development of a new technique for … · dimensional mom was used to solve the rotationally...

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UNIVERSITI PUTRA MALAYSIA

METHOD OF MOMENT ANALYSIS USING OPEN-ENDED COAXIAL SENSOR IN DETERMINATION OF CORN REFLECTION COEFFICIENT

HOJJATOLLAH SOLEIMANI

IPM 2010 16

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METHOD OF MOMENT ANALYSIS USING OPEN-ENDED

COAXIAL SENSOR IN DETERMINATION OF CORN REFLECTION

COEFFICIENT

By


Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia,

in Fulfilment of the Requirement for the Degree of Doctor of Philosophy

August 2010

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DEDICATION

To my mother

And

In memory of my father

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Abstract of thesis presented to the Senate of Universiti Putra Malaysia in fulfilment of the

requirement for the degree of Doctor of Philosophy

METHOD OF MOMENT ANALYSIS USING OPEN-ENDED AXIAL

SENSOR IN DETERMINATION OF CORN REFLECTION

COEFFICIENT

By


August 2010

Chairperson : Zulkifly Abbas, PhD

Institute : Mathematical Research

The present thesis is a critical study on the use of an open-ended coaxial sensor for the

estimation of moisture content of corn with various degrees of fruit ripeness at 125 oC.

The fruit’s state of ripeness depends on moisture content. The permitivity is in direct

relation with the amount of water in corn texture’ in other words, The higher the amount

of water in the corn texture is, the higher the permittivity goes. An open-ended co-axial

line has been used as an electromagnetic sensor or probe for various industrial and

scientific applications. These applications are based on the principle that the

characteristics of the echo signal produced by the co-axial opening depend upon the

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sample material terminating the probe. Thus, if the aperture admittance characteristics can

be precisely formulated, then the electrical parameters of the sample can be found.

The sensor was studied based on the calculation of reflection coefficient using an integral

admittance approach and Method of Moment (MOM). The Method of Moment is one of

the most important general methods which are used for solving electromagnetic-field

problems. It begins with a brief mathematical foundation of the general method.

Then, the various specializations are described, accompanied with relevant references to

illustrate the pitfalls and shortcomings, as well as the advantages, as compared to other

methods. So finally, their algorithms are easily programmable on computer.

The computation of reflection coefficient of the corn was programmed using MATLAB

software for the admittance approach and Method of Moment (MOM). The results were

compared with the measured reflection coefficient using the open-ended coaxial sensor in

conjunction with a vector network analyzer (VNA). The sensor operating between 1 GHz

and 5 GHz was fabricated from a 2.05 mm and 0.65 mm, outer and inner diameters

respectively. The measuring end of the sensor was calibrated by a transmission line

procedure.

The integral admittance formulation was simplified into a series expression. The local

truncation errors of the series approximation were critically analyzed. The two-

dimensional MOM was used to solve the rotationally symmetric region of the open-ended

coaxial line. The MOM results are closed to the measurements data than calculated

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admittance formulation. The maximum absolute errors of MOM and measurement results

for magnitude and phase reflection coefficient are less than 0.02 and 0.1 rad, respectively,

compared with 0.05 and 0.2 rad of admittance formulation and measurement results,

respectively.

A calibration equation has been developed based on the relationship between the

measured moisture content obtained by the oven drying method and the phase of the

reflection coefficient of the sensor. The moisture content predicted by the sensor was in

good agreement with those obtained using the standard oven drying method with its

absolute error within 5 % moisture content, when tested on 114 different corn samples.

The model successfully evaluated the complex permittivity for different ripeness stages of

corn mesocarp as a function of frequency, moisture and ionic conductivity, as well as the

bulk density.

The software is also used to calculate reflection coefficient from complex permittivity in

frequency between 1 GHz and 5 GHz.

