedal is an electronic device that alters the sound of a musical instrument or other audio source through audio signal processing.
Common effects include distortion/overdrive, often used with electric guitar in el ...
.
The name derives from the fact that the
analog circuit
Analogue electronics ( en-US, analog electronics) are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term "analogue" describes the proportional relat ...
of
diodes originally used to implement this technique takes the shape of a ring: a diode ring. The circuit is similar to a
bridge rectifier
A diode bridge is a bridge rectifier circuit of four diodes that is used in the process of converting alternating current (AC) from the input terminals to direct current (DC, i.e. fixed polarity) on the output terminals. Its function is to con ...
, except that instead of the diodes facing left or right, they face clockwise or counterclockwise.
Ring modulation is quite similar to
amplitude modulation, with the difference that in the latter the modulator is shifted to be positive before being multiplied with the carrier, while in the former the unshifted modulator is multiplied with the carrier. This has the effect that ring modulation of two sine waves having frequencies of 1,500 Hz and 400 Hz will produce as output signal the sum of a sine wave with frequency 1,900 Hz and one with frequency 1,100 Hz. These two output frequencies are known as
sidebands. If one of the input signals has significant
overtones
An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental i ...
(which is the case for
square waves), the output will sound quite different, since each
harmonic will generate its own pair of sidebands that won't be harmonically-related.
Operation
Denoting the carrier signal by
, the modulator signal by
and the output signal by
(where
denotes time), ring modulation is described by the formula
:
If
and
are sine waves with frequencies
and
, respectively, then
will be the sum of two (
phase-shifted) sine waves, one of frequency
and the other of frequency
. This is a consequence of the
trigonometric identity
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involvin ...
:
Alternatively, one can use the fact that multiplication in the
time domain
Time domain refers to 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 c ...
is the same as
convolution
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' ...
in the
frequency domain
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a s ...
.
Ring modulators thus output the
sum and difference of the frequencies present in each waveform. This process of ring modulation produces a signal rich in
partials. As well, neither the carrier nor the incoming signal are prominent in the output, and ideally, not present 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. When the oscillators' frequencies are ''not'' harmonically related, ring modulation creates
inharmonic
In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency ( harmonic series).
Acoustically, a note perceived to have a singl ...
s, often producing bell-like or otherwise metallic sounds.
If the carrier signal is a
square wave of frequency
, whose
Fourier expansion
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or '' ...
contains the
fundamental
Fundamental may refer to:
* Foundation of reality
* Fundamental frequency, as in music or phonetics, often referred to as simply a "fundamental"
* Fundamentalism, the belief in, and usually the strict adherence to, the simple or "fundamental" idea ...
and a series of reducing-amplitude odd
harmonics:
:
and the carrier frequency
is at least twice the maximum frequency of the modulating signal ''
'', then the resulting output is a series of duplicates of ''
'' at increasing regions of the frequency spectrum.
For example, let ''
'' represent a sine wave at 100 Hz, and the carrier ''
'' be an ideal square wave at 300 Hz. The output will then include sine waves at 100±300 Hz, 100±900 Hz, 100±1500 Hz, 100±2100 Hz, etc., at decreasing amplitudes according to the Fourier expansion of the carrier square wave. If the carrier frequency is less than twice the upper frequency of the signal then the resulting output signal contains spectral components from both the signal and the carrier that combine in the time domain.
Because the output contains neither the individual modulator or carrier components, the ring modulator is said to be a ''double-balanced'' mixer, where both input signals are suppressed (not present in the output)—the output is composed entirely of the sum of the products of the frequency components of the two inputs.
History
The ring modulator was invented by Frank A. Cowan in 1934 and patented in 1935 as an improvement on the invention of Clyde R. Keith at
Bell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984),
then AT&T Bell Laboratories (1984–1996)
and Bell Labs Innovations (1996–2007),
is an American industrial Research and development, research and scientific developm ...
. The original application was in the field of
analogue telephony for
frequency-division multiplexing
In telecommunications, frequency-division multiplexing (FDM) is a technique by which the total bandwidth available in a communication medium is divided into a series of non-overlapping frequency bands, each of which is used to carry a separat ...
for carrying multiple voice signals over telephone cables. It has since been applied to a wider range of uses, such as
voice inversion
Voice inversion scrambling is an analog method of obscuring the content of a transmission. It is sometimes used in public service radio, automobile racing, cordless telephones and the Family Radio Service. Without a descrambler, the transmission ma ...
, radio
transceiver
In radio communication, a transceiver is an electronic device which is a combination of a radio ''trans''mitter and a re''ceiver'', hence the name. It can both transmit and receive radio waves using an antenna, for communication purposes. Thes ...
s, and
electronic music
Electronic music is a genre of music that employs electronic musical instruments, digital instruments, or circuitry-based music technology in its creation. It includes both music made using electronic and electromechanical means ( electroa ...
