[sdiy] Yet more questions: best VC drive approach

Richie Burnett rburnett at richieburnett.co.uk
Tue Feb 15 17:04:34 CET 2022 

The OTA in a cascaded OTA low-pass filter (like the Roland Juno 106 filter) 
works like this...  In each stage the OTA inputs measure the instantaneous 
difference between the input voltage and the capacitor voltage.  This 
measurement is then scaled by the control current and finally converter to a 
current output that is fed to the capacitor.  In this way the behaviour of 
the OTA approximates that of a resistor between the input and the capacitor. 
i.e. The current out of the OTA is a scaled version of the voltage 
difference between the input voltage and the capacitor voltage.  And that's 
exactly what a resistor would do if it was also connected between the input 
voltage and the capacitor.  The difference here is that the scaling factor 
(or "gain") of the OTA is variable and is determined by the control current 
into the OTA.

Now all of that assumes that the OTA's input stage behaves completely 
linearly.  But it doesn't!  The front end of the OTA is a long-tailed pair 
differential amplifier and exhibits the tanh() distortion we mentioned 
earlier in this thread.  For small signals everything said in the first 
paragraph holds true.  But as the signals get larger we start to see a 
reduction in the incremental gain of the OTA as we start to use more of the 
tanh() curve.  The effect is that even for a fixed control current (cutoff 
frequency setting,) the scaling factor for the output current ("gain" of the 
OTA) decreases when there is a large difference between the input voltage 
and the capacitor voltage.  If the scaling factor decreases it is as if the 
resistor value somehow got larger for big signals.  And an increase in this 
"virtual resistance" moves the instantaneous cutoff frequency of the 
resulting RC filter downwards to a lower frequency.

The scaling resistors around the inputs of OTA circuits are an attempt to 
make the differential input voltage relatively small compared to the thermal 
voltage so that the OTA mostly operates in the reasonably linear region 
around the origin of the tanh() curve.  But if you drive the filter hard 
enough or mess about with the resistor values, you can easily drive the OTA 
input stage with signal large enough to drive into the saturation regions of 
the tanh() curve.

I hope this explanation helps.  And I hope others also think it is valid and 
technically sound.  The key takeaway from this analysis for me is that it is 
not the signal amplitude itself that saturates, but rather the rate of 
change of the signal that is limited when the OTA input is driven hard. 
This results in a more subtle distortion than basic saturation.

-Richie,



-----Original Message----- 
From: Rutger Vlek
Sent: Tuesday, February 15, 2022 2:43 PM
To: Richie Burnett
Cc: SDIY
Subject: Re: [sdiy] Yet more questions: best VC drive approach


Thanks for the helpful replies since I brought this thread back to life!

@Richie Burnett  Thanks for the wonderful summary of knowledge on this! I 
was already aware of the tanh characteristic involved, but mainly struggle 
to understand the interaction of it with the capacitor (capacitive load) in 
each stage of the ladder filter. Is the math behind it described somewhere? 
The audio-rate modulation of the filter's cutoff frequency that occurs as a 
consequence of this interaction (if I'm right?) as what fascinates me 
particularly. I already did some experiments on a Nord Modular to see if I 
could somewhat replicate this type of saturation with a feedback (from 
output) or feedforward (from input) signal at each filter stage to the 
control input for frequency (thereby modulating cutoff at audio rate with 
the input or output of each stage). It sounds interesting, when applied in 
modest amounts, but does not quite get to Moog smoothness territory. I'd 
like to understand if there are ways to get closer to the actual behaviour 
inside a ladder filter, and if I could extrapolate that to other (analog) 
topologies, such as a 2164-based filter.

The case for an OTA-C filter seems a bit different, if I understand 
correctly, as it's saturation in the output stage that interacts with the 
capacitor to cause the cutoff modulation described above. Additionally 
there's more tanh saturation happening in the input stage of the OTA, 
without consequences for the cutoff frequency? I presume that this last 
effect is happening in almost all OTA filters, since inputs are so 
sensitive, but the first effect (cutoff modulation) is only happening in 
some OTA filters, depending on OTA output loading?

Rutger



Op ma 14 feb. 2022 om 12:14 schreef <rburnett at richieburnett.co.uk>:
Hi Rutger,

Wow, that is an old thread.  I've slept since then! ;-)

They are both based around a "long tailed pair," which is a differential
amplifier made up of two transistors.  If you read up about this
arrangement you will find that there is a tanh() function in its
transfer function, that leads to a soft saturation behaviour.  Both the
Moog ladder filter and the input stage of a bare OTA exhibit similar
tanh() soft distortion.  Although the exact effect on the cutoff
frequency in each type of filter may be subtly different.

