# Ring modulation

Schematic diagram of a ring modulator, showing ring of diodes

In electronics, ring modulation is a signal-processing function, an implementation of frequency mixing, performed by multiplying two signals, where one is typically a sine wave or another simple waveform and the other is the signal to be modulated. A ring modulator is an electronic device for ring modulation. A ring modulator may be used in music synthesizers and as an effects unit.

The function derives its name from the fact that the analog circuit of diodes originally used to implement this technique takes the shape of a ring.[1] The circuit is similar to a bridge rectifier, except that instead of the diodes facing left or right, they face clockwise or counterclockwise.

## Operation

Double balanced high level frequency mixer Mini-Circuits SBL-1 with four Schottky diodes. LO level +7 dBm (1.41 Vp-p) and RF 1–500 MHz (ADE-1: 0.5–500 MHz).

Ring modulators frequency mix or heterodyne two waveforms, and 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 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. When the oscillators' frequencies are not harmonically related, ring modulation creates inharmonics, often producing bell-like or otherwise metallic sounds.

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 f2f1 = 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 techniques by simply multiplying the time domain 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 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 f1 and f2 (f1 < f2) are multiplied, two new sine waves are created, with one at f1 + f2 and the other at f2f1. 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 products can be generated by carefully selecting and changing the frequency 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.

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.

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, creating a polarity inversion between the transformers.

Ring modulators frequency mix or heterodyne two waveforms, and output the sum and difference of the frequencies present in each waveform. Multiplication in the time domain is the dual of convolution in the frequency domain, so the output waveform contains the sum and difference of the input spectral components. For the basic case where two sine waves of frequencies fcarrier and fvoice are multiplied, two new sine waves are created, one at fcarrier + fvoice and the other at fcarrierfvoice.

In a ring modulator—being a switching modulator—the carrier signal is ideally a square wave, whose Fourier expansion contains the fundamental and a series of reducing-amplitude odd harmonics:

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

In frequency terms:

${\displaystyle C=f_{c}+{\frac {1}{3}}3f_{c}+{\frac {1}{5}}5f_{c}+{\frac {1}{7}}7f_{c}+\ldots }$

When the carrier frequency is at least twice the maximum frequency of the modulating signal V(t) then the result is a series of duplicates of V(t) at increasing regions of the frequency spectrum. [2] When the carrier 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. For example, let V(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.

Because the output contains neither the individual voice or carrier components the ring modulator is said to be a double-balanced mixer, [3] 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[4] as an improvement on the invention of Clyde R. Keith at Bell Labs.[5] 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.

## 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.

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 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. (See also Integrated circuit methods of ring modulation)

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

On the C64 SID chip, ring modulation multiplies the triangle wave of oscillator 1 and oscillator 3. Ring modulation is muted unless oscillator 1 is set to produce a triangle wave but oscillator 3 can be set to generate any of its available waveforms.[6]

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 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.

## 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. [7]

Imperfections in the diodes and transformers introduce artefacts of the two input signals. In practical ring modulators this leakage can be reduced by introducing opposing imbalances (e.g., variable resistors or capacitors).

## Refinements

The original Cowan patent describes a circuit with a ring of four diodes. Later implementations use FETs as the switching elements.

## Use in music

One of the earliest musical instruments utilizing a ring modulator may be 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.[8] The early Melochord was extensively used by Werner Meyer-Eppler in the early days of the electronic music studio at Bonn University.[9]

Meyer-Eppler mentioned the musical application of ring modulator in his book "Elektrische Klangerzeugung", published in 1949[10] (also described in Elena Ungeheuer's book[11]). In 1951, he joined to the successive proposal on establishment of WDR Studio for Electronic Music in Cologne, and at the beginning of the studio, already ring modulator was equipped along with the sound sources and audio gadget including sine wave oscillators, noise generator, etc.[12] Then in 1953, the above-mentioned Melochord by Harald Bode, along with the Electronic Monochord by Friedrich Trautwein, was specifically commissioned by the WDR Studio to upgrade their synthesis modules,[13] and used by the Elektronische Musik group especially in the first half of the 1950s.[9][14] Also Meyer-Eppler demonstrated his experiments in June 1953 in Delft.[15][verification needed]

Meyer-Eppler's student, Stockhausen also used ring modulation in 1956 for some sounds in Gesang der Jünglinge and his realization score for Telemusik (1966) also calls for it. Indeed, whole compositions 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 (1970, where the sounds from two pianos are routed through ring modulators), and Licht-Bilder (2002) from Sonntag aus Licht, which ring-modulates flute and trumpet.[16][17][18]

A ring-modulator was the major component used in Louis and Bebe Barron's music for the film Forbidden Planet (1956).

