[sdiy] Polymoog resonator question

[rsdio at audiobanshee.com]

Hi Don,

I feel bad asking yet again, but I can’t figure out how to enter those equations with the condition operator.

Mostly, I think I’m having problems because I don’t see a closing ‘}’ to balance the ‘{‘
In addition, there seems to be a mix of characters that should be entered into Grapher versus text that simply describe what’s being configured.

I do have the first equation entered. One thing I notice is that the range seems to be 0 to 1 for x, as you point out, and from 0 to 1 for y, as well. Since the scale is logarithmic, that works out in the Frame Limits to y: from 10^-1 to 10^0

If you care to help further, I’m very interested in learning more about how to use Grapher. In fact, I seem to recall running across the condition operator before, but maybe that’s just the DSP textbooks that I’ve been reading…

Brian


On Oct 6, 2018, at 7:51 PM, Donald Tillman <don at till.com> wrote:
> 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
>