Appendix A - The Steinhart-Hart Equation - ILX Lightwave LDT-5525 User Manual

Appendix A
The 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:
3
1/T = A + B(Ln R) + C(Ln R) 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 °C over the range -20 C to 50 °C.
A-1