Finding all DC equilibrium points of nonlinear circuits

The details of a continuation algorithm for systems of real polynomial equations which is suitable for calculating all their zeros is described. Some properties of this algorithm are shown by means of a simple example. Such a numerical method is helpful to circumvent the problems connected with bifurcations and turning points occurring in systems of parameterized polynomial equations. Applications of this algorithm enable the determination of all DC operational points of nonlinear resistive networks and the solving of nonlinear design equations with more than one solution.<<ETX>>

[1]  F. Drexler.  Eine Methode zur berechnung sämtlicher Lösungen von Polynomgleichungssystemen , 1977 .

[2]  Tien-Yien Li.  Solving polynomial systems , 1987 .

[3]  C. B. García,et al.  Finding all solutions to polynomial systems and other systems of equations , 1979, Math. Program..

[4]  J. Yorke,et al.  Finding zeroes of maps: homotopy methods that are constructive with probability one , 1978 .

[5]  Layne T. Watson,et al.  Finding all isolated solutions to polynomial systems using HOMPACK , 1989, TOMS.

[6]  R. Saeks,et al.  Continuation methods in circuit analysis , 1977, Proceedings of the IEEE.

[7]  L. Chua,et al.  A new approach to overcome the overflow problem in computer-aided analysis of nonlinear resistive circuits , 1975 .

[8]  D. A. Zein.  Solution of a set of nonlinear algebraic equations for general-purpose CAD programs , 1985, IEEE Circuits and Devices Magazine.

[9]  Gene H. Golub,et al.  Matrix computations , 1983 .

[10]  B. C. Haggman,et al.  Geometric properties of nonlinear networks containing capacitor-only cutsets and/or inductor-only loops. Part I: Conservation laws , 1986 .

[11]  Christian H. Bischof,et al.  Computing the Singular Value Decomposition on a Ring of Array Processors , 1986 .

[12]  H. Shichman,et al.  Computation of DC Solutions for Bipolar Transistor Networks , 1969 .

[13]  Fathi M. A. Salam,et al.  Parallel processing for the steady state solutions of large-scale non-linear models of power systems , 1989, IEEE International Symposium on Circuits and Systems,.

[14]  I. Cermak.  DC solution of nonlinear state-space equations in circuit analysis , 1971 .

[15]  S. Richter,et al.  Continuation methods: Theory and applications , 1983 .