There are some good papers out there discussing the non-linearities in
the Moog ladder filter arrangement.  Ones by Antti Huovilainen, Tim
Stinchcombe and to a lesser extent Tim Stilson are the ones that
immediately come to mind.  Some of the stuff in those papers is about
making a digital "DSP" model of the filter, but the first bits about how
the analogue filter works discusses the non-linear behaviour for large
signals.

I don't have a reference for OTA operation immediately at hand but I
would have thought the non-linearities for large input signal amplitudes
would be discussed in the datasheet, or documented somewhere.  As I
said, the first stage is just a long-tailed pair diff amp, so assuming
the OTA doesn't have any fancy linearising diodes, it will have a tanh()
shape to its transfer function that starts to kick in once the
differential input signal amplitude goes over a few tens of millivolts.

Hope this helps...

-Richie,



On 2022-02-12 20:15, Rutger Vlek wrote:
> Hi Richie,
>
> I hope you don't mind me bumping up an old thread. I was reading back
> what you wrote in 2018 and wondered if you could refer me to more
> background information on filter saturation. I'd like to understand
> what happens in a ladder filter, and weather something musically
> similar could also be recreated in other ways (e.g. in other
> topologies than a ladder). If you have an opinion on the latter,
> please share!
>
> Regards,
>
> Rutger
>
> Op vr 9 nov. 2018 10:51 schreef <rburnett at richieburnett.co.uk>:
>
>> When you over-drive OTA based 1-pole "leaky integrator" stages, you
>> actually get a signal dependent shift in the cutoff frequency as the
>> OTA
>> saturates, rather than what you would typically describe as
>> "clipping".
>> This behaviour is down to the way in which the OTA and filter
>> capacitor
>> are wrapped up inside a negative feedback loop.  The behaviour is
>> quite
>> like how the cutoff frequency of the Moog ladder filter changes
>> dynamically with drive signal level.  It is much more musical that
>> simple signal clipping.
>>
>> -Richie,
>>
>> On 2018-11-09 08:48, Rutger Vlek wrote:
>>> Hi Jacob,
>>>
>>>> This also ensures that the clipping happens in the chip used for
>> the
>>>> integrators, and not in the OTA's, which sound bad when
>> overdriven.
>>>
>>> I presume you refer to the OTA in the VCA that controls the drive
>>> level? Or do you mean OTAs inside your integrators? In the latter
>> case
>>> I don't understand what you're saying (sorry)...
>>>
>>> Rutger
>>>
>>>> JACOB WATTERS
>>>> Web & Multimedia Specialist
>>>>
>>>> JacobWatters.com [1]
>>>> Tel: 226-886-3526
>>>>
>>>> On Thu, Nov 8, 2018 at 3:32 PM Rutger Vlek <rutgervlek at gmail.com>
>>>> wrote:
>>>>
>>>>> Hi guys,
>>>>>
>>>>> I've been wondering about many things lately, hence the flood of
>>>>> emails to the list :). I also have to admit feeling a bit stupid
>>>>> about having to ask this.. but here goes:
>>>>>
>>>>> What's the best approach to designing a voltage controlled
>>>>> overdrive? The obvious solution I can think of is having a
>>>>> saturation element preceded by a VCA. While I haven't fully done
>>>>> my homework on it yet, my guts tell me that this isn't the best
>>>>> circuit in terms of noise behaviour, as it would require the
>>>>> saturation element to be at high gain constantly while the VCA
>>>>> various input level. Meaning that any VCA noise would be
>> amplified
>>>>> by the full gain of the saturation element. In guitar stomp
>> boxes,
>>>>> some design place a pot in the feedback loop of an opamp to
>> change
>>>>> gain. Could a similar approach work well for a VC-drive unit and
>>>>> would it perform better/worse than the first solution I
>> proposed?
>>>>>
>>>>> Finally, I've been thinking about making drive level voltage
>>>>> controlled via power supply to the saturation element
>> (transistor
>>>>> in this case). Feeding the control voltage into a buffer that
>> puts
>>>>> out the supply to a transistor would also allow to change drive
>>>>> level.
>>>>>
>>>>> What do you think? How it this typically done? I just bought a
>>>>> Novation Peak, and am impressed with it's three stages of
>>>>> overdrive although it suffers from noise issues due to the
>> amounts
>>>>> of again at hand. It makes me wonder how I would design such a
>>>>> stage myself.
>>>>>
>>>>> Rutger
>>>>> _______________________________________________
>>>>> Synth-diy mailing list
>>>>> Synth-diy at synth-diy.org
>>>>> http://synth-diy.org/mailman/listinfo/synth-diy
>>>
>>>
>>>
>>> Links:
>>> ------
>>> [1] http://jacobwatters.com/
>>> _______________________________________________
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