Verification of the phase-noise model for MEMS oscillators operating in the nonlinear regime

Lee, H.K.; Ward, Paul A. S.; Duwel, Amy; Salvia, J.; Qu, Yu Qiao; Melamud, R.; Chandorkar, Saurabh A.; Hopcroft, Matthew A.; Kim, B.; Kenny, Thomas W.

doi:10.1109/transducers.2011.5969667

Cited by 23 publications

(8 citation statements)

References 11 publications

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“…Currently, micro-and nano-mechanical oscillators are being developed as an alternative to conventional oscillators, such as quartz oscillators, supported by their intrinsic compatibility with standard semiconductor processing and by their unprecedented sensitivity and time response as miniaturized sensing devices 8,9 . Unfortunately, as the dimensions of the vibrating structures are reduced to the micro-and nano-scale, their dynamic response at the amplitudes needed for operation frequently becomes nonlinear, with large displacement instabilities and excessive frequency noise considerably degrading their performance [10][11][12][13] .…”

mentioning

confidence: 99%

Frequency stabilization in nonlinear micromechanical oscillators

2012

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mechanical oscillators are present in almost every electronic device. They mainly consist of a resonating element providing an oscillating output with a specific frequency. Their ability to maintain a determined frequency in a specified period of time is the most important parameter limiting their implementation. Historically, quartz crystals have almost exclusively been used as the resonating element, but micromechanical resonators are increasingly being considered to replace them. These resonators are easier to miniaturize and allow for monolithic integration with electronics. However, as their dimensions shrink to the microscale, most mechanical resonators exhibit nonlinearities that considerably degrade the frequency stability of the oscillator. Here we demonstrate that, by coupling two different vibrational modes through an internal resonance, it is possible to stabilize the oscillation frequency of nonlinear self-sustaining micromechanical resonators. our findings provide a new strategy for engineering low-frequency noise oscillators capitalizing on the intrinsic nonlinear phenomena of micromechanical resonators.

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confidence: 99%

Frequency stabilization in nonlinear micromechanical oscillators

2012

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“…On the other hand, the recent model proposed by [9] acknowledges the possibility of improved PN due to proper phase tuning of a nonlinear resonator, where the expected results are determined by the phase-frequency slope at the selected operating phase, and captures the PN term and additive noise contributions. The experimental results reported in [10] demonstrate this characteristic under nonlinear operation with amplitude limiting enabled. This paper presents an empirical PN model for resonatorbased oscillators that encompasses both linear and nonlinear operation of the resonator, as demonstrated in [2] and [4], where the improvement to the PN in nonlinearity derives from the high-order phase filter action [3].…”

Section: Introductionmentioning

confidence: 62%

“…MEMS resonators can be forced into the nonlinear elastic regime when sufficiently high power is applied to the device structure, creating regions of high energy density [1], [10], [18], [19]. Intrinsic nonlinearities are dependent on effective acoustic velocity, stiffness coefficients, and propagation of the acoustic wave within the device, while induced nonlinearities may arise due to temperature, force, pressure, acceleration, and vibration, among other sources [5].…”

Section: Nonlinearity Of Mems Resonatorsmentioning

confidence: 99%

“…Dielectric materials present in the resonator (e.g., AlN) can exhibit hysteretic damping [28]. A resonator exhibits flicker noise given by (10) where is a coefficient capturing the hysteresis in the film due to dielectric loss, and is the capacitance of the piezoelectric stack [28]. For the case of AlN, is related to the dielectric loss tangent, which is approximately constant down to a few hundred Hertz [29], contributing additional flicker noise.…”

Section: B Noise Of the Nonlinear Resonatormentioning

confidence: 99%

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An Empirical Phase-Noise Model for MEMS Oscillators Operating in Nonlinear Regime

Pardo

Sorenson

Ayazi

2012

IEEE Trans. Circuits Syst. I

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Nonlinearity of a silicon resonator can lead to improved phase-noise performance in an oscillator when the phase shift of the sustaining amplifier forces the operating point to a steeper phase-frequency slope. As a result, phase modulation on the oscillator frequency is minimized because the resonator behaves as a high-order phase filter. The effect of the increased filtering translates into phase-noise shaping that reflects superior overall performance. Nonlinear effects in MEMS oscillators can be induced via sufficient driving power, generating low-frequency nonwhite noise processes that need to be considered in a phase-noise description. Since the phase-frequency response is not symmetric for a nonlinear detuned resonator, an empirical model based on power series is proposed to describe its effect in the noise sources and to account for the observed higher effective quality factor of the oscillator, the reduction in the corner frequency, and elevated levels of flicker noise very close-to-carrier. The applicability of the presented phase-noise model is shown for three piezoelectric MEMS oscillators, producing a relative fitting error below 1% in all cases.

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“…Recently, stable oscillators have been reported that drive the resonator into the nonlinear operation range [1,2]. Preliminary results show that the oscillator noise continues to improve even in the resonator's nonlinear range of operation [2].…”

Section: Introductionmentioning

confidence: 99%

Fracture limit in thin-film piezoelectric-on-substrate resonators: Silicon VS. diamond

Fatemi

Abdolvand

2013

2013 IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS)

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In this work, lateral-extensional thin-film piezoelectricon-substrate (TPoS) resonators, fabricated on both silicon and diamond, are driven beyond their bifurcation point in order to study the maximum allowable energy density before the resonator fractures. A method is presented to measure the stored energy of the resonator at different drive levels. The average measured critical energy density of the resonator (the stored energy at bifurcation) on silicon substrate is ~5.2×10 5 J/m 3 for a specific resonator design while it is ~2.7×10 5 J/m 3 for a similar device fabricated on ultrananocrystalline diamond. On the other hand, the resonator on diamond withstands energy densities more than 2 times larger than the resonator on silicon before devices fracture and fail mechanically.

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Verification of the phase-noise model for MEMS oscillators operating in the nonlinear regime

Cited by 23 publications

References 11 publications

Frequency stabilization in nonlinear micromechanical oscillators

Frequency stabilization in nonlinear micromechanical oscillators

An Empirical Phase-Noise Model for MEMS Oscillators Operating in Nonlinear Regime

Fracture limit in thin-film piezoelectric-on-substrate resonators: Silicon VS. diamond

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