REPORT. EUROMET project no EUROMET.EM-S18 supplementary comparison of 1Ω and 10 kω resistance standards. P.O.Hetland, T. Sørsdal (JV, pilot 1 Ω)

Transcription

1 REPORT EUROMET project no. 710 EUROMET.EM-S18 supplementary comparson of 1Ω and 10 kω resstance standards P.O.Hetland, T. Sørsdal (JV, plot 1 Ω) G. Eklund, O. Gunnarsson (SP, plot 10 kω), H. D. Jensen (DFM), A. Satrapnsk (MIKES) May 005 Abstract: Ths report presents the result of the supplementary comparson of measurements on 1 Ω and 10 kω resstance standards performed by the natonal nsttutes of Sweden, Norway, Denmark and Fnland. 1

2 Content 1. Introducton Partcpants and schedule Comparson schedule Organsaton of the comparson The travellng standards and measurement nstructons Descrpton of the travellng standards Measurement nstructons Method of measurements Behavour of the travellng standards Measurement results Results of the partcpatng nsttutes Calculaton of the reference value and ts uncertanty Degree of equvalence (DoE) of the partcpatng nsttutes wth respect to the reference value Summary and concluson... 1 References... 1 Appendx A: Method of measurements Appendx B: Uncertanty budgets... 15

3 1. Introducton Many natonal laboratores use the quantum Hall effect as a means to establsh a reference standard of dc resstance. When the lowest possble uncertanty s desrable for the scalng from the Quantum Hall Resstance (QHR) to conventonal resstance standards a cryogenc current comparator (CCC) s often used. The scalng from QHR to a 100 Ω resstance standard s often the frst step n the scalng process. A EUROMET key comparson of Resstance at 100 Ω, EUROMET.EM- K10 began n the sprng of 003 and wll soon be completed. Comparson of the scalng from QHR or 100 Ω to 1 Ω and 10 kω s also very mportant. Such a BIPM comparson was carred out n In May to November 003 the natonal nsttutes of Denmark, Fnland, Norway and Sweden performed a supplementary comparson on 1 Ω and 10 kω resstance standards. Ths comparson allows for a clear and unequvocal comparson of the measurement results and wll show the equvalence of measurng results obtaned wth varous quantzed Hall systems or other measurement systems for resstance n the partcpatng natonal nsttutes.. Partcpants and schedule There were four laboratores partcpatng n ths comparson. The laboratores are lsted n Table 1. Laboratory Country JV Norwegan Metrology Servce Norway DFM Dansh Insttute for Fundamental Metrology Denmark MIKES Centre for Metrology and Accredtaton Fnland SP Swedsh Natonal Testng and Research Insttute Sweden Table 1: Lst of partcpants.1 Comparson schedule Crculaton Tme Schedule Supplementary Comparson EUROMET project 710 ( ) Set A1 & A Insttuton Country Start date Tme for Comment measurement and transportaton SP (start 10 kω) Sweden May weeks 10 kω JV (start 1 Ω) Norway June weeks 10 kω +1 Ω DFM Denmark July weeks 10 kω +1 Ω MIKES Fnland August weeks 10 kω +1 Ω SP (plot 10 kω) Sweden September weeks 10 kω +1 Ω JV (plot 1 Ω) Norway November weeks 1 Ω 3

