DESIGN AND ANALYSIS OF MEMS CAPACITIVE ACCELEROMETER WITH OPTIMIZED SENSITIVITY

KHAIRUN NISA BT KHAMIL

RESEARCH PROJECT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF MASTER OF ENGINEERING

FACULTY OF ENGINEERING UNIVERSITY OF MALAYA

KUALA LUMPUR

2014

UNIVERSITI MALAYA

ORIGINAL LITERARY WORK DECLARATION

Name of Candidate: KHAIRUN NISA BT KHAMIL (I.C/Passport No: 850101146334)

Registration/Matric No: KGK 110014

Name of Degree: Master of Engineering (Industrial Electronics and Control)

Title of Project Paper/Research Report/Dissertation/Thesis (“this Work”):

DESIGN AND ANALYSIS OF MEMS CAPACITIVE ACCELEROMETER WITH OPTIMIZED SENSITYVITY Field of Study: MICROELECTROMECHANICAL SYSTEM (MEMS)

I do solemnly and sincerely declare that:

(1) I am the sole author/writer of this Work; (2) This Work is original; (3) Any use of any work in which copyright exists was done by way of fair dealing

and for permitted purposes and any excerpt or extract from, or reference to or reproduction of any copyright work has been disclosed expressly and sufficiently and the title of the Work and its authorship have been acknowledged in this Work;

(4) I do not have any actual knowledge nor do I ought reasonably to know that the making of this work constitutes an infringement of any copyright work;

(5) I hereby assign all and every rights in the copyright to this Work to the University of Malaya (“UM”), who henceforth shall be owner of the copyright in this Work and that any reproduction or use in any form or by any means whatsoever is prohibited without the written consent of UM having been first had and obtained;

(6) I am fully aware that if in the course of making this Work I have infringed any copyright whether intentionally or otherwise, I may be subject to legal action or any other action as may be determined by UM.

Candidate’s Signature Date

Subscribed and solemnly declared before,

Witness’s Signature Date

Name:

Designation:

ii

ABSTRACT

Nowadays, numerous research studies have been done on MEMS based micro-

accelerometer that focuses on optimizing the device sensitivity. With a smaller size

compared to the conventional design of the accelerometer, it weighs lesser, functions

more efficiently which then contributes to cheaper manufacturing cost. The selection of

type and model of the MEMS accelerometer is important before the design parameter

can be determined. The relationship between mass width, beam (length and width) and

the device sensitivity are investigated. After the theoretical analysis has been calculated,

the FEM simulation is then done by constructing three dimensional model structures

and the displacement sensitivity of the device is simulated. The result from the

simulation proved that it matches the theoretical analysis. The optimization analysis

concluded that desired sensitivity can be achieved by adding number of fingers and

adjusting the length of the beam. The optimizing method used in this project is based on

trial and error technique. From the simulation result, the device has a displacement

sensitivity of 3.5301 nm/g which showed that the MEMS accelerometer sensitivity has

been optimized. By using this recommended MEMS capacitive accelerometer, an airbag

deployment system in automobiles with the capability to withstand extensive range of

shock can be designed.

iii

ABSTRAK

Pada masa kini, terdapat banyak kajian dan penyelidikan mengenai pecutan

meter mikro dalam teknologi sistem elektromekanik mikro (MEMS) yang

mengoptimumkan prestasi dengan kaedah peningkatan sensitiviti untuk peranti. Dengan

saiz yang lebih kecil dan padat berbanding dengan reka bentuk konvensional meter

pecutan, meter pecutan mikro adalah lebih ringan, cekap dan seterusnya menjadikan kos

pengeluaran jauh lebih murah. Permilihan struktur model dan jenis meter pecutan

MEMS yang bersesuaian adalah penting sebelum parameter reka bentuk dapat

ditentukan. Hubungan diantara lebar jisim, panjang dan lebar rasuk, sensitiviti peranti

