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Applied Physics Letters

Measurement of the input impedance of a RF biased SQUID

Franco Bordoni, P. Carelli, I. Modena, Gian Luca Romani

Published Oct 15, 1979• 3 citations
Publisher

Abstract

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.

DOI
10.1063/1.91236

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•Jan 1, 1978•1 citation
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.
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.
The spectral density of the low-frequency open-circuit intrinsic input noise of the hysteretic rf-biased SQUID is calculated. The noise level, which affects the optimized power sensitivity of the SQUID, is found to be strongly model dependent and thus also constitutes an interesting probe of device physics. The results of the calculation are significantly different from previous predictions. A direct measurement of the total input noise of a typical rf-biased SQUID system is reported. The results, which are consistent our calculation, correspond to a system noise temperature of 3.1±0.4 mK at a frequency of 1 kHz. This value is consistent with the Manley-Rowe equations and with previous experimentally determined upper limits.
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.
The theory of rf SQUID operation, including the effects of fluctuations, is discussed. The theory is in agreement with the large signal and small signal behavior of real devices under optimum conditions. The noise levels of many existing rf SQUID systems are substantially above those predicted on the basis of amplifier noise temperatures. All rf SQUIDs seem to exhibit excess noise of unknown origin at low input frequencies. The limitations of devices and future directions of development are considered.