Equivalence Checking of System-Level and SPICE-Level Models of Static Nonlinear Circuits

Recently, Signal Flow Graphs (SFGs) have been successfully leveraged to show equivalence for linear analog circuits at system-level and SPICE-level. However, this is clearly not sufficient as the true complexity stems from nonlinear analog circuits. In this paper, we go beyond linear analog circuits, i.e., we extend the SFGs and develop the Modified Signal-Flow Graph (MSFG), to show equivalence between system-level and SPICE-level representations of static nonlinear analog circuits. First, we map the nonlinear circuits to MSFGs. Afterwards, graph simplification and functional approximation (in particular Legendre polynomials) techniques are used to create minimal MSFG and canonical MSFG. This enables us to compare the MSFGs even if they have vastly different structures. Finally, we propose a similarity metric that calculates the similarity between SPICE-level and system-level models. By successfully applying the proposed equivalence checking technique to benchmark circuits, we demonstrate its applicability.