Transient simulation of lossy interconnects based on the recursive convolution formulation

An approach for transient simulation of lossy interconnects terminated in arbitrary nonlinear elements based on convolution simulation is presented. The Pade approximations of each line's characteristics or each multiconductor line's modal functions are used to derive a recursive convolution formulation, which greatly reduces the amount of computation used to perform convolutions. The approach can handle frequency-varying effects, such as skin effects, and general coupling situations. The errors introduced by Pade approximations are analyzed, and a scheme for determining the necessary order for an approximation is developed. The approach has been incorporated in the stepwise equivalent conductance timing simulator (SWEC) for digital CMOS circuits. Comparisons with SPICE3.e indicate that SWEC, which gives accurate results, can be one to two orders of magnitude faster.>