dapat dianalisa. Selepas analisa teori, simulasi FEM membina struktur model tiga

dimensi dan analisasensitiviti anjakan dapat dilakukan. Hasil dari simulasi, analisis dari

teori dapat dibuktikan. Analisis tersebut menunjukkan sensitiviti yang dikehendaki

boleh dicapai dengan penambahan bilangan jari meter pecutan dan menetapkan panjang

rasuk yang bersesuaian. Teknik mengoptimumkan peranti adalah berasaskan kaedah

cuba jaya. Berdasarkan keputusan simulasi, peranti mempunyai sensitiviti anjakan

3.5301 nm/g. Dengan itu, sistem beg udara dalam kereta mempunyai keupayaan untuk

menahan pelbagai kejutan yang direka dengan menggunakan teknologi MEMS meter

pecutan mikro kapasitif yang disyorkan ini.

iv

ACKNOWLEDGEMENT

Alhamdulillah. All praise to Allah s.w.t. Thanks to Allah s.w.t for His blessing

so that I can complete this research project of “Design and Analysis of MEMS

Capacitive Accelerometer with Optimized Sensitivity”. This research project is done

as for the requirements to complete the Master of Engineering in University Malaya.

With this opportunity, I would like to express my appreciation to my supervisor,

Assoc. Prof. Dr. Norhayati Soin that helps me with guidance and advice throughout the

entire research. Her experiences in Microelectromechanical system pointed me into the

right direction to conduct my research. I thank her for the thoughtful, perseverance and

trust she has put in me to complete this research.

Next, I would like to thank my sponsor and employer, Kementerian Pengajian

Tinggi Malaysia and Universiti Teknikal Malaysia Melaka for giving me the chance to

further my studies with the Skim Latihan Akademik Bumiputera (SLAB) scholarship.

Most importantly, I would like to thank my husband, Ahmad Nizam B. Isa for

giving me the permission to pursue my studies. I could not thank him enough with all

his helps especially taking care of our kids during the weekends when I went to class

and his patience when I need to do my research. Not to forget, thanks to my family that

helped me taking care of my kids and with the house work while I’m busy with studies

and this project.

I also want to thank my colleagues at Universiti Malaya Norshahida, Nurul Ain,

Suziana for helping with the simulation and giving inputs on how to solve the problem

occurred to complete this research project. Last but not least, my proof read checker,

Shireen Zaki that helps checked the thesis.

v

TABLE OF CONTENTS

TITLE i

DECLARATION ii

ABSTRACT ................................................................................................................................ iii

ABSTRAK .................................................................................................................................... iv

ACKNOWLEDGEMENT ............................................................................................................. v

TABLE OF CONTENTS .............................................................................................................. vi

LIST OF FIGURES ................................................................................................................... viii

LIST OF ABBREVIATIONS ........................................................................................................ x

LIST OF NOMENCLATURES .................................................................................................... xi

CHAPTER 1 ................................................................................................................................ 13

1.1 Overview ...................................................................................................................... 13 1.2 Background Studies ..................................................................................................... 14 1.3 Structure device design of MEMS capacitive accelerometer ...................................... 15 1.4 Finite element analysis and optimization method ........................................................ 16 1.5 Thesis Objectives ......................................................................................................... 17 1.6 Scope and Limitation ................................................................................................... 17 1.7 Project Methodology .................................................................................................... 17 1.8 Thesis Outline .............................................................................................................. 18

CHAPTER 2 ................................................................................................................................ 19

2.1 Introduction .................................................................................................................. 19 2.2 Literature surveys ........................................................................................................ 20 2.3 Principle of operation ................................................................................................... 23 2.4 Device Design .............................................................................................................. 26

vi

2.5 Mechanical Suspension ................................................................................................ 28 2.6 Damping and Quality Factor ........................................................................................ 30 2.7 Basic knowledge for capacitive MEMS ...................................................................... 31

2.7.1 Capacitive Sensing technique .............................................................................. 31 2.8 Analysis of the device .................................................................................................. 35 2.9 Performance Analysis of the device ............................................................................ 38

