Abstract
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.
Résumé
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.
Similar content being viewed by others
References
Klapper (J.) andFrankle (J. T.), Phase-locked and frequency-feedback systems,Academic Press, New York, (1972).
Adler (R.), A study of locking phenomena in oscillators,Proc. IRE,34, p. 351, 1946, Reprinted inProc. IEEE,61, 1380 (1973).
Cresser (J. D.), Louisell (W. H.), Meystre (P.), Schleich (W.), Scully (M. O.), Quantum noise in ring-laser gyros. i. theoretical formulation of problem,Physical Review A. (1982),25, p. 2214.
Vanier (J.), Audoin (C.), The quantum physics of atomic frequency standards, vol. 1 et 2,Adam Hilger, (1989).
Dos Santos (S.), Planat (M.), Arithmetical fractals in an electronic loop, inFractals and Beyond, M. M. Novak, Ed. (1998), Word Scientific, p. 299.
Dos Santos (S.), Étude non linéaire et arithmétique de la synchronisation des systèmes: application aux fluctuations de basse fréquence des oscillateurs ultra-stables,PhD thesis, Besançon, (1998).
Stratanovich (R. L.), Theory of random noise,Gordon and Breach, New York, (1967).
Planat (M.), Dos Santos (S.), Ratier (N.), Cresson (J.), Perrine (S.), Close to resonance interaction of radiofrequency waves in a schottky diode mixer: 1/f noise and number theory, inProc. of VII Van der Ziel Symposium on Quantum 1/f noise, St. Louis. (1999), AIP Press.
Arecchi (F. T.), Badii (R.), Politi (A.), 1/f spectra in nonlinear systems with many attractors,Noise in Physical systems and 1/f noise. (1983), p. 127.
Arecchi (F. T.), Califano (A.), Noise-induced trapping at the boundary between two attractors: a source of 1/f spectra in nonlinear dynamics,Europhysics Letters. (1987),3, p. 5.
Yamaguchi (Y), Sakai (K.), 1/f noise spectrum of the chaotic motion in a whisker mapping,Physics Letters A. (1986),117, p. 387.
Takagi (K.) The power spectrum of a white noise passed through a nonlinear transmission line,Jpn. J. Appl. Phys. (1983),22, p. 1446.
Handel (P. H.), The nature of fundamental 1/f noise, inNoise in Physical Systems and 1/f fluctuations, Saint-Louis, (1993), p. 162, Peter H. Handel and Alma L. Chung.
Kawai (T.), Mihira (Y.), Basis of universal existence of 1/f fluctuations, inNoise in Physical Systems and 1/f fluctuations, SaintLouis, (1993), p. 639, Peter H. Handel and Alma L. Chung.
Leeson (D. B.), A simple model of feedback oscillator noise spectrum,Proc. of the IEEE (1966),54, p. 329.
Sauvage (G.), Phase noise in oscillators: A mathematical analysis of Leeson's model,IEEE Trans. Instrum. Meas. (1977),IM-26, p. 408.
Planat (M.), Ed.,Oscillators,Special issue of Annals of Telecom-munications. (1996)51, no 7–8, pp. 293–436.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1007/BF02998594
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02998594