Calibrating Thermistor Sensors
Thermistors have the advantage of a very high sensitivity to temperature changes, but the disadvantage of an aggressively nonlinear characteristic. Here is a characteristic curve showing the resistance of a typical negative temperature coefficient thermistor device over a temperature range from 0 to 100 degrees C.
Figure 1 - Typical thermistor curve
As you can see, the value changes from over 15k ohms to under 100 ohms. The change is most rapid at low temperatures, giving great resolution for determining the corresponding temperature values there. At the other end of the range, resistance levels change relatively less with temperature and measurement resolution is relatively poor.
Curve forms are available that describe the nonlinear shape of
the thermistor characteristic quite well. The most commonly used form is the
Steinhart-Hart Equation. The resistance measurement of the
thermistor is not normalized, so just use the measured value of
Thermistor Linearization Curves
It is relatively easy to calibrate your own response curves, if you have an accurate temperature measurement standard. Convert the temperature values to Kelvins, and invert. Take the corresponding measured resistance values and compute the natural logarithm. Now, fit the coefficients of a third order polynomial in the log-resistance values to best match the inverse-temperature values.
For the following example, three points are selected, two close to the ends of the operating range and one near the center. We know that measurements will not be completely accurate, so artificial errors have been inserted into the data to result in temperature errors of magnitude 0.1 degrees C with alternating sign at the three measured points.
Data with artificial 0.1 degree errors added
Powers of log-resistance are collected in a matrix,
and the inverses of temperature in Kelvins are collected in a
vector. The model coefficients
Both of these formulas produce curves that are virtually indistinguishable from Figure 1. The following shows the differences — the calibration errors — that resulted from the data errors deliberately included for the the 3-point fit.
Deviations of 0.1 degrees appear, as we know they should, where they were injected at the locations of the measured points used for the fit. At intermediate locations, the fit error is well behaved. We can conclude that the fit is about as good as the measurement errors that went into making it — but don't extrapolate much beyond the range that you measure. To reduce sensitivity to noise during calibration try the following steps.
Balancing measurement resolution
The linearization takes care of the problem of interpreting the highly nonlinear response, but not the problem of uneven measurement resolution.
If the range is not too large, you can balance the resolution significantly by measuring in a voltage divider configuration. Power the thermistor from a regulated voltage supply, connect the other end to ground through an accurately measured load resistance, and observe the output voltage where the thermistor and load resistor join.
The goal is to obtain a relatively uniform relationship between temperature and measured voltage. The linearization curves will take care of the rest. The following shows the relationship between temperature and measured voltage with a load resistor that is about half of the nominal room-temperature resistance.
The slope doesn't change much through the operating range. This is very different from the drastic nonlinear behavior you see in Figure 1. How does this work? The voltage divider has a saturating characteristic that responds less as thermistor resistance grows. The growth and saturation effects approximately balance.
Measure a temperature using a thermistor device in the voltage divider configuration by doing the following.
You can use the