Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges

A new traceability chain for the derivation of the farad from dc quantum Hall effect has been implemented at INRIM. Main components of the chain are two new coaxial transformer bridges: a resistance ratio bridge, and a quadrature bridge, both operating at 1541 Hz. The bridges are energized and controlled with a polyphase direct-digital-synthesizer, which permits to achieve both main and auxiliary equilibria in an automated way; the bridges and do not include any variable inductive divider or variable impedance box. The relative uncertainty in the realization of the farad, at the level of 1000 pF, is estimated to be 64E-9. A first verification of the realization is given by a comparison with the maintained national capacitance standard, where an agreement between measurements within their relative combined uncertainty of 420E-9 is obtained.Comment: 15 pages, 11 figures, 3 table

A fully digital bridge towards the realization of the farad from the quantum Hall effect

This paper presents the implementation of an electronic fully-digital impedance bridge optimized for RC comparisons with equal impedance magnitudes, together with an evaluation of the uncertainty. This bridge has been designed with the goal of realizing the farad directly from the quantum Hall effect with a bridge uncertainty component at the 1E-7 level. Thanks to its simple design, ease of operation and affordability, this bridge is suitable to be industrially manufactured. Together with the increasing availability of graphene quantum Hall resistance standards, this can provide an affordable quantum realization of the unit farad for metrology institutes and calibration centres. In this paper we present the uncertainty budget of an example measurement and the results of the validation of the bridge against a suitably modified version of the traceability chain of the Italian national standard of capacitance. The combined uncertainty of the bridge resulted from repeated measurements (overall measurement time of about 200 min) is 9.2 × 10^−8, suitable for the primary realization of the unit of capacitance from a quantized Hall resistance standard. The crosstalk among the channels of the electrical generator is the most significant uncertainty component, possibly reducible with internal shielding and filtering of the electronic generator

New proposed method for traceability dissemination of capacitance measurements

Capacitance measurements at the National Institute of Standards (NIS), Egypt, are traceable to the Bureau International des Poids et Mesures (BIPM). It calibrates the main NIS standard capacitors, AH11A. In this paper, traceability of the BIPM capacitance measurements could be used to evaluate a new accurate measurement method through an Ultra-Precision Capacitance Bridge. The new method is carefully described by introducing some necessary equations and a demonstrating chart. Verification of this new method has been realized by comparing its results for the 10 pF and 100 pF capacitance standards with the results obtained by the conventional substitution method at 1 kHz and 1.592 kHz. The relative differences between the two methods are about 0.3 µF/F, which reflect the accuracy of the new measurement method. For higher capacitance ranges, the new measurement method has been applied for the capacitance measurements up to 1 μF at 1 kHz. The relative differences between the two methods are in the range of 5.5 µF/F on the average which proves the acceptable accuracy and the reliability of the new method to be used

Programmierbare Josephson-Arrays für Impedanzmessungen

An innovative way of networking two programmable Josephson arrays generating synchronous waveforms for impedance ratio measurements, as the first of its kind, is presented. This pioneering approach of the Josephson Impedance Bridges is far more flexible than conventional bridges at the same level of measurement uncertainty. Results prove that aside from having the capability of measuring over a wider frequency range, the Josephson bridge permits measurements on two impedances with any value of phase angle between them. In the two-terminal-pair Josephson bridge setup, measurements are made for a 1:1 resistance ratio at the 10-k level in the frequency range between 25 Hz and 10 kHz. Uncertainties reach to levels of better than a few parts in 108 and results agree to the values measured from conventional impedance bridges. Two methods for four-terminal impedance measurements have been investigated, the potential comparison circuit and the coaxial setup. Both methods are capable of measuring from DC to 6 kHz with uncertainties to 10−8. The four-terminal-pair coaxial setup has potential to decrease the relative uncertainty down to 10−9 once systematic errors are analyzed and canceled. Thermal converter measurements have been made to investigate the effects of transients on stepwise approximated sinewaves. Rms measurements show that transients limit the uncertainty to about 10−6 at 1 kHz. A simple model with an equivalent time constant is presented to evaluate the influence of different parameters on the shape of the transients. It has been experimentally established, at the 10−8 level of uncertainty for the determination of impedance ratios, that the variations of the transients in stepwise approximated waveforms can be neglected when using the fundamental component of rectangular waveforms. Quantization at up to 10 kHz has been confirmed by varying the bias current of the Josephson arrays resulting in constant resistance ratios within the measurement resolution.Ein innovativer Weg, zwei programmierbare Josephson-Schaltungen für Impedanz-Verhältnismessungen zu verknüpfen, wird erstmals in dieser Arbeit präsentiert. Dieser neuartige Ansatz einer Josephson-Impedanzmessbrücke ist flexibler als konventionelle Impedanzmessbrücken bei gleicher Messunsicherheit. Es wird gezeigt, dass neben der Möglichkeit, über einen wesentlich größeren Frequenzbereich zu messen, die Josephson-Impedanzmessbrücke auch Messungen sehr unterschiedlicher Impedanzverhältnisse und beliebiger Phasenwinkel erlaubt. In einer Zwei-Tor-Anordnung der Josephson-Impedanzmessbrücke wurden Messungen für ein 1:1 Widerstandsverhältnis bei 10 k im Frequenzbereich von 25 Hz bis 10 kHz durchgeführt. Die Ergebnisse stimmen mit denen einer konventionellen Messbrücke im Rahmen der Unsicherheit von wenigen 10−8 überein. Für eine Vier-Tor-Anordnung wurden zwei unterschiedliche Methoden untersucht, eine Spannungsverhältnisschaltung und eine koaxiale Vier-Tor-Anordnung. Letztere hat das Potential, Unsicherheiten von 10−9 zu erreichen, sobald systematische Fehler eliminiert sind. Um Effekte der Transienten in stufenförmig approximierten Sinuswellen zu untersuchen, wurden Messungen an Thermokonvertern durchgeführt. Diese Effektivmessungen zeigen, dass Transienten die relative Messunsicherheiten auf etwa 10−6 bei einer Frequenz von 1 kHz beschränken. Es wird ein einfaches Modell vorgestellt, das die Form der Transienten in Abhängigkeit der wesentlichen Parameter beschreibt. Experimentell konnte bei Impedanzverhältnismessungen mit einer relativen Messunsicherheit von 10−8 nachgewiesen werden, dass die Variation der Transienten in stufenförmig approximierten Wellenformen vernachlässigbar ist, wenn die fundamentale Komponente eines Rechtecksignals verwendet wird. Quantisierte Plateaus wurden bis zu Frequenzen von 10 kHz gefunden, bei denen die Variation des angelegten Stroms durch die Josephson-Schaltungen keine Veränderung des Impedanzverhältnisses zur Folge hatte

