Solvability and analysis of linear active networks by use of the state equations

A study of the reduction process used to obtain the state equations for a network containing capacitors, resistors, inductors, and controlled and incontrolled sources of all types, gives the necessary and sufficient conditions for such a network to possess a solution. These conditions involve both the topology of the network and its element values. The formation of the state equations also depends both on the network's topology and its element values. It is shown that the state variables can be chosen from the variables associated with the controlled sources, and any set of state variables chosen for the passive network, formed by removing all the sources. A topological restriction on the active network, which ensures that the maximum order of complexity of the active network is the same as that of this passive network, is given.