A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is implemented in finite-element method software and is based on a recently developed 3-D formulation for general electromagnetic problems with solid conductors. It has been adapted for modeling of superconductors with nonlinear resistivity in 3-D, characterized by a power-law E-J relation. It has first been compared with an existing and verified two-dimensional (2-D) model: Compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Second, the model has been tested for computing the current distribution with typical 3-D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2-D models.

This paper presents a new physical model for shielded slow-wave coplanar waveguide structures. This lossy electrical model is based on physical behavior of the transmission lines. It allows a better understanding of the losses distribution along the structure. The ohmic losses in the coplanar strips, as well as the ohmic losses and the eddy current losses in the floating shield strips are studied for transmission lines having different geometrical dimensions and hence electrical characteristics. The model is then validated on different CMOS technologies and leads to the efficient optimization of the slow-wave transmission lines, especially concerning the floating shield dimensions.