[sdiy] Interpreting four-pole-w-feedback circuits

[Aaron Lanterman]

In lecture, I've talked about four-pole filters, and we've done the  
analysis of how you get a 180 degree phase shift around the cutoff, so  
if you run a negative loop back to the input, you get this cool  
resonance spike around the cutoff.

In another lecture, I've talked about how to built one-pole VCFs with  
OTAs, caps, resistors, and op amps.

So tomorrow (Thursday) in lecture I'm talking about filter circuits.  
Here are my slides:

http://users.ece.gatech.edu/~lanterma/ems/filters.pdf

For the SSM2040 filter, I see each stage is inverting, but there's  
four of them, so the entire sequence should be noninverting  
(-1*-1*-1*-1 = 1). I see the LF356 is in an inverting configuration;  
hence it looks like the whole circuit does invert, and you get a  
negative feedback path through the SSM2020.

In Ray WIlson's circuit, I see all the stages are also inverting.  
There's a noninverting configuration op amp at the output, so the  
whole circuit is noninverting. The feedback path has an op amp in an  
inverting configuration, so that gives you the negative feedback you  
want.

The Polyfusion makes sense to me too. A noninverting buffer at the  
input, a noninverting buffer at the output, each individual stage is  
inverting, but it all adds up to something noninverting. The feedback  
loop hits the - terminal of a 3080, and the current is turned to a  
volage by dropping the current down a resistor, and then buffering  
that with an op amp in a voltage voller configuration, and that's  
brought back to the input. The use of the - terminal on the 3080 gives  
me the negative feedback I expect to see.

BUT... I'm bewildered by the four-pole arp patent circuit. The stages  
look inverting (since the opamp-cap-in-feedback is an inverting  
configuration), the four of them in casecade should give total  
noninverting behavior, that's OK... but... it looks to be like the  
feedback loop is POSITIVE. I'd expect the input to either go through  
an inverting opamp before being fed back, or for it to go to the  
negative terminal of the first OTA (so that first stage would be  
noninverting, but the other three inverting, so it would all go  
through with a minus sign).

What am I missing? Where is my thinking going wrong?

- Aaron