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Self-Calibrate Your Thermistors for Higher Accuracy

Use the Steinhart-Hart Equation for High-Precision Readings

Technicians and engineers often use thermistors to log temperature in applications which require increased accuracy for more demanding projects. To accomplish this, they use the Steinhart–Hart equation to convert a thermistor sensor’s resistance to temperature. When compared against other methods, Steinhart-Hart models will give you much more precise readings across the sensors’ temperature ranges, often within a few hundredths of a degree of accuracy. Although the Steinhart-Hart equation is not universally known, users most commonly work with it in applications measuring water or machine temperatures, including liquid temperature sensors and solar hot water applications. As part of our free tech support, we at CAS Data Loggers often provide help in this area for customers who call in asking how to convert the measured resistance to temperature.

Thermistor manufacturers don’t always provide users with Steinhart–Hart coefficients for their sensors, or they may not be presented clearly enough for users to plug them into the equation. In the absence of a manufacturer-provided table, it’s not immediately obvious how to derive the necessary coefficients. However, even when you do have to derive these, the formula doesn’t take very long to complete. To speed up the process, there are several Steinhart-Hart temperature calculators online which you can use to save time by just entering the coefficients and resistance. You’ll find a download to our own online calculator here and an example table, at the end of this article.

Plotting a Coefficient Table into Microsoft Excel:

If your thermistor manufacturer has provided them, the sensor tables give the resistance versus temperature at several reference points and temperature ranges. In this case you can input them into Excel and perform a line fit. Using Excel to plot it out, you can perform a line fit using a 2nd order logarithmic curve to show the results in graph form by adding a trend line, for example. You can also test it by performing a spreadsheet calculation. Once you program the coefficients into the datalogger, it automatically gives you the temperature.

Deriving Steinhart–Hart Coefficients:

In cases where the Steinhart–Hart coefficients are not provided by your thermistor manufacturer, you can derive them yourself. First you’ll gather at least 3 accurate measures of resistance data made at 3 known temperatures and then insert them into the formula to derive the A, B and C coefficients.

The Steinhart-Hart equation is commonly defined as:

steinhart-hart-equation1

where:

  • T is the temperature (given in kelvins)
  • R is the resistance at T (given in ohms)
  • A, B, and C are the Steinhart–Hart Coefficients which differ according to your thermistor model/type and its particular temperature range
  • Ln is the natural logarithm

The equation is sometimes presented as containing a (ln(R))2 term, but this results in a lesser value than the other coefficients and is therefore not as useful for obtaining higher sensor accuracy.

To find the Steinhart–Hart coefficients, you need to know at least three operating points. For this, we use three values of resistance data for three known temperatures.

steinhart-hart-equation2

After inputting the values R1, R2 and R3 giving resistance at the temperatures at T1, T2 and T3, you can determine the Steinhart-Hart coefficients A, B and C:

steinhart-hart-equation3

If instead you want to find the resistance of a semiconductor given its temperature, you must use the inverse of the Steinhart–Hart equation:

steinhart-hart-equation4

where:

steinhart-hart-equation5

 

Our Engineering Tech Support developed the below tool which shows an example of how to enter your actual temperature in Celsius and Kelvin (Col. B and C) and your sensor’s resistance (Col. D) at 3 reference points (T1-T3) to derive the 3 Steinhart-Hart coefficients (A, B, C).

tactual in C tactual in K Resistance Tcalc Y R L
T1 10 283 1991.4 283 0.003534 1991.4 7.596593
T2 60 333 248.7 333 0.003003 248.7 5.516247
T3 122 395 37 396 0.002532 37 3.610918
G2 0.000255037
G3 0.000251381
Steinhart-Hart Coefficients C 5.48534E-08
B 0.000247904
A 0.001626295

To get more information on several data logger models which connect to thermistors and many other sensor types, and which include software to make it easier to convert resistance to temperature, contact a CAS Data Logger Applications Specialist at (800) 956-4437.