CAD model of high-Tc superconducting coplanar waveguide resonator on isotropic and anisotropic substrate

A closed form model of the effective dielectric constant of a coplanar waveguide (CPW) on anisotropic sapphire substrate is derived in a quasistatic approach using a perturbation method and the conformal mapping technique. A CPW high-Tc (HTS) resonator on isotropic and anisotropic substrates was modeled using a surface resistance model, a current distribution model, and a CPW gap model. The models were verified by measurements of temperature dependence of resonant frequency and insertion loss of HTS resonators on sapphire and MgO substrates.