Unconditionally stable implicit schemes for transient analysis of lossy multiconductor lines

This article shows the advantages provided by implicit time stepping schemes for the study of multiconductor transmission lines. Implicit schemes allow for choosing time and space steps independently by attending only to resolution criteria, without the limitation imposed by the Courant–Friedrich–Levy stability condition. Hence, they behave favorably whenever a large time step would be preferable, for instance when a massive number of simulations is required for sensitivity analyses. We focus our attention on two common schemes in electromagnetics, Crank-Nicolson and Newmark- β methods, that are shown to have the same accuracy and to lead to the same solving-equation structure. We illustrate how to include frequency-dependent losses in the algorithms, and we show the influence of dispersion on fast transients. Results show that implicit formulations can be favorably compared with the classical explicit leap-frog scheme