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Journal of Applied Physics

Design and High-Frequency Response of Resistive SQUID Frequency Converters

Alistair A. Fife, Suso Gygax

Published May 1, 1972• 19 citations
Publisher

Abstract

Several resistive SQUID frequency converters (R-SQUID) have been constructed and their properties studied in the frequency regimes 26.5–40 and 67–73 GHz. A brief outline of the theory of the device is presented together with constructional details for a Nb–Nb point-contact version. The device response is complicated by the effects on the ac Josephson current of distributed circuit elements, and a broad range of complex behavior is presented which is only partially understood. A useful amplification effect for the detected signal has been discovered, which gives the device good broad range sensitivity (∼ 10−7–∼ 10−12 W/Hz1/2) and reasonably narrow linewidths (Q-values of ∼ 104 at 70 GHz).

DOI
10.1063/1.1661509

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IEEE Transactions on Electron Devices•Oct 1, 1980•88 citations
Several resistive SQUID frequency converters (R-SQUID) have been constructed and their properties studied in the frequency regimes 26.5–40 and 67–73 GHz. A brief outline of the theory of the device is presented together with constructional details for a Nb–Nb point-contact version. The device response is complicated by the effects on the ac Josephson current of distributed circuit elements, and a broad range of complex behavior is presented which is only partially understood. A useful amplification effect for the detected signal has been discovered, which gives the device good broad range sensitivity (∼ 10−7–∼ 10−12 W/Hz1/2) and reasonably narrow linewidths (Q-values of ∼ 104 at 70 GHz).
A pair of high-temperature-superconducting (HTS) step-edge Josephson junctions connected in the ‘resistive-SQUID’ (R-SQUID) configuration has been previously shown to generate a heterodyne oscillation which is frequency-tunable by a control current across the resistor. A method is described which enables the R-SQUID to act both as the local oscillator (LO) and simultaneously as a radio- frequency down-converter element. For the first time the autonomous Josephson mixer–local oscillator device for signal frequencies between 1–5 GHz, over a temperature range of 20–70 K, is demonstrated.
We have already seen, in Chapter 2 , that the complex response of a Josephson junction to applied electromagnetic radiation forms a basis for both broad-band and heterodyne detection modes, ranging from low frequencies to the far-infrared. Greater detail of actual working devices of this type will be given in this chapter. The second topic dealt with is digital applications of squid s. This is already a significant, and may in the future become a dominant, use of low-power superconducting technology. At first sight the contents of this chapter may seem to divide into two rather disconnected areas. However, logic devices have two important characteristics in common with radiation detectors: first, both involve very high-frequency operation, since slow digital devices are of little or no practical interest. Second, both applications demand the use of well characterised and reproducible small-area junctions with similar parameters. In what follows, more details of junction fabrication methods will be given than have been discussed earlier in the book. This reflects the fact that well defined junction properties are of the utmost importance in achieving high performance in these areas. It seems paradoxical that squid s, for all their unparalleled sensitivity, will operate very satisfactorily with far from ideal Josephson junctions. This is mainly because squid s have only been used in rather low-frequency applications, for which the low resistive and reactive impedances associated with poor-quality junctions do not limit performance.
The well-developed technique of a toroidal point-contact rf SQUID has been extended to a dc SQUID. Two point-contacts are made on the symmetry axis of the toroid. A large Nb cavity containing a signal coil is connected to the junctions via a narrow gap. Such geometry allows good coupling of the SQUID to a high-inductance signal coil without increasing the effective SQUID inductance at the Josephson frequency. It is expected that both the shot-noise-limit performance and a high signal coupling will be achieved in this SQUID. We discuss the status of design and the result of preliminary test of the device.
We report continuing investigations into practical applications of the AC Josephson effect as the basis for a voltage-tunable radio-frequency oscillator. We have previously demonstrated experimentally that useful power levels (10 s of nW) and linewidths of a few kHz can be achieved in the heterodyne output from a high-temperature-superconducting resistive SQUID (HTS-RSQUID) operating in the frequency range 1-50 MHz. Those results were achieved with 2-junction R-SQUIDs incorporating current-biased shunt resistors of a few micro-ohms. We have now modified the fabrication procedures, and adjusted the shunt resistors and bias current values so that higher frequencies can be achieved. The Josephson junctions are of step-edge type, rather than the bi-crystal type used in our earlier work. The step-edge technique permits much more flexibility in the geometrical lay-out and utilizes the more cost-effective single-crystal MgO substrates. In the present paper, we report numerical simulations and experimental measurements on these devices in the frequency range up to 2 GHz.
The output voltage of a dc superconducting quantum interference device (SQUID) containing a resistive section Rs oscillates at a frequency νq =Vs/ φ0 (φ0=flux quantum) when a current controlled voltage Vs is maintained across Rs. These oscillations have been observed from ∼10−1 to 1011 Hz, using Rs values ranging from ∼10−10 to ∼10−3 Ω in low inductance (∼10−10 H) point contact SQUID loops. At high frequencies, they manifest themselves in the dc current-voltage characteristics by inducing extra current steps.
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.