Characteristic Modes
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List of Figures ix
List of Tables xvii
Preface xix
1 Introduction 1
1.1 Backgrounds 1
1.2 An Introduction to Characteristic Mode Theory 3
1.2.1 Traditional Modal Analysis in Antenna Engineering 3
1.2.2 Definition of Characteristic Modes 6
1.2.3 Primary Properties of Characteristic Modes 7
1.2.4 Variants of Characteristic Modes 7
1.3 Characteristic Modes in Antenna Engineering 10
1.3.1 Pioneering CM Studies (1965-1990) 12
1.3.2 Recent CM Developments (1991-2014) 13
1.4 Characteristic Modes in Scattering Computation 19
1.5 Outline of this Book 20
References 22
2 Characteristic Mode Theory for PEC Bodies 37
2.1 Backgrounds 37
2.2 Surface Integral Equations 39
2.2.1 Maxwell's Equations 39
2.2.2 Electromagnetic Boundary Condition 39
2.2.3 Magnetic Vector Potential and Electric Scalar Potential 40
2.2.4 Electric Field Integral Equation 41
2.2.5 Magnetic Field Integral Equation 43
2.3 Method of Moments 43
2.4 EFIE Based CM Formulation 47
2.4.1 Conventional Derivation 47
2.4.2 Poynting's Theorem Based Derivation 48
2.4.3 Othogonality of Characteristic Modes 49
2.4.4 Physical Interpretation of Eigenvalues 51
2.4.5 Physical Interpretation of Modal Significances 52
2.4.6 Physical Interpretation of Characteristic Angles 54
2.5 MFIE Based CM Formulation 55
2.5.1 MFIE Based CM Formulation 55
2.5.2 Approximate MFIE-Based CM Formulation 57
2.6 CFIE-Based CM Formulation 59
2.7 Applicability of the CM Formulations 60
2.7.1 Closed and Open Objects 60
2.7.2 Electrically Small and Large Problems 60
2.8 Computation of Characteristic Modes 61
2.8.1 Solution of Generalized Eigenvalue Equation 61
2.8.2 Characteristic Mode Tracking 65
2.9 Numerical Examples 70
2.9.1 PEC Sphere 70
2.9.2 Rectangular PEC Patch 81
2.9.3 Numerical Aspects of Mesh Density 82
2.10 A First Glance on CM Excitations 88
2.11 Summary 95
References 95
3 Characteristic Mode Theory for Antennas in Multilayered Medium 99
3.1 Backgrounds 99
3.2 cm Formulation for PEC Structures in Multilayered Medium 103
3.3 Relationship Between Cavity Model and Characteristic Modes 105
3.4 Physical Investigations on Microstrip Patch Antennas 111
3.4.1 Equilateral Triangular Patch Antenna 112
3.4.2 Concentric Circular Microstrip Antenna 115
3.4.3 Corner-Truncated Circularly Polarized Antenna 117
3.4.4 Dual Band Stacked Microstrip Patch Antenna 120
3.5 Applications to Circularly Polarized Microstrip Antenna Design 125
3.5.1 U-Slot Microstrip Antenna 126
3.5.2 E-Shaped Microstrip Antenna with Low Cross Polarization 131
3.5.3 Summary 138
3.6 Conclusions 139
References 139
4 Characteristic Mode Theory for Dielectric Resonators 143
4.1 Backgrounds 143
4.1.1 A Brief Introduction to DRA 144
4.1.2 Importance of Modal Analysis and its Challenges 146
4.1.3 Early Attempts to DRA Modal Analysis Using Characteristic Mode Theory 147
4.1.4 Contributions of this Chapter 148
4.2 CM Formulations for Dielectric Bodies 149
4.2.1 PMCHWT Surface Integral Equations 149
4.2.2 MoM Matrix Equation 152
4.2.3 Generalized Eigenvalue Equation for Characteristic Electric Current 152
4.2.4 Important CM Quantities 154
4.2.5 Generalized Eigenvalue Equation for Characteristic Magnetic Current 155
4.3 Analysis and Design of DRAs Using CM Theory 156
4.3.1 Cylindrical Dielectric Resonator Antennas 157
4.3.2 Spherical Dielectric Resonator Antennas 164
4.3.3 Rectangular Dielectric Resonator Antennas 170
4.3.4 Triangular Dielectric Resonator Antennas 175
4.3.5 Notched Rectangular Dielectric Resonator Antenna 178
4.4 Computational Efficiency 181
4.5 Conclusions 181
References 182
5 Characteristic Mode Theory for N-Port Networks 187
5.1 Backgrounds 187
5.2 Characteristic Mode Formulations For N-Port Networks 188
