Order of complexity of active networks

The topological properties of networks containing resistors, capacitors, self inductors and controlled current generators are considered. A restriction is found on the positioning of such generators so that the network may have a solution. The determinant of the node-admittance matrix of such a network is expanded in terms of some tree-admittance products. The order of complexity is related to a particular tree associated with such an expansion, and a method of calculation is given. It is shown that, for a broad class of networks, the order of complexity can be calculated by considering only the simpler RLC subnetwork.