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Applied Physics Letters

Measurement of forward and reverse signal transfer coefficients for an rf-biased SQUID

R. P. Giffard, J. N. Hollenhorst

Published Jun 1, 1978• 24 citations
Publisher

Abstract

Comprehensive measurements of the parameters characterizing an rf-biased SQUID as a linear twoport are described. The behavior of the device corresponds in detail to the predictions of a recently published model of SQUID operation and is unexpectedly similar to that of a conventional reactive parametric amplifier. The measurements have been used to make the first reliable predictions of the noise temperature and optimum source impedance of an rf-biased SQUID.

DOI
10.1063/1.89888

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Comprehensive measurements of the parameters characterizing an rf-biased SQUID as a linear twoport are described. The behavior of the device corresponds in detail to the predictions of a recently published model of SQUID operation and is unexpectedly similar to that of a conventional reactive parametric amplifier. The measurements have been used to make the first reliable predictions of the noise temperature and optimum source impedance of an rf-biased SQUID.
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.
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.
The theory of rf SQUID opteration, 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.
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.
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.