Modeling of radio wave propagation is indispensable for the design and analysis of wireless communication systems. The use of the Finite-Difference Time-Domain (FDTD) method for wireless channel modeling has gained significant popularity due its ability to extract wideband responses from a single simulation. FDTD-based techniques, despite providing accurate channel characterizations, have often employed point sources in their studies, mainly due to the large amounts of resources required for modeling fine geometrical details or features inherent in antennas into a discrete spatial domain. The underlying influences of the antenna on wave propagation have thus been disregarded. This work presents a possible approach for the efficient space-time analysis of antennas by deducing FDTD-compatible macromodels that completely encapsulate the electromagnetic behaviour of antennas and then incorporating them into a standard FDTD formulation for modeling their interactions with a general environment.

Modeling of radio wave propagation is indispensable for the design and analysis of wireless communication systems. The use of the Finite-Difference Time-Domain (FDTD) method for wireless channel modeling has gained significant popularity due its ability to extract wideband responses from a single simulation. FDTD-based techniques, despite providing accurate channel characterizations, have often employed point sources in their studies, mainly due to the large amounts of resources required for modeling fine geometrical details or features inherent in antennas into a discrete spatial domain. The underlying influences of the antenna on wave propagation have thus been disregarded. This work presents a possible approach for the efficient space-time analysis of antennas by deducing FDTD-compatible macromodels that completely encapsulate the electromagnetic behaviour of antennas and then incorporating them into a standard FDTD formulation for modeling their interactions with a general environment.

