Macromodel-Based Iterative Solvers for Simulation of High-Speed Links With Nonlinear Terminations

Data transmission on high-speed channels may be affected by several undesired effects, including coupling from nearby interconnects, dispersion, losses, signal reflections from terminations and from internal discontinuities, and nonlinear/dynamic effects of drivers and receivers. The latter are often neglected, leading to very fast solvers, whose results may, however, be questionable when driver/receiver nonlinearities are important. This paper presents a framework for the transient analysis of complex high-speed channels with arbitrary nonlinear termination circuits. The approach is based on decoupling channel and terminations through a scattering-based waveform relaxation (WR) formulation. The channels are here cast as delay-rational macromodels, which are solved in discrete time domain through fast delayed recursive convolutions. The terminations can be either arbitrary circuits, solved by SPICE, or nonlinear behavioral macromodels, which are here formulated in discrete-time scattering representations. To overcome the known convergence issues of standard WR methods, we apply here more general iterative solution schemes, such as generalized minimal residual and biconjugate gradient stabilized, integrated into inexact Newton iterations, obtaining a set of numerical schemes with guaranteed convergence. The excellent performance of the proposed approach is illustrated on a large set of benchmarks.