Dynamical Model of Tunable MEMS Energy Harvester1

Dynamical Model of Tunable MEMS Energy Harvester1 -...

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Modeling of Tunable MEMS Energy Harvester 1.0. Introduction In work, [1] a possible implementation of a tunable filter structure using variable MEMS capacitors is considered. Tunable bandpass filters are crucial component in a variety of radar and communication systems. While existing tunable filters are fabricated using resonators, active inductors, and semiconductor varactor diodes [2], improvements in MEMS technology have made it possible to use MEMS variable capacitors instead [6]. For a specific cantilever with a certain resonant frequency, the output signal on the piezoelectrics is large only near the resonant frequency of the cantilever, and decreases rapidly away from resonance. Thus as a filter, a single cantilever device has a narrow bandwidth. The unable bandpass filters presented in this paper consist of 2.0. Description of MEMS structure and electronic feedback A AC DC A Fig. 1. Structure of self tunable MEMS energy harvester 2.0. Dynamic model of the self tunable energy harvester with serial capacitive circuit The scheme of the lumped parameter model of the system is shown in Figure 2. The absolute displacement of the mass is denoted by coordinate z . The coordinate y is used for denotation of relative mass displacement with respect to the harvester body. The absolute displacement of the vibrating object is denoted by X . The relation between these three coordinates is z y X = + (1
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) The displacement of the mass is determined by the well known [ Priya S. at all, 2009 ] differential equation p C mz by ky F F + + = + & && (2 ) where m is the inertial mass of the cantilever, b – damping coefficient, k –stiffness of the cantilever beam, p F - piezoelectric force, C F - force of the differential capacitor. Since the piezoelectric layer is used as a sensor its force is negligible, and it can be assumed that 0 p F = because the piezoelectric layer only changes the stiffness of the cantilever. Taking in account relation (1) the differential equation (2) can be rewritten in the form C my by ky F mX + + = - & . (3 ) The force of the differential capacitor is sum of both electrostatic forces of the capacitors with capacitance C 1 and C 2 or 1 2 C C C F F F = + where the capacitive forces of the two capacitors if the output feedback voltage V p is constant ε is permittivity of the air, A is the area of the capacitor electrodes, 0 g is the initial air gap, p V is the transferred voltage of the piezoelectric through feedback circuit. Then the total electrostatic force is ( 29 ( 29 ( 29 2 2 0 2 2 2 2 2 0 0 0 1 1 2 2 p C p AV g y F AV g y g y g y = - = - + - . (6 ) 3.0 Determining the piezoelectric voltage of the cantilever The free body diagram of the cantilever, the bending moment My, and the top view of the cantilever with interdigitated electrodes is shown in Figure 3. The voltage between two teeth can be calculated by [Jeon Y.B, at all, 2005], [ Choi, W.J, et all, 2006] the formula Fig. 2. Scheme of the self tunable MEMS harvester m d k b C 1 A AC DC PID y Ф C 2 X z v v p Feedback circuit ( 29 1 2 2 0 2 p C AV F g y = - + (4 ) ( 29 2 2 2 0 2 p C AV F g y = - (5 )
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33 i i xxm V tg σ = (7 ) where i xxm
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Dynamical Model of Tunable MEMS Energy Harvester1 -...

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