# Log-Taper Variable Resistor from Linear-Taper

I'll start by saying: I've read quite a bit about how to make a "log taper potentiometer" using a resistor and linear-taper potentiometer, but I'm not sure if that will work in my case.

I'm working on an all-pass filter to use as a corrective phase-shift for an active-noise-cancellation circuit I'm designing. This circuit will be used primarily to filter out car noises from a nearby highway when I'm trying to sleep.

I'm using this diagram for my phase-shift/all-pass filter:

I figure I should be able to modify VR1 and R6 to give me the frequency response I'm looking for.

As I understand it, the 90-degree (center) frequency is calculated by f=1/(2*pi*R*C). I want that frequency to be user-variable between ~30hz and 3kHz. I figure it's easier (and probably more reliable/cheaper) to use a variable resistor than it is to use a variable capacitor, but maybe I'm wrong - I don't have a lot of experience with variable capacitors. For the capacitance provided in the diagram (100nF) I've calculated I'll need ~500 ohms of resistance for the top of my frequency range, and ~50Kohms of resistance for the bottom. Thus I need to use a variable resistor that ranges approximately 50Kohm - pretty good, pretty standard.

When I graph the frequency vs linear rheostat position, however, I don't get a very good response:

It looks like the first 1/5 of the range of the rheostat/potentiometer will cover 90%+ of my frequency range, though - so I guess I'd better use a log-taper potentiometer. I want it to closely approximate the log curve rather than a cheap 2-line approximation (though maybe it's better to just give up on this count) - which means either:

• A) find an expensive accurate log-taper potentiometer,
• B) Approximate it myself

Here I run into another problem: from my research, it's easy to do a reverse-log taper variable resistor, but I can only make a linear-taper potentiometer into a log-taper if I'm using it as a voltage divider. I don't know if a voltage divider is appropriate for my intended use. If so, I'm not sure how to visualize it.

My question, then, is: What are my options? Is it possible to make a log-taper variable resistor that's not in a voltage divider configuration? If so, how? If not so, is it appropriate to use a voltage divider configuration here? If so, what values would you recommend, and how best to hook it up? If neither is possible/acceptable, what other options remain to me (aside from giving up)?

And, as a side, if you see anything wrong with my overall idea/proposition for this active-noise-cancellation circuit, let me know!

• A few Questions. Since this is for audio filtering, do you want true log or audio (human sensitivity log) taper? What is difficult about picking up an audio grade log pot? They are a couple of bucks... How bad is the taper from optimal? I would look for guitar electronics brands like bourns , they are used to change passive filters ("tone") in professional instruments and on professional amplifiers all the time... – crasic Aug 24 '18 at 0:16
• It's not impossible to get audio-grade log pots, but the taper is usually approximated with 2 or 3 lines (linear subsections). Those that aren't approximated that way have proven tricky (not in stock) or expensive (\$10+ for a single potentiometer) to find. Part of my hope in "making" a solution was that I could control the amount of taper, too - I need a pretty severe/steep slope to counteract the way the frequency response (1/(2pi*R*C*)) works for the filter. – Helpful Aug 24 '18 at 0:31
• Your frequency scale should be exponential, to the power of 2 as each ocatave is a doubling of frequency. It will linearlse your curve somewhat. – Transistor Aug 24 '18 at 6:21