Phase noise in capacitively coupled micromechanical oscillators

Kaajakari, V.; Koskinen, J.K.; Mattila, T.

doi:10.1109/tuffc.2005.1563277

Cited by 80 publications

(56 citation statements)

References 19 publications

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“…The micromechanical resonator is attracted due to electrostatic forces creating a capacitive coupling between the resonator and the input electrode (Kaajakari et al, 2005). A large electrode area that covers the resonator is desirable where the capacitance C is described as,…”

Section: The Electromechanical Analogy 421 the Electromechanical Comentioning

confidence: 99%

“…However, when a beam is too soft, non-linear effects become more dominant. We can classify two different types of resonator non-linearities (Kaajakari et al, 2005;):…”

Section: Nonlinear Behaviormentioning

confidence: 99%

“…From equation 24, we can see that the spring stiffness consists of higher order terms that all are related to the displacement x (Kaajakari et al, 2005). The k e0 term is the first term and is linear.…”

Section: Nonlinear Behaviormentioning

confidence: 99%

See 2 more Smart Citations

Low-power Sensor Interfacing and MEMS for Wireless Sensor Networks

Michaelsen¹,

Ramstad²,

Wisland³

et al. 2011

Wireless Sensor Networks

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Section: The Electromechanical Analogy 421 the Electromechanical Comentioning

confidence: 99%

“…However, when a beam is too soft, non-linear effects become more dominant. We can classify two different types of resonator non-linearities (Kaajakari et al, 2005;):…”

Section: Nonlinear Behaviormentioning

confidence: 99%

See 1 more Smart Citation

Low-power Sensor Interfacing and MEMS for Wireless Sensor Networks

Michaelsen¹,

Ramstad²,

Wisland³

et al. 2011

Wireless Sensor Networks

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“…This value is "optimal" in the sense that small variations of the amplitude will not affect the value of osc ω : thus, one may achieve large amplitude oscillations and good frequency stability, both of which would be very desirable features in MEMS/NEMS reference oscillator applications [18][19].…”

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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“…Nonlinearities can limit the maximal optical power modulation through bifurcation, distortion, and noise aliasing effects. 1,16 The strong dependence of transmission on waveguide separation quoted makes our system more prone to noise aliasing and distortion induced by the optical transduction. The transduction technique only affects the maximum optical power modulation when optical-induced nonlinearities dominate the mechanical and electrical nonlinear effects.…”

Section: -mentioning

confidence: 99%

Detection of nanomechanical motion by evanescent light wave coupling

Vlaminck

Roels

Taillaert

et al. 2007

Applied Physics Letters

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The authors demonstrate a technique allowing sensitive nanomechanical motion detection based on the evanescent light wave coupling between two photonic nanowires. Any relative motion between the nanowires results in a change in light coupling, providing a means of registering motion. The in-plane vibrations of a 220 nmϫ 400 nmϫ 10 m nanomechanical resonator were recorded using this method. An analysis of the sensitivity reveals the potential of this integrated technique to provide fast and sensitive motion detection. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2746067͔ Nanoelectromechanical systems ͑NEMSs͒ have received great attention in recent years. Most research has focused on resonant devices for sensor applications. 1,2 Through scaling of the mechanical sensing element from the micron-to the nanoscale, researchers were able to improve the detection limits in force and mass sensing drastically. Devices sensitive enough to measure the magnetic moment of a single electron spin 3 or to perform zeptogram scale mass sensing 4 have resulted from efforts in scaling. A central problem in the development of even more sensitive mechanical sensors is the fast and high-precision detection of motion. In many cases, the performance of the sensor is restricted by the efficiency of the motion detection method employed, more so than by the inherent capabilities of the mechanical element. Much research has been devoted to solving this problem and a myriad of optical and electronic techniques has been developed. 5 Optical motion detection techniques have the inherent advantage that optical signals can be communicated with very large bandwidth. 6-8 Unfortunately, for conventional optical techniques, diffraction effects limit the attainable detection limits when the mechanical devices are scaled. It has been anticipated that these issues can be overcome by integration of mechanical sensors with nanophotonics and by exploiting optical near-field effects. 1,5 Recently, it was shown that motion of micron-scale devices can be monitored through changes in end-to-end alignment of optical waveguides. [9][10][11] In this letter, we propose an integrated and near-field optical motion detection technique that exploits near-field optical evanescent-wave coupling. We demonstrate that the technique works efficiently for nanoscale mechanical resonators, with greater sensitivity than conventional optical techniques.The approach offers potential for applications where robust and sensitive measurement of motion is required and applications requiring remote detection or detection of motion in harsh environments. The integration of the device with photonic circuitry reduces the complexity of addressing large arrays of devices.The detection of nanomechanical motion is achieved through the near-field coupling of light from a photonic waveguide to a mechanical resonator. The mechanical resonator acts as a photonic waveguide; when the evanescent tails of the guided modes of the resonator and waveguide overlap, photons tunnel from one wavegu...

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Phase noise in capacitively coupled micromechanical oscillators

Cited by 80 publications

References 19 publications

Low-power Sensor Interfacing and MEMS for Wireless Sensor Networks

Low-power Sensor Interfacing and MEMS for Wireless Sensor Networks

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

Detection of nanomechanical motion by evanescent light wave coupling

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