5.3 Reactively Controlled Antenna Array Designs Using Characteristic Modes 192
5.3.1 Problem Formulation 192
5.3.2 Design and Optimization Procedure 194
5.3.3 Design Examples 199
5.3.4 Efficiency of CM-Based Approach 202
5.4 Yagi-Uda Antenna Designs Using Characteristic Modes 203
5.4.1 CM-Based Design Method 204
5.4.2 Design Examples 208
5.4.3 Efficiency Investigation 212
5.5 Wideband Array Excitation Design Using Characteristic Modes 214
5.5.1 Tightly Coupled Wideband Arrays 214
5.5.2 Computation of Quasi-Excitations from Characteristic Modes 215
5.6 Conclusions 217
References 217
6 Platform-Integrated Antenna System Design Using Characteristic Modes 221
6.1 Backgrounds 221
6.2 Electrically Small UAV Antenna System Design Using Characteristic Modes 223
6.2.1 Reconfigurable Radiation Pattern Synthesis Using Characteristic Modes 223
6.2.2 Feeding Designs for the Excitation of the Synthesized Currents 235
6.2.3 Experimental Validations 238
6.2.4 Summary 241
6.3 HF Band Shipboard Antenna System Design Using Characteristic Modes 245
6.3.1 CM-Based Broadside Radiation Pattern Synthesis 246
6.3.2 Feeding Structure Design 254
6.3.3 Experimental Validations 258
6.3.4 Practical Implementation 260
6.3.5 Summary 262
6.4 Conclusions 263
References 263
Index 267
LIST OF FIGURES
Figure 1.1 The cavity model of a microstrip antenna. Figure 1.2 An isolated rectangular dielectric resonator antenna. Figure 1.3 Yearly publications on characteristic modes. The statistical data comes from the Scopus database [64]. Figure 1.4 CM research topics and their publication percentages after the year 1980. Figure 2.1 Surface equivalence principle of a 3D PEC structure. Figure 2.2 Triangular element mesh of a ship. Figure 2.3 RWG basis function defined over a pair of adjacent triangle elements. Figure 2.4 Example of closed and open objects (a) Closed sphere and (b) open surface of a parabolic reflector. Figure 2.5 Flowchart of the CM computer code. Figure 2.6 Association in the first round. Figure 2.7 The reduced correlation coefficient matrix. Figure 2.8 The association relationship between the eigenvectors at two different frequencies. Figure 2.9 Configuration of a double-layered stacked microstrip antenna. Figure 2.10 Modal significances with and without CM tracking. (a) CM analysis without CM tracking and (b) CM analysis with CM tracking. Figure 2.11 Characteristic currents of the (a) first and (b) fourth mode at the resonant and non-resonant frequencies. Figure 2.12 Characteristic modes of the PEC sphere with 0.2 wavelength radius. (a) Modal currents of the TM01 mode, (b) modal fields of the TM01 mode, (c) modal currents of the TE01 mode, (d) modal fields of the TE01 mode, (e) modal currents of the TM12 mode, (f) modal fields of the TM12 mode, (g) modal currents of the TM22 mode, (h) modal fields of the TM22 mode, (i) modal currents of the TE02 mode, (j) modal fields of the TE02 mode, (k) modal currents of the TE12 mode, (l) modal fields of the TE12 mode, (m) modal currents of the TE22 mode, (n) modal fields of the TE22 mode, (o) modal currents of the TM03 mode, and (p) modal fields of the TM03 mode. Figure 2.13 Eigenvalues of the 100 mm × 40 mm rectangular PEC plate. Figure 2.14 Characteristic modes of the 100 mm × 40 mm rectangular PEC plate at 1300 MHz. (a) J1 & E1, (b) J2 & E2, (c) J3 & E3, and (d) J4 & E4. Figure 2.15 Inductive and capacitive coupling elements for the excitation of the first mode in Figure 2.14a. Figure 2.16 Eigenvalues of closed sphere surface for varying mesh density in EFIE-based CM formulation. Figure 2.17 Eigenvalues of closed sphere surface for varying mesh density in the MFIE-based CM formulation. Figure 2.18 Eigenvalues of the PEC plate for varying mesh