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 Back Home to Earth".

On Miles Davis' 1975 live album Agharta, guitarist Pete Cosey ran the sounds he played through a ring modulator.[19] Deep Purple's Jon Lord fed the signal from his Hammond through a Gibson Ring Modulator unit live on stage.[20][21] 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.[22] Black Sabbath's 1970 hit "Paranoid" and the 1978 Never Say Die! album track "Johnny Blade" both have a ring mod panned against the dry track on the guitar solos.[citation needed] The 1974 Devo track "Mechanical Man" which appears on Hardcore Devo Vol. 1 has the lead vocal highly treated with the effect.[citation needed]

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.[23] These devices were designed to be controlled by voltage, for today's modern modular synthesizer architecture also advocated by him,[24] and these modules were licensed to R.A. Moog for their Moog modular synthesizers started in 1963–1964.[25] In 1963, Don Buchla included an optional ring modulator in his first modular synthesizer, the Model 100.[26] Also Tom Oberheim built a ring modulator unit for his musician friend in the late 1960s,[27][28] and it became an origin of Oberheim Electronics Music Modulator[29] and Maestro Ring Modulator,[30] one of the earliest ring modulator effect products for guitarists. The EMS VCS3, Synthi A, ARP 2600, Odyssey, Rhodes Chroma and Yamaha CS-80 synthesizers also featured built-in ring modulators.

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 Doctor Who, starting in 1963.[31]

## Other applications

Ring modulation has also been extensively used in radio receivers, for example to demodulate an FM stereo signal, and to down-convert 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.[32][33] A ring modulator can be used to generate a double-sideband suppressed-carrier (DSB-SC) wave used in radio transmission.[34]

### Analogue telephone systems

The original application of the ring modulator was for combining multiple analogue telephone voice channels into a single wideband signal to be carried on a single cable using frequency-division multiplexing.

Early attempts at securing analogue 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.

Ring modulation has also been extensively used in radio receivers, for example to demodulate an FM stereo signal, and to down-convert 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.[32] [33] A ring modulator can be used to generate a double-sideband suppressed-carrier (DSB-SC) wave used in radio transmission. [34]

### Electronic music

Ring modulators have been used in the field of electronic music since the 1950s where the effect they create is known as ring modulation.

As of 2016, electronic instruments usually provide an effect called "ring modulation" using some other circuitry (such as an analog multiplier) instead of an actual diode ring; careful design can produce similar results.[2]

