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Applied Physics Letters

Measurement of the dynamic input impedance of a dc superconducting quantum interference device at audio frequencies

P. Falferi, R. Mezzena, Stefano Vitale, MASSIMO CERDONIO

Published Aug 18, 1997• 21 citations
Publisher

Abstract

The coupling effects of a commercial dc superconducting quantum interference device (SQUID) to an electrical LC resonator which operates at audio frequencies (≈1 kHz) with quality factors Q≈106 are presented. The variations of the resonance frequency of the resonator as functions of the flux applied to the SQUID are due to the SQUID dynamic inductance in good agreement with the predictions of a model. The variations of the quality factor point to a feedback mechanism between the output of the SQUID and the input circuit.

DOI
10.1063/1.119700

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Tapani Ryhänen, Heikki Seppä, R. Cantor

Practical thin-film dc superconducting quantum interference devices (SQUIDs) are often built with an integrated input coil which leads to the formation of various parasitic elements. We have designed and fabricated several square washer-shaped dc SQUID test devices with various amounts of parasitic capacitance formed by covering the washer slits with superconducting coverplates of various widths. In the simplest approximation, the parasitic capacitance Cp appears entirely across the Josephson junctions; in a better approximation, Cp divides the total inductance into two parts, an effective SQUID loop inductance L and a small parasitic inductance Lp. For both models, noise-free and noise-rounded current-voltage and voltage-flux characteristics are calculated for various values of the ratios L/Lp and Cp/C, where C is the Josephson junction capacitance. The SQUID dynamics are significantly affected by Cp and Lp. The energy resolution ε at first deteriorates with increasing Cp for Cp/C ≲ 2, but as Cp/C becomes large, ε improves to less than twice the value for Cp/C ≊ 0. The optimal points of operation for large Cp, however, are found at voltages above the low-frequency resonance determined by L and Cp where the flux-to-voltage transfer function is low. Furthermore, for devices with Cp/C ≫ 1 and Lp≠0, the double-loop geometry leads to an additional resonance determined by Lp and C that appears at high frequencies. The energy resolution inside this high-frequency resonance is nearly independent of Cp and comparable to the energy resolution of a device having the same total inductance but with Cp/C ≪ 1. Extensive noise mappings on several different test devices have been carried out using a computer-controlled measurement system. The measured characteristics and noise performance are shown to be in good agreement with the simulations.

