Tunable microwave components based on dielectric nonlinearity by using HTS/ferroelectric thin films

This study provides the possibility of developing tunable microwave components based on the dielectric substrate nonlinearity, with the conducting surfaces made of a superconductor. The displacement vector, the dipole moment, polarization, polarizability, susceptibility, and relative permittivity concepts are used for ferroelectrics; and for superconductors, Bose statistics and the Gorter and the Casimir model for a two-fluid model, London's equations, and the classical skin effect for the normal component of the current are used. A sinusoidal wave solution is found for a planar superconducting transmission line. This solution gives expressions for the phase velocity and attenuation coefficient which are used to characterize the tunability of microwave components. The measured data in the literature have been used to compute the relative phase velocities and phase shift per cm versus temperature and the dc bias electric field E (kV/cm). It is shown that with a ferroelectric film of thickness of 140 nm, with /spl epsiv//sub /spl tau//=2/spl times/10/sup 3/ and tan /spl delta/=10/sup -3/ phase shifts and attenuation of the order of tens of degrees per centimeter and 5.76/spl times/10/sup -3/ dB/cm, respectively, at 10 GHz, can be obtained with tens of millivolts at 4 K.