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March 03, 2012

Comments

Richard Mayo

It's just a hunch, but temperature related phenomena generally have an exponential function. Have you tried fitting an exponential series ae^t + be^2x ... me^it + ne^i2t ? You might get a better fit with fewer terms and less bad behaviour outside the data range.

John Dunn

I got the equation from an Omega catalog. I didn't derive it.

Gustavo Castro

Richard,
For most practical purposes, this is good enough. Sometimes, piece-wise linear approximations are used, in order to simplify the math even further in systems that have limited computing power. For better accuracy, RTDs have better linearity and yield more accurate results.

Andy Fierman

Another useful source of information on thermistors can be found here:

http://www.meas-spec.com/product/t_resources.aspx?id=592;

The note on the Steinhart-Hart Thermistor Equation and the associated Excel calculator are particularly good.

http://www.meas-spec.com/downloads/MEAS_Steinhart-Hart_Thermistor_Equation.pdf;

and the calculator is here:

http://www.meas-spec.com/WorkArea/DownloadAsset.aspx?id=6651.

About 10 years ago I wrote an Octave script to derive the Steinhart-Hart (SH) coefficients for an NTC thermistor used in a temperature compensated power supply for an Avalanche Photo Detector. The SH based calculations gave considerably closer correlation between modelled and measured performance than the simple exponential model:

R = Ro exp( Beta/T - Beta/To)

A bit of background can be found here:

http://en.wikipedia.org/wiki/Thermistor

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