Nonlinear circuits

This tutorial paper presents a sample of some interesting and practical results from three fundamental areas in nonlinear circuit theory; namely, nonlinear circuit analysis, nonlinear circuit synthesis, and nonlinear device modeling. The first area covers both resistive and dynamic circuits. The former includes the following 5 topics: existence and uniqueness of solution, bounds on solutions, symmetry properties, stationary properties, and geometric properties. The latter includes the following topics: no finite forward-escape-times, existence of a unique periodic steady-state response, dc steady-state response of capacitor-diode circuits, nonlinear dynamics, and energy-related concepts. The second area covers driving-point and transfer characteristics, nonlinear n-port resistors, mutators, nonlinear algebraic elements, and the Hodge decomposition. The third area covers nonlinear model validation and nonlinear model structure.