Programmable Josephson Arrays for Impedance Measurements

Arbitrary impedance ratios can be determined with high accuracy by means of a programmable Josephson system. For a 1 : 1 resistance ratio at 10-kΩ level, we demonstrate that the novel system allows measurements over a wide frequency range from 25 Hz to 6 kHz. Uncertainties are in the range of a few parts in 10⁸ and thus comparable to those of conventional impedance bridges. Two methods for four-terminal-pair impedance measurements have been investigated, i.e., the potential comparison circuit and the coaxial setup. Both methods are capable of measuring from dc to 6 kHz with uncertainties to a few parts in 10⁸. The potential comparison circuit has an upper bound at 6 kHz due to the use of the sampling method. The four-terminal-pair coaxial setup has the potential to decrease the relative uncertainty down to 10^-9 once systematic errors are analyzed and canceled.