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Journal of Applied Physics

Noise characteristics of a dc SQUID with a resistively shunted inductance. II. Optimum damping

Keiji Enpuku, Keiji Yoshida, Satoshi Kohjiro

Published Dec 15, 1986• 66 citations
Publisher

Abstract

Effects of a damping resistance on noise characteristics of a dc SQUID are studied theoretically, where the damping resistance is in shunt with a loop inductance of the SQUID. An analytical expression for the energy resolution of the SQUID is obtained, with which the relation between the damping resistance and the energy resolution is studied in detail. It is shown that an optimum value of the damping resistance exists, which is determined by the tradeoff between the improvement of the transfer function and the additional noise due to the damping resistance. Optimum values of the damping resistance are about twice the shunt resistance of the SQUID and vary slightly with SQUID modulation parameter β. For optimum damping, the energy resolution is improved, compared with the case without the damping resistance. This means that the SQUID with large β can be used without significant degradation of the performance, i.e., the previous restriction of β=1 can be loosened. The analytical results agree quantitatively with numerical ones.

DOI
10.1063/1.337510

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Chinese Physics•Mar 1, 2005•0 citations
Effects of a damping resistance on noise characteristics of a dc SQUID are studied theoretically, where the damping resistance is in shunt with a loop inductance of the SQUID. An analytical expression for the energy resolution of the SQUID is obtained, with which the relation between the damping resistance and the energy resolution is studied in detail. It is shown that an optimum value of the damping resistance exists, which is determined by the tradeoff between the improvement of the transfer function and the additional noise due to the damping resistance. Optimum values of the damping resistance are about twice the shunt resistance of the SQUID and vary slightly with SQUID modulation parameter β. For optimum damping, the energy resolution is improved, compared with the case without the damping resistance. This means that the SQUID with large β can be used without significant degradation of the performance, i.e., the previous restriction of β=1 can be loosened. The analytical results agree quantitatively with numerical ones.
Noise characteristics of a dc SQUID with an inductance shunted by a damping resistance are studied numerically. It is shown that the damping resistance improves considerably the resolution of the SQUID in the case of large β, where β=2LI0/Φ0, I0 is a critical current, L is a loop inductance and Φ0 is the flux quantum. The energy resolutions for β=4 and β=10 are only about 2 and 4 times larger than that for β=1, respectively. Furthermore, the ranges of both the bias current and the external flux, where good resolution is obtained, become very wide compared with the conventional SQUID. Therefore, the SQUID with the damping resistance can be used for large β (or L) without the significant degradation of the resolution, and will much improve the coupling properties between the SQUID and the input circuitry. The numerical simulation results are also compared with analytical ones, and a reasonable agreement is obtained.
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.
The conversion efficiency between a signal magnetic flux and the output power of a large-β dc SQUID, i.e., a SQUID with a modulation parameter β larger than unity, have been studied theoretically. In our investigation the inductance of the SQUID was shunted by using a damping resistor. The dependence of the output power on such SQUID parameters as β, the McCumber parameter βc and the damping parameter γ=R s /R d (R s and R d are the shunt and the damping resistances, respectively) was investigated in detail. It has been shown that an order-of-magnitude increase in the output power can be realized with a large-β SQUID without a degradation of noise characteristics, compared with the case of β=1. It has also been shown that the values of βc=0.4 and γ=1 are optimum with regard to a large output power and a low-noise operation of the SQUID.
We have fabricated and characterized the noise performance of well-coupled Nb-Pb alloy edge junction dc superconducting quantum interference devices (SQUIDs) with a resistively shunted inductance. The extra damping resistor removes the resonances in the current-voltage characteristics resulting in a very low value of the extrinsic energy sensitivity in flux-locked-loop operation. Numerical simulations, with the junction capacitance included, indicate that the damping resistance does not degrade noise performance until it is significantly less than the junction-shunting resistance. We also tested different SQUID designs and demonstrated that a large SQUID inductance, proposed earlier to be desirable when resistively shunted, can seriously affect the low-frequency flux noise.
The noise characteristics of a large- beta DC SQUID (superconducting quantum interference device) have been studied experimentally in the case where the SQUID inductance is resistively shunted. Energy resolutions of the SQUIDs, epsilon , have been measured for various beta values up to beta =19. It is shown experimentally that the energy resolution of these large- beta SQUIDs is as small as that of the conventional SQUID with beta =1. For example, an energy resolution of 25h was obtained for beta =12 (L= 340 pH and I/sub 0/=37 mu A), where h is Planck's constant. The experimental results agree quantitatively with theoretical ones. It is also shown that the present resistivity shunted inductance scheme is very useful in developing SQUIDs operating at T=77 K with high-T/sub c/ superconductors, where the value of beta will necessarily be large in order to avoid noise effects. Numerical simulations of the performance of the high-T/sub c/ SQUID are presented.>
An analytical expression for the stationary probability distribution of the DC superconducting quantum interference device (SQUID) with a resistively shunted inductance driven by thermal noise is derived from the two-dimensional Fokker–Planck equation. The effects on the SQUID characteristics subject to a large thermal fluctuation with a noise parameter Γ>0.20 are discussed by taking into account the thermal noise in the accuracy of numerical simulation. This theory is valid for a reduced inductance β⩽1. The analytical formulae for the SQUID characteristics, e.g. the circulating current, the average voltage and the voltage modulation, are obtained and discussed. The theory shows that the voltage modulation increases with the shunted inductance more efficiently for a large inductance parameter β and small fluctuation parameter Γ.