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Speed-up hyperspheres homotopic path tracking algorithm for PWL circuits simulations.

A Ramirez-Pinero1, H Vazquez-Leal1, V M Jimenez-Fernandez1

  • 1Facultad de Instrumentación Electrónica, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Veracruz Mexico.

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Summary
This summary is machine-generated.

This study presents an improved hyperspheres path tracking method for piecewise linear circuits, enhancing the homotopy continuation method (HCM). The new approach significantly speeds up circuit analysis and reduces convergence issues with Newton-Raphson methods.

Keywords:
Homotopy continuation methodMultiple operating pointsNonlinear circuitsPath tracking algorithmPiecewise linear

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Area of Science:

  • Electrical Engineering
  • Computational Science

Background:

  • Nonlinear circuit analysis is computationally intensive.
  • Existing homotopy continuation methods (HCM) face challenges with convergence and speed.

Purpose of the Study:

  • To introduce an improved hyperspheres path tracking method for piecewise linear (PWL) circuits.
  • To enhance the performance and speed of the homotopy continuation method (HCM).

Main Methods:

  • Adapted hyperspheres path tracking for PWL circuits.
  • Utilized modified nodal analysis for equilibrium equations.
  • Developed a starting point criteria and a technique to avoid reversion.

Main Results:

  • Achieved faster path tracking by leveraging PWL characteristics.
  • Reduced Newton-Raphson method divergence by applying it only twice per linear region.
  • Demonstrated up to twelve times speed improvement compared to the original method.
  • Successfully avoided several reversion cases encountered with the original scheme.

Conclusions:

  • The improved method offers significant speedups for nonlinear circuit analysis.
  • Enhanced robustness against convergence issues in numerical methods.
  • Effective for analyzing complex circuits with bipolar (BJT) and CMOS transistors.