Realization of the Farad From the AC Quantum Hall Resistance at PTB—14 Years of Experience

Since 2008, the capacitance unit, the farad, has been realized at the Physikalisch-Technische Bundesanstalt (PTB) successfully and routinely using a measurement chain starting at two quantum Hall resistance (QHR) devices operated at ac. After the first years of practice, a systematic scatter became apparent which indicated an increased measurement uncertainty. This was not due to systematic errors in bridge circuitries (which were fixed in 2014) but accidental incidents. Since then, valuable operational experience has been gained on how to avoid them. As a result, the current uncertainty of the calibration of a 10-pF capacitance standard is back to the initially published relative uncertainty of
$6\times 10^{-9}$
(
$k = 1$
), which is still unmatched. In this article, we report the findings from the operational experience gained during this time, in particular the effect of charge carriers trapped in a QHR device due to accidental discharging incidents. Besides helping practitioners to avoid the pitfalls, the low uncertainty provides a basis for improving the capacitance standards and for reducing the calibration period. Furthermore, we present a new and unique digital sinewave generator. Finally, we show that precision ac measurements of gallium arsenide (GaAs)-based QHRs do not require a
³
He cryo-magnet system but can be carried out in a cheaper and easier-to-operate
⁴
He cryo-magnet system at 2.1 K.