Related papers: Optimal operating points of oscillators using nonl…

We use the strong intrinsic non-linearity of a microwave superconducting qubit with a 4 GHz transition frequency to directly detect and control the energy of a micro-mechanical oscillator vibrating at 25 MHz. The qubit and the oscillator…

For atomic frequency standards in which fluctuations of the local oscillator (LO) frequency are the dominant noise source, we examine the role of the servo algorithm that predicts and corrects these frequency fluctuations. We derive the…

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator subjected to weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase…

Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…

The problem of estimating an unknown force driving a linear oscillator is revisited. When using linear measurement, feedback is often cited as a mechanism to enhance bandwidth or sensitivity. We show that as long as the oscillator dynamics…

This paper presents a system-level analytical framework for modeling and minimizing phase noise in body-biased cross-coupled LC-tank voltage-controlled oscillators (LC-VCOs). Building upon Impulse Sensitivity Function (ISF) theory, the…

This paper addresses important control and observability aspects of the phase synchronization of two oscillators. To this aim a feedback control framework is proposed based on which issues related to master-slave synchronization are…

Despite recent progress in nonlinear optics in wavelength-scale resonators, there are still open questions on the possibility of parametric oscillation in such resonators. We present a general approach to predict the behavior and estimate…

Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess…

We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the…

Photonic microring resonators are used in a variety of chip-integrated sensing applications where they allow one to measure transmission intensity changes upon external signals with a sensitivity that scales linearly with the Q factor. In…

We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly…

This paper addresses the analysis of oscillator phase-noise effects on the self-interference cancellation capability of full-duplex direct-conversion radio transceivers. Closed-form solutions are derived for the power of the residual…

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…

The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\varepsilon$. It is well known that,…

As a model of coupled nano-electromechanical resonantors we study two nonlinear driven oscillators with an arbitrary coupling strength between them. Analytical expressions are derived for the oscillation amplitudes as a function of the…

Amplitude amplification provides a quadratic speed-up for an array of quantum algorithms when run on a quantum machine perfectly isolated from its environment. However, the advantage is substantially diminished as the NISQ-era quantum…

We implement a capacitorless model of a VO2 oscillator by introducing into the circuit of a field-effect transistor and a VO2 thermal sensor, which provide negative current feedback with a time delay. We compare the dynamics of current and…

In this paper, we discuss the definition of Q factor for nonlinear oscillators. While available definitions of Q are often limited to linear resonators or oscillators with specific topologies, our definition is applicable to any oscillator…

Error correction is essential for modern computing systems, enabling information to be processed accurately even in the presence of noise. Here, we demonstrate a new approach which exploits an error correcting phase that emerges in a system…