Advanced modeling of nonuniform interconnects

A class of numerical schemes for the transient simulation of nonuniform interconnects loaded with arbitrary terminations is presented. The approach is based on a weak formulation of the Nonuniform Multiconductor Transmission Lines (NMTL) equations through expansion and testing with suitable basis functions sets. Depending on the choice of these basis functions, it is possible to tune the behavior of the numerical scheme to the form of the expected solution, which can be predicted a priori from the type of excitation. When the exciting pulse is a regular function, it is preferable to use high-order basis functions, leading to fast convergence to the exact solution. Instead, when the exciting pulse presents some regions of fast variations being elsewhere smooth, it is possible to design simple adaptive algorithms based on the use of wavelets as trial and test functions. Adaptivity reduces the number of operations required to compute the solution. Several examples illustrate the behavior of both high-order and adaptive schemes.