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Sensors & Transducers<br />

Volume 127, Issue 4,<br />

April 2011<br />

www.sensorsportal.com ISSN 1726-5479<br />

Editors-in-Chief: pr<strong>of</strong>essor Sergey Y. Yurish, tel.: +34 696067716, fax: +34 93 4011989, e-mail: editor@sensorsportal.com<br />

Editors for Western Europe<br />

Meijer, Gerard C.M., Delft University <strong>of</strong> Technology, The Netherl<strong>and</strong>s<br />

Ferrari, Vittorio, Universitá di Brescia, Italy<br />

Editor South America<br />

Costa-Felix, Rodrigo, Inmetro, Brazil<br />

Editor for Eastern Europe<br />

Sachenko, Anatoly, Ternopil State Economic University, Ukraine<br />

Editors for North America<br />

Datskos, Panos G., Oak Ridge National Laboratory, USA<br />

Fabien, J. Josse, Marquette University, USA<br />

Katz, Evgeny, Clarkson University, USA<br />

Editor for Asia<br />

Ohyama, Shinji, Tokyo Institute <strong>of</strong> Technology, Japan<br />

Editor for Asia-Pacific<br />

Mukhopadhyay, Subhas, Massey University, New Zeal<strong>and</strong><br />

Editorial Advisory Board<br />

Abdul Rahim, Ruzairi, Universiti Teknologi, Malaysia<br />

Ahmad, Mohd Noor, Nothern University <strong>of</strong> Engineering, Malaysia<br />

Annamalai, Karthigeyan, National Institute <strong>of</strong> Advanced Industrial Science<br />

<strong>and</strong> Technology, Japan<br />

Arcega, Francisco, University <strong>of</strong> Zaragoza, Spain<br />

Arguel, Philippe, CNRS, France<br />

Ahn, Jae-Pyoung, Korea Institute <strong>of</strong> Science <strong>and</strong> Technology, Korea<br />

Arndt, Michael, Robert Bosch GmbH, Germany<br />

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Atghiaee, Ahmad, University <strong>of</strong> Tehran, Iran<br />

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Azamimi, Azian binti Abdullah, Universiti Malaysia Perlis, Malaysia<br />

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Barford, Lee, Agilent Laboratories, USA<br />

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Beck, Stephen, University <strong>of</strong> Sheffield, UK<br />

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Hern<strong>and</strong>ez, Wilmar, Universidad Politecnica de Madrid, Spain<br />

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Jiang, Wei, University <strong>of</strong> Virginia, USA<br />

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Kalach, Andrew, Voronezh Institute <strong>of</strong> Ministry <strong>of</strong> Interior, Russia<br />

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Kim, Min Young, Kyungpook National University, Korea South<br />

Ko, Sang Choon, Electronics. <strong>and</strong> Telecom. Research Inst., Korea South<br />

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Kratz, Henrik, Uppsala University, Sweden<br />

Kockar, Hakan, Balikesir University, Turkey<br />

Kong, Ing, RMIT University, Australia


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Lin, Paul, C<strong>level</strong><strong>and</strong> State University, USA<br />

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Liu Changgeng, Louisiana State University, USA<br />

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Oberhammer, Joachim, Royal Institute <strong>of</strong> Technology, Sweden<br />

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Zhang, Xueji, World Precision Instruments, Inc., USA<br />

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Zhu, Qing, Fujifilm Dimatix, Inc., USA<br />

Zorzano, Luis, Universidad de La Rioja, Spain<br />

Zourob, Mohammed, University <strong>of</strong> Cambridge, UK<br />

Sensors & Transducers Journal (ISSN 1726-5479) is a peer review international journal published monthly online by International Frequency Sensor Association (IFSA).<br />

Available in electronic <strong>and</strong> on CD. Copyright © 2011 by International Frequency Sensor Association. All rights reserved.


Sensors & Transducers Journal<br />

Contents<br />

Volume 127<br />

Issue 4<br />

April 2011<br />

www.sensorsportal.com ISSN 1726-5479<br />

Research Articles<br />

Going Fabless with <strong>MEMS</strong><br />

Bhaskar Choubey ............................................................................................................................... 1<br />

Micromachined Polycrystalline Si Thermopiles in a T-shirt<br />

Vladimir Leonov, Yvonne van Andel, Ziyang Wang, Ruud J. M. Vullers <strong>and</strong> Chris Van Ho<strong>of</strong>........... 15<br />

Virtual Fabrication <strong>of</strong> Silicon Nitride Based Multifunctional <strong>MEMS</strong> Pressure Sensor<br />

Mahesh Kumar Patankar.................................................................................................................... 27<br />

General Development <strong>of</strong> a New Hall Effect Sensor<br />

Vlassis N. Petoussis, Panos D. Dimitropoulos, George Stamoulis.................................................... 36<br />

Inspection <strong>of</strong> Pipe Inner Surface using Advanced Pipe Crawler Robot with PVDF Sensor<br />

based Rotating Probe<br />

Vimal Agarwal, Harutoshi Ogai, Kentarou Nishijima <strong>and</strong> Bishakh Bhattacharya............................... 45<br />

Ultrasonic <strong>System</strong> Approach to Obstacle Detection <strong>and</strong> Edge Detection<br />

Yin Thu Win, Hla Thar Htun, Nitin Afzulpurkar, Chumnarn Punyasai ................................................ 56<br />

Monitoring <strong>of</strong> Various Glucose Concentrations Based on Optical Spectroscopic<br />

Reflectometry<br />

Hariyadi Soetedjo ............................................................................................................................... 69<br />

Studies <strong>of</strong> Gas Sensing Performance <strong>of</strong> Barium Zirconate (BaZrO 3 )<br />

