[sdiy] 1-pole LPF using a differential integrator?

[Aaron Lanterman]

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, as expertly redrawn  
by Marjan Urekar:

http://members.tripod.com/urekarm/synth/eml101vcf.pdf

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: http://users.ece.gatech.edu/~lanterma/eml_inspired_vcf_sketch.jpg 
, 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