# Exponential conversion

Hi Guys, I was interested to see that the anushri uses an SSM2164 for its exponential conversion. How well do these track and how temperature stable are they? I am just asking as it seems like a pretty neat solution to the problem. The last module I built that needed to do that used unobtainium hyper matched transistors chips and a tempco resistor to do the same job.

Just find the datasheet for the ssm2164/V2164 and look it up?

I more wondered what peoples experiences were. I guess there probably aren’t that many experiences yet though, as no-one has the boards.

The LP2+Delay filter board uses 2164’s, as does the dual SVF board, so there should be people who have used them… Anyways, i would still recommend looking at the datasheet…

The circuit comes from Osamu Hoshuyama’s collection of unusual synth circuits
I think he gave some precisions about the quality of tracking of this solution, tested on breadboard. Actually, he tells us that between 0 and 40°C it’s 1% precision over 10 octaves.

He provides other neat circuits for doing the same as well

By itself, a SSM2164 cell is just like a traditional expo pair - good conformance to the “theoretical” log response ; but temperature dependence.

The formula I use for my SSM2164 designs is:

gain = exp(- (cv / 10.4) / kT)

The 10.4 value was empirically obtained, it looks like there’s something fishy with the resistor values given in the datasheet anyway.

Anushri uses Osama Hoshuyama’s trick in which one SSM2164 cell is used as an expo current source (constant current in ; control voltage modulating it with an expo response) ; and the other is used to slightly scale the CV in order to multiply the temperature dependence curves. Instead of a line, it becomes a parabola - so effectively there’s no temperature variation in the neighborhood of a center temperature. The “magic” control voltage of 0.268 yields the flattest temperature dependence in a neighborhood of about 20°. Parabolas being parabolas, it grows horribly when getting into negative temperatures or above 40°. I have decided not to use this value but rather a higher one - it gives a narrower “zone of flat temperature dependence”, but it’s centered around 30° which will more accurately represent the temperature in the Anushri case.

Regarding tracking, Anushri tracks over 5 octaves ; things go awry above 3kHz. This is not due to the expo converter itself, but to two other factors:

• The reset time of the integrator, which I have moderately compensated with a “De Franco” resistor.
• (This one is a bitch and took me days to find). The input of the SSM2164 is not a virtual ground! It’s more like a smallish (say 80 ohm) resistor to ground. The consequence is that when big voltages are summed into the input pin of the SSM2164 a tiny error is added, because the input pin won’t be at 0V but at 40 or so mV. I got fooled with this because my original design used 30k resistors to the input of the tempco cell. Even 100k is not optimal ; but then you get away of the “100k input impedance” implicit standard of modular stuff…

I understand what you are saying. I am not looking for perfect tracking. I was only interested in how the 2164 performed as an exponential converter.

I maintain though, that people will expect their synth to basically track well over a few octaves whether it is doing it digitally or through analogue means.

It does amuse me somewhat that people want absolutely perfect tracking, tuning etc. from analog when it is these little variations that give it the character. Which is probably why virtual analog doesn’t sound as good.

Just like pitch correcting vocals can result in more of a bland result.

I hate to say it, I suspect more people would complain about bad tracking than would embrace it. I know what you mean though. It will never be as pin-point accurate as a digital solution and will probably sound better for it.

If you want perfect pitch tracking with Anushri over dozen of octaves, you can enable sync The sync master is a digital square oscillator (1.25 MHz master clock), dead accurate.

Indeed, that’s how the JX3P/MKS30/JX8P sawtooth oscillators work

Is the DCO stuff just in addition to the VCO? Presumably the current charging the integrator has to be broadly related to the frequency or you would have amplitude drift.

The DCO is a second oscillator which can FM, Sync the VCO, or just be routed in the audio path. When sync is not enabled the VCO is, well, a VCO, nothing digital in it…

>I hate to say it, I suspect more people would complain about bad tracking than would embrace it

Depends how much it is out by and it would vary depending on temp. Just like some of the “classic” analog synths did.

People try to add this sort of small variation into soft synths or VA synths.

Well yes, but not 100% perfect

@pichenettes So does the VCO auto calibration just sample the vco output pitch and scale the cv it sends to the exponential converter front end to maintain pitch? ie the VCO is basically not tracking 1v per octave, but the pitch (note) to cv conversion is done in software?

edit: actually never mind, I looked at the build instructions again and the description there pretty much answers all my questions

You can make the VCO track at 1V/Oct if you play with the trimmers - in this case the software correction is not needed. If you don’t really care about external CV I/O at a precise 1 V/Oct standard, you can let the software correction do the job.

Thats what I thought. That is a pretty clever solution!
In my experience tuning a VCO can be pretty fiddly, but you have provided a means to side step the problem.