R. M. Chaudhari, V. B. Gaikwad, P. D. Hire, R. L. Patil,S. D. Shinde, N. U. Patil, G. H. Jain. .......... 76<br />

<strong>Modeling</strong> <strong>and</strong> <strong>System</strong>-<strong>level</strong> <strong>Simulation</strong> <strong>of</strong> <strong>Force</strong>-<strong>balance</strong> <strong>MEMS</strong> Comb Accelerometers<br />

Hao Chen, Limei Xu ........................................................................................................................... 88<br />

Design <strong>and</strong> Fabrication <strong>of</strong> a Lab-on-a-chip for Point-<strong>of</strong>-care Diagnostics<br />

Anne Balck, Monika Michalzik, Laila Al-Halabi, Stefan Dübel, <strong>and</strong> Stephanus Büttgenbach............ 102<br />

Authors are encouraged to submit article in MS Word (doc) <strong>and</strong> Acrobat (pdf) formats by e-mail: editor@sensorsportal.com<br />

Please visit journal’s webpage with preparation instructions: http://www.sensorsportal.com/HTML/DIGEST/Submition.htm<br />

International Frequency Sensor Association (IFSA).


Sensors & Transducers Journal, Vol. 127, Issue 4, April 2011, pp. 88-101<br />

Sensors & Transducers<br />

ISSN 1726-5479<br />

© 2011 by IFSA<br />

http://www.sensorsportal.com<br />

<strong>Modeling</strong> <strong>and</strong> <strong>System</strong>-<strong>level</strong> <strong>Simulation</strong> <strong>of</strong> <strong>Force</strong>-<strong>balance</strong><br />

<strong>MEMS</strong> Comb Accelerometers<br />

Hao CHEN, Limei XU<br />

Institute <strong>of</strong> Astronautics & Aeronautics<br />

University <strong>of</strong> Electronic Science <strong>and</strong> Technology <strong>of</strong> China<br />

Chengdu, Sichuan 611731, China<br />

Tel.: 028-83205198<br />

E-mail: scuch@uestc.edu.cn<br />

Received: 10 April 2011 /Accepted: 22 April 2011 /Published: 30 April 2011<br />

Abstract: This paper presents a quick system-<strong>level</strong> modeling <strong>and</strong> simulation <strong>of</strong> force-<strong>balance</strong> <strong>MEMS</strong><br />

comb accelerometers. The derivation <strong>of</strong> the system-<strong>level</strong> model including the sense element <strong>and</strong><br />

interface electronics is elaborated <strong>and</strong> the simulation results are obtained from COVENTOR <strong>and</strong><br />

MATLAB respectively. The force-<strong>balance</strong> <strong>MEMS</strong> comb accelerometer, with the size <strong>of</strong> 1920 µm<br />

960 µm 50 µm, the static capacitance <strong>of</strong> 2.25 pF, <strong>and</strong> the inertial mass <strong>of</strong> 5.47 µg, can endure with<br />

over load <strong>of</strong> 2000 g. Through the system-<strong>level</strong> simulation, the sensitivity is 100 mv/g, the full scale<br />

range is 50<br />

g, the nonlinear distortion is smaller than 0.5 % <strong>and</strong> the system b<strong>and</strong>width is 2.2 kHz.<br />

Copyright © 2011 IFSA.<br />

Keywords: Micro-accelerometer; <strong>System</strong>-<strong>level</strong> simulation; Closed-loop system; Differential<br />

capacitive.<br />

1. Introduction<br />

Now, micro-machined sensors are widely used in many different aspects <strong>of</strong> inertial navigation system<br />

as well as the center <strong>of</strong> the vibration examination system for their small size, low cost <strong>and</strong> low power<br />

consumption. Especially, micro-machined accelerometers have been more <strong>and</strong> more popular since the<br />

safety requirement for automobiles has tightened, such like seat belts <strong>and</strong> air-bag systems. This leads<br />

to a high dem<strong>and</strong> for low-cost <strong>and</strong> small-size accelerometers capable <strong>of</strong> sensing up to 50 g (where 1 g<br />

is the acceleration due to earth gravitational force). Thus, integrated capacitive accelerometers that<br />

meet the requirements are well received [1-4]. There are many different types <strong>of</strong> micro-machined<br />

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accelerometers, such as piezoresistive, piezoelectric, <strong>and</strong> capacitive accelerometer. But, most<br />

accelerometers use the capacitive-based mechanism because <strong>of</strong> its structural simplicity, high accuracy,<br />

low temperature sensitivity, low noise performance, good DC response, <strong>and</strong> compatibility with CMOS<br />

readout electronics. Capacitive accelerometers are typically implemented as a differential capacitance,<br />

using the linear relationship between the capacitance change <strong>and</strong> the acceleration [5]. Moreover, force<strong>balance</strong><br />

<strong>MEMS</strong> accelerometers based on capacitive mechanism can improve the system stability <strong>and</strong><br />

widen the measurement range using a closed loop structure [6].<br />

As <strong>MEMS</strong> technology continues to grow, to design <strong>and</strong> simulate <strong>MEMS</strong> device is becoming an<br />

interesting <strong>and</strong> important research issue. FEA/BEA is a commonly used numerical simulation method<br />

in <strong>MEMS</strong> simulation; firstly this method meshes the entity model <strong>and</strong> produces the system matrix, <strong>and</strong><br />

then solves the system matrix to get simulation result. In order to analyze the interaction between<br />

mechanical <strong>and</strong> electrostatic field, we must carry out the iterative calculation on both mechanical <strong>and</strong><br />

electrostatic field until the results <strong>of</strong> these two fields are consistent [8 - 10], but using this method will<br />

cost too much time <strong>and</strong> have a poor convergence performance as the author indicated in [10], so it’s<br />

