Topological Analysis for Active Networks

It is shown that a general network determinant and its cofactors can be evaluated by means of "directed trees" and "directed two-trees". There is no sign problem. The products of such directed trees and directed two-trees will automatically give the correct signs. Furthermore, this new method can be applied to either the node-admittance matrix or the loop-impedance matrix. In case the given network is passive and contains no magnetic coupling, the digraph associated with the node-admittance matrix reduces to the original network; the directed trees and directed two-trees reduce to ordinary trees and two-trees, respectively