Some Considerations on the State Equations of Linear Active Networks and the Network Topology

Abstract

The state equations as a characterization of a linear active network involve two factors, the network topology and the properties of the network elements. In this paper the way these two factors influence the formulation of the state equations is studied. A set of state equations for the networks with certain topological restrictions is derived based on an overnormal tree. Furthermore the order of complexity of a linear active network is investigated in connection with the network topology, and an upper bound on the order of complexity is stated with respect to a particular common tree. Several examples are given to illustrate the investigation.