A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering, 2016 / The work presented extends and contributes to the research of modelling lightning return stroke (RS) electromagnetic (EM) fields in the time domain. Although previous work in this area has focused on individual lightning electromagnetic pulse (LEMP) modelling techniques, there has not been an investigation into the strengths and weaknesses of different methods, as well as the implementation considerations of the models. This work critically compares three unique techniques (Finite Antenna, FDTD, and Single Cell FDTD) under the same ideal simulation parameters. The research presented will evaluate the EM fields in the range of 50m to 500m from the lightning channel. This range, often referred to as the near field distance, has a significant effect on lightning induced overvoltages on distribution lines, which are primarily created by the horizontal EM fields of the RS channel. These close distances have a significant effect on the model implementations, especially with the FDTD method. Each of these modelling methods is explained and tested through examples. The models are implemented in C++ and have been included in the Appendix to aid in future implementation. From the model simulations it is clear that the FDTD method is the most comprehensive model available. It allows for non-ideal ground planes, as well as complex simulation environments. However, FDTD has a number of numerical related errors that the Finite Antenna method does not suffer from. The Single Cell FDTD method is simple to implement and does not suffer from the same numerical errors as a full FDTD implementation, but is limited to simple simulation environments. This work contributes to the research field by comparing and evaluating three techniques and giving consideration to the implementation and the applicability to lightning EM simulations. / MT2017

Ho Kwok Ching. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 107-111). / Abstracts in English and Chinese. / Content --- p.5 / Chapter 1 --- Introduction --- p.7 / Chapter 2 --- Background Theory --- p.9 / Chapter 2.1 --- Background history --- p.9 / Chapter 2.2 --- Finite Difference Time Domain Method --- p.10 / Chapter 2.2.1 --- Basic Formulation --- p.10 / Chapter 2.2.2 --- Finite Difference Expression: --- p.11 / Chapter 2.2.3 --- Courant Stability Criterion --- p.13 / Chapter 2.3 --- Absorbing Boundary Condition (PML) --- p.13 / Chapter 2.3.1 --- "Field -Splitting Modification of Maxwell's equation, TE case" --- p.14 / Chapter 2.3.2 --- Propagation of a TE Plane Wave in a PML Medium --- p.15 / Chapter 2.3.3 --- Transmission of a wave through PML-PML Interfaces --- p.19 / Chapter 2.3.4 --- PML for FDTD in 2D domain --- p.23 / Chapter 2.3.5 --- Extension to Three Dimension Case --- p.25 / Chapter 2.3.6 --- Obtaining S-parameters for General Microwave circuit --- p.26 / Chapter 2.4 --- Extended Finite Difference Time Domain Method --- p.29 / Chapter 2.4.1 --- Direct Implementation of Lumped Elements --- p.30 / Chapter 2.4.2 --- Equivalent-Source Techniques --- p.31 / Chapter 2.5 --- EMC --- p.37 / Chapter 3 --- Novel Techniques for Extended FDTD Method --- p.38 / Chapter 3.1 --- Introduction --- p.38 / Chapter 3.2 --- The Improved FDTD-SPICE Interface --- p.38 / Chapter 3.3 --- The Improved DC Bias Source --- p.48 / Chapter 3.4 --- The Improved DC Biasing Component --- p.50 / Chapter 3.5 --- Example --- p.51 / Chapter 3.6 --- Program Architecture --- p.55 / Chapter 3.7 --- Conclusion --- p.57 / Chapter 4 --- Example Design --- p.58 / Chapter 4.1 --- Introduction --- p.58 / Chapter 4.2 --- Internal Antenna Design --- p.58 / Chapter 4.2.1 --- Half-wavelength Patch --- p.58 / Chapter 4.2.2 --- Quarter-wavelength patch --- p.63 / Chapter 4.3 --- RF Power Amplifier Circuit Design --- p.73 / Chapter 4.4 --- Active Internal Antenna Design --- p.88 / Chapter 4.4.1 --- Design --- p.88 / Chapter 4.4.2 --- Surface Wave Analysis 一 Transient state analysis --- p.91 / Chapter 4.4.3 --- Surface wave analysis -AC analysis --- p.95 / Chapter 4.4.4 --- Far Field Pattern --- p.101 / Chapter 4.5 --- Conclusion --- p.105 / Chapter 5 --- Conclusion: --- p.106 / Chapter 6 --- Reference List --- p.107 / Publication --- p.111

