Main Results of GULFMET . EMS 4 Supplementary Comparison of Inductance for 10 and 100 mH at 1 kHz

A Supplementary Comparison of Regional Metrology Organizations (RMOs) is a comparison, usually carried out by an RMO to meet specific metrological needs not covered by Key Comparison of Consultative Committee of the International Committee for Weights and Measures (CIPM) or RMOs. The outcomes of the CIPM Mutual Recognition Arrangement (MRA) are the internationally recognized Calibration and Measurement Capabilities (CMCs) of the participants of comparisons and CMCs of National Metrology Institutes published in Key Comparison Database (KCDB) of the International Bureau for Weights and Measures (BIPM). Main results of the participating laboratories which have been measuring the same inductance travelling standard for 10 and 100 mH at 1 kHz in a framework of GULFMET.EM-S4 Supplementary Comparison of Inductance are presented. The paper describes the evaluation of drift effect of the travelling standard and Reference Value of a Supplement Comparison. Degrees of Equivalence and Expanded Uncertainties of NMI participants are determined. En number was calculated for each NMI participating in GULFMET.EM-S4 comparison with the aim of determining data consistency. Linked results of COOMET.EM-S14 and GULFMET.EM-S4 supplementary comparisons for inductance were presented. Obtained results of both comparisons have good data consistency for all NMI participants.


Introduction
Key comparisons (KC) are the special comparisons for National Metrology Institutes (NMIs) in a frame of Consultative Committee (CC) and Regional Metrology Organizations (RMOs) around the world, which are carried out within the framework of the International Committee for Weights and Measures (CIPM) of Mutual Recognition Arrangement (MRA) [1,2]. The main purpose of KC is the determination of the equivalence between laboratories of different NMIs. A supplementary comparison (SC) of RMO is a comparison, usually carried out by a RMO to meet specific metrological needs not covered by KC of CC or RMOs.
The CIPM MRA describes in general how the data of KC should be evaluated but it does not provide enough specifics to define an unambiguous analysis. Consequently, many different ways of evaluating KC data have been suggested over the years [3][4][5]. The degree of equivalence (DoE) of a laboratory is obtained as the deviation of its measurement result from the KC reference value (RV), together with the uncertainty associated with this deviation according to the CIPM MRA [6].
RMOs have procedures for carry out of comparisons, but only the Euro-Asian Cooperation of National Metrological Institutions (CООМЕТ) has guidelines on KC and SC data evaluation [7,8]. The outcomes of the CIPM MRA are the internationally recognized Calibration and Measurement Capabilities (CMCs) of the participants of comparisons and CMCs of NMIs published in Key Comparison Database (KCDB) of the International Bureau for Weights and Measures (BIPM) [9,10].

Brief review of carried out comparisons of inductance
The Consultative Committee for Electricity and Magnetism (CCEM) of CIPM was a sponsor of international comparisons of the national measurement standards of electromagnetic quantities between laboratories of different NMIs in the CIPM-MRA framework. From 1989 to 1999, CCEM-K3 KC [11] for inductance of 10 mH at 1 kHz was carried out. 11 NMIs that are the members of four RMOs: EURAMET, APMP, COOMET and SIM, participated in this KC. The PTB was the pilot laboratory of this KC.  [15] SC for inductance 100 mH at 1 kHz was carried out. 7 NMIs participated in this SC and SENAM (Mexico) was the pilot laboratory. SE "UKRMETRTESTSTAN-DART" (UMTS, Ukraine) took part as the participant in EURAMET.EM-S26 SC with the aim of publishing CMCs for inductance in the KCDB of the BIPM.
From 2013 to 2014, the COOMET.EM-S14 [16] SC for inductance 10 and 100 mH at 1 kHz was carried out in the CIPM-MRA framework. The SC was carried out between 4 NMIs which are the members of two RMOs: COOMET and GULFMET. The UMTS (Ukraine) was the pilot laboratory of this SC.
The procedure was proposed for linking results of EURAMET.EM-S20, EURAMET.EM-S26 and COOMET.EM-S14 SCs to those NMIs which have also taken part in those comparisons [17].

Participants of supplementary comparison of inductance
The GULFMET.EM-S4 [18] SC for inductance 10 and 100 mH at 1 kHz was carried out in the CIPM-MRA framework from June to October 2018. The SC was carried out between 3 NMIs which are the members of two RMOs: COOMET and GULFMET.
The travelling standards (TSs) were compared at UMTS (Ukraine), QCC EMI (United Arab Emirates), and SASO-NMCC (Saudi Arabia). UMTS was a pilot laboratory responsible for providing the TSs, coordinating the schedule, collecting and analysing the comparison data, preparing the draft report, etc.

