Surpassing Fundamental Limits of Oscillators Using Nonlinear Resonators

Abstract

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 resonator’s 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 nano-electromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator’s phase noise, as predicted by our model.

Phase noise of oscillators with unsaturated amplifiers

“…Some time ago, Greywall et al demonstrated an interesting noise quenching effect in the operation of a self-oscillating system [1,2], a discovery that has an important potential impact for the design of high frequency, low noise electronic oscillators [3,4]. In addition to its practical consequences, the noise quenching phenomenon is of fundamental interest because it appeared when the system operated in the nonlinear regime, i.e., the quenching apparently relies on the inherent nonlinearity of the resonating element.…”

Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators

“…Nonlinear effects strongly restrict the dynamic range within which the system operates linearly, even making it vanishingly small in NEMS, and limit the scope for applications. However, recent works focus on directly using nonlinearities to improve the sensitivity of parametrically amplified detectors [16,18,19]. For instance, though quartic (Duffing) nonlinearities stabilize the parametric oscillator, it retains a "memory" of the underlying instability tongue structure in its frequency dependent response [20].…”

High-sensitivity linear piezoresistive transduction for nanomechanical beam resonators

“…However, one of the most limiting difficulties for the practical development of batch-fabricated SiNW resonators with performance characteristics approaching those of CNTs is to establish highly sensitive transduction schemes that efficiently convert mechanical vibrations into functional electrical signals. The small amplitude of the mechanical vibrations, in combination with their very high frequency and the natural tendency of high-aspect ratio beams to operate in a nonlinear regime, represents formidable obstacles for such purpose 11,12 . The application of the most sensitive transduction schemes reported so far for nanomechanical resonators, such as piezoelectric 13 , electrothermal 14 or optomechanical 15 , results either impossible or impractical for simple beams made of silicon with dimensions deep down in the nanoscale and resonant frequencies in the very high-frequency range.…”