Σκοπός της παρούσας διπλωματικής είναι η εξέταση των προτεινόμενων συστημάτων γείωσης για ανεμογεννήτριες σύμφωνα με την IEC και η προσομοίωση με Matlab της συμπεριφοράς τους σε πλήγμα κεραυνού στην κατασκευή μέσω της μεθόδου FDTD. Στο πρώτο κεφάλαιο αναπτύσσεται σύντομα το φαινόμενο του κεραυνού και οι ανανεώσιμες πηγές ενέργειας. Στη συνέχεια δίνονται στοιχεία για την αιολική ενέργεια και την εκμετάλλευσή της στον κόσμο και στην Ελλάδα. Επίσης αναλύονται τα βασικά μέρη και η λειτουργία μιας ανεμογεννήτριας. Στο δεύτερο κεφάλαιο αναλύεται η αντικεραυνική προστασία ανεμογεννητριών όπως προτείνεται στο διεθνές πρότυπο IEC-61024 και η διαδικασία αξιολόγησης της επικινδυνότητας μιας τέτοιας κατασκευής. Δίνονται οι βασικοί ορισμοί για συστήματα γείωσης. Διεξοδικότερα εξετάζονται οι δύο τύποι συστημάτων γείωσης για ανεμογεννήτριες, σύμφωνα πάντα με την IEC. Στο τρίτο κεφάλαιο αναλύεται η μέθοδος FDTD (Finite Difference Time Domain ) και ο αλγόριθμος του Yee. Η καινοτομία του αλγορίθμου αυτού ήταν η γεωμετρική απεικόνιση για τη δειγματοληψία των τιμών του ηλεκτρικού και του ηλεκτρομαγνητικού πεδίου η οποία αντιπροσωπεύει τις ολοκληρωτικές και τις διαφορικές μορφές των εξισώσεων του Maxwell. Για την προσομοίωση χρησιμοποιήθηκε επίσης η μέθοδος λεπτού αγωγού (thin wire) η οποία επιτρέπει την ακριβή μοντελοποίηση ενός λεπτού αγωγού(όπου λεπτός αγωγός ορίζεται ως αγώγιμο καλώδιο η ακτίνα του οποίου είναι μικρότερη από το μέγεθος του κελιού που χρησιμοποιεί η FDTD) και περιγράφεται στη συνέχεια του κεφαλαίου. Στο τέταρτο κεφάλαιο εξετάζουμε δυο προτεινόμενες διατάξεις γείωσης σύμφωνα με το πρότυπο της IEC. Εξηγείται αναλυτικά πως υλοποιήθηκε ο αλγόριθμος FDTD στο Matlab και αναφέρονται οι παραδοχές που έγιναν για τη σύγκλιση της μεθόδου .Παρουσιάζεται με γραφική απεικόνιση από το MAtlab η μοντελοποίηση του χώρου για τις 2 διατάξεις. Μελετάμε την αύξηση δυναμικού ,την βηματική τάση και την μεταβατική αντίσταση για τη διάταξη τύπου Α με ένα κάθετο ηλεκτρόδιο . Εξετάζουμε πως επηρεάζει τα παραπάνω μεγέθη η μεταβολή του βάθους του ηλεκτροδίου και πως μεταβάλλονται σε διαφορετικούς τύπους εδαφών. Ακόμα εξετάζουμε την συμπεριφορά ενός συστήματος γείωσης για τη διάταξη τύπου Β με ένα οριζόντιο δακτύλιο και τέσσερα κάθετα ηλεκτρόδια συγκριτικά με τη διάταξη Α. Στο τελευταίο κεφάλαιο σχολιάζονται τα αποτελέσματα των προσομοιώσεων και γίνεται σύγκριση των δύο προτεινόμενων διατάξεων γείωσης από την IEC. Συνοψίζονται τα πλεονεκτήματα και τα μειονεκτήματα της μεθόδου FDTD για προσομοίωση συμπεριφοράς συστημάτων γείωσης σε πλήγμα κεραυνού. Επίσης προτείνονται διαφορετικές προσεγγίσεις στην υλοποίηση της μεθόδου για την αντιμετώπιση των μειονεκτημάτων. / The subject of this essay is the analysis of the suggested by IEC grounding systems for wind turbines and the simulation of these systems using the FDTD method .The software used for the simulations was MATLAB. First chapter is a brief but essential theoretical approach on the lightning phenomenon. Moreover facts and figures are given for renewable energy and particularly wind power in Greece and worldwide. Furthermore the components and the function of a wind turbine are analyzed. The second chapter is a thorough study of the lightning protection systems for wind turbines as suggested by the international standard IEC-61204.The standard defines the risk assessment process of a wind turbine. The components of grounding systems are introduced and the two types of grounding systems for wind turbines according to IEC are analyzed. FDTD (Finite Difference Time Domain) method is analyzed in the third chapter along with Yee’s algorithm. The novelty of this method is the geometrical representation of the electrical and magnetic fields and the equations of Maxwell. The thin wire method was also used for the simulation in order to model precisely the conductors (as thin wire we define a wire with radius smaller than the cell used in the FDTD) and is described in this chapter. Along with writing this essay various grounding systems were simulated with MATLAB. In the forth chapter some brief comments about the development of the simulation are stated along with the description of the FTDT algorithm implementation. We study the potential rise, the step voltage and the transient resistance for the two types of grounding systems suggested by IEC and we observe how the depth of the rods and the resistivity of the soil affect them. In addition to that we also examine some variations of the two types of grounding systems in order to conclude to the optimal grounding system for a wind turbine. In the last chapter results are examined and conclusion are extracted and presented. The suggested by the IEC grounding systems are compared. Further optimizations of the simulation process are discussed leading to possible, future improvement. The advantages and disadvantages of the FTDT method for simulation of grounding systems after a lightning are presented.

<p> This thesis contributes to the development of a novel electromagnetic (EM) time-domain computational approach, the self-adjoint variable method, for the scattering parameter (S-parameter) sensitivity analysis of high frequency problems. </p> <p> The design sensitivity analysis provides sensitivity information in the form of the response gradient (response Jacobian). For that, various techniques are used, ranging from finite-difference approximations to quadratic and spline interpolations. However, when the number of design parameters becomes large, the simulation time would become unaffordable, which is especially the case with EM simulations. The proposed self-adjoint sensitivity analysis (SASA) approach aims at providing sensitivity information efficiently without sacrificing the accuracy. Its efficiency lies in the fact that regardless of the number of design parameters, only one simulation of the original structure is required- the one used to compute the S-parameters. Thus, the sensitivity computation has negligible overhead. At the same time, it has second-order accuracy. </p> <p> Currently, commercial EM simulators provide only specific engineering responses, such as Z- or S-parameters. No sensitivity information is actually made available. With the SASA approach, the only requirement for the EM solver is the ability to access the field solution at the perturbation grid points. This feature is generally available with all time-domain EM simulators. The manipulation of the field solutions in this approach is simple and it adds practically negligible overhead to the -simulation time. </p> <p> We confirm the validity of this approach for both the shape and constitutive parameters of the design structures. 2-D examples including metallic and dielectric details are presented, using the field solutions from an in-house time-domain solver. We also explore the feasibility of implementing this approach with one of the commercial solvers, XFDTD v. 6.3. </p> <p> Suggestions for future research are provided. </P> / Thesis / Master of Applied Science (MASc)

