Resonant Pull-In Condition in Parallel-Plate Electrostatic Actuators

Fargas-Marques, A.; Casals‐Terré, Jasmina; Shkel, Andrei M.

doi:10.1109/jmems.2007.900893

Cited by 70 publications

(56 citation statements)

References 31 publications

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“…They show that dynamic pull-in obtained by adding a resonant ac actuation force to the static DC component helps pull-in happen at lower voltages. Fargas-Marques et al [24] studied pull-in instability under resonant excitation, considering the nonlinear mechanical stiffness effect that appears with large amplitude oscillations. They used energy methods to derive analytical expressions for static and dynamic pull-in voltages.…”

Section: Resonant Pull-in Conditionmentioning

confidence: 99%

“…Using energy analysis and first-order approximation of X o (t), (X o (t) = X o cos(ωt)), the steady-state vibration amplitude (X 0 ) can be found from the energy balance of an energy oscillation loop as follows [24]:…”

Section: Resonant Pull-in Conditionmentioning

confidence: 99%

“…where D = 0 identifies the transition between all-real solutions and the existence of complex solutions [24]. There are several mechanisms of damping associated with micromechanical resonators, including extrinsic (air damping, anchor loss) and intrinsic losses (thermoelastic damping).…”

Section: Resonant Pull-in Conditionmentioning

confidence: 99%

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Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators

2012

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Abstract:A distributed modeling approach has been developed to describe the dynamic behavior of ring resonators. The model includes the effect of large amplitudes around primary resonance frequencies, material and electrostatic nonlinearities. Through a combination of geometric and material nonlinearities, closed-form expression for third-order nonlinearity in mechanical stiffness of bulk-mode ring resonators is obtained. Moreover, to avoid dynamic pull-in instability, the choices of the quality factor, ac-drive and DC-bias voltages of the ring resonators, with a given geometry are limited by a resonant pull-in condition. Using the perturbation technique and the method of harmonic balance, the expressions for describing the effect of nonlinearities on the resonance frequency and displacement are derived. The results are discussed in detail, showing the effect of varying operating conditions and the quality factor on the harmonic distortions and third-order intermodulation distortion. The detailed nonlinear modeling and distortion analysis are applied as appropriate tools to design bulk-mode ring resonators with low motional resistance and high linearity.

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Section: Resonant Pull-in Conditionmentioning

confidence: 99%

Section: Resonant Pull-in Conditionmentioning

confidence: 99%

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Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators

2012

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“…Thus, the value of max A that can be inferred from (31) is out of the range of validity of DFA. This shows that one should be very careful when trying to determine the onset of electrostatic instability under sinusoidal motion assumptions [16][17], because the two notions (instability and sinusoidal motion) are somehow contradictory. This is confirmed by a stability analysis based on DFA: the oscillatory regime defined by (30) is stable provided (24) is satisfied.…”

Section: Analysis Of the Closed-loop Systemmentioning

confidence: 99%

Large amplitude dynamics of micro-/nanomechanical resonators actuated with electrostatic pulses

Jerome

Bonnoit

Avignon

et al. 2010

Journal of Applied Physics

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Abstract. In the field of resonant NEMS design, it is a common misconception that large-amplitude motion, and thus large signal-to-noise ratio, can only be achieved at the risk of oscillator instability. In the present paper, we show that very simple closed-loop control schemes can be used to achieve stable largeamplitude motion of a resonant structure, even when jump resonance (caused by electrostatic softening or Duffing hardening) is present in its frequency response. We focus on the case of a resonant accelerometer sensing cell, consisting in a nonlinear clamped-clamped beam with electrostatic actuation and detection, maintained in an oscillation state with pulses of electrostatic force that are delivered whenever the detected signal (the position of the beam) crosses zero. We show that the proposed feedback scheme ensures the stability of the motion of the beam much beyond the critical Duffing amplitude and that, if the parameters of the beam are correctly chosen, one can achieve almost full-gap travel range without incurring electrostatic pull-in. These results are illustrated and validated with transient simulations of the nonlinear closed-loop system. 2 1. Introduction Resonant sensing consists in measuring the frequency shift of a system subject to the variation of a given physical quantity. Because of its moderate complexity, this measurement technique is becoming commonplace in the context of MEMS and NEMS devices [1][2][3]. This paper focuses on closed-loop resonant sensors, where the micromechanical structure is brought to oscillate by being placed inside a feedback loop [4][5][6]. In the present work, the structure is a clamped-clamped beam, the motion of which is sensed capacitively. It is maintained in an oscillation state with pulses of electrostatic force that are delivered whenever the detected signal (the position of the beam) crosses zero [7][8]. In order to maximize the signal-to-noise ratio (SNR) and, thus, to relax the constraints on the electronic design, the detected signal must be as large as possible, which means that, for a given set of structural parameters and a given bias voltage, the oscillation amplitude of the resonant beam must also be as large as possible. This raises questions concerning what oscillation amplitude can be sustained without incurring mechanical [9-10] or electrostatic [11][12] instability. We show in this paper that, in spite of the nonlinearities, the proposed feedback scheme ensures the stability of the motion of the beam much beyond the critical Duffing amplitude. We also show that, if the parameters of the beam are correctly chosen, one can realistically achieve almost full-gap travel range without incurring electrostatic pull-in. In section 2, the sensing cell of the resonant accelerometer that is the basis of our work is briefly described. The focus is brought on the capacitive detection and actuation schemes. In section 3, a simplified one-degree-offreedom (1-DOF) model of the beam is derived. In particular, an approximate expression of the first modal ...

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“…The pull-in instability phenomenon is still a wellknown yet challenging problem that needs to be solved [3]. The main challenge is to extend the travel range of the parallel plate micro electrostatic actuator beyond the pull-in limit that is one third of its full capacitive gap.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Control Techniques for Micro Electrostatic Actuators in the Presence of Parasitics and Parametric Uncertainties

Salah¹,

Al-Jarrah²,

Tatlıcıoğlu³

2011

Control and Applications

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In this paper, nonlinear control techniques are developed to control parallel-plate micro electrostatic actuators in the presence of parasitics and parametric uncertainties. The movable plate of the micro actuator is actively controlled utilizing the measurements of internal charge and movable plate's displacement. A velocity observer is designed to estimate the velocity of the plate that is needed for the control algorithm since it is difficult to be measured practically. The proposed backstepping nonlinear control strategies are developed based on a Lyapunov-based analysis, which proves that the desired plate's displacement can be obtained accurately. The proposed nonlinear controllers are capable of controlling the movable plate beyond the pull-in limit in the presence of parametric uncertainties. Representative numerical simulations are presented to demonstrate the performance of the developed nonlinear control strategies in accurately tracking desired deflections of the movable plate within the entire capacitive gap. Finally, a comprehensive performance comparison is performed to examine the effectiveness of the control designs.

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Resonant Pull-In Condition in Parallel-Plate Electrostatic Actuators

Cited by 70 publications

References 31 publications

Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators

Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators

Large amplitude dynamics of micro-/nanomechanical resonators actuated with electrostatic pulses

Nonlinear Control Techniques for Micro Electrostatic Actuators in the Presence of Parasitics and Parametric Uncertainties

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