# Electrical – Log-Taper Variable Resistor from Linear-Taper

filteroperational-amplifierphase shiftpotentiometerresistors

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!