[sdiy] Non-linear properties of SSM2040

[René Schmitz]

Hi Rutger and all,


The TANH comes from the input side, i.e. the long tail pair transistors, 
this is more or less symmetric as one would expect.

(If you ignore minor effects such as the different Vce voltages, Vbe 
matching, source resistances etc.)


For a single stage:

The asymmetry comes from the output of the one-mirror OTA. It can't sink 
past -0.6V (The collector of the output transistor can't go lower than 
it's emitter voltage, with the bases near GND thats about -0.6V).

Thus you see clipping at -0.6V.

It really only makes a difference if you're *not* summing the current 
into a virtual ground. As was done in the 2040 of course, which uses 
emitter followers.

(But you can run the 2040 gain stage into an opamp integrator and do not 
get any of the clipping at all.)


BTW the 2164 also has voltage compliance limits for its output current 
(albeit different).

So you can run the 2164 into an "open" load, and get extra 
nonlinearities. Thats mentioned in AN701.


If you cascade several inverting 2040 stages, then at the output you get 
(more or less) symmetric clipping because you alternately treat the 
positive and negative input swings at consecutive stages.

I think this was what JH was talking about. But also look at a single 
stage to understand what the root behaviour is.



Best,

  René




Am 08.09.2024 um 12:34 schrieb Rutger Vlek via Synth-diy:
> Dear all,
>
> In the sparse moments between day time job and fatherhood I'm trying 
> to push forward with an idea I've had for a long time. I'm trying to 
> capture the variation in favourable non-linear characteristics from 
> well-known filters (read SSM2040 and Moog Ladder) and implement them 
> in a more modern topology (read SSI2164). Would also be great to be 
> able to select between them, while using the same filter core. I'm not 
> necessarily aiming for perfectly cloning the response of vintage 
> filters, but rather hope to take inspiration from them and perhaps to 
> discover other pleasant non-linearities.
>
> I've been approaching this with Spice as well as with mathematical 
> modelling in Python, using a multi-dimensional Newton-Raphson solver 
> with the system of equations needed to describe the various filters.
>
> Right now I'm trying to understand the character of the SSM2040, and 
> am a bit puzzled. I am familiar with the inverting cascaded topology 
> of this filter. And with the typical math that describes the 
> non-linearities of an OTA-based filter:
> Vout = g * tanh(Vin-Vout).
>
> I have been reading across the internet about the asymmetrical 
> saturation of this filter, most notably in the application notes for 
> making filters with the SSI2164: 
> https://www.soundsemiconductor.com/downloads/AN701.pdf. Based on this 
> information, I had assumed that the tanh only operates in one 
> direction, something like this:
> y = tanh(x)    if x < 0
> y =x               if x > 0
>
> However, in Spice, when simulating the internals of the SSM2040 using 
> Jurgen Haible's schematic 
> (http://jhaible.com/legacy/tonline_stuff/jh2040.gif), I don't see that 
> happening. Instead, I see tanh distortion in both directions.
>
> Only when I push the input harder (beyond 1Vpp), I see one side of the 
> output clipping much sooner than the other. This seems in line with 
> the effect described in AN701, but is the SSM2040 really driven that 
> hard in real world applications, and is it really *this* additional 
> effect, on top of the already present tanh distortion, that explains 
> the SSM2040's character? And if so... how would one model it 
> mathematically?
>
> Rutger
>
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