On the application of the no-gain property in nonlinear resistive networks

The necessary and sufficient topological conditions under which one can transfer all independent sources of a no-gain nonlinear resistive network to the branches with positive linear resistors are derived. Such a relocation of sources allows an estimate, practically without computation, of the greatest possible voltage and current in the circuit. The main theorem proved here shows that the simple localization of the solutions can, practically without computation, be made for a very large class of nonlinear circuits