4 . Organsaton of the comparson For ths supplementary comparson JV was plot laboratory for the 1Ω travellng standards and SP for the 10 kω travellng standard. The comparson was performed n parallel wth the ongong 100 Ω EUROMET key comparson, EUROMET.EM-K10. The 1 Ω and 10 kω travellng standards were crculated together wth two 100 Ω resstors. All travellng standards were transported by car and kept n temperature regulated enclosures. After crculaton the travellng standards were returned to the plot laboratores. Each laboratory had 4 weeks to perform the measurements. 3. The travellng standards and measurement nstructons 3.1 Descrpton of the travellng standards The travellng resstance standards were one 10 kω ESI standard and two CSIRO 1Ω standards. The 10 kω standard had a temperature stablsed enclosure wth nternal temperature measurement usng a Pt 100 thermometer. The 1Ω standards where kept n olbaths at each laboratory but transported n a temperature regulated box. DFM used the temperature regulated box nstead of an olbath. Set A1, 10 kω (SP): Standard Resstor 10 kω ESI, QHR transfer standard wth temperature stablsed enclosure, S/N SP91010 Pt 100 measurement cable Power supply 1V Instructon Manual. Set A, CSIRO 1 Ω (JV): Standard Resstor 1 Ω CSIRO, S/N 64179, Standard Resstor 1 Ω CSIRO, S/N Temperature regulated transport box 3. Measurement nstructons The measurand s the value of the resstance at DC, based on the conventonal value of the von Kltzng constant R K-90 = 5 81,807 Ω. In practce, DC means that the watng tme between the end of a current reversal and the start of data acquston should not be shorter than 8 s for the 10 kω travellng standard and 4 s for the 1 Ω travellng standards. It s up to the partcpants to ether make a guarded measurement where the resstor case s guarded, leave the resstor floatng wth respect to the case, or connect one pont of the resstor to ts case. The soluton adopted should be reported. A short descrpton of the methods used should be ncluded n the fnal report together wth the measurement results. After nstallaton of the travellng standards n ther respectve bath and thermostat n the laboratory, a mnmum settlng tme of two days s requred for the 1Ω travellng 4

5 standards and three days for the 10 kω travellng standard. The measurements should be carred out wth the followng preferred condtons: drect or ndrect (usng a 100 Ω resstor) comparson wth the QHR usng a CCC brdge, amed uncertanty less than (95% confdence level), 50 ma through the 1 Ω resstor, appled measurement voltage 10 kω standard 0.5V 1V (max appled 3 V) ol bath temperature for the 1Ω standards (3,00 ± 0,01) C ambent temperature for the10 kω enclosure (0,0 4,0) C Laboratores not usng the QHR as ther prmary standard of resstance shall measure the resstors wth ther respectve best measurement capablty. For these measurements the source of traceablty has to be ncluded n the measurement report. The travellng standard temperature and ambent pressure should be recorded and reported as well as the heght of ol above the top plate of the resstors n the ol bath. If known, the densty of the ol n the ol bath should be reported. Resstors may have a long thermal tme constant (several hours)! The measurements should be made at dfferent dates durng the perod n the laboratory. The temperature and pressure coeffcents of the travellng standard have been determned to allow for correctons. They are not gven n the protocol. 4. Method of measurements Dfferent measurement set-ups were used n the comparson. One of the laboratores used a conventonal DCC brdge and has traceablty to BIPM through 10 kω resstor standards. The scalng from 10 kω to 1 Ω s acheved prmarly va two Hamon transfer devces. The three remanng laboratores have traceablty to ther own QHR standards. The travellng standards were compared drectly aganst 100 Ω standards usng CCC resstance brdges. The 100 Ω standards were calbrated aganst QHR. The 10 kω travellng standard plot laboratory (SP) measurements was drectly aganst the QHR usng the dc-ccc brdge. Two of these three laboratores use the same type of commercal dc-ccc brdge. These brdges are based upon a Natonal Physcal Laboratory (NPL) desgn [1]. The thrd laboratory uses a self desgned ac-ccc brdge (0.1 Hz to 0.3 Hz) []. Further detals are gven n appendx A. 5. Behavour of the travellng standards The plot laboratores measured the respectve travellng standards before and after the crculaton. From these measurements the drft and stablty of the travellng standards have been evaluated. The estmated drft rate has also been compared wth the hstorcal drft rate of the travellng standards. All three travellng standards had a drft rate as expected from the hstorcal data durng the comparson. The temperature regulaton of the 10 kω standard also showed a very good behavour 5

