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

Event-driven methods are very promising for simulating large-scale linear and nonlinear circuits but they may suffer some drawbacks, such as spurious numerical oscillations and have difficulties in convergence to equilibrium points. To overcome these drawbacks a pseudoanalytical method is presented that is based on the staircase approximation of v-i characteristics of linear and nonlinear resistors, on the piecewise-linear approximation of v-q characteristics of nonlinear capacitors and t-v characteristics of time-varying voltage sources. At a generic time instant, these approximations allow 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 pathological situations, the model does no longer hold and then a rigorous and in general more complex analysis is needed. Even if this analysis yields a conceptual effort, its computational execution is not complex. This algorithm works successfully on circuits composed of linear and nonlinear resistors and capacitors, time-varying voltage and time-invariant current sources. Some applications of this method to the analysis of interconnects and power-grids in VLSI circuits are presented.