AMPLITUDE NOISE INDUCED PHASE NOISE IN ELECTROSTATIC MEMS RESONATORS

This article's focus is on the numerical estimation of the overall instability of microelectromechanical-system-based (MEMS) resonators, caused by intrinsic noise mechanisms that are different in nature (electrical, mechanical or chemical). Heterogeneous intrinsic noise sources in MEMS resonators that have been addressed here are Johnson–Nyquist noise, 1/f noise, noise caused by temperature fluctuations and adsorptiondesorption induced noise. Their models are given first (based on analytical modeling or based on empirical expressions with experimentally obtained parameters). Then it is shown how each one contributes to the phase noise, a unique figure of merit of resonators instability. Material dependent constants  and knee position in noise spectrum, needed for empirical formulae referring to 1/f noise, have been obtained experimentally, by measurements of noise of MEMS components produced in the Centre of Microelectronic Technologies of the Institute of Chemistry, Technology and Metallurgy in Belgrade. According to these measurements,  varies in the range from 0.776.10-4 to 2.26.10-4 and cut off frequency for 1/f noise varies from 147 Hz to 1 kHz. The determined values are then used for the modeling of micro-resonator phase noise with electrical origin and overall phase noise of a micro-resonator. Numerical example for calculation of overall phase noise is given for a micro-cantilever, produced by the same technology as measured components. The outlined noise analysis can be easily extended and applied to noise analysis of MEMS resonator of an arbitrary shape.

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Analysis of the Orbits of Electrostatic MEMS Resonators

Volume 13: Nano-Manufacturing Technology; and Micro and Nano Systems, Parts A and B ◽

10.1115/imece2008-68042 ◽

2008 ◽

Cited By ~ 1

Author(s):

F. Najar ◽

E. M. Abdel-Rahman ◽

A. H. Nayfeh ◽

S. Choura

Keyword(s):

Initial Conditions ◽

Order Approximation ◽

Differential Quadrature Method ◽

Basin Of Attraction ◽

Mems Resonator ◽

Mems Resonators ◽

Electrostatic Mems ◽

Differential Integral Equation ◽

First Order Approximation ◽

The Basin Of Attraction

We study the dynamic behavior of an electrostatic MEMS resonator using a model that accounts for the system nonlinearities due to mid-plane stretching and electrostatic forcing. The partial-differential-integral equation and associated boundary conditions representing the system dynamics are discretized using the Differential Quadrature Method (DQM) and the Finite Difference Method (FDM) for the space and time derivatives, respectively. The resulting model is analyzed to determine the periodic orbits of the resonator and their stability. Simultaneous resonances are identified for large orbits. Finally, we develop a first-order approximation of the microbeam dynamic response, which reveals an erosion of the basin of attraction of the stable orbits that depends heavily on the amplitude and frequency of the AC excitation. Simulations show that the smoothness of the boundary of the basin of attraction can be lost to be replaced by fractal tongues, which increase the sensitivity of the microbeam response to initial conditions. As a result, the locations of the stable and unstable fixed points are likely to be disturbed.

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