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Title: Analysis of a Horizontal Thin-Wire Antenna in the Vicinity of a Lossy Ground, Using Complex-Time Green’s Functions
Other Titles: Analyse van horizontale dunne-draad antennes in de nabijheid van een grond met verliezen gebruik makende van complexe-tijd greense functies
Authors: Firouzeh, Zaker Hossein
Issue Date: 18-Apr-2017
Abstract: Transient analysis of objects residing above or inside a dielectric half-space is of great importance due to more recent applications that require analysis of wideband phenomena and fast EM analysis in the time domain. Concrete examples are the problem of antennas operating in the vicinity of an earth interface, the study of lightning effects, the detection of buried land mines and unexploded ordnance by ground penetration radar (GPR). This research is focusing on the analysis of a horizontal thin-wire structure in the vicinity of a lossy ground, using complex-time Green’s functions.
In this dissertation, firstly, time-domain methods based on differential and integral equations are considered and their advantages and disadvantages are compared. Moreover, a complete literature survey in the area of Green's function calculation of multi-layered media in time domain is presented. In next chapter, a novel technique is proposed to calculate Sommerfeld integrals of a half space based on the expansion wave concept. In addition, a new scheme is introduced to obtain closed-form Green's functions of multi-layered media using complex images theory. The results of the new technique are compared with previous methods in regard to accuracy and computation time.
In the third chapter, the transient response of a horizontal thin-wire structure above/inside a lossy ground is analyzed by the complex-time method. Firstly, the complex-time Green's functions of a horizontal electric dipole above/inside the ground are calculated and used in a novel time-domain mixed-potential integral equation (TD-MPIE) formulation of the problem. An accurate and fast converging time-domain method of moments (TD-MoM) is developed for solving the TD-MPIE. The final matrix equation is solved by a marching-on-in-time (MOT) scheme leading to the space-time current distribution on the radiator/scatterer. The resulting TDIE solution is efficient in terms of memory usage and computation time. In addition, it is illustrated that the accuracy, stability and computation time can be improved using causal and non-causal temporal basis functions such as Lagrange and B-spline functions, respectively. Meanwhile, the spatial integrals can be computed significantly faster by using Gaussian quadrature rules.
Finally, conclusions are given and future work is proposed in the last chapter. This study introduces new efficient techniques to analyze thin-wire structures above/inside a lossy ground. The proposed complex-time method can be extended to a lossy multi-layered medium.
Description: This PhD thesis has been fulfilled according to the co-operation agreement for ioint supervision of a double doctoral degree between Amirkabir University of Technology, Tehran, Iran and the Katholieke Universiteit Leuven.
Table of Contents: Table of Contents xii
Table of Figures ix
Table of Tables xv
1 Introduction 1
1.1 Time Domain Analysis of Electromagnetic Waves in the Vicinity of a half-space medium 2
1.1.1 Inverse Fourier Transform Method 2
1.1.2 Approximation Methods 3
1.1.3 Exact Image Theory Method 3
1.1.4 Cagniard-de Hoop Method 3
1.1.5 Complex Time Method 4
1.2 Time Domain Analysis and Applications 5
1.2.1 Variations of TD Models 6
1.3 Specific Issues Related to Time-Domain Integral Equations 8
1.3.1 The late-time instability 8
1.3.2 Computational Complexity 8
1.3.3 Frequency Dispersion and Loading 10
1.4 Thesis Objectives 10
1.5 Structure of the Thesis 11
2 Analysis of Layered Media in Frequency domain 12
2.1 Introduction 13
2.2 The analysis of electromagnetic waves in the vicinity of the ground 13
2.3 The analysis of multi-layered media 16
2.3.1 The spectral Green's functions of multi-layered media 16
2.3.2 The numerical calculation of Sommerfeld integrals 17
2.3.3 Asymptotic approximation methods for the calculation of Sommerfeld integrals 22
2.3.4 Complex Images Theory 23
2.4 The calculation of Sommerfeld integrals by the Expansion Wave Concept 29
2.4.1 Efficient Calculation of the Half-Space Green's Functions 29
2.4.2 Numerical Results 33
2.5 The Computation of Potentials by New Closed-Form Green’s Functions 38
2.5.1 The New Closed-Form Green’s Functions for Symmetrical Potentials 38
2.5.1.1 Theory 38
2.5.1.2 Numerical Results 41
2.5.2 The New Closed-Form Green’s Functions for Nonsymmetrical Potentials 50
2.5.2.1 Theory 51
2.5.2.2 Numerical Results 52
2.6 Summary and Conclusion 58
3 Time-Domain Analysis of a Thin Wire in the Vicinity of a Lossy Half-Space 60
3.1 Introduction 61
3.2 The Formulation of a Thin-Wire above an Imperfect Ground 61
3.2.1 Formulation of the Problem in Time Domain 62
3.2.2 Numerical Solution Approach for the TD-MPIE 64
3.2.3 Complex-Time Green’s Functions 67
3.2.3.1 The Calculation of the Wide-Band Closed-Form Green’s Functions for an HED over a Half-Space 67
3.2.3.2 The Calculation of the Complex-Time Green’s Functions for an HED over a Lossy Half-Space 69
3.2.3.3 The Calculation of the Complex-Time Green’s Functions for an HED over a Lossless Half-Space 71
3.2.4 Simplifying the Calculation of the Elements of Matrix Φk-i 71
3.2.5 Numerical Results 72
3.2.5.1 The Lossless Ground 74
3.2.5.2 Lossy Ground 81
3.3 The Improvement of TD-MoM Using the Complex-Time Green’s Functions 89
3.3.1 Lagrange Temporal Basis Functions 90
3.3.2 B-Spline Temporal Basis Functions 94
3.3.3 Speeding up the Calculation of Spatial Integrals 99
3.4 A Thin-Wire within an Imperfect Ground 102
3.4.1 Formulation of the Problem in the Time Domain 102
3.4.2 Complex-Time Green’s Functions 104
3.4.2.1 The Calculation of the Wide-Band Closed-Form Green’s Functions for an HED within a Half-Space 104
3.4.2.2 Calculation of the Complex-Time Green’s Functions for an HED within a Lossy Half-Space 106
3.4.2.3 Calculation of the Complex-Time Green’s Functions for an HED within a Lossless Half-Space 107
3.4.3 Numerical Solution Approach for the TD-MPIE 107
3.4.4 Simplifying of the Calculation of the Elements of Matrix Φk-i 108
3.4.5 Numerical Results 109
3.4.5.1 The Lossless Ground 109
3.4.5.2 The Lossy Ground 118
3.5 Summary and Conclusion 125
4 Conclusion and Future Work 127
4.1 Conclusion 127
4.2 Future Work 129
Appendix 1 130
Appendix 2 132
Appendix 3 133
Appendix 4 135
Appendix 5 139
References 140
List of Publications 153
Publication status: published
KU Leuven publication type: TH
Appears in Collections:ESAT- TELEMIC, Telecommunications and Microwaves

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