General review of travelling standards
The UMTS as pilot laboratory has performed repeated measurements on the TSs of types Р5109 10 mH and P5113 100 mH during the course of this comparison as well as COOMET.EM-S14 comparison [16]. TSs of inductance are shown on Fig. 1. Thermostatically regulated standards of inductance of types P5109 and P5113 allow the monitoring of critical parameters: the temperature difference of values within each standard thermostat and internal supply voltage. The standards contain inbuilt precision thermostat with dual temperature sensors, which provides increased reliability and accuracy of the measurement results.

Behaviour of the travelling standard
Connection of TSs in accordance with connection schemes for 2-and 3-terminal is shown on Fig. 2. From these measurements, the behaviour of the TSs can be seen in Fig. 3-6.
As the values of the inductance are time-dependent they were measured before and after each visit so that a drift curve for each one could be established. The drift of the TSs by using all results weighted with the variance of the measurements was checked. The drift was neglected.

The reference values of comparison
The RV x ref calculated as the mean of participant results with GULFМЕТ.EM-S4 data are given by [3][4][5] x The UMTS as pilot laboratory has provided the traceability to the SI of the national measurement standards. All of the participating NMIs made measurements at the same measurement points for 10 and 100 mH at 1 kHz.

Degrees of equivalence of participants
Only one value is reported for each of NMI participants. Degrees of equivalence of the NMI participants are reported with respect to the measu-rement for 10 and 100 mH at 1 kHz for 2-and 3-terminals.
The degrees of equivalence of the i-th NMI and its expanded uncertainties with respect to the comparison reference value are estimated as [8] D The declared uncertainties are judged as confirmed if the following equation is satisfied The Degrees of Equivalence (DoE) of the NMI participants and their expanded uncertainties (k = 2) with respect to the KCRV for 10 and 100 mH at 1 kHz for 2-and 3-terminal are also presented in Table 1 and the graphs in Fig. 7-10.

Results of participants of comparison
The maximum E n number and declared uncertainties for degrees of equivalence of all NMIs for 10 and 100 mH ( Table 2)
DoE of GULFMET.EM-S4 SC needs to be corrected by a value d [17], which is determined from the results of the participant linking NMI: where: D UMTS-S14 is the DoE of linking NMI (UMTS) in COOMET.EM-S14 SC; D UMTS-S4 is the DoE of linking NMI in GULFMET.EM-S4 SC and standard uncertainty of corrected factor: where: u D UMTS-S14 is standard uncertainty of linking NMI in COOMET.EM-S14 SC; u D UMTS-S4 is standard uncertainty of linking NMI in GULFMET. EM-S4 SC. The corrected DoE for i-th NMI participants [17] in GULFMET.EM-S4 SC in terms of COOMET.EM-S14 SC RV are then is given by: and corrected standard uncertainty of DoE: where: D S4i is the DoE of i-th NMI in GULFMET. EM-S4 SC; u D ( ).

S4i
The results from NMIs in COOMET.EM-S14 and GULFMET.EM-S4 SCs for 100 mH in terms of RV S14 are shown in Table 3 and Fig. 11. The sign "*" in Table 3 and Fig. 11 indicates those NMIs that participated in both comparisons and have two different results.  In Fig. 1 red dashed lines indicate the boundaries of the minimum expanded uncertainty of the linking laboratory.

Conclusion
A SC of inductance for 10 and 100 mH at 1 kHz has been carried out between participating GULFMET and COOMET member laboratories. In general, there is good agreement between participating laboratories for this quantity at a nominal value of 10 mH and acceptable agreement at a nominal value of 100 mH. It is expected that this comparison will be able to provide support for participants' entries in Appendix C of the CIPM MRA.
The calculated values of drift effect for GULFMET. EM-S4 TS were linear and small for all measurement points, so it was neglected. Also the RV of SC and its expanded uncertainties were calculated. The RV of SC lies in the range from 0.448 mH/H (2-terminal) to 0.435 mH/H (3-terminal) for 10 mH with expanded uncertainty 0.020 mH/H, and from 0.977 mH/H (2-terminal) to 0.833 mH/H (3-terminal) for 100 mH with expanded uncertainty 0.020 mH/H. DoE and its expanded uncertainties of NMI participants were calculated. The E n numbers lies in the range from 0.07 to 0.99 for all NMI participants that satisfies the condition of performance E n ≤ 1.0 and characterizes good data consistency.
Linked results of COOMET.EM-S14 and GULFMET.EM-S4 SCs for inductance were presented. Obtained results for all NMI participants of both comparisons have good data consistency.