Surpassing fundamental limits of oscillators using nonlinear resonators

Abstract

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 signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic, regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonators anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nanoelectromechanical system (NEMS)-based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables a significant reduction of the oscillators phase noise, as predicted by our model.

14 pages, 2 figures, 1 table

References in corpus (8)

• Nonlinear damping in mechanical resonators based on graphene and carbon nanotubes
• Nonlinear modal interactions in clamped-clamped mechanical resonators
• A Nanoscale Parametric Feedback Oscillator
• Nonlinearity in nanomechanical cantilevers
• Stress-Induced Variations in the Stiffness of Micro- and Nanocantilever Beams
• Frequency and phase noise of ultra-high Q silicon nitride nanomechanical resonators
• Optimal operating points of oscillators using nonlinear resonators
• A Passive Phase Noise Cancellation Element

Cited by in corpus (37)

• Thermal nonlinearities in a nanomechanical oscillator
• Graphene mechanical oscillators with tunable frequency
• Synchronization of two anharmonic nanomechanical oscillators
• Nanotube mechanical resonators with quality factors of up to 5 million
• Mesoscopic physics of nanomechanical systems
• Optically levitated nanoparticle as a model system for stochastic bistable dynamics
• Nonlinear mode-coupling and synchronization of a vacuum-trapped nanoparticle
• Stabilization of a linear nanomechanical oscillator to its ultimate thermodynamic limit
• Quantum limit-cycles and the Rayleigh and van der Pol oscillators
• Self-sustained micromechanical oscillator with linear feedback
• Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators
• Phase-Locked Loop based Resonant Sensors: A Rigorous Theory and General Analysis Framework for Deciphering Fundamental Sensitivity Limitations due to Noise
• Non-equilibrium steady state of a driven levitated particle with feedback cooling
• Resolution Limits of Resonant Sensors with Duffing Non-Linearity
• Understanding Fundamental Tradeoffs in Nanomechanical Resonant Sensors
• Non-linear Frequency Transduction of Nano-mechanical Brownian Motion
• Coherent interplay between surface acoustic waves and coupled mechanical resonators: transition from plasmon-like to surface mediated coupling
• Cubic singularities in binary linear electromechanical oscillators
• Spin detection via parametric frequency conversion in a membrane resonator
• Generating Giant and Tunable Nonlinearity in a Macroscopic Mechanical Resonator from Chemical Bonding Force
• Charge sensitivity enhancement via mechanical oscillation in suspended carbon nanotube devices
• Systematic Synthesis and Design of Ultra-Low Threshold Parametric Frequency Dividers
• Precision calibration of the Duffing oscillator with phase control
• Frequency stabilization of self-sustained oscillations in a sideband-driven electromechanical resonator
• Phase noise of oscillators with unsaturated amplifiers
• Suppressing Frequency Fluctuations of Self-Sustained Vibrations in Underdamped Nonlinear Resonators
• Method to Determine the Closed-Loop Precision of Resonant Sensors from Open-Loop Measurements
• Devil's Staircase in an Optomechanical Cavity
• On the effect of linear feedback and parametric pumping on a resonators frequency stability
• Size Effects on Mechanical Properties of Micro/Nano Structures
• Hidden vibrational bistability revealed by intrinsic fluctuations of a carbon nanotube
• Determining the source of phase noise: Response of a driven Duffing oscillator to low-frequency damping and resonance frequency fluctuations
• Network and Phase Symmetries Reveal That Amplitude Dynamics Stabilize Decoupled Oscillator Clusters
• Frequency Stability of Graphene Nonlinear Parametric Oscillator
• High Stability Mechanical Frequency Sensing beyond the Linear Regime
• On-Chip Frequency Noise Cancellation in Nanomechanical Resonators using Cavity Optomechanics
• Coherent response of a stochastic nonlinear oscillator to a driving force: analytical characterization of the spectral signatures