# Linearity problem

Posted: 7/1/2013 7:31:19 PM

From: UK

Joined: 7/1/2013

Hi, I'm attempting to construct only the volume side of the EW theremin to produce a DC output of 0 to 10v. Have successfully constucted the oscillator, VCA and antenna circuits and added the mod from the Hot Rodding pdf to convert this to 0 to 10V. Have removed the oscillator tuning circuit as it's not really needed in this situation. The problem I'm having is one of linearity. It's not at all linear. I suppose my question is, what makes the pitch circuit give a more linear response than the volume and how can I alter the volume circuit to give a similar response curve?

Posted: 7/1/2013 10:15:33 PM

From: Eastleigh, Hampshire, U.K. ................................... Fred Mundell. ................................... Electronics Engineer. (Primarily Analogue) .. CV Synths 1974-1980 .. Theremin developer 2007 to present .. soon to be Developing / Trading as WaveCrafter.com . ...................................

Joined: 12/7/2007

Hi rikiow..

EDIT >> I wont delete this post - But I advise you to bypass it and go directly to Thierry's post which follows this.. as what I write in the following probably isnt worth reading!! - and may in fact be completely wrong with regard to the EW's volume CV response..

If I understand what you are doing correctly, you are using the theremin to provide a linear CV (1V/Octave) from the pitch antenna, and using the voltage from the volume antenna for some function -

But please understand that the volume antenna circuit of the EW is not something I have explored much, so I dont know what kind of response one could expect from this particular circuit (I have my own circuit which uses the reference oscillator and has no oscillator of its own, so removes all problems of possible harmonic interactions) - What I say in the following is my guess as to where your problem be:

The Pitch to voltage converter (in the hotrodding manual)  has an exponential converter at its final stage (the period-to-pitch section) The period voltage is a direct V/HZ output from the SAH, and the period-to-pitch circuit converts this to a linear V/Octave. The difference frequency is a non-linear function (we / our hearing, for both pitch and volume, are non-linear.. When we talk of a linear theremin response, we are actually talking about a musically linear response, as in, we hear a "linear" change in pitch, but in fact the frequency change is exponential)..

Mini tutorial on voltage control:

In order to deal simply with the problems of interfacing multiple modules, Bob Moog invented (or at least I think he invented) a scheme wherebye a linear voltage is used to convey pitch and expression data - this scheme is that a change of 1 volt gives a change of 1 octave for the pitch (this equals 83.333mV per semitone) . Each module has its own independent exponential converter, so that, for example, 1V into a module causes a current (into the control node of the VCO for example) of (say) 100uA, 2V would then cause a current of 200uA, 3V would give 400uA, 4V gives 800uA etc - The current would determine the frequency, so at 1V one may have 40Hz, 2V = 80Hz, 3V = 160Hz, 4V = 320Hz .... as in, each 1V added to the input doubles the current and therebye doubles the frequency.

The beauty of the above scheme is that one can add voltages independently to each module, and have these modules track a common control voltage - so they can be detuned from each other and modulated without losing their musical relationship to other modules... The 'problem' with this scheme is the expense and hassle of requiring an exponential converter for each module.. This problem is even more of a pain with an instrument like the theremin, where one has a good V/Hz that one must convert to V/Octave (using an exponential converter), just to be converted back, effectively, to V/Hz ot I/Hz by the exponential converter in the module being driven.

The volume response also needs to be non-linear for us to hear it as "linear" - This is the reason why volume control potentiometers are log, not linear..

On the EW, the voltage from the volume antenna circuit is converted to a current which drives a linear VCA formed from the LM13700 - so the volume response one hears is (reasonably) musically linear - ie, how it should be.. but the voltage is deliberately non-linear!

If you are using the volume output voltage with anything requiring a actually linear relationship (as is required if you are driving a 1V/Octave VCF or VCO, or you are driving a LOG VCA) then you need to convert the voltage using a log or exponential converter before you feed it (the resultant linear voltage) to your circuits.

