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

A theory is formulated which shows how transistor networks can, for the purpose of analysis, be broken apart into smaller subnetworks, which can then be analyzed individually. It is 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 the solutions to the dc equations of the subnetworks. It is shown, moreover, that the amount of effort required for the analysis of the original circuit is thereby reduced, in many cases by enormous proportions. Furthermore, it is shown how the theory can be used to identify circuits whose topological structure is such as to require that the circuit's dc equations possess a unique solution. For such circuits, therefore, the required analysis becomes nothing more than a trivial inspection of the circuit's topology; that is, no computation is required.