New signal flow graph topological formulas for linear active networks

The paper is concerned with topological analysis for a certain electrical network. The element admittance matrix of this linear active or passive electrical network exists and is diagonal, and a procedure is presented for the topological analysis of the signal flow graph associated with the hybrid system of equations for this network. Term cancellation in Mason's topological formulas is considered, and necessary and sufficient conditions for certain terms either to cancel or not cancel are established. In a new approach which is described, signal flow graph topological formulas for the graph determinants and cofactors are proved. No term cancellation occurs in these formulas, which are readily adaptable to computer implementation. The number of terms is independent of the network tree used to formulate the signal flow graph. Examples of formula application are provided.