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

Realization of an Inductance Scale Traceable to the Quantum Hall Effect Using an Automated Synchronous Sampling System

In this paper, the realization of an inductance scale from 1~$\mu$H to 10~H for frequencies ranging between 50~Hz to 20~kHz is presented. The scale is realized directly from a series of resistance standards using a fully automated synchronous sampling system. A careful systematic characterization of the system shows that the lowest uncertainties, around 12~$\mu$H/H, are obtained for inductances in the range from 10~mH to 100~mH at frequencies in the kHz range. This new measurement system which was successfully evaluated during an international comparison, provides a primary realization of the henry, directly traceable to the quantum Hall effect. An additional key feature of this system is its versatility. In addition to resistance-inductance (R-L) comparison, any kind of impedances can be compared: R-R, R-C, L-L or C-C, giving this sampling system a great potential of use in many laboratories around the world

Primary Realization of Inductance and Capacitance Scales With a Fully Digital Bridge

This article describes an automated electronic fully digital bridge for the comparison of four-terminal-pair (4TP) impedance standards in the audio frequency range. The bridge relative accuracy, which is on the order of 10-6, makes it suitable as a reference bridge for the realization of primary scales of inductance and capacitance in metrology institutes and calibration laboratories. The performances of this bridge were validated by comparing the results of the calibrations of inductance and capacitance standards with those obtained from an existing analog reference system based on the three-voltage method. The article also reports the results of this validation

A CIRCULAR LOOP TIME CONSTANT STANDARD

A time constant standard, developed for the phase angle measurement of precision current shunts is developed and described, and its time constant has been determined. Based on a single circular loop placed in an air thermostat, its construction is very simple and it gives accurate results in the frequency band of interest, e.g. for frequencies between 50 Hz and 100 kHz. The influence of the shielding is calculated using numerical Finite Element Analysis (FEA). The thermostatic stability is analyzed, and the time-constant of the thermostat is determined using temperature measurement and Butterworth filtering. The power coefficient of the standard is determined, and limits of errors are discussed

A CIRCULAR LOOP TIME CONSTANT STANDARD

A time constant standard, developed for the phase angle measurement of precision current shunts is developed and described, and its time constant has been determined. Based on a single circular loop placed in an air thermostat, its construction is very simple and it gives accurate results in the frequency band of interest, e.g. for frequencies between 50 Hz and 100 kHz. The influence of the shielding is calculated using numerical Finite Element Analysis (FEA). The thermostatic stability is analyzed, and the time-constant of the thermostat is determined using temperature measurement and Butterworth filtering. The power coefficient of the standard is determined, and limits of errors are discussed

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

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