Finite-pole macromodels of transmission lines for circuit simulation

A simple method for macromodeling transmission lines for circuit simulation is presented. Finite-pole y-parameter approximations in the frequency domain are derived for these infinite-order interconnects using either the AWE (asymptotic waveform evaluation) technique or closed-form expression for an iterative ladder circuit model. Macromodels are then applied to transform these rational functions in the s-domain to time-domain stencils which can be easily incorporated into SPICE. One difficulty with all finite-pole models of transmission lines has been the accurate handling of the time-of-flight delay. In the present work, the pure delay is shown to be handled directly by the iterative ladder y-parameters. For the case of `lumped´ transmission line circuits, a pseudo-time-of-flight delay is developed and calculated for incorporation in the time-domain macromodel