6 wth small temperature varatons between the measurements at the partcpatng laboratores. 6. Measurement results 6.1 Results of the partcpatng nsttutes Each laboratory has reported a mean value, R lab, the temperature, the mean date, ambent condtons and the measurement uncertanty for each travellng standard. The sngle values from whch the mean values are estmated and complete uncertanty budgets are also reported. The travellng standards have small temperature dependences. The two 1 Ω travellng standards also have a small pressure dependence. These two effects are corrected for n tables -4. The corrected values for all three resstors are shown n fgures 1-3. Due to the small varatons of the temperature of the 10 kω travellng standard enclosure the temperature correctons were for all laboratores below 3 nω/ω for the 10 kω travellng standard. Laboratory Date 1 Ω sn (Ω) Exp. uncertanty (nω) JV , DFM , MIKES , SP , JV , Table : Corrected measurement results for 1Ω travellng standard sn Laboratory Date 1 Ω sn (Ω) Exp. uncertanty (nω) JV , DFM , MIKES , SP , JV , Table 3: Corrected measurement results for 1Ω travellng standard sn Laboratory Date 10 kω sn. SP91010 (Ω) Exp. uncertanty (mω) SP , ,6 JV , ,09 DFM , ,78 MIKES , ,50 SP , ,6 Table 4: Corrected measurement results for 10 kω travellng standard sn.sp

7 Nordc 1 Ω (sn ) EUROMET.EM-S18 supplementary comparson 100 Devaton from nomnal value µω/ω JV (before/after) DFM MIKES SP Ref.value Measurement date Fgure 1: Results for 1Ω travellng standard, sn , wth expanded uncertanty Nordc 1 Ω (sn ) EUROMET.EM-S18 supplementary comparson Devaton from nomnal value µω/ω JV (before/after) DFM MIKES SP Ref.value Measurement date Fgure : Results for 1Ω travellng standard, sn , wth expanded uncertanty 7

8 Nordc 10 kω EUROMET.EM-S18 supplementary comparson 80 Devaton from nomnal value -6.9 µω/ω SP JV DFM MIKES Ref. value Measurement date Fgure 3: Results for 10 kω travellng standard, sn. SP91010, wth expanded uncertanty 6. Calculaton of the reference value and ts uncertanty For a stable reference standard t s possble to estmate the reference value usng the method of least squares. Stablty of the travellng standards was provded by organsaton of careful transportaton and we assume that change of the resstors was small. The reference value can be determned by the weghted mean of the laboratores measurements n that case. The measurements results from the plot laboratores and old drft data ndcate that some drft n the standards has to be ncluded n the evaluaton of the reference values. Our proposal for the determnaton of the reference value s to determne the weghted ft to a straght lne, Y=a+bX, where only parameter a s ftted. The parameter b s calculated from the plot laboratory results. a = w y b w w x where the weght w s c w = u x ) ( wth c=0,5 for the plot laboratory and c=1 for the other laboratores. 8

9 In addton to the weght based on the measurement uncertanty, the plot laboratores are gven a weght of 0,5 because they contrbute wth two measurement results. The calculated reference values are shown as a dashed lne n fgure 1-3. The standard uncertanty of the reference value s determned from u 1 ( x = ) u 1 ( x ) ( ref 1 x N u ) 6.3 Degree of equvalence (DoE) of the partcpatng nsttutes wth respect to the reference value The laboratores degree of equvalence wth respect to the reference value are calculated accordng to the CCEM gudelnes [3]. For nsttute =1,., N the degree of equvalence s gven by d = x x ref wth the expanded uncertanty U ( d ) = u( d ) when u(d ) s gven by u ( d ) = u ( x ) u ( x ref ) Laboratory DoE ± U(DoE) 1Ω sn Ω sn kω sn SP91010 JV 19 ±7 17 ±5 0 ± 3 DFM 35 ±540 4 ± ± 178 MIKES -6 ±9-14 ±7 0 ± 49 SP -19 ±33-3 ±68 5 ± 5 Table 5: Degrees of equvalence (DoE) wth expanded uncertanty for the ndvdual travellng standards. Snce two travellng standards have been used n the 1 Ω measurements, t s normal to report only one combned DoE. The two 1 Ω results for each laboratory can be defned to be R 1, and R,. The measurants we want to compare are the average results from the two 1 Ω measurements. 9