2.9.1 Displacement Sensitivity analysis ........................................................................ 38 2.9.2 Optimization Analysis ......................................................................................... 41

2.10 Finite Element Modelling tools. .................................................................................. 42

CHAPTER 3 ................................................................................................................................ 46

3.1 Introduction .................................................................................................................. 46 3.2 Selection of Model Structure ....................................................................................... 47 3.3 Determination of Design Parameters ........................................................................... 49 3.4 COMSOL Multiphysics® Simulation ......................................................................... 50

CHAPTER 4 ................................................................................................................................ 52

4.1 Introduction .................................................................................................................. 52 4.2 Simulation Results of Sensitivity Analysis .................................................................. 53

4.2.1 Variation of Beam Width (Part a) ........................................................................ 53 4.2.2 Variation of Beam Length (Part b) ...................................................................... 55 4.2.3 Variation of Mass Width (Part c) ......................................................................... 56

4.3 Simulation Results of Optimization Analysis .............................................................. 58 4.4 Comparison between Optimized Result with Published models ................................. 65

CHAPTER 5 ................................................................................................................................ 67

5.1 Conclusion ................................................................................................................... 67 5.2 Recommendation for Future Work .............................................................................. 68

REFERENCES ............................................................................................................................ 69

APPENDIX A .............................................................................................................................. 73

vii

LIST OF FIGURES

Figure 1.1 Airbag system (Brain, 2013) ......................................................................... 14

Figure 1.2 Accelerometer structure (Lyshevski, 2002)................................................... 16

Figure 2.1 Basic accelerometer (K.H Denishev, 2007) .................................................. 23

Figure 2.2 Schematic of accelerometer (W.C.Wong, 2007) ........................................... 26

Figure 2.3 Differential capacitance of accelerometer (K.Sharma et al 2008) ................. 27

Figure 2.4 Type of suspension design model (W.C.Wong, 2007) .................................. 28

Figure 2.5 Suspension beam structure features (LC, 2008) ............................................ 29

Figure 2.6 Basic capacitance model of displacement sensors (Stephen Beeby, 2004) ... 31

Figure 2.7 Schematic Diagram of capacitive MEMS (Xiong, 2005).............................. 32

Figure 2.8 One of the COMSOL’s examples (COMSOL, 2013) ................................... 43

Figure 3.1 Flowchart of project ...................................................................................... 47

Figure 3.2 Side view of the overall device...................................................................... 48

Figure 3.3 Top view of the overall device ..................................................................... 48

Figure 3.4 Flowchart of COMSOL Multiphysics® simulation process ......................... 51

Figure 4.1 The displacement sensitivity versus beam width .......................................... 53

Figure 4.2 The displacement sensitivity versus beam length ......................................... 55

Figure 4.3 The displacement sensitivity versus Mass Width .......................................... 56

Figure 4.4 Sensitivity versus Beam Length for each of number of fingers .................... 59

Figure 4.5 Stress versus Acceleration ............................................................................. 62

Figure 4.6 Top View Stress Simulation .......................................................................... 63

Figure 4.7 Side View Stress Simulation ......................................................................... 63

Figure 4.8 Capacitance versus Acceleration for Original Model and Optimized Model 64

viii

LIST OF TABLES

Table 2.1 Summary of other researchers Capacitive Accelerometer studies

(W.C.Wong, 2007) ......................................................................................... 22

Table 2.2 Length of proof mass, Lm for number of fingers, Nsf ..................................... 41

Table 2.3 Physics Groups in the Model Wizard (COMSOL, 2013) ............................... 44

Table 3.1 Structure Label and Dimension ...................................................................... 49

Table 3.2 Material Properties .......................................................................................... 49

Table 3.3 Design Specification ....................................................................................... 50

Table 4.1 The Percentage differences between each of the Beam Width ....................... 54

Table 4.2 Percentage difference between each of the Beam Length .............................. 55

Table 4.3 Percentage difference between each of the Mass Width ................................ 57

