Line impedance and propagation coefficient of narrow superconducting coplanar lines made of YBaCuO

The microwave properties of coplanar waveguides with line widths from 1 μm to 40 μm made of superconducting YBaCuO films with a thickness t=180 nm on LaAlO₃ are investigated. The line impedance Z_L and the normalized propagation coefficient β/β₀ of these waveguides are measured between 45 MHz and 26.5 GHz at temperatures between 77.4 K and 92 K. The ratio of the line width w to the distance of the ground layers d is constant with w/d=0.2. Therefore, Z_L and β/β₀ are independent of w for perfectly conducting waveguides. For superconducting waveguides it is found that Z_L and β/β₀ differ from the values of perfectly conducting waveguides. They increase for smaller line widths at a constant temperature. At w=1 μm and T=80 K, Z_L and β/β ₀ are nearly twice as high as calculated for perfect conductors. Furthermore, Z_L and β/β₀ increase with the temperature. It is shown that these effects are attributed to an increase of the inductance per unit length L´ due to the superconducting material, whereas the capacitance per unit length C´ behaves like C´ of perfectly conducting waveguides. Using these results, the dimensions of the superconducting waveguides, which are necessary to obtain a desired Z_L at a given line width w, are calculated