vii
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xi
LIST OF FIGURES
xii
LIST OF SYMBOLS
xvi
LIST OF ABBREVIATIONS
xix
LIST OF APPENDICES
xx
INTRODUCTION
1.1 Background of Study
1
1.1.1
Effective Permittivity of Dielectric Mixtures
2
1.1.2
Transmission Line Method
3
1.2 Problem Statement
4
1.3 Objective of Research
4
1.4 Scope of Study
5
viii
1.5 Significance of Study
2
5
THEORY
2.1 Electromagnetic Theory
6
2.2 Coaxial and Shielding of Transmission Lines
8
2.3 Principle of The Transmission Line Method
11
2.4 Scattering Matrices S-Parameters
14
2.5 Plane Wave Reflection and Transmission at an
Interface
16
2.6 Material Properties
18
2.6.1
Material Classifications
2.6.2
Intrinsic Impedance
Coefficient
19
and
Propagation
20
2.7 Dielectrics, Permittivity, and The Electric Field in a
Dielectric
20
2.7.1 Dielectric Properties of Inhomogeneous
Media
21
2.7.2
22
Dielectric Properties Measuring Technique
2.8 Transmission and Reflection Line Measurements
Method
24
2.9 Dielectric Mixtures
25
2.9.1
Three- Dimensional Mixing Models
2.9.2
Theoretical Bounds
Permittivity
Effective
28
2.9.3
Principle of Numerical Mixture Calculations
28
2.9.4
Maxwell-Garnett Formula for Multiphase
Composites
30
for
The
27
2.10 FDTD Simulation
32
2.10.1 Time Domain Measurements
33
2.10.2 Stability Requirements and Boundary
Conditions
34
ix
3
METHODOLOGY
3.1 EastFDTD
36
3.2 Modelling Steps
37
3.2.1
Modelling In Windows
37
3.3 Simulation Steps
38
3.3.1 Step 1: Establish The Project and Set Project
Properties
38
3.3.2
General Parameters
39
3.3.3
Boundary Parameters
40
3.3.4
Calculation Domain and Mesh Grid Setting
42
3.3.5
Calculation Model
44
3.4 Step 2: Establish Simulation Model
45
3.5 Step 3: Create Source
47
3.6 Step 4: Create Records and Data PostProcessing
48
3.6.1 Point
3.7 Source (Natural Parameter in The Domain)
48
49
3.7.1
Gaussian Pulse
49
3.7.2
Spatial Character Parameter
50
3.7.2.1 3D Gaussian Beam
3.8 Utilities
50
52
3.8.1
Calculation In LINUX
52
3.8.2
Visualization Tools
53
3.8.3
Calculating The Transmission and
Reflectance Spectra
53
3.9 Transmission Line Measurements
3.9.1 Transmission Line Modeling
3.10 Measuring S-parameters From FDTD Simulation
55
55
60
x
3.10.1 Effective Material Properties
61
3.11 Three - Dimensional Mixing Models
62
3.11.1 Simulation Setup
62
3.12 Random Mixtures
63
3.12.1 Local Permittivity Near Material Interfaces
4
RESULTS
4.1 Properties of TEM Waves in Coaxial Transmission
Line
4.1.1
5
64
TEM Waves Along
Transmission Line
z-axis
on
66
The
67
4.1.2 TEM Waves around of The Transmission
Line
69
4.1.2.1 Three Points Check TEM Waves at
Four Difference Axis (X and Y)
69
4.2
Air–Filled Transmission Line
70
4.3
Material-Filled Transmission Line
71
4.4 Calculations of Transmission and Reflection
Coefficient
72
4.5 Random Mixtures
77
4.5.1 Mixture without Clustering (Dilute Mixture)
77
4.5.2 Three Phase Mixture
78
4.6 Soil and Sand Mixture Models
79
4.7 Wet Granular Materials
83
CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions
90
5.2 Recommendations
92
REFERENCES
94
Appendices A - F
99 - 112
xix
LIST OF ABBREVIATIONS
ABC
-
Absorbing Boundary Conditions
3D
-
Three dimensional
FDTD
-
Finite Difference Time Domain
PML
-
Perfectly match layer
UPML
-
Unixial anisotropic perfectly match layer
PEC
-
(Ideal electric conductor)
PMC
-
(Ideal magnetic conductor)
ta
-
Polarization in the next direction of the axis of the light incident
-
Polarization in the more next direction of the axis of the light
-
Reflection in the next direction of the axis of the light incident
-
Reflection in the more next direction of the axis of the light
-
Transverse electromagnetic
axis
tb
incident axis
ra
axis
rb
incident axis
TEM
xx
