Lightwave Communications LDT-5525 manual STEINHART-HART Equation

A P P E N D I X A

STEINHART-HART EQUATION

Two-terminal thermistors have a nonlinear relationship between temperature and resistance. The resistance verses temperature characteristics for a family of similar thermistors is shown in Figure A.1. It has been found empirically that the resistance versus 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:

1/T = A + B(Ln R) + C(Ln R)3 Equation 1

- where T is expressed in KELVIN.

Once the three constants A, B, and C are accurately determined, Equation 1 introduces small errors in the calculation of temperature over wide temperature ranges. Table A.1 shows the results of using equation 1 to fit the resistance verses temperature characteristic of a common 10K ohm (at room temperature) thermistor. Equation 1 will produce temperature calculation errors of less than 0.01 oC over the range -20 oC to 50 oC.

Table A.1 Comparison of Curve Fitting Equations

		Error T (°C)	Error T (°C)
R1	T	Third Order Fit Eq 1	First Order Fit Eq 2
	Actual
32128	0.00	-0.0000	-0.23
19549	10.00	0.0005	-0.11
12262	20.00	-0.0001	-0.06
9814	25.00	-0.0002	-0.06
7908	30.00	0.0009	-0.07
5331	40.00	0.0003	-0.15
3542	50.00	-0.0030	-0.30

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