Superconducting resonator circuits at frequencies above the gap frequency

The frequency response of three superconductive niobium resonating circuits, formed by a Nb microstrip and a Nb tunnel junction, is measured and analyzed at frequencies above the superconducting gap frequency. The circuits are placed in a waveguide system and the frequency response is determined with a Fourier transform spectrometer. The calculated and measured resonance frequencies and bandwidths are in good agreement with the extreme anomalous limit of the Mattis–Bardeen theory on the anomalous skin effect in superconductors [D.C. Mattis and J. Bardeen, Phys. Rev. 111, 412 (1958)]. The observed loss is higher than predicted by this theory, in agreement with previous observations on Nb films. The use of other materials for striplines as tuning circuits for heterodyne superconducting tunnel junction mixers is analyzed