[sdiy] OTA filter stage transfer function

[Olivier Gillet]

One more thing: whether the cap is grounded and followed by a buffer,
with negative feedback to the OTA ; or in the feedback loop of an
op-amp with positive feedback to the OTA, the transfer function is the
same (with just a sign flip).

The feedback is required because a resistor has two "ends": if we want
to replace the resistor in a RC filter by an OTA, and expect the OTA
to behave like a current-controlled resistor, the OTA needs to "know"
the voltage at those two ends.

Regarding David's document:
What about setting up a wiki / google site to compile and publish such
a "cookbook" of sub-circuits - with a focus on small, reusable,
general purpose "cells", with their analysis/transfer functions --
rather than full circuits with every component value already in place.
Filter stages, exponential converters, current sources, the "bipolar
modulation amount" topic discussed yesterday... This information is
probably out there in books, electronotes, class material -- it's only
a matter of putting it together in one place.

On Tue, Jul 20, 2010 at 9:19 AM, David G. Dixon
<dixon at interchange.ubc.ca> wrote:
>> Can anyone clear up a question I'm having?  When an OTA like the 13700
>> has a capacitor to ground on the output in a typical filter stage
>> (rather than feeding an opamp with the cap in the feedback loop), is the
>> normalized transfer 1/s because it's a current output, rather than
>> 1/(s+1)?
>
> If the output of the cap (via the buffer) is fed back to the negative input
> terminal of the OTA with the same gain (i.e., through an identical divider)
> as the input which is fed to the positive terminal, then it's a lowpass
> filter with a TF of 1/(s+1).  Without that feedback, it's a non-inverting
> integrator with a TF of 1/s.
>
> The fact that the OTA produces a current output has nothing to do with it.
> Any filter or integrator requires a current source, even if it's simply a
> voltage source across a resistor.
>
> (I've sent you a document via private email which explains these concepts in
> detail, and much else besides, with derivations of the transfer functions
> for many different filters and integrators based on OTAs and VCAs; refer to
> items 4 and 5.)
>
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