Appendix; The Callendar - Van Dusen Method - Endress+Hauser iTEMP HART TMT162 Bedienungsanleitung

Appendix

102
11 Appendix
11.1

The Callendar - van Dusen Method

It is a method to match sensor and transmitter to improve the accuracy of the measurement
system. According to IEC 60751, the non-linearity of the platinum thermometer can be
expressed as (1):
R
T
in which C is only applicable when T < 0 °C.
The coefficients A, B, and C for a standard sensor are stated in IEC 60751. If a standard
sensor is not available or if a greater accuracy is required than can be obtained from the
coefficients in the standard, the coefficients can be measured individually for each sensor.
This can be done e.g. by determining the resistance value at a number of known
temperatures and then determining the coefficients A, B, and C by regression analysis.
However, an alternative method for determination of these coefficients exists. This method
is based on the measuring of 4 known temperatures:
• Measure R at T = 0 °C (the freezing point of water)
0 0
• Measure R at T = 100 °C (the boiling point of water)
100 100
• Measure R at T = a high temperature (e.g. the freezing point of zink, 419.53 °C)
h h
• Measure R at T = a low temperature (e.g. the boiling point of oxygen, -182.96 °C)
l l
Calculation of 
First the linear parameter  is determined as the normalized slope between 0 and 100 °C (2):
If this rough approximation is enough, the resistance at other temperatures can be
calculated as (3):
and the temperature as a function of the resistance value as (4):
Calculation of 
Callendar has established a better approximation by introducing a term of the second order,
 , into the function. The calculation of  is based on the disparity between the actual
temperature, T , and the temperature calculated in (4) (5):
h
With the introduction of  into the equation, the resistance value for positive temperatures
can be calculated with great accuracy (6):
R
T
Calculation of 
At negative temperatures (6) will still give a small deviation. Van Dusen therefore
introduced a term of the fourth order,  , which is only applicable for T < 0 °C. The calculation
2
= R [ 1 AT BT + + +
0
R –
-------------------- - 100
a =
100 R ·
R = R + R
T 0
0
R – R
------------------- -
T =
T
R ·
0
RT
h
---------------------- -
T –
h
R
------------------------------------- - 0
d =
T ö T
æ æ
-------- - 1 h
–
è ø è
100
æ
-------- - 1
= R + R a T ( + – d
0
0 è
100
3
C T 100 ( – )T ]
R
0
0
a T ·
0
a
– R
0
· a
ö
h
-------- -
ø
100
T
T
ö æ ö ö
-------- -
–
ø è ø ø
100
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