Optimal synthesis of finite difference models for multiconductor transmission lines via Gaussian spectral rules

We present an algorithm for the generation of optimal, nonuniform finite difference grids for the analysis of multiconductor transmission lines (MTL). Such MTL segments are the basic constitutive elements of large interconnect networks used for broadband signal transmission in state-of-the-art, GHz processor-based, computing systems. The algorithm is based on a Padé-Chebyshev approximation of the input impedance, implemented via the Lanczos procedure, and results in compact, multi-port, frequency-dependent representations of MTLs. A dramatic reduction of computational time is possible, using just over two points per wavelength to achieve superexponential convergence in the response at the input of the line. Moreover, the generated models have the advantage to be passive by construction, which enables their efficient incorporation into SPICE-based simulation tools for circuit design.