Table 4.4 Calculated data for each number of fingers and Beam Length. ...................... 58

Table 4.5 Percentage differences between the sensitivity for each number of fingers and

beam length .................................................................................................... 60

Table 4.6 Percentage of error between Analytical and Simulated result for both

Optimized and Original models...................................................................... 61

Table 4.7 Percentage of increase between Analytical and Simulated result for both

Optimized and Original models...................................................................... 62

Table 4.8 Stress Analysis ................................................................................................ 63

Table 4.9 Benchmarking to other researcher's finding ................................................... 66

ix

LIST OF ABBREVIATIONS

MEMS Microelectromechanical systems

SRS Supplemental Restraint System

FEA Finite Element Analysis

IC Integrated Circuit

FEM Finite Element Modelling

ODE Ordinary differential Equation

MOSFET Metal Oxide Semiconductor Field Effect Transistor

x

LIST OF NOMENCLATURES

C: Capacitance

d: Distance

ε, εo : Electric Constant

A: Area

m: Mass

Ms: Movable Mass

Kfold, Ks: Spring Constant

aext: External Acceleration

D: Damping Coefficient

x: Displacement

f0, 𝜔𝑟: Resonant Frequency

Q: Quality Factor

Vx: Voltage Output

Nf: Total Sensing Finger Number

neff : Effective Viscosity of Air

lb: Beam Length

Wb: Beam Width

t: Thickness

xi

E: Young’s modulus

S: Join Area Between Mass and The Fingers

Vm: Voltage Modulation

d0: Stationary Gap of the Capacitance

𝜔: Frequency of Modultaion voltage

t0: Time of operation

Fd: Electrostatic Force

V0: Voltage Input

Wm : Proof Mass Width

Lm: Proof Mass Length

Nsf: Total of Sensing Finger

Nff : Total of Fixed Finger

Wf: Fingers Width

Lf: Fingers Length

Finertial: Inertia Force

Ktotal: Total of Spring Constant

𝜌: Density of Polysilicon

Ib: Inertial Momentum

Sd: Displacement Sensitivity

Sc: Capacitance Sensitivity

xii

CHAPTER 1

INTRODUCTION

1.1 Overview

This chapter aims to discuss the background of the Microelectromechanical

systems or MEMS with the outline of the thesis which presented as follows:

• Background studies

• Structure device design of MEMS capacitive accelerometer

• Finite element analysis and improvisation method

• Thesis objective

• Scope and limitation

• Thesis outline

Nowadays, numerous research studies are made on MEMS based micro-

accelerometer that focus on optimizing the device sensitivity. With a smaller size

compared to the conventional design of the accelerometer, it weighs lesser, functions

more efficiently which then contributed to cheaper manufacturing cost..

MEMS accelerometers can be found used in most of our everyday life items

which ranging from telecommunication to health and safety like airbag deployment

systems used in vehicles. By detecting the negative acceleration of the automobile,

accelerometers are the sensor to use. These sudden changes of the negative acceleration

are depend on the changes to the types of the sensor that will be used in this project

which is the capacitance.

13

1.2 Background Studies

In most automobiles these days, airbag has become the most important features

due to its safety purposes. For Toyota Motor Corporation, the Supplemental Restraint

System (SRS) of the Airbag System increases vehicle user’s safety and aimed to

enhance the seatbelt method (Toyota Motor Corporation, 2013).

For SRS airbag to be deployed, the amount of the collision needed is calculated

for the sensor to sense the impact. The time taken for the airbag to complete deploying

must be around 0.03 seconds as the human eye can blink from 0.1 to 0.3 seconds which

made the completion period took 0.1 seconds. After that, the airbag deflated.

The deployed and deflated process occurred rapidly where the vehicle’s user

have no chance to do anything. This shows that the sensitivity of the sensor used in the

airbag system is vital since it is served safety purposes.

Figure 1.1 Airbag system (Brain, 2013)

14

1.3 Structure device design of MEMS capacitive accelerometer

The interface of capacitance sensors have some remarkable features which are

very sensitive and not easily effected by temperature. This shows why the capacitance is

commonly chosen for accelerometer (Andrejašic, 2008).