.
While the original Cowan patent describes a circuit with a ring of four diodes, later implementations used
FETs as the switching elements.
Circuit description
The ring modulator includes an input stage, a ring of four diodes excited by a carrier signal, and an output stage. The input and output stages typically include
transformers
''Transformers'' is a media franchise produced by American toy company Hasbro and Japanese toy company Tomy, Takara Tomy. It primarily follows the Autobots and the Decepticons, two alien robot factions at war that can transform into other forms ...
with centre-taps towards the diode ring. It is important to note that while the diode ring has some similarities to a
bridge rectifier
A diode bridge is a bridge rectifier circuit of four diodes that is used in the process of converting alternating current (AC) from the input terminals to direct current (DC, i.e. fixed polarity) on the output terminals. Its function is to con ...
the diodes in a ring modulator all point in the same clockwise or counterclockwise direction. (See the schematic of a ring modulator in the upper right.)
The carrier, which alternates between positive and negative current, at any 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
In electrical engineering, a switch is an electrical component that can disconnect or connect the conducting path in an electrical circuit, interrupting the electric current or diverting it from one conductor to another. The most common type of ...
(''double pole, double throw'') switch wired for reversing connections.
A particular elegance of the ring modulator is that it is bidirectional: the signal flow can be reversed allowing the same circuit with the same carrier to be used either as a
modulator
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
or
demodulator, for example in low-cost radio transceivers.
Integrated circuit methods of ring modulation
Some modern ring modulators are implemented using
digital signal processing techniques by simply multiplying the time domain signals, producing a nearly-perfect signal output.
Intermodulation
Intermodulation (IM) or intermodulation distortion (IMD) is the amplitude modulation of signals containing two or more different frequencies, caused by nonlinearities or time variance in a system. The intermodulation between frequency comp ...
products can be generated by carefully selecting and changing the
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of the two input waveforms. If the signals are processed digitally, the frequency-domain convolution becomes
circular convolution Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discre ...
. If the signals are
wideband
In communications, a system is wideband when the message bandwidth significantly exceeds the coherence bandwidth of the channel. Some communication links have such a high data rate that they are forced to use a wide bandwidth; other links ma ...
, this will cause
aliasing
In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or ''aliases'' of one another) when sampled. It also often refers to the distortion or artifact that results when ...
distortion, so it is common to
oversample the operation or low-pass filter the signals prior to ring modulation.
The
SID chip found in the
Commodore 64 allows for
triangle wave
A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.
Like a square wave, the triangle wave contains only odd harmonics. However, ...
s to be ring modulated. Oscillator 1 gets modulated by oscillator 3's frequency, oscillator 2 by oscillator 1's frequency, and oscillator 3 by oscillator 2's frequency. Ring modulation is disabled unless the carrier oscillator is set to produce a triangle wave, but the modulating oscillator can be set to generate any of its available waveforms. However, no matter what waveform you set the modulating oscillator to, the ring modulation will always have the effect of modulating a triangle wave with a square wave.
On an
ARP Odyssey synthesizer (and a few others from that era as well) the ring modulator is an
XOR function (formed from
four NAND gate
In digital electronics, a NAND gate (NOT-AND) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the ...
s) 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 as ring modulators, of course with regard to such matters as their operating limits and scale factors. Use of multiplier 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.
Limitations
Any DC component of the carrier will degrade the suppression of the carrier and thus in radio applications the carrier is typically transformer- or capacitor-coupled; in low frequency (e.g., audio) applications the carrier may or may not be desired in the output.
Imperfections in the diodes and transformers introduce artifacts of the two input signals. In practical ring modulators, this leakage can be reduced by introducing opposing imbalances (''e.g.'', variable resistors or capacitors).
Applications
Radio communications
Ring modulation has also been extensively used in
radio receivers, for example, to
demodulate
Demodulation is extracting the original information-bearing signal from a carrier wave. A demodulator is an electronic circuit (or computer program in a software-defined radio) that is used to recover the information content from the modulated c ...
an
FM stereo signal, and to heterodyne microwave signals in mobile telephone and wireless networking systems. In this case, the circuit is sometimes called a ''ring demodulator'', one of many possible
chopper circuits.
A ring modulator can be used to generate a double-sideband suppressed-carrier (DSB-SC) wave used in radio transmission.
Music and sound effects
One of the earliest musical instruments utilizing a ring modulator was the ''Melochord'' (1947) built by
Harald Bode. It was a two-tone melody keyboard instrument with foot controllers and later added a second keyboard for timbre control, featuring a white-noise generator, envelope controller, formant filters and ring modulators for harmonics.
