Theory of amplifier-noise evasion in an oscillator employing a nonlinear resonator

Abstract

Resonators driven into self-oscillation via active feedback often form the basis of clocks and other sensitive measurement instrumentation.The phase stability of such an oscillator is ultimately limited by the noise associated with the resonator s intrinsic losses. However, it is often the case that amplifier noise is the dominant cause of the oscillator's phase diffusion. Here it is shown that when the resonator possesses a suitable nonlinearity, the phase diffusion due to amplifier noise can be suppressed, allowing one to achieve a long-term phase stability comparable to the ultimate noise limit.PACS number(s): 42.50.Ne, 05.40. +j, 06.20.Dk, 03.65.Bz

Nonlinear Dynamics of Nanomechanical Resonators

“…We can treat this equation perturbatively [49,69]. We first consider the linear part of the equation, which has the form of (8.5) with T 0 in place of T, separate the variables, 8) and find its spatial eigenmodes φ n (z).…”

“…The existence of the saddle-node bifurcation has also been exploited for applications because the response of the resonator at the bifurcation point can change dramatically if one changes the drive frequency, or any of the resonator's physical parameters that can alter the response curve. This idea has been used for signal amplification [10] as well as squeezing of noise [3,69].…”

Phase noise of oscillators with unsaturated amplifiers

“…Greywall et al considered a nonlinear resonator typified by a thin, electrically conducting beam of mass M in a uniform magnetic field and driven by an alternating feedback current [1,2]. The beam dynamics are governed by the equation [2] …”

“…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.…”

Addressing geometric nonlinearities with cantilever microelectromechanical systems: Beyond the Duffing model

“…When used in the linear regime, non-linearity limits the dynamic range of a device [3]. One can also exploit non-linearity with for instance frequency mixing [4], synchronization [5], amplification using bifurcation points [6], suppression of amplifier noise in oscillator circuits [7][8][9], and mass (homodyne) detection [10]. Moreover, the non-linear component proves to be essential to complex, useful and efficient designs, with for instance the diode in conventional electronics and the Josephson junction in superconducting circuitry [11].…”