The limits of modeling of nonlinear circuits

Interconnected circuit models of physical electric devices must have at least the following Properties when they are used for circuit analysis: A: existence of at least one dc solution, B: uniqueness of the transient response, C: no forward escape time, D: the uniqueness of the numerical integration formula when the transient response is to be calculated. A circuit analysis problem is considered well-posed if it has Properties A and B and C and D. Based on the recent results published on the four different fields described above the basic properties of the models ensmuing the four requirements together are presented and the practical consequences in electric circuit modeling are summarized. Furthermore, a characteristic circuit example is shown, when Property D is not met and general conditions ensuring Property D are given. New Theorem is given, for a broad class of practical nonlinear networks, which show conditions under which they are well-posed analysis problems. These conditions are derived in terms of network functions as well as in terms of the set of the allowable device modeling characteristics.