User's Manual

LDT-5525 27
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APPENDIX A
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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
o
C over the range -20
o
C to 50
o
C.
Table A.1 Comparison of Curve Fitting Equations
Error T (°C) Error T (°C)
R
1
T
Actual
Third Order Fit Eq 1 First Order Fit Eq 2
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