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
INSTALLATIONS
99
B
INPUT SOURCE
101
C
RAW DATA OUTPUT
102
D
GNU OCTAVE SCRIPT
103
E
CALCULATIONS
(DIELECTRIC
PERMITTIVITY
108
AND CONDUCTIVITY)
F
MATERIAL-FILLED RESULTS
112
xii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
2.1
Cross section of coaxial cable
8
2.2
Coaxial line (shielded)
9
2.3
E and H field in a coaxial transmission line
13
2.4
Signal Flows in a Two-Port Network
15
2.5
Plane wave reflection and transmission in a medium
18
interface
3.1
Linux server IP setting dialog box
37
3.2
EastFDTD modeling interface
37
3.3
Create project document
38
3.4
Global preferences setting
40
3.5
Specific parameter setting
41
3.6
Computational domain and time setting
43
3.7
Calculation modes
44
3.8
Symbol setting
45
3.9
Material parameter setting
46
3.10
Structure parameter setting
46
3.11
Gauss source parameter setting
47
3.12
Point record setting
48
3.13
The time domain parameter meaning of Gaussian pulse.
50
3.14
Parameter setting of Gaussian pulse
51
3.15
The field distribution schematic diagram of the field of each
52
component of the electric field at the cross section of beamwaist of 3D Gaussian beam.
3.16
The styles of data files
54
3.17
Dimensions of coaxial transmission line sample holder
56
xiii
3.18
Three different readings at the X-axis (620 mm, 500 mm,
57
and 580 mm) to calibrate the simulation process on the
coaxial transmission line holder. Five difference points to
record each fields along the transmission lines at z-axis
where Point 1 (290 mm), Point 2 (445 mm), Point 3 (600
mm), Point 4 (755mm), and Point 5 (910 mm)
3.19(a)
Four different points along the circular Z-axis to calibrate
57
the simulation process on the coaxial transmission line
holder. Four difference points (Point A, B, C and D) to
record each fields around the center of cylinder model (600
mm along z-axis)
3.19(b)
Three different points along the Z-axis to calibrate the
58
simulation process on the coaxial transmission line holder
(Point A at 350 mm along z-axis, Point B at 600 mm along
z-axis and Point C at 850 mm along z-axis.
3.20
Empty specimen coaxial transmission line holder
58
3.21
Coaxial transmission line holders with presence of material
59
3.22
Dielectric conformal approximations for a small gap
65
4.1
The signal at Point 3 at 600 mm along z-axis for reading 1
67
4.2
The signal from five different points on all three readings
68
(P=Point record)
4.3
The signal at Point B along the z-axis (-X, +X, -Y, and +Y
69
axis) to record each fields around the center of cylinder
model (600 mm along z-axis)
4.4
The signal at Point A (350 mm), Point B (600 mm) and
70
Point C (850 mm) along z-axis
4.5
Transmission and reflection signals on the air-filled
71
transmission line
4.6
Transmission and reflection signals on the material-filled
72
transmission line
4.7
Spectra of reflected signals for the air filled and material
74
xiv
filled transmission lines
4.8
Spectra of transmitted signals for the air filled and material
74
filled transmission lines
4.9
Magnitude of the transmission and reflection coefficients
75
versus frequency
4.10
Phases of the transmission and reflection coefficients versus
75
frequency
4.11
Real (red line) and imaginary (green line) part of the
76
relative dielectric permittivity calculated from the FDTD
simulations
4.12
DC conductivity calculated from the FDTD simulations
76
4.13
The effective relative permittivity of dilute mixtures from
77
FDTD simulation compared to those mixture formulas at
500 MHz
4.14
The effective relative permittivity of three mixtures (air-
78
solid-water) from FDTD simulation compared to those
mixture formulas at 500 MHz
4.15
