
Page 24 · TC-3 Temperature Controller User’s Manual
required temperature range. The typical setting is 100μA, but your
application will determine the actual needs.
The Steinhart-Hart Equation
As can be seen from the temperature versus resistance graph above,
resistance varies inversely with temperature in a non-linear fashion.
This relationship can be accurately modeled by polynomial equations,
and one such being the Steinhart-Hart equation:
1
T
=A+B *ln ( R )+C *ln ( R)
3
The coefficients A, B, and C can usually be obtained from the
thermistor manufacturer. The TC-3 defaults to the coefficients for the
BetaTHERM 10K3A1 thermistor (A = 1.12924x10
-3
, B = 2.34108x10
-4
, C
= 0.87755x10
-7
). You can change the coefficients under the Sensor
Coeffs menu.
Working With RTDs
Like thermistors, RTDs also function by converting temperature into
resistance, but unlike thermistors, RTDs increase in resistance as
temperature increases. RTDs are also a fairly linear device, meaning
they can be used across a much broader temperature control range.
According to IEC751, the resistance/temperature relationship is
determined using one of two equations, dependent on the temperature
or resistance value being measured. For resistances above the R
0
value
(resistance at 0°C, typically 100Ω) of the RTD, the following equation is
used:
Below R
0
, an additional term is added to the equation:
R=R
0
[1+AT+BT
2
+C (T −100 ) T
3
]
In both of these equations, R
0
is the resistance of the RTD at 0°C, and
A, B, and C are the coefficients as defined by IEC751, through
regression analysis, or by using the Callendar-van Dusen method. By
default, the TC-3 uses the Laboratory standard coefficients, which are
for a 0.003926Ω/ Ω/°C curve (A = 3.9848x10
-3
, B = -0.58700x10
-6
, C =
4.0000x10
-12
, and R
0
= 100).
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