How to Model the Near-to-the-Carrier Regime and the Lower Knee Frequency of Real RF Oscillators

Numerous empirical data demonstrate that real noisy RF oscillators are affected by power-law phase noise. However, until recently, the robust analytic modeling of the deep-into-the-carrier spectral regime of RF oscillators was intangible due to the infinities involved in the relevant power-law regions. In this letter we demonstrate how recent advances in oscillator spectral modeling can be applied to extrapolate the near-to-the-carrier regime as well as estimate the oscillator lower knee frequency of transition between the deep-into-the-carrier regime and the power-law regions of real RF oscillators.</jats:p

Determination of phase noise spectra in optoelectronic microwave oscillators: a Langevin approach

We introduce a stochastic model for the determination of phase noise in optoelectronic oscillators. After a short overview of the main results for the phase diffusion approach in autonomous oscillators, an extension is proposed for the case of optoelectronic oscillators where the microwave is a limit-cycle originated from a bifurcation induced by nonlinearity and time-delay. This Langevin approach based on stochastic calculus is also successfully confronted with experimental measurements.Comment: 18 pages, 7 figures, 11 references. Submitted to IEEE J. of Quantum Electronics, May 200

A spectral model for RF oscillators with power-law phase noise

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High spectral purity microwave sources based on optical resonators

L'optique constitue aujourd'hui une solution performante pour la réalisation de sources très pures en hyperfréquences, en particulier grâce à l'approche de l'oscillateur électro-optique (OEO). La pureté spectrale de ces sources est essentielle pour les applications spatiales, militaires et pour la métrologie du temps et des fréquences. Durant cette thèse, nous avons réalisé et étudié différents types d'OEO à résonateur optique en vue d'optimiser le bruit de phase de ce système. Nous avons en particulier orienté nos travaux vers une approche originale utilisant un anneau résonant fibré (ARF) passif. Ce type de résonateur présente en effet des coefficients de qualité optiques supérieurs à 109 pour des longueurs de fibre restant relativement faibles (L ~ 10 m) et facilement intégrables dans un support planaire. En parallèle, nous avons mené un travail important sur les oscillateurs à base de résonateurs optiques 3D. Concernant l'OEO à ARF, des progrès spectaculaires ont pu être obtenus grâce à une meilleure compréhension des phénomènes de bruit intrinsèques à ce système. Les deux types de bruit prépondérants étaient la conversion du bruit du laser (FM et AM) en bruit de phase RF par différentes non-linéarités (dont la photodiode) et le déclenchement d'effets non-linéaires optiques à l'intérieur du résonateur. Le contrôle de ces effets a permis en particulier d'éliminer des remontées importantes de bruit sur le spectre de l'oscillateur, et d'atteindre un niveau de bruit de phase de -128 dBc/Hz à 10 kHz de la porteuse à 10.2 GHz en utilisant un OEO à base d'un ARF passif de 100 mètres de longueur, optimisé et immunisé contre les effets non-linéaires optiques.Optics represents an elegant and reliable solution to generate high spectral purity microwave signals, especially the approach using the optoelectronic oscillator (OEO). The spectral purity of these sources is very important for space and military applications and also for time and frequency domain metrology. During this thesis, we have fabricated and studied many types of resonator based OEO in order to optimize the system phase noise. We have especially investigated an original approach using a passive fiber ring resonator (FRR). This resonator type can feature optical quality factors higher than 109 when only few meters of optical fibers are used (L ~ 10 m) and it can be easily integrated in a planar setup. Moreover, we have performed an important work on 3D WGM resonators based oscillators. In the FRR based OEO, spectacular progresses have been achieved thanks to a good understanding of the system intrinsic noise phenomena. Actually, we have found that the most important noise parameters were the laser FM and AM noise conversion into RF phase noise by means of different nonlinearities in the system (like the photodiode nonlinearity), but also by the generation of nonlinear optical effects inside the resonator. By controlling these effects, we have been able to reduce the OEO phase noise level and to reach a -128 dBc/Hz noise level at 10 kHz offset frequency from a 10.2 GHz carrier. This has been achieved using an OEO based on a 100m-long passive FRR, which has been optimized and immunized against different nonlinear optical effects

Homodyne detection for laser-interferometric gravitational wave detectors

Gravitational waves are ripples of space-time predicted by Einstein\u27s theory of General Relativity. The Laser Interferometer Gravitational-wave Observatory (LIGO), part of a global network of gravitational wave detectors, seeks to detect these waves and study their sources. The LIGO detectors were upgraded in 2008 with the dual goals of increasing the sensitivity (and likelihood of detection) and proving techniques for Advanced LIGO, a major upgrade currently underway. As part of this upgrade, the signal extraction technique was changed from a heterodyne scheme to a form of homodyne detection called DC readout. The DC readout system includes a new optical filter cavity, the output mode cleaner, which removes unwanted optical fields at the interferometer output port. This work describes the implementation and characterization of the new DC readout system and output mode cleaner, including the achieved sensitivity, noise couplings, and servo control systems

Low-frequency noise in downscaled silicon transistors: Trends, theory and practice

By the continuing downscaling of sub-micron transistors in the range of few to one deca-nanometers, we focus on the increasing relative level of the low-frequency noise in these devices. Large amount of published data and models are reviewed and summarized, in order to capture the state-of-the-art, and to observe that the 1/area scaling of low-frequency noise holds even for carbon nanotube devices, but the noise becomes too large in order to have fully deterministic devices with area less than 10nm×10nm. The low-frequency noise models are discussed from the point of view that the noise can be both intrinsic and coupled to the charge transport in the devices, which provided a coherent picture, and more interestingly, showed that the models converge each to other, despite the many issues that one can find for the physical origin of each model. Several derivations are made to explain crossovers in noise spectra, variable random telegraph amplitudes, duality between energy and distance of charge traps, behaviors and trends for figures of merit by device downscaling, practical constraints for micropower amplifiers and dependence of phase noise on the harmonics in the oscillation signal, uncertainty and techniques of averaging by noise characterization. We have also shown how the unavoidable statistical variations by fabrication is embedded in the devices as a spatial “frozen noise”, which also follows 1/area scaling law and limits the production yield, from one side, and from other side, the “frozen noise” contributes generically to temporal 1/f noise by randomly probing the embedded variations during device operation, owing to the purely statistical accumulation of variance that follows from cause-consequence principle, and irrespectively of the actual physical process. The accumulation of variance is known as statistics of “innovation variance”, which explains the nearly log-normal distributions in the values for low-frequency noise parameters gathered from different devices, bias and other conditions, thus, the origin of geometric averaging in low-frequency noise characterizations. At present, the many models generally coincide each with other, and what makes the difference, are the values, which, however, scatter prominently in nanodevices. Perhaps, one should make some changes in the approach to the low-frequency noise in electronic devices, to emphasize the “statistics behind the numbers”, because the general physical assumptions in each model always fail at some point by the device downscaling, but irrespectively of that, the statistics works, since the low-frequency noise scales consistently with the 1/area law