General dispersive multiconductor transmission line model for interconnect simulation in SPICE

Although numerous methods have been proposed for interconnect simulation, no single model exists for all kind of transmission line problems. This paper presents a new, single, general dispersive coupled uniform/nonuniform transmission line model which can be used for interconnect simulation in SPICE. The mathematical model is based on the use of Chebyshev polynomials for the representation of the spatial variation of the transmission-line voltages and currents. A simple collocation procedure is used to obtain a matrix representation of the transmission line equations with matrix coefficients that are first polynomials in s, and in which terminal transmission-line voltages and currents appear explicitly. Thus, the model is compatible with both the SPICE's numerical integration algorithm and the modified nodal analysis formalism.