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Chapter 5
Temperature Controller Operation
63
5.4.4.1.6
The Steinhart-Hart Equation
The Steinhart-Hart equation is used to derive temperature from the non-linear
resistance of an NTC (Negative Temperature Coefficient) thermistor.
The following section contains an explanation of the Steinhart-Hart equation and the
values of these constants for some common thermistors.
Two terminal thermistors have a non-linear relationship between temperature and
resistance. The resistance verses temperature characteristics for a family of similar
thermistors is shown in Figure 32. It has been found empirically that the resistance
verses temperature relationship for most common negative temperature coefficient
(NTC) thermistors can be accurately modeled by a polynomial expansion relating the
logarithm of resistance to inverse temperature. The Steinhart-Hart equation is one
such expression and is given as follows:
3
1/T = A + B (Ln R) + C (Ln R)
Where T is in KELVIN. To convert T to °C, subtract 273.15.
Once the three constants A, B, and C are accurately determined, only small errors in
the calculation of temperature over wide temperature ranges exist. Table 6 shows the
results of using the equation to fit the resistance verses temperature characteristic of a
common 10 k Ohm (at room temperature) thermistor. The equation will produce
temperature calculation errors of less than 0.01°C over the range -20 °C to 50 °C.
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