Calibration of temperature sensors within Length Standard Section of NMIJ Dr. Akiko Hirai Length Standard Section National Metrology Institute of Japan (NMIJ) 1
Contents Temperature measurement system with PRT and thermometry bridge Comparative calibration of temperature sensors within Length Standard Section Calibration system Calibration procedures Example of calibration result Uncertainty analysis of temperature sensors 2
Temperature measurement by Pt resistance thermometers and precision thermometry bridge Group of SPRTs (100 ) Standard resistor (100 ) Thermometry bridge PRTs (100 ) 3
Temperature measurement by Pt resistance thermometer and resistance thermometry bridge R 1 R 3 R1 R 3 R 2 R 4 R 2 R 4 4
Temperature measurement by Pt resistance thermometer and resistance thermometry bridge R 1 R 3 R R 1 3 R x R s R x R s R R x s R R 1 3 PRT Standard resistor When R x R s 100 1 x 10-4 1 ppm 0.25 mk 5
Traceability of temperature sensor National primary standard, NMIJ Triple point of water Quantum Hall effect resistance standard Accredited calibration laboratory Triple point of water Melting point of Gallium Standard resistor 1 SPRT PRT Thermometry bridge Standard resistor 100 Length standard section, NMIJ 6
Calibration system of temperature sensors within Length Standard Section Calibrate PRT sensors with reference to SPRT Required calibration uncertainty of PRT is several mk Just a few degree of temperature range around 20 is enough Linear approximation of relationship between temperature and resistance is satisfactory 7
History of calibration system of temperature sensors within Length Standard Section Cu blocks for comparative calibration of different types of temperature sensors 8
History of calibration system of temperature sensors within Length Standard Section 1st Generation Dewar flasks (1997~2001) 2nd Generation Thermal insulation box (2002~2005) 3rd Generation Temp. controlled Cu block (2006~Present) 9
Calibration system of temperature sensors, 1G Double Dewar flasks Change temperature by surrounding heating pads and refrigerants Temperature change was too fast Caused temperature gradient Heating pad Double Dewar flasks Refrigerant 10
Calibration system of temperature sensors, 2G Cupper block in double Dewar flasks set in thermal insulation box Change temperature by air conditioner of laboratory Temperature change was slow enough Too slow! (a few weeks in total!) Double Dewar flasks in thermal insulation box 11
Calibration system of temperature sensors, 3G Cu block in Cu chamber Actively control temperature of block by Peltier controller Temperature was set stable at each calibration point SPRT PRT Cu chamber Water Insulator Cu block Cu block in Cu chamber Peltier device 12
Prevention of heat penetration Heat penetration through leads Better to lay leads in Cu chamber 13
Calibration procedures -measurement - Attach SPRT and PRT probes in/on Cu block Set Cu block in temperaturecontrolled Cu chamber Change temperature of Cu block and keep it for a while Repeat at several temperature 14
Calibration procedures - analysis - Get resistance ratios of SPRT and PRT, to standard resistor Convert resistance ratio of SPRT into temperature Find coefficients of linear model between resistance ratio and temperature of PRT by least-square algorithm 15
Example of calibration - stepwise change of temp.- 1.084000 1.083000 SPRT PRT_Ch0 1.082000 1.081000 Use 40 data from each plateau Resistance ratio 1.080000 1.079000 1.078000 1.077000 1.076000 1.075000 1.074000 2009/2/27 12:00:00 2009/2/28 0:00:00 2009/2/28 12:00:00 Date, Time 2009/3/1 0:00:00 2009/3/1 12:00:00 2009/3/2 0:00:00 Profile of resistance ratio of SPRT and PRT throughout calibration 16
Example of calibration - convert into temp. - 21 Around 19.0, 19.5, 20.0, 20.5, 21.0 20.5 Temp. SPRT 20 19.5 19 18.5 2009/2/27 12:00:00 2009/2/28 0:00:00 2009/2/28 12:00:00 2009/3/1 0:00:00 2009/3/1 12:00:00 2009/3/2 0:00:00 Date, Time Temperature change of SPRT 17
Example of calibration - resistance ratio vs. temp. - 21.0 20.5 Temp. SPRT 20.0 19.5 T ar b 19.0 18.5 1.074000 1.076000 1.078000 1.080000 1.082000 1.084000 Resistance ratio of PRT_Ch0 Relationship between resistance ratio and temperature 18
Example of calibration -residual error - 0.4 0.3 0.2 Residual error [mk] 0.1 0-0.1-0.2-0.3-0.4 18.5 19 19.5 20 20.5 21 Temperature [K] Residual error after linear approximation 19
Uncertainty factors in calibration of PRT Reference SPRT Calibration at TPW Calibration at melting point of Ga Interpolation by ITS-90 Self heating Standard resistor Calibration Temperature dependency Thermometry bridge Repeatability Complement Linearity Calibration procedure Residual error of linear approximation Repeatability Temperature uniformity of Cu block 20
