Models of superconducting microstrip and coplanar elements for submillimeter applications

Some models which predict the microwave properties of superconducting microstrip lines, radial stubs, coplanar lines and coplanar waveguides are presented. These models take into account the dispersion which occurs in superconducting lines when the frequency of operation becomes close to the gap frequency of the superconductors (700 GHz for niobium). The effects of fringing fields are also taken into consideration. These models are also valid for high-temperature superconductors. They have been developed in the specific case of elements for which the characteristic dimension (the dielectric thickness for microstrip lines, the spacing between conductors for coplanar elements) is of the same order of magnitude as the typical length of penetration of the magnetic field in the metal. The length of penetration is the skin depth for normal metals and the London penetration depth for superconductors. The consequence of this particular topology is that the propagation of signals in such a transmission line is slow-wave and its microwave properties are modified. These models are also valid for classical line configurations (dielectric thickness much higher than penetration length).