----- Original Message -----
From: "Albert Otten" <aodiversen@concepts.nl>
To: <TekScopes@groups.io>
Sent: Sunday, January 19, 2020 12:28 PM
Subject: Re: [TekScopes] Risetime calculator (in tekwiki)


Actually the math appears to be surprisingly simple and in theory the instrument shows EXACT results with LINEAR pots..
Suppose all fixed (plus their trimpots) and variables have equal resistance R (5 k in our case).
Each pot is in parallel with one fixed resistor.
The wiper of a pot splits the pot resistance in xR (top part) and (1 - x)R (bottom part) where x varies linearly with angle from 0 (ccw) to 1 (cw).
The effective resistance, say z, of one pot circuit is seen between wiper and bottom terminal. The path consists of parallel (1 -x)R and xR + R = (1 + x)R.
Hence z = (1 - x)R*(1 + x)R / [(1 - x)R + (1 + x)R] = (1 - x^2)R^2 / (2R) = R(1 - x^2)/2.
There is the quadratic function we need!
To make it complete:
F branch including the extra R to the meter: R + zF = R + R(1 - xF^2)/2 = (3/2)R - (R/2)*xF^2,
A+B+C branch: zA + zB + zC = R(1 - xA^2)/2 + R(1 - xB^2)/2 + R(1 - xC^2)/2 = (3/2)R - (R/2)*(xA^2 + xB^2 +xC^2)
Balance when xF^2 = xA^2 + xB^2 +xC^2.
Q.E.D.

Albert


On Sun, Jan 19, 2020 at 04:15 PM, Roger Evans wrote:

Albert,

Thanks for pointing that out, the calculator is quite different to what I had
imagined. I thought the resistance would increase in the clockwise direction
and each pot would just be connected as a two terminal variable resistor.
That does rely on having a good approximation to a square law for the taper of
the pot. As you pointed out the resistance increases ccw and I can't see
immediately why the maths works for the combination of fixed resistor in
parallel with the three terminal connected pot. It might be a rather clever
piece of algebra or an approximation that is good enough for the intended
application.

Roger