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Behavior of the dc impedance of an rf-biased resistive SQUID. Final report

Deborah van Vechten, Robert J. Soulen, Rick Peterson

Published Jan 1, 1980• 0 citations
OpenAlex

Abstract

The authors measured the dc impedance of an rf-biased R-SQUID as a function of applied dc bias current, rf frequency and amplitude, and the critical current of the weak link. They conclude that the inclusion of an rf driving current, as required for parametric upconversion influences, in an as-yet incompletely modeled way, the dc impedance of an R-SQUID.

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AIP conference proceedings•Jan 1, 1978•0 citations
The authors measured the dc impedance of an rf-biased R-SQUID as a function of applied dc bias current, rf frequency and amplitude, and the critical current of the weak link. They conclude that the inclusion of an rf driving current, as required for parametric upconversion influences, in an as-yet incompletely modeled way, the dc impedance of an R-SQUID.
The dc -impedance of an rf-biased R-SQUID is studied analytically for the nonhysteretic regime. A mathematical analysis of the intrinsic behavior of an R-SQUID, including the mutual interaction between the tank circuit and the SQUID loop, is presented. The results obtained give good agreement with some experimentally observed features. Although the main aim of the present paper was to find an analytic solution for the dc -impedance of an R-SQUID, the results given here can also be used to estimate the R-SQUID parameters and to optimize the performance of a R-SQUID noise thermometer. The theory presented here also provides a good basis for modelling the noise properties of a Josephson junction noise thermometer.
We have measured with high accuracy (100 ppm) and high precision (5--10 ppm) the impedance of a rf-driven resistive superconducting quantum interference device (SQUID) as a function of the amplitude and frequency of the radio-frequency (rf) bias, as a function of the current bias, and as a function of several other circuit parameters. We have developed the coupled differential equations for the resistive SQUID and for the rf tank circuit. The fit of the solutions of these equations to the data for nonhysteretic junctions is excellent. We were unable to develop solutions for the hysteretic case and thus simply present examples of typical data obtained in order to illustrate the differences with the nonhysteretic case. The relationship of this study to noise thermometry using resistive SQUID's is indicated.