by Wai-Chung Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 121-124). / Abstract also in Chinese. / Acknowledgement --- p.i / Abstract --- p.ii / Table of contents / Chapter Chapter 1: --- Introduction --- p.1 / Chapter Chapter 2: --- Background Theories --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Maxwell's Equations --- p.5 / Chapter 2.3 --- Basic Formulation --- p.8 / Chapter 2.4 --- Plane Wave Formulation --- p.13 / Chapter 2.4.1 --- Total-Field / Scattered-Field Algorithm --- p.14 / Chapter 2.4.2 --- Pure Scattered-Field Algorithm --- p.16 / Chapter 2.4.2.1 --- Application to PEC Structures --- p.16 / Chapter 2.4.2.2 --- Application to Lossy Dielectric Structures --- p.17 / Chapter 2.5 --- Incident Plane Wave Components Generation --- p.20 / Chapter 2.6 --- Source and Termination Modeling in FD-TD model --- p.24 / Chapter 2.6.1 --- Resistive source --- p.25 / Chapter 2.6.2 --- Resistor Formulation --- p.27 / Chapter 2.7 --- PML Formulation --- p.28 / Chapter 2.7.1 --- Two-Dimensional TE Case --- p.28 / Chapter 2.7.2 --- Extension to the Full-vector Three-Dimension Case --- p.32 / Chapter 2.8 --- Time Domain Extrapolation --- p.33 / Chapter 2.8.1 --- Prony's Model --- p.34 / Chapter 2.8.2 --- Auto-regressive Model and Performance Comparison with Prony's Method --- p.36 / Chapter 2.9 --- Summary --- p.42 / Chapter Chapter 3: --- Verification of FD-TD Method --- p.43 / Chapter 3.1 --- Introduction --- p.43 / Chapter 3.2 --- Microstrip Patch Antenna: An Introduction --- p.44 / Chapter 3.2.1 --- Direct Fed Patch --- p.45 / Chapter 3.2.2 --- EMC Patch --- p.50 / Chapter 3.2.3 --- Aperture-Coupled Patch --- p.53 / Chapter 3.3 --- Verification of FD-TD: S11 Analysis --- p.55 / Chapter 3.3.1 --- Analysis of Direct Fed Rectangular Patch Antenna --- p.56 / Chapter 3.3.2 --- Analysis of EMC Patch Antenna --- p.60 / Chapter 3.3.3 --- Analysis of Aperture-Coupled Patch Antenna --- p.63 / Chapter 3.4 --- Verification of FD-TD: Radiation Pattern Analysis --- p.66 / Chapter 3.4.1 --- The Absolute and Relative Approaches --- p.67 / Chapter 3.4.2 --- The Inset Fed Patch Antenna --- p.69 / Chapter 3.5 --- Summary --- p.71 / Chapter Chapter 4: --- Space Diversity Design --- p.73 / Chapter 4.1 --- Introduction --- p.73 / Chapter 4.2 --- How Space Diversity Antenna Works --- p.74 / Chapter 4.3 --- Criteria for Evaluation and Optimization of Diversity Performance --- p.77 / Chapter 4.4 --- Simple Approach for Two-Patch Diversity Array --- p.82 / Chapter 4.4.1 --- Performance as a Function of Antenna Separation --- p.83 / Chapter 4.5 --- Novel Designs for Performance Improvement --- p.89 / Chapter 4.5.1 --- Shorting Post Isolation --- p.90 / Chapter 4.5.2 --- Offset-positioned Configuration --- p.101 / Chapter 4.6 --- Three-Patch Diversity Array --- p.106 / Chapter 4.6.1 --- Co-aligned Configurations --- p.107 / Chapter 4.6.2 --- Offset-Positioned Configurations --- p.112 / Chapter 4.7 --- Summary --- p.117 / Chapter Chapter 5: --- Conclusion --- p.118 / Appendix A: Publication --- p.121 / Appendix B: References List --- p.122

