Property calculations of a superconducting coplanar waveguide resonator

We present calculations of the properties of the first coplanar waveguide transmission line resonators patterned from high-T_c superconducting films at 8.8 and 6.5 GHz [1, 2]. Based on field calculations of the corresponding coplanar waveguides with infinite conductivity, performed by a partial wave synthesis (mode-matching method) [3], we obtain the superconductor losses subsequently using London's theory. Due to the high conductivity of the superconductive material both the electric and magnetic fields within the superconductor may be assumed to be parallel to the surface planes. For the small conductor thickness the tangential electrical field on each surface plane depends on the tangential magnetic fields on both surface planes. This relation is modelled by the surface impedance matrix Z_s. The substrate losses are treated in the field calculations and are also taken into account. The calculated overall Q values are compared with the measured values and it has to be pointed out, that the superconducting thin films are due to the available material datas of the YBaCuO superconductor and the used substrate materials of a very good quality, because they reach nearly their upper limit given by the known material datas.