A general method to predict the amplitude of oscillation in nearly sinusoidal oscillators

Author

Maggio, Gian Mario ; De Feo, Oscar ; Kennedy, Michael P.

Author_Institution

Adv. Syst. Technol., STMicroelectronics, San Diego, CA, USA

Volume

51

Issue

8

fYear

2004

Firstpage

1586

Lastpage

1595

Abstract

In this paper, a general methodology for predicting the amplitude of oscillation in nearly sinusoidal oscillators is presented. The method relies on the recently proposed projection technique for the computation of the center manifold and on the Hopf normal form theory to approximate the corresponding limit cycle in state space. The Colpitts oscillator is selected as a case study and, for this circuit, a closed-form expression for the amplitude of oscillation is derived as a function of the circuit parameters.

Keywords

bifurcation; eigenvalues and eigenfunctions; limit cycles; oscillators; state-space methods; Colpitts oscillator; Hopf normal form theory; center manifold theorem; limit cycle; nearly sinusoidal oscillators; oscillation amplitude; state space; Bifurcation; Circuits; Closed-form solution; Eigenvalues and eigenfunctions; Failure analysis; Frequency; Information analysis; Limit-cycles; Oscillators; State-space methods; Center manifold theorem; Colpitts oscillator; Hopf normal form theorem; oscillation amplitude;

fLanguage

English

Journal_Title

Circuits and Systems I: Regular Papers, IEEE Transactions on

Publisher

ieee

ISSN

1549-8328

Type

jour

DOI

10.1109/TCSI.2004.832793

Filename

1323210