<strong>of</strong>ten restricted in practical application. To solve the problem <strong>of</strong> force-<strong>balance</strong> <strong>MEMS</strong> comb<br />

accelerometers, three widely used methods have been proposed: signal flow method; multi-emulator<br />

coupling analysis method; unified modeling method.<br />

The signal flow method emphasizes using general principles <strong>of</strong> perspective to simulate the system<br />

behavior, such as simplifying the spring-mass-damper system <strong>and</strong> RLC oscillation circuit to a secondorder<br />

system. The disadvantage <strong>of</strong> the above method is that it can’t directly reflect some local<br />

characteristics <strong>of</strong> the device (like motion parameters etc.) <strong>and</strong> structure parameters (like dimension<br />

parameters etc.), it is very difficult to use this method to research the impact <strong>of</strong> these local<br />

characteristics <strong>and</strong> structure parameters on system performance.<br />

Multi-emulator coupling analysis method uses the coupling <strong>of</strong> different special emulators including<br />

fields <strong>of</strong> circuit, machinery <strong>and</strong> fluid to achieve the overall behavior’s simulation <strong>of</strong> <strong>MEMS</strong> [11, 12], it<br />

has high accuracy <strong>and</strong> also can take the device’s local characteristics into account, but this method has<br />

some disadvantages: non-unified abstract <strong>level</strong>s in coupled fields; poor convergence performance;<br />

relatively long computing time.<br />

The unified modeling method uses the same modeling approach <strong>and</strong> language (such as VHDL-AMS<br />

etc.) to model <strong>and</strong> describe the whole system, hence one can simulate the entire system just by a single<br />

simulator. The models <strong>of</strong> functional structure components constituting the system can be obtained on<br />

the basis on numerical analysis, <strong>and</strong> they can be inserted into the system-<strong>level</strong> simulation model [13].<br />

The models based on numerical analysis have high accuracy, suit for functional structure components<br />

in different shape <strong>and</strong> can realize the top-down verification in <strong>MEMS</strong> design [14, 15], but the models<br />

must be recalculated after changes in geometry dimension or topology <strong>of</strong> the functional structure<br />

components, resulting in long design circle, <strong>and</strong> can’t meet the requirement <strong>of</strong> rapid design.<br />

In order to realize rapid design <strong>of</strong> <strong>MEMS</strong> comb accelerometer <strong>and</strong> analyze the system-<strong>level</strong> behaviors<br />

<strong>of</strong> it, on one h<strong>and</strong>, we use pr<strong>of</strong>essional <strong>MEMS</strong> design s<strong>of</strong>tware to simulate <strong>and</strong> optimize the sensor<br />

part <strong>of</strong> <strong>MEMS</strong> comb accelerometers; on the other h<strong>and</strong>, we use numerical analysis to establish the<br />

system-<strong>level</strong> model <strong>of</strong> force-<strong>balance</strong> accelerometers including interface circuit. This mixed rapid<br />

modeling method has the following advantages: reflecting the impact <strong>of</strong> these local characteristics <strong>and</strong><br />

structure parameters on system performance comparing to signal flow method; less computing time<br />

comparing to multi-emulator coupling analysis method; short design circle comparing to unified<br />

modeling method.<br />

This paper proposes a quick design method on system-<strong>level</strong> simulation <strong>of</strong> <strong>MEMS</strong> comb<br />

accelerometers. Section II describes the derivation <strong>of</strong> the system-<strong>level</strong> model including the sense<br />

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element <strong>and</strong> interface electronics. <strong>Simulation</strong> results are obtained from COVENTOR <strong>and</strong> MATLAB in<br />

Section III. The conclusions are reported in Section IV.<br />

2. Theoretical Principles <strong>of</strong> <strong>MEMS</strong> Comb Accelerometers<br />

The <strong>MEMS</strong> comb accelerometer system consists <strong>of</strong> two main parts: the sense element <strong>and</strong> the interface<br />

electronics. As shown in Fig. 1, the sense element comprises a pro<strong>of</strong> mass suspended by two folded<br />

beams on each end, differential sensing <strong>and</strong> feedback capacitances. Movable fingers are mounted on<br />

the mass, <strong>and</strong> stator fingers are attached to substrate. The movable fingers <strong>and</strong> the stators establish<br />

differential sensing capacitances that can be evaluated by a signal pick-<strong>of</strong>f circuit. In the initial state,<br />

there is no acceleration <strong>and</strong> the pro<strong>of</strong> mass rests in the null position. The differential capacitances are<br />

equal, <strong>and</strong> the output voltage is zero. If an external acceleration is applied on the pro<strong>of</strong> mass in the x<br />

direction, the <strong>balance</strong> breaks <strong>and</strong> position variation <strong>of</strong> the pro<strong>of</strong> mass is sensed, causing relative<br />

changes <strong>of</strong> differential capacitances ( C ). With proper interface electronics, C can be converted to<br />

a voltage signal, which is proportional to the magnitude <strong>of</strong> the external acceleration. In order to<br />

improve the system stability <strong>and</strong> widen the measurement range, we use a closed loop structure, <strong>and</strong><br />

this can be realized by applying the feedback voltage signal to the pro<strong>of</strong> mass, which can pull back the<br />

deflected pro<strong>of</strong> mass to the null position.<br />

Anchor<br />

F EXT<br />

Anchor<br />

C a1<br />

C b1<br />

y<br />

x<br />

Pro<strong>of</strong> Mass: M<br />

Air Damping: B<br />

Spring Constant: K<br />

Movable fingers<br />

Stator fingers<br />

C a2<br />

C b2<br />

Anchor<br />

X<br />

Anchor<br />

Fig. 1. Simplified model <strong>of</strong> the <strong>MEMS</strong> comb accelerometer.<br />

2.1. Sense Element<br />

The structure design <strong>of</strong> a <strong>MEMS</strong> comb accelerometer is shown in Fig. 2. Lateral accelerometers have<br />

been developed using comb electrodes <strong>and</strong> differentially detecting parallel electrodes to obtain linear<br />

output. The movable parts <strong>of</strong> this sense element consist <strong>of</strong> four U-shape folded beams, a pro<strong>of</strong> mass<br />

