# [sdiy] how to calculate cutoff in an OTA filter?

Chris McDowell declareupdate at gmail.com
Fri Dec 11 19:18:06 CET 2020

```So this makes sense, but when I work it all out I get confused.

> take into account attenuation at the
> input of the OTA.

How would I go about this without making the cutoff frequency seem voltage dependent? If I derive gm from Vin/Iout, then the resulting frequency is dependent on the input voltage, but we know it is not. Is it just some algebra I'm overlooking to separate it out?

I took a peek in my copy of Barry Klein's book (thank you list for bringing it up recently so it could rejoin the shelf) and he actually does this, but it leads to a cutoff that is dependent on input voltage. I'm a little lost ¯\_(ツ)_/¯

What I tried to do was use gm = 19.2*Iabc, from the LM13700 datasheet. But that ends up quite wrong. If I use the method you describe an in Barry's book, it agrees with LTSpice quite well if I use 5V as the input, but again I'm not seeing how the voltage input relates. If I change that input voltage to 2V, everything is wrong (the values are all in a spreadsheet currently)

Cheers,
Chris

> On Dec 11, 2020, at 11:25 AM, Guy McCusker <guy.mccusker at gmail.com> wrote:
>
> Unless I have become confused again, the centre frequency of the SVF
> bandpass (which is not the same as the 3dB point of the lowpass, but
> is probably the right frequency to think about) is the same as the
> unity gain frequency of the integrators. This assumes you have the
> integrators set for the same gain, which you don't have to, and fun
> can be had if you don't.
>
> So for a typical OTA integrator, I think you would use your equation
> but the gm would be calculated to take into account attenuation at the
> input of the OTA.
>
> Guy.
>
> On Fri, Dec 11, 2020 at 5:06 PM Chris McDowell <declareupdate at gmail.com> wrote:
>>
>> The subject says it. How do we calculate the cutoff frequency in a filter with OTAs, or VCAs for that matter. Maybe this is more obvious than I think but I'm not making sense out of it.
>>
>> So for a state variable filter, if transconductance, gm = 1/R, then R = 1/gm, then why is the cutoff not just 1 / ( 2 * PI * (1/gm) * C) ?
>>
>> Cheers and thanks in advance,
>> Chris
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