Modeling of frequency response in vortex state of high temperature superconducting microstrip and slotline

A modeling technique to study the frequency response of electromagnetic signal fed to High Temperature Superconducting (HTS) microstrip and slotline exposed to a constant dc magnetic field is presented. The computation is done for a temperature close to the critical temperature where the vortex effects significantly influence the signal propagation. The flux related effects are modeled using a modified two-fluid theory proposed by Coffey and Clem (CC). The complex penetration depth obtained by CC model is used to derive a complex resistive boundary condition which, in turn, incorporates the HTS effects and modifies the dyadic Green´s functions derived for microstrip and slotline using Spectral Domain Method (SDM). The propagation parameters are obtained using Galerkin procedure for a wide range of applied dc field and microwave signal frequency. Both the strip lines are of same geometrical dimensions for a comparative study. Phase constant of the signal varies with signal frequency whereas the attenuation constant is largely influenced by vortex movements. The study presents a comparative modeling method for microstrip and slotline and relates vortex physics with microwave signal propagation for a wide range of applied dc field and signal frequency.