Using continuation methods to improve convergence of circuits with high impedance nodes

The use of continuation methods has been shown to be more effective than standard Newton-Raphson-based methods in finding the operating point(s) of circuits possessing multiple operating points or in dealing with circuits exhibiting convergence problems in DC. In this paper we propose a method of dealing with numerical problems caused by a singular or nearly singular Jacobian matrix along a zero curve resulting from the use of a continuation method. This method has been implemented in a circuit simulator that uses a continuation method. Using the implementation we were able to achieve a much better convergence rate for some circuits. The proposed method is not limited to simulators based on homotopy methods only; it can be used with any ODE solution algorithm based on a predictor-corrector mechanism. Several circuit examples are given.