Woo, Kat Choi = 以時域有限差分法模擬貴金屬的納米結構 / 胡吉才. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 84-86). / Abstracts in English and Chinese. / Woo, Kat Choi = Yi shi yu you xian cha fen fa mo ni gui jin shu de na mi jie gou / Hu Jicai. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Importance of Nanoscale Plasmonic Physics --- p.1 / Chapter 1.2 --- The Driving Forces behind Plasmon Physics --- p.2 / Chapter 1.3 --- Computation Method --- p.3 / Chapter 1.4 --- Conclusion and Interesting Topics --- p.5 / Chapter 2 --- The FDTD Mechanism --- p.6 / Chapter 2.1 --- Algorithm Method --- p.6 / Chapter 2.2 --- The Dielectric Function --- p.9 / Chapter 2.2.1 --- Drude Model Definition --- p.9 / Chapter 2.2.2 --- Drude Model Discretization --- p.10 / Chapter 2.2.3 --- Discussion on Models --- p.11 / Chapter 2.3 --- Accuracy and Stability --- p.12 / Chapter 2.3.1 --- Numerical Dispersion --- p.12 / Chapter 2.3.2 --- Courant Condition --- p.14 / Chapter 2.4 --- Time Dependence of the Methods --- p.15 / Chapter 2.5 --- Perfectly Matched Layer (PML) --- p.16 / Chapter 2.5.1 --- Boundaries Problem --- p.16 / Chapter 2.5.2 --- PML Main Theme --- p.17 / Chapter 2.5.3 --- Different Types of PMLs --- p.20 / Chapter 2.6 --- Conclusion: Simulation Laboratory --- p.20 / Chapter 3 --- Software Comparison and Scaling Usage --- p.22 / Chapter 3.1 --- Physical Quantity Interested --- p.22 / Chapter 3.1.1 --- Cross-sections and Relation to Surface Plasmon Excitation --- p.23 / Chapter 3.2 --- Mie Theory --- p.24 / Chapter 3.2.1 --- Spherical Harmonics --- p.24 / Chapter 3.2.2 --- Expressing the terms in Spherical Harmonics --- p.26 / Chapter 3.2.3 --- Matching Boundaries --- p.27 / Chapter 3.2.4 --- Scattering and Extinction Cross-sections --- p.28 / Chapter 3.3 --- Software Used --- p.29 / Chapter 3.3.1 --- Meep --- p.29 / Chapter 3.3.2 --- Lumerical FDTD Solution --- p.30 / Chapter 3.4 --- Machines Used for Comparison --- p.30 / Chapter 3.5 --- Ease of Usage --- p.30 / Chapter 3.5.1 --- Installation --- p.31 / Chapter 3.5.2 --- Support --- p.32 / Chapter 3.5.3 --- Parallel Computation --- p.33 / Chapter 3.6 --- The Check Case Building --- p.33 / Chapter 3.6.1 --- Monitor Measurement Related to Time for Simulation --- p.34 / Chapter 3.6.2 --- Meep's Implementation --- p.34 / Chapter 3.6.3 --- Total Field Scattering Field (TFSF) Source --- p.35 / Chapter 3.6.4 --- Lumerical FDTD Solutions' Implement at ion --- p.36 / Chapter 3.7 --- Comparison --- p.37 / Chapter 3.7.1 --- Accuracy of the Programs --- p.37 / Chapter 3.7.2 --- Time Needed for the Programs --- p.43 / Chapter 3.8 --- Conclusion: How to Build Reasonable Running Cases --- p.46 / Chapter 4 --- The Projects on Nanorods --- p.47 / Chapter 4.1 --- Basic Understanding of Nanorods --- p.47 / Chapter 4.1.1 --- Geometry Dependence on Localized Surface Plasmon Resonance in Au Nanorods --- p.48 / Chapter 4.1.2 --- Plasmonic Coupling in Au Nanorod Dimers --- p.49 / Chapter 4.2 --- Size-Dependent Scattering and Absorption Cross-sections for Au Nanocrystals --- p.51 / Chapter 4.2.1 --- Measurement of Data --- p.51 / Chapter 4.2.2 --- Setup of Simulation --- p.52 / Chapter 4.2.3 --- Results and Conclusion --- p.54 / Chapter 4.3 --- Angle-Dependent Plasmon Coupling in Au Nanorod Dimers --- p.56 / Chapter 4.3.1 --- Setup of Experiment --- p.56 / Chapter 4.3.2 --- Setup of Simulation --- p.57 / Chapter 4.3.3 --- Results of Simulation --- p.59 / Chapter 4.3.4 --- The Dipolar Model Discussion --- p.62 / Chapter 4.3.5 --- Conclusion --- p.65 / Chapter 4.4 --- Plasmon Coupling in Linear Au Nanorod Dimers --- p.65 / Chapter 4.4.1 --- Experimental Results --- p.66 / Chapter 4.4.2 --- Energy Dependent Plasmon Coupling of Au Nanorod Dimers --- p.67 / Chapter 4.4.3 --- Dependency of the Plasmon Coupling on the Inter-particle Distance --- p.70 / Chapter 4.4.4 --- Dependency of the Plasmon Coupling on the Head Shape of Au Nanocrystals --- p.74 / Chapter 4.4.5 --- Coupling-induced Fano-Resonance in Au Nanorod Het- erodimers --- p.74 / Chapter 4.4.6 --- Conclusion --- p.78 / Chapter 4.5 --- Conclusion --- p.80 / Chapter 5 --- Conclusion --- p.81 / Bibliography --- p.84

