Efficient generation of compact symbolic network functions in a nested rational form

This paper presents the extension of generalized parameter extraction method for direct circuit function generation in a fully symbolic form of rational expressions or a nested s-expanded polynomial. The new formula for implicit extraction of parameters that allows effective factoring by grouping of determinants of circuits containing any linear models of active elements, such as controlled sources, nullors, and pathological mirrors, is proposed. The concept of nullor with parameter is used for implicit extraction. The rules of optimal selection of parameters for extraction are presented. The proposed algorithm of symbolic analysis is implemented in the CirSym program, which is available online. The paper discusses the results of automatic analysis of several large active circuits, as well as determinants of matrixes and passive topologies, in terms of compact size and minimization of the number of arithmetic operations. Experimental results demonstrate that the expressions of determinants derived by CirSym are more compact than the results of the factorization algorithms of commercial computer algebra systems. The comparison with several other symbolic analysis algorithms shows that CirSym is the only available program that provides the exact calculation of the symbolic function of large circuits in the s-expanded form with every coefficient being a compact-nested expression.