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IEEE Transactions on Magnetics

Input impedance of the RF SQUID in high frequency regime

S.S. Tinchev

Published May 1, 1983• 0 citations
Publisher

Abstract

A simple method is developed for analysis of the RF SQUID in regime, where the bias frequency ω is comparable to the natural R/L frequency of the SQUID ring. The input impedance of the RF SQUID is calculated for various values of the parametersq = \omega L/R\leq \leq \pi/4, signal frequency and detuning of the rf bias frequency from tank circuit resonant frequency. It is shown, that both the input resistance and the input inductance may be positive or negative. Measurement of the real part of the input impedance of a hysteretic RF SQUID are described. The experimental data are in qualitative agreement with the prediction of the theory.

DOI
10.1109/tmag.1983.1062481

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Physical review. B, Condensed matter•Jul 1, 1987•13 citations
A simple method is developed for analysis of the RF SQUID in regime, where the bias frequency ω is comparable to the natural R/L frequency of the SQUID ring. The input impedance of the RF SQUID is calculated for various values of the parametersq = \omega L/R\leq \leq \pi/4, signal frequency and detuning of the rf bias frequency from tank circuit resonant frequency. It is shown, that both the input resistance and the input inductance may be positive or negative. Measurement of the real part of the input impedance of a hysteretic RF SQUID are described. The experimental data are in qualitative agreement with the prediction of the theory.
An experimental method to measure the imaginary and real part of the input impedance of an rf biased SQUID is described. The experimental results are in good agreement with the predictions of a detailed theoretical model of the rf SQUID, recently published. In particular it seems confirmed that the real part of the input impedance has a negative value which depends on the square of the input signal frequency. This effect must be taken into account whenever a SQUID is used to measure high frequency signals.
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)
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.