[sdiy] Non-linear properties of SSM2040

[rburnett at richieburnett.co.uk]

Interesting stuff Rutger. And I will be interested to follow the replies 
to this thread.

What are you using to characterise your 2040 filter? Sinewaves, 
impulses, steps, sawtooths...?

-Richie,



On 2024-09-08 11:40, Rutger Vlek via Synth-diy wrote:
> By the way, forgot to mention that I dug through our list's history
> and it seems Jurgen Haible observed something similar, questioning if
> the SSM2040 is symmetric after all....
> 
> https://synth-diy.org/pipermail/synth-diy/1996-April/035864.html
> 
> Also, the clipping effect that I see at higher levels seems much
> different between the implementation of Jurgen Haible and that of Rene
> Schmitz: https://www.schmitzbits.de/rs2040.html. If it is crucial for
> the character of the SSM2040, these two implementations should sound
> very differently, unless I'm mistaken?
> 
> Finally, I'm hoping that Andrew Simper will chime in, as I love his
> digital implementation of the SSM2040! Of course I'm also
> understanding in case you cannot share too many details, Andrew :).
> 
> Regards,
> 
> Rutger
> 
> Op zo 8 sep 2024 om 12:34 schreef Rutger Vlek <rutgervlek at gmail.com>:
> 
>> 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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