DocumentCode :
3437054
Title :
Exploitation of the phasor approach for closed-form solution of the Van der Pol´s oscillator and sinusoidal oscillators with high-order nonlinearity
Author :
Palumbo, Gaetano ; Pennisi, Melita ; Pennisi, Salvatore
Author_Institution :
DIEES - Dipt. di Ing. Elettr., Elettron. e dei Sist., Univ. of Catania, Catania, Italy
fYear :
2009
fDate :
13-16 Dec. 2009
Firstpage :
155
Lastpage :
158
Abstract :
In this paper the phasor approach is applied to find the solution of the well-known Van der Pol´s equation for both quasi-sinusoidal and relaxation oscillation regimes. It allows to find simple closed-form relationships for the output harmonics of a LC oscillator whose behavior is described by the Van der Pol´s equation. Furthermore, the validity of the phasor approach is extended to analyze also oscillators with nonlinearity of order higher than three. As an example a LC oscillator with a polynomial nonlinearity of fifth order is considered and closed-form relationships for the output harmonics are found. The analysis developed, both for the Van der Pol´s equation and for oscillators with high-order nonlinearity, is verified by means of simulations performed with Spectre.
Keywords :
harmonics; nonlinear network analysis; relaxation oscillators; LC oscillator; Van der Pol oscillator; closed form solution; high order nonlinearity; phasor approach; quasisinusoidal oscillation; relaxation oscillation; sinusoidal oscillator; Analytical models; Circuits; Closed-form solution; Harmonic analysis; Linearity; Nonlinear equations; Oscillators; Performance analysis; Polynomials; Software performance;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Electronics, Circuits, and Systems, 2009. ICECS 2009. 16th IEEE International Conference on
Conference_Location :
Yasmine Hammamet
Print_ISBN :
978-1-4244-5090-9
Electronic_ISBN :
978-1-4244-5091-6
Type :
conf
DOI :
10.1109/ICECS.2009.5410963
Filename :
5410963
Link To Document :
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