Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Applied Physics

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

Sergio Nicola Erne, H.-D. Hahlbohm, H. Lübbig

Published Dec 1, 1976• 30 citations
Publisher

Abstract

The SQUID response φ (φe) is studied analytically for the nonhysteretic regime, 2πLsIc<φ0, and low-frequency excitation, ω?108 s−1. The influence of the weak-link parameters on the voltage at the tank circuit is demonstrated. The calculations including the cos(2πφ/φ0) term are compared with the experimental results of Nisenoff and Wolf.

DOI
10.1063/1.322574

Related papers

A method for determining the SQUID parameter β and the coupling coefficient K in a nonhysteretic rf SQUID

Sergio Nicola Erne, Holger M. Luther

A method for determining the superconducting-quantum-interference-device (SQUID) parameter β = LsIc/Φo and the coupling coefficient K between the SQUID loop and tank circuit based on the general theory for the nonhysteretic rf SQUID is derived. Analysis of the periodic dependence of the amplitude of the tank-circuit voltage on applied dc flux leads to explicit expressions for β and K. Important advantages of the method are that, during measurements, the SQUID loop has neither to be opened nor decoupled from the tank circuit, and the temperature of the sample does not have to be changed. Measurements with a Nb-point-contact SQUID at 4.2 K to verify the method in practice are reported. Intrinsic errors were estimated to be less than 10%.

Journal of Applied Physics•Apr 1, 1981•3 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

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

Detailed measurements of the response of an rf SQUID in the regime LIc< Φ0/2π

Robert Rifkin, Daniel A. Vincent, Paul K. Hansma +1 more

Using a superconducting ring containing a Nb point contact inductively coupled to a resonant circuit fed with an rf current source, (typical rf SQUID configuration) we have measured the tank voltage as a function of frequency in the regimeLI_{c}< \Phi_{0}/2\pi. ForLI_{c} \ll \Phi_{0}/2\pi, the curves of tank voltage versus drive current for various values of external flux\Phi_{x}through the ring agree with the calculations of Hansma. For higher critical currents, there is an asymmetry in these curves for frequencies above and below ω0, the resonant frequency of the circuit. Calculations using an expanded theory including the effects of a conductanceG_{o}(1+\alpha \cos \phi)and of screening flux give good agreement with the data. In principle α can be determined from these measurements, however the\cos \phiterm and the screening flux produce qualitatively similar effects. A quantitative determination of α requires a precise knowledge of Go/Ic. Using values of Goand Icfrom independent impedance measurements, the data yield a negative value of α in agreement with another experiment.

IEEE Transactions on Magnetics•Mar 1, 1975•5 citations

Detailed measurements of the response of an rf SQUID in the regime LI/sub c/ < PHI/sub 0//2. pi

Robert Rifkin, Daniel A. Vincent, Paul K. Hansma +1 more

A superconducting ring containing a Nb point contact inductively coupled to a resonant circuit fed with an rf current source (typical rf SQUID configuration) was used to measure the tank voltage as a function of frequency in the regime LI/sub c/ less than PHOI/sub 0//2..pi... For LI/sub c/ much less than PHI/sub 0//2..pi.., the curves of tank voltage versus drive current for various values of external flux PHI/sub x/ through the ring agree with the calculations of Hansma. For higher critical currents, there is an asymmetry in these curves for frequencies above and below ..omega../sub 0/, the resonant frequency of the circuit. Calculations using an expanded theory including the effects of a conductance G/sub 0/(1 + ..cap alpha.. cos phi) and of screening flux give good agreement with the data. In principle, ..cap alpha.. can be determined from these measurements, but the cos phi term and the screening flux produce qualitatively similar effects. A quantitative determination of ..cap alpha.. requires a precise knowledge of G/sub 0//I/sub c/. Using values of G/sub 0/ and I/sub c/ from independent impedance measurements, the data yield a negative value of ..cap alpha.., in agreement with another experiment. (auth)

IEEE Transactions on Magnetics•Mar 1, 1975•0 citations

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
The SQUID response φ (φe) is studied analytically for the nonhysteretic regime, 2πLsIc<φ0, and low-frequency excitation, ω?108 s−1. The influence of the weak-link parameters on the voltage at the tank circuit is demonstrated. The calculations including the cos(2πφ/φ0) term are compared with the experimental results of Nisenoff and Wolf.
A method for determining the superconducting-quantum-interference-device (SQUID) parameter β = LsIc/Φo and the coupling coefficient K between the SQUID loop and tank circuit based on the general theory for the nonhysteretic rf SQUID is derived. Analysis of the periodic dependence of the amplitude of the tank-circuit voltage on applied dc flux leads to explicit expressions for β and K. Important advantages of the method are that, during measurements, the SQUID loop has neither to be opened nor decoupled from the tank circuit, and the temperature of the sample does not have to be changed. Measurements with a Nb-point-contact SQUID at 4.2 K to verify the method in practice are reported. Intrinsic errors were estimated to be less than 10%.
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.
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.
Using a superconducting ring containing a Nb point contact inductively coupled to a resonant circuit fed with an rf current source, (typical rf SQUID configuration) we have measured the tank voltage as a function of frequency in the regimeLI_{c}< \Phi_{0}/2\pi. ForLI_{c} \ll \Phi_{0}/2\pi, the curves of tank voltage versus drive current for various values of external flux\Phi_{x}through the ring agree with the calculations of Hansma. For higher critical currents, there is an asymmetry in these curves for frequencies above and below ω0, the resonant frequency of the circuit. Calculations using an expanded theory including the effects of a conductanceG_{o}(1+\alpha \cos \phi)and of screening flux give good agreement with the data. In principle α can be determined from these measurements, however the\cos \phiterm and the screening flux produce qualitatively similar effects. A quantitative determination of α requires a precise knowledge of Go/Ic. Using values of Goand Icfrom independent impedance measurements, the data yield a negative value of α in agreement with another experiment.
A superconducting ring containing a Nb point contact inductively coupled to a resonant circuit fed with an rf current source (typical rf SQUID configuration) was used to measure the tank voltage as a function of frequency in the regime LI/sub c/ less than PHOI/sub 0//2..pi... For LI/sub c/ much less than PHI/sub 0//2..pi.., the curves of tank voltage versus drive current for various values of external flux PHI/sub x/ through the ring agree with the calculations of Hansma. For higher critical currents, there is an asymmetry in these curves for frequencies above and below ..omega../sub 0/, the resonant frequency of the circuit. Calculations using an expanded theory including the effects of a conductance G/sub 0/(1 + ..cap alpha.. cos phi) and of screening flux give good agreement with the data. In principle, ..cap alpha.. can be determined from these measurements, but the cos phi term and the screening flux produce qualitatively similar effects. A quantitative determination of ..cap alpha.. requires a precise knowledge of G/sub 0//I/sub c/. Using values of G/sub 0/ and I/sub c/ from independent impedance measurements, the data yield a negative value of ..cap alpha.., in agreement with another experiment. (auth)