Technical assessment of novel digital impedance bridges

Project Description

Technical assessment of novel digital impedance bridges able to calibrate a capacitance standard against a resistance standard in the frequency range around 1 kHz with an uncertainty lower than few parts in 10^-7. 
A travelling bridge from INRIM will be moved to the other partner sites; the comparison will be performed by verifying the compatibility of the calibration outcomes of the travelling bridge and the onsite bridge.

Final Report 2024-10-18

The results of the comparison between INRIM-POLITO’s fully-digital impedance bridge (FDIB) [1] and the PTB’s dual Josephson impedance bridge (DJIB) [2] performed at PTB in 2021 were published in 2022 as a journal paper [3] together with the upgraded version of the bridges according to the bridges’ assessment. 

In 2023 CMI joined the project and in the second half of the year a second round of comparisons took place in Bern, where the INRIM-POLITO FDIB (from October to December) and the CMI FDIB [4] (mid October) were moved to and compared with the METAS DJIB [5]. The target uncertainties of the bridges are at the 10^−8 to 10^−7 (FDIB) and 10^−9 to 10^−8 (DJIB) level.

The comparisons of the bridges were performed at 1 : 1 ratio magnitude for R : R and R : C standards with nominal magnitudes of 12.9 kΩ, and for QHR : R with a quantum Hall resistance (QHR) standard, in measurement conditions proper of the primary realisation of the impedance units from the AC QHR or from a quadrifilar resistance standard in turn calibrated against the DCQHR.
The results were fully compatible at the expected level of uncertainty for what concerns the magnitude ratio, but phase measurements with R : C standards showed some incompatibilities.

The employed standards are a temperature-controlled 10 nF capacitance standard developed by GUM and SUT, two 12.9 kΩ quadrifilar calculable resistance standards, temperature-controlled 8nF capacitance standard developed by INRIM and a graphene AC QHR standard developed by PTB operated in a liquid helium cryostat at 4.2 K in a magnetic field between 8 T and 10 T.

The results for the R : C comparison at a frequency of such that 2πf RC ≈ 1 were presented in the 2024 Conference on Precision Electromagnetic Measurements (CPEM) in Denver (CO), US, and published in the proceedings of the conference [6].
In the measurements, there were employed a temperature-controlled 10 nF capacitance standard developed by GUM and SUT and a 12.9 kΩ quadrifilar calculable resistance standard, and the working frequency is 1233.147 Hz. This frequency is of practical interest, being close to the ones typically adopted for the representation of the farad and in international comparisons. The calibration of a 10 nF capacitance standard against a 12.9 kΩ calculable resistance standard at 1233 Hz is a measurement condition suitable for the primary direct realisation of the impedance units ohm and farad from AC quantum Hall resistance standards or from AC/DC calculable transfer resistance standards calibrated against DC quantum Hall resistance standards. Fig.2 of [6] shows the relative deviation from the nominal ratio 1 : 1 of the magnitude of the measured impedance ratio obtained with the three bridges in the campaign, with their combined standard uncertainties.
Most measurements are compatible within the standard uncertainty and all are compatible within an expanded uncertainty with a coverage factor of 2. 

The full results for the R : R, R : C and QHR : R comparisons, both in magnitude and phase, have been submitted as a journal paper [7], where some technical difficulties that arose during the comparisons are also discussed. The main additional results are herewith briefly summarised.

• Although the results for the R : C ratio measurements of the 10 nF capacitance standard and the 12.9 kΩ calculable resistance standard were compatible for all INRIM-POLITO FDIB, CMI FDIB and METAS DJIB, there was an incompatibility between the measurements of the phase. The discrepancies of the results of the INRIM-POLITO FDIB and CMI FDIB from those of the METAS DJIB were then reduced by changing the FDIB configuration, but further investigations on these effects will be performed in the future.
   
• The results for the R : R ratio measurements with the 12.9 kΩ calculable resistance standards at 1233.147 Hz show that the magnitude ratio results are compatible for both CMI FDIB and INRIM-POLITO FDIB from those of the METAS DJIB within the expanded uncertainties with coverage factor k = 2. At 5000 Hz, the magnitude ratio results are compatible for CMI FDIB and METAS DJIB within the expanded uncertainties with coverage factor k = 2. Also in this case, the phase measurements for the INRIM-POLITO FDIB deviate significantly from the other measurements at the beginning, but after the change in the bridge configuration there is full compatibility also on the phase measurements (also at 5000 Hz).
   
