A Study of the Korg MS10 & MS20 Filters - Tim Stinchcombe

1 A Study of the KorgMS10 & MS20 FiltersTimothy E. Stinchcombe 30 August 2006 Comments, suggestions and corrections can be emailed to me good place to seek answers to questions on the internals of synthesizers in generalis the Synth DIY mailing list: Corrections to links and minor typos, 13 Dec 200912 Contents1 Introduction42 Filter Schematics, Structures and Transfer Transfer function of the OTA version .. Transfer function of the Korg35 version .. 103 Korg35 Voltage Control of the Cut-Off Reverse saturation mode .. 204 Asymmetrical Frequency and Resonance Responses of the Korg35 295 Non-Linear Effects of the Feedback Diodes306 Exponential Control in the OTA Version367 The High-Pass Filter Variants are 6dB, not 12!

2 398 Sallen-Key Myths Discredited409 Conclusion4310 Acknowledgements, Rights and Copyrights45 References4634 Introduction1 IntroductionThis paper contains a reasonably thorough analysis of the Filters used in the KorgMS10 and MS20, concentrating for the most part on the low-pass variants of thosefilters. The Filters have a reputation for having lots of character , and if we attemptto attribute this to some facet of the Filters topology, we immediately run into muchconfusion: Filters in the ms10 and early MS20s were built around a Korg-proprietary,resin-sealed device, the Korg35 ; in later MS20s, the filter was re-designed aroundthe LM13600 operational transconductance amplifier (OTA).

3 Korg finally divulged thecircuitry inside the Korg35 in 2000, confirming that the Filters topology was indeedone of the standard Sallen-Key types, as had been suspected for some time; the laterOTA-based filter however is basically two cascaded, buffered first-order sections, whichwhilst still being a second-order filter, does not share the same Sallen-Key topology ofthe are several purposes to my Study . Firstly there is the mechanism by whichthe transistors in the Korg35 chip are used to provide voltage-control of the filter cut-offfrequency: barring simple substitution of vactrols for resistors, adding voltage-controlto a standard filter topology such as the Sallen-Key types may require a good dealof ingenuity.

4 Korg have demonstrated such ingenuity by biasing two transistors in theKorg35 in thereversesaturation mode, thus essentially using them as current-controlledresistors, and I was keen to better understand how on earth this , when mention is made of the MS20 filter and its legendary sound , itis often unclear justwhichof the two filter types is being referred to: do they havesuch similar aural characteristics that it is immaterial which one is actually meant?It will be shown in this paper that, analytically at least, the two filter designs havesimilarities, but there are also differences, and these are shown too.

5 Ultimately the besttest of their similarity/difference will be to listen to actual hardware: this will form thenext phase in my Study , that of building copies of both types of and simulation:all schematics in this document have been producedin SIMetrix, [11], a SPICE-type simulation package. Where possible I have used rec-ognized models for the Japanese transistors: I was unable to find one for the 2SK94 JFET, and so have used a BF245A instead, as it has a similar threshold voltage have generated my own OTA symbol, whose pin-outs areA Study of the Korg ms10 & MS20 5 Figure 1: ms10 version of the Korg35-based filteras when I imported the National LM13600/13700 models, the symbol SIMetrix assignedwas a bit generic.

6 2 Filter Schematics, Structures and Transfer FunctionsFigures 1 and 2 are schematics for the two filter types: the earlier Korg35-based one inthe former, and the later OTA-based filter in the latter. The Korg35-based schematictakes the ms10 component values, mainly for the simple expedient that the copy ofthe ms10 schematic I found on the web was easier to read than that which I foundfor the MS20. I ve not yet seen either an ms10 or MS20 in the flesh, but it seemsthe later OTA-based filter was constructed around a daughterboard PCB, the KLM-307 , for which I also found a readable schematic. In both figures I have tried to keepthe nomenclature of the discrete components as the original schematics, for ease of6 Filter Schematics, Structures and Transfer FunctionsFigure 2: OTA-based version of later MS20sA Study of the Korg ms10 & MS20 7 Figure 3: Sallen-Key low-pass structure of the Korg35-based Figure 1:V3is the input voltage;V4the cut-off frequency control voltage; theoutput is taken atC19/R62;VR13is the resonance control pot.

7 In Figure 2:V2is theinput;V4the cut-off voltage (V5is an offset-adjustment for the cut-off); the output isC7/R29;VR1is the resonance of the most obvious differences between the two filter types is that the non-linearity-producing diodes in the early filter is in the forward path, whilst in the OTAversion they are in the feedback loop. If we ignore these diodes for the moment (theyare covered in detail in Section 5 later), and disregard the cut-off frequency controlcircuitry, then the basic structure of the Korg35-based filter is as in Figure 3: hereresistorsR1andR2are actually formed byQ2andQ3in the real thing, which areacting as current-controlled resistors; gain blockk1is formed from the JFET buffer andthe non-inverting op amp set-up aroundX1; gaink2consists ofVR13/R62and potentialdividerR61/R60.

8 This is easily recognizable as the main low-pass filter topology of theSallen-Key family of Filters , [3].The basic structure of the OTA-based filter is shown in Figure 4, which is slightlyharder to see due to the use of the OTAs and supporting circuitry (more on this in amoment). In the figure:R1andR2represent the variable-resistor roles performed bythe OTAs (X1andX2); gaink1is basically the (unity gain) buffer atX2 OTA s output;gaink2isR8x/VR1and non-inverting op amp set-upX5. The noteworthy differencewith Figure 3 is the inclusion of the unity gain buffer at the output of the first OTA(X1): this means that there is no loading effect of the second filter stage upon thefirst, as there is in the Sallen-Key set-up.

9 The effect on the derivation of the transferfunction is not great, as we ll see below, but I do not believe this set-up corresponds toany of those in [3], and so therefore I do not regard it as being a Sallen-Key function of the OTA versionFigure 4: Basic filter structure of the OTA Transfer function of the OTA versionThe equivalence of the OTA set-ups to simpleRCsections is not immediately obviousto me. Whether with sufficient intuition and familiarity with OTAs it is possible toquickly establish what such a circuit does, or simply with enough exposure one merelyrecognizeswhat it is, I do not know, and in any case with my limited electronicsexperience I do not possess the ability to do either: thus I shall do what many do whenfaced with apparently such a complex situation resort to some mathematics!

10 ([9].)Consider the following simple situation:and we require an expression forV2in terms ofVinandVo. By nodal analysis (currentin = current out) at theV2node, we getVinR+k2 VosC=V2R+V2sC,(1)thenVin+k2 VosCR=V2+V2sCR,which easily leads toV2(1+s c)=Vin+k2 Vos c(2)on putting c=1 grounded, 0, this gives the familiar firstorder low-pass transfer functionV2 Vin=1(1+s c).A Study of the Korg ms10 & MS20 9 Now consider this diagrammatic representation of the first OTA stage:Nodal analysis at theV innode givesVinR1+V2R3=V in(1R1+1R2+1R3),and forR1=R3 Vin+V2=V in(2+R1R2),which further simplifies toV in=k(Vin+V2)wherek R2/R1whenR1 R2, which is usually the case.