A Resistance Bridge Based on a Cryogenic Current Comparator Achieving Sub-10⁻⁹ Measurement Uncertainties

A new resistance bridge has been built at the Laboratoire national de metrologie et d’essais (LNE) to improve the ohm realization in the Systeme International (SI) of units from the quantum Hall effect. We describe the instrument, the performance of which relies on two synchronized and noise-filtered current sources, an accurate and stable current divider, and a cryogenic current comparator (CCC) having a low noise of $\mathrm {80~pA.t/Hz^{1/2}}$ . The uncertainty budget for the measurement of the 100- $\Omega /(R_{\textrm {K}}/2)$ resistance ratio, where $R_{\textrm {K}}$ is the von Klitzing constant, amounts to a few parts in $10^{10}$ only.