Rigorous event-driven (RED) analysis of large-scale nonlinear RC circuits

Event-driven methods are very promising for simulating large-scale linear a nd nonlinear circuits but they may suffer of some drawbacks, such as spurio us numerical oscillations and have difficulties in convergence to equilibri um points. To overcome these drawbacks a pseudoanalytical method is present ed that is based on the staircase approximation of v-i characteristics of l inear and nonlinear resistors, on the piecewise-linear approximation of v-q characteristics of nonlinear capacitors and t-v characteristics of time-va rying voltage sources. At a generic time instant, these approximations allo w us to represent the original circuit with a very simple model composed of only linear capacitors, voltage and current sources. The solution of this circuit model is straightforward but, when the operating point meets some p athological situations, the model does no longer hold and then a rigorous a nd in general more complex analysis is needed. Even if this analysis yields a conceptual effort, its computational execution is not heavy. This algori thm works successfully on circuits composed of linear and nonlinear resisto rs and capacitors, time-varying voltage and time-invariant current sources. Some applications of this method to the analysis of interconnects and powe r-grids in VLSI circuits are presented.