Simulation of multiconductor transmission lines using Krylov subspace order-reduction techniques

A mathematical model for lossy, multiconductor transmission lines is introduced to facilitate the efficient application of Krylov subspace order-reduction techniques to the analysis of linear networks with transmission line systems. The model is based on the use of Chebyshev polynomial expansions for the approximation of the spatial variation of the transmission-line voltages and currents. The exponential convergence of Chebyshev expansions, combined with a simple collocation procedure, leads to a low-order matrix representation of the transmission line equations with matrix coefficients that are first polynomials in the Laplace variable s, and in which terminal transmission-line voltages and currents appear explicitly. Thus, the resulting low-order model is compatible with both Krylov subspace order-reduction methods (such as the Lanczos and the Arnoldi processes) and the modified nodal analysis formalism. The accuracy and efficiency of the proposed model, as well as its compatibility with Krylov subspace order reduction, are demonstrated through its application to the numerical simulation of several interconnect circuits.