RC cutoff formula for multipule stages

[pqt_bach]

Hi there,

I was wondering what is the correct way to calculate the low and hi roll-off frequency of a multipule gain stages. To clarify that, in a single inverting OA stage the low-cut point is calculated by: 1/(2*pi*R*C) - the how to I calculate the comulative effect on the roll-off points for a multi stage circuit, like two OA stage is series?



Cheers

[WGTP]

Wondered the same thing a while back.   

http://www.diystompboxes.com/smfforum/index.php?topic=58312.0

[pqt_bach]

I use multi-pole filters quite a bit, but I meant how do I calculate the overall frequency shaping of a number of gain stages in series, like the Marshall Blues Breaker, or Boss Blues-Driver, for example. Is it the same as passive multi-pole filters?

[R.G.]

Well, let's think.

The "cutoff frequency" of any filter is arbitrarily defined as the half power point in the rolloff, -3db in power. Power has no real meaning in voltage-only circuits where the impedance is not specified, but in circuits where there are equal impedances to compare, you get to -3db power at a voltage ratio of 6db; half the voltage. That is what gives us the "formula" that the cutoff point in a single RC is F = 1/(2*pi*R*C). It's just ohm's law rearranged for the frequency where the voltage across the R and the C are the same.

When you cascade RCs, you can have four cases. These are identical vs non-identical sections either separated by buffers to not interact, or not separated so they interact. It's only when they are identical and separated by buffers that you can quote a specific formula. In other cases, it's always going to be the process of writing out the loop equations, setting the voltage ratio at the output equal to 0.5, and solving the loop equations.

For identical, isolated sections, you will divide -6db by the number of stages, and solve for the frequency where the voltage ratio is equal to that. For instance, for two identical, isolated sections, the "cutoff point" is the frequency where each section is contributing -1.5db.

[pqt_bach]

Thanks alot

[WGTP]

Oh, your wanting to get all fancy with it.  I was doing well to calculate 65%.