# Transfer function of OTA based neural signal amplifier

I was reading about OTA based neural signal amplifiers and reached this schematic Based on the book's description the transfer function for this circuit design is : but unfortunately couldn't find any description on where this equation has come from, neither in the book, nor online.

Can you help me through understanding this equation and maybe suggesting some resources ?

Figuring out how circuits work in depth is not intention of the book and maybe this is why it hasn't been mentioned, but an explanation or a link to some brief explications are very much appreciated.

• Calculate, as usual, and apply superposition. DC Vnia, Vnr not used. Band-pass EE&O. Jul 27 at 13:49
• Formulas seem to be "low entropy". Use EET or FACTS ... Some assumptions were done. Don't know "what". Jul 27 at 15:10
• Thanks @Antonio51 , shall i just short circuit Vnia and Vnr ? Jul 27 at 15:28
• They seem to be DC components. Here, it is AC analysis. So you can short it. I did not use it in the AC simulation. MFS is used to "short" or "reset", did not use. Jul 27 at 15:36

Anyway, to help, the simulation shows something like this, one pole is CL driven.
Note that the values of the components are not exactly what they should be ... Only for example.

The plot is "confirmed" with Maple sheet (will insert it later), but does not give the same "formula" ("brute force", "high entropy").

[ ]

Here is what I get (same assumptions as the above circuit) with a Maple sheet.
I expanded the "gain" formula to show/make "simplification" easier. function plot (CL parameter) :

• animate(evalf(20*log(abs(gain))), ff=-3..12,CL=1e-9..1e-6);
One can note there are 1 zero and 2 poles (not calculated). EE&O.
No simplification made on transfer function (left to OP for checking). In case of noise (X1 10mV) ... Harmonic analysis ... 