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Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai

memenuhi keperluan untuk ijazah Doktor Falsafah

ANALISIS KAEDAH MOMEN TERHADAP PENDERIA HUJUNG

TERBUKA DALAM PENENTUAN PEKALI PANTULAN JAGUNG

Oleh


August 2010

Pengerusi : Zulkifly Abbas, PhD

Institut : Penyelidikan Matematik

Tesis ini mengemukakan kajian kritikal tentang penggunaan pengesan sepaksi hujung

terbuka untuk menganggar kandungan kelembapan jagung pada peringkat matang yang

pelbagai pada suhu (25±1)o

C. Pengesan sepaksi hujung terbuka telah digunakan sebagai

deria atau pengesan untuk pelbagai aplikasi industri dan saintifik. Aplikasi ini adalah

berdasarkan prinsip sifat isyarat gema yang terhasil dari sepaksi terbuka bergantung

kepada bahan yang menamatkan pengesan. Oleh itu, jika sifat kebenaran masuk bukaan

boleh diungkapkan dengan tepat, maka parameter elektrik bagi sampel boleh diketahui.

Pengesan telah dikaji berdasarkan pengiraan pemalar pantulan menggunakan pendekatan

kamiran kebenaran masuk dan Kaedah bagi Ketika (MOM). Kaedah ini adalah salah satu

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daripada kaedah umum yang penting yang mana digunakan untuk menyelesaikan masalah

medan elektromagnet. Ia dimulakan dengan asas matematik yang mudah bagi kaedah

umum tersebut. Kemudian, pelbagai pengkhususan digambarkan, diiringi oleh rujukan

yang relevan untuk menjelaskan kesukaran dan kelemahan, termasuk juga kelebihan,

berbanding kaedah yang lain. Akhirnya, algoritma terbabit diprogramkan dengan mudah

dalam komputer.

Perkomputeran bagi pemalar pantulan jagung telah diprogramkan menggunakan perisian

MATLAB untuk pendekatan kebenaran kemasukan dan Kaedah bagi Ketika (MOM).

Keputusannye telah dibandingkan dengan pemalar pantulan yang diukur menggunakan

pengesan sepaksi hujung terbuka bersama dengan analisis rangkaian vektor (VNA). Deria

ini beroperasi diantara 1GHz dan 5GHz yang mana telah dihasilkan pada diameter dalam

dan luar masing-masing 2.05mm dan 0.65mm. Hujung pengukur deria telah dilaraskan

melalui prosedur garis pemancaran.

Formula kamiran kebenaran kemasukan telah dipermudahkan kepada ungkapan bersiri.

Ralat pemendekan setempat bagi anggaran siri-siri telah dianalisis dengan kritikal. MOM

dua dimensi telah digunakan untuk menyelesaikan kawasan simetri putaran bagi garisan

sepaksi hujung terbuka. Keputusan bagi MOM adalah hampir kepada nilai ukuran

berbanding nilai yang telah dikira daripada formulasi kebenaran kemasukan. Ralat mutlak

yang maksimum bagi MOM dan keputusan pengukuran bagi magnitud dan fasa pemalar

pantulan adalah kurang daripada 0.02 dan 0.1 rad berbanding dengan formulasi kebenaran

kemasukan dan keputusan pengukuran masing-masing adalah 0.05 dan 0.2 rad.

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Persamaan yang selaras telah dihasilkan berasaskan hubungan di antara kandungan

kelembapan yang diukur dengan yang diperoleh daripada teknik pengeringan oven dan

fasa pemalar pantulan bagi deria. Kandungan kelembapan yang dianggar oleh deria adalah

berkadar baik dengan kandungan kelembapan yang telah diperoleh menggunakan teknik

pengeringan oven dengan nilai multak ralat diantara 5% kandungan kelembapan apabila

diuji dengan 114 sampel jagung yang berbeza.

Model ini telah berjaya menilai permitiviti kompleks bagi peringkat kematangan mesocarp

jagung yg berbeza bagi fungsi kepada frekuensi, kelembapan dan konduktiviti ion, dan

juga ketumpatan bahagian utama. Perisian juga digunakan untuk mengira pemalar

pantulan daropada permitiviti kompleks dala frekuensi antara 1 GHz dan 5 GHz.

