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Japanese Journal of Applied Physics

Noise Characteristics of dc Superconducting Quantum Interference Device with Additional Positive Feedback

Youichi Takada, Gen Uehara Kado

Published Dec 1, 1994• 3 citations
Publisher

Abstract

We investigated the flux noise characteristics of a superconducting quantum interference device (SQUID) with additional positive feedback (APF) by comparing calculated results with experimental results. Equations for the minimum flux noise of a SQUID with APF and the optimum condition of APF gain (βa) are deduced. We examined the relationship of flux noise versus βaand experimentally confirmed that it has a minimum point. The deduced equations agree well with experimental results. From the viewpoint of total flux noise of SQUID, it is useful to employ the APF technique for a low-intrinsic-noise SQUID, but not for a high-intrinsic-noise SQUID.

DOI
10.1143/jjap.33.l1665

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We investigated the flux noise characteristics of a superconducting quantum interference device (SQUID) with additional positive feedback (APF) by comparing calculated results with experimental results. Equations for the minimum flux noise of a SQUID with APF and the optimum condition of APF gain (βa) are deduced. We examined the relationship of flux noise versus βaand experimentally confirmed that it has a minimum point. The deduced equations agree well with experimental results. From the viewpoint of total flux noise of SQUID, it is useful to employ the APF technique for a low-intrinsic-noise SQUID, but not for a high-intrinsic-noise SQUID.
The relationship between superconducting quantum interference device (SQUID) voltage swing and additional positive feedback (APF) parameters has been investigated. Voltage swing is depressed as APF gain increases. In a symmetric-bias-injection SQUID, the voltage depression can be explained by the voltage divider action of APF resistance and the SQUID dynamic resistance. On the other hand, the voltage depression in an asymmetric-bias-injection SQUID is expressed as the effect of the voltage divider action multiplied by the effect of thermal noise of APF resistance. These two effects should be considered when designing SQUIDs with an APF.
Distortion of voltage versus flux (V–Φ) relation of a dc superconducting quantum interference device (SQUID) coupled to a multiturn input coil is studied. First, resonant behavior of the coupled SQUID due to the so-called input coil resonance is clarified. It is shown that large rf noise flux is produced by the input coil resonance. This rf flux is added to the SQUID, and results in large rf voltage across the SQUID. In the case where parasitic capacitance exists between the input coil and the ground of the SQUID, this rf voltage produces the rf flux again, i.e., a feedback loop for the rf flux is formed. Taking into account this capacitive feedback, we study the V–Φ relation of the coupled SQUID. Numerical simulation shows that the V–Φ relation is distorted considerably by the feedback mechanism. The simulation result explains well the experimental V–Φ relation of the coupled SQUID. The combination of the input coil resonance with the capacitive feedback is the most likely mechanism for the distorted V–Φ curve of the coupled SQUID. The condition for occurrence of the distorted V–Φ curve due to the capacitive feedback is also obtained, and methods to prevent degradation are discussed.
The flux noise in a long superconducting quantum interference device (SQUID) array consisting of at least 100 dc-SQUID elements connected in series was characterized analytically, and then compared with measurements. In the analysis, noise sources in the array were shunt resistors for Josephson junctions, a damping resistor for a SQUID loop, the dynamic resistance of the SQUID array, and the noise of electronics at room temperature. The flux noise of the array was calculated analytically as a function of the number of dc-SQUID elements. The results reveal that the flux noise is significantly influenced by the dynamic resistance of the array, although the influence by the dynamic resistance for a single SQUID is negligibly small. The dynamic resistance becomes dominant for the flux noise when the number of SQUID elements in the array exceeds 100. These results agree well with the measured flux noise for a long SQUID array constructed using a Nb/AlO x /Nb fabrication process.
Effects of thermal noise on the characteristics of the dc superconducting quantum interference device (SQUID) have been studied. Numerical simulation on the SQUID characteristics operating at T=77 K has been performed by taking into account the thermal noise. It is shown that the voltage versus flux relation of the dc SQUID is degraded considerably with the thermal noise. The degradation becomes significant when the inductance of the SQUID increases. Due to this degradation, there exists significant limitation for the range of the inductance available at T=77 K, unlike the case at T=4.2 K. The maximum inductance should be around 200 pH in order to avoid significant degradation of the transfer function. This limited value of the inductance must be taken into account when we realize the SQUID coupled to an input coil. The analytical expression for the degradation of the transfer function due to the thermal noise is also obtained. The theoretical result explains experimental results reported recently.
We investigate niobium thin film superconducting quantum interference devices (SQUIDs) with different Steward—McCumber parameters βc operated in both current- and voltage-bias modes. We experimentally prove that there is no difference between the two bias modes with respect to the SQUID intrinsic noise and the noise contribution from the preamplifier. Furthermore, the relationships of the SQUID dynamic parameters, (Rd)current bias ≈ (Rd)voltage bias and (∂V/∂Φ)current bias ≈ [(∂i/∂Φ)Rd]voltage bias, are always satisfied. For a strongly damped SQUID with βc ≈ 0.25, additional positive feedback (APF) and noise cancellation (NC) were employed to enhance ∂V/∂Φ, the former showing a degradation in the linear flux range but otherwise the same with NC. For a weakly damped SQUID with βc ≈ 3, it is directly connected to the preamplifier without APF or NC, and a low SQUID system noise of about 4 μΦ0/√Hz is measured, which is close to its intrinsic noise.
Noise characteristics of dc SQUIDs in large β regimes have been studied experimentally in the case when a SQUID inductance is resistively shunted. Here, β=2L I 0/Φ0 is the modulation parameter, L is the SQUID inductance, I 0 is the critical current of the Josephson junction and Φ0 is the flux quantum. It is shown experimentally that the performance of the SQUID does not degrade significantly even for large β values; for example, the minimum energy resolution of the SQUID is as small as ε=25h and the flux region where ε<50h is as wide as 0.1Φ0, even for the case β=12, where h is the Planck constant. The experimental results agree quantitatively with the theoretical ones.