## References

1. ^ Richard Orton, "Ring Modulator", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001): "the ring modulator takes its name from the characteristic ring formation of four diodes in its analog circuit."
2. ^ a b "Multipliers vs. Modulators".
3. ^ "Double Balanced Mixer - Theory; Circuit; Operation - Tutorial - Radio-Electronics.Com".
4. ^ U.S. Patent 2,025,158
5. ^ U.S. Patent 1,855,576
6. ^ Commodore Programmer's Reference Guide, page 463
7. ^ "Synth Secrets, Part 11: Amplitude Modulation".
8. ^ Rebekkah Palov (July 2011), "Harald Bode—A Short Biography", eContact!, Canadian Electroacoustic Community, 13 (4)
9. ^ a b "The "Melochord" (1947–9)", The Keyboardmuseum Online, archived from the original on 2007-11-14 (description and history)
10. ^ Werner Meyer-Eppler, Elektronische Klangerzeugung: Elektronische Musik und synthetische Sprache, (Bonn: Ferdinand Dümmlers, 1949)
11. ^ Elena Ungeheuer, Wie die elektronische Musik "erfunden" wurde. Quellenstudie zu Werner Meyer-Epplers Entwurf zwischen 1949 und 1953, (Mainz, inter al.: Schott, 1992), p. 208, ISBN 3-7957-1891-0
12. ^ Thom Holmes, Electronic and Experimental Music (second ed.), (New York: Routledge, 1985), p. 96, ISBN 0-203-42706-8 (Master e-book), ISBN 0-203-43926-0 (Adobe eReader), ISBN 0-415-93643-8 (hard cover), ISBN 0-415-93644-6 (pbk)
13. ^ Tom Rhea (May 2004), "Harald Bode", Video History Project, Experimental Television Center, archived from the original on 2011-07-19 (also broken format page remains in here)
14. ^ Marietta Morawska-Büngeler, Schwingende Elektronen: Eine Dokumentation über das Studio für Elektronische Musik des Westdeutschen Rundfunks in Köln, 1951–1986, Cologne-Rodenkirchen: P. J. Tonger Musikverlag, 1988, p. 13
15. ^ Werner Meyer-Eppler (1953). "Welche Möglichkeiten bestehen für eine sinnvolle Anwendung elektronischer Musikinstrumente ?" [Which Possibilities Exist for the Meaningful Application of Electronic Music Instruments?]. Musical Acoustics. 1st ICA-Congress. Electro-Acoustics [Delft, 1953] (in German).; published on: Cornelis Willem Kosten; M. L. Kasteleyn (eds.). Electro-acoustics: Proceedings of the First ICA-congress (PDF). [held in the Netherlands from 16th to 24th June 1953]. Netherlands. pp. 239–241. ASIN B0000EFZ68.[full citation needed] — features the Bode Melochord of the WDR Studio for Electronic Music in Cologne.
16. ^ Ludger Brümmer, "Stockhausen on Electronics, 2004", Computer Music Journal 32, no. 4 (2008):10–16.
17. ^ Karlheinz Stockhausen, "Electroacoustic Performance Practice", translated by Jerome Kohl, Perspectives of New Music 34, no. 1 (Winter, 1996): 74–105. Citation on 89.
18. ^ Karlheinz Stockhausen, "Einführung"/"Introduction", English translation by Suzanne Stephens, in booklet accompanying Karlheinz Stockhausen, Licht-Bilder (3. Szene vom SONNTAG aus LICHT), 2-CD set, Stockhausen Gesamtausgabe/Complete Edition 68A–B (Kürten: Stockhausen-Verlag, 2005): 10 & 51
19. ^ Trzaskowski, Andrzej (1976). Jazz Forum: The Magazine of the International Jazz Federation: 74. Most of the selections are kept in the rock-jazz climate with the rhythm course being interrupted now and again by an overflowing patch of accumulated layers of electronic and percussive effects (Theme from Jack Johnson, Prelude). In fact, electronic effects appear repeatedly in the form of 'bruitistic' whizzes and grinds of the synthi resembling a buzz saw and of the guitar steered through a ring modulator. Missing or empty |title= (help)
20. ^ "Lord Almighty". Keyboard Magazine. 24. 1998. Retrieved 21 January 2016.
21. ^ "Interview with Jon Lord". Modern Keyboard. January 1989. Retrieved 21 January 2015.
22. ^ Abrahams, Ian (2004). Hawkwind: Sonic Assassins. SAF Publishing. p. 20. ISBN 9780946719693.
23. ^ Harald Bode—A Lifetime for Sound (PDF), Harald Bode News, retrieved 2011-01-27
24. ^ Harald Bode, "European Electronic Music Instrument Design", Journal of the Audio Engineering Society 9 (1961): 267.
25. ^ Tom Rhea, Harald Bode Biography, (New York: Experimental Television Center Ltd, 2004), archived from the original on 2011-07-19 (also broken format page remains)
26. ^ Buchla Electronic Musical Instruments—Historical Overview, Buchla & Associates, retrieved 2011-01-27
27. ^ Thomas E. Oberheim, "A Ring Modulator Device for the Performing Musician", AES Convention 38 (May 1970), No. 708 (G-4).
28. ^ "Session Transcript: Tom Oberheim", Red Bull Music Academy Barcelona 2008
29. ^ Oberheim Music Modulator (photo). Edison Music Corporation.
30. ^ Maestro RM-1A Ring Modulator, DiscoFreq's Effects Database
31. ^ Jeremy Bentham, Doctor Who: The Early Years, (London: W.H. Allen, 1986), p. 127, ISBN 0-491-03612-4
32. ^ a b Meikle, Hamish (2008). Modern Radar Systems. Artech House. p. 336. ISBN 978-1-59693-243-2.
33. ^ a b Yadav, Abhishek (2008). Analog Communication System. Firewall Media. p. 83. ISBN 978-81-318-0319-6.
34. ^ a b T G Thomas S Chandra Sekhar (2005). Communication Theory. Tata McGraw-Hill Education. p. 37. ISBN 978-0-07-059091-5.