[sdiy] OTA filter stage transfer function

[David G. Dixon]

> Well, the difference in my mind is that the OTA without feedback will
> continue to deliver a constant current regardless of the voltage across
> the cap (within supply limits, etc.).  It doesn't 'sense' the voltage on
> the cap.  Whereas a voltage source through a resistor will not supply
> constant current. It does sense the voltage on the cap and supplies
> current based on the voltage difference across the resistor.  Applying
> the feedback from the cap to the OTA input gives it that same 'sense'
> that the unbuffered resistor sees, which correlates to the 1/s+1.  And
> constant current implies integrator or 1/s, the same way a cap in an
> opamp feedback loop receives a constant charging current.

Yes, you are absolutely correct.  The feedback makes the OTA into a
resistor.  That's why an OTA wired up that way is often called a
"voltage-controlled resistor."  This is explained in item 4 of the document.

The difference between a passive filter + buffer and a standard opamp
integrator is that the former has the output voltage at the end of the
resistor, and the latter has virtual ground at the end of the resistor.  In
the latter case, there is nothing for the resistor to "sense".  However, if
a feedback resistor of equal value is added in parallel with the cap, we now
have the equivalent (albeit inverting) lowpass filter again.