3 band active tone control - need some math help

[ubersam]

anyone know the math for the filters in this 3 band active tone control?

[PRR]

Bigger caps make lower frequencies.

[alanlan]

It's best to break these things down a bit. Forget dc conditions and the input buffer and coupling caps and concentrate on each of the bands separately ( even though there may be some interaction). Then consider the pot at each end and somewhere in the middle. That will make the maths easier. If you really want to solve symbolically by hand considering all 3 bands then it's difficult but not impossible. For me I would use Kirchoffs law and solve using matrices in Mathcad. Even simpler, bung it into PSpice but I suppose that wouldn't really do if you really want to grasp the maths.

[liquids]

This is a great way to enter the world of LTspice.  The learning curve is rough, but EQ is a great area to get started.  One can build this circuit, sim it, and get a frequency plot every time one changes the values of the caps or resistor values (for potentiometer settings).

Gaussmarkov(?) has a good 'primer' that helps to get one going with LTspice via the passive BMP tonestack.  The only thing more complicated than that here is, in essense, the addition of an (arbitrary) op amp of some ilk in LTspice.


MAybe a too-far ahead side note, but one can use the generic op amp (and one then only needs to include a clause to do so, which I forgot since it's been a while, but that shouldn't be hard to find), or once can use one of the a "specific" op amps in the LTspice catalog, then add power supplies for the op amps + and - connections.  Either way, the op amp you pick or way you go about it should have little to no effect on this kind of circuit, which is cool.   

From there, one can take and run with it.

Why do "math" when one can "sim and see"!