Finding the DC operating points of a nonlinear circuit is one of the most important and difficult tasks in electrical circuit simulation and thus has been an active area of research for many years. In the vast majority of circuit simulations ( e.g., SPICE and its variants) the Newton-Raphson algorithm is used. However, this algorithm is not guaranteed to converge. A better approach to finding the solution of a set of nonlinear equations is the use of a continuation method. Recent work in this field by the speaker and others has shown that proper use of a continuation method makes possible global convergence; that is, an operating point is guaranteed to be found. In this talk the following research will be discussed:

1. Development of an algorithm, based on a novel continuation method, that automatically searches for multiple DC operating points of a circuit without any intervention from the user.

2. Automatic diagnosis and rectification of convergence problems using continuation methods.

3. Generalization of algorithms used for DC operating point analysis to steady--state analysis of autonomous dynamic circuits. This research has the potential of constructing a globally convergent algorithm that allows the user to avoid the trivial (i.e., DC) state and is capable of searching for multiple modes of oscillation.

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