Four Terminal Pair Impedance Bridge based on two pulse-driven Josephson Arrays and a Graphene Quantum Hall System

This research presents the successful development and comprehensive characterizations of a four-terminal-pair Josephson impedance bridge based on a pulse-driven Josephson voltage standard. The four-terminal-pair configuration reduces cable and connector errors and ensures that the bridge is immune from external disturbances.
The pulse-driven Josephson voltage standard, also known as Josephson arbitrary waveform synthesizer (JAWS), produces quantum-based voltages with superior amplitude stability. Using two Josephson junction arrays to generate pure sine wave voltages in impedance bridges, offering various advantages. This approach simplifies the bridge setup compared to traditional inductive voltage divider (IVD) networks. Additionally, the JAWS provides voltages with a broad range of frequencies compared to a single IVD-based source, expanding the operational frequency range of the Josephson Bridge from 53 Hz to 50 kHz, depending on the compared impedances.
Furthermore, by controlling phase angles and amplitude ratios between both JAWS arrays, versatile impedance measurements can be performed across a wide integer and non-integer ratio range from 1:1 to 1:10. The bridges facilitate both ratio and quadrature measurements and establish a direct Connection between an impedance standard and a graphene-based quantum Hall resistance (QHR) standard. These flexibility and adaptability overcome the limitations of traditional impedance bridges, which typically operate at fixed ratios and frequencies within a few kHz.
The Josephson bridge is developed in two configurations. In an earlier phase, the bridge requires manual balancing, while the present bridge is fully automated with enhanced current sourcing and detecting approaches. Both configurations undergo thorough evaluation, validation, and extensive uncertainty assessments. The automated bridge yields highly accurate results and demonstrates excellent stability, reducing uncertainties to levels comparable with those of conventional bridges.
The bridges are utilized to measure capacitance ratios between two 10 nF capacitance standards across a frequency range from 53 Hz to 50 kHz. The bridge achieves uncertainties ranging from 2 nF/F to 185 nF/F. The ratios obtained from the Josephson bridges exhibit excellent agreement with results achieved from a PTB's IVD-based impedance bridge, with the smallest deviation being -2 nF/F ± 3 nF/F (k =1) at 1,233.15 Hz.
Moreover, the bridges are capable of measuring resistance ratios between 12.9 kO and 10 kO resistance standards spanning a frequency range from 53 Hz to 50 kHz. The bridge achieves uncertainties ranging from 4 nO/O to 24 nO/O. At the lowest frequency of 53 Hz, the deviation of the value achieved by the bridge from a DC value obtained from a PTB's 14-bit cryogenic current comparator bridge is -4 nO/O± 5 nO/O (k =1).
The Josephson bridges demonstrate remarkable versatility by enabling ratio and quadrature measurements without the need for additional components, thereby simplifying the setup compared to traditional bridges that require complex quadrature networks. With the quadrature configuration, two sets of measurements are conducted, each involving a 10 nF capacitance standard and a 12.9 kO resistance standard, to estimate an indirect capacitance ratio. The calculated ratios are compared with the values obtained from the IVD-based impedance bridge. The results demonstrate a minimum deviation of -5 nF/F ± 13 nF/F (k =1). The indirect ratio evaluation serves as an indicator to assess the quadrature bridge's performance by comparing it with a reference value from a conventional bridge.
Furthermore, measurements with an AC graphene QHR, including resistance ratio and quadrature measurements are carried out over a frequency range from 246 Hz to 30 kHz contingent on the impedances being compared. The measurements yield uncertainties in the range of 23 nO/O to 0.5 µO/O. The primary source of uncertainty is attributed to the frequency-dependence characteristics of the AC QHR, as the double-shielding technique has not yet been implemented.
All measurements exhibit high reproducibility within their respective uncertainty ranges. Additionally, the Josephson impedance bridges are observed to operate without unexpected noise sources, as confirmed by Allan deviation analyses.