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

Abstract

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 10−7 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.

Design and development of a coaxial cryogenic probe for precision measurements of the quantum Hall effect in the AC regime

“…Measurements in the AC regime will be performed with a fully-digital bridge [16], using the triple-connection series; the approximate electrical modelling of the connections reported in the paper predicts a maximum connection error of a few parts in 10 8 . A more accurate modelling of such error, in progress, will allow to perform a correction of the measurement reading.…”

“…Table 1 summarizes the result of the calculations performed at the frequency f = 1541 Hz, which is of particular interest for the realisation of the farad unit from the quantized resistance [16]. It can be appreciated that, even for the case of a high contact resistance, a triple-series connection reduces the measurement error to about one part in 10 8 .…”

“…impedance standards based on electronic fully-digital impedance bridges [8], [14]- [16] associated to individual QHE devices operating in a simple cryogenic environment.…”

“…The probe will be employed with a new fully-digital coaxial impedance bridge developed in [16]. The bridge is optimised to perform RC comparisons with a 1:1 magnitude ratio, with a comparison uncertainty around 10 -7 .…”

Comparison of a 100-pF Capacitor With a 12 906-Ω Resistor Using a Digital Impedance Bridge

“…The latter still provide measurements with the highest accuracy for the most demanding applications, including the realization of the capacitance unit from calculable capacitors or the ac quantized Hall resistance (QHR) through a quadrature bridge [2][3][4]. However, the digital bridges have been noticeably improving for impedance comparisons, offering many advantages through computer control and automation [5][6][7][8][9][10][11]. In particular, Josephson arbitrary waveform synthesizers establish a quantum-based voltage ratio standard that can be used for impedance comparisons at any phase angle [5,6].…”