<strong>and</strong> some movable fingers. The fixed parts include four anchors <strong>and</strong> stator fingers. The pro<strong>of</strong> mass is<br />

connected to four anchors through four folded beams. The stator fingers <strong>and</strong> the movable fingers form<br />

four capacitances, which are C a1 , C a2 , C b1 <strong>and</strong> C b2 respectively.<br />

The specific structure parameters <strong>of</strong> the sense element are shown in Table 1.<br />

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Fig. 2. 3D model <strong>of</strong> the sense element.<br />

Table 1. Structure parameters for the sense element.<br />

Serial<br />

number<br />

1<br />

2<br />

3<br />

4<br />

5<br />

6<br />

Name<br />

Length <strong>of</strong><br />

mass L<br />

Width <strong>of</strong><br />

mass B<br />

Length <strong>of</strong><br />

superposition<br />

l fr<br />

Length <strong>of</strong><br />

comb finger<br />

l f<br />

Width <strong>of</strong><br />

comb finger<br />

w f<br />

Length <strong>of</strong><br />

girder l b<br />

Value<br />

Serial<br />

number<br />

1880 7<br />

200 8<br />

270 9<br />

300 10<br />

5 11<br />

300 12<br />

Name<br />

Width <strong>of</strong> girder<br />

w b<br />

Plate distance<br />

1 d f1<br />

Plate distance<br />

2 d f2<br />

Ratio <strong>of</strong> plate<br />

distance η<br />

Thickness <strong>of</strong><br />

accelerometer<br />

h<br />

Number <strong>of</strong><br />

comb fingers n<br />

Value<br />

6<br />

4<br />

40<br />

10<br />

50<br />

50<br />

Dynamic behavior <strong>of</strong> the sense element is governed by the Newton’s second law <strong>of</strong> motion:<br />

2<br />

d x dx<br />

M B Kx F<br />

2 ext<br />

Ma<br />

(1)<br />

dt dt<br />

The effective spring constant (K) <strong>of</strong> the sense element is expressed by [16]<br />

K K K<br />

(2)<br />

mechanical<br />

electrical<br />

The mechanical <strong>and</strong> electrical stiffness <strong>of</strong> the structure are given by [17]<br />

K<br />

mechanical<br />

3<br />

2Eb h<br />

(3)<br />

l<br />

3<br />

b<br />

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K<br />

electrical<br />

1<br />

V<br />

2<br />

2<br />

DC<br />

n<br />

hl<br />

d<br />

f<br />

2<br />

1<br />

,<br />

(4)<br />

where E is the Young’s modulus <strong>of</strong> silicon in the sense direction; b, h, l b are the width, height <strong>and</strong><br />

length <strong>of</strong> the U-shape folded beams, respectively; n is the total number <strong>of</strong> movable fingers; is the<br />

dielectric constant; the initial distances between movable finger <strong>and</strong> fixed are shown as d 1 <strong>and</strong> d 2<br />

(d 1


2.2. Interface Electronics<br />

Sensors & Transducers Journal, Vol. 127, Issue 4, April 2011, pp. 88-101<br />

n order to measure the capacitance change, it’s not only to apply the excitation signal on the sense<br />

element, but also need to pick up signals from it for subsequent conditioning circuit’s processing. The<br />

excitation signal can be either a voltage or current signal, <strong>and</strong> also are the picked signals. When using<br />

the current signal as the excitation signal, the magnitude <strong>of</strong> the current signal through the sense<br />

element is determined by the admittance <strong>of</strong> the excitation node, which means it’s related to the<br />

magnitude <strong>of</strong> the parasitic capacitance. Hence, it’s better to use the voltage signal as the excitation<br />

signal. If the picked signals are voltage signal, it’s also affected by the parasitic capacitance, so it’s<br />

more <strong>of</strong>ten used to pick up current signals from the sense element. To sum up, it’s a suitable way to use<br />

a voltage signal to excite the sense element <strong>and</strong> pick up current signals from it.<br />

Based on the above reasons, we build the interface electronics in Fig. 3. The capacitances changes<br />

( C1, C2<br />

) can be converted into two voltage signals at the input terminals <strong>of</strong> the high pass filter.<br />

The signals are filtered <strong>and</strong> then sent to the differential operational amplifier, <strong>and</strong> the output <strong>of</strong> the<br />

differential operational amplifier is demodulated, amplified, <strong>and</strong> then filtered by a low pass filter. The<br />

output <strong>of</strong> the low pass filter is the output signal <strong>of</strong> circuit, which we can use a PID controller to<br />

improve the dynamic characteristics <strong>of</strong> the whole system. Proportional to the output signal, the<br />

feedback voltage is continuously applied to the pro<strong>of</strong> mass, <strong>and</strong> then the deflected is pulled back to the<br />

original position.<br />

C 1<br />

U drive<br />

C 2<br />

Fig. 3. The schematic diagram <strong>of</strong> interface electronics in a force-<strong>balance</strong> <strong>MEMS</strong> comb accelerometer.<br />

The voltage signals coming out <strong>of</strong> the high pass amplifier can be expressed as:<br />

C<br />

U () t - Acos( t)<br />

(11)<br />

1<br />

1 0<br />

CCA<br />

C<br />

U () t - Acos( w t)<br />

(12)<br />

2<br />

2 0<br />

CCA<br />

where C CA is the magnitude <strong>of</strong> feedback capacitance in charge amplifier; U drive is the excitation signal,<br />

which frequency is w 0 <strong>and</strong> amplitude is A.<br />

The differential operational amplifier can translate the two voltage signals (U 1 <strong>and</strong> U 2 ) into one voltage<br />

signal, which is U pos . It can be expressed as:<br />

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C C C<br />

U<br />

pos<br />

K Acos( w t) K Acos( w t)<br />

(13)<br />

C<br />

1 2<br />

1 0 1 0<br />

CCA<br />

CA<br />

The synchronous demodulator is composed <strong>of</strong> the multiplier <strong>and</strong> low pass filter, which can demodulate<br />

the dc flow signal related to the acceleration signal. The output signal <strong>of</strong> the multiplier can be<br />

expressed as:<br />

KA C<br />

U U Acos( w t) [1 cos(2 w t)]<br />

(14)<br />

mult<br />

pos<br />

2<br />

1<br />

0 0<br />

2 CCA<br />

In order to filter out the high frequency signal in it, we select the second voltage-controlled voltage<br />

type low pass filter, which amplitude-frequency characteristics is closer to the ideal low pass filter <strong>and</strong><br />

has some gain amplification. The output signal <strong>of</strong> this low pass filter is:<br />

1<br />

2 C<br />

Uout<br />

K1Alp<br />

A<br />

2 C<br />

CA<br />

(15)<br />

where A lp is the amplification <strong>of</strong> the low pass filter. In general, the greater open-loop gain <strong>of</strong> the<br />

system, the higher the accuracy <strong>of</strong> it, but the system is prone to oscillation when the gain is very large.<br />

Hence, it’s very important to have an appropriate gain <strong>of</strong> the system, <strong>and</strong> usually we use the amplitudefrequency<br />

characteristics <strong>of</strong> the system to determine it. If open-loop gain amplification <strong>of</strong> the system is<br />

K 2 , we can express the feedback voltage as:<br />

1<br />

2 C<br />

U<br />

fb<br />

K2K1Alp<br />

A<br />

2<br />

C<br />

CA<br />

(16)<br />

3. <strong>System</strong>-<strong>level</strong> <strong>Simulation</strong> <strong>of</strong> the <strong>Force</strong>-<strong>balance</strong> <strong>MEMS</strong> Comb Accelerometer<br />

Section II describes the derivation <strong>of</strong> the system-<strong>level</strong> model including sensor part <strong>and</strong> interface<br />

electronics, <strong>and</strong> we use pr<strong>of</strong>essional <strong>MEMS</strong> design s<strong>of</strong>tware COVENTOR to model, simulate <strong>and</strong><br />

optimize the sensor element. After that we use numerical analysis s<strong>of</strong>tware MATLAB to establish <strong>and</strong><br />

simulate the system-<strong>level</strong> model <strong>of</strong> force-<strong>balance</strong> accelerometers including interface circuit.<br />

The design way <strong>of</strong> our quick system-<strong>level</strong> modeling <strong>and</strong> simulation method is shown in Fig. 4. In the<br />

beginning, we have an initial design for a <strong>MEMS</strong> comb accelerometer, including the sensor part’s<br />

structural parameters <strong>and</strong> the interface electronics; after that, we use COVENTOR to establish the<br />

architect model <strong>of</strong> the sensor part according to its parameters. We can get the macro model’s<br />

parameters from the architect model, <strong>and</strong> also can analyze the parameters’ influence on the macro<br />

model; Using the macro model from the COVENTOR <strong>and</strong> the transfer functions <strong>of</strong> interface<br />

electronics we can build the system-<strong>level</strong> model <strong>of</strong> the <strong>MEMS</strong> comb accelerometer in MATLAB, <strong>and</strong><br />

get the performance parameters <strong>of</strong> it; Finally, if the performance parameters cannot meet the<br />

requirements, we can change the parameters in the architect model until we get the performance<br />

parameters that meet the requirement.<br />

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Fig. 4. The quick system-<strong>level</strong> modeling <strong>and</strong> simulation method in <strong>MEMS</strong> comb accelerometers.<br />

3.1. <strong>Simulation</strong> <strong>of</strong> the Sense Element<br />

We build the architect model <strong>of</strong> the sense element in COVENTOR, which is shown in Fig. 5. Using<br />

this architect model we can easily simulate the sense element, if some parameters <strong>of</strong> the sense element<br />

change, we can easily analyze the parameters’ influences on the sense element, unlike CAE traditional<br />

way that we need to reestablish the three-dimensional model <strong>and</strong> analyze it in finite element analysis<br />

s<strong>of</strong>tware. Architect model can quickly model <strong>and</strong> analyze the sense element, <strong>and</strong> also doesn’t lose<br />

accuracy.<br />

Fig. 5. The architect model <strong>of</strong> a <strong>MEMS</strong> comb accelerometer in COVENTOR.<br />

According the known, the sense element <strong>of</strong> <strong>MEMS</strong> comb accelerometer was a mass-spring system, the<br />

vibration was occurred on the condition <strong>of</strong> acceleration. So the significant limitation <strong>of</strong> accelerometer<br />

sensor was the narrow range for frequency response, whose main factors were the resonant frequency.<br />

We did the modal analysis <strong>of</strong> the sense element in COVENTOR, <strong>and</strong> the modal results are shown in<br />

Fig. 6. The first mode is lateral vibration in the sense direction x, which is preferable for stable device<br />

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operation, <strong>and</strong> the modal frequency is 7.72 kHz; the second mode is lateral vibration in the direction z,<br />

which modal frequency is 32.06 kHz; the third mode is torsional vibration in the direction z, which<br />

modal frequency is 70 kHz; the fourth mode is torsional vibration in the direction y, which modal<br />

frequency is 72.75 kHz. The result <strong>of</strong> theoretical analysis was about 7.1 kHz, <strong>and</strong> the error was below<br />

10 % compared with the data <strong>of</strong> simulation, which was in the range <strong>of</strong> error for engineering.<br />

Fig. 6. Resonant modes <strong>of</strong> the sense element (by COVENTOR).<br />

