Non-linear techniques with filters

[jh.]

Von: Grant Richter <grichter at asapnet.net>

> It appears the ladder filter design introduces distortion at the crossover
> point. The ladder introduces non-linearities at the input transistor,
which
> are compensated for by complimentary non-linearities on the output
> transistor, except at the cross over point. It is generally agreed this
> sounds good (perceptual advantage).
>
> Since we know the mechanism, can it be applied to other filter topologies?
> If a non-linear process is applied to the audio before filtering and a
> complimentary process used after filtering to re-linearize, will a
> perceptual advantage be gained?
>
> One example immediately springs to mind. A CA3080 has a very limited
linear
> range. To extend the range, diodes are used as compensation on the input
> side. But what if the compensation were done on the OUTPUT side?
[...]

Hi Grant,

May I say that the OTA-type filter already has this "crossover point"
distortion
built it ?!

I remember I tried to work out the difference between OTA filters and
Ladder filters some years ago, thinking in the very same direction, just
the other way round. I thought it was clear that OTAs have that kind
of distortion, but I thought the Moog ladder had not. (It was Don Tillman
who put me right on the Moog ladder - I vividly remember the "click"
in my head when he wrote "cascode at low frequencies".)

Back to the OTA filter: Consider an OTA stage with buffer and feedback
loop to get the 1/(1+s) response, and let's assume the resistor dividers
are chosen such that it *is* possible to overdrive the OTA input.
At low frequencies, however, you will get (almost) no distortion, because
of the feedback loop. The whole thing (OTA, cap, buffer) acts like an
opamp with one dominating pole from the capacitor. At low frequencies,
the OTA output and capacitor provide a high voltage gain. The external
feedback loop reduces the distortion. For slow input changes, the output
will follow the input, but the OTA input is almost zero (from +in to
-in that is).
Higher frequencies, less feedback, more distortion. As in Ladder filter.
Even higher frequencies, following LPF stages will filter out the distortion
products.

So where is the big difference ? Not sure, but this may be one reason:
The Ladder input can be overdriven beyond recovery by the upper stage.
At 100mV peak the tops of the peaks are *flat*, no way to restore them
with a complementary function.
Emulate with OTAs ? Put a limiter in *front* of the filter (but inside
the feedback loop!) perhaps. (I modified my Prophet 5 rev. 3 to have
the mixing stage befor the filter overdriven. The sound is not bad
for the highly linearized CEM3320 chip ! Feedback loop was not
included, though.)
SSM2040 limits amplitude after 1st OTA stage. Still 3 stages to filter
distortion products - can sound quiteMoog-like. (But the 2040 has
features that take it beyond the Moog, IMO.)

Unfiltered bubbling of mine that was - I type and run.

JH.