IB IL TEMP 4/8 RTD ...
7079_en_05 PHOENIX CONTACT 24
19.2 Systematic errors during temperature measurement using 2-wire technology
Figure 8 Systematic temperature measuring error ΔT
depending on the cable length l
Curves depending on cable cross section A
(Measuring error valid for: copper cable χ = 57 m/Ωmm
2
,
T
A=
25°C and Pt 100 sensor)
Figure 9 Systematic temperature measuring error ΔT
depending on the cable cross section A
(Measuring error valid for: copper cable χ = 57 m/Ωmm
2
,
T
A=
25°C, l = 5 m,and Pt 100 sensor)
Figure 10 Systematic temperature measuring error ΔT
depending on the cable temperature T
A
(Measuring error valid for: copper cable χ = 57 m/Ωmm
2
,
l=5m, A=0.25mm
2
, and Pt 100 sensor)
All diagrams show that the increase in cable resistance
causes the measuring error.
A considerable improvement is made through the use of Pt
1000 sensors. Due to the 10 times higher temperature coef-
ficient α (α =0.385 Ω/K for Pt100 to a = 3.85 Ω/K for Pt1000)
the effect of the cable resistance on the measurement is de-
creased by a factor of 10. All errors in the diagrams above
would be reduced by factor 10.
Figure 8 clearly shows the effect of the cable length on the
cable resistance and therefore on the measuring error. The
solution is to use the shortest possible sensor cables.
Figure 9 shows the influence of the cable cross-section on
the cable resistance. It can be seen that cables with a cross
section of less than 0.5 mm
2
cause errors to increase expo-
nentially.
Figure 10 shows the influence of the ambient temperature
on the cable resistance. This parameter is of minor impor-
tance and can hardly be influenced. It is mentioned here
only for the sake of completeness.
The formula for calculating the cable resistance is as fol-
lows:
Where:
Since there are two cable resistances in the measuring sys-
tem (forward and return), the value must be doubled.
The absolute measuring error in Kelvin [K] is provided for
platinum sensors according to DIN using the average tem-
perature coefficient α (α =0.385Ω/K for Pt100; α =3.85Ω/
K for Pt1000).
(1) Temperature measuring error for A = 0.14 mm
2
(2) Temperature measuring error for A = 0.25 mm
2
(3) Temperature measuring error for A = 0.50 mm
2
0 . 0
3 . 0
6 . 0
9 . 0
1 2 . 0
1 5 . 0
0 . 0 2 . 5 5 . 0 7 . 5 1 0 . 0 1 2 . 5 1 5 . 0 1 7 . 5 2 0 . 0
K
l
m
5 7 5 5 1 0 1 4
( 1 )
( 2 )
( 3 )
,
T
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1.0
K
A
mm²
70790015
DT
K
T
A
°C
0.0
0.5
1.0
1.5
2.0
2.5
-30 -20 -10
0
+10 +20 +30 +40 +50 +60
57550016
T
R
L
Cable resistance in Ω
R
L20
Cable resistance at 20°C in Ω
l Cable length in m
χ Specific electrical conductivity of copper in
Ωmm
2
/m
A Cable cross section in mm
2
0.0039 1/K Temperature coefficient for copper
(degree of purity of 99.9%)
T
A
Ambient temperature (cable temperature)
in °C
R =
L
1
K
x ( 1 + 0.0039 x (T )
A
- 20°C)
R = R x ( 1 + 0.0039 x (T
L L20 A
- 20°C))
l
c x A
1
K
