Cuong Phu Le

Microscale electrostatic energy harvester using internal impacts

This article presents a new concept for electrostatic energy harvesting devices that increase output power under displacement limited inertial mass motion at sufficiently large acceleration amplitudes. The concept is illustrated by two demonstrated electrostatic energy harvesting prototypes in the same die dimension: a reference device with end-stops and an impact device with movable end-stops functioning as slave transducers. Both devices are analyzed and characterized in small and large excitation regimes. We found that significant additional energy from the internal impact force can be harvested by the slave transducer. The impact device gives much higher, up to a factor of 3.7, total output power than the reference device at the same high-acceleration amplitude. The bandwidth of the response to frequency sweeps is beneficially enlarged by up to a factor of 20 by the nonlinear mechanisms of the impact device.

Wideband excitation of an electrostatic vibration energy harvester with power-extracting end-stops

An electrostatic energy harvester with two-stage transduction is investigated for enhancement of bandwidth and dynamic range. The harvester includes a primary proof mass with two main transducers and end-stops for the proof mass functioning as secondary transducers. In the small acceleration regime, the power is primarily obtained from the main transducers. In the high acceleration regime, the mass impacts the end-stops and actuates the secondary transducers, generating additional output power. The device is designed and fabricated using the SOIMUMPs process and has a total active area of 4 5 mm 2 . Under wideband acceleration at high levels, the experimental results show that the total output power increases to about twice the output power of the main transducers, while the 3 dB-bandwidth is enlarged by a factor of 6.7 compared to the linear-response bandwidth at low levels. In comparison with a reference device made with the same die dimensions, the two-stage device improves output power instead of saturating when the maximum mass displacements of both devices reach the same limit. Measurement of output power demonstrates that the device with the transducing end-stops give an efficiency of 23.6%, while this value is 14.1% for the reference device with the conventional end-stops, at an acceleration spectral density of SaD 19:2 10 3 g 2 Hz 1 . The efficiency is improved about by 9.5% in the impact regime. (Some figures may appear in colour only in the online journal)

Architecture-independent power bound for vibration energy harvesters

The maximum output power of energy harvesters driven by harmonic vibrations is well known for a range of specific harvester architectures. An architecture-independent bound based on the mechanical input-power also exists and gives a strict limit on achievable power with one mechanical degree of freedom, but is a least upper bound only for lossless devices. We report a new theoretical bound on the output power of vibration energy harvesters that includes parasitic, linear mechanical damping while still being architecture independent. This bound greatly improves the previous bound at moderate force amplitudes and is compared to the performance of established harvester architectures which are shown to agree with it in limiting cases. The bound is a hard limit on achievable power with one mechanical degree of freedom and can not be circumvented by transducer or power-electronic-interface design.

Power optimization and effective stiffness for a vibration energy harvester with displacement constraints

This paper presents experiments on how to approach the physical limits on power from vibration energy harvesting under displacement-constrained operation. A MEMS electrostatic vibration energy harvester with voltage-control of the system stiffness is used for this purpose. The power saturation problem, when the proof-mass displacement reaches a maximum amplitude for sufficient acceleration amplitude, is shifted to higher accelerations by use of load optimization. In addition, we demonstrate the effect of varying the electromechanical coupling k 2. Measurement results show that harvested power can also be made to follow the optimal power of the velocity-damped generator for a range of accelerations, which implies displacement constraints. Compared to the saturated power, the power increases 1.5 times with the optimal load for electromechanical coupling at k 2 = 8.7%. This is improved 2.3 times for a higher coupling of . The obtained system effectiveness exceeds 60%. This work shows a first demonstration of reaching optimal power in the intermediate acceleration-range between the two extremes of maximum efficiency and maximum power transfer. The experimental results follow the theoretical results for a device with both load and stiffness tuning surprisingly well, despite only optimizing the load here. We compared a linearized lumped-model of the device with the same augmented by end-stop nonlinearities. The comparison shows that an effective stiffness due to end-stop impacts in the latter model closely matches the optimal stiffness for the former model, and therefore can explain why the experimental output power is close to optimal despite the lack of deliberate stiffness tuning.

