Chaos on Phase Noise of Van Der Pol Oscillator

Gang Feng Yan, Xian He Huang


 Phase noise is the most important parameter in many oscillators. The proposed method in this paper is based on nonlinear stochastic differential equation for phase noise analysis approach. The influences of two different sources of noise in the Van Der Pol oscillator adopted this method are compared. The source of noise is a white noise process which is a genuinely stochastic process and the other is actually a deterministic system, which exhibits chaotic behavior in some regions. The behavior of the oscillator under different conditions is investigated numerically. It is shown that the phase noise of the oscillator is affected by a noise arising from chaos than a noise arising from the genuine stochastic process at the same noise intensity.

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Edson WA. Noise in oscillators. Proc. of IRE. 1960; 48(8): 1454-1466.

Mullen JA. Background Noise in Nonlinear Oscillators. Proc. of IRE. 1960; 8: 1467-1473.

Leeson DB. A Simple Model of Feedback Oscillator Noise Spectrum. Proc. of IEEE. 1966; 54(2): 329-330.

Robins WP. Phase Noise in Signal Sources. London: Peter Peregrinus. 1982.

Hajimiri A, Lee TH. Ageneral theory of phase noise in electrical oscillators. IEEE J Solid-State Circuits. 1998; 33(2): 179–194.

Kaertner FX. Determination of the correlation spectrum of oscillators with low noise. IEEE Transactions on Microwave Theory and Techniques. 1989; 37(1): 90-101.

Demir A. Fully Nonlinear Oscillator Noise Analysis: An Oscillator with no Asymptotic Phase. International Journal of Circuit Theory and Applications. 2007; 35(2): 175–203.

Demir A. Nonlinear Phase Noise in Optical Fiber Communication Systems. IEEE Journal of Lightwave Technology. 2007; 25(8): 2002-2032.

Liu SK, Liu SD. Nonlinear Equations in Physics. Beijing: Peking University Press. 2000.

Wolf A, Swift JB. Determining Lyapunov exponents from a time series. Physica D. 1985; 16(3): 285-317.

Burrage PM. Runge–Kutta methods for stochastic differential equations. Thesis. Queensland: University of Queensland; 1999.


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