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 produces 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 Josephson standard 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, impedance measurements can be performed across a wide integer and non-integer ratio range from 1:1 to 1:10. 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 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 kΩ and 10 kΩ resistance standards spanning a frequency range from 53 Hz to 50 kHz. The bridge achieves uncertainties from 4 nΩ/Ω to 24 nΩ/Ω. 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 nΩ/Ω ± 5 nΩ/Ω (k = 1). The Josephson bridges demonstrate remarkable versatility by enabling ratio and quadrature measurements without the need for additional components. Two sets of measurements are conducted, each involving a 10 nF capacitance standard and a 12.9 kΩ 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).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 from 23 nΩ/Ω to 0.5 µΩ/Ω.