The Ringmodulator

Ring modulators are electronic circuits stemming from early telephony. They are at the essence of the possibility to send and receive many simultaneous telephone conversations through one and the same couple of wires. Soon enough the circuit has found abundant applications throughout 20th century music production and performance. They are fundamental also to the working of radio receivers and emitters, both for AM and FM. The historical ring modulator circuit looks like this:

[ref.69.10]

There are two inputs and a single output. The two signals get multiplied in the diode-ring configuration between the two transformers. Input signals for this circuit must be kept smaller than 25mV. That's why there are four resistors in thye circuit. Their value must be calculated such that they are larger then the conducting resistance of the diodes used under voltage conditions specified. The diodes must be matched withing fractions of a percent. The ideal transformers for this circuit must be of the toroidal type. Hard to find for audio applications but if you are lucky you can every so often recycle them from old professional audio equipment stemming from physics labs or electronic music studios.

 

It is a purely analog circuit and its functioning can be analysed as follows.

- Two input signals are required. The output signal contains all sum and difference tones between both input signals, the input signals themselves disappearing from the output signal. From a mathematical point of view, the transfer function seen in the time-domain is:

Uout= (Uin_x * Uin_y) / k

How this connects to the statement about resulting sum and difference tones is a bit more involved. The circuit behaves as a multiplier in the time-domain. Let's suppose the input signals are periodic functions such as:

Uin_x= Upx * COS((wx+ phi_x).t)

Uin_y= Upy * COS((wy+ phi_y).t)

wherein
wx = 2 * Pi * fx

and

wy = 2 * Pi * fy

Thus fx en fy represent the respective frequencies of the input signals and where phi_x, phi_y represent the phase-angles of these signals. Upx and Upy are the peak amplitudes of both signals.

Further development of this product leads to:

Uout = Upx*Upy * {COS[(wx-wy)* t - ph ] + COS[(wx+wy)*t + ph] } * COS(wx+ph* t)

= (Upx*Upy/2) * {COS[wy*t + ph] + COS[-wy* t - ph] + COS[(2*wx +/- wy)* t +/- ph)

(suppose ph = phi_x - phi_y)

Expressed in words, this means that at the output we are getting nothing but the sum and difference tones between the input signals. The transfer function becomes even intuitive of we imagine both input signals being the same. In this case we would get:

 

Ui = Um * SIN(wx*t) input signal

[Um * SIN(wx*t)] * [ Um * SIN(wx*t)] = (Um * SIN(wx*t))^2

If we now apply a standard rule in goniometry we derive that:

[Um * SIN(wz*t)]^2 = ((Um^2) / 2)) * [1- COS(2*wx*t)]

Or, expressed in words, the output of the circuit offers us a periodic signal with twice the frequency of the input signal. Simply said, we just made an octave doubler. For those amongst our readers wanting to dig further into the internal guts of such modulators and demodulators, we refer to the exhaustive technical literature available on the subject. The printed data books published by Analog Devices and Burr-Brown are invaluable sources of information. A thorough understanding of these devices is essential for a proper understanding of FM-synthesis as it has been fundamental for the development of electronic synthesizers since about 1970. FM-synthesis is entirely based on the multiplication of wave forms.

For pure sine wave input signals, the characteristics of the resulting output signal can be predicted easily, as shown in a few examples:

  • suppose U1= 440 Hz (la) and U2= 660 Hz (mi)

    gives: Uout+=1100Hz (do#)

    as well as Uout-= 220Hz (la)

  • A pure fifth interval thus undergoes a transformation to the interval of an octave plus a natural major third.

  • suppose:. U1 = 440 Hz (la)

    U2 = 880 Hz (la')

    gives: Uout+=1320Hz (mi)

    as well as: Uout-= 440Hz (la)

  • In this example, the octave between the input signals, gives us an octave and a pure fifth at the output

  • vb. U1 = 440Hz (la)

    U2 = 466Hz (sib)

    geeft: Uout+= 906Hz (la+)

    + Uout-= 26Hz (la-)

  • In this case we get at the output an A raised a quartertone together with a very low A, a quartertone down. The latter however will be perceived as a fast tremolo. As soon as we try to feed the ringmodulator with more complex waveforms such as those stemming from acoustic musical instruments, the results can get very complex. This is caused by the fact that the multiplier applies its transformation to the entire spectrum found in the input signals. If we feed at least one of the inputs with spikes or pulses, we can easily obtain sounds refering to metal percussion instruments such as gongs and bells. Needless to say that this has fascinated generations of composers and musicians using technology.

    A special application of the ringmodulator is the octave doubler, obtained by shorting both inputs together and feeding it with a single periodic signal, as demonstrated earlier mathematically.

    Also, we can feed one of the inputs with a wide band noise signal and the other input with a sine wave. At the output colored noise centered around the frequency of the sine wave will be obtained.

    We can also use the ringmodulator as a VCA (voltage controlled amplifier). It is enough to use one of the inputs as very low frequency input or even feed it with ADSR signals. As a matter of fact, the VCA is nothing but a specialised application of the fundamental ringmodulator circuit.

    Functionally, we encounter the circuit an many very old as well as new electronic instruments: the Theremin as well as the theremin derived Ondes Martenot.

