The impact of damping on the frequency stability of nonlinear MEMS oscillators

Linear models for oscillator noise predict an improvement in frequency stability with increasing Quality factor. Although it is well known that this result does not apply to non-linear oscillators, systematic experimental investigations of the impact of damping on frequency stability of non-linear MEMS oscillators has not been previously reported. This paper studies the frequency stability of a nonlinear MEMS oscillator under variable damping conditions. Analytical and experimental investigation of a MEMS square-wave oscillator embedding a double-ended tuning fork resonator driven into the non-linear regime is introduced. The experimental results indicate that for a pre-set drive level, the variation of air-damping changes the onset of nonlinear behaviour in the resonator, which not only impacts the output frequency but also the phase/frequency noise of a nonlinear MEMS square wave oscillator. The random walk frequency noise and flicker frequency noise levels are strongly correlated with the non-linear operating point of the resonator, whereas the white phase and white frequency noise levels are impacted both by the output power and by operative nonlinearities.This is the accepted manuscript. The final version is available from IEEE at http://dx.doi.org/10.1109/JMEMS.2015.2391832

An auto-parametrically excited vibration energy harvester

Parametric resonance, as a resonant amplification phenomenon, is a superior mechanical amplifier than direct resonance and has already been demonstrated to possess the potential to offer over an order of magnitude higher power output for vibration energy harvesting than the conventional direct excitation. However, unlike directly excited systems, parametric resonance has a minimum threshold amplitude that must be attained prior to its activation. The authors have previously presented the addition of initial spring designs to minimise this threshold, through non-resonant direct amplification of the base excitation that is subsequently fed into the parametric resonator. This paper explores the integration of auto-parametric resonance, as a form of resonant amplification of the base excitation, to further minimise this activation criterion and realise the profitable regions of parametric resonance at even lower input acceleration levels. Numerical and experimental results have demonstrated in excess of an order of magnitude reduction in the initiation threshold amplitude for an auto-parametric resonator (∼0.6 ms−2) as well as several folds lower for a parametric resonator with a non-resonant base amplifier (∼4.0 ms−2), as oppose to a sole parametric resonator without any threshold reduction mechanisms (10's ms−2). Therefore, the superior power performance of parametric resonance over direct resonance has been activated and demonstrated at much lower input levels.This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/I019308/1].This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.sna.2014.09.01

Five topologies of cantilever-based MEMS piezoelectric vibration energy harvesters: a numerical and experimental comparison

In the realm of MEMS piezoelectric vibration energy harvesters, cantilever-based designs are by far the most popular. For cantilever-based vibration energy harvesters, the active piezoelectric area near the clamped end is able to accumulate maximum strain-generated-electrical- charge, while the free end is used to house a proof mass to improve the power output without compromising the effective area of the piezoelectric generator since it experiences minimal strain anyway. However, despite while other contending designs do exist, this paper explores five selected micro-cantilever (MC) topologies, namely: a plain MC, a tapered MC, a lined MC, a holed MC and a coupled MC, in order to assess their relative performance as an energy harvester. Although a classical straight and plain MC offers the largest active piezoelectric area, alternative MC designs can potentially offer larger deflection and thus mechanical strain distribution for a given mechanical loading. Numerical simulation and experimental comparison of these 5 MCs (0.5 μ AlN on 10 μm Si) with the same practical dimensions of 500 μm and 2000 μm, suggest a cantilever with a coupled subsidiary cantilever yield the best power performance, closely followed by the classical plain cantilever topology.This work was supported by EPSRC (Grant EP/L010917/1).This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s00542-015-2599-

Power Optimization by Mass Tuning for MEMS Piezoelectric Cantilever Vibration Energy Harvesting

A cantilever with an end mass is one of the most popular designs for piezoelectric MEMS vibration energy harvesting. The inclusion of a proof mass near the free end of a micro-cantilever can significantly enhances the power responsiveness of a vibration energy harvester per unit acceleration. However, the accommodation of the proof mass comes at the expense of the active piezoelectric area. This paper numerically and experimentally investigates this compromise and explores the optimal proof-mass-to-cantilever-length ratio for power maximisation. It was found that an end mass occupying about 60% to 70% of the total cantilever length is optimal within linear response, and they notably outperform comparable cantilevers with 40% and 50% of end mass. Additionally, nonlinear squeeze film air damping within the chip package was found to adversely affect the cantilevers with larger mass more significantly. A harvester prototype with 70% of the length covered by end mass (5.0 mm^3 ) was able to generate 1.78 μW at 0.6 ms^-2 and up to 20.5 μW at 2.7 ms^-2 and 210 Hz when not limited by nonlinear damping. This result outperforms the previously reported counterparts in the literature by nearly an order of a magnitude in terms of power density normalised against acceleration squared.This work was supported by Innovate UK and GE Aviation.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/JMEMS.2015.249634

Edge-anchored mode-matched micromachined gyroscopic disk resonator

© 2017 IEEE. This paper reports on a vacuum packaged circular disk gyroscopic resonator with T-shape anchors fabricated in a (100) single crystalline silicon substrate. This device topology simplifies the fabrication process as compared to previous approaches to realize center-anchored disk gyroscopes. Mode-matching of the trigonal modes of the disk is realized with open-loop characterization results demonstrating a Quality factor exceeding 1.5 million with an initial modal frequency split of 4.7 Hz and a natural frequency of approximately 0.976 MHz (4.81 ppm split). An approach to effective mode matching of such devices is described

