A new signal flowgraph formulation of symbolic network functions

Abstract

Symbolic topological analysis of the closed primitive signal flowgraph corresponding to a linear active or passive network having an edge admittance matrix is considered. First, necessary and sufficient conditions for the occurence of term cancellation in Mason's formula for the graph determinant are established. Then, a new signal flowgraph topological formula for the graph determinant in which no term cancellation occurs is proved. A computer program to implement the new formula is described. It is shown that this program is more efficient than existing programs based on Mason's formula.