In order to scale the anti-shock ability <strong>of</strong> the sense element, we simulated the sense element with an<br />

external acceleration <strong>of</strong> 2000 g in x, y, z direction. The result shows that the maximum stress is<br />

47 MPa. Because the maximum stress <strong>of</strong> the silicon can hold is 7 GPa, so the sense element can endure<br />

with over load <strong>of</strong> 2000 g.<br />

From the above data we can have a conclusion that the first mode <strong>of</strong> the sense element is isolated with<br />

the second, third <strong>and</strong> fourth mode. So we can see that the design <strong>of</strong> the sense element can meet the<br />

basic requirements <strong>of</strong> the modal analysis.<br />

Although the above analysis can meet the requirements <strong>of</strong> the modal analysis, it is necessary to be sure<br />

that the sense element has good linearity in working range, which means we should be sure that the<br />

applied load has linear relationship with the pro<strong>of</strong> mass’s displacement. By using the architect model,<br />

we can easily change the applied load for analysis. Therefore, we applied external acceleration from<br />

0-40 g (1g=9.8 m 2 /s), the displacement <strong>of</strong> the pro<strong>of</strong> mass is shown in Fig. 7. From Fig. 7 we can say<br />

that the sense element has good linearity when the external acceleration is in the range <strong>of</strong> 40 g.<br />

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60 Displacement[nm] Acceleration(g)<br />

50<br />

40<br />

30<br />

20<br />

10<br />

0<br />

0 5 10 15 20 25 30 35 40<br />

Fig. 7. The relationship between external acceleration <strong>and</strong> the displacement <strong>of</strong> the pro<strong>of</strong> mass.<br />

From the dc analysis, we can get the initial capacitances C1 <strong>and</strong> C2 are 2.25 pF. Through applying<br />

different external acceleration, we can get the capacitance change (C1-C2), the relationship between<br />

them is shown in Fig. 8. From Fig. 8 we can see that when the external acceleration is in the range <strong>of</strong><br />

4g, the relationship is linear between them. But when the external acceleration is above 4 g, the<br />

relationship is not linear. If the sense element is controlled by open-loop system, the work range <strong>of</strong><br />

<strong>MEMS</strong> comb accelerometer will be subject to the nonlinear effect <strong>of</strong> capacitor plates. So we use closeloop<br />

system to sense <strong>and</strong> feedback the sense element, which the work range will not be affected by the<br />

nonlinear effect <strong>of</strong> capacitor plates.<br />

10<br />

Capacitance Change [10 -2 pF]<br />

8<br />

6<br />

4<br />

2<br />

Real relationship<br />

Linear relationship<br />

0<br />

0 2 4 6 8 10<br />

Acceleration [g]<br />

Fig. 8. The relationship between external acceleration <strong>and</strong> the capacitance change.<br />

Through the modal analysis, we found that the first mode is also the sense direction, which can<br />

improve the sensitivity <strong>of</strong> the detection axis, <strong>and</strong> its second <strong>and</strong> high order modes are isolated with the<br />

first mode, that can avoid cross-coupling; through the static analysis, we found that when the<br />

acceleration is in the range <strong>of</strong> 40 g, the displacement <strong>of</strong> the pro<strong>of</strong> mass has good linear relationship<br />

with it.; finally, we analyzed the relationship between the capacitance change <strong>and</strong> the external<br />

acceleration, <strong>and</strong> found the nonlinear effect <strong>of</strong> capacitor plates.<br />

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3.2. <strong>System</strong>-<strong>level</strong> <strong>Simulation</strong> <strong>of</strong> the <strong>Force</strong>-<strong>balance</strong> <strong>MEMS</strong> Comb Accelerometer<br />

The above analysis <strong>of</strong> the sense element proved that the design structure <strong>and</strong> parameters are<br />

appropriate, <strong>and</strong> from the architect model’s analysis we can get the macro model’s parameters <strong>of</strong> the<br />

sense element: the mass is 5.47 µg; the damping is 2.1 mNm/s; the mechanical spring constant is<br />

357.8 N/m; the initial capacitances (C1 <strong>and</strong> C2) are 2.25 pF. So we can use these parameters to derive<br />

corresponding transfer function <strong>of</strong> the sense element. We also designed the electronic circuits in Fig. 3,<br />

which are the charge amplifier, the high pass filter, the differential operation amplifier, the<br />

synchronous demodulator, <strong>and</strong> the PID controller, <strong>and</strong> derived the transfer functions <strong>of</strong> them. Thus we<br />

established the system-<strong>level</strong> model <strong>of</strong> the <strong>MEMS</strong> comb accelerometer using the transfer functions<br />

according to the real parts in the numerical analysis s<strong>of</strong>tware MATLAB, which is shown in Fig. 9.<br />

a<br />

Acceleration<br />

Subtract1<br />

Subtract<br />

-K-<br />

Gain<br />

Gain1<br />

1<br />

x'<br />

s<br />

Integrator<br />

1 x<br />

s<br />

Integrator1<br />

x<br />

-K-<br />

Gain2<br />

-K-<br />

f(u)<br />

x to c1<br />

C1<br />

Signal<br />

Generator<br />

f(u)<br />

x to c<br />

Product<br />

-1.64E-3s 2<br />

den(s)<br />

Transfer Fcn<br />

Delta C<br />

f(u)<br />

x to c2<br />

C2<br />

-10<br />

-1<br />

Gain4<br />

Switch<br />

Gain3<br />

Subtract2<br />

Demodulation V<br />

Switch1<br />

Signal<br />

Generator1<br />

Sign<br />

-K-<br />

Gain7<br />

1<br />

s<br />

Integrator2<br />

butter<br />

-10<br />

Analog<br />

Filter Design<br />

Gain5<br />

-K-<br />

du/dt<br />

Subtract3<br />

Vf<br />

Gain8<br />

Derivative<br />

signal before PI<br />

Gain6<br />

-K-<br />

Fig. 9. <strong>System</strong>-<strong>level</strong> model <strong>of</strong> the force-<strong>balance</strong> <strong>MEMS</strong> comb accelerometer system in MATLAB.<br />

