Conductor loss in superconducting planar structures: Calculations and measurements

We present closed-form expressions of the attenuation constant due to condu ctor loss far superconducting coplanar waveguide and microstrip transmissio n lines. These expressions, valid for arbitrary conductor thickness, make u se of a numerically determined quantity (the stopping distance Delta) that depends on the material properties and edge Shape of the superconducting tr ansmission line. Once Delta is determined; the attenuation constant for any planar geometry can be obtained without further numerical calculation, mak ing, this technique attractive for use in the design of circuits incorporat ing superconducting planar elements. The results of this calculation compar e favorably with full numerical calculations and also with experimental dat a on high-temperature superconducting coplanar transmission lines, illustra ting the accuracy and applicability of the calculation for determining the conductor loss of superconducting circuit elements.