handbook of modern sensors

16.1 Thermoresistive Sensors 471
Fig. 16.7. Errors of a simple model and Fraden model for four thermistors calibrated at two
temperature points (t 0 and t 1 ) to determine β m . Errors of a Steinhart–Hart model are too small
to be shown on this scale.
A practical selection of the appropriate model depends on the required accuracy
and cost constraints. The cost is affected by the number of points at which the sensor
must be calibrated. A calibration is time-consuming and thus expensive. A complexity
of mathematical computations is not a big deal thanks to the computational power
of modern microprocessors. When the accuracy demand is not high, or cost is of a
prime concern, or the application temperature range is narrow (typically ±5–10 ◦ C
from the calibrating temperature), the simple model is sufficient. The Fraden model
is preferred when low cost and higher accuracy is a must. The Steinhart–Hart model
should be used when the highest possible accuracy is required but the cost is not a
major limiting factor (Fig. 16.7).
To use the simple model, you need to know the values of β m and the thermistor
resistance S 0 at a calibrating temperature T 0 . To use the Fraden model, you need to
know the value of γ also, which is not unique for each thermistor but is unique for
a lot or a type. For the Steinhart–Hart model, you need to know three resistances at
three calibrating temperatures. Table 16.3 provides the equations for calibrating and
computing temperatures from the thermistor resistances. For all three models, a series
of computations is required if the equations to be resolved directly. However, in most
practical cases, these equations can be substituted by look-up tables. To minimize the
size of a look-up table, a piecewise linear approximation can be employed.