Realization of the farad from the quantum Hall effect with a fully-digital bridge: progress report

On 16 November 2018, the General Conference on Weights and Measures approved a major revision of the International System of Units (SI), so that all the units are now defined by fixing the values of seven fundamental constants. In particular, the unit of electrical capacitance, the farad, is defined by the exact value of the von Klitzing constant [1] and by the unit of time. This opens the possibility of realizing the farad directly from the quantum Hall effect by means of suitable impedance bridges. We present here the design, the implementation and a preliminary validation against the Italian national capacitance scale of a four terminal-pair fully-digital impedance bridge optimized for the direct comparison of an 8 nF standard capacitor with a quantum Hall resistance standard at a frequency of about 1541 Hz, where the impedance magnitude ratio is 1:1. The impedance bridge is based on a polyphase digital sine wave generator developed by Janusz Kaczmarek and Ryszard Rybski, University of Zielona Góra, Poland: two channels produce the voltage ratio reference against which the impedance ratio is compared; three other channels are used to drive the auxiliary circuits realizing the four terminal-pair impedance definition; and one channel is used as auxiliary injection to minimize the uncertainty for the 1:1 comparison. The bridge balance is detected by a phase-sensitive detector and the bridge balance procedure is automated. The bridge balancing time is of about 20 min. The uncertainty of the 1:1 comparison, according to a preliminary evaluation, is at the level of 1E-7.