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1/f spectrum in a nonlinear electronic loop: consequences in frequency standards and signal processing

Spectre en 1/f dans une boucle électronique non linéaire: conséquences en traitement du signal et sur la caractérisation des oscillateurs

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We study an electronic loop in which we can observe two different behaviors: the frequency locking and the free-run mode. Two ultrastable RF oscillators are compared in an electronic loop whose phase error follows the Adler model. This model presents a separatrix yielding a chaotic behavior under small perturbations. We study experimentally and numerically the effects of perturbations given by the intermodulation products generated by the mixer, or by the intrinsic instability of oscillator under measurement. Power spectral density and Allan variance measurements are in agreement with theoretical results which predict an increasing instability close to the separatrix. Furthermore, we find that the most important noise contribution follows a 1/f dependence. In our experiment we attribute the 1/f fluctuations to the presence of nonlinear effects predicted from the Adler equation under time depending perturbations.


Une boucle électronique dont on observe deux comportements différents: le régime de battement et le régime synchronisé est présentée. Deux oscillateurs RF ultra-stables sont comparés en utilisant le modèle non lineaire d’Adler. Ce système présente une séparatrice conduisant, sous l’effet d’une perturbation, à une évolution chaotique de la phase. L’effet d’une perturbation périodique issue des produits d’intermodulation générés par le mélangeur, et d’une perturbation stochastique issue de l’instabilité intrinsèque de l’oscillateur est étudiée expérimentalement et numériquement. Les mesures de densité spectrale et de variance d’Allan confirment cette augmentation de l’instabilité essentiellement constituée de bruit en 1/f et qui peut être attribué à la présence d’effets non linéaires établis à partir du modèle d’Adler perturbé.

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Correspondence to Serge Dos Santos or Michel Planat.

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Dos Santos, S., Planat, M. 1/f spectrum in a nonlinear electronic loop: consequences in frequency standards and signal processing. Ann. Télécommun. 53, 488–494 (1998).

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Key words

  • Phase locked loop
  • Nonlinear circuit
  • 1/f noise
  • Oscillator
  • Intermodulation products
  • White noise

Mots clés

  • Boucle verrouillage phase
  • Circuit non linéaire
  • bruit 1/f
  • Oscillateur
  • Produits intermodulation
  • Bruit blanc