10 R avg, = R 1, + R, wth the uncertanty ( u ( R ) + u ( R )) 1 u( Ravg ) = u ( R0, ) + 1,, 4, R 0, are the type B components wth an uncertanty u(r 0, ) whch represent the system uncertanty common for both 1 Ω measurements. δr 1, and δr, are the type A components for each 1 Ω measurements wth the uncertanty u(δr 1, ) and u(δr, ). Then wth R avg, and u(r avg, ) for each laboratory a reference value and DoE among the laboratores are calculated n the same way as for the ndvdual 1 Ω standards shown above. Laboratory DoE ± U(DoE) 1Ω 10 kω sn SP91010 JV 19 ± 5 0 ± 3 DFM 40 ± ± 178 MIKES -9 ± 8 0 ± 49 SP -0 ± 38 5 ± 5 Table 6: Degrees of equvalence (DoE) wth expanded uncertanty for the 1Ω and 10 kω measurements. 10

11 Degrees of equvalence - 1 Ω Degrees of equvalence (n Ω ) Date JV DFM MIKES SP Degrees of equvalence - 10 kω sn. SP91010 Degrees of equvalence (m Ω ) Date JV DFM MIKES SP Fgure 4: DoE wth respect to the reference value for the 1Ω and 10 kω measurements. 11

12 7. Summary and concluson The comparson ndcates that t s possble to compare resstance standards and estmate systematc effects n measurement equpment wth uncertantes of parts n 10-8 for 1Ω and 10 kω usng conventonal resstance standards and careful transport. Personally transported standards, mantaned at stable temperature, showed very stable behavour. Ths s mportant for the possblty to check for systematc uncertantes n resstance scalng n the range 1Ω - 10 kω wth CCC-brdges of dfferent desgn. The results of the 1 Ω comparson show good agreement among the partcpants. The agreement of the 10 kω comparson s excellent. References [1] J.M. Wllams and A. Hartland, An Automated Cryogenc Current Comparator Resstance Rato Brdge, IEEE Trans. Instrum. Meas., Vol. 40, pp 67-70, [] H. Seppä and A. Satrapnsk, AC Resstance Brdge Based on the Cryogenc Current Comparator, IEEE Trans. Instrum. Meas., Vol. 46, No., pp , 1997 [3] M.G. Cox, The evaluaton of key comparson data, Metrologa, 00, 39,

13 Appendx A: Method of measurements The measurement method of SP The measurements are based on the quantum Hall effect. The QHE cryostat has a varable temperature nsert and QHE samples can be cooled to 1,6 K. The magnet can produce operatng felds to 1 Tesla at 4, K. The Hall sample s mounted on a header of the TO-8 type and the room temperature connectons are gold plated bnd post termnals. The used QHE sample s charactersed wth a constant current source connected to the current termnals. The measurements have been performed followng the techncal gudelnes n Delahaye F 1989 Metrologa The realsed QHE resstance, the QHR, s compared wth room temperature resstance standards wth nomnal values 100 Ω and 10 kω wth a cryogenc current comparator (CCC) or a Josephson potentometer (10 kω measurements). All results reported here are from CCC measurements. The CCC system s manufactured by Oxford Instruments under a technology transfer agreement wth Natonal Physcal Laboratory UK [1]. The CCC measurements are performed n a postve-negatve-postve sequence wth two current reversals. The total number of measurements s the same n postve and negatve polarty. For measurements below the 100 Ω level the CCC measurements have to be made n two steps. In the case of the measurements on the 1 Ω standards reported here, a temperature controlled 100 Ω resstance standard s used as a transfer standard. The measurement method of MIKES The 1 Ω travellng standards were measured wth the MIKES ac Cryogenc Current Comparator (CCC) Resstance Brdge. The 1 Ω resstors were compared drectly wth the two 100 Ω transfer standards, Tr1 and Tr. These 100 Ω resstors were measured n July 003 aganst the MIKES QHR standard. The 1 Ω standards were measured at the frequences 0,1 Hz 0,3 Hz, and wth the currents (rms value) n the 100 Ω: 0,35 ma, 0,5 ma and 0,7 ma, (or equvalent dc currents n 1 Ω 35 ma, 50 ma, and 70 ma). The temperature of the 1 Ohm resstors was measured by temperature meter Hart Scentfc (model 159R), wth the calbrated Pt100 sensors placed nsde the wells of the resstors. The 100 Ω references are n ther own enclosures wth the mantaned temperatures: T Tr1 = 30,73 C, and T Tr = 30,5 C. These temperatures are mantaned permanently wth the nstabltes of 0,003 C and, at these temperatures the temperature coeffcents are close to zero. 13