The ampere and the electrical units in the quantum era

By fixing two fundamental constants from quantum mechanics, the Planck constant $h$ and the elementary charge $e$, the revised Syst\`eme International (SI) of units endorses explicitly quantum mechanics. This evolution also highlights the importance of this theory which underpins the most accurate realization of the units. From 20 May 2019, the new definitions of the kilogram and of the ampere, based on fixed values of $h$ and $e$ respectively, will particularly impact the electrical metrology. The Josephson effect (JE) and the quantum Hall effect (QHE), used to maintain voltage and resistance standards with unprecedented reproducibility since 1990, will henceforth provide realizations of the volt and the ohm without the uncertainties inherited from the older electromechanical definitions. More broadly, the revised SI will sustain the exploitation of quantum effects to realize electrical units, to the benefit of end-users. Here, we review the state-of-the-art of these standards and discuss further applications and perspectives.Comment: 78 pages, 35 figure

Compendium for precise ac measurements of the quantum Hall resistance

In view of the progress achieved in the field of the ac quantum Hall effect, the Working Group of the Comite Consultatif d'Electricite et Magnetisme (CCEM) on the AC Quantum Hall Effect asked the authors of this paper to write a compendium which integrates their experiences with ac measurements of the quantum Hall resistance. In addition to the important early work performed at the Bureau International des Poids et Mesures and the National Physical Laboratory, UK, further experience has been gained during a collaboration of the authors' institutes NRC, METAS, and PTB, and excellent agreement between the results of different national metrology institutes has been achieved. This compendium summarizes the present state of the authors' knowledge and reviews the experiences, tests and precautions that the authors have employed to achieve accurate measurements of the ac quantum Hall effect. This work shows how the ac quantum Hall effect can be reliably used as a quantum standard of ac resistance having a relative uncertainty of a few parts in 10^8.Comment: 26 pages, 8 figure

An international comparison of phase angle standards between the novel impedance bridges of CMI, INRIM and METAS

partially_open8We report here the results of a comparison of electrical impedance standards aimed at evaluating four novel digital impedance bridges developed by the national metrology institutes CMI, INRIM and METAS. This comparison, which is the first of its kind, involved phase angle impedance standards developed by TÜBITAK UME with phase angles of  ± 30° and  ± 60°, and magnitudes ranging from about 100 Ω to 1 MΩ. The comparison demonstrated agreement among the measurement results obtained with the different bridges, and allowed us to gather information on the stability of the phase standards and on more critical aspects related to the characterization of the bridges.partially_openOrtolano, Massimo; Palafox, Luis; Kučera, Jan; Callegaro, Luca; D’Elia, Vincenzo; Marzano, Martina; Overney, Frédéric; Gülmez, GülayOrtolano, Massimo; Palafox, Luis; Kučera, Jan; Callegaro, Luca; D’Elia, Vincenzo; Marzano, Martina; Overney, Frédéric; Gülmez, Güla