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ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my supervisor, Dr. Zulkifly Abbas for his

great scientific points and tips given with friendly guidance and advice during this study.

His encouragement, moral and technical support made this study possible. My gratitude

also goes to my respected co-supervisors, Professor Dr. Kaida bin Khalid and Associate

Professor Dr. Jumiah Hassan, who gave me strong moral and scientific supports during

the research. I also would like to express my thanks to staffs and postgraduate students at

the Institute Mathematical Research (INSPEM) of University Putra Malaysia as well as

the colleagues and postgraduate students, Mr. Ashry, Meng, Kong and Ahmad at the

Microwave Laboratory at the Department of Physics in UPM. Dr. You Kok Yeow and is

highly acknowledged for his advice in the Finite Element Method Simulation. Also I

would like to express my thanks to my dear friend Mr. Kasra Behzad for his kindly

support.

Last but not least, My dear brother Dr. Hassan Soleimani and his wife Dr. Leyla

Khodapanah are acknowledged for their invaluable technical and moral support.

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I certify that an Examination Committee has met on to conduct

the final examination of Hojjatollah Soleimani on his Doctor of Philosophy thesis entitled

“METHOD OF MOMENT ANALYSIS USING OPEN-ENDED COAXIAL SENSOR IN

DETERMINATION OF CORN REFLECTION COEFFICIENT” in accordance with the

Universiti Pertanian Malaysia (Higher Degree) Act 1980 and Universiti Pertanian

Malaysia (Higher Degree) Regulations 1981. The Committee recommends that the

candidate be awarded the relevant degree.

Members of the thesis Examination Committee are as follows:

W. Mahmood Mat Yunus, PhD Professor

Faculty of Science

Universiti Putra Malaysia

(Chairman)

Mohd Maarof Hj. Abd Moksin, PhD Professor

Faculty of Science


(Internal Examiner)

Alyani bt. Ismail, PhD

Associate Professor

Faculty of Engineering


(Internal Examiner)

Kaharudin bin Dimyati, PhD

Professor

Faculty of Science

Universiti Kebangsaan Malaysia

(External Examiner)

__________________________________

NORITAH OMAR, PhD

Associate Professor and Deputy Dean

School of Graduate Studies


Date: 27 June 2011

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This thesis was submitted to the Senate of Universiti Putra Malaysia has been accepted as

fulfillment of the requirement for the degree of Doctor of Philosophy. The members of the

Supervisory Committee were as follows:

Zulkifly Abbas, PhD

Lecturer

Faculty of Science


(Chairman)

Kaida Khalid, PhD

Professor

Faculty of Science


(Member)

Jumiah Hassan, PhD

Lecturer

Faculty of Science


(Member)

______________________________

HASANAH MOHD GHAZALI, PhD

Professor and Dean

School of Graduate Studies


Date:

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DECLARATION

I declare that the thesis is based on my original work except for quotations and citations

which have been duly acknowledged. I also declare that it has not been previously and is

not concurrently, submitted for any other degree at Universiti Putra Malaysia or other

institutions.


Date: 17 August 2010

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TABLE OF CONTENTS

Page

DEDICATION ii

ABSTRACT iii

ABSTRAK vi

ACKNOWLEDGEMENTS ix

APPROVALS x

DECLARATION xii

LIST OF TABLES xvi

LIST OF FIGURES LIST OF SYMBOLS xxiii

LIST OF ABBREVIATIONS xxx

CHAPTER

1 INTRODUCTION 1

1.1 Background of the Study

1.2 Microwave Moisture Measurements 2

1.3 Open-Ended Coaxial Sensor

1.4 Numerical Solutions

1.5 Method of Moments as Applied to Electromagnetic Problems 10

1.6 Problem statement 11

1.7 Objectives of Thesis 14

1.8 Thesis Outline 15

2 LITERATURE REVIEW 17

2.1 Microwave Measurement Technique for the Determination 17

of Moisture Content in sample

2.1.1 Transmission-Reflection Technique 18

2.1.2 Transmission technique 20

2.1.3 Reflection Technique 23

2.2 Modeling of Coaxial Sensor 25

2.3 Analytical Model 26

2.3.1 Capacitance model 27

2.3.2 Antenna Model 29

2.3.3 Virtual Line Model 32

2.3.4 Rational Function Model 34

2.3.5 Modification Models: Short Monopole Probe Models 36

2.4 Numerical Models 39

2.4.1 Finite Element Method (FEM) 40

2.4.2 Finite Difference Time-Domain (FD-TD) 47

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2.4.3 Method of Moment (MOM) 50

