[sdiy] OTA filter stage transfer function

[David Moylan]

David G. Dixon 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.
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.

Might be a different approach to thinking about it but it jives with the 
theory.  Thanks for sending the document, it's bringing my memory back. 
  I was doing some state variable derivations when the question arose in 
my mind.  It sure is easier to do the math with 1/s terms than having to 
expand 1/s+1 terms.  And I think it's safe to treat the stages as 
integrators without feedback, then calculate the feedback coefficients 
for the desired response....for example, the SVF in the 13700 datasheet 
doesn't have local feedback around the second integrator.


>  
> (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.)
> 
>