The Generalized Topological Formula for Transfer Function Generation by Two-Graph Tree Enumeration

Analog Signal Processing

Abstract

In this paper the topological approach for transfer function generation by two-graph tree enumeration is presented. The generalized topological formula with homogeneous parameters is proved for all the circuit functions, and a simple representation of the four types of controlled sources by admittances is proposed, that allows a uniform treatment of the entire circuit in terms of admittances. To implement our procedure, the rules to automatically generate the two graphs and to enumerate the common spanning trees are presented. Some simplifications in the circuit and in the two graph structure before tree generation and a graph representation on levels, improve the efficiency of the tree enumeration procedure. An illustrative example is presented and a reduced symbolic form of the network function is obtained by some simplifications after generation.

Key Words

two-graph tree enumeration topological formula transfer function homogeneous parameters 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Electrical Engineering Department“Politehnica” University of BucharestBucharestRomania

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