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AIP conference proceedings

rf SQUIDSs: The state of the science

R. P. Giffard

Published Jan 1, 1978• 5 citations
Publisher

Abstract

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.

DOI
10.1063/1.31327

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Rf SQUIDs: the state of the science

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The operation and noise limitations of de and RF SQUID's are outlined, and recent advances in their sensitivity are discussed. A model of the dc SQUID predicts an energy noise level per hertz referred to the SQUID of approximately8 k_{B}TL/R \approx 8 k_{B}T(\piLC)^{1/2}, whereL, R,andCare the SQUID inductance and the shunt resistance and capacitance of each Josephson junction. Some examples of dc SQUID's are described to show that their performance is generally in reasonable agreement with the model. The noise energy has improved from about 2 × 10-30J. Hz-1for a device withL = 1nH and a tunnel junction area of 104µm2to about 2 × 10-33J . Hz-1for a device withL = 0.1nH and a microbridge resistance of 40 Ω. Further improvements axe expected in the near future. The model of the RF SQUID predicts a noise energy per hertz referred to the SQUID of[(\pi\alpha^{2}\phi\min{0}\max{2}/2L) + 2 \pi \alpha k_{B}T\min{a}\max{(eff)}]/\omega_{RF}, where α is the intrinsic width of the distribution of flux transitions,T\min{a}\max{(eff)}is an effective amplifier noise temperature, and ωRFis the pump frequency. With one exception, the performance of the seven types of RF SQUID listed is in reasonable agreement with the model. The noise energy ranges from about 1.5 × 10-29J . Hz-1for a 20-MHz toroidal SQUID to 3.5 × 10-31J . Hz-1for 9-GHz reentrant toroidal SQUID; a somewhat better sensitivity has been reported for a 430-MHz device, apparently in conflict with the theory. In both dc and RF SQUID's, 1/fnoise (fis frequency) is likely to extend to higher frequencies as the white-noise level is decreased.

IEEE Transactions on Electron Devices•Oct 1, 1980•88 citations
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 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.
In this paper a discussion is given of the noise sources and sensitivity limits of the rf biased SQUID. Both the low critical current inductive and the higher critical current hysteretic devices are considered. The intrinsic SQUID noise is treated by considering the internal flux response of a SQUID ring to an applied rf flux. While approximate, this approach yields the most direct picture of the nature of the intrinsic noise. Circuit optimization procedures for maximizing SQUID performance under various operating conditions are also outlined. Finally the effects of non-ideal weak link behavior upon SQUID operation are treated. (Author)
SQUIDs are an attractive candidate for the amplification of low-level rf and microwave signals. Compared to semiconductor amplifiers, they offer lower noise and much lower power dissipation. Especially at frequencies below 1 GHz, the improvement in noise temperature compared to the best cold semiconductor amplifiers can be as high as 50; noise temperatures only slightly above the quantum limit have been achieved in this frequency range. This article will review the current status of radio-frequency amplifiers based on dc SQUIDs and provide detailed discussions of amplifier noise temperature, input and output impedance, and nonlinearities.
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 operation and noise limitations of de and RF SQUID's are outlined, and recent advances in their sensitivity are discussed. A model of the dc SQUID predicts an energy noise level per hertz referred to the SQUID of approximately8 k_{B}TL/R \approx 8 k_{B}T(\piLC)^{1/2}, whereL, R,andCare the SQUID inductance and the shunt resistance and capacitance of each Josephson junction. Some examples of dc SQUID's are described to show that their performance is generally in reasonable agreement with the model. The noise energy has improved from about 2 × 10-30J. Hz-1for a device withL = 1nH and a tunnel junction area of 104µm2to about 2 × 10-33J . Hz-1for a device withL = 0.1nH and a microbridge resistance of 40 Ω. Further improvements axe expected in the near future. The model of the RF SQUID predicts a noise energy per hertz referred to the SQUID of[(\pi\alpha^{2}\phi\min{0}\max{2}/2L) + 2 \pi \alpha k_{B}T\min{a}\max{(eff)}]/\omega_{RF}, where α is the intrinsic width of the distribution of flux transitions,T\min{a}\max{(eff)}is an effective amplifier noise temperature, and ωRFis the pump frequency. With one exception, the performance of the seven types of RF SQUID listed is in reasonable agreement with the model. The noise energy ranges from about 1.5 × 10-29J . Hz-1for a 20-MHz toroidal SQUID to 3.5 × 10-31J . Hz-1for 9-GHz reentrant toroidal SQUID; a somewhat better sensitivity has been reported for a 430-MHz device, apparently in conflict with the theory. In both dc and RF SQUID's, 1/fnoise (fis frequency) is likely to extend to higher frequencies as the white-noise level is decreased.