Pot Tapering Math!! Including charts and graphs

[R.G.]

I had to go refresh myself on my "Secret Life of Pots" article at geofex.com recently, and wound up re-creating all the math-scribble behind it. It occurred to me that some of you might like to read through it, so I cased it up in a pdf document (linked below).

The math is not too bad, just the parallel resistors formula, and there are three pages of pretty graphs of what happens when you add tapering resistors to a pot. I did both the voltage-divider use of a pot and the two-terminal variable resistor form on the graphs.

It's funny. I had a tiny mental breakthrough in doing this. I realized that all pots have two tapering resistors, all the time. For no obvious resistors attached, the tapering "resistors" are just the resistance of the air between the terminals, some giga-ohms for average values of air. The two-terminal variable resistor case has one of its tapering resistors set to zero ohms - a short circuit. When I put that in, the charts and graphs just fell out.
In the top graph, I made the terminal 1-2 tapering resistor be huge, and the terminal 2-3 tapering resistor be 1/10 of the nominal pot rated resistance. This makes it into a pseudo-audio-taper divider.


In the bottom graph, I reversed the tapering. The taper resistor from terminals 1-2 were set to 1/10 of the pot nominal value, and the tapering resistor across terminals 2-3 was made giga-ohms. This made it approximate a reverse-log pot divider.

 

The pdf is four pages. The last page has the graphs showing tapering a two-terminal-connected pot by making one "tapering resistor" be microscopically small compared to the nominal pot value.

Pot Tapering Math

Here's the original article at geofex.com:
The Secret Life of Pots

[m7b52000]

when I download the pdf it has only 1 page with trial #5 to trial #7.

[R.G.]

aaccckkkk!!

debugging

[R.G.]

I think I fixed it:

Pot Tapering Math PDF

[davent]

I think I fixed it:

Pot Tapering Math PDF

Yup, I get the four pages now.

[Morocotopo]

I read the original Geofex article many many years ago, and some others regarding alteration of pot tapers with resistors. But I´ve never been able to use these resistor tricks to get a pot I could use in a real circuit. Maybe I´ll try to do it again, it´s true that years ago I was in more of a learning phase in electronics.
Thanks R.G. for your generous sharing.

[m7b52000]

yes, thanks indeed!

[StephenGiles]

For the benefit of those speaking UK English - he means Maths!!!