Evaluation of each uncertainty factor Reference SPRT Calibration at TPW 0.5 mk Provided in calibration certificate Calibration at melting point of Ga 1.0 mk Provided in calibration certificate Interpolation by ITS-90 1.0 mk Estimate propagation from TPW and MP of Ga Self heating 0.25 mk Evaluate by changing measurement current 21
Evaluation of each uncertainty factor (Cont'd) Standard resistor Calibration 5.5 x 10-6 0.01 mk Calculate from calibration certificate Temperature dependency 0.6 x 2 ppm/ =1.2 ppm 0.3 mk Calculate from specification 22
Evaluation of each uncertainty factor (Cont'd) Thermometry bridge Error sources: ADC, amplifier, switches, and stray conductance in the electronic circuits Repeatability 1.5 ppm 0.4 mk Evaluate by repeating reconnection of standard resistors Complement 5.5 ppm / 3 0.8 mk Evaluate by exchanging Rs and Rx Linearity 6 ppm / 3 0.9 mk Evaluate from check data by manufacturer 23
Evaluation of complement of thermometry bridge R 1 R 3 R A Standard resistor A R B Standard resistor B 24
Evaluation of complement of thermometry bridge (Cont'd) Assume complement error of the bridge as. RA r and RB R RA r Therefore, RB RB 1 1 r RA RA r 2 2 B 1 1 2 25
Evaluation of complement of thermometry bridge (Cont'd) Standard resistor I: 100.000739 Standard resistor II: 99.99948 Standard resistor III: 99.99984 Resistance ratio A B I II III I 0.999980 0.999985 II 1.000010 1.000001 III 1.000005 0.999990 26
Evaluation of complement of thermometry bridge (Cont'd) Combination (II / I) x (I / II) - 1 Complement error Average Standard deviation of 10 measurements -1.1 x 10-5 1.6 x 10-6 (III / I) x (I / III) - 1 (II / III) x (III / II) - 1-1.0 x 10-5 -9.2 x 10-6 1.3 x 10-6 1.9 x 10-6 5 6 1.1 10 / 2 5.5 10 5.5 ppm / = 3.2 ppm 3 Corresponds to 0.8 mk 27
Another uncertainty factor of thermometry bridge The error associated with the digits of binary and decimal divider stages in bridge. 1st digit, 0~9 R 1 2nd digit, 0~9 3rd digit, 0~9 Variation in contact resistance 'Sawtooth' shaped error 28
'Sawtooth' error of thermometry bridge Measured resistance ratio 1.081 1.080 1.079 Error from difference of contact resistances between '7' and '8' r Actual Ideal 19.6 19.8 20.0 20.2 Temperature [ ] 29
Measured resistance ratio of SPRT 1.081 1.080 1.079 'Sawtooth' error of thermometry bridge (Cont'd) Ideal One is over 1.08, the other is under 1.08 Actual r r r 1.079 1.080 1.081 Measured resistance ratio of PRT Both are in the same range 30
Resistance ratio 'Sawtooth' error of thermometry bridge (Cont'd) Discontinuous change occurs when the ratio acrosses 1.08 1.09 1.088 1.086 1.084 1.082 SPRT PRT_Ch0 Residual error 4.0 2.0 0.0-2.0-4.0 Residual error [mk] 1.08-6.0 1.078 2005/8/2 22:00 2005/8/3 4:00 2005/8/3 10:00 2005/8/3 16:00 Date, Time 2005/8/3 22:00-8.0 2005/8/4 4:00 2005/8/4 10:00 Residual error of linear approximation obtained from mixed data with different digits. 31
Evaluation of each uncertainty factor (Cont'd) Calibration procedure Residual error of linear approximation 0.2 mk Evaluate by data Repeatability Temperature uniformity of Cu block 0.3 mk Evaluate by repeating measurement while changing PRT position Set control limit of uncertainty of calibration procedure as 1.5 mk in standard deviation. 32
Uncertainty budget Category Factor u(xi) ci ui SPRT TPW 0.5 mk 1 0.5 mk Melting point of Ga 1.0 mk 1 1.0 mk ITS-90 1.0 mk 1 1.0 mk Self heating 0.25 mk 1 0.25 mk Standard resistor Calibration 5.5 x 10-6 2.5 K/ 0.01 mk Temperature dependence 0.6 0.5 mk / 0.3 mk Bridge Repeatability 1.5 ppm 0.25 mk / ppm 0.4 mk Complement 5.5 ppm / 3 0.25 mk / ppm 0.8 mk Linearity 6 ppm / 3 0.25 mk / ppm 0.9 mk Calibration Residual error 1.5 mk 1 1.5 mk Repeatability Uniformity Combined standard uncertainty 2.5 mk 33
Other uncertainty factors when using PRT Secular change of PRT Self heating of PRT Contact to the artefact Temperature distribution Temporal change of temperature 34
Conclusion Calibration system and procedures of temperature sensors within Length Standards Section are introduced. Just a few degree of temperature range around 20 is enough Linear model is enough Uniformity and slow change of temperature of Cu block are the most important Uncertainty analysis Evaluate uncertainty of thermometry bridge 35
References Evaluation of thermometry bridge R. Walker, "Automatic linearity calibration in a resistance thermometry b ridge," Int. J. Thermophys. 32, 215 (2011). D.R. White, "A method for calibrating resistance thermometry bridges," Success in the 21st century depends on modern metrology, 1-2, 471 (1997). 36
Thank you for your kind attention. 37