We have constructed a new finite-difference time-domain (FDTD) method in this project. Our new algorithm focuses on the most important and more challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media. We use an electric permittivity that stays as a constant in each medium, and magnetic permittivity that is constant in the whole domain. To handle the interface between different media, we introduce new effective permittivities that incorporates electromagnetic fields boundary conditions. That is, across the interface between two different media, the tangential component, Er(x,y), of the electric field and the normal component, Dn(x,y), of the electric displacement are continuous. Meanwhile, the magnetic field, H(x,y), stays as continuous in the whole domain. Our new algorithm is built based upon the integral version of the Maxwell's equations as well as the above continuity conditions. The theoretical analysis shows that the new algorithm can reach second-order convergence O(∆x2)with mesh size ∆x. The subsequent numerical results demonstrate this algorithm is very stable and its convergence order can reach very close to second order, considering accumulation of some unexpected numerical approximation and truncation errors. In fact, our algorithm has clearly demonstrated significant improvement over all related FDTD methods using effective permittivities reported in the literature. Therefore, our new algorithm turns out to be the most effective and stable FDTD method to solve Maxwell's equations involving multiple media.

Graduation date: 1999

A new second order accurate nonuniform grid spacing technique which does not depend on supraconvergence is developed for Finite Difference Time Domain (FDTD) simulation of general three dimensional structures. The technique is useful for FDTD simulations of systems which require finer details in small regions of the simulation space by providing the ability to utilize nonuniform grid spacing. The stability conditions of the new technique are derived and shown to be consistent with uniform grid formulation and the accuracy of the technique is investigated and shown to be second order. The advantage of the new technique is that it allows for greater simulation detail while reducing the computational and memory requirements compared to the current uniform grid FDTD techniques. Additionally, the derivation of the expressions associated with the inclusion of material properties in the FDTD simulation with nonuniform grids is presented allowing for the development of a nonuniform FDTD simulator for general lossy 3D systems associated with on and off chip interconnects, electronic packages and microwave circuits. In order to illustrate the utility of this simulator, time domain electromagnetic simulation of a 3-D lossy interconnect structure associated with a generic surface mount IC package is presented. The time domain currents and fields are computed in the structure to investigate ground bounce, signal degradation, and crosstalk associated with the interconnects and packaging structure. The supply plane conductivities are included in the simulation allowing the observation of the current densities in the power/ground planes as a function of time. Finally, the FDTD simulation tool is proposed and used as a Virtual TDR (V-TDR) to extract the circuit models associated with complex 3D structures. The time domain response of a multiport structure is used to extract the equivalent circuit parameters to characterize the multiport by using the multiport time domain reflection (TDR) based general deconvolution algorithm. Examples of coupled interconnects and transmission lines are presented to illustrate this technique. / Graduation date: 1997

Thesis (Ph. D.)--University of Texas at Dallas, 2006. / Includes vita. Includes bibliographical references (leaves 253-256).

Thesis (Ph. D.)--West Virginia University, 2000. / Title from document title page. Document formatted into pages; contains xiii, 325 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 138-144).

Thesis (Ph. D.)--Washington State University. / Includes bibliographical references.