Experiments on power optimization for displacement-constrained operation of a vibration energy harvester

This paper presents experiments on how to approach the physical limits on power from vibration energy harvesting under displacement-constrained operation. A MEMS electrostatic vibration energy harvester with voltage-control of the system stiffness is used for this purpose. The power saturation problem, when the proof mass displacement reaches maximum amplitude for sufficient acceleration amplitude, is shifted to higher accelerations by use of load optimization and tunable electromechanical coupling k2. Measurement results show that harvested power can be made to follow the optimal velocity-damped generator also for a range of accelerations that implies displacement constraints. Comparing to the saturated power, the power increases 1.5 times with the optimal load and an electromechanical coupling k2=8.7%. This value is 2.3 times for a higher coupling k2=17.9%. The obtained system effectiveness is beyond 60% under the optimization. This work also shows a first demonstration of reaching optimal power in the intermediate acceleration-range between the two extremes of maximum efficiency and maximum power transfer.

Low power electronic interface for electrostatic energy harvesters

This paper presents design and simulation of a power electronic interface circuit for MEMS electrostatic energy harvesters. The designed circuit is applicable to highly miniaturized electrostatic harvesters with small transducer capacitances below 10 pF. It is based on comb- drive harvesters with two anti-phase capacitors that are connected as charge pumps and uses a flyback-path scheme. Controlled activation and deactivation of sub-circuits, some by help of clocking, were exploited to reduce power consumption down to 1.03 μW. Net power generation can be achieved with as low initial voltage as 3.0 V.

Electric control of power extracting end-stop for MEMS vibration energy harvesting

This experimental work investigates a technique to further improve performance of vibration energy harvesters under displacement-constrained operation. Previously, a device concept based on end-stops acting as additional transducers was developed so that the harvested power can be increased beyond the power obtained from a conventional harvester of the same size. However, there is a range of tested acceleration amplitudes in which the transducing end- stop device performs worse than the conventional device. In this paper, an approach using electric control is used to optimize the end-stop transducer performance and thereby further improve the system effectiveness under displacement constrained operation. For example, the maximum power increases by a factor of 2.4 compared to that of a conventional prototype under the same operating conditions and constrained displacement amplitude, while this value was about 1.3 for the previous technique.

MEMS electrostatic influence machines

This paper analyses the possibility of MEMS electrostatic influence machines using electromechanical switches like the historical predecessors did two centuries ago. We find that a generator design relying entirely on standard silicon-on-insulator(SOI) micromachining is conceivable and analyze its performance by simulations. The concept appears preferable over comparable diode circuits due to its higher maximum energy, faster charging and low precharging voltage. A full electromechanical lumped-model including parasitic capacitances of the switches is built to capture the dynamic of the generator. Simulation results show that the output voltage can be exponentially bootstrapped from a very low precharging voltage so that otherwise inadequately small voltage differences or charge imbalances can be made useful.

Capacitance calculation for electrostatic transducer applications

An approach for accurate calculation of the capacitance coefficient matrix in electrostatic transducer applications is presented in this article. We consider transducers consisting of a fixed and a moving set of metal strips where strong fringing field effects may occur. The calculation method is based on an expansion of the surface charge distribution on each metal finger in terms of orthogonal functions that capture the singularity effects at the edge of the fingers. We analyze the errors both due to neglect of end effects and due to truncation of the series expansion. The complexity of the capacitance matrix calculation is significantly reduced by truncation to the first three terms of the expansion, giving errors below 1%. An example capacitance structure is analyzed in detail. The capacitance/induction coefficients roughly vary as a cosine function of the horizontal relative displacement between two electrodes. This motivates a simple approximation formula that can be used to calculate the capacitance coefficient matrix of electrostatic transducers. It gives a maximum error of 1.5% compared to the full calculation for a gap g = 5 µm and a microstrip width a = 50 µm in the example structure.

Comparative performance of voltage multipliers for MEMS vibration-based energy harvesters

This paper investigates by numerical simulation the performance of an electrostatic vibration energy harvester when it is electrically configured in two different diode-capacitor multiplier topologies. The complete lumped-model of an overlap-varying generator along with power electronic interface circuit is constructed for analysis using a crcuit simulator. Parasitic capacitance of the transducers and nonideal diode traits such as leakage current and junction capacitance are incorporated. We find that both configurations are able to efficiently operate with a ratio of capacitance variation much lower than 2, which overcomes a challenging obstacle of MEMS-based devices. Other advantages and disadvantages of the two topologies are compared and discussed.