Quote of the Day
People don't care how much you know until they know how much you care.
I had a job this week that required that I use the Steinhart-Hart equation for modeling a thermistor's resistance versus temperature relationship. The requirement was driven by the customer's need for high accuracy. Most thermistor applications do not demand high accuracy, but this application can tolerate no more than ±0.5 °C of error. This means that I cannot use the β-based thermistor model, which in this application would have an error of more than ±2 °C. This page will show you how how to perform an efficient 3-point calibration using Excel and a bit of matrix math. As a side benefit, I am using this workbook as an example of matrix math in my Excel tutoring at a local library.
The Steinhart-Hart thermistor equation is shown in Equation 1.
- A, B, C are calibration parameters.
- R is the thermistor resistance (Ω).
- T is the thermistor temperature (K).
Because there are three unknowns, calibration consists of measuring the thermistor resistance at 3 temperatures and solving the linear system shown in Equation 2.
Because my customer is Excel-focused, I solved this problem in Excel. The workbook is straightforward to use:
- Adjust the columns "Temperature (°C)" and "Mfg Spec (Ω)" to match the manufacturer's thermistor specifications for temperature versus resistance.
- Select the desired calibration temperatures. The resulting maximum error is displayed.
- The spreadsheet calculates the A, B, and C coefficients needed for using this specific thermistor.
My spreadsheet is available here. The thermistor included in the spreadsheet was an arbitrary choice for use as an example.