title: Modified hyperspheres algorithm to trace homotopy curves of nonlinear circuits composed by piecewise linear modelled devices.
abstract: 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.
authors.affiliation: Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico.
authors.forename: H
authors.initials: H
authors.lastname: Vazquez-Leal
authors.affiliation: Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico.
authors.forename: V M
authors.initials: VM
authors.lastname: Jimenez-Fernandez
authors.affiliation: Higher Colleges of Technology, Abu Dhabi Men's College, P.O. Box 25035 Abu Dhabi, UAE.
authors.forename: B
authors.initials: B
authors.lastname: Benhammouda
authors.affiliation: Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico.
authors.forename: U
authors.initials: U
authors.lastname: Filobello-Nino
authors.affiliation: National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro No. 1, Santa María Tonantzintla, 72840 Puebla, PUE, Mexico.
authors.forename: A
authors.initials: A
authors.lastname: Sarmiento-Reyes
authors.affiliation: Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico.
authors.forename: A
authors.initials: A
authors.lastname: Ramirez-Pinero
authors.affiliation: Department of Artificial Intelligence, Universidad Veracruzana, Sebastián Camacho No. 5, 91000 Xalapa, VER, Mexico.
authors.forename: A
authors.initials: A
authors.lastname: Marin-Hernandez
authors.affiliation: Facultad de Ingeniería Civil, Universidad Veracruzana, Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, Mexico.
authors.forename: J
authors.initials: J
authors.lastname: Huerta-Chua
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical