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Analytic study on the influence of the weak link parameters on the resonant circuit of the nonhysteretic rf SQUID (W less than or equal to 10/sup 8/ s/sup -1/)

H. Luebbig

Published Jan 1, 1978• 0 citations
OpenAlex

Abstract

An analytic expression for the ac impedance of a one-junction SQUID is derived for the nonhysteretic mode of operation. This impedance involves completely the nonlinear influence of the weak links' current phase relationship on the driving resonant circuit.

Related papers

Analytic study on the influence of the weak link parameters on the resonant circuit of the nonhysteretic rf SQUID (ω?108s−1)

H. Lübbig

An analytic expression for the ac impedance of a one‐junction SQUID is derived for the nonhysteretic mode of operation. This impedance involves completely the nonlinear influence of the weak links’ current phase relationship on the driving resonant circuit.

AIP conference proceedings•Jan 1, 1978•0 citations

Theory of rf-biased superconducting quantum interference device for nonhysteretic regime

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Journal of Applied Physics•Dec 1, 1976•30 citations

Influence of the tank circuit on the low frequency impedance of an rf-biased R-SQUID

Heikki Seppä

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.

Journal of Applied Physics•Mar 15, 1984•10 citations

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

Deborah van Vechten, Robert J. Soulen, Rick Peterson

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.

•Jan 1, 1980•0 citations

Impedance of radio-frequency-biased resistive superconducting quantum interference devices

Robert J. Soulen, Deborah van Vechten

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.

Physical review. B, Condensed matter•Jul 1, 1987•13 citations

Basic properties of an rf SQUID involving two Josephson junctions connected in series

Bo Mao, Tan Zhong-Kui, Meng Shu-Chao +2 more

We have studied the basic characteristics of a radio frequency superconducting quantum interference device (rf SQUID) involving two Josephson junctions connected in series, the case for the widely used grain boundary junction (GBJ) rf SQUID. It is found that the SQUID properties are determined mainly by the weaker junction when the critical current of the weaker junction is much lower than that of the other junction. Otherwise, the effect of the other junction is not negligible. We also find that only when the hysteresis parameter β is less than 1−α, where α is the critical current ratio of the two junctions, will the SQUID operate in the nonhysteretic mode.

Chinese Physics•Jul 29, 2004•7 citations
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.
We have studied the basic characteristics of a radio frequency superconducting quantum interference device (rf SQUID) involving two Josephson junctions connected in series, the case for the widely used grain boundary junction (GBJ) rf SQUID. It is found that the SQUID properties are determined mainly by the weaker junction when the critical current of the weaker junction is much lower than that of the other junction. Otherwise, the effect of the other junction is not negligible. We also find that only when the hysteresis parameter β is less than 1−α, where α is the critical current ratio of the two junctions, will the SQUID operate in the nonhysteretic mode.