286
TECMount
User’s Manual · Page 13
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:
3
)
ln(
*
)
ln(
*
1
R
C
R
B
A
T
The coefficients for the BetaTHERM 10K3A1 thermistor are:
A = 1.12924x10
-3
B = 2.34108x10
-4
C = 0.87755x10
-7
These are the default coefficients for Arroyo Instruments temperature controllers.
Using the RTD on 150°C Versions
The
286-xx-150
LaserMount
is equipped with a RTD sensor with a 0.00385
Ω
/
Ω
/ °C sensitivity.
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.
As per 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 100
Ω
,
as is the case with the RTD used in the
286-xx-150
) of the RTD, the following
equation is used:
)
1
(
2
0
BT
AT
R
R
Below R
0
, an additional term is added to the equation:
]
)
100
(
1
[
3
2
0
T
T
C
BT
AT
R
R
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.
