A regularity-based hierarchical symbolic analysis method for large-scale analog networks

Summary form only given. The main challenge for any symbolic analysis method is the exponential size of the produced symbolic expressions (10¹¹ terms for an op amp). Current research considers two ways of handling this limitation: approximation of symbolic expressions and hierarchical methods. Approximation methods retain only the significant terms of the symbolic expressions and eliminate the insignificant ones. The difficulty, however, lies in identifying what terms to eliminate and what the resulting approximation error could be. Hierarchical methods tackle the symbolic analysis problem in a divide-and-conquer manner. They consider only one part of the global network at a time and then recombine partial expressions for finding overall symbolic formulas. Existing hierarchical methods have a main limitation in that they are not feasible for addressing networks that are built of tightly coupled blocks, i.e. operational amplifiers. The originality of our research stems from exploiting regularity aspects for addressing the exponential size of produced symbolic expressions. As a result, polynomial-size models are obtained for any network, including networks formed of tightly coupled blocks. Two kinds of regularity aspects were identified