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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
HOJJATOLLAH SOLEIMANI
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
HOJJATOLLAH SOLEIMANI
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
HOJJATOLLAH SOLEIMANI
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
Universiti Putra Malaysia
(Internal Examiner)
Alyani bt. Ismail, PhD
Associate Professor
Faculty of Engineering
Universiti Putra Malaysia
(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
Universiti Putra Malaysia
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
Universiti Putra Malaysia
(Chairman)
Kaida Khalid, PhD
Professor
Faculty of Science
Universiti Putra Malaysia
(Member)
Jumiah Hassan, PhD
Lecturer
Faculty of Science
Universiti Putra Malaysia
(Member)
______________________________
HASANAH MOHD GHAZALI, PhD
Professor and Dean
School of Graduate Studies
Universiti Putra Malaysia
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.
HOJJATOLLAH SOLEIMANI
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
r