14 The 10 kω was compared also drectly wth the two 100 Ω transfer standards, Tr1 and Tr wth the MIKES ac Cryogenc Current Comparator (CCC) Resstance Brdge. The applcaton of low frequency currents allows comparng the magnary components of the measured standards. Durng measurements wth the 10 kω a bgger magnary part and a hgher frequency dependence n the real part was notced, compared to other types of 10 kω. Ths ndcates probably addtonal dsspaton n capactve components of that standard. The ncreased frequency dependence and the uncertanty of nterpolaton were the reasons of an addtonal contrbuton to the uncertanty budget of that resstor. The measurement method of JV JV s system s an automatc QHR-system from Oxford Instruments. It conssts of a 16T magnet wth a top loadng 3 He nsert and a Cryogenc Current Comparator (CCC). The CCC-brdge s produced by Oxford Instruments under a technology transfer agreement wth NPL [1]. The CCC brdge s used n the calbraton of the 1 Ω and 10 kω resstors usng a 100 Ω resstor as reference standard. Ths reference standard s calbrated aganst the QHR standard. The measurement method of DFM DFM acheves at present ts traceablty for resstance from BIPM. A set of three ESI SR kω resstors serve as DFM reference standard, and each of these are n turn calbrated by BIPM over a three year perod. Scalng over the range 1 Ω to 10 kω s acheved prmarly va two Hamon transfer devces, Guldlne 9350/1 kω and Guldlne 9350/10 kω. The scalng s ndependently checked va a set of thermalsed resstors n a 1::5 sequence. Workng standards at 10 kω, 100 Ω, etc. are used as check standards. Resstance rato measurements are performed usng a Guldlne 6675A Drect Current Comparator Brdge. The resstors are connected to a Measurement Internatonal 40A Four-Termnal Matrx scanner. The case of the ESI and Hamon transfer resstors s connected to the reference potental va the screen of the potental carryng nterconnectng cable. The screen of the current carryng cable s connected to the reference pont at the scanner sde. A program connect the resstors, set up the measurement parameters of the brdge, start the measurement, and read the resstance rato measured by the brdge. Temperature measurements, Pt 100 sensor readngs, as well as recordng of the envronmental condtons are performed smultaneously. 14

15 Appendx B: Uncertanty budgets The uncertanty budget of MIKES for 1Ω Source Table II Error budget n determnaton of 1 Ω from the 100 Ω by CCC brdge. Input Quantty X Estmate x I Standard Uncertanty of nput u(x ) Probablty Dstrbuton / method of evaluaton (A,B) Senstvty Coeffcent c I (ΔR x / ΔX ) Uncertanty Contrbuton u (R x ) = u(x )* (ΔR x / ΔX ) Degree of Freedom ν I 100 Ohm Reference resstance, Calbraton from QHR, low frequency fluctuaton. Reference resstance, Current dependence, 100 Ω Square / B Infnte Power coeffcent µω/ω / mw Square / B Infnte Rato, compensaton current error I comp / I Square / B Infnte Rato, CCC wndng error, dc -1 Hz N 1 / N, 16: Square / B Infnte Rato, dynamc error, FB gan I 1 / I Square / B Infnte CCC brdge Nose rectfcaton, squd voltage Voltage V Square / B 10-7 / V Infnte bas changes, flux jumps, nonlnearly of null-detector Error due to uncompensated ac Voltage Square / B Infnte currents and leakage currents n voltage lnk Zero offset n brdge Voltage Square / B Infnte Extrapolaton to dc Rato Square / B Infnte Contact resstance n rotary Resstance Normal / A swtch of I comp µω/ω Temperature* 3.0 C C Square / B 0.5 µω/ω / C* Infnte 1 Ohm Resstor Temperature coeffcents (α, β)* 0.5* µω/ω / C Current dependence* Power coeffcent <0.5 µω/ω / C < µω/ω / mw 1 µω/ω/ < Infnte Square / B (µω/ω/ C) Square / B 1 < Infnte Pressure* 1013 hpa 0.1 hpa Square / B < / hpa < Infnte Low frequency fluctuaton** Resstance Square / B Infnte Measurement*** Voltage Normal / A R1 Ω ν eff = 8984 The expanded uncertanty s 36 nω/ω for k=. 15

