[sdiy] Polymoog resonator question

[Donald Tillman]

> On Oct 6, 2018, at 5:56 PM, rsdio at audiobanshee.com wrote:
> 
> I tried this is Grapher, but need some hints. Is C in farads or nanofarads? What about s? Also, there aren’t enough parentheses for me to tell whether sC is in the numerator or denominator.

No, I totally goofed.  Let's try that again:

This is for the pots tuning the integrators on the Polymoog filters:

Open up a new graph plot, lin-log.

Use this equation:

    y = Rmin / (Rpot(1-x) + Rmin)

Or for this case, a 2.4K resistor in series with a 10K pot:

    y = 2400 / (10000(1-x) + 2400)

X is the pot turning (0 to 1).
Y is the log of the attenuation.

Set it to only show the x values from 0 to 1 (View -> Frame Limits).

This is the loss the pot adds, going from full CCW to full CW.

It's not a straight line, but it's plenty close.

And you can compare it to a regular passive attenuator with the same values.  Add a second equation, use the condition operator:
               
y = (1/(Rpot + Rmin)){(2x-1)Rpotright + Rpotleft + Rmin   for 0.5 <= x
                      (2x)Rpotleft + Rmin                 for x < 0.5

For a 10K audio taper pot split 17%/83%  (pot left, pot right), and a resistor Rmin to ground:

y = (1/(10000 + 2400) {(2x-1)8300 + 1700 + 2400 for 0.5 <= x
                       (2x)1700 + 2400          for x < 0.5 

Compare the two, and the first looks much better.

(They should begin and end at the same points.)

  -- Don
--
Donald Tillman, Palo Alto, California
http://www.till.com

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