Modeling nonlinear dynamics in analog circuits via root localization

An algorithm for determining when electrical circuit poles and zeros (i.e., roots) are topologically localized to a node or coupled-pair of nodes is described. Discovering this relationship provides insight to designers for circuit optimization, and is a basis upon which nonlinear dynamic behavioral models can be built. This root localization algorithm, the main contribution of this paper, facilitates the creation of models that more accurately reflect the distinctive behavior of a circuit. This is accomplished by identifying when poles and zeros can be modeled as localized effects whose values change with circuit operating conditions. The underlying modeling approach is described to provide a context for this research. The algorithm is illustrated through several examples.