[sdiy] Yet more questions: best VC drive approach

Tue Feb 15 17:32:34 CET 2022

Thanks Richie, that's a great explanation! :-)

/mr

Richie Burnett <rburnett at richieburnett.co.uk> skrev:

> 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
> >>>>> _______________________________________________
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> >>>
> >>>
> >>>
> >>> Links:
> >>> ------
> >>> [1] http://jacobwatters.com/
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>
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