• The results for the C : R ratio measurements of the 8 nF capacitance standard and the 12.9 kΩ calculable resistance standard at 1541.434 Hz performed with both the INRIM-POLITO FDIB and the METAS DJIB became compatible after solving an initial issue due to the shorter cables used to connect the standards to the METAS DJIB compared to those employed with the INRIM-POLITO FDIB, and thus to the thermal transient in the capacitance standard due to the change in the thermal load toward the ambient, changing the capacitance during the measurement. This problem was solved employing the same long cables with both bridges so that the capacitance value remained stable.
   
• The results for the QHR : R ratio measurements performed at 1233.147 Hz with only the INRIM-POLITO FDIB and the METAS DJIB. The magnitude ratio results are compatible, whereas the phase results are incompatible. Later measurements with the QHR standard revealed a malfunction of the INRIM-POLITO FDIB when connected to the QHR network due to an interaction with the active current equalizers employed at METAS, likely caused by an unwanted ground loop current that shifted the balance of the bridge, and which unfortunately couldn’t be eliminated during the time of the comparison. For this reason, these results should be considered with caution.
   

In conclusion, the results of the FDIB and DJIB assessments performed in the framework of the project EURAMET TC-EM 1501 confirm the significance of onsite comparisons as invaluable tools to validate and improve measuring systems, highlighting issues that could go undetected otherwise, and validate the DJIBs and FDIBs with state-of-the-art accuracy in the kilohertz frequency range and their employment in the realisation of the unit of capacitance directly from a calculable resistance standard or, with more technical difficulties, from the ACQHR. 

With the employed techniques it is also possible to consider as quantities of interest not only the primary parameters of the compared impedances (resistance, capacitance or inductance), but also the secondary parameters (time constant, dissipation factor or series resistance), which are related to the impedance phase angle. Furthermore, as highlighted in the comparison, the phase angle measurements need to be considered for a complete characterisation of the impedance measuring systems.

[1] M. Marzano, M. Ortolano, V. D’Elia, A. Müller, and L. Callegaro, “A fully digital bridge towards the realization of the farad from the quantum Hall effect,” Metrologia, vol. 58, p. 015002, 2020.

[2] Y. Pimsut, S. Bauer, M. Kraus, R. Behr, M. Kruskopf, O. Kieler and L. Palafox, “Development and implementation of an automated four-terminal-pair Josephson impedance bridge,” Metrologia, vol. 61, p. 025007, 2024.

[3] M. Marzano, Y. Pimsut, M. Kruskopf, Y. Yin, M. Kraus, V. D’Elia, L. Callegaro, M. Ortolano, S. Bauer, and R. Behr, “PTB-INRIM comparison of novel digital impedance bridges with graphene impedance quantum standards,” Metrologia, vol. 59, p. 065001, 2022.

[4] J. Kučera and J. Kováč, “A reconfigurable four terminal-pair digitally assisted and fully digital impedance ratio bridge,” IEEE Trans. Instrum. Meas., vol. 67, no. 5, pp. 1199–1206, 2018.

[5] F. Overney, N. E. Flowers-Jacobs, B. Jeanneret, A. Rüfenacht, A. E. Fox, P. D. Dresselhaus, and S. P. Benz, “Dual Josephson impedance bridge: towards a universal bridge for impedance metrology,” Metrologia, vol. 57, no. 6, p. 065014, 2020.

[6] M. Marzano, M. Ortolano, F. Overney, A. L. Eichenberger, J. Kucera, V. D’Elia, L. Bartova, J. Medved, and L. Callegaro, "Trilateral Comparison Among Digital and Josephson Impedance Bridges," 2024 Conference on Precision Electromagnetic Measurements (CPEM), Denver, CO, USA, pp. 1-2, 2024.

