3 2 Influence of Surrounding Electrostatic FieldIn this paper, w

3.2. Influence of Surrounding Electrostatic FieldIn this paper, we assume the surrounding electrostatic field is comparatively small, thus its sellckchem influence was omitted. To ensure the validity of the assumption, the influence of surrounding electrostatic field was evaluated by simulation analysis using CoventorWare software. Figure 2(a) shows the model on which we performed the evaluation. A comb-drive actuator using the proposed actuation mechanism was sandwiched between two imaginary parallel plates. A dc voltage was applied onto the parallel plates to create a surrounding electrostatic field. Two factors, i.e., the distance between the actuator and the upper or lower plate, gcp, and the applied voltage, Vsef, were taken into consideration. Figure 2(b) shows the simulation results.
The value of gcp and Vsef refer to actual conditions of IC packaging and operation. Typically, gcp is larger Inhibitors,Modulators,Libraries than 500 ��m and Vsef is less than 25 volts. In this case, the actuator is surrounded by an electrostatic field of 50 kV/m, and then about 0.9% Vr difference will be induced. Hence, the influence of outside electrostatic field can be ignored.Figure 2.(a) The testing model: a proposed actuator is sandwiched between a pair of parallel plates. A voltage of Vsef is applied on the upper plate, and the lower plate is grounded. A surrounding electrostatic field will be created as a possible outside interference. …3.3. Static DisplacementTo simplify modeling, the electrostatic field between the movable and fixed fingers is approximated by the parallel plate model between the engaged parts of the comb fingers.
Due to the configuration of the comb-drive, the capacitances Inhibitors,Modulators,Libraries between movable and fixed fingers in the high-voltage (V1) and low-voltage (V2) sides, as shown in Figure 1, can be derived as:C1=2n?airh(x+a1)g(4)and:C2=2n?hair(?x+a2)g(5)where x is the displacement of the rotor, n is the numbers of finger pairs, ��air is the permittivity of air, h is the finger height, g is the spacing between movable and fixed comb fingers.The capacitance between the rotor and the handle layer can be written as:Cr=?airAsusd+?oxAanchd(6)where Inhibitors,Modulators,Libraries Asus and Aanch are the areas of the rotor’s suspended part and anchor, respectively. ��ox is the permittivity of silicon dioxide. d is the thickness of the silicon dioxide layer. Note Inhibitors,Modulators,Libraries that Cr is a constant because of the constant Asus and Aanch.
Assuming the rotor is a good conductor and the actuator is operated to obtain a Entinostat static Navitoclax CAS displacement, in the capacitive circuit shown in Figure 1, the total potential U existing in C1, C2 and Cr can be expressed as:U=12[C1(V1?Vr)2+C2(V2?Vr)2+CrVr2](7)The longitudinal force induced by the electrostatic potential is:Fex=?U?x(8)The restoring force of the folded spring [12] can be expressed as:Fsx=kx?x=2Ehb3L3?x(9)where kx, E, b and L represent the spring constant (longitudinal direction), Young’s modules, width and length, respectively.

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