An accelerated Poincaré-map method for autonomous oscillators

A novel time-domain method for finding the periodic steady state of a free-running electrical oscillator is introduced. The method is based on the extrapolation technique MPE. The new method is applied to a family of artificial benchmark problems and to a real circuit (Colpitt's oscillator). It turns out to have super-linearly convergence properties in both cases. Full implementational details are provided.

[1]  Kenneth S. Kundert,et al.  Simulation methods for RF integrated circuits , 1997, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[2]  Leon O. Chua,et al.  Computer-Aided Analysis Of Electronic Circuits , 1975 .

[3]  E. Hairer,et al.  Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .

[4]  A. Sidi,et al.  Extrapolation methods for vector sequences , 1987 .

[5]  Michael R. Osborne,et al.  Numerical solution of boundary value problems for ordinary differential equations , 1995, Classics in applied mathematics.

[6]  T. Aprille,et al.  Steady-state analysis of nonlinear circuits with periodic inputs , 1972 .

[7]  Paolo Antognetti,et al.  Semiconductor Device Modeling with Spice , 1988 .

[8]  R. Laur,et al.  Minimization of the error in the calculation of the steady state by shooting methods , 2001 .

[9]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[10]  Claude Brezinski,et al.  Convergence acceleration during the 20th century , 2000 .

[11]  Jacob K. White,et al.  Fast simulation algorithms for RF circuits , 1996, Proceedings of Custom Integrated Circuits Conference.

[12]  H. Sadok,et al.  Vector extrapolation methods. applications and numerical comparison , 2000 .

[13]  L. Petzold.  An Efficient Numerical Method for Highly Oscillatory Ordinary Differential Equations , 1978 .

[14]  Caren Tischendorf,et al.  Structural analysis of electric circuits and consequences for MNA , 2000, Int. J. Circuit Theory Appl..

[15]  C. Tischendorf,et al.  Structural analysis of electric circuits and consequences for MNA , 2000 .

[16]  S. Skelboe,et al.  Time-domain steady-state analysis of nonlinear electrical systems , 1982, Proceedings of the IEEE.

[17]  Kenneth S. Kundert,et al.  The designer's guide to SPICE and Spectre , 1995 .

[18]  Aurelio Medina,et al.  Computation of the periodic steady state in systems with nonlinear components using a hybrid time and frequency domain methodology , 1995 .