Asymptotic Waveform Evaluation

Summary

Asymptotic waveform evaluation (AWE), with its many extensions for controlling stability, provides an effective moment matching approximation methodology for interconnect circuits. Although it has clear limitations and problems, we believe that AWE is the best technique for waveform analysis for on-chip interconnection circuits --- particularly those that are modeled as RC (or RL) circuits. Even for most on-chip RLC interconnect circuits, AWE works very well. However, as the strong coupling and transmission line effects start to dominate the behavior of the waveform propagation, AWE, as a single point moment matching method, suffers from accuracy and stability problems. Circuits with strong coupling and reflection effects generally require more poles than AWE can provide. Although we addressed the stability issues of the reduced order models we have not considered the passivity. For linear circuit analysis, passivity is not a concern. But when reduced order linear models and nonlinear devices are combined together in a circuit simulation environment, for a stable simulation, the reduced order blocks have to be passive too. In the next chapter, we present the PRIMA method which guarantees passivity and stability. Furthermore, PRIMA uses Krylov vectors instead of moments and therefore does not suffer from the numerical problems that occur in AWE.