The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposed by the Courant–Friedrich–Lewy (CFL) stability condition. Therefore, there is a growing interest in overcoming this limitation by employing unconditionally stable FDTD methods for which time-step and space-step can be independently chosen. Unconditionally stable Crank Nicolson method has not been widely used in time domain electromagnetics despite its high accuracy and low anisotropy. There has been no work on the Crank Nicolson FDTD (CN–FDTD) method for frequency dependent medium. In this thesis a new three-dimensional frequency dependent CN–FDTD (FD–CN–FDTD) method is proposed. Frequency dependency of single–pole Debye materials is incorporated into the CN–FDTD method by means of an auxiliary differential formulation. In order to provide a convenient and straightforward algorithm, Mur’s first-order absorbing boundary conditions are used in the FD–CN–FDTD method. Numerical tests validate and confirm that the FD–CN–FDTD method is unconditionally stable beyond the CFL limit. The proposed method yields a sparse system of linear equations which can be solved by direct or iterative methods, but numerical experiments demonstrate that for large problems of practical importance iterative solvers are to be used. The FD–CN–FDTD sparse matrix is diagonally dominant when the time-stepis near the CFL limit but the diagonal dominance of the matrix deteriorates with the increase of the time-step, making the solution time longer. Selection of the matrix solver to handle the FD–CN–FDTD sparse system is crucial to fully harness the advantages of using larger time-step, because the computational costs associated with the solver must be kept as low as possible. Two best–known iterative solvers, Bi-Conjugate Gradient Stabilised (BiCGStab) and Generalised Minimal Residual (GMRES), are extensively studied in terms of the number of iteration requirements for convergence, CPU time and memory requirements. BiCGStab outperforms GMRES in every aspect. Many of these findings do not match with the existing literature on frequency–independent CN–FDTD method and the possible reasons for this are pointed out. The proposed method is coded in Fortran and major implementation techniques of the serial code as well as its parallel implementation in Open Multi-Processing (OpenMP) are presented. As an application, a simulation model of the human body is developed in the FD–CN–FDTD method and numerical simulation of the electromagnetic wave propagation inside the human head is shown. Finally, this thesis presents a new method modifying the frequency dependent alternating direction implicit FDTD (FD–ADI–FDTD) method. Although the ADI–FDTD method provides a computationally affordable approximation of the CN–FDTD method, it exhibits a loss of accuracy with respect to the CN-FDTD method which may become severe for some practical applications. The modified FD–ADI–FDTD method can improve the accuracy of the normal FD–ADI–FDTD method without significantly increasing the computational costs.

Silicon-on-Insulator (SOI) micro-ring resonators (MRRs) are versatile elements in high-density integrated optics telecommunication systems. However, small inaccuracies in the fabrication process intensely deteriorate the response of SOI MRRs. By utilizing the racetrack resonator structures with strong coupling abilities, one can improve the fabrication tolerance. For the SOI racetrack resonators, the FSR is usually large. By introducing gratings into SOI racetrack resonators, the mutual mode coupling between the clockwise and counterclockwise modes can be induced and result in the resonance splitting. The grating-assisted SOI racetrack resonators can increase the operation wavelength and open up the possibility to overcome this limitation. In this thesis, we first use the 2-D FDTD method with the effective index method (EIM) to obtain the transmission spectra of the SOI racetrack resonators. The transmission spectra are then fitted by using the time-domain coupled mode theory (CMT) to obtain the quality factor and optical parameters of the SOI racetrack resonators. Next, we demonstrate the characteristics of mode splitting resulted from the mutual mode coupling between the clockwise and counterclockwise modes in the grating-assisted racetrack resonators by utilizing both the CMT and the 2-D FDTD method with the EIM. By tuning the grating configurations, such as the length or the structure of sidewall gratings, one can obtain the desired transmission spectrum of the grating-assisted racetrack resonators. Finally, we numerically investigate the temperature-dependent spectral characterics of the grating-assisted SOI racetrack resonator by taking the thermal-optic responce of the SOI materials into account. The thermal sensitivity of this device is 95.38 pm/¢XC, and the calculted properties can help the further designs based on the grating-assisted SOI racetrack resonators.

