HOME

TheInfoList



OR:

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 electronics, a mixer, or frequency mixer, is an electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals are applied to a mixer, and it produces new signals at the sum and di ...
, in which two signals 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, ''Electron ...
; the other signal is typically more complicated and is called the input or the modulator signal. A ring modulator is an electronic device for ring modulation. A ring modulator may be used in music
synthesizer A synthesizer (also spelled synthesiser) is an electronic musical instrument that generates audio signals. Synthesizers typically create sounds by generating waveforms through methods including subtractive synthesis, additive synthesis ...
s 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 e ...
. The name derives from the fact that the analog circuit 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, 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 (which is the case for
square waves A square wave is a non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square wave, the transitions ...
), 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 c(t), the modulator signal by x(t) and the output signal by y(t) (where t denotes time), ring modulation is described by the formula :y(t)=x(t)\cdot c(t). If c(t) and x(t) are sine waves with frequencies f_c and f_x, respectively, then y(t) will be the sum of two ( phase-shifted) sine waves, one of frequency f_c+f_x and the other of frequency f_c-f_x. This is a consequence of the trigonometric identity :\sin(u)\cdot \sin(v)=\frac\left(\cos(u-v)-\cos(u+v)\right). 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 ...
is the same as 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 ...
. 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 inharmonics, often producing bell-like or otherwise metallic sounds. If the carrier signal is a
square wave A square wave is a non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square wave, the transitions b ...
of frequency f_c, whose Fourier expansion contains the fundamental and a series of reducing-amplitude odd harmonics: :c(t) = \sin f_ct + \frac 1 3 \sin 3f_ct + \frac 1 5 \sin 5f_ct + \frac 1 7 \sin 7f_ct + \ldots and the carrier frequency f_c is at least twice the maximum frequency of the modulating signal ''x(t)'', then the resulting output is a series of duplicates of ''x(t)'' at increasing regions of the frequency spectrum. For example, let ''x(t)'' represent a sine wave at 100 Hz, and the carrier ''c(t)'' 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 scientific development company owned by mult ...
. The original application was in the field of analogue telephony for frequency-division multiplexing for carrying multiple voice signals over telephone cables. It has since been applied to a wider range of uses, such as voice inversion, radio transceivers, and
electronic music Electronic music is a Music genre, genre of music that employs electronic musical instruments, digital instruments, or electronics, circuitry-based music technology in its creation. It includes both music made using electronic and electromech ...
. 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 with centre-taps towards the diode ring. It is important to note that while the diode ring has some similarities to a bridge rectifier 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 (''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 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 Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner ar ...
techniques by simply multiplying the time domain signals, producing a nearly-perfect signal output. Intermodulation 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 ...
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 low-pass filter the signals prior to ring modulation. The SID chip found in the Commodore 64 allows for triangle 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 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 th ...
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 receiver In radio communications, a radio receiver, also known as a receiver, a wireless, or simply a radio, is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna. T ...
s, for example, to demodulate 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 used ring modulation in 1956 for some sounds in '' Gesang der Jünglinge'' 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 (Sunday from Light) 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'' (Light). Its stage premiere in 20 ...
'' (2003), which ring-modulates flute and trumpet. Other Stockhausen pieces employing ring modulation include '' Kontakte'' (1960), ''Mikrophonie I'' (1964), '' Hymnen'' (1969), ''
Prozession ''Prozession'' (Procession), for tamtam, viola, electronium, piano, microphones, filters, and potentiometers (six performers), is a composition by Karlheinz Stockhausen, written in 1967. It is Number 23 in the catalogue of the composer's works. C ...
'' (1967), and '' Kurzwellen'' (1968). A ring-modulator was the major component used in
Louis and Bebe Barron Bebe Barron ( – ) and Louis Barron ( – ) were two American pioneers in the field of electronic music. They are credited with writing the first electronic music for magnetic tape composed in the United States, and the first entirely elec ...
'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 of the BBC Radiophonic Workshop to produce the distinctive voice of the Daleks 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 ...
'' 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 synthesizers started in 1963–1964. In 1963, Don Buchla included an optional ring modulator in his first modular synthesizer, the
Model 100 The TRS-80 Model 100 is a portable computer introduced in April 26th, 1983. It is one of the first notebook-style computers, featuring a keyboard and liquid crystal display, in a battery-powered package roughly the size and shape of a notepad or ...
. Also Tom Oberheim 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 ubi ...
Ring Modulator'', one of the earliest ring modulator effect products for guitarists. The EMS
VCS3 The VCS 3 (or VCS3; an initialism for ''Voltage Controlled Studio, version #3'') is a portable analog synthesizer with a flexible modular voice architecture introduced by Electronic Music Studios (London) Limited (EMS) in 1969. EMS released ...
,
Synthi A The VCS 3 (or VCS3; an initialism for ''Voltage Controlled Studio, version #3'') is a portable analog synthesizer with a flexible modular voice architecture introduced by Electronic Music Studios (London) Limited (EMS) in 1969. EMS released ...
, ARP 2600,
Odyssey The ''Odyssey'' (; grc, Ὀδύσσεια, Odýsseia, ) is one of two major Ancient Greek literature, ancient Greek Epic poetry, epic poems attributed to Homer. It is one of the oldest extant works of literature still widely read by moder ...
, 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 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 Agartha (sometimes Agartta, Agharti, Agarath, Agarta, Agharta, or Agarttha) is a legendary kingdom that is said to be located in the Earth's core. It is related to the belief in a hollow Earth and is a popular subject in esotericism. History The ...
'', guitarist Pete Cosey ran the sounds he played through a ring modulator. Deep Purple's Jon Lord fed the signal from his Hammond through a Gibson Ring Modulator unit live on stage, which he described in 1989. Founding member of Hawkwind, 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 Centre Pompidou (), more fully the Centre national d'art et de culture Georges-Pompidou ( en, National Georges Pompidou Centre of Art and Culture), also known as the Pompidou Centre in English, is a complex building in the Beaubourg area of ...
. 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, 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 f_0 (n) of the voice. Then the child voice passes through a ring modulator, where the frequency of the carrier f_c is set to f_0 (n)/2. 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. A ring modulator in combination with carrier wave 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