The early Melochord was extensively used by
Werner Meyer-Eppler in the early days of the electronic music studio at
Bonn University.
Meyer-Eppler mentioned the musical application of ring modulator in his book "''Elektrische Klangerzeugung''", published in 1949.
Meyer-Eppler's student
Karlheinz Stockhausen
Karlheinz Stockhausen (; 22 August 1928 – 5 December 2007) was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th-century classical music, 20th and early 21st-century ...
used ring modulation in 1956 for some sounds in ''
Gesang der Jünglinge
''Gesang der Jünglinge'' (literally "Song of the Youths") is an 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. The vo ...
'' and his realization score for ''
Telemusik'' (1966
[ Collins, Nick (2010). ]
Introduction to Computer Music
', pp. 124-125. John Wiley & Sons. .) also calls for it. Indeed, several entire compositions by Stockhausen 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
A mantra ( Pali: ''manta'') or mantram (मन्त्रम्) is a sacred utterance, a numinous sound, a syllable, word or phonemes, or group of words in Sanskrit, Pali and other languages believed by practitioners to have religious, ...
'' (1970),
where the sounds from two pianos are routed through ring modulators; and ''Licht-Bilder'' (2002) from ''
Sonntag aus Licht'' (2003),
which ring-modulates flute and trumpet.
Other Stockhausen pieces employing ring modulation include ''
Kontakte
''Kontakte'' ("Contacts") is an electronic music work by Karlheinz Stockhausen, realized in 1958–60 at the ''Westdeutscher Rundfunk'' (WDR) electronic-music studio in Cologne with the assistance of Gottfried Michael Koenig. The score is Nr. 12 ...
'' (1960),
''Mikrophonie I'' (1964),
''
Hymnen
''Hymnen'' (German for "Anthems") is an electronic and concrete work, with optional live performers, by Karlheinz Stockhausen, composed in 1966–67, and elaborated in 1969. In the composer's catalog of works, it is No. 22.
The extended work is ...
'' (1969),
''
Prozession'' (1967),
and ''
Kurzwellen'' (1968).
A ring-modulator was the major component used in
Louis and Bebe Barron's music for the film ''
Forbidden Planet'' (1956). One of the best-known applications of the ring modulator may be its use by
Brian Hodgson
Brian Hodgson (born 1938) 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 program ...
of the
BBC Radiophonic Workshop
The BBC Radiophonic Workshop was one of the sound effects units of the BBC, created in 1958 to produce incidental sounds and new music for radio and, later, television. The unit is known for its experimental and pioneering work in electroni ...
to produce the distinctive voice of the
Dalek
The Daleks ( ) are a fictional extraterrestrials in fiction, extraterrestrial race of mutants principally portrayed in the British science fiction on television, science fiction television programme ''Doctor Who''. They were conceived by write ...
s in the
television series
A television show – or simply TV show – is any content produced for viewing on a television set which can be broadcast via over-the-air, satellite, or cable, excluding breaking news, advertisements, or trailers that are typically placed be ...
''
Doctor Who'', starting in 1963.
One of the first products dedicated for music was the ''Bode Ring Modulator'' developed in 1961 by
Harald Bode. 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, compatible with modular synthesizer architecture also advocated by him,
and these modules were licensed to
R.A. Moog for their
Moog modular synthesizer
The Moog synthesizer is a modular synthesizer developed by the American engineer Robert Moog. Moog debuted it in 1964, and Moog's company R. A. Moog Co. (later known as Moog Music) produced numerous models from 1965 to 1981, and again from 20 ...
s started in 1963–1964.
In 1963,
Don Buchla
Donald Buchla (April 17, 1937 – September 14, 2016) was an American pioneer in the field of sound synthesis. Buchla popularized the "West Coast" style of synthesis. He was co-inventor of the voltage controlled modular synthesizer along with Rob ...
included an optional ring modulator in his first modular synthesizer, the
Model 100.
Also
Tom Oberheim
Thomas Elroy Oberheim (born July 7, 1936, Manhattan, Kansas), known as Tom Oberheim, is an American audio engineer and electronics engineer best known for designing effects processors, analog synthesizers, sequencers, and drum machines. He has ...
built a ring modulator unit for
his musician friend in the late 1960s,
and it became an origin of
Oberheim Electronics ''Music Modulator''
and ''
Maestro
Maestro (; from the Italian '' maestro'' , meaning "master" or "teacher") is an honorific title of respect (plural: maestros or maestri). The term is most commonly used in the context of Western classical music and opera, in line with the ubiqu ...
