EML-101 Multimode VCF Schematic

via Aaron on the sdiy list:
"One project idea that I tossed out to my students, which one student is trying to get work, is to use the idea of an NPN differential amp driving a "differential integrator" to build a 1-pole LPF, which you could then do four times to get a usual 4-pole LPF.

I got the idea from the EML-101 filter schematic [mirror], as expertly redrawn by Marjan Urekar:

The EML-101 is a state variable filter, and said diff amp/diff integrator configurations form the variable gain integrators.

My thought was that we could take the output of such an integrator, and feed it into the opposite input terminal of the diff pair, and that feedback should form a 1-pole LPF, as follows:

The NPN pair driving the differential integrator forms a variable gain integrator with transfer function A/RCs, where A is the voltage gain of the diff pair and R and C are the resistor values used in the integrator. Let's denote wo = A/RC. Now imagine we take the output of this integrator and feed it back into the input with a minus sign. You get something like this:

Y(s) = (wo/s) [X(s) - Y(s)]

Y(s)[1 + wo/s] = (wo/s) X(s)

Y(s)/X(s) = (wo/s) / (1+wo/s) = wo/(s+wo)

Which is the transfer function of a single-pole LPF with cutoff wo with unity gain at DC. (This is the same idea as a usual OTA-C filter 1-pole LPF).

Three questions:

1) I sent my student, Justin, this sketch to get him started, where I just blindly ganked the resistor and cap values from the EML circuit.

Anyway, I just realized I drew that wrong - the EML integrating stage is _inverting_, so we should actually either:

A) Swap the inputs on the differential integrator, to make a noninverting stage, or

B) Take the feedback to the left NPN instead of the right NPN

Does (A) or (B) sound like the safer option?

2) Given the way the "differential integrator" is going to load the differential amp, should I even be thinking of this as a differential amp followed by a differential integrator? Or are they interacting so much such thinking breaks down?

3) Does this whole crazy idea of mine sound like a decent idea at all or is it doomed to insanity?

- Aaron

P.S. This got me wondering if there's an "integrating version" of the standard 3-op-amp instrumentation amplifier? A differential integrator with high input impedance, but something more elegant than just slapping noninverting op amp buffers at the inputs to the above differential integrator?

http://en.wikipedia.org/wiki/Image:Opampinstrumentation.svg"