2.5 Comparison of Numerical Methods 52

2.6 Sensitivity Coefficient, S

of Open-Ended Coaxial Sensor

2.7 Mixture Materials 55

2.8 Reviews of Fruits Ripeness Measurements Using

Microwave Sensors

3 THEORY 62

3.1 Electromagnetic fields in open-ended coaxial line 62

3.1.1 Formulation of the problem 63

3.1.2 The Magnetic Field in a Coaxial Line 69

3.1.3 Integral Equation for the Radial Electric Field at the

aperture of a Coaxial Line 75

3.1.4 Apparent Admittance of a Coaxial Line 76

3.1.5 Electromagnetic Fields for z≥0 80

3.2 Variational Principles, Stationary Formulation, and Quasi Static

Analysis of open Ended Coaxial Lines 84

3.2.1 Variational Principles 85

3.2.2 Stationary Formulation 89

3.2.3 Quasi-Static Approximation

3.3 Numerical Solution of the Integral Equation by the Method

of Moments (MoM) 93

3.3.1 Evaluatuion of the Matrix Elements 95

3.3.2 Discretization and Normalization Aspects in

the MoM Method 99

4 METHODOLOGY 101

4.1 Materials and Methods 101

4.1.1 Open-Ended Coaxial Sensor 102

4.1.2 Calibration and Measurement Procedures of PNA 103

4.1.3 Corn Sample Preparation 107

4.1.4 Oven Drying Procedures 108

4.2 Measurement and Computational Procedures 109

4.3 Computation Procedures of Method of Moment (MoM) 110

4.3.1 Program Procedure and Flow Diagram 111

4.3.2 The program flow 112

5 RESULTS AND DISCUSSION 119

5.1 Effect of number of zone on the admittance of reference

liquids with frequency 1 to 5 GHz

5.2 Variation of normalized conductance and susceptance with

frequency for 4 liquid and air 126

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5.3 Variation in reflection coefficient with frequency

5.3.1 Air 134

5.3.2 Water

5.3.3 Propanol

5.3.4 Ethanol

5.3.5 Methanol

5.4 Proof and Design Rules for Corn Measurement

5.4.1 Variation in the Reflection Coefficient of Fruit Samples

with Frequency and Moisture Content 155

5.4.2 Comparison between MOM and Quasi Static Model 158

5.5 Effect of number of zone on the error of magnitude and phase 171

5.5.1. m.c. =10% 172

5.5.2. m.c. =30% 175

5.5.3. m.c.=55% 178

5.5.4. m.c.=85% 181

5.6 Effect of number of zone and root on the computation time

5.7 Simulations Performance 186

5.8 Normalized Susceptance and Conductance of Corn Mesocarp 188

5.9 Comparison of Various Size Probe Using MoM 190

5.10 The variation of normalized conductance and susceptance with

aspect ratio, b/a and frequency 192

5.11 Complex permittivity with moisture contents, m.c. in corn 201

5.11.1 Variation of relative complex permittivity of corn

mesocarp, with frequency for different m.c. 201

5.11.2 Variation in Dielectric Constant and Loss Factor with

Moisture Content in Corn 203

5.12 Conclusion 211

6 SUMMARY AND FUTURE WORK 213

6.1 Summary of the Study 213

6.2 Main Contributions 215

6.3 Suggestions for Further Studies 216

REFERENCES 218

APPENDICES 229

BIODATA OF STUDENT 248

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