Blocage par injection de modes sous- harmoniques d’un oscillateur utilisant une ligne à retard à ondes de surface

A nonlinear regeneration pulsed oscillator driven by a monochromatic source has been built. Subharmonics of the resonance carrier/modulation are measured with an accuracy of 10^-10 thanks to the use of a double beats measurement set-up. The multiscale analysis of frequency readings reveals a rich fine structure which is in agreement with the nonlinear topological approach of synchronized states.     

On the frequency and amplitude spectrum and the fluctuations at the output of a communication receiver

A mixer cascaded with a low-pass filter is the basic piece of any communication receiver. The frequency and amplitude fluctuations of beat signals recorded at the output of the mixer plus filter set-up are investigated experimentally and explained on the basis of number theory in relation to the Riemann problem concerning the distribution of prime numbers. The frequency of the beat signal is obtained from a diophantine approximation of the frequency ratio of the input oscillators. The amplitude is defined globally from the position of resolved fractions with respect to an equally spaced graduation. Time series analysis methods show that frequency fluctuations present a transition from white frequency noise to 1/f frequency noise close to resonance; the latter is compatible with an underlying fractal attractor. The same transition is observed in the case of time series computed from continued fraction expansions.     

Synchronization,topology and oscillators

The synchronization of oscillators is defined step by step from the exemple of an electronic phase-locked loop. Besides, an injection-locked pulsed delay oscillator is built in which the signal is synchronized both in its frequency and its duration : the local behaviour (the carrier) is thus resonating with the global behaviour (the envelope). A model of the electronic wave function in terms of the fundamental groups of punctured Riemann surfaces is attempted. The structure of synchronization zones goes in favour of that hypothesis.     

Bulk waves radiated from an interdigital metallic transducer deposited on an anisotropic substrate

The whole acoustic field emanating from a metallic interdigital transducer (IDT) deposited on an anisotropic half-space is computed. Extending the classical Lamb approach, it is shown that the field can be expressed by an integral whose singularities give rise to both Rayleigh surfaces waves (SAWs) and well collimated bulk waves (BAWs). For a Y-cut, Z-propagation quartz crystal a horizontal shear wave is excited; it is shown that the orientation and width of the main lobe can be chosen by changing the frequency.     

Generation of 1/f noise in locked systems working in nonlinear mode

Properties of the phase fluctuations of a nonlinear oscillator were investigated. The multiscale aspect of synchronization is experimentally confirmed with the observation of lockings at any rational ratio. This global property of synchronization is associated with a local one by the study of the phase locked loop (PLL) under nonlinear conditions. We show that the discontinuity between the locking and the free-run state is characterized by the presence of slow temporal variations that induce a low frequency spectrum. An experimental verification of the increase of fluctuations confirms the classical results, which associate 1/f noise to nonlinearity, autosimilarity and regularity, represented here by the synchronization.     

Is the frequency noise of an oscillator of deterministic origin?

We report on a new multifractal type approach of low-frequency noise in oscillators. The time sequence is interrogated by means of a multiscale local stability exponent which acts in a sliding filtering window. Its discontinuities are reflected into a binary coding in which the correlations are analyzed. The mapping of binary data into a devil's staircase is used to emphasize the correlated and possibly deterministic origin of frequency fluctuations in quartz oscillators     

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

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.     

Oscillator phase noise measurements by picosecond synchroscanstreak camera

A new method-with picosecond resolution-allowing the recording of the instantaneous time phase fluctuations of a crystal controlled oscillator is presented. The oscillator under test drives the acoustooptic modelocker of a CW Nd:YAG laser associated with a synchronously pumped dye laser. By means of a streak camera illuminated by the ps dye laser pulses and synchronized by the oscillator signal the statistics of its zero crossings is analyzed     

Intermodulation in X-cut lithium tantalate resonators

The analysis of intermodulation in X-cut lithium tantalate resonators is performed and applied to the evaluation of the fourth-order nonlinear elastic coefficient. A comparison with an AT-cut quartz resonator indicates that lithium tantalate nonlinearities are much lower.