Re: Risetime calculator (in tekwiki)
Albert,toggle quoted messageShow quoted text
That's great, but where do you use such an instrument. I'm trying to figure out where three risetimes, or two as the case may be, react to give me a single total risetime. It's a neat calculator, but where do you use it?
----- Original Message -----
From: "Albert Otten" <aodiversen@...>
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.
On Sun, Jan 19, 2020 at 04:15 PM, Roger Evans wrote: