Generation of sequential symbolic network functions for large-scale networks by circuit reduction to two-port

The major stumbling block in symbolic analysis of large-scale circuits is the exponential growth of expression complexity with the circuit size. Sequential techniques, introduced more than a decade ago, reduced that growth to quasi-linear. The fundamental assumption in all sequential methods developed so far is that the circuit must be decomposed in order to reduce the complexity or the final expression. In this paper we show conclusively that this is not the case. We describe a new algebraic approach to symbolic analysis of large-scale networks, based on the reduction of the compacted modified node admittance matrix to a two-port matrix. No circuit partitioning is required. Internal variables are suppressed one by one using Gaussian elimination. To minimize the number of symbolic operations we employ a locally optimal pivoting strategy. Formula complexity is estimated to grow quasi-linearly with circuit size. The technique is conceptually very simple and produces sequential formulae of significantly lesser complexity than any exact method published to date