Journal of Applied Physics•Jun 15, 1992•32 citations
The coupling effects of a commercial dc superconducting quantum interference device (SQUID) to an electrical LC resonator which operates at audio frequencies (≈1 kHz) with quality factors Q≈106 are presented. The variations of the resonance frequency of the resonator as functions of the flux applied to the SQUID are due to the SQUID dynamic inductance in good agreement with the predictions of a model. The variations of the quality factor point to a feedback mechanism between the output of the SQUID and the input circuit.
The measured input impedance of an amplifier involving a coil tightly coupled to a dc superconducting quantum interference device (SQUID) is found to depend on the current and flux biases of the SQUID. Variations in the input inductance arise from the reflected dynamic inductance of the SQUID, and are in reasonable agreement with the predictions of an analog simulator. Variations in the input resistance, on the other hand, arise from feedback between the output of the SQUID and the input circuit, and are in approximate agreement with the predictions of a simple model.
The dynamics and noise of a dc superconducting quantum interference device (SQUID) with the McCumber parameter βc=2πR2IcC/Φ0 close to the unity (where Ic, R, C are the critical current, the shunt resistance, and the capacitance of the Josephson junctions comprising the SQUID, respectively, and Φ0=2.07×10−15 Wb is the magnetic flux quantum) integrated with a planar spiral input coil have been experimentally studied. The length of the spiral input coil was chosen to match its λ/4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance enhances the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, increases the dynamic resistance Rd and the gradient of the flux-to-voltage characteristics ∂V/∂Φ without hysteresis. This relaxes the tolerance for the βc parameter, simplifies the technological process, and improves the yield of devices. A dc SQUID with loop inductance L=31.4 pH, βc=0.72, and a six turn input coil has demonstrated a nondistorted quasisinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of approximately 140 μV peak-to-peak. A spectral density of the intrinsic magnetic flux noise as low as 3.5×10−7 Φ0/Hz1/2 has been measured in the double stage configuration at a temperature of 4.2 K using direct read-out electronics. This corresponds to the intrinsic energy resolution of ε=12.5h. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz1/2 with an input coil inductance of 58 nH. The coupled energy resolution is εc=45h in the white noise region.
The forward scattering parameters of an amplifier based on a dc superconducting quantum interference device are directly measured at 4.2K as functions of the applied magnetic flux. These parameters are equivalent to the real and imaginary components of the input impedance and forward gain of the amplifier. The results can be described using an equivalent circuit model of the fundamental resonance of the microstrip resonator which forms the input of the amplifier. The circuit model is used to determine the series capacitance required for critical coupling of the microstrip to the input circuit.
The dynamics and noise of a dc SQUID (the Superconducting Quantum Interference Device), with the McCumber parameter /spl beta//sub c/=2/spl pi/R/sup 2/l/sub c/C//spl Phi//sub 0/ close to the unity (where I/sub c/, R, C is the critical current, the shunt resistance and the capacitance of the Josephson junctions comprising the SQUID, respectively, /spl Phi//sub 0/=2.07 10/sup -15/ Wb is the magnetic flux quantum) integrated with a planar spiral input coil, have been experimentally studied. The length of the spiral input coil was chosen so as to match its /spl lambda//4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance is found to enhance the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, to increase the dynamic resistance R/sub d/ and the gradient of the flux-to-voltage characteristics, /spl delta/V//spl delta//spl Phi/, without hysteresis. A dc SQUID with a loop inductance L=30.5 pH, /spl beta//sub c/=0.72, and a 6 turn input coil demonstrated a non-distorted quasi-sinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of 140 /spl mu/V peak-to-peak. The spectral density of the magnetic flux noise was as low as 3.5/spl times/10/sup -7/ /spl Phi//sub 0//Hz/sup 1/2/ in the double stage configuration, measured at a temperature 4.2 K using direct read out electronics. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz/sup 1/2/ with an input coil inductance of 100 nH.
Practical thin-film dc superconducting quantum interference devices (SQUIDs) are often built with an integrated input coil which leads to the formation of various parasitic elements. We have designed and fabricated several square washer-shaped dc SQUID test devices with various amounts of parasitic capacitance formed by covering the washer slits with superconducting coverplates of various widths. In the simplest approximation, the parasitic capacitance Cp appears entirely across the Josephson junctions; in a better approximation, Cp divides the total inductance into two parts, an effective SQUID loop inductance L and a small parasitic inductance Lp. For both models, noise-free and noise-rounded current-voltage and voltage-flux characteristics are calculated for various values of the ratios L/Lp and Cp/C, where C is the Josephson junction capacitance. The SQUID dynamics are significantly affected by Cp and Lp. The energy resolution ε at first deteriorates with increasing Cp for Cp/C ≲ 2, but as Cp/C becomes large, ε improves to less than twice the value for Cp/C ≊ 0. The optimal points of operation for large Cp, however, are found at voltages above the low-frequency resonance determined by L and Cp where the flux-to-voltage transfer function is low. Furthermore, for devices with Cp/C ≫ 1 and Lp≠0, the double-loop geometry leads to an additional resonance determined by Lp and C that appears at high frequencies. The energy resolution inside this high-frequency resonance is nearly independent of Cp and comparable to the energy resolution of a device having the same total inductance but with Cp/C ≪ 1. Extensive noise mappings on several different test devices have been carried out using a computer-controlled measurement system. The measured characteristics and noise performance are shown to be in good agreement with the simulations.