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

Chris McDowell declareupdate at gmail.com
Fri Dec 11 19:50:30 CET 2020

```Totally, I've actually built and sold many filters like this and am as familiar as one could say they are without being able to make the math match the simulation or pcb, haha. I've always picked the range empirically after setting the range of current from an expo converter to something sane. Here is the circuit I'm trying to get to match my spreadsheet. I stripped down everything fancy for this. I simply want to be able to confidently calculate the expected center frequency (yes, of the bandpass, why not :) )

example:

Let's say the input voltage is 5V, to get gm this way.

For one LM13700;

Vin = 5 * 220 / (100k + 220)

Iabc = 13uA

Iout = 19.2 * Iabc * Vin

Iout = 0.2739e-6		 (this seems really low...)

R equivalent = Vin / Iout = 182,510 ohms

C = 220pf

1 / 2*PI*R*C = 396.5, just about spot on in LTSpice.

so pretty obviously, if I cut the input voltage in half, that frequency goes up by 2.

And Tom, I think I do understand that, but I want to be able to reconcile what is stated in Barry's book Electronic Music Circuits, pg 140, with what I'm seeing here.

> On Dec 11, 2020, at 12:24 PM, Michael E Caloroso <mec.forumreader at gmail.com> wrote:
>
> Make sure you do not exceed the maximum control signal.  IE for
> LM13700 OTA max is 2mA.
>
> MC
>
> On 12/11/20, 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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