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Sensors & Transducers Journal, Vol. 127, Issue 4, April 2011, pp. 88-101<br />

When the external step acceleration is 1 g, 2 g, 4 g, 6 g, 8 g, the displacement <strong>of</strong> the pro<strong>of</strong> mass is<br />

shown in Fig. 10-a. We can see that the displacement <strong>of</strong> the pro<strong>of</strong> mass gradually increases firstly<br />

because <strong>of</strong> the external acceleration, but the displacement starts to decrease after a very short time,<br />

which is caused by the influences <strong>of</strong> feedback electrostatic force <strong>and</strong> the beam’s spring force. After<br />

about 0.008 second, the displacements decrease to zero.<br />

The according output voltage, which is also the feedback electrostatic voltage, is shown in Fig. 10-b.<br />

When the external step acceleration is 1 g, after a very short vibration (about 0.003 second) the output<br />

voltage can hold a stable value <strong>of</strong> 0.1 V; as is shown in Fig. 10-b, the stable value <strong>of</strong> the output voltage<br />

has a good linear relationship with the external acceleration. From Fig. 10, we can get the sensitivity <strong>of</strong><br />

the <strong>MEMS</strong> comb accelerometer is 100 mV/g.<br />

14<br />

Displacement [nm]<br />

Output Voltage(V)<br />

1.2<br />

12<br />

10<br />

8<br />

6<br />

4<br />

8g<br />

6g<br />

4g<br />

1.0<br />

0.8<br />

0.6<br />

0.4<br />

8g<br />

6g<br />

4g<br />

2 2g<br />

0.2 2g<br />

1g<br />

0<br />

1g<br />

0.000 0.002 0.004 0.006 0.008 0.010 0.0<br />

Time[s] 0.000 0.002 0.004 0.006 0.008 0.010<br />

Time(s)<br />

(a)<br />

(b)<br />

Fig. 10. (a) the displacement response <strong>of</strong> the pro<strong>of</strong> mass in 1 g step external acceleration Fig.10-b;<br />

(b) the output voltage response <strong>of</strong> the accelerometer system in 1 g step external acceleration.<br />

The relationship between the external acceleration <strong>and</strong> the final output voltage is shown in Fig. 11.<br />

Because we defined the bias voltage <strong>of</strong> the <strong>MEMS</strong> comb accelerometer as 5 V, so the output voltage is<br />

constrained to [-5 V, 5 V]. From Fig. 11, we can see that when the external acceleration is in the range<br />

<strong>of</strong> [-50 g, 50 g], it can hold a very good linear relationship with the output voltage, <strong>and</strong> we can get the<br />

range <strong>of</strong> the <strong>MEMS</strong> comb accelerometer is 50g , <strong>and</strong> the nonlinear distortion is smaller than 0.5 %. If<br />

we want to extend the range <strong>of</strong> the <strong>MEMS</strong> comb accelerometer, we can reduce the feedback<br />

coefficient <strong>of</strong> the output voltage, which will reduce the sensitivity; <strong>and</strong> if we want to increase the<br />

sensitivity <strong>of</strong> the <strong>MEMS</strong> comb accelerometer, we need to enlarge the feedback coefficient <strong>of</strong> the<br />

output voltage, but this will cause the loss the range that the <strong>MEMS</strong> comb accelerometer can measure.<br />

So when we design the real electronic interfaces <strong>of</strong> the <strong>MEMS</strong> comb accelerometer, one resistance <strong>of</strong><br />

the differential operation amplifier can be designed as an adjustable resistance in order to adjust the<br />

sensitivity <strong>and</strong> range <strong>of</strong> the accelerometer manually.<br />

The amplitude-frequency response <strong>of</strong> the <strong>MEMS</strong> comb accelerometer is shown in Fig. 12. When we<br />

load 20 acceleration signals on the <strong>MEMS</strong> comb accelerometer with the same amplitude but different<br />

frequencies, the final output voltage changes as the frequency change. As is shown in Fig. 12, in the<br />

low frequency scale (


Sensors & Transducers Journal, Vol. 127, Issue 4, April 2011, pp. 88-101<br />

4<br />

3<br />

2<br />

1<br />

0<br />

-1<br />

-2<br />

-3<br />

-4<br />

-5<br />

-50 -40 -30 -20 -10 0 10 20 30 40 50<br />

5 Output voltage[V] Acceleration[g]<br />

Fig. 11. the relationship between the external acceleration <strong>and</strong> the output voltage.<br />

Output Voltage(V)<br />

0.32<br />

0.30<br />

0.28<br />

0.26<br />

0.24<br />

0.22<br />

0.20<br />

0.18<br />

0.16<br />

0.14<br />

0.12<br />

0.10<br />

1 10 100 1000 10000<br />

Frequency[Hz]<br />

Fig. 12. The amplitude-frequency response <strong>of</strong> the force-<strong>balance</strong> <strong>MEMS</strong> comb accelerometer system.<br />

