Closed Form Formulas for Distributed Circuit Model of Discontinuities in HTS Microstrip Transmission Lines

Abstract

A distributed circuit model for different kinds of discontinuities in high temperature superconducting (HTS) microstrip transmission lines (TLs), is proposed. In each case, closed form formula for lumped element model is presented based on the configuration of the discontinuity and the characterizations of HTS microstrip TLs. These discontinuities consist of steps in width, open ends, gaps and 90-degree bends. In the case of normal conductor microstrip TLs there are a lot of numerical and analytical equations that can accurately model them, however those formulas are not efficient for HTS TLs. Thus modified relations are extracted utilizing the superconducting characterizations to obtain much more accurate formulas. Additionally temperature dependence of HTS TLs is considered in the relations. Moreover regarding the kinetic inductance in HTS TLs a closed form formula is proposed for characteristic impedance of HTS TLs. Furthermore correction factors based on fringe fields is used to optimize all formulas. Using these formulations can lead to modeling and analysis of some superconducting microwave devices such as resonators, microwave filters, couplers, etc. In contrast to EM analysis, using the distributed circuit model is much easier for analysis of HTS microwave devices. The accuracy of the proposed model is confirmed in comparison with some electromagnetic full-wave simulations. This full analytical approach shows great accuracy in this test case as well.