Appendix TMT162
52 Endress+Hauser
Calculation of β
At negative temperatures (6) will still give a small deviation. Van Dusen therefore introduced a term
of the fourth order, β , which is only applicable for T < 0 °C. The calculation of β is based on the
disparity between the actual temperature, t
l
, and the temperature that would result from employing
only α and δ (7):
With the introduction of both Callendar's and van Dusen's constant, the resistance value can be
calculated correctly for the entire temperature range, as long as one remembers to set β = 0 for
T > 0 °C (8):
Conversion to A, B and C
Equation (8) is the necessary tool for accurate temperature determination. However, seeing that the
IEC 751 coefficients A, B and C are more widely used, it would be natural to convert to these
coefficients.
Equation (1) can be expanded to (9):
and by simple coefficient comparison with equation (8) the following can be determined (10):
(11)
(12)
The device accepts the coefficients to be specified as α, β, δ and A, B, C.
Information on the coefficients can be requested from the sensor manufacturers in question.
β
T
l
RT
l
R
0
–
R
0
α•
---------------------
δ
T
l
100
-------- -
⎝
⎛
1
)
T
l
100
-------- -
⎝⎠
⎛⎞
–+–
T
l
100
-------- -
1–
⎝⎠
⎛⎞
T
l
100
-------- -
⎝⎠
⎛⎞
3
--------------------------------------------------------------------------------------
=
R
T
R
0
R
0
α
T
δ
T
100
-------- -
1–
⎝⎠
⎛⎞
T
100
-------- -
⎝⎠
⎛⎞
–
β
T
100
-------- -
1–
⎝⎠
⎛⎞
T
100
-------- -
⎝⎠
⎛⎞
3
–+=
R
T
R
0
1
AT BT
2
100
CT
3
–
CT
4
++ +
()
=
A
α
αδ•
100
------------
⎝⎠
⎛⎞
+=
B
αδ•
100
2
------------
=
C
αβ•
100
4
------------
=
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