Characteristics of smooth and periodic HTS coplanar resonators on ferroelectric/dielectric substrates

Characteristics of smooth and periodic (consisting of sections with different dimensions) high temperature superconducting (HTS) thin film coplanar waveguide (CPW) resonators with a ferroelectric component were calculated. Frequency tunability and microwave (MW) losses of the structure were analyzed using the obtained formulas. It was shown that for the ferroelectric layer thickness less than 100 nm, the MW losses are determined by the losses of HTS electrodes, while for thicker layers, the MW losses are completely determined by the loss tangent of the ferroelectric. Experimental aspects of the problem were investigated in the example of a YBCO/Ba_xSr_1-xTiO₃ smooth CPW resonator at 77 K and information about the permittivity and the loss tangent of the ferroelectric was obtained.