Custom Hi-Pass Filter Stompbox

[artifus]

i'm down with that and i'm all ears - diiiive! (as brian blessed once bellowed)

[R.G.]

Actually, I've talked you through the hard part already. It was a trick.    Once you get to where you can imagine that there's always a clot of internal Rs, Cs, and Ls inside every signal source, you know how to treat it.

Good design work has a principle that says that whatever cannot be controlled must be made irrelevant.

Imagine you have simple lowpass filter, single R in series with the signal, single C to ground. Input through the R and output across the C.

We know that the capacitor's impedance to AC current flow declines linearly with frequency, and that the R (ignoring for the moment the non-perfect nature of the insides of a real-world R) is constant with frequency. The nominal "rolloff frequency for this combination is taken to be where the impedance of the C is the same as the R, and that happens at F = 1/(2*pi*R*C).  No problem. For R = 10K and C = 0.1uF, then F = 1/(2*3.14*10k*0.0000001) = 159Hz.

So we connect this up to a signal source which has a 10K ohm internal resistance. The capacitor can't tell that there is one real-world and one hidden internal 10K resistors feeding it. All it knows is that its current is coming through 20K, not 10K. And the rolloff frequency of the filter now acts like it has a 20K resistor, not a 10K, and so its real measured rolloff will be 79.6Hz, not 159. The source impedance has changed the effective filter frequency.

ACK! How do we ever design filters?

Make the source impedance irrelevant. We do this sometimes by putting a buffer on the signal. Buffers are things with high input impedances (they don't load down the signal source much, and we still have a discussion of input impedance coming later) and low or even very, very low output impedances. If we buffer that signal source with a 10K internal impedance by putting a buffer after it that has a 1M internal input impedance and a 1 ohm output impedance, then the filter acts like it has a series resistor of 10,001 ohms, not 10,000 ohms, and we can safely ignore the effect of the source impedance because our meter's not good enough to measure the difference anyway.

Buffers change high impedance sources into low impedance sources.

Another way we can make the source impedance irrelevant is to be a textbook on filters, where we can simply say "... of course, the source impedance for this class of filters is assumed to be very small... " and leave the reader to wonder what the devil that meant, anyway; what it really meant was "you better use a buffer in front of this...".

So - sources got impedances. For audio considerations, we can usually think of them as internal resistors, but they can also be internal inductances and capacitances too, and guitar pickups are an important - to us! - class where internal inductance and capacitance matter. And you have to take the source impedance into account, or assure yourself somehow that it won't matter, or fix it so it can't matter to your filters.

[artifus]

Once you get to where you can imagine that there's always a clot of internal Rs, Cs, and Ls inside every signal source, you know how to treat it...

...The capacitor can't tell that there is one real-world and one hidden internal 10K resistors feeding it. All it knows is that its current is coming through 20K, not 10K.

So - sources got impedances. For audio considerations, we can usually think of them as internal resistors, but they can also be internal inductances and capacitances too, and guitar pickups are an important - to us! - class where internal inductance and capacitance matter. And you have to take the source impedance into account, or assure yourself somehow that it won't matter, or fix it so it can't matter to your filters.

i think this is what i was missing and had not considered before. thanks again, rg, a lot of stuff is starting to (slowly) fall into place now.