16 Source The uncertanty budget of MIKES for 10 kω Table II Error budget n determnaton of 10 kω from the 100 Ω by ac CCC brdge. Input Quantty X Estmate x I Standard Uncertanty of nput u(x ) Probablty Dstrbuton / method of evaluaton (A,B) Senstvty Coeffcent c I (ΔR x / ΔX ) Uncertanty Contrbuton u (R x ) = u(x )* (ΔR x / ΔX ) Degree of Freedom ν I 100 Ohm Reference resstance, Calbraton from QHR, low frequency fluctuaton. 100 Ω Square / B Infnte Rato, compensaton current error I comp / I Square / B Infnte Rato, CCC wndng error, dc -1 Hz N 1 / N, 16: Square / B Infnte Rato, dynamc error, FB gan I 1 / I Square / B Infnte CCC brdge Nose rectfcaton, squd Voltage 10 - V Square / B 10-7 / V Infnte voltage bas changes, flux jumps Error due to Voltage Square / B Infnte uncompensated ac currents and leakage currents n voltage lnk Zero offset n brdge Voltage Square / B Infnte Extrapolaton to dc Rato Square / B Infnte 10 kohm Resstor Contact resstance n Resstance Normal / A rotary swtch of I comp µω/ω Temperature coeffcents 30 C C Square / B 0.1 µω/ω / C* Infnte Temperature coeffcents µω/ω 1 µω/ω/ Infnte (α, β)* µω/ω / C / C square / B (µω/ω/ C) Pressure* 1013 hpa 0.1 hpa Square / B < / hpa < Infnte Low frequency Resstance Square / B Infnte fluctuaton** Measurement*** Voltage Normal / A R10 kω ν eff = 8984 The expanded uncertanty s 50 nω/ω for k=. * temperature and pressure coeffcents are not known and the uncertanty are estmated approxmately. ** estmate of possble combned maxmum nfluence. *** Estmate for typcal parameters n one run of measurements: current (rms) n 100 Ω 5 ma, frequency 0.1 Hz, tme of measurement - 0 mn (degree of freedom 180). 16

17 The uncertanty budget of SP for 1 Ω The model for the measurements s: Rx = Rs (1+ δtsd) r ( 1+ δcwr + δclr + δcsr + δrxl ) Where Rx s the unknown 1 Ω resstor. Rs s the 100 Ω QHR transfer resstor. δtsd s the relatve error due to the QHR 100 Ω transfer standard drft. r s the rato Rx/Rs measured by the CCC brdge. δcwr s the relatve error due to the CCC wndng rato devaton from nomnal. δclr s the relatve error due the CCC leakage resstance. δcsr s the relatve error due to the error of the shunt resstor value. δrxl s the relatve error due to the error of the nternal lead resstance of the shunted resstor. The relatve standard uncertanty s gven by : u( Rx) = Rx u( R S) u( r) + RS r + u( δ ) Where u ( r) r s the relatve standard devaton of the mean for the measurement results. Uncertanty budget for R X = 1 Ω travellng standard s/n Quan- Estmate Relatve Probablty Senstvty Relatve Degree tty standard dstrbuton coeffcent uncertanty of X x uncertanty u(x ), (10-9 ) / method of evaluaton (A,B) c contrbuton u (R x ), freedom ν Rs Ω 13.0 Normal/A+B δtsd Normal/B r Normal/A δqpl Rectangular/B δcwr Normal/A δclr Rectangular/B δcsr Normal/B δrxl Normal/B R X Ω The expanded uncertanty s 39 nω/ω for k=.1 17

