Finding DC operating points of transistor circuits using homotopy methods

Finding the DC operating points of transistor circuits is one of the most important tasks in electrical circuit simulation. To resolve DC convergence difficulties that often arise when simulating bipolar and MOS transistor circuits, the authors use homotopy methods to solve nonlinear circuit equations. The authors exploit the properties of the equations and construct various homotopies that prove useful in finding their solutions. Criteria are provided for choosing homotopy parameters and a good starting point for homotopy paths. Homotopy methods are robust, accurate, and capable of finding multiple operating points. The authors present a circuit that could not be simulated using techniques available in current circuit simulators, while the solutions were successfully obtained using homotopy methods.