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The Scientific World Journal
Volume 2014, Article ID 938598, 11 pages
Research Article

Modified Hyperspheres Algorithm to Trace Homotopy Curves of Nonlinear Circuits Composed by Piecewise Linear Modelled Devices

1Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico
2Higher Colleges of Technology, Abu Dhabi Men’s College, P.O. Box 25035 Abu Dhabi, UAE
3National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro No. 1, Santa María Tonantzintla, 72840 Puebla, PUE, Mexico
4Department of Artificial Intelligence, Universidad Veracruzana, Sebastián Camacho No. 5, 91000 Xalapa, VER, Mexico
5Facultad de Ingeniería Civil, Universidad Veracruzana, Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, Mexico

Received 22 April 2014; Accepted 2 July 2014; Published 11 August 2014

Academic Editor: Ishak Altun

Copyright © 2014 H. Vazquez-Leal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a homotopy continuation method (HCM) for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL) representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation.