Hierarchical approach to exact symbolic analysis of large analog circuits

Abstract

This paper provides a novel approach to exact symbolic analysis of very large analog circuits. The new method is based on determinant decision diagrams (DDDs) to represent symbolic product terms. But instead of constructing DDD graphs directly from a flat circuit matrix, the new method constructs DDD graphs in a hierarchical way based on hierarchically defined circuit structures. The resulting algorithm can analyze much larger analog circuits exactly than before. Theoretically, we show that exact symbolic expressions of a circuit are cancellation-free expressions when the circuit is analyzed hierarchically. Practically we propose a novel hierarchical DDD graph construction algorithm. Our experimental results show that very large analog circuits, which can't be analyzed exactly before like μA725 and other unstructured circuits up to 100 nodes, can be analyzed by the new approach for the first time. The new approach significantly improves the exact symbolic capacity and promises huge potentials for the new applications of symbolic analysis in analog circuit design automation.