Article

# Path Following Circuits--SPICE-Oriented Numerical Methods Where Formulas are Described by Circuits--

Faculty of Science and Engineering, Chuo University, Edo, Tōkyō, Japan
(Impact Factor: 0.23). 04/2005; DOI: 10.1093/ietfec/e88-a.4.825
Source: OAI

ABSTRACT

Path following circuits (PFC's) are circuits for solving nonlinear problems on the circuit simulator SPICE. In the method of PFC's, formulas of numerical methods are described by circuits, which are solved by SPICE. Using PFC's, numerical analysis without programming is possible, and various techniques implemented in SPICE will make the numerical analysis very efficient. In this paper, we apply the PFC's of the homotopy method to various nonlinear problems (excluding circuit analysis) where the homotopy method is proven to be globally convergent; namely, we apply the method to fixed-point problems, linear programming problems, and nonlinear programming problems. This approach may give a new possibility to the fields of applied mathematics and operations research. Moreover, this approach makes SPICE applicable to a broader class of scientific problems.

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##### Conference Paper: An efficient and globally convergent homotopy method for finding DC operating points of nonlinear circuits
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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.
Preview · Conference Paper · Feb 2006
• ##### Article: A SPICE-Oriented Method for Finding DC Operating Points of Nonlinear Circuits Containing Piecewise-Linear Macromodels*This paper was presented at the 49th IEEE International Midwest Symposium on Circuits and Systems, Puerto Rico, August 6--9, 2006.
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ABSTRACT: Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear (PWL) resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a PWL resistor that is neither voltage nor current controlled. By modeling often used one-port subcircuits by such resistors (macromodels), large scale circuits can be analyzed efficiently. In this paper, an efficient method is proposed for finding DC operating points of nonlinear circuits containing such neither voltage nor current controlled resistors using the SPICE-oriented approach. The proposed method can be easily implemented on SPICE without programming.
No preview · Article · Nov 2006 · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
• ##### Article: An Efficient Homotopy Method That Can Be Easily Implemented on SPICE
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ABSTRACT: Recently, an efficient homotopy method termed the variable gain Newton homotopy (VGNH) method has been proposed for finding DC operating points of nonlinear circuits. This method is not only very efficient but also globally convergent for any initial point. However, the programming of sophisticated homotopy methods is often difficult for non-experts or beginners. In this paper, we propose an effective method for implementing the VGNH method on SPICE. By this method, we can implement a "sophisticated VGNH method with various efficient techniques" "easily" "without programming," "although we do not know the homotopy method well."
No preview · Article · Nov 2006 · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences