检测电压对一种新型谐振式微加速度计的影响

静电作用在在平行板电容器上会产生等效静电负刚度,介绍了基于静电刚度的谐振式微加速度计设计原理,建立了其动力学模型.根据检测电压的约束条件,求解了其可行范围.同时分析了检测电压对系统灵敏度、可靠性和量程及输出电压的影响.分析结果表明:检测电压越大,灵敏度越大,但可靠性和量程会相应减少,反之亦然;直流检测电压的存在使得输出电压不受检测电容并行的寄生电容影响.理论分析结果为谐振式微传感器的系统设计提供了重要依据.     

A resonant microstructure tunability analysis for an out-of-plane capacitive detection MEMS magnetometer

In this paper, the method of tuning the resonant frequency of a micro-resonant clamped–clamped beam has been successfully applied to a MEMS capacitive magnetometer. The resonant structure frequency, which presents the vital component of the sensor, was tuned by applying a bias voltage between the interdigitated capacitive comb-fingers in order to control its spring constant. It has been proved that an applied DC voltage increases the structure stiffness and as a result the resonance frequency to higher values, especially for low motion magnitude. The shifting causes were described through an accurate analytic analysis using the generated electrostatic force between movable and fixed combs, and thereafter have been proved by characterization. The measured resonance frequency of the clamped–clamped beam structure was changed by up to 38 % from the original value (around 18.2 kHz) when a bias voltage of 52 V was applied. Tuning the resonant frequency of the resonating structure has many advantages for the magnetometer since it can serve as a feedback mechanism for error compensation.

     

静电刚度式谐振微加速度计设计

运用梁的横向振动特性分析了梁振动频率与平行板电容形成的静电刚度的关系,并以此设计了静电刚度式谐振微加速度计。在加速度作用下,检测质量产生的惯性力使电容器极板发生位移来改变电容结构的间隙大小,从而使谐振频率发生变化,通过检测频率变化量来测量输入加速度的大小。根据加速度计的工作原理说明检测过程中梁的机械刚度保持不变,只与产生静电刚度的电容间隙变化相关,减小了检测信号对机械误差与残余应力的依赖性。运用加工参数进行理论计算得出加速度计的灵敏度为21．17Hz／gn,在CoventorWare2005中进行仿真表明：加速度计的固有频率为23．94kHz,灵敏度约为20Hz／gn,与理论设计值相近。     

Numerical analysis on snapping induced by electromechanical interaction of shuffling actuator with nonlinear plate

When a voltage is applied between two electrodes consisting of a rigid ground and a deformable rectangular plate that has two parallel free edges, and one movable edge and one fixed edge, the plate bends under the electrostatic force generated in it. Accompanying to the bending deformation, the movable edge of the plate results in some displacement along the movable direction, which is the main clue of the MEMS actuator of shuffling movement. As the control voltage is applied up to a critical value, the phenomenon of snapping occurs at the plate electrode under the interaction of electromechanical coupling such that the shuffling displacement is obtained as possibly as large. Based on the nonlinear theory of plates with the von Karman’s type deformation and the electrostatic theory, a theoretical analysis for the snapping behavior is quantitatively displayed in this paper. For this purpose, a numerical code is proposed by associating the increment finite element methods for deformation with the moment method for electrostatic fields as well as the arc-length control approach in the quantitative calculations. The numerical results for some case studies show that the path of bending deformation from stability into instability passing through the snapping criterion can be tracked well by this numerical code, while the characteristic curves of the maximum deflection in the plate and the shuffling displacement versus the control voltage, which are mainly concerned in the design of the MEMS shuffling actuator, are obtained additionally.     

静电刚度谐振式微加速度计及其接口电路分析

根据静电加载在平板电容器上产生等效静电负刚度原理,分析了基于静电刚度的谐振式微加速度计的敏感过程.针对有效信号检测中存在的同频干扰问题,建立了接口电路的等效模型,并根据干扰源提出在信号处理电路采用方波调制、开关解调的抑制方法.仿真和实验表明制造的加速度计检测端静态电容约为0.4pF,实验条件下变化的检测电容为3.1fF...     

Dynamic pull-in of parallel-plate and torsional electrostatic MEMS actuators

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.     

Current drive methods to extend the range of travel ofelectrostatic microactuators beyond the voltage pull-in point

When a voltage source drives an electrostatic parallel plate actuator, the well-known pull-in instability limits the range of displacement to 1/3 of the gap. Different strategies have been reported to overcome this limitation. More recently, experimental results have been presented using a capacitor in series with the actuator. Nevertheless, this strategy requires higher voltage than the pull-in voltage value to achieve full range of travel. In order to reduce the operating voltage, a switched-capacitor configuration has been also proposed. In this paper, two different approaches are introduced to control charge in the actuator by means of current driving. Theoretical equations derived for each method show that full range of travel can be achieved without voltage penalty. Both approaches are based on the use of current pulses injecting the required amount of charge to fix the position of the movable plate. Experimental measurements, showing that displacement beyond the pull-in point can be achieved, are in good agreement with the theoretical and the predicted simulated behavior     

A MEMS-based tracking milli-mirror for high-density optical disk drives

We present a new MEMS-based milli-mirror for precise tracking in high-density optical disk drives (ODDs). The device consists of a torsionally suspended mirror plate, one pair of torsion springs, which support the mirror plate and offer a restoring torque, and two pairs of electrodes attached to the mirror plate and glass substrate. The dimensions of mirror plate and torsion springs were determined so that a 5 V dc bias ±4.5 V ac drive voltage would provide the mirror with ±0.02° rotation to transmit laser beam spot on spinning disk. The MEMS-based milli-mirror was successfully fabricated using MEMS technology. Displacement–voltage linearization scheme was implemented by differential voltage driving. The static and dynamic performances of mirror prototype, such as capacitance versus driving voltage, rotation angle versus driving voltage, and resonant frequency were characterized and compared well with the simulation solutions. The mechanical resonant frequency of the mirror is expected to be high enough to satisfy the requirement of the servo bandwidth of precise tracking-control in high-density blue-laser optical disk drive.     

Vertically-Shaped Tunable MEMS Resonators

We report the development of tunable comb-resonators that use vertically-shaped comb-fingers as electrostatic springs. By restricting our design modifications to the vertical dimension, the tunability is achieved without increasing the device footprint. Three-dimensional finite element analysis was used to evaluate the effects of geometry and design on electrostatic spring strength and linearity. All structural components were fabricated using gray-scale technology, simultaneously defining all vertical levels using a single lithography and dry-etching step. Subsequent testing achieved bidirectional resonant frequency tuning (> 17%) through the creation of electrostatic spring constants as high as 1.06 N/m (at 70 V) and 1.45 N/m (at 120 V). While the current resonant devices show evidence of nonlinear stiffness coefficients at large oscillation amplitudes (> 10 mum), multiple design options are introduced and simulated as potential solutions.     

Position control of parallel-plate microactuators for probe-based data storage

In this paper, we present the use of closed-loop voltage control to extend the travel range of a parallel-plate electrostatic microactuator beyond the pull-in limit. Controller design considers nonlinearities from both the parallel-plate actuator and the capacitive position sensor to ensure robust stability within the feedback loop. Desired transient response is achieved by a pre-filter added in front of the feedback loop to shape the input command. The microactuator is characterized by static and dynamic measurements, with a spring constant of 0.17 N/m, mechanical resonant frequency of 12.4 kHz, and effective damping ratio from 0.55 to 0.35 for gaps between 2.3 to 2.65 /spl mu/m. The minimum input-referred noise capacitance change is 0.5 aF//spl radic/Hz measured at a gap of 5.7 /spl mu/m, corresponding to a minimum input-referred noise displacement of 0.33 nm//spl radic/Hz. Measured closed-loop step response illustrates a maximum travel distance up to 60% of the initial gap, surpassing the static pull-in limit of one-third of the gap.     

Pull-In Analysis of Torsional Scanners Actuated by Electrostatic Vertical Combdrives

This paper presents pull-in analysis of torsional MEMS scanners actuated by electrostatic vertical combdrives with general comb gap arrangements and cross sections. The analysis is based on a 2-DOF actuator with a single voltage control. Three failure modes of the scanners are identified as in-plane twist, transversal motion, and out-of-plane twist. For each failure mode, analytical expressions of pull-in deflection are obtained by applying 2D analytical capacitance models to the derived pull-in equations. From these, the dominant pull-in mechanism is shown to be in-plane twist for scanners with high-aspect-ratio torsional springs. The analytical calculations for both symmetric and asymmetric capacitances are shown to be in good agreement with simulation results. The optimum scanner design is achieved when the pull-in deflection matches the capacitance maximum angle. The condition can be expressed in terms of the ratio of the comb thickness to the comb gap, which is smaller than the typical aspect ratio of deep reactive ion etching. The optimum tradeoff between the maximum deflection angle and the number of movable combs is achieved by adjusting the overlap of the movable and fixed combs and the distance of the comb sets from the axis of the rotation.     

Electrostatic model for an asymmetric combdrive

This paper presents an analytical solution to the electrostatic actuation of an asymmetric combdrive in out-of-plane and torsional motions. The exact solutions to force in the out-of-plane motion and the integral for torque in the torsional motion are obtained. The dependence of the peak force on the thickness of the movable fingers and the amount of overlap of the combs is given in closed form. Using our model, the shift of the natural resonant frequency due to a dc bias is analyzed. Furthermore, our solution also applies to the in-plane motion of an in-plane interdigitated combdrive. We found that an in-plane interdigitated combdrive generates a constant force within 0.1% when the minimum initial engagement length of the combs is twice the separation gap     

Design of nonrecursive FIR filters with simultaneously MAXFLAT magnitude and prescribed cutoff frequency

Maximally-flat (MAXFLAT) FIR filter design still has a problem in overcoming the cutoff-frequency error due to approximation of the desired frequency response by some closed-form solution. In order to overcome such a difficulty, this paper describes a new method for the design of nonrecursive FIR filters with simultaneously MAXFLAT magnitude and accurate cutoff frequency. The proposed method provides a general formula to find interpolation coefficients for a new closed-form expression of this filter type, obtained by solving solutions of linear differential equations that are derived from the maximal flatness and cutoff-frequency conditions. In addition, this method efficiently determines the optimal degree of flatness by using a powerful objective error function derived from this closed-form solution, and allows direct and simple computation of the coefficients of the filter with the desired frequency response. The design examples are shown to provide a complete and accurate solution for the design of such filters.     

Laterally driven electrostatic repulsive-force microactuators usingasymmetric field distribution

We present a new electrostatic actuation method using a lateral repulsive-force induced by an asymmetric distribution of planar electrostatic field. The lateral repulsive-force has been characterized by a simple analytical equation, derived from a finite element simulation. Quality-factors are estimated from the computer simulation based on creep flow model. A set of repulsive-force polycrystalline silicon microactuators has been designed and fabricated by a four-mask surface-micromachining process. Static and dynamic response of the fabricated microactuators has been measured at the atmospheric pressure for the driving voltage range of 0-140 V. The static displacement of 1.27 μm is obtained at the dc voltage of 140 V. The resonant frequency of the repulsive-force microactuator increases from 11.7 kHz to 12.7 kHz when the dc induction voltage increases from 60 V to 140 V. The measured quality-factors are increased from 12 to 13 in the voltage range of 60-140 V. Fundamental characteristics of the force, frequency and quality-factor of the electrostatic repulsive-force microactuator have been discussed and compared with those of the conventional electrostatic attractive-force microactuator     

Closed-form forward kinematics solutions of a 4-DOF parallel robot

It is well known that the forward kinematics of parallel robots is a very difficult problem. Closed-form forward kinematics solutions have been reported only to a few special classes of parallel robots. This paper presents closed-form forward kinematics solutions of a 4-DOF parallel robot H4. A 16th order polynomial in a single variable is derived to solve the forward kinematics of the H4. The 16 roots of the polynomial lead to at most 16 different forward kinematics solutions. A numerical verification is also presented.     

Coupled electrostatic and mechanical FEA of a micromotor

The electrostatic forces occurring in a novel double stator axial-drive variable capacitance micromotor (VCM) are studied as a function of rotor-stator overlap, applied voltage, rotor support morphology, and rotor thickness. Analytical equations are developed using parallel plate assumptions, and results are compared with those obtained with 3D Finite Element Analysis (FEA) for tangential, axial, and radial electrostatic forces. The influence of the axial forces on the rotor deflections are studied using iterative indirect coupled field analysis, where the axial forces obtained from the electrostatic 3D FE model are iteratively applied to a structural FE model until stable rotor deflections are obtained. It was found that the axial forces, taking the rotor deflection into account, are twice as high as those obtained by analytical evaluation neglecting rotor deflections and about 70 times higher than the radial forces at a typical operating voltage of 100 V. Inclusion of bushing supports results in lower axial forces and decreases the influence of rotor tilt. Tangential forces likely to be exerted on the rotor at start-up are also examined and compared with analytical predictions. The study demonstrates that FEA provides more accurate results than analytical equations due to the geometry and field simplifications assumed in the latter     

微机械加速度计挠性梁机械刚度的实验研究

在使用开环频率响应实验求取微机械加速度计挠性梁机械刚度时,不可避免地受到静电负刚度的影响。通过分析预载电压和扫频信号幅值对静电负刚度的影响,提出了从系统刚度中分离出挠性梁机械刚度的计算方法。通过不同实验条件下得到的实验结果,验证了该方法的正确性。     

A novel high tuning ratio MEMS cantilever variable capacitor

This paper presents a novel cantilever-type MEMS variable capacitor with high tuning ratio. In previous works, the cantilever is used as a switch but in our design, it is applied as a variable capacitor. For increasing the maximum achievable capacitance of the cantilever, the suspended capacitive plate should be moved as parallel with fixed plate. The parallel movement can be obtained using the novel structure which utilized two additional lateral beams. Also to overcome the pull-in phenomenon in new structure, the different membrane thickness technique is used. The novelty of our design is adding the lateral beams to make parallel movement of the suspended plate to increase the variable capacitor of the cantilever. The new device is designed on a thick silicon substrate with a thin poly silicon membrane. The results show the tuning range of tunable capacitor with initial capacitance of 560.1 fF can be improved from 6:1 for conventional cantilever to 22.5:1 for the new cantilever. In other words the capacitance tuning range increased three times.     

Dynamic response of a torsional micromirror to electrostatic force and mechanical shock

In this paper dynamic characteristics of a capacitive torsional micromirror under electrostatic forces and mechanical shocks have been investigated. A 2DOF model considering the torsion and bending stiffness of the micromirror structure has been presented. A set of nonlinear equations have been derived and solved by Runge–Kutta method. The Static pull-in voltage has been calculated by frequency analyzing method, and the dynamic pull-in voltage of the micromirror imposed to a step DC voltage has been derived for different damping ratios. It has been shown that by increasing the damping ratio the dynamic pull-in voltage converges to static one. The effects of linear and torsional shock forces on the mechanical behavior of the electrostatically deflected and undeflected micromirror have been studied. The results have shown that the combined effect of a shock load and an electrostatic actuation makes the instability threshold much lower than the threshold predicted, considering the effect of shock force or electrostatic actuation alone. It has been shown that the torsional shock force has negligible influence on dynamic response of the micromirror in comparison with the linear one. The results have been calculated for linear shocks with different durations, amplitudes, and input times.     

MEMS Electrostatic Actuation in Conducting Biological Media

We present design and experimental implementation of electrostatic comb-drive actuators in solutions of high conductivity relevant for biological cells. The actuators are operated in the frequency range 1-10 MHz in ionic and biological cell culture media, with ionic strengths up to 150 mmol/L. Typical displacement is 3.5 mum at an applied peak-to-peak signal of 5 V. Two different actuation schemes are presented and tested for performance at high frequency. A differential drive design is demonstrated to overcome the attenuation due to losses in parasitic impedances. The frequency dependence of the electrostatic force has been characterized in media of different ionic strengths. Circuit models for the electric double layer phenomena are used to understand and predict the actuator behavior. The actuator is integrated into a planar force sensing system to measure the stiffness of cells cultured on suspended structures.