An efficient and globally convergent homotopy method for finding dc operating points of nonlinear circuits

Abstract

Finding DC operating points of nonlinear circuits is an important problem in circuit simulation. The Newton-Raphson method employed in SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. There are several types of homotopy methods, one of which succeeded in solving bipolar analog circuits with more than 20000 elements with the theoretical guarantee of global convergence. In this paper, an improved version of the homotopy method is proposed that can find DC operating points of practical nonlinear circuits smoothly and efficiently. It is also shown that the proposed method can be easily implemented on SPICE without programming.

An efficient and globally convergent homotopy method for finding DC operating points of nonlinear circuits

“…Now we show some numerical examples. We consider the circuit containing n tunnel diodes discussed in [5].…”

“…By these studies, the application of the homotopy methods in practical circuit simulation has been remarkably developed, and the homotopy method termed the Newton homotopy (NH) method succeeded in solving bipolar analog circuits with more than 20000 elements (that belong to a class of the largest-scale circuits available with the current bipolar analog LSI technology) with the theoretical guarantee of global convergence [1]- [5]. However, since the NH method is globally convergent only when we choose an initial point on which the uniform passivity holds, we cannot choose a good initial point (e.g., point in the forward active operation region of transistors).…”

Accelerating the solving of nonlinear equations using the homotopy method: application on finding the operating point of complex circuits

“…It compares the proposed method (Alg. (02)) to two other methods; the first method is the VGNH (variable gain Newton homotopy) implemented with the SPICE software [7,8] while the second is the method (Alg. (01)) proposed in [12].…”

“…These circuits consist of an Ebers-Moll BJT and have convergence issues in the SPICE software but are frequently used as a test circuits [7,8]:…”

“…The continuation method, proposed in [3][4][5][6][7][8][9][10][11], is an effective method to solve nonlinear circuits. The continuation method is based on 3 steps:…”