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Superconductor Science and Technology

Simulation and comparison of the influence of metal on the tank circuits of rf SQUIDs

Dongfeng He, Hideo Itozaki

Published Mar 7, 2006• 1 citation
Publisher

Abstract

In rf SQUID operation, nearby metal may influence the field distribution and the resonant frequency of the tank circuit, and then cause low frequency noise in the rf SQUID. Using an electromagnetic simulation method, we analysed the influence of metal on the resonant frequencies of three kinds of tank circuit: coplanar resonator, dielectric resonator and lumped-element tank circuit. The simulation results show that metal has the biggest influence on the coplanar resonator and the smallest influence on the dielectric resonator. This is why the high-Tc rf SQUID with a dielectric resonator has less low frequency noise than that with a coplanar resonator.

DOI
10.1088/0953-2048/19/4/029

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In rf SQUID operation, nearby metal may influence the field distribution and the resonant frequency of the tank circuit, and then cause low frequency noise in the rf SQUID. Using an electromagnetic simulation method, we analysed the influence of metal on the resonant frequencies of three kinds of tank circuit: coplanar resonator, dielectric resonator and lumped-element tank circuit. The simulation results show that metal has the biggest influence on the coplanar resonator and the smallest influence on the dielectric resonator. This is why the high-Tc rf SQUID with a dielectric resonator has less low frequency noise than that with a coplanar resonator.
Characteristics of a lumped element L-C tank circuit resonator of high-Tc rf-SQUIDs, which plays an important role in the device operation, have been experimentally investigated, according to the corresponding simulations obtained by COMSOL Multiphysics. We experimentally investigated the characteristics of the resonators by measuring their scattering parameters, as well as evaluating the rf-SQUID signal. Our SQUIDs are made of sputtered YBCO thin films with 3-mm-diameter washer areas. Different configurations of the resonator are investigated, and it is observed that, by increasing the thickness of the dielectric in a specific range, the reflection coefficient (S11) increases. For the experimental verifications, we constructed resonators with different dielectric thicknesses and different configurations. The resonators are made of a dielectric board with a hole in its middle to hold the inductors for close coupling to the SQUID mounted on the backside. An increase in the thickness of the dielectric board confines the RF field distribution close to the SQUID, while also making further distance between the contact pads and the SQUID reducing their parasitic effects on the device signal. This is observed to improve the stability of the operating point of the SQUIDs, while also reducing the noise for measured frequency range of 0.1 to 100 Hz.
We have developed a matching scheme for the operation of a rf superconducting quantum interference device (SQUID) with a lumped-element tank circuit at pumping frequencies up to 1 GHz. This conventional LC resonant circuit is inductively coupled to a matching coil, which is connected to the 50 Ω transmission line. We characterized the flux noise of high-temperature rf SQUIDs at resonant frequencies between 221 and 950 MHz. At about 900 MHz, we obtained the white flux noise of about 14.6 μφ0/Hz with a SQUID inductance LS=150 pH and 20 μφ0/Hz with LS=260 pH. Several of such tank circuits can be driven in parallel or in series with only one cable.
We simulate the dielectric SrTiO3 (STO) resonator for radio frequency superconducting quantum interference devices (rf SQUIDs) using electromagnetic analysis software. The simulated values of the resonant frequencies, the unloaded quality factor, the loaded quality factor under 50Ω matching, and the coupling with the SQUID are in good agreement with the experimental results. The simulation also shows that the strength of the electromagnetic field outside the resonator decreases exponentially with the distance from the resonator, which proves that the field is confined to a small volume near the resonator. Due to the strong temperature dependence of the permittivity of STO, the resonant frequency changes with the temperature fluctuations of liquid nitrogen, which may cause the low frequency noise of rf SQUIDs with dielectric resonators.
Understanding the coupling mechanism between SQUID (superconducting quantum interference device) loop and resonator in high-frequency SQUIDs is essential for the application of these devices in sensitive magnetometers or controllable microwave devices. We have investigated, therefore, two kinds of planar microstrip tank circuit resonators: (1) S-shaped λ/2-resonators with direct or indirect coupling to the SQUID loop with optional flux-focussing pads and (2) conventional rf-washer-SQUID structures for which we have found resonant modes of the washer providing a coupling to the SQUID loop. A lumped element representation of SQUID loop and resonator is presented in order to describe the effective SQUID-resonator coupling in case of direct or indirect coupling. According to this approach, the square of the effective coupling constant k in both cases is equal to the ratio of the magnetic energy stored in the SQUID loop to that stored in the resonator. For the indirect coupled S-shaped λ/2-resonators, k can be described in terms of a geometry-defined mutual inductance. The predictions of the lumped element description are compared with simulations using a standard full-wave analysis computer program in order to quantify the effect of the different layouts on microwave current distribution and on k. A method for the determination of k by simulation is described, leading to useful design rules for the optimization of high-frequency SQUIDs. The simulation results will also be compared with experimental data.
The dc -impedance of an rf-biased R-SQUID is studied analytically for the nonhysteretic regime. A mathematical analysis of the intrinsic behavior of an R-SQUID, including the mutual interaction between the tank circuit and the SQUID loop, is presented. The results obtained give good agreement with some experimentally observed features. Although the main aim of the present paper was to find an analytic solution for the dc -impedance of an R-SQUID, the results given here can also be used to estimate the R-SQUID parameters and to optimize the performance of a R-SQUID noise thermometer. The theory presented here also provides a good basis for modelling the noise properties of a Josephson junction noise thermometer.
A number of applications of high-temperature superconductor radio frequency superconducting quantum interference devices (rf SQUIDs) require a certain immunity of these sensors against electromagnetic interference (EMI). We have investigated effects of electromagnetic radiation in the high-frequency and ultrahigh-frequency range on various types of rf SQUIDs. It has been found that EMI of sufficient field strength reduces the voltage versus flux transfer function, and thus increases the flux noise of the SQUIDs. SQUIDs with a wire wound tank circuit coil have been found to be more sensitive to EMI than SQUIDs integrated into a superconducting microstrip resonator.