    If we use the ringmodulator to multiply two signals in the ultrasonic audio range and if their difference tone falls in the audio band, then we can use it to detect just this difference tone as the co-existent sum tone a fortiori will be out of the audio range.

    As soon as electronic music studios started rising up in the beginning of the fiftees of the 20th century, the ringmodulator became a standard component for the production of electronic music. Early composers that made extensive use of them are Karlheinz Stockhausen (Telemusik, Mantra, Hymnen, Mixtur...), Wladimir Ussachewsky, Gordon Mumma, John Cage... The analog electronic synthesizers as they were build since the seventies, almost all contained at least one patchable ringmodulator (Synket, Putney of VCS3, Korg, R.Moog, ARP, Buchla, Synthelog, Serge etc).

    Even in some orchestral compositions one may encounter requests for ringmodulators, for instance the Flemish composer Luc Brewaeys uses them in 'Trajet' and 'Due Cose'.


    Although the original ringmodulator -or with its more technical name the double balanced modulator/demodulator- was build using transformers or coils, nowadays we would invariably make use of specialised analog chips. Of course, digital implementations are also possible and have become even commonplace.

    Usefull analog integrated circuits are:

    LM1496 of LM1596 (Philips, National Semiconductor e.a.)

    HA2546, HA2547, ICL8013 (Harris)

    AD532, AD534, AD539, AD632, AD633, AD743 (Analog Devices)

    MPY534 (Burr Brown)

    Good quality chips (with 0.5% precision) combined with a wide frequency bandwidth are not cheap. The MPY534 used to go for some 150 Euro. If you can live with 2% precision, you can go for the AD633 at ca. 20 Euro.

    `

    In de meest algemene vorm moet de ringmodulator beschouwd worden als een analoge komputer. De meest geavanceerde chips zijn dan ook opgebouwd als algemeen inzetbare analoge komputerbouwstenen, waarmee naast vermenigvuldigers, ook talloze andere overdrachtfunkties (deling, worteltrekking, log- en antilog funkties ...) gerealiseerd kunnen worden.

    Technische problemen:

      Hoewel de teorie wil dat van de ingangssignalen niets in het uitgangssignaal aanwezig is, blijkt dit in de praktijk zeer moeilijk te realiseren. Zeker wie een ringmodulator volgens de klassieke technieken (gebruik makend van spoelen of transformatoren en een diode- vermenigvuldiger) wil opbouwen, zal zich geplaatst zien voor kwazi onoverkomelijke doorlekproblemen. Pas onder gebruikmaking van de modernste chips -die echter nogal prijzig zijn- is dit goed te voorkomen. Deze problemen gaven in het verleden aanleiding tot het gebruik van 'gating'-technieken voor een van beide ingangssignalen. Hierbij werd het signaal van de A ingang dan alleen naar de schakeling gevoerd, wanneer ook op de B ingang een signaal aanwezig was. De VCA geschakeld in het signaalpad van de A ingang en spanningsgestuurd vanuit de B ingang was de standaard oplossing voor dit probleem bij analoge synthesizers. In partituren uit de jaren '70 zullen we wanneer ringmodulatoren worden voorgeschreven dan ook steeds een dergelijke patch aantreffen.

     

    Bibliographical references:

    - ORTON, Richard "Ring Modulator" in: Groves Dictionary of Musical Instruments, dl3.,p.249 (1984)

    - BODE, Harald "The Multiplier type Ringmodulator in: Electronic Music Review,nr.1, 1967

    - STRANGE, Allen "Electronic Music" ed.:New York, 1972

    - RAES, Godfried-Willem "Een Onzichtbaar Muziekinstrument" , Doktorale dissertatie R.U.G., Gent 1993.


    Moderne praktische schakelingen geschikt voor nabouw

    LM1496 schakeling met enkelvoudige voeding [cfr.archief- geschrapt 1997]

    zie: Elektuur, Formant-boek, deel 1 & 2

    AD633 schakeling met symmetrische voeding:

    [ref.:93-04]

    In dit ontwerp wordt een dubbele opamp toegepast, eentje voor elke modulator ingang. Hiermee kunnen de ingangsnivos optimaal worden aangepast. Noteer dat de blokkeerkondensator van 1mF in serie met de ingangssignalen alle DC spanningen blokkeren. Voor audiogebruik is dit prima. Wil je echter het ontwerp ook als gate of VCA gebruiken, dan moet je deze kondensator door een draadbrug vervangen. Je krijgt dan wel af te rekenen met een mogelijke DC offset op de uitgang.

    De signalen op de ingangen van de AD633 mogen niet veel groter worden van 10V pk-pk. Merk op dat de dynamiek van het uitgangssignaal een kwadratisch verloop heeft in verhouding tot die van de ingangssignalen. Het is Uo = (Uix*Uiy)/10. Om die reden wordt een ringmodulator vaak gebruikt in kombinatie met een limiter of zelfs een kompressorschakeling.


    Filedate: 8601121/950310 updated: 2015-04-30

     

     

    dr.Godfried-Willem Raes

    This article is part of a research project on Experimental Legacy financed by the Orpheus Institute in Ghent.

    www.orpheusinstituut.be

    to home page Godfried-Willem Raes