Etude non linéaire et arithmétique de la synchronisation des systèmes : application aux fluctuations de basse fréquence des oscillateurs ultra-stables

Abstract : We study the nonlinear behavior of electronical systems such as oscillators or phase locked loops (PLL). After a brief sum-up of the existence of oscillator intrinsic nonlinearities, we recall
classical statistical methods of signal processing and phase noise measurement. We adapt new modern tools of nonlinear signal processing (Poincaré sections, phase space, Arnold mapping,
arithmetic) on the Van der Pol model of oscillator. This model (Adler's model) allow us to study the PLL under nonlinear behavior in which multiscale properties of synchronization and high
transient time are identified. The experimental study is realized from the nonlinear synchronization of two ultrastable radiofrequency oscillators (5 MHz) perturbed with white frequency noise and periodic perturbations due to the modulator. A white frequency noise to l/f frequency noise (flicker noise) transformation is observed when the system exhibits a high nonlinear behavior; results confirmed by numerical integration (Runge-Kutta) .The experimental verification of multiscale properties exhibits a diophantine property of the intermodulation spectrum due to the arithmetical rules governing the frequencies. This arithmetical approach is again verified with a carrier-envelope experiment where a carrier (97 MHz) is modulated from the detection of an acoustic response (300 kHz) of a surface acoustic wave delay line. The same nonlinear properties
(chaos, synchronization, devil staircase, scale invariance) of the system are identified.
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https://tel.archives-ouvertes.fr/tel-00009255
Contributor : Serge dos Santos <>
Submitted on : Friday, May 13, 2005 - 12:03:32 PM
Last modification on : Friday, July 20, 2018 - 3:02:03 PM
Long-term archiving on : Friday, April 2, 2010 - 9:36:31 PM

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  • HAL Id : tel-00009255, version 1

Citation

dos Santos Serge. Etude non linéaire et arithmétique de la synchronisation des systèmes : application aux fluctuations de basse fréquence des oscillateurs ultra-stables. Traitement du signal et de l'image [eess.SP]. Université de Franche-Comté, 1998. Français. ⟨tel-00009255⟩

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