The spreadsheet in figure C10b works like a calibration curve - the slope
(m) and intercept (b) of the best fit straight line is determined , then
best-fit temperature values are calculated automatically from slope and
intercept of the best-fit line.
This section is quite technical. If you don't understand it, don't worry,
you don't need to. We include it just to be complete. This math is powerful
and if you can master it, you will be able to use these ideas again and
again. Here is the math behind fitting to the thermistor equation. The trick
is, to convert that awful thermistor equation into a straight line equation.
Sounds difficult, but you can take the natural log of both sides of this
equation to get ln(R) = a/(T+To) + ln(Ro) If you define the following three
new variables ln(R) = y, 1/(T+To) = x, ln(Ro) = b then the equation becomes
y = a*x +b the equation of a straight line! The spreadsheet can convert
the R,T pairs into x,y pairs, fit the data to this straight line, determine
a and b, and then use these to compute the temperature for any resistance
R using T = ­p;To + a/(ln(R)-b) Quite a mess, but all perfectly good
algebra incorporated in the spreadsheet.