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.