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Journal of Applied Physics

Modeling the dc superconducting quantum interference device coupled to the multiturn input coil

Keiji Enpuku, Keiji Yoshida

Published May 15, 1991• 34 citations
Publisher

Abstract

In order to study the effect of a multiturn input coil on superconducting quantum interference device (SQUID) characteristics, the radio frequency (rf) properties of the coupling circuit between the SQUID coil and the input coil are studied. For the measurement of rf properties of the coupling circuit, the so-called expanded model of the coupling circuit using normal metals was adopted, which is shown to be very useful for this purpose. It is shown that the SQUID coil cannot be expressed by a simple inductance when the SQUID coil is coupled to the input coil, i.e., many resonant structures are observed in rf properties of the coupling circuit. It is also shown that the damping resistance is useful in suppressing the resonant structures. Using the experimental results, a circuit model of the SQUID coupled to the multiturn input coil is proposed.

DOI
10.1063/1.347576

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Review of Scientific Instruments•Mar 1, 1999•9 citations
In order to study the effect of a multiturn input coil on superconducting quantum interference device (SQUID) characteristics, the radio frequency (rf) properties of the coupling circuit between the SQUID coil and the input coil are studied. For the measurement of rf properties of the coupling circuit, the so-called expanded model of the coupling circuit using normal metals was adopted, which is shown to be very useful for this purpose. It is shown that the SQUID coil cannot be expressed by a simple inductance when the SQUID coil is coupled to the input coil, i.e., many resonant structures are observed in rf properties of the coupling circuit. It is also shown that the damping resistance is useful in suppressing the resonant structures. Using the experimental results, a circuit model of the SQUID coupled to the multiturn input coil is proposed.
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.
Properties of washer resonances in dc superconducting quantum interference devices (SQUIDs) coupled to a multiturn input coil have been studied using an expanded model of the coupled SQUID. The condition of resistances required to suppress the washer resonance is clarified. In the coupled SQUID, junction shunt resistances should be determined by taking into account this condition in addition to the conventional condition βc<1, where βc is the McCumber parameter. In the case of small junction capacitances, it is shown that the washer resonance limits the value of junction shunt resistances, and prevents the use of large resistances given by βc<1. In order to solve this problem, a new washer geometry of the SQUID is proposed. From the experiment using the expanded model of the new washer, it is shown that the new washer can control the washer resonances, and enables the use of large resistance in the coupled SQUID. Therefore, the new washer will be useful for the improvement of the performance of the coupled SQUID.
Arrays of dc-superconducting quantum interference devices (dc-SQUIDs) were investigated, in which each dc-SQUID element has a multiturn input coil. The dependence of flux noise on the number of turns of the input coil was studied for current amplifiers. SQUID arrays were fabricated by a Nb/AlO x /Nb Josephson tunnel junction fabrication process. Results show that the flux noise of the SQUID array amplifier does not depend on the turn number of the input coil. A SQUID array amplifier consisting of 128 dc-SQUID elements was fabricated, in which each element had a 7-turn input coil and a mutual inductance between the input coil and the SQUID loop of 460 pH. This amplifier showed an ultrahigh current resolution of 1 pA/Hz0.5 and a maximum input current of 11 µA for signals of 50 kHz, which is sufficient bandwidth for X-ray detection applications. These values correspond to a large dynamic range of 87 dB. The flux-voltage characteristics of this SQUID array, however, showed asymmetric behavior, which originated from electronic resonance in stray capacitance and the mutual inductance between the SQUID loop and the multiturn input coil.
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.
This article describes three planar layouts of superconducting multiturn flux transformers integrated with a coplanar resonator for radio frequency (rf) superconducting quantum interference device (SQUID) magnetometers. The best magnetic field noise values of 22 and 11.5 fT/Hz1/2 in the white noise regime were obtained for the layout with two input coils and the layout with the labyrinth resonator, respectively. Excess low-frequency noise (about 200 fT/Hz1/2 at 10 Hz) was present. Computer simulation showed that the loss in this trilayer system was dominated by the high loss tangent of the dielectric film used for the separation of the upper and lower superconducting films. The rf coupling coefficient krf between the resonator and the flip-chip-coupled SQUID was also estimated. The values krf2≈14×10−3 obtained for the layout with two input coils, and krf2≈45×10−3 for the layout with the labyrinth resonator were considerably higher than the typical value of krf2≈7×10−3 for the single-layer coplanar resonator. These high coupling coefficients have compensated the somewhat degraded unloaded quality factor of the resonator, thus securing the optimum operation of the rf SQUID.
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.