The Josephson two-terminal-pair impedance bridge

Abstract

We present the connection of two programmable Josephson arrays generating synchronous waveforms to measure impedance ratios—the Josephson two-terminal-pair impedance bridge. This approach is more flexible than conventional bridges at the same level of uncertainty. The Josephson bridge can measure over a wider frequency range, over a wider range of impedance ratios than conventional two-terminal-pair bridges. Furthermore, the phase angle between the two impedances can take any value. As a first application, we present measurements of a 1 : 1 resistance ratio at the 10 kΩ level in the frequency range between 25 Hz and 10 kHz. The uncertainties are better than a few parts in 108 and hence comparable to those of conventional impedance bridges. Quantization at up to 10 kHz was confirmed by varying the bias current of the Josephson arrays, resulting in constant resistance ratios within the measurement resolution.

Josephson impedance bridges as universal impedance comparators

“…Building on from the results in the proof-of-concept experiment [1], the two-terminal-pair (2TP) Josephson impedance bridge has been used to determine the ratio of two 100-pF capacitance standards, as shown in Fig.1. Similarly to the case of the two 10-kΩ resistors, the measurements extend over a large frequency range from 25 Hz to 10 kHz.…”

“…Josephson impedance bridges [1,2] have been shown to measure the ratio of two resistors at frequencies ranging from a few hertz to 10 kHz with an accuracy close to that of the best conventional impedance bridges [3]. As the Josephson Waveform Synthesizers (JWS) can supply any voltage accurately within their working range and their relative phase can be controlled very precisely, any kind of impedances whether predominately resistive, capacitive or inductive can be compared with the same or any other kind.…”

Josephson Junctions for Present and Next Generation Voltage Metrology

“…A two terminal pair impedance bridge has achieved an accuracy of one part in 10 8 in a frequency range from 25 Hz to 10 KHz, limited mainly by contact resistance changes at the bridge terminals [57]. Further progress is expected when a four terminal connection to the resistances can be provided.. Also quantum sampling of waveforms is made possible, by realization of Josephson DAC with quantum accuracy, and using them with a proper electronics which enclose in the same circuit conventional and quantum based DAC.…”

Development of Josephson voltage standards

“…Internally the lock-in amplifier multiplies the rectangular waveform with a sine wave heavily weighting the quantized plateaus and almost neglecting the transients (Jeanneret et al, 2010). The influence of the transients is suppressed to below parts in 10 8 which is being utilized fully for impedance ratio measurements (Lee et al, 2010). However, the only way to completely avoid transients at all is to use the so-called pulsedriven Josephson arbitrary waveform synthesizer.…”