Guitar Tone Circuit Analysis Part 3

Introduction
Well I had a very impressive bit of research put together based on adding a parallel resistor to linearize my 1-pole tone circuit from Part 2.  I was putting together the post when I realized that the resistance was almost exactly the same as a log pot alone.  But the plot looked so different from the one I had posted before!  What was going on?

I eventually realized that the plot I put up for the 1-pole circuit was by far the wrong plot.  The information is accurate, but I shouldn't have plotted Cutoff Frequency vs. Resistance for a log pot!  That gives us no indication of how the log pot will perform in comparison to a linear pot.  What I should have graphed was cutoff frequency vs. wiper position.  This is the plot that follows.

As you can see, it's much prettier.  Oddly enough, the Sallen-Key plot seems to be pretty unaffected by the change.  Not sure why, but I'm tired of looking at it now.

The result of my research tonight is that you can put a 100 ohm resistor in parallel with the top half of the pot and achieve essentially the same result.  That should have been pretty obvious in the first place.  I will re-examine whether anything is actually gained from that configuration at a later date and possibly post back.

*** Update ***
I've looked again, and the benefit of using a parallel resistor is completely non-existent.  On the bright side, I've figured out how to flatten out the curve more at the expense of loosing out on the lowest frequency possible. 

I've run the numbers for all pots currently offered at Futurlec.  By the way, Futurlec is amazing!  I've used them before, but I thought I'd give them some props for having ridiculous prices and a surprisingly good and growing pot selection.  It's the only place I've seen with anti-log pots.  They are all mini-pots, but that's not too big a deal. 

Based on the plot above, I think I'll be going with a 20K for the tone pot (dual ganged).  I'll have to figure out this triple pot for the volume later.  Right now I'm working on the prototype.  Back to having everything breadboarded and alligator clipped into the amp. 

Thanks for reading,
Bill