18 Uncertanty budget for R X = 1 Ω travellng standard s/n Quan- Estmate Relatve Probablty Senstvty Relatve Degree tty standard dstrbuton coeffcent uncertanty of X x uncertanty u(x ), (10-9 ) / method of evaluaton (A,B) c contrbuton u (R x ), freedom ν Rs Ω 13.0 Normal/A+B δtsd Normal/B r Normal/A δqpl Rectangular/B δcwr Normal/A δclr Rectangular/B δcsr Normal/B δrxl Normal/B R X Ω The expanded uncertanty s 7 nω/ω for k=.87 The uncertanty budget of SP for 10 kω The model for the measurements s: Rx = QHR (1+ δqhr + δqpl) r ( 1+ δcwr + δclr + δcsr + δrxl ) Where Rx s the unknown 10 kω resstor. QHR s the realsed quantum Hall resstance at plateau = wth the exact numercal value 1906,4035 Ω. δqhr s the relatve error of the realsed Hall resstance due to mperfect quantzaton and effects of mperfect contacts on the Hall sample. δqpl s the relatve error due to the QHR probe leakage resstance. r s the rato Rx/QHR measured by the CCC brdge. δcwr s the relatve error due to the CCC wndng rato devaton from nomnal. δclr s the relatve error due the CCC leakage resstance. δcsr s the relatve error due to the error of the shunt resstor value. δrxl s the relatve error due to the error of the nternal lead resstance of the shunted resstor. 18

19 The relatve standard uncertanty s gven by : u( Rx) = Rx u( r r) + u( δ ) Where u ( r) r s the relatve standard devaton of the mean for the measurement results. Uncertanty budget for R X = 10 kω travellng standard s/n SP91010 Quantty X Estmate x Relatve standard uncertanty u(x ), (10-9 ) Probablty dstrbuton / method of evaluaton (A,B) Senstvty coeffcent c Relatve uncertanty contrbuton u (R x ), Degree of freedom ν QHR 1906,4035 Ω r Normal/A δqhr Normal/B δqpl Rectangular/B δcwr Normal/A δclr Rectangular/B δcsr 0.0 Normal/B 1.0 δrxl 0 0. Normal/B 1 0. R X Ω The expanded uncertanty s 5 nω/ω for k= 19

20 Uncertanty budget for R X = 10 kω travellng standard s/n SP91010 Quantty X Estmate x Relatve standard uncertanty u(x ), (10-9 ) Probablty dstrbuton / method of evaluaton (A,B) Senstvty coeffcent c Relatve uncertanty contrbuton u (R x ), Degree of freedom ν QHR 1906,4035 Ω r Normal/A δqhr Normal/B δqpl Rectangular/B δcwr Normal/A δclr Rectangular/B δcsr 0.0 Normal/B 1.0 δrxl 0 0. Normal/B 1 0. R X Ω The expanded uncertanty s 6 nω/ω for k= 0

21 Budget of uncertanty of JV for 1 Ω The model for the measurement s: R x = R r s ( wnd leak bal shunt rect p 1+ δ + δ + δ + δ + δ + δ ) The components are: R x : the unknown resstor R s : the 100 Ω reference standard: 100, Ω r : the rato measured by the CCC-brdge δ wnd : the relatve wndng rato error δ leak : the relatve error due to leakage resstance δ bal : the relatve error due to brdge balancng δ shunt : the relatve error due to the stablty and calbraton of the shunt resstor δ rect : the relatve error due to nose rectfcaton δ p : the relatve error due to change n power dsspaton n the 100 reference standard The relatve standard uncertanty s then gven by : u( R R x x ) = u( R Rs s ) u( r + r ) + u ( δ ) Whch gve the followng uncertanty budget for R x : Uncertanty budget for R X = 1 Ω travellng standard s/n Quantty Estmate Relatve Probablty Senstvty Relatve Degree standard dstrbuton coeffcent uncertanty of X x uncertanty / method of u(x ), evaluaton(a,b) c contrbuton u (R x ), freedom R s Ω 3.6 normal r normal δ wnd 0 1 normal 1 1 δ leak 0 1 rectangular 1 1 δ bal 0.0 normal δ shunt normal δ rect 0 1 rectangular 1 1 δ p 0 15 rectangular 1 15 R X Ω The expanded uncertanty s 34 nω/ω for k=. ν 1

