Finding all characteristic curves of nonlinear resistive circuits using linear programming
Kiyotaka Yamamura, Fitrah Gunawan, Koji Yomogita · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 2001
This paper presents an efficient algorithm for finding all characteristic curves of nonlinear resistive circuits. This algorithm is based on interval analysis and a new computational test for nonexistence of a characteristic curve in a given region X. In this test, the simplex method is applied to a linear programming (LP) problem whose feasible region contains all characteristic curves in X. Such an LP problem can be formulated by replacing the component nonlinear functions with auxiliary variables and linear inequalities that are obtained by using interval extensions. If the feasible region of the LP problem is empty (that can be easily checked by the simplex method), then there is no characteristic curve in X. This test is much more powerful than the conventional nonexistence test, which makes the number of analyzed regions much smaller. By numerical examples, it is shown that the proposed algorithm can find all characteristic curves of nonlinear resistive circuits much more efficiently than the conventional algorithm. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(6): 1–11, 2001