[7] M. Ortolano, M. Marzano, F. Overney, A. L. Eichenberger, J. Kucera, V. D’Elia, L. Bartova, J. Medved, and L. Callegaro, “An international trilateral comparison among the newest generations of digital and Josephson impedance bridges,” submitted.

Progress Report 2022-10-04

The aim of the project is to perform onsite comparisons of two different digital impedance bridges when performing measurements on a quantum Hall resistance standard with the purpose of realising the SI unit of capacitance, the farad. A travelling bridge from INRIM will be moved to the other partner sites

The travelling INRIM’s electronic-digital impedance bridge has been moved to the PTB to be compared with the PTB’s Josephson-digital impedance bridge.

At the beginning of September 2021, the INRIM’s bridge was reassembled at PTB by the coordinator of the project and the technical assessment was performed by verifying the compatibility of the calibration outcomes of the travelling bridge and the onsite bridge by measuring both temperature-controlled standards and a graphene AC quantised Hall resistance standard. The temperature-controlled standards employed in the assessment are: two PTB’s 10 nF capacitance standards, two 12.9 kΩ resistance standards, one from INRIM and one from PTB.

The impedances are compared in R:R and R:C configurations with a 1:1 magnitude ratio to optimise the INRIM’s bridge accuracy.
The working frequencies are chosen consequently (1233 Hz and 2466 Hz). The uncertainties for the calibration of 10 nF capacitance standards at 1233 Hz are within 1 × 10^-8 for the PTB's bridge and around 1 × 10^-7 for the INRIM-POLITO's bridge. The comparison mutually validates the two bridges within the combined uncertainty.
The comparison has been very fruitful since it allowed to discover issues in the INRIM’s bridge implementation. In particular, the current equalizers number, position and efficiency, the switches involved in the balance automatisation and temperature dependence of the digital signal source have been investigated.

The performance of the bridges in the comparison of the impedance standards against the graphene ACQHR (quantum Hall Resistance in AC regime) were also investigated.
First, the graphene ACQHR developed by PTB was characterised in both the DC and AC regime to prove its quantisation and to choose the best measurement conditions. Then, triangle measurements were performed with both bridges to verify their performances in the calibration of a capacitance standard against the ACQHR.
The results of the assessments can be found in M. Marzano et al, Metrologia, 2022, accepted for publication, https://iopscience.iop.org/article/10.1088/1681-7575/ac9187/pdf. 

Because of already planned research activities, we couldn't schedule the comparison of the travelling INRIM’s bridge with the bridge of the second participating partner, METAS, within the 2022. We plan to perform the activity in the second half of the next year (2023) before the new proposed expected completion date, 31/12/2023.

Progress Report 2021-10-12

The travelling INRIM’s electronic-digital impedance bridge has been moved to the PTB to be compared with the PTB’s Josephson-digital impedance bridge.

At the beginning of September 2021, the INRIM’s bridge was reassembled at PTB by the coordinator of the project and a preliminary technical assessment has been performed by verifying the compatibility of the calibration outcomes of the travelling bridge and the onsite bridge. The standards employed in the assessment are: two PTB’s 10 nF capacitance standards, an INRIM’s 8 nF capacitance standard and two 12.9 kΩ resistance standards, one from INRIM and one from PTB. The impedances are compared in R:R and R:C configurations with a 1:1 magnitude ratio to optimise the INRIM’s bridge accuracy. The working frequencies are chosen consequently (1233 Hz, 2466 Hz and 1541 Hz). The relative deviation between the calibrations performed with the INRIM’s and the PTB’s bridges are of few parts in 10⁸ with a combined type A uncertainty of the same order, lower than the target one.

The comparison has been very fruitful since it allowed to discover issues in the INRIM’s bridge implementation. In particular, the current equalizers number, position and efficiency, the switches involved in the balance automatisation and temperature dependence of the digital signal source have been investigated. A further assessment of the performance of the bridges in the comparison of the impedance standards against the graphene ACQHR (quantum Hall Resistance in AC regime) is now ongoing.

Due to the pandemic restrictions, the comparison of the travelling INRIM’s bridge with the bridge of the second participating partner, METAS, has to be delayed and has not been scheduled yet. We expect to be able to perform the activity during the next year (2022) before the new proposed expected completion date, 31/12/2022.