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.I.
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:
In
=
A
+
B(Ln
R)
+
C(Ln
R)3
Equation
1
Where
T
is is expressed in
KELVIN.
Once the three constants
A,
B,
and
C
are accurately determined, Equation
1
introduces small errors in the calcu-
lation
of
temperature over wide temperature ranges. Table
A.l
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
\u11
produce temperature calculation errors of less than 0.01 OC over the range -20 C to 50 OC.
CURVE-FITTING
EQUATION
COMAPARISON
I
Error
T
(OC) Error
T
(OC)
T
Actual
-20.00
-10.00
0.00
10.00
20.00
25.00
30.00
40.00
50.00
First Order Fit Eq
22
Third Order Fit Eq
l3
Table
A1
Comparison of Curve
Fitting
Equations
Rtsistnnce
of
a
10
kR,
Fenwal UUA41J1
thermistor.
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