So you need to determine the law you require to suit the function, and then build a suitable converter. If you are driving a log VCA, the simplest solution would be to use a linear VCA.

If you give details about your application I may be able to give more specific help.

Fred

Posted: 7/1/2013 10:49:03 PM

From: Colmar, France

Joined: 12/31/2007

Actually, taking away the tuning circuit which allows a fine tuning (compared to the coarse tuning which is possible with L11) was not a good idea. The volume oscillator produces a fixed frequency. The volume control voltage is taken from the (more or less) resonant current through the big coils and the volume loop. Varying ambient capacitance (yes, 0.05pF play a role!) and temperature drift have to be meticulously compensated by the volume tuning circuit which allows to alter the volume oscillator's frequency by +/- 0.1% which makes already a huge difference in the volume response (once the oscillator is basically tuned with L11).

When you follow the coarse primary volume CV (0 to -4V) behind D1, you will see that it is amplified and shifted by the second half of the LM13700 to run from -12V to +12V. This "control voltage processor" has an additional negative feedback through a diode which will approach a kind of exponential characteristic (together with the non-linear response of the resonant circuit since the loop capacitance increases the more, the more your hand is approaching).

Thus the steps are:

- put the fine tuning circuit back in its place.
- Tune L11 (and then the volume tuning pot) to give a smooth transition from -12V (hand at 1/2" above the volume loop) to +12V (hand at 8" above the volume loop) at pin 12 of the LM13700
- Make sure that the CA 3080 "level shifter" from the hot rod manual translates these -12V to +12V correctly into 0 to +10V using 2 multimeters.

Posted: 7/1/2013 11:12:12 PM

From: Eastleigh, Hampshire, U.K. ................................... Fred Mundell. ................................... Electronics Engineer. (Primarily Analogue) .. CV Synths 1974-1980 .. Theremin developer 2007 to present .. soon to be Developing / Trading as WaveCrafter.com . ...................................

Joined: 12/7/2007

Oooh La!

Just had another look at the circuit - I have never actually given it any attention before, and never even noticed that it was a fixed frequency resonant scheme.. Ouch! LOL ;-)

Thanks Thierry -

Once again, clear proof that Mr Frenkel is the undisputed master of the EW!  ;-) - and once again clear proof that at times I am an idiot!!

Fred.

Posted: 7/2/2013 12:39:32 AM

From: UK

Joined: 7/1/2013

Thank you both for your quick replies, I'll reinstate the fine tuning circuit as you suggest and see if this makes things better.

The output voltage is read by a pc and used in some software I am working on. Ideally it would be nice if the decrease in voltage output was directly proportional to hand movement towards the antenna. I realise this probably won't be achievable using the Volume circuit from the EW, (just looked alot easier to make than the pitch circuit) but there must be some way of preventing it dropping off as quickly as it does.

Thanks Again

Rik

Posted: 7/2/2013 9:00:58 AM

From: Colmar, France

Joined: 12/31/2007

Fred wrote:

Oooh La!

Just had another look at the circuit - I have never actually given it any attention before, and never even noticed that it was a fixed frequency resonant scheme.. Ouch! LOL ;-)

Thanks Thierry -

Once again, clear proof that Mr Frenkel is the undisputed master of the EW!  ;-) - and once again clear proof that at times I am an idiot!!

Fred.

No! You aren't an idiot, you just have other priorities and a different viewing angle. :-)

That's why the teamwork here on TW works fine in general, since the different "views" add up to a beautiful picture, or should I say "think tank"?

Posted: 7/2/2013 11:52:58 AM

From: Canada

Joined: 8/1/2008

I think the think tank tanked!

Thanks

Posted: 7/2/2013 1:21:50 PM

From: Eastleigh, Hampshire, U.K. ................................... Fred Mundell. ................................... Electronics Engineer. (Primarily Analogue) .. CV Synths 1974-1980 .. Theremin developer 2007 to present .. soon to be Developing / Trading as WaveCrafter.com . ...................................

