Alternative Traceability Chains of Impedance Units With Fully Digital Impedance Bridges

We discuss alternative calibration schemes for disseminating the capacitance unit farad from the reference resistance standard using digital impedance bridges. The impedance ratio measurements are performed with a fully digital (FD) bridge. High stability and low crosstalk of the involved generators SWG enable us to perform extreme impedance ratio scaling up to 129:1. Such ratio enables direct linkage even of 100-pF capacitor to the von Klitzing constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {R}_{\mathrm {H}}$ </tex-math></inline-formula>/2 (12.9 k<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula>). We introduce the idea of involving calculable resistance standards, enabling the laboratory to realize the capacitance scale from dc quantum Hall effect (QHE) with only one dc resistance bridge and one digital bridge. Furthermore, an alternative involvement of a single ac Josephson source in a digital bridge is proposed. Finally, experimental measurements as practical examples are given to demonstrate the discussed traceability chains.