Frequency dependency of effective relative permittivity of
79
sandy loam at soil volumetric wetness of 4.3%
4.16
Frequency dependency of effective relative permittivity of
80
sandy loam at soil volumetric wetness of 24.3%
4.17
Frequency dependency of the effective relative permittivity
81
of soils calculated from FDTD simulations
4.18
Effective relative complex permittivity on volumetric
82
wetness at frequency 100 MHz and 400 MHz
4.19
Effective relative complex permittivity of sand
82
dependencies on volumetric wetness at a frequency of 100
MHz and 400 MHz
4.20(a)
Measured relative permittivity vs. volumetric moisture
content of pure sand from FDTD simulation compared to
Maxwell-Garnett formula at 400 MHz frequency
84
xv
4.20(b)
Measured relative permittivity vs. volumetric moisture
84
content of pure sand from FDTD simulation compared to
Maxwell-Garnett formula at 100 MHz frequency
4.21(a)
Measured relative permittivity vs. volumetric moisture
85
content of sand + 10% clay from FDTD simulation
compared to Maxwell-Garnett formula at 400 MHz
frequency
4.21(b)
Measured relative permittivity vs. volumetric moisture
85
content of sand + 10% clay from FDTD simulation
compared to Maxwell-Garnett formula at 100 MHz
frequency
4.22(a)
Measured relative permittivity vs. volumetric moisture
86
content of sand + 20% clay FDTD simulation compared to
Maxwell-Garnett formula at 400 MHz frequency
4.22(b)
Measured relative permittivity vs. volumetric moisture
86
content of sand + 20% clay FDTD simulation compared to
Maxwell-Garnett formula at 100 MHz frequency
4.23(a)
Conductivity vs. volumetric moisture content of pure sand
87
from FDTD simulation compared to Maxwell-Garnett
formula at 400 MHz frequency
4.23(b)
Conductivity vs. volumetric moisture content of sand + 10%
88
clay from FDTD simulation compared to Maxwell-Garnett
formula at 400 MHz frequency
4.23(c)
Conductivity vs. volumetric moisture content of sand + 20%
clay from FDTD simulation compared to Maxwell-Garnett
formula at 400 MHz frequency
88
xvi
LIST OF SYMBOLS
α
-
Polarizability
β
-
Fitting parameter for constant phase element
ɛ
-
Dielectric permittivity or dielectric constant
ɛr
-
Complex dielectric permittivity
ɛeff
-
Effective dielectric permittivity
σ
-
Conductivity
μ
-
Relative permeability
μr
-
Complex relative permeability
μeff
-
Effective relative permeability
n
-
Refractive index
neff
-
Effective refractive index
λ
-
Wavelength
λn
-
Wavelength in the medium
δ
-
Loss angle
c
-
Speed of light in vacuum or air (300mm/ns)
v
-
Phase velocity
xvii
π
-
Radian
θ
-
Phase angle
t
-
Time
k
-
Phase constant or wave number
f
-
Frequency
fc
-
Centre frequency
fco
-
Cut – off frequency
fmax, fm
-
Maximum frequency
fmin
-
Minimum frequency
Γ
-
Reflection coefficient
Δ
-
Delta or interval
Δt
-
Time interval
ω
-
Angular frequency
rin
-
Inner radius
rout
-
Outer radius
Nt
-
Fitting parameter for constant phase element
B
-
Magnetic induction vector
D
-
Electric displacement vector
E
-
Electric field
Ei
-
Incident electric field
Er
-
Reflected electric field
xviii
Et
-
Transmitted electric field
H
-
Magnetic field
J
-
Current density vector
L
-
Length of transmission line
S
-
Pointing vector
S11
-
Reflection coefficient
S21
-
Transmission coefficient
│S11│ , │S21│-
Magnitude of the S-parameters (Complex S-parameters)
T
-
Transmission coefficient
Z
-
Impedance
z
-
Effective impedance
xi
LIST OF TABLES
TABLE NO.
TITLE
PAGE
2.1
Comparison Between The Measurement Methods
23
2.2
Polarization Factors For Ellipsoids
31
4.1
Composition For Soil Model
84
F.1
Attenuation and Relative Permittivity of Subsurface
113
Material Measured at 500 MHz
F.2
Dielectric Constant of Soil at Various Porosity Values
114