Inelectronics,ring modulation is asignal processing function, an implementation offrequency mixing, in which twosignals are combined to yield an output signal. One signal, called the carrier, is typically asine wave or another simplewaveform; the other signal is typically more complicated and is called the input or themodulator signal.

Thering modulator takes its name from the original implementation in which theanalog circuit ofdiodes takes the shape of a ring, adiode ring.^[2] The circuit is similar to abridge rectifier, except that all four diodes are polarized in the same direction.

Ring modulation is similar toamplitude 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 signal 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 produce an output signal that is the sum of a sine wave with frequency 1,900 Hz and one with frequency 1,100 Hz. These two output frequencies are known assidebands. If one of the input signals has significantovertones (which is the case forsquare waves), the output sounds quite different, since eachharmonic generates its own pair of sidebands that is not harmonically-related.^[3]

Denoting the carrier signal by${\displaystyle c(t)}$, the modulator signal by${\displaystyle x(t)}$ and the output signal by${\displaystyle y(t)}$ (where${\displaystyle t}$ denotes time), ring modulation approximatesmultiplication:

${\displaystyle y(t)=x(t)c(t).}$

If${\displaystyle c(t)}$ and${\displaystyle x(t)}$ are sine waves with frequencies${\displaystyle f_c}$ and${\displaystyle f_x}$, respectively, then${\displaystyle y(t)}$ is the sum of two (phase-shifted) sine waves, one of frequency${\displaystyle f_c+f_x}$ and the other of frequency${\displaystyle f_c-f_x}$. This is a consequence of thetrigonometric identity:

${\displaystyle \sin (u)\sin (v)=\frac{1}{2}\left(\cos (u-v)-\cos (u+v)\right).}$

Alternatively, one can use the fact that multiplication in thetime domain is the same asconvolution in thefrequency domain.

Ring modulators thus output thesum and difference of the frequencies present in each waveform. This process of ring modulation produces a signal rich inpartials. 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 makeup. When the oscillators' frequencies arenot harmonically related, ring modulation createsinharmonics, often producing bell-like or otherwise metallic sounds.

If the carrier signal is asquare wave of frequency${\displaystyle f_c}$, whoseFourier expansion contains thefundamental and a series of reducing-amplitude oddharmonics:

${\displaystyle c(t)=\sin f_{c}t+\frac{1}{3}\sin 3f_{c}t+\frac{1}{5}\sin 5f_{c}t+\frac{1}{7}\sin 7f_{c}t+\dots }$

and the carrier frequency${\displaystyle f_c}$ is at least twice the maximum frequency of the modulating signal${\displaystyle x(t)}$, then the resulting output is a series of duplicates of${\displaystyle x(t)}$ at increasing regions of the frequency spectrum.^[4] For example, let${\displaystyle x(t)}$ represent a sine wave at 100 Hz, and the carrier${\displaystyle c(t)}$ be an ideal square wave at 300 Hz. The output then includes 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 adouble-balanced mixer,^[5] 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.

The ring modulator was invented by Frank A. Cowan in 1934 and patented in 1935^[6] as an improvement on the invention of Clyde R. Keith atBell Labs.^[7] The original application was in the field ofanalog telephony forfrequency-division multiplexing for carrying multiple voice signals over telephone cables. It has since been applied to a wider range of uses, such asvoice inversion, radiotransceivers, andelectronic music.

While the original Cowan patent describes a circuit with a ring of four diodes, later implementations usedFETs as the switching elements.

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 includetransformers with center-taps towards the diode ring. While the diode ring has some similarities to abridge rectifier the diodes in a ring modulator all point in the same clockwise or counterclockwise direction.

The carrier, which alternates between positive and negative current, at any given time makes one pair of diodes conduct, andreverse-biases the other pair. The conducting pair carries 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 aDPDT (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 amodulator ordemodulator, for example in low-cost radio transceivers.

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Some modern ring modulators are implemented usingdigital signal processing techniques by simply multiplying the time domain signals, producing a nearly-perfect signal output.Intermodulation products can be generated by carefully selecting and changing thefrequency of the two input waveforms. If the signals are processed digitally, the frequency-domain convolution becomescircular convolution. If the signals arewideband, this causesaliasing distortion, so it is common tooversample the operation or low-pass filter the signals prior to ring modulation.

TheSID chip found in theCommodore 64 allows fortriangle waves 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 which waveform the modulating oscillator is using, the ring modulation always has the effect of modulating a triangle wave with a square wave.^{[8][failed verification]}

On anARP Odyssey synthesizer (and a few others from that era as well) the ring modulator is anXOR function (formed fromfourNAND 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 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.

Any DC component of the carrier degrades 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.^[9]

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).

