DC Operating Point Analysis – A Formal Approach

If the inputs to a circuit are held constant, then the state of some circuits settle to a unique equilibrium: the DC operating point. Many circuit analysis techniques seek to determine or use this state and assume that it is unique. However, for some constant input some circuits may settle to one of several different operating points, while still others may never settle. In this paper we describe a procedure that uses symbolic circuit models generated from a netlist level circuit description to rigorously locate and classify all of the equilibria of a circuit model in order to determine the existence, location and number of DC operating points. Implemented with a collection of public tools (HySAT, INTLAB and EigTool) and our own MATLAB circuit modeling system OOmspice, we demonstrate that the technique can deduce the hysteresis of a Schmitt trigger and the lack of DC operating points for a ring oscillator with an odd number of stages.