Symbolic analyzer for large lumped and distributed networks

Abstract

A symbolic linear analyzer that integrates the analysis of both lumped and distributed networks is presented in this paper. This is achieved by implementing a consistent set of notations and a unified mathematical framework. The merits of sparse symbolic matrices are utilized to develop a complete symbolic sparse toolbox that includes all basic elements of electrical circuits. A new storage scheme called Row-Indexed Semi-Symetric (RISS) sparse is proposed and implemented for symbolic network matrices. Several existing and newly developed matrix solvers are implemented and their performances are compared. These solvers are used in the proposed symbolic solver to provide a multi-path analysis root that can be optimized for a particular problem. The overall performance of the proposed symbolic analyzer is assessed practically using several application examples. The obtained results are found in agreement with the results obtained from previously reported analyses and thus confirm validity of the adopted formula approximation method. A polynomial fitting shows that the time complexity of a variable size RC network is super-quadratic with the number of network sections. A substantial reduction in the analysis time of a large ladder RC network is demonstrated with the implementation of macromodeling techniques.