Joined: 12/7/2007

Was that thanks or tanks Peter ? ;-)

but back to the linearity -

I have a problem understanding the problem... In a moment of shock as I realised my error WRT the volume antenna operation, I wrote off all I had said regarding the lin / log relationships required for satisfactory operation of external devices vs satisfactory operation of the volume response..

But reflecting back, I cannot see that (or how) my core analysis of the problem could be "wrong" - despite the fact that my assumption regarding the volume circuit operation was wrong, and that my proposed possible solution probably wouldnt be much good..

IMO/AFAIKS, one requires a log distance-volume relationship to get smooth "linear" response from the volume antenna. And AFAICS there is no independent pre-processor applied to the voltage from the volume circuit before it is fed to the linear LM13700 VCA..

So - As I see it, in order to get a reasonable volume response from the EW, the volume CV MUST be non-linear - as in, exponential / log with respect to distance..

The original question was "what makes the pitch circuit give a more linear response than the volume and how can I alter the volume circuit to give a similar response curve?"

My answer was wrong inasmuch as the 'raw' curve from the volume circuit will not be the same as the 'raw' curve from the pitch to period section of pitch voltage output circuit - so feeding the volume voltage into the following exponential converter will not produce an identical output and may not even produce a remotely similar output curve...

But likewise, I do not see any way that one will get a similar output curve directly from the volume voltage, unless the EW's volume response is actually abysmal! - The reason why the pitch CV is linear (as in actually linear = 1V/Octave) is due to the deliberate conversion of the exponential function via the log converter circuit.. As I see it, some similar conversion process is required to get a linear output from what I believe must be an exponential / log (or at least, a deliberate non-linear curve of some kind, to facilitate smooth usable volume control from the volume antenna) volume voltage

Am I missing something ? The whole CV side of things is an area where I feel quite competent - its my primary methadology for my current theremin developments (although I use entirely different front-end topology), so the idea that there is any chance that I have a fundamental missunderstanding about any aspect really bothers me.

I have never built the EW volume circuit, never even simulated it (If I had, I would not have made the error I did) - I never understood why anyone opted for a seperate volume oscillator (or in some cases two oscillators) when a trouble-free fixed frequency can be obtained from the existing pitch reference oscillator, and one only needs to change the tuning control and make the pitch VFO tunable rather than making the reference oscillator tunable (or far better IMO, make the pitch antenna resonator tunable, as this maintains best linearity when tuning is requited due to changes in the capacitive environment), and implement some simple tuning mechanism on the volume antenna resonant circuit... but anyway - there must be some reason I havent seen!

Seeing that the EW volume oscillator is fixed frequency, I am even more puzzled as to why Bob implemented it the way he did, and never used the reference oscillator...

Fred.

Added ->

Rick, if you are feeding the CV to some digital processing via an ADC, and you are developing your own software / firmware for this, it seems to me that you may be best sticking with simple hardware giving a non-linear curve, and use digital processing to linearize that curve..

A useful technique to achieve this (particularly if using a PC and there are no constraints on memory and interfacing the distance measurement is simple) is to use a distance measuring instrument such as ultrasonic or optical, place this at the antenna, then feed the data from this simultaniously with the voltage from the 'theremin' to the PC. Under controlled conditions, you should be able to plot distance against voltage, and derive a look-up table you can put in your software.. You probably only need to collect data for 1cm or 5cm points and extrapolate between them - an array with one byte index should be more than enough, using the 8 most significant bits from the ADC to index into the array, and the less significant bits to extrapolate between the values. (in fact, you probably only need 6 bits for the index and a small array - if you have a 12 bit ADC or greater, this should give enough resolution I think..... But dont trust me on any of this - I suspect that someone more into digital / software will give better advice)

I have NOT done the above! - But I have used voltage and distance inputs to evaluate the linearity of test circuits.

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