Ring Modulator'',
one of the earliest ring modulator
effect products for guitarists. The
EMS VCS3,
Synthi A,
ARP 2600
The ARP 2600 is a semi-modular analog subtractive audio synthesizer produced by ARP Instruments, Inc.
History
Developed by a design team headed by ARP namesake Allen R. Pearlman and engineer Dennis Colin, the ARP 2600 was introduced in 1971 ...
,
Odyssey
The ''Odyssey'' (; grc, Ὀδύσσεια, Odýsseia, ) is one of two major ancient Greek epic poems attributed to Homer. It is one of the oldest extant works of literature still widely read by modern audiences. As with the ''Iliad'', th ...
,
Rhodes Chroma and
Yamaha CS-80 synthesizers also featured built-in ring modulators.
John McLaughlin employs the ring modulator heavily in the 1974
Mahavishnu Orchestra
The Mahavishnu Orchestra were a jazz fusion band formed in New York City in 1971, led by English guitarist John McLaughlin. The group underwent several line-up changes throughout its history across its two periods of activity, from 1971 to 1976 ...
album
Visions of the Emerald Beyond Especially on the track "On the Way Home to Earth". On
Miles Davis
Miles Dewey Davis III (May 26, 1926September 28, 1991) was an American trumpeter, bandleader, and composer. He is among the most influential and acclaimed figures in the history of jazz and 20th-century music. Davis adopted a variety of musi ...
' 1975 live album ''
Agharta'', guitarist
Pete Cosey
Peter Palus Cosey (October 9, 1943 – May 30, 2012) was an American guitarist who played with Miles Davis' band between 1973 and 1975. His fiercely flanged and distorted guitar invited comparisons to Jimi Hendrix. Cosey kept a low profile for ...
ran the sounds he played through a ring modulator.
Deep Purple's
Jon Lord
John Douglas Lord (9 June 194116 July 2012) was an English orchestral and rock composer, pianist, and Hammond organ player known for his pioneering work in fusing rock with classical or baroque forms, especially with the British rock band Deep ...
fed the signal from his Hammond through a Gibson Ring Modulator unit live on stage, which he described in 1989.
Founding member of
Hawkwind
Hawkwind are an English rock band known as one of the earliest space rock groups. Since their formation in November 1969, Hawkwind have gone through many incarnations and have incorporated many different styles into their music, including hard ...
, Dik Mik, a self-confessed non-musician, used a ring modulator as his main instrument during his time with the band (1969-1973).
Vangelis
Evangelos Odysseas Papathanassiou ( el, Ευάγγελος Οδυσσέας Παπαθανασίου ; 29 March 1943 – 17 May 2022), known professionally as Vangelis ( ; el, Βαγγέλης, links=no ), was a Greek composer and arranger of ...
used a ring modulator with his
Yamaha CS-80 to improvise his 1978 avant-garde-experimental album
Beaubourg. The music on the album is often atonal, with the ring modulator converting the synthesizer's sound into complex metallic timbres.
It remains the most experimental released work by the artist, with reviewers calling it "difficult listening at best".
Ring modulation is used in the piece ''Ofanim'' (1988/1997) by
Luciano Berio
Luciano Berio (24 October 1925 – 27 May 2003) was an Italian composer noted for his experimental work (in particular his 1968 composition ''Sinfonia'' and his series of virtuosic solo pieces titled '' Sequenza''), and for his pioneering work ...
, and in the first section is applied to a child's voice and a
clarinet: "The transformation of the child voice into a clarinet was desired. For this purpose, a pitch detector computes the instantaneous frequency
of the voice. Then the child voice passes through a ring modulator, where the frequency of the carrier
is set to
. In this case odd harmonics prevail which is similar to the sound of a clarinet in the low register."
[Zölzer, Udo; ed. (2002). ]
DAFX - Digital Audio Effects
', p.76-7. John Wiley & Sons. .
Analogue telephone systems
An early application of the ring modulator was for combining multiple analog telephone voice channels into a single wideband signal to be carried on a single cable using
frequency-division multiplexing
In telecommunications, frequency-division multiplexing (FDM) is a technique by which the total bandwidth available in a communication medium is divided into a series of non-overlapping frequency bands, each of which is used to carry a separat ...
. A ring modulator in combination with
carrier wave
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has ...
and filter was used to assign channels to different frequencies.
Early attempts at
securing analog telephone channels used ring modulators to modify the spectrum of the audio speech signals. 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.
See also
*
Theremin
The theremin (; originally known as the ætherphone/etherphone, thereminophone or termenvox/thereminvox) is an electronic musical instrument controlled without physical contact by the performer (who is known as a thereminist). It is named afte ...
References
External links
*
{{music technology
Audio effects
Electronic musical instruments
Frequency mixers
Radio modulation modes