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Applied Physics Letters

Numerical modeling of superconducting coplanar resonators for radio frequency superconducting quantum interference devices

H. R. Yi, Yanwen Zhang, A. I. Braginski

Published Oct 19, 1998• 6 citations
Publisher

Abstract

We have simulated the superconducting coplanar resonators of different designs that we have fabricated and tested as the tank circuit of radio frequency superconducting quantum interference devices. The coplanar resonator is formed by two microstrip lines surrounding a flux concentrator with each line having a slit. The simulated resonant frequencies agreed well with the experimental values, where frequencies decreased with an increasing mutual angular position between the two microstrip slits, and with a short circuit between the two microstrip lines. The simulation also showed that the loss in the system is mainly contributed by the dielectric loss of the substrate materials.

DOI
10.1063/1.122460

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We have simulated the superconducting coplanar resonators of different designs that we have fabricated and tested as the tank circuit of radio frequency superconducting quantum interference devices. The coplanar resonator is formed by two microstrip lines surrounding a flux concentrator with each line having a slit. The simulated resonant frequencies agreed well with the experimental values, where frequencies decreased with an increasing mutual angular position between the two microstrip slits, and with a short circuit between the two microstrip lines. The simulation also showed that the loss in the system is mainly contributed by the dielectric loss of the substrate materials.
We have developed a novel coplanar resonator serving as a tank circuit for radio frequency washer superconducting quantum interference devices (SQUIDs). Two coplanar lines surrounded the circular flux concentrator washer, 13.4 mm in diameter. The SQUID, 3.5 mm in diameter, was coupled to the concentrator in the flip-chip configuration. All parts were fabricated from single-layer epitaxial YBa2Cu3O7 films on LaAlO3 substrates. In this layout, the resonant frequency could be set between 600 and 850 MHz. With SQUID loops of 100×100 μm2 (SQUID) inductance Ls=150 pH or 10×500 μm2 (Ls=260 pH), we determined at 77 K white flux noise levels Sφ1/2 of 1.0×10−5 and 1.5×10−5φ0/Hz, respectively. Both figures corresponded to the field resolution of about 30 fT/Hz.
At present, the high-transition-temperature radio frequency superconducting quantum interference device (High- T c RF SQUID) is usually coupled to a dielectric resonator which is a standard 10 mm×10 mm× 1 mm SrTiO3 (STO) substrate with a YBa2Cu3O7-δ (YBCO) thin-film flux focuser deposited on it. The dielectric resonator for the High- Tc RF SQUID has a high quality factor and a resonant frequency in the microwave range. In order to find out the effect of the flux focuser’s geometry on the dielectric resonator’s resonant frequency, we used ANSOFT high frequency structure simulator (ANSOFT HFSS) to simulate the resonance characteristics of some dielectric resonators with different flux focuser geometries. Our simulation results show that when the width of the flux focuser’s slit increases or the radius of the flux focuser’s inner hole decreases, the dielectric resonator’s resonant frequency increases. To estimate the reliability of our simulation results, we selectively prepared a few dielectric resonators and measured their resonance characteristics. The experimental results are virtually consistent with the simulation results. Our study shows that changing the flux focuser geometry is an effective way to adjust the dielectric resonator’s resonant frequency.
The analysis of the structure of a superconducting multiturn flux transformer integrated with a coplanar resonator for radio-frequency superconducting quantum interference devices is described. Electromagnetic simulations indicate that the loss is dominated by the high loss tangent of the dielectric film used for the separation of the upper and lower superconducting films. The simulated current distribution at its resonant frequency shows that the highest current density is distributed on the multiturn input coil. This current distribution leads to a very high loss when the loss tangent of the dielectric film is high. However, for the same loss tangent of the dielectric film, it is possible to get a reasonably high unloaded quality factor by providing a normal shunt for the multiturn input coil.
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 coupling coefficient (k/sup 2/) between the superconducting coplanar resonator and the flip chip coupled washer radio frequency SQUID was calculated using computer simulation. The coplanar resonator is formed by two coplanar lines surrounding a flux concentrator with each line having a slit. For a 3 mm/spl times/3 mm washer SQUID with a 100 /spl mu/m/spl times/100 /spl mu/m loop coupled to a coplanar resonator with the slits on opposite sides, we estimated k/sup 2/=7.1/spl times/10/sup -3/. However, if the same SQUID is coupled to a coplanar resonator with parallel slits and with a short circuit at the 90/spl deg/ position with respect to the opening slit, k/sup 2/ of only 0.5/spl times/10/sup -3/ is obtained, which indicates that the k/sup 2/ is strongly dependent on the resonator layout. The simulation also shows that k/sup 2/ is dependent on the SQUID washer size and the separation distance between the washer SQUID and the coplanar resonator.
We developed a novel magnetic coupling module, formed of a monolayer superconducting flux concentrator that is integrated with a coplanar resonator, strongly coupled to high-temperature superconducting radio frequency superconducting quantum interference device (SQUID). Three types of resonators, including a long stripline resonator between the input loop and the pick-up loop of the flux concentrator, a complementary split ring resonator, and a spiral shape inside the input loop, are explored. The resonance quality factor of different patterns of these three types of the resonators, as well as their coupling to the SQUID, is evaluated using finite-element-method simulations. Several readout methods are tested to couple the electronic system to the resonators by inductive (coil) or capacitive (transmission line) methods, and the optimum readout is reported for each of the resonators. Among the evaluated resonator types, a spiral shape with an optimal behavior at the resonance frequency of 836 MHz, showing the highest quality factor together with the strongest coupling to the SQUID, compared to other types of the resonators, is fabricated using a 200-nm-thick YBCO film on a 1-mm-thick crystalline LaAlO3substrate. The flux concentrator of the module is optimized by the variation of the linewidth of its different parts and also its input loop radius to obtain the maximum flux transformation efficiency.