A high-resolution micro-electro-mechanical resonant tilt sensor

This paper reports on the design and experimental evaluation of a high-resolution Micro-Electro-Mechanical (MEM) tilt sensor based on resonant sensing principles. The sensors incorporate a pair of double-ended tuning fork (DETF) resonant strain gauges, the mechanical resonant frequencies of which shift in proportion to an axial force induced by variations in the component of gravitational acceleration along a specified input axis. An analysis of the structural design of such sensors (using analytical and finite element modelling) is presented, followed by experimental test results from device prototypes fabricated using a silicon-on-insulator (SOI) MEMS technology. This paper reports measurement conducted to quantify sensor scale factor, temperature sensitivity, scale factor linearity and resolution. It is demonstrated that such sensors provide a ±90 degree dynamic range for tilt measurements with a temperature sensitivity of nearly 500 ppb/K (equating to systematic sensitivity error of approximately 0.007 degree/K). When configured as a tilt sensor, it is also shown that the scale factor linearity is better than 1.4% for a ±20° tilt angle range. The bias stability of a micro-fabricated prototype is below 500 ng for an averaging time of 0.8 seconds making these devices a potentially attractive option for numerous precision tilt sensing applications.This is the author's accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0924424714004385

Piezoelectric vibration energy harvesting: A connection configuration scheme to increase operational range and output power

For a conventional monolithic piezoelectric transducer (PT) using a full-bridge rectifier, there is a threshold voltage that the open-circuit voltage measured across the PT must attain prior to any transfer of energy to the storage capacitor at the output of the rectifier. This threshold voltage usually depends on the voltage of the storage capacitor and the forward voltage drop of diodes. This article presents a scheme of splitting the electrode of a monolithic piezoelectric vibration energy harvester into multiple ( n) equal regions connected in series in order to provide a wider operating voltage range and higher output power while using a full-bridge rectifier as the interface circuit. The performance of different series stage numbers has been theoretically studied and experimentally validated. The number of series stages ([Formula: see text]) can be predefined for a particular implementation, which depends on the specified operating conditions, to achieve optimal performance. This enables the system to attain comparable performance compared to active interface circuits under an increased input range while no additional active circuits are required and the system is comparatively less affected by synchronized switching damping effect. </jats:p

Electrostatic Frequency Tuning of Bulk Acoustic Wave Disk Gyroscopes

Bulk acoustic wave gyroscopes have been researched for potential benefits such as immunity to shock and vibration and the high Q factors achievable with the bulk modes. This paper outlines an approach to address mode matching in bulk acoustic wave (BAW) disk gyroscopes using electrostatic frequency tuning. Electrostatic frequency tuning is achieved by varying the potential difference between the body of the resonator and electrodes surrounding the disk resonator. Tuning of the frequencies of both drive and sense modes is demonstrated in this work as a means to achieving mode matching. The experimental results are also compared to COMSOL simulations reporting mode matching

A Cold-Startup SSHI Rectifier for Piezoelectric Energy Harvesters with Increased Open-Circuit Voltage

Piezoelectric vibration energy harvesting has drawn much research interest over the last decade towards the goal of enabling self-sustained wireless sensor nodes. In order to make use of the harvested energy, interface circuits are needed to rectify and manage the energy. Among all active interface circuits, SSHI (synchronized switch harvesting on inductor) and SECE (synchronous electric charge extraction) are widely employed due to their high energy efficiencies. However, the cold-startup issue still remains since an interface circuit needs a stable DC supply and the whole system is completely out of charge at the beginning of implementations or after a certain period of time without input vibration excitation. In this paper, a new cold-startup SSHI interface circuit is presented, which dynamically increases the open-circuit voltage generated from the piezoelectric transducer (PT) in cold-state to start the system under much lower excitation levels. The proposed circuit is designed and fabricated in a 0.18 um CMOS process and experimentally validated together with a custom MEMS (microelectromechanical systems) harvester, which is designed with split electrodes to work with the proposed power extraction circuit. The experiments were performed to start the system from the cold state under variable excitation levels. The results show that the proposed system lowers the required excitation level by at least 50% in order to perform a cold-startup. This aids restarting of the energy harvesting system under low excitation levels each time it enters the cold state

Mode-localized sensing in micro- and nano-mechanical resonator arrays

Micromachined resonant sensors have been researched for several decades for a variety of applications with potential benefits in terms of improved sensitivity and scalability relative to other transduction principles. Conventional implementations usually involve detection elements monitoring resonant frequency and/or dissipation shift in a single degree-of-freedom or several independent degrees-of-freedom. This paper discusses a complementary approach to resonant sensing in which the eigenstates in coupled array structures can be employed as a read-out mechanism offering the potential for both increased sensitivity and excellent common mode rejection. The technique, dubbed 'mode-localized sensing', is based on the spatial localization of vibration in an array of nearly identical weakly coupled resonators wherein the eigenstates are seen to be sensitive signatures of symmetry-breaking perturbations in structural parameters. The sensing methodology has been applied to a range of applications including gravimetric sensing, electrometry, inertial sensors and force sensors where in high accuracy approaches to physical transduction are often of interest. The paper concludes with a discussion of the current challenges in the field and an outlook on future developments