Ring modulation has also been extensively used inradio receivers, for example, todemodulate anFM stereo signal, and to heterodyne microwave signals in mobile telephone and wireless networking systems. In this case, the circuit is sometimes called aring demodulator, one of many possiblechopper circuits.^[10][11] A ring modulator can be used to generate a double-sideband suppressed-carrier (DSB-SC) wave used in radio transmission.^[12]

Audio samples of the ring modulation effect:

Unprocessed original sample

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Ring modulation with a 2500 Hz sound

Notice the bell-like sound.

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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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One of the earliest musical instruments utilizing a ring modulator was theMelochord (1947) built byHarald 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.^[13] The early Melochord was extensively used byWerner Meyer-Eppler in the early days of the electronic music studio atBonn University.^[14] Meyer-Eppler mentioned the musical application of ring modulator in his bookElektrische Klangerzeugung, published in 1949.^[15]

Meyer-Eppler's studentKarlheinz Stockhausen used ring modulation in 1956 for some sounds inGesang der Jünglinge and his realization score forTelemusik (1966^[16]) also calls for it. Indeed, several entire compositions by Stockhausen are based around it, such asMixtur (1964), one of the first compositions for orchestra and live electronics;Mikrophonie II (1965), where the sounds of choral voices are modulated with aHammond organ;Mantra (1970),^[16] where the sounds from two pianos are routed through ring modulators; andLicht-Bilder (2002) fromSonntag aus Licht (2003),^[1] which ring-modulates flute and trumpet.^[17][18][19] Other Stockhausen pieces employing ring modulation includeKontakte (1960),^[1]Mikrophonie I (1964),^[1]Hymnen (1969),^[1]Prozession (1967),^[1] andKurzwellen (1968).^[1]

A ring-modulator was the major component used inLouis and Bebe Barron's music for the filmForbidden Planet (1956). One of the best-known applications of the ring modulator may be its use byBrian Hodgson of theBBC Radiophonic Workshop to produce the distinctive voice of theDaleks in thetelevision seriesDoctor Who, starting in 1963.^[20]

One of the first products dedicated for music was theBode Ring Modulator developed in 1961 byHarald Bode. Also in 1964 he developed theBode Frequency Shifter, which produced a clearer sound by eliminating a side band.^[21] These devices were designed to be controlled by voltage, compatible with modular synthesizer architecture also advocated by him,^[22] and these modules were licensed toR.A. Moog for theirMoog modular synthesizers started in 1963–1964.^[23] In 1963,Don Buchla included an optional ring modulator in his first modular synthesizer, theModel 100.^[24] AlsoTom Oberheim built a ring modulator unit forhis musician friend in the late 1960s,^[25][26] and it became an origin ofOberheim ElectronicsMusic Modulator^[27] andMaestro Ring Modulator,^[28] one of the earliest ring modulatoreffect products for guitarists. TheEMSVCS3,Synthi A,ARP 2600,Odyssey,Rhodes Chroma andYamaha CS-80 synthesizers also featured built-in ring modulators.

John McLaughlin employs the ring modulator heavily in the 1974Mahavishnu Orchestra albumVisions of the Emerald Beyond, especially on the track "On the Way Home to Earth". OnMiles Davis' 1975 live albumAgharta, guitaristPete Cosey ran the sounds he played through a ring modulator.^[29]Deep Purple'sJon Lord fed the signal from his Hammond through a Gibson Ring Modulator unit live on stage, which he described in 1989.^[30][31] Founding member ofHawkwind, Dik Mik, a self-confessed non-musician, used a ring modulator as his main instrument during his time with the band (1969-1973).^[32]

Vangelis used a ring modulator with hisYamaha CS-80 to improvise his 1978 avant-garde-experimental albumBeaubourg. The music on the album is often atonal, with the ring modulator converting the synthesizer's sound into complex metallic timbres.^[33] It remains the most experimental released work by the artist, with reviewers calling it "difficult listening at best".^[34]

Ring modulation is used in the pieceOfanim (1988/1997) byLuciano Berio, and in the first section is applied to a child's voice and aclarinet: "The transformation of the child voice into a clarinet was desired. For this purpose, a pitch detector computes the instantaneous frequency${\displaystyle f_0(n)}$ of the voice. Then the child voice passes through a ring modulator, where the frequency of the carrier${\displaystyle f_c}$ is set to${\displaystyle f_0(n)/2}$. In this case odd harmonics prevail which is similar to the sound of a clarinet in the low register."^{[35][failed verification]}

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 usingfrequency-division multiplexing. A ring modulator in combination withcarrier wave and filter was used to assign channels to different frequencies.

Early attempts atsecuring 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.

• Theremin

• Scott Lehman."Effects Explained: Ring Modulation". Harmony Central. Archived fromthe original on 1 December 2005.

• Audio effects
• Electronic musical instruments
• Frequency mixers
• Radio modulation modes

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