𝐶 =𝜀0𝜀𝐴𝑑

(1.1)

Referring to equation 1.1, εoε is permittivity, C is equivalent to Capacitance,

distance as d and the area as A. When the housing (main part for the capacitive

accelerometer) that sometimes can be referred as seismic mass or proof mass moved the

“comb-like” part back and forth so that the acceleration can be calculated. As the result

from the movement of the center section, the fingers on the accelerometer structure

made up a differential capacitance and allowing the current to flow (G.H.Y. I. Lee,

2005).

𝑎 =𝐾𝑠𝑑𝑚𝑉0

𝑉𝑥

(1.2)

The voltage of the proof mass is the output voltage, Vx and x is the displacement. While

the spring constant will be Ks and the mass is m. Therefore, the acceleration can be

found (Sharma et al., 2008) .

15

Figure 1.2 Accelerometer structure. The spring’s constant is attached to proof mass at substrate where it moved up and down. From the movable and fixed plates, the capacitor is determined (Lyshevski, 2002)

1.4 Finite element analysis and optimization method

By using the Finite Element Analysis (FEA), the product can be designed and

analyzed virtually where the computer simulation predicts a detailed outcome of the

design before manufacturing it. This technique can save the manufacturing cost without

even manufactured the real design over and over again. Three dimensional is commonly

used to see a more realistic and accurate effects (Widas, 1997). The testing will able to

show how much the device can take the stress using a certain material or how much the

displacement is given at certain amount of force at each of the axis and so on. FEA lets

engineers understand the product design entirely and verify the theoretical method.

Through FEA, optimization method for the design can be easily done. For this

research project, trial and error method is used by re-designing the published structure

to get higher sensitivity of the device.

16

1.5 Thesis Objectives

The objective of this project is to optimize MEMS accelerometer structure by

enhancing the device sensitivity.

1.6 Scope and Limitation

Even though the micromachined of the device with certain parameter can

certainly increase the sensitivity, the structure of the device only focuses on simulation

of the design and also the analytical analysis.

As for the simulation part, it will cover the Solid Mechanic studies to check the

displacement of the device and how much stress the accelerometer can withstand.

Another study is the Electrostatic Studies where the capacitance can be achieved.

1.7 Project Methodology

In general, methodology used in this project is shown in Figure 3.1. It can be

divided into three main parts, which are the literature reviews that consist of the

background studies and the theoretical research and analysis. Next is the selection of the

model structure. After the right type and model structure is chosen, the design

parameter can be determined. The Finite Element simulation comprises the

construction of three dimensional model structures and the analysis of the device’s

displacement sensitivity. These simulations were first made using the published model’s

dimension. After the simulations confirmed the theoretical analysis, the next simulation

is to optimize the device sensitivity after the structure is re-designed. Last but not least,

to document the whole process in a report. The project methodology will be explained

in detail in Chapter 3.

17

1.8 Thesis Outline

This thesis comprises five chapters which includes Introduction in Chapter 1,

Literature Review in Chapter 2, the project Methodology in Chapter 3, Results and

Discussion in Chapter 4 and last but not least the Conclusion in Chapter 5.

Chapter 1 provides the overview of the background studies of the example

accelerometer, its structure and the finite element analysis used. The objective and

scopes of the project are also explained in this chapter.

Chapter 2 will present the literature review of MEMS accelerometer and all the

concise theoretical analysis used in this project. This chapter contains ten main parts,

which are the literature suvey, principles of operation, the device’s design, mechanical

suspension, damping and quality factor, basic knowledge on capacitive MEMS, analysis

of the device, performance analysis of the device and the finite element analysis tools.

In Chapter 3, the methodology of the project presented will be on the selection

of the model structure chosen from the published model, determination of design

parameters and the FEM simulation process.

As for Chapter 4, the results will be presented in graph and in tables. Each result

will be elaborated and discussed in detail.

