Abstract
The paper offers a universal method for finding a unique or multiple DC operating points of nonlinear circuits. The developed method is based on the theory known as a linear complementarity problem (LCP) and the homotopy concept. It is a combination of Lemke’s method for solving LCP and some variant of the homotopy method. To express the problem of finding DC operating points in terms of LCP, an appropriate piecewise–linear approximation of diode characteristic is proposed. Although the method does not guarantee finding all the DC operating points, usually it finds them. The method is very fast and remarkably efficient. Numerical examples, including practical BJT and CMOS circuits having a unique or multiple DC operating points are given.
Highlights
The basic question of the analysis of nonlinear electronic circuits is finding DC operating points (DC solutions) [2, 23]
In the SPICE simulator [8, 12], where different concepts and techniques have been implemented in order to overcome the convergence problems
The homotopy method is a powerful tool for finding a unique or multiple DC operating points. Another interesting approach to the analysis of nonlinear DC circuits is based on the theory known as a linear complementarity problem (LCP) [3, 5]
Summary
The basic question of the analysis of nonlinear electronic circuits is finding DC operating points (DC solutions) [2, 23]. The homotopy method is a powerful tool for finding a unique or multiple DC operating points Another interesting approach to the analysis of nonlinear DC circuits is based on the theory known as a linear complementarity problem (LCP) [3, 5]. The problem of finding a unique or multiple DC operating points of BJT and CMOS circuits is expressed in terms of LCP and solved using an algorithm being a combination of Lemke’s method and some variant of the homotopy method [3, 5]. The algorithm is easy for computer implementation, very fast and remarkably efficient This approach is entirely different than the method proposed in [22], for finding multiple DC operating points, being a combination of deflation technique, enabling us to avoid the solutions earlier determined, with some variant of the Newton–Raphson nodal analysis.
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