In this work, we utilized the CMOS-MEMS technique to make the tunable in-plane resonator. The commercial 0.35 ��m CMOS process of the Taiwan Semiconductor Manufacturing Company (TSMC) was used to fabricate the micromechanical resonator. The post-process employed a wet etching treatment to remove the sacrificial layer and release the suspended structures in the resonator. The tunable resonator contains three parts: the driving, sensing, and tuning parts. The sensing part senses a change in capacitance when a voltage is applied to the driving part, and the resonant frequency of the resonator can be tuned by the tuning part. Experimental results depict that the resonant frequency was about 183 kHz, and increased by 14 kHz when a tuning voltage of 30 V was applied.2.

?Design and SimulationFigure 1 illustrates the structures of the micromechanical resonator, which includes a driving part, a sensing part and a turning part. The sensing and driving parts have a constant-length comb configuration that consists of the moveable and fixed combs. The driving voltage depends on the number of comb-finger of driving part and the stiffness of supported beams. In order to reduce the driving voltage, the driving part of the resonator is designed with four comb-finger rows. There are eight support beams arranged symmetrically. Each beam is 260 ��m long, 2 ��m wide and 2.6 ��m thick, and it is fixed to the 20��40 ��m2 anchor. The resonator is a suspended membrane with a thickness of 5.8 ��m; the gap between the membrane and the substrate is approximately 1.3 ��m.

Anacetrapib The area of the resonator is about 460��260 ��m2.Figure 1.Schematic structure of the tunable resonator.The resonator is actuated by the electrostatic force. When applying an ac voltage, Vs(t)=V0 sin��t, to the driving part, the driving force produced by the comb-fingers of the driving part can be expressed as [14],Fd (t)=F0sin��t(1)andF0=n��thV022d(2)where n represents the number of fingers in the driving-comb; �� is the permittivity constant of air, th is the comb thickness and d is the inter-finger gap of the comb. The equation of motion of the micromechanical tunable resonator is given by,mx��+cx�B+kx=Fd (t)(3)where m represents the mass of the resonator; c is the damp; k is the stiffness of the resonator and x is the dynamic displacement of the resonator. The particular solution of Equation (3) can be expressed as [15],x(t)=Xsin(��t??)(4)andX=F0k(1?r2)2+(2?r)2(5)where X and ? are the amplitude and phase angle of the response, respectively; r is the frequency ratio and r=��/��n; �� is the damping ratio and ��=c/2m��n; ��n is the natural frequency of the resonator. The maximum amplitude occurs when r=1?2?2 [15].