Finally, the thesis will be finished with conclusions in Chapter 5 that

summarized the project methods and results and the potential recommendation for

future improvement.

18

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

MEMS (Micro Electromechanical System) has become an emerging technology

that covers from house appliance to automotive and even in the medical industry. The

remarkable development with MEMS is initiated from the integrated circuit

technologies and then evolved into a highly functional system in miniaturized version.

MEMS sensor comes from an input of mechanical signal which is converted using an

interface circuit to a corresponding electrical signal that is used to produce the required

control function (B.P. Gogoi (2002).

This incorporation between MEMS sensor with the help of the interface circuit

can be done using silicon or packaged it completely. Most MEMS devices are prepared

from silicon wafer which are similar to integrated circuit (IC) where MEMS fabrication

also shares the same standard processes like etching, photolithography oxidation,

diffusion and deposition.

19

2.2 Literature surveys

As mention in previous chapter, the model structure are based on the published

model that similar to Analog Device Inc, ADXL 150 accelerometer (Sharma et al.,

2008). Before optimizing the accelerometer, several researchers model are also

investigated but the scope of the studies only focus on capacitive accelerometer. In

(Chae, Kulah, & Najafi, 2002), the comb finger type of accelerometer was optimized

using analytical derivation and the model structure is novel design with a large

thickness due to DRIE fabrication. For (Lüdtke, Biefeld, Buhrdorf, & Binder, 2000), the

capacitance sensitivity are investigated using only basic comb finger type of

accelerometer with six sensing fingers. While in (Luo, Zhang, Carley, & Fedder, 2002),

the model structure are based on ADXL 202 from Analog Devices Inc. and the scope

focusing on electrically isolated multimetal routing on microstrctures and minimizing

parasitic capacitance. This factors created a full-bridge capacitive sensors and an

integration to increase transducer sensitivity. The other researchers that also using the

same model structure as (K.Sharma et al 2008) is (Benmessaoud & Nasreddine, 2013)

that uses the same optimization method but different FE tool.

The review of the existing MEMS capacitive accelerometer analysis has been

summarized in Table 2.1. This comb finger type capacitive accelerometer proved in

each of the research studies to be most successful type accelerometer since it gives high

sensitivity in capacitance due to its large sensing area. However, the researches on

comb finger type accelerometer are limited. By tracing back to the application of comb

finger type device, this design has been used in actuator for a long time (W.C.Wong,

2007). The study successes in comb finger as used in actuator can be used as the

reference for comb finger type as being used in accelerometer. Regardless of what type

being used in accelerometer or actuators, resonant frequency and the variation of the

20

structure in comb finger type are the interested parameters that are being considered in

the structural analysis and to optimize the sensitivity.

Thus, the current work tries to fill the absence in the above study and the aim is

to develop a methodology comprising the analytical and numerical study for structural

analysis and optimization of the sensitivity for comb finger type accelerometer. In this

project, the finding will be referred closely to simulated result of (Sharma et al, 2008)

and (Benmessaoud & Nasreddine, 2013) since both published model are also optimized

the device displacement sensitivity (Benmessaoud & Nasreddine, 2013). The

displacement sensitivity is an important element of the sensing process, and it is part

of the open-loop gain of the sensor. So, it is a strong inverse relationship between

sensitivity and bandwidth for any class of sensors (Bernstein, 2003).

21

Researcher Device Sensing Type

Suspention Beam Type

Device Shape

Research Type Input Parameter Output Parameter Tool Contribution

Chae, Kulah, &

Najafi,2002

Accelerometer Capacitive Folded Beam Comb Finger

Analytical, Otimazation,

FE, Fabrication, Testing

Spring Constant Of Beams, No Of Comb

Finger, Length Of Comb Finger (Other

Devices Geometry and Material Properties As

Dependent Parameters)

High Sensitivity, Low Noise, K, Fn, Cross Axis Sensitivity (FE Simulation), Shock

Resistance (FE Simulation), Stress(FE

Simulation)