density. Figure 2.19 Geometry of a multiband planar inverted-F antenna. Figure 2.20 VSWR of the multiband planar inverted-F antenna. Figure 2.21 Current distributions and radiation patterns at resonant frequencies. (a) 1.9 GHz, (b) 3.3 GHz, (c) 4.1 GHz, and (d) 4.7 GHz. Figure 2.22 Eigenvalues of the PIFA. Figure 2.23 Dominant characteristic modes at resonant frequencies. (a) Characteristic currents at 1.9 GHz, (b) characteristic currents at 3.3 GHz, (c) characteristic currents at 4.1 GHz, and (d) characteristic currents at 4.7 GHz. Figure 3.1 Basic configuration of a microstrip patch antenna. Figure 3.2 Typical feeding structures for microstrip patch antennas. (a) Coaxial probe feed, (b) microstrip line feed, (c) proximity coupled feed, and (d) aperture coupled feed. Figure 3.3 Geometry of an irregularly shaped patch antenna. Figure 3.4 Configuration of a rectangular microstrip patch antenna. Figure 3.5 S-parameters of the rectangular microstrip patch antenna. Figure 3.6 HFSS-simulated radiating currents at the resonant frequencies. (a) 1.05 GHz, (b) 1.55 GHz, (c) 1.90 GHz, and (d) 2.10 GHz. Figure 3.7 HFSS-simulated radiation patterns at the resonant frequencies. (a) 1.05 GHz, (b) 1.55 GHz, (c) 1.90 GHz, and (d) 2.10 GHz. Figure 3.8 Modal significances obtained from (a) CM theory for antennas in multilayered medium and (b) CM theory for PEC objects. Figure 3.9 Characteristic currents and far fields of the dominant modes at the resonant frequencies, (a) TM10, 1.08 GHz; (b) TM01, 1.60 GHz; (c) TM11, 1.95 GHz; and (d) TM20, 2.13 GHz. Figure 3.10 Dimensions of an equilateral triangular patch. Figure 3.11 Modal significance for the equilateral triangular patch antenna. Figure 3.12 Characteristic currents and far-fields of the dominant modes at the resonant frequencies. (a) TM01, 1.299 GHz; (b) TM10, 1.299 GHz; (c) TM11, 2.249 GHz; (d) TM02, 2.573 GHz; (e) TM20, 2.573 GHz; (f) TM21, 3.438 GHz; and (g) TM12, 3.438 GHz. Figure 3.13 Configurations of the concentric circular patch antenna. Figure 3.14 Characteristic currents and characteristic fields of the concentric circular patch at 5.0 GHz. (a) J1 & E1, (b) J2 & E2, and (c) J3 & E3. Figure 3.15 Configurations of the corner-truncated CP antenna. Figure 3.16 Modal significances (a) and characteristic angles (b) for the three corner-truncated CP antennas. Figure 3.17 Characteristic currents for antenna 1: (a) mode 1 and (b) mode 2. Figure 3.18 Characteristic fields for antenna 1: (a) mode 1 and (b) mode 2. Figure 3.19 Configuration of the dual band stacked microstrip antenna. Figure 3.20 Simulated reflection coefficient of the dual band stacked microstrip antenna. Figure 3.21 Measured axial ratio of the dual band stacked microstrip antenna. Figure 3.22 The current distributions on the stacked patches in two different bands: (a) 1.225 GHz band and (b) 1.575 GHz band. Figure 3.23 Modal significance of the stacked patches. Figure 3.24 Characteristic currents and characteristic fields of the modes indicated in Figure 3.23, (a) The first mode at 1.15 GHz; (b) the second mode at 1.15 GHz; (c) the third mode at 1.5 GHz, (d) the fourth mode at 1.5 GHz. Figure 3.25 The circularly polarized U-slot antenna with offset feed: (a) the geometry and (b) prototype. From Ref. [39]. © 2012 by IEEE. Reproduced by permission of IEEE. Figure 3.26 Horizontal and vertical modes of the U-slot antenna: (a) characteristic angle and (b) modal significance. Figure 3.27 Characteristic currents of the U-slot antenna at 2.3 GHz. (a) Normalized horizontal mode J1, (b) normalized vertical mode J2, and (c) "H-V" current J1 - J2. The color scale is in dB and is applicable to all the three figures. Figure 3.28 The axial ratio of the U-slot antenna with offset...
