A UNIFIED APPROACH TO THE APPROXIMATE SYMBOLIC ANALYSIS OF LARGE ANALOG INTEGRATED-CIRCUITS

This paper describes a unified approach to the approximate symbolic an alysis of large linearized analog circuits in the complex frequency do main, It combines two new approximation-during-computation strategies with a variation of the classical two-graph tree enumeration method, T he first strategy is to generate common trees of the two-graphs, and t herefore the product terms in the symbolic network function, in the de creasing order of magnitude, This is made possible by our algorithm fo r generating color-constrained spanning trees in the order of weight, It avoids the burden of computing all the product terms only to find m ost of them numerically negligible, The second approximation strategy is the sensitivity-based simplification of two-graphs, which excludes from the two-graphs many of the insignificant circuit elements that ha ve little effect on the network function being derived. It significant ly reduces the complexity of the two-graphs before tree enumeration, O ur approach is therefore able to symbolically analyze much larger anal og integrated circuits than previously reported, using complete small signal models for the semiconductor devices. We show accurate yet reas onably sized symbolic network functions for integrated circuits with u p to 39 transistors whereas previous approaches were limited to less t han 15, For even larger circuits, the limit is imposed mainly by the i nterpretability of the generated symbolic network function.