zbMATH — the first resource for mathematics

An accelerated Poincaré-map method for autonomous oscillators. (English) Zbl 1027.65109
Summary: 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.

65L80 Numerical methods for differential-algebraic equations
65L05 Numerical methods for initial value problems
34A09 Implicit ordinary differential equations, differential-algebraic equations
78A55 Technical applications of optics and electromagnetic theory
34C25 Periodic solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
Full Text: DOI
[1] Telichevesky, R.; Kundert, K.; Elfadel, I.; White, J., Fast simulation algorithms for RF circuits, (), 437-444
[2] Aprille, T.J.; Trick, T., Steady state analysis of nonlinear circuits with periodic inputs, (), 108-114
[3] Skelboe, S., Time-domain steady-state analysis of nonlinear electrical systems, (), 1210-1228
[4] ter Maten, E., Numerical methods for frequency domain analysis of electronic circuits, Survey on mathematics for industry, 8, 171-185, (1999) · Zbl 1085.94514
[5] K. Kundert, Simulation methods for RF integrated circuits, in: Proceedings of ICCAD’97, 1997
[6] Semlyen, A.; Medina, A., Computation of the periodic steady state in systems with nonlinear components using a hybrid time and frequency domain method, IEEE transactions on power systems, 10, 3, 1498-1504, (1995)
[7] G. Welsh, H. Brachtendorf, C. Sabelhaus, R. Laur, Minimization of the error in the calculation of the steady state by shooting methods, Technical Report, Institute of Electromagnetic Theory and Microelectronics, University of Bremen, Germany
[8] Petzold, L.R., An efficient numerical method for highly oscillatory ordinary differential equations, SIAM journal on numerical analysis, 18, 455-479, (1981) · Zbl 0474.65053
[9] Brambilla, A.; D’Amore, D.; Santomauro, M., Simulation of autonomous circuits in the time domain, (), 399-402
[10] Chua, L.O.; Lin, P.-M., Computer-aided analysis of electronic circuits, (1975), Prentice-Hall Englewood Cliffs, NJ · Zbl 0358.94002
[11] Massobrio, G.; Antognetti, P., Semiconductor device modeling with SPICE, (1993), McGraw-Hill New York
[12] Kundert, K., The designer’s guide to SPICE & SPECTRE, (1995), Kluwer Academic Publishers Dordrecht · Zbl 0834.94002
[13] Schwarz, D.E.; Tischendorf, C., Structural analysis for electric circuits and consequences for MNA, International journal of circuit theory and applications, 28, 131-162, (2000) · Zbl 1054.94529
[14] Ascher, U.; Mattheij, R.; Russell, R., Numerical solution of boundary value problems for ordinary differential equations, (1988), Prentice-Hall Englewood Cliffs, NJ
[15] Hairer, E.; Nørsett, S.; Wanner, G., Solving ordinary differential equations I, (1987), Springer Berlin · Zbl 0638.65058
[16] Smith, D.A.; Ford, W.F.; Sidi, A., Extrapolation methods for vector sequences, SIAM review, 29, 2, 199-233, (1987) · Zbl 0622.65003
[17] Brezinski, C., Convergence acceleration during the 20th century, Journal of computational and applied mathematics, 122, 1-21, (2000) · Zbl 0976.65003
[18] Jbilou, K.; Sadok, H., Vector extrapolation methods. applications and numerical comparison, Journal of computational and applied mathematics, 122, 149-165, (2000) · Zbl 0974.65034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.