[sdiy] Formula for Audio & Log-taper pots?

[Tim Stinchcombe]

> I've read that audio taper pots have 15% resistance at the half-way 
> point in their rotation, and that log taper pots have 10% resistance 
> at the half-way point. Is this generally correct? I seem to remember 
> that there was more than one taper being used by some engineers for 
> audio, but I think these are the common ones.
> 
> Does anyone know of a more precise way to describe the "curve" of 
> either the resistance vs rotation, or more importantly, the 
> attenuation vs rotation? I would really like to find a formula to 
> calculate either the resistance or the signal attenuation for a given 
> amount of rotation.

Here's what I cobbled together for use in SPICE some while back. Basically
two resistors which sum to the total value of the pot, and the resistance of
each depends on a 'factor' which varies from 0 to 1 (i.e. represents angle
of rotation), so the junction between them is the 'wiper'.

linear:

X$VR1 V1_P VR1_Wiper 0  VR1$TP_POT pinnames: Max Wiper Min
.subckt VR1$TP_POT 1 2 3
R1 1 2 "10k*(1-VR1factor)"
R2 2 3 "10k*VR1factor"
.ENDS

reverse log:

X$VR1 V1_P VR1_Wiper 0  VR1$TP_POT pinnames: Max Wiper Min
.subckt VR1$TP_POT 1 2 3
R1 1 2 "10k*(1-.16*ln(535.14*VR1factor+1))"
R2 2 3 "10k*.16*ln(535.14*VR1factor+1)"
.ENDS

log:

X$VR1 V1_P VR1_Wiper 0  VR1$TP_POT pinnames: Max Wiper Min
.subckt VR1$TP_POT 1 2 3
R1 1 2 "10k*(1-.0155*(exp(4.18*VR1factor)-1))"
R2 2 3 "10k*.0155*(exp(4.18*VR1factor)-1)"
.ENDS

I seem to have taken the data I used from here:

http://www.omeg.co.uk/lawp16ct.htm

and then 'fitted' my chosen 'law' to two points, the full value and that 'at
15%' (whatever, as from the Omeg data) using a calculator, hence the funny
numbers that are seen. (Looks like I said assume the basic law is e.g.
A*(exp(B*factor)-1), then solved for A and B from the two points).

Works nicely enough for simulations when a non-linear pot is called for -
the attached gif shows the voltage at the 'wiper' for each type.

Hopefully this may give you some ideas for how to implement something in
whatever it is you are doing!

Tim
__________________________________________________________
Tim Stinchcombe 

Cheltenham, Glos, UK
email: tim102 at tstinchcombe.freeserve.co.uk
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