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IEEE Transactions on Applied Superconductivity

Analysis of Nonlinearity in Step in Width Discontinuity of Superconducting Coplanar Waveguide Structures

Abolfazl Mostaani, Seyed Mohammad Hassan Javadzadeh

Published Apr 6, 2017• 2 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2017.2691582

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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.
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.
Superconducting planar circuits possess properties that can be very different from their normal-metal counterparts, which makes modeling efforts more complicated for superconducting components. In this paper we present closed-form expressions for the resistance and internal inductance per unit length of superconducting planar transmission lines in terms of the relevant material parameters. We also include a simple calculation of the nonlinear response of superconducting devices based on a current-dependent superconducting penetration depth. Taken together, these two descriptions can be used to predict the linear and nonlinear response of superconducting planar devices in a manner that is conducive to use in circuit design. The results of these calculations compare well with 76 K measurements of coplanar waveguide transmission lines and resonators fabricated from thin films of the high T/sub c/ superconductor YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta//.
We present a method for the numerical analysis of superconducting quantum circuits combining lumped elements, either linear or nonlinear (i.e., Josephson junctions), and distributed coplanar waveguide (CPW) structures. CPW transmission lines and multiline couplers are directly modeled without discretizing them into lumped-element equivalents, and the circuit Hamiltonian parameters are extracted by using the energy-participation ratio (EPR) method. This approach enables fast and accurate extraction of mode frequencies, anharmonicities, cross-Kerr interactions, and Purcell decay rates without relying on full electromagnetic simulations, while naturally accounting for higher-order modes of distributed components. We have implemented the proposed method in a Python framework, QuLTRA (Quantum hybrid Lumped and TRansmission lines circuits Analyzer), which we have used to validate the approach against full electromagnetic simulations (Ansys HFSS, pyEPR), existing circuit-analysis tools (QuCAT), and designs reported in the literature. The comparisons show excellent agreement with orders-of-magnitude reductions in computational time relative to full-wave solvers. We demonstrate applications including Purcell-protected readout, multimode ultrastrong coupling, and multiplexed qubit readout, illustrating how the method can support fast and reliable early-stage circuit design.
Superconducting coplanar waveguide (SCPW) resonators have a wide range of applications due to the combination of their planar geometry and high quality factors relative to normal metals. However, their performance is sensitive to both the details of their geometry and the materials and processes that are used in their fabrication. In this paper, we study the dependence of SCPW resonator performance on materials and geometry as a function of temperature and excitation power. We measure quality factors greater than 2 × 106 at high excitation power and 6 × 105 at a power comparable to that generated by a single microwave photon circulating in the resonator. We examine the limits to the high excitation power performance of the resonators and find it to be consistent with a model of radiation loss. We further observe that while in all cases the quality factors are degraded as the temperature and power are reduced due to dielectric loss, the size of this effect is dependent on resonator materials and geometry. Finally, we demonstrate that the dielectric loss can be controlled in principle using a separate excitation near the resonance frequencies of the resonator.
Superconducting coplanar-waveguide (CPW) resonators are one of the key devices in circuit quantum electrodynamics (cQED). Their performance can be limited by dielectric losses in the substrate and in the material interfaces. Reliable modeling is required to aid in the design of low-loss CPW structures for cQED. We analyze the geometric dependence of the dielectric losses in CPW structures using finite-element modeling of the participation ratios of the lossy regions. In a practical scenario, uncertainties in the the dielectric constants and loss tangents of these regions introduce uncertainties in the theoretically predicted participation ratios. We present a method for combining loss simulations with measurements of two-level-system-limited quality factors and resonance frequencies of CPW resonators. Namely, we solve an inverse problem to find model parameters producing the measured values. High quality factors are obtainable by properly designing the cross-sectional geometries of the CPW structures, but more accurate modeling and design methods for low-loss CPW resonators are called for major future improvements. Our nonlinear optimization methodology for solving the aforementioned inverse problem is a step in this direction.