22 Budget of uncertanty of JV for 10 kω The model for the measurement s: R x = Rs r ( 1 + δ wnd + δ leak + δ bal + δ shunt + δ rect ) The components are: R x : the unknown resstor R s : the 100 Ω reference standard: Ω r : the rato measured by the CCC-brdge δ wnd : the relatve wndng rato error δ leak : the relatve error due to leakage resstance δ bal : the relatve error due to brdge balancng δ shunt : the relatve error due to the stablty and calbraton of the shunt resstor δ rect : the relatve error due to nose rectfcaton The relatve standard uncertanty s then gven by : u( R R x x ) = u( R Rs s ) u( r + r ) + u ( δ ) Whch gve the followng uncertanty budget for R x : Uncertanty budget for R X = 10 kω travellng standard s/n SP91010 Quantty Estmate Relatve Probablty Senstvty Relatve Degree X x standard dstrbuton uncertanty / method of u(x ), evaluaton(a,b) coeffcent uncertanty of c contrbuton u (R x ), freedom R s Ω 3.6 normal r normal δ wnd 0 1 normal 1 1 δ leak 0 1 rectangular 1 1 δ bal 0.0 normal δ shunt normal δ rect 0 1 rectangular 1 1 R X Ω The expanded uncertanty s 9.0 nω/ω for k=. ν

23 The uncertanty budget of DFM for 1 Ω The model for the measurement s: ε X = ε + δε S SP + δ ( + δrs + δrc ) T X T, S + r δ, where ε X s the relatve devaton from nomnal (RDN) of the unknown resstor, ε S s the RDN of the reference resstor. The δε SP s the seres-parallel transfer error of the Hamon transfer devce. The term δ T,S s the temperature correcton of the reference, r s the rato as measured, δr S s the specfcaton of the current comparator brdge, δr C s the correcton of the brdge error, and δ T,X s the temperature correcton of the unknown resstor. The uncertanty budget becomes: Quantty (unt) Dstrbuton x U(x ) n c u (y) 1 ε s, rel.dev. from nomnal of standard (10-6 ) Normal , ,150 δε SP, Seres-parallel transfer error (10-6 ) Rectangular 0,000 0,058 nfnty 1 0,058 3 δ T,S, Temp devaton standard ±0,1 C (10-6 ) Rectangular 0,000 0,080 nfnty 1 0,080 4 r, Rato devaton as determned (10-6 ) Normal -4,547 0, ,005 5 δr S, Specfcaton for Guldlne brdge (10-6 ) Rectangular 0,000 0,058 nfnty 1 0,058 δr C, Correcton of brdge error (10-6 ) Normal 0,000 0, ,001 y ε X, Rel. dev. From nom. of unknown (10-6 ) Normal -0,9757 0,73 37 The expanded uncertanty s 540 nω/ω for k=. The uncertanty budget of DFM for 10 kω The model for the measurement s: ε X = ε ( r + δrs + δrc ) T, X ref, A + ε ref, B + δε + δt, S + δ ε S where ε X s the relatve devaton from nomnal (RDN) of the unknown resstor, ε S s the RDN of the reference resstor, contanng the value obtaned from BIPM (type-a and type-b components) and the drft snce calbraton. The term δ T,S s the temperature correcton of the reference, r s the rato as measured, δr S s the specfcaton of the current comparator brdge, δr C s the correcton of the brdge error, and δ T,X s the temperature correcton of the unknown resstor. Quantty (unt) Dstrbuton x u(x ) n c u (y) 1 ε s, rel.dev. from nomnal of standard (10-6 ) Normal 0,668 0, ,0151 δ T,S, Temp devaton standard ±0,1 C (10-6 ) Rectangular 0 0,017 nfnty 1 0, r, Rato devaton as determned (10-6 ) Normal -7,778 0, , δr S, Specfcaton for Guldlne brdge (10-6 ) Rectangular 0 0,058 nfnty 1 0, δr C, Correcton of brdge error (10-6 ) Normal 0,141 0, ,010 y ε X, Rel. dev. From nom. of unknown (10-6 ) Normal -6,969 0,089 nfnty The expanded uncertanty s 180 nω/ω for k=. 3

24 It s further estmated that there s a correlaton of the DFM result for resstor SP91010 to the BIPM workng standards of r = 0,17 (estmated from the quoted type-b relatve uncertanty of BIPM of 1, ) 4