Related papers: Another approach to the study of phase noise in el…
The oscillator, inherently, turns the phase noise of its internal components into frequency noise, which results into a multiplication by 1/f^2 in the phase-noise power spectral density. This phenomenon is known as the Leeson effect. This…
Time, and equivalently frequency, is the most precisely measured physical quantity. It is therefore inevitable that virtually all domains of engineering and physics need reference oscillators. The oscillator noise can be decomposed into…
We present an analytical calculation of the response of a driven Duffing oscillator to low-frequency fluctuations in the resonance frequency and damping. We find that fluctuations in these parameters manifest themselves distinctively,…
We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the stochastic oscillator dynamics onto a…
This paper augments the existing macroscopic circuit noise model for phase noise in relaxation oscillators by showing the microscopic origins of the noise and explains temperature dependency. The noise arises from fluctuation of the energy…
The frequency flicker of an oscillator, which appears as a 1/f^3 line in the phase noise spectral density, and as a floor on the Allan variance plot, originates from two basic phenomena, namely: (1) the 1/f phase noise turned into 1/f…
The phase description is a powerful tool for analyzing noisy limit cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to the Gaussian noise while noise in the…
Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the…
We review the state space decomposition techniques for the assessment of the noise properties of autonomous oscillators, a topic of great practical and theoretical importance for many applications in many different fields, from electronics,…
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for…
Synchronization of coupled oscillators is a paradigm for complexity in many areas of science and engineering. Any realistic network model should include noise effects. We present a description in terms of phase and amplitude deviation for…
We theoretically study the frequency stability of an opto-mechanical radio frequency oscillator based on resonant interaction of two optical and one mechanical modes of the same optical microcavity. A generalized expression for the phase…
We analyze the amplitude and phase noise of limit-cycle oscillations in a mechanical resonator coupled parametrically to an optical cavity driven above its resonant frequency. At a given temperature the limit-cycle oscillations have lower…
A new mechanism of low frequency (1/f-like) noise generation is described and analyzed. It is attributed to higher frequency asymmetric resonance modes, which are stimulated by a random factor, e.g. due to thermal excitation.…
We address the exploitation of an optical parametric oscillator (OPO) in the task of mitigating, at least partially, phase noise produced by phase diffusion. In particular, we analyze two scenarios where phase diffusion is typically…
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic…
We introduce a new method for reducing phase noise in oscillators, thereby improving their frequency precision. The noise reduction device consists of a pair of coupled nonlinear resonating elements that are driven parametrically by the…
We study the role of amplifier saturation in eliminating feedback noise in self-sustained oscillators. We extend previous works that use a saturated amplifier to quench fluctuations in the feedback magnitude, while simultaneously tuning the…
The output of oscillators is usually not stable over time. In particular, phase variations---or \emph{phase noise}---corrupts the oscillations. In this letter, we describe a circuit that designed to average the phase noise processes and…
An effective description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by invariant probability density or via first passage times. While the first approach…