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IEEE Transactions on Applied Superconductivity

Current Distribution and Kinetic Inductance of Coplanar Waveguide Transmission Lines

Mohammad Hossein Amini, Zahra Davoodi-Rad, Amirhossein Ghasemi, Mohsen Khaliliy, Alireza Mallahzadeh

Published Sep 2, 2022• 4 citations
Publisher

Abstract

Analysis of superconducting circuits requires knowledge of current density distribution in the film cross section. This article aims to investigate the current density distribution in superconducting coplanar waveguides (SCPWs), a basic component with increasing use in microwave integrated circuits. In this regard, first, the CPW is mapped to a pair of parallel plates and the vector potential is described through the Green's function concept. Then, based on the Green's function and utilizing London's second equation, an integral equation is formed which yields the current density distribution. The procedure is verified by COMSOL Multiphysics software. Examining the current density for several SCPWs shows that as the gap is reduced, the SCPW experiences much more current density especially at the edges. Based on the proposed procedure, the kinetic inductance of SCPW is examined, which is another focus of the article. In this article, for several CPWs with different aspect ratios, the kinetic inductance is evaluated and discussed. Results show that as the ratio is increased, the kinetic inductance is decreased.

DOI
10.1109/tasc.2022.3203029

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Analysis of superconducting circuits requires knowledge of current density distribution in the film cross section. This article aims to investigate the current density distribution in superconducting coplanar waveguides (SCPWs), a basic component with increasing use in microwave integrated circuits. In this regard, first, the CPW is mapped to a pair of parallel plates and the vector potential is described through the Green's function concept. Then, based on the Green's function and utilizing London's second equation, an integral equation is formed which yields the current density distribution. The procedure is verified by COMSOL Multiphysics software. Examining the current density for several SCPWs shows that as the gap is reduced, the SCPW experiences much more current density especially at the edges. Based on the proposed procedure, the kinetic inductance of SCPW is examined, which is another focus of the article. In this article, for several CPWs with different aspect ratios, the kinetic inductance is evaluated and discussed. Results show that as the ratio is increased, the kinetic inductance is decreased.
Several studies have been conducted on field solutions of superconducting planar transmission lines; however, no study has been performed on superconducting grounded coplanar waveguides (GCPWs) which is a promising element, from the viewpoint of immunity to electromagnetic interference, in superconducting circuits. The purpose of this article is to analyze the superconducting GCPW to achieve the electrical parameters of the transmission line. In this regard, first, the magnetic field within the superconducting film is described through a 2-D wave equation. By introducing the proper boundary conditions acquired through the field solution of the structure, the proposed wave equation is solved and the magnetic field is obtained. Accordingly, the current distribution and the inductance of the line are evaluated which are of interest in the superconducting community. Compared with conventional coplanar waveguide (CPW), the GCPW structure experiences less current density at the edges. Hence, it supports a much more sustainable current. Further, it is shown that the GCPW exhibits less kinetic inductance during data transmission.
In this paper, the nonlinearity in superconducting coplanar waveguides (SCPWs) with step in width discontinuities has been analyzed using a distributed nonlinear circuit model. In such structures, nonlinearities depend on the current distribution of the central strip of the SCPW. A numerical electromagnetics approach based on the method of moments, which analyzes high-frequency planar circuits, determines the current distribution. This is used to obtain the nonlinear circuit elements of a discontinued SCPW structure. The equivalent nonlinear circuit model can be solved using the harmonic balance method as has been done in an example of a step in width SCPW. The accuracy of the model is shown by comparison of results from an experiment for a SCPW transmission-line structure. Moreover, all different types of step discontinuities in a SCPW have been compared and the efficient structure, which has the minimum nonlinearity has been defined.
Advancements in the fabrication of superconducting quantum devices have highlighted tantalum as a promising material, owing to its low surface oxidation microwave loss at low temperatures. However, tantalum films exhibit significantly larger kinetic inductances compared to materials such as aluminum or niobium. Given the inevitable variations in film thickness, this increased kinetic inductance leads to considerable, uncontrolled frequency variances and shifts in components like superconducting coplanar waveguide (SCPW) resonators. Achieving high precision in resonator frequencies is crucial, particularly when multiple resonators share a common Purcell filter with limited bandwidth in superconducting quantum information processors. Here, we tackle this challenge from both fabrication and design perspectives, achieving a reduction in resonator frequency fluctuation by a factor of more than 100. Concurrently, the internal quality factor of the SCPW resonator remains at high level. Our findings open up new avenues for the enhanced utilization of tantalum in large-scale superconducting chips.
An analytical expression for the kinetic inductance of the superconducting coplanar waveguide is given using the conformal mapping technique. This expression is shown to be in good agreement with experimental results obtained from the temperature dependence of the resonant frequency of the NbN coplanar waveguide resonators, especially in the case of a film thickness smaller than the magnetic penetration depth. It is also shown that the magnetic penetration depth of the superconducting thin films can be evaluated by this method.
Abstract We measured the microwave transmission characteristics of coplanar waveguides (CPWs) fabricated using YBa2Cu3O7−δ (YBCO) thin films with DC current biases. Kinetic inductances ( L K ) and nonlinear parameters ( I * ) were evaluated for CPWs with film thicknesses of 20, 50, and 200 nm. The results indicate that the experimental values closely follow the second-order nonlinearity exhibited by the L K . To operate as a superconducting parametric amplifier with a standard gain of 20 dB and a pump power of −10 dBm, we introduced a step-impedance structure into the transmission line. As a result, when using an MgO substrate, the required line length was estimated to be approximately 1.25 m, corresponding to approximately 29 times the wavelength of the CPW.
Abstract We fabricated a coplanar waveguide (CPW) using high temperature superconductor YBa2Cu3O7-δ (YBCO) and evaluated its characteristics for the realization of a superconducting parametric amplifier. A YBCO thin film with a film thickness of 200 nm was formed by the PLD method using a YAG laser on a 10 × 10 mm MgO substrate. The YBCO thin films were processed into the CPW shape with a line width of 8 μm, a gap width of 8 μm and a line length of 5 mm by photolithography and sputter etching. Using a network analyzer, phase differences of microwave were measured at dc current bias from 0 mA to 14 mA. From the measurement results, it was found that the phase difference decreased with increasing temperature. In addition, it was found that the phase shifts greatly varied near the superconducting transition temperature at each current bias. We observed a maximum phase difference Δθ of -0.08 rad at a bias current of 14.0 mA, which is the closest to the transition temperature. A parametric gain was estimated to be 0.15 dB from the measured maximum phase difference.