MATLAB, ANSYS

Micro-G Performance,

High- Precision Accelerometer, High Sensitivity With Low Noise

Chae, Kulah, & Najafi,

2002

Accelerometer Capacitive Folded Beam Comb Finger

Length Of Finger, No Of Finger, K, Initial

Gap, Thickness

Resolution: Sensitivity/TNEA,

Simulation

MATLAB, ANSYS

Fabrication Process, System

Lüdtke Et Al. 2000

Accelerometer Capacitive Folded Beam Comb Finger

FE Simulated, Designed And

Fabricated

Structure Height Oscillation and Frequency, Capacitance

Sensitivity (Cap/D)

ANSYS New Fabrication Method For High Aspect

Accelerometer Luo Et Al.

2002 Accelerometer Capacitive Multi-Layer

Suspending Springs, Corner

Attachment Serpentine Spring. Two Turns Each

Serpentine Spring

Comb Finger

Analytical, Experimental

K, Fn (exp), Displacement

Sensitivity(exp), Capacitive

Sensitivity(exp), Noise, Shock Performance

And Cross Axis Sensitivity

Fabrication Process Using

Post-Cmos Process

K. Sharma Et Al. 2008

Accelerometer Capacitive Folded Beam Comb Finger

Analytical, Otimazation,

FE, Fabrication

Spring Constant Of Beams, Beam Length

And Width, Mass Width And Length

Displacement Sensitivity

ANSYS Sensitivity

M. Benmessaoud Et Al. 2013

Accelerometer Capacitive Folded Beam Comb Finger

Analytical, Otimazation,

FE

Spring Constant Of Beams, Beam Length

And Width, Mass Width And Length

Displacement Sensitivity, Capacitance

Sensitivity And Sensibility

MATLAB Sensitivity

Table 2.1 Summary of other researchers Capacitive Accelerometer studies (W.C.Wong, 2007)22

2.3 Principle of operation

Interface in capacitance sensor have some great features where it can function

equally as an actuator and a sensor. It is highly sensitive but naturally unaffected to

Curretemperature (Stilson, 1996).

To understand the operation of accelerometer is by simply using the principle of a mass

spring system which is the second order mass-spring-damper system (Vijayakumar S,

2011).

𝑀𝑠.𝑑2𝑥𝑑𝑡2

+ 𝐷.𝑑𝑥𝑑𝑡

+ 𝐾𝑠.𝑥 = 𝑀𝑠.𝑎𝑒𝑥𝑡

(2.1)

given the spring constant, 𝐾𝑠, the damping coefficient as D, the movable mass as Ms

and the external acceleration as 𝑎𝑒𝑥𝑡.

Figure 2.1 Basic accelerometer (K.H Denishev, 2007)

23

If the equation (2.1) changes to transfer function of second order using the Laplace

transform:

𝑋(𝑠)𝐴(𝑠)

=1

𝑠2 + 𝑠. 𝐷𝑀𝑠 + 𝐾𝑠𝑀𝑠

=1

𝑠2 + 𝑠.𝜔𝑟𝑄 + 𝜔𝑟2

(2.2)

given the resonant frequency as 𝜔𝑟 and the quality factor as Q.

So, at low frequency where (𝜔 ≪ 𝜔𝑟), it will be:

𝑋𝐴≈

1𝜔𝑟2

(2.2)

This shows that the device will get a high sensitivity with low resonant frequency

because it is inversely proportional to each other.

The total of the spring constant that has been extended or retracted at a certain

displacement will give a reinstating force which is relative to:

𝐹 = 𝑘𝑠𝑥

(2.3)

In equation 2.3, Ks, the spring constant and displacement, x is proportional to force, F

(Sharma et al.). There’s another main principle that will show a force functioning on a

mass with acceleration, Newton's second law of motion:

𝐹 = 𝑀𝑠𝑎

(2.4)

This mass is attached to a spring and when it goes into acceleration, then by Newton's

law, there will be a resultant force equal to Msa.

24