An analytical solution of the London equation for the weakly coupled grain model of high Tc superconducting thin films has been obtained in the case of finite thickness by taking full account of anisotropic conductivities. Using the solution, we provide general expressions for the transmission-line parameters of high Tc superconducting transmission lines. Dependences of the inductance and resistance on the grain size, coupling strength and film thickness have been numerically evaluated and discussed.

The complex conductivities of high Tc superconducting YBa2Cu3Ox thin films have been studied using the coplanar waveguide resonator technique. In order to evaluate the magnetic penetration depth precisely, we measured the temperature dependence of the resonant frequency and compared it with the numerical results self-consistently. The observed temperature dependence of the complex conductivities is shown to be able to distinguish the effects of the weaklink from the intrinsic property of the grain of an epitaxial thin film and demonstrate the weakly coupled grain model of YBa2Cu3Ox thin films.

In order to explain the temperature and frequency characteristics of high-Tc superconductors, a new model is proposed, which will be called the improved three-fluid model, where the momentum relaxation time τ is assumed to depend on temperature in the superconducting and normal states, respectively, although τ has been assumed to be independent of temperature for the conventional three-fluid model. According to this model, the complex conductivity σ1jσ2 and the surface impedance ZsRsjXs, where Rs is the surface resistance and Xs is the surface reactance, are expressed as a function of temperature. The temperature dependences of Zs and for a YBCO bulk estimated using this model agree very well with ones measured by the dielectric-loaded cavity method in room to cryogenic temperature. In particular, a peak of σ1 observed just below the critical temperature Tc in experiments, appeared in the calculated results based on this model. This phenomenon has been already known in the BCS theory. Thus, it is verified that this model is useful to explain the microwave characteristics of high-Tc superconductors in room to cryogenic temperature. On the other hand, the residual normal electron density nres4.2541023 m-3 and the total electron density nt7.3081024 m-3 are obtained by calculation. The ratio nres/nt0.058 can be used as figure of merit to evaluate material quality of high-Tc superconductors; thus it means that there is 5.8% nonpairing electron in this YBCO bulk.