4. Conclusions<br />

To aid system designers, the system-<strong>level</strong> modeling <strong>and</strong> simulation <strong>of</strong> force-<strong>balance</strong> <strong>MEMS</strong> comb<br />

accelerometers is studied. A mathematical model, which involves both the sense element <strong>and</strong> interface<br />

electronics, is developed <strong>and</strong> governing equations are derived. The sense element is designed <strong>and</strong><br />

simulated in COVENTOR. The modal analysis shows that the resonance frequency <strong>of</strong> the sense<br />

element in detecting direction is 7.1 kHz; the static analysis shows that the sense element can endure<br />

with over load <strong>of</strong> 2000 g, <strong>and</strong> the displacement <strong>of</strong> the pro<strong>of</strong> mass has a very good linear relationship<br />

with the external acceleration in the range <strong>of</strong> ±40 g. The whole accelerometer system is derived <strong>and</strong><br />

simulated in MATLAB. The results show that the force-<strong>balance</strong> <strong>MEMS</strong> comb accelerometer system’s<br />

sensitivity is 100 mv/g, the full scale range is ±50 g, the nonlinear distortion is smaller than 0.5 % <strong>and</strong><br />

the system b<strong>and</strong>width is 2.2 kHz.<br />

References<br />

[1]. ADXL50 – Monolithic Accelerometer With Signal Conditioning, Data Sheet Analog Devices Inc., 1996.<br />

[2]. ADXL150/ADXL250 – ±5 g to ±50 g, low Noise, low Power, Single/Dual Axis i<strong>MEMS</strong> Accelerometers,<br />

Data Sheet Analog Devices Inc., 1998.<br />

[3]. ADXL78 – full range <strong>of</strong> ±35 g, ±50 g, ±70 g, low Noise, low Power, Single Axis i<strong>MEMS</strong> Accelerometers,<br />

Data Sheet Analog Devices Inc., 2005.<br />

[4]. MMA2202D – Surface Mount Micromachined Accelerometer, Data Sheet Motorola, 2001.<br />

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[5]. J. Bernstein, An Overview <strong>of</strong> <strong>MEMS</strong> Inertial Sensing Technology, Sensors Magazine Online, Feb. 2003.<br />

[6]. Van Kampen, R. P. <strong>and</strong> Wolffenbuttel, R. F., Application <strong>of</strong> electrostatic feedback to critical damping <strong>of</strong> an<br />

integrated silicon accelerometer, Sensors <strong>and</strong> Actuators, A, 43, 1994, pp. 100-106.<br />

[7]. Gilbert J R, Legtenberg R, Senturia S D., 3D Coupled Electro – Mechanics for <strong>MEMS</strong>: Applications <strong>of</strong><br />

Cosolve_EM, Micro Electro Mechanical <strong>System</strong>s, Proceedings, IEEE, Jan 29 – Feb, 1995, pp. 122-127.<br />

[8]. Zhulin V I, Owen S J, Ostergaard D F, Finite Element Based Electrostatic—Structural Coupled Analysis<br />

with Automated Mesh Morphing, in Proceedings <strong>of</strong> the international Conference on <strong>Modeling</strong> <strong>and</strong><br />

<strong>Simulation</strong> <strong>of</strong> Microsystems (MSM’ 2000), San Diego, CA, 2000.<br />

[9]. Zheng Ying-bin, Su Wei, He Xiao-ping, Coupled electrostatic-mechanical analysis for a multi-finger microaccelerometer,<br />

Journal <strong>of</strong> Transducer Technology, 05, 2002.<br />

[10]. Robert M. K., George E. K., Mikulchenko O., et al. An integrated simulator for coupled domain problems,<br />

Journal <strong>of</strong> Micro electromechanical <strong>System</strong>s, 10, 3, 2001, pp. 379-391.<br />

[11]. Ramaswamy D, Aluru N, White J., Fast coupled-domain, mixed regime electromechanical simulation, In:<br />

Proc. Int Conf Solid-State Sensors <strong>and</strong> Actuators, Japan: The Institute <strong>of</strong> Electrical Engineers <strong>of</strong> Japan,<br />

1999, pp. 314 - 317.<br />

[12]. Gabbay L D, Senturia S D. Computer-aided generation <strong>of</strong> nonlinear reduced-order dynamic macromodels.<br />

I. Non-stress stiffened case, Journal <strong>of</strong> Micro electromechanical <strong>System</strong>s, 9, 2, 2000, pp. 262 - 269.<br />

[13]. Romanowicz B F, Bart S F, Gilbert J R. Integrated CAD tools for top-down design <strong>of</strong> <strong>MEMS</strong>/MOEMS<br />

systems, SPIE, 3680, 1999, pp. 171 - 178.<br />

[14]. Nguyen Linh, Lee Hee Jung, Maher Marr Ann, et al. Structured CAD methodology for integrated <strong>MEMS</strong><br />

<strong>and</strong> IC design, Proceedings <strong>of</strong> SPIE, 3680, 1999, pp. 259 - 265.<br />

[15]. S. D. Senturia, Microsystem Design, Kluwer Academic Publishers, 2001.<br />

[16]. A. M. Lemkin, Micro accelerometer design with digital feedback control, Doctoral Thesis, U. C. Berkeley,<br />

1997.<br />

[17]. James B. Starr, Squeeze film damping in solid-state accelerometers, in Tech. Dig. IEEE Solid State Sensor<br />

<strong>and</strong> Actuator Workshop, June 1990, pp. 44 – 47.<br />

[18]. T. Veijola, H. Kuisma, <strong>and</strong> J. Lahdenperä, Model for gas film damping in a silicon accelerometer, in Proc.<br />

<strong>of</strong> the Transducers'97, June 1997, pp. 1097 – 1100.<br />

[19]. A. Selvakumar, A multifunctional silicon micromachining technology for high performance microsensors<br />

<strong>and</strong> microactuators, Doctoral Thesis, U. Michigan, 1997.<br />

[20]. R. P. Van Kampen, Bulk-micromachined capacitive servo-accelerometer, Doctoral Thesis, Delft University,<br />

Netherl<strong>and</strong>s, 1995.<br />

[21]. Zheng Ying-bin, Coupled-Field Analysis for comb finger accelerometer, Master Degree Thesis, China<br />

academy <strong>of</strong> engineering physics, 2, 2002, pp. 13-17.<br />

___________________<br />

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