[sdiy] Polymoog resonator question

Donald Tillman don at till.com
Sat Oct 13 20:08:01 CEST 2018


In the upper right corner of the Grapher window is a funky sigma symbol.  
    Click on that, 
    click on "Show Equation Palette", 
    click on "Operators", 
    admire all the fancy possibilities, 
    click on the condition operator (the next to last one), 
    select two conditions, 
    and use that, 
    and fill out the four fields there.

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


> On Oct 12, 2018, at 7:27 PM, rsdio at audiobanshee.com wrote:
> 
> 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



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