Topological criteria for establishing the uniqueness of solutions to the dc equations of transistor networks

The presence of a certain topological structure was shown to be a necessary and sufficient condition for a network to possess a unique solution to its dc equations for any choice of network parameter values. An important result in this theory showed how transistor networks could, for the purpose of analysis, be broken apart into smaller subnetworks, which could then be analyzed individually. It was shown how one can then deduce that the original circuit possesses a unique solution to its dc equations, as a consequence of the uniqueness of solutions to the dc equations of the subnetworks. In the event that a given transistor network does not possess the topological structure mentioned previously, results are presented which show how the computational effort required to verify a certain well-known set of necessary and sufficient conditions, which guarantees the uniqueness of solutions to the dc equations of transistor networks, can be reduced.