Transcript M105 Liedberg - PRT ohm to temp

Platinum resistance
thermometers: converting
ohms to degrees Celsius
Hans LIEDBERG
© NMISA 2010
Overview
If converting resistance to temperature by hand, remember:
• PRTs are not all that linear.
If using a readout that calculates temperature for you,
remember:
• PRTs come in different sensitivities.
© NMISA 2010
Resistance-temperature relationship of a
PRT
PRTs are commonly characterised using two numbers,
• the resistance at the ice point (R(0 °C) = 100 Ω for all
PRTs discussed in this paper)
and
R(100C )  R(0C )
• the alpha value  
R(0C )  (100C  0C )
(alpha ranges from (0.00385 to 0.00393) Ω/Ω/°C for
platinum of increasing purity).
For example, “Pt100(385)” is used to describe a 100 Ω PRT
with alpha = 0.00385 Ω/Ω/°C.
© NMISA 2010
Resistance-temperature relationship of a
PRT (cntd)
Non-linearity:
Resistance of a Pt100 (385) sensor
•PRTs decrease in
260
240
sensitivity with
a Pt100(385) from
Resistance (Ω)
increasing temperature,
220
200
180
160
140
120
0.397Ω/°C at -50°C to
100
80
0.385Ω/°C at 50°C and
-50
0
50
100
150
200
250
300
350
Temperature (°C)
Straight line (0.385 Ω/°C)
0.345Ω/°C at 400°C.
© NMISA 2010
Real Pt100(385)
400
Resistance-temperature relationship of a
PRT (cntd)
Sensitivity of a Pt100 (385) sensor
Sensitivity (Ω/°C)
0.405
0.385
0.365
0.345
-50
0
50
100
150
200
250
300
350
400
Temperature (°C)
IEC751
Real Pt100(385)
Decreasing sensitivity of a PRT with increasing temperature.
© NMISA 2010
Resistance-temperature relationship of a
PRT (cntd)
Different sensitivities:
Sensitivities of PRTs of different purity
•The higher the purity
0.405
higher the alpha
value of the PRT.
Sensitivity (Ω/°C)
of the platinum, the
0.385
0.365
0.345
-50
0
50
100
150
200
250
300
350
Temperature (°C)
IEC751
© NMISA 2010
JEMIMA (3916)
SAMA RC4:1966 (3923)
400
Errors arising from non-linearity
Calibration data for a Pt100(385) sensor:
Actual
temperature (°C)
-49.598
0.000
50.126
100.057
150.047
200.113
251.347
298.288
350.634
401.971
Resistance
of UUT (Ω)
80.4480
100.0000
119.4563
138.5448
157.3647
175.9228
194.6156
211.4796
229.9924
247.8461
To calculate temperature from measured resistance, the
first reaction is to interpolate linearly between these data
pairs.
© NMISA 2010
Errors arising from non-linearity (cntd)
Linear interpolation results in errors proportional to ΔT2:
Various R(T) models minus actual resistance of a Pt100
(385) sensor
0.05
0
Error (°C)
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
-0.4
-0.45
-50
0
50
100
150
200
250
300
350
400
Temperature (°C)
IEC751
Fitted CvD
Linear interpol (50°C interval)
Linear interpol (100°C interval)
© NMISA 2010
Solutions to the non-linearity problem
1. Use a reference function that models the decreasing
sensitivity of PRTs with increasing temperature well (e.g., ITS-
90 or IEC 751).
• The deviations of a real PRT from such a reference
function should be fairly linear.
OR
2. Fit a 2nd order polynomial to the data (e.g., using Excel’s
“Add trendline” function).
© NMISA 2010
Errors arising from different sensitivities
Calibration data for a Pt100(385) sensor:
Actual
temperature (°C)
-49.598
0.000
50.126
100.057
150.047
200.113
251.347
298.288
350.634
401.971
Indicated
temperature of UUT (°C)
-49.643
0.000
50.154
100.104
150.106
200.182
251.430
298.395
350.789
402.189
Correction
(°C)
0.045
0.000
-0.028
-0.047
-0.059
-0.069
-0.083
-0.106
-0.155
-0.217
These data were measured with the readout using IEC 751
(which describes “385” PRTs) to calculate temperature.
© NMISA 2010
Errors arising from different sensitivities
(cntd)
If the readout is mistakenly set to “‘Pt100(3916)” or
“Pt100(3923)” during use, large errors will result:
Differences of some standards from IEC751 am2:1995
8
Error (°C)
6
4
2
0
-2
-50
0
50
100
150
200
250
300
350
Temperature (°C)
JEMIMA (3916)
© NMISA
SAMA RC4:1966
(3923)2010
IEC751:1983
400
Verifying the readout sensitivity setting
•Checking the PRT + readout system at the ice point only
verifies that R(0°C) or R(0.01°C) is correct.
•To verify A, B and C coefficients, check the system at a
temperature away from 0°C, using
• a simple fixed point (e.g., boiling point of water or
sublimation point of carbon dioxide)
or
• a PRT + readout system for which the correct resistanceto-temperature conversion method is not in doubt.
© NMISA 2010
Conclusions
PRTs capable of ±0.01°C accuracy are readily available. To
achieve this, take care to
• use an appropriate method to interpolate between
resistance-temperature data pairs
or
• set your readout to the same function as was used
during calibration.
Cal lab and client should agree on the method of resistancetemperature conversion during contract review.
© NMISA 2010