Realizing the farad from two ac quantum Hall resistances

Abstract

Since the quantum Hall resistance (QHR) measured with alternating current (ac) has reached the state of an excellent quantum standard of impedance, we have realized a quadrature bridge with two ac QHRs to accurately calibrate capacitance standards in terms of the SI value of the von-Klitzing constant, without the need for any calculable artefact. The advantages of the realized measuring chain, experimental tests of the coaxial ac bridges involved and the achieved relative uncertainty of 6 × 10 −9 (k = 1) are discussed.

Quantum Hall Effect: Discovery and Application

“…Simultaneously a worldwide agreed value for the conventional Josephson constant K J−90 ≡ 483597.9 × 10 9 Hz/V was fixed such that all electrical units can be reproduced anywhere in the world with extremely high precision. With the implementation of the AC QHE, not only the resistance but also capacitances (48) and inductances (49) can be directly calibrated relative to the quantized Hall resistance. Unfortunately, as of 2017, these units are still disconnected from the official international system of seven base units (SI units).…”

Josephson impedance bridges as universal impedance comparators

“…In order to establish the deviation presented by a particular capacitance standard from its ideal behaviour with frequency, its impedance needs to be compared to frequency independent impedance at several frequencies. The ultimate goal would be to perform these multi-frequency quadrature measurements relative to the impedance of an AC Quantum Hall Resistor [4].…”

Calculated frequency behaviour of the PTB calculable capacitor in audio frequency range

“…By comparing a frequency-characterized calculable capacitor and an AC-QHR with a quadrature bridge, the frequency dependence being observed in AC-QHR devices can be checked. At present, the ohm can be traced back to the farad via the AC-QHE with a measurement uncertainty of 6×10 -9 (k = 1) at a frequency of 1233 Hz [2]. Furthermore, a capacitance standard based on a single electron tunneling (SET) device can be investigated.…”