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SUMMARYAn efficient algorithm is proposed for finding all DC solutions of transistor circuits where characteristics of transistors are represented by piecewise-linear (PWL) convex monotone functions. This algorithm is based on a simple test (termed the linear programming, LP, test) for non-existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem by surrounding component PWL functions by rectangles. Then the dual simplex method is applied, by which the number of pivotings per region becomes very small. In this letter, we propose a new LP test using the dual simplex method and triangles. The proposed test is not only efficient but also more powerful than the conventional test using the simplex method or rectangles.

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits with high approximation accuracy, namely, circuits where the characteristics of PWL resistors are approximated by PWL functions with a very large number of segments. By numerical examples, it is shown that the proposed algorithm could find all solutions of a circuit where the number of PWL resistors is 4000 and the number of linear regions is 100004000 for the first time.

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An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits with high approximation accuracy, namely, circuits where the characteristics of PWL resistors are approximated by PWL functions with a very large number of segments. This algorithm is based on the LP test using the dual simplex method, the contraction method, and a special technique that makes the algorithm not require large memory space and not require copying tableaus. By numerical examples, it is shown that the proposed algorithm could find all solutions of a circuit where the number of PWL resistors is 4000 and the number of linear regions is 10 0004000.