Neste trabalho é realizada a otimização de antena de microfita banda larga de formato E utilizando o método de Diferenças Finitas no Domínio do Tempo (FDTD). Um programa desenvolvido em C é usado para analisar e aperfeiçoar a antena em projeto, tamanho, largura de banda e polarização. Inicialmente é feita a introdução sobre o assunto, abordando aspectos de comunicações e de antenas de microfita, além de se fazer revisão bibliográfica e resumir o estado da arte sobre o tema do trabalho. O próximo item, visando a sistematizar o projeto da antena, é a caracterização da antena de formato E, obtida ao variar seus parâmetros e verificar o desempenho por meio da análise do comportamento das freqüências que compõem a largura de banda. O trabalho prossegue com simulações numéricas e medidas da largura de banda, do ganho, dos níveis de polarização e da eficiência da antena. A tese é concluída com observações sobre o analisado e sugestões para prosseguimento e aperfeiçoamento das investigações técnicas realizadas. / The optimization of wideband E-format microstrip antenna employing the Finite Difference Time Domain (FDTD) method is shown in this work. This developed software is used to optimize different design parameters and characteristics of the antenna, such the dimensions, the bandwidth, the input impedance and the polarization. Firstly, an introduction considering the main issues related to wireless communications and antennas is done. Then, a review of the wideband antennas theory and conventional methods to the antenna analysis, with emphasis on the FDTD method, are described. The following topic is a parametric study, where the antenna parameters are being changed and performance variations are considered. Next, simulations using the FDTD method and measurements are compared and the relevant characteristics are optimized, e.g., in terms of dimensions, bandwidth, input impedance, gain, efficiency and polarization. Finally, the main contributions and conclusion of this thesis are described and some suggestions for further works are presented.

Neste trabalho é realizada a otimização de antena de microfita banda larga de formato E utilizando o método de Diferenças Finitas no Domínio do Tempo (FDTD). Um programa desenvolvido em C é usado para analisar e aperfeiçoar a antena em projeto, tamanho, largura de banda e polarização. Inicialmente é feita a introdução sobre o assunto, abordando aspectos de comunicações e de antenas de microfita, além de se fazer revisão bibliográfica e resumir o estado da arte sobre o tema do trabalho. O próximo item, visando a sistematizar o projeto da antena, é a caracterização da antena de formato E, obtida ao variar seus parâmetros e verificar o desempenho por meio da análise do comportamento das freqüências que compõem a largura de banda. O trabalho prossegue com simulações numéricas e medidas da largura de banda, do ganho, dos níveis de polarização e da eficiência da antena. A tese é concluída com observações sobre o analisado e sugestões para prosseguimento e aperfeiçoamento das investigações técnicas realizadas. / The optimization of wideband E-format microstrip antenna employing the Finite Difference Time Domain (FDTD) method is shown in this work. This developed software is used to optimize different design parameters and characteristics of the antenna, such the dimensions, the bandwidth, the input impedance and the polarization. Firstly, an introduction considering the main issues related to wireless communications and antennas is done. Then, a review of the wideband antennas theory and conventional methods to the antenna analysis, with emphasis on the FDTD method, are described. The following topic is a parametric study, where the antenna parameters are being changed and performance variations are considered. Next, simulations using the FDTD method and measurements are compared and the relevant characteristics are optimized, e.g., in terms of dimensions, bandwidth, input impedance, gain, efficiency and polarization. Finally, the main contributions and conclusion of this thesis are described and some suggestions for further works are presented.

Neste trabalho é realizada a otimização de antena de microfita banda larga de formato E utilizando o método de Diferenças Finitas no Domínio do Tempo (FDTD). Um programa desenvolvido em C é usado para analisar e aperfeiçoar a antena em projeto, tamanho, largura de banda e polarização. Inicialmente é feita a introdução sobre o assunto, abordando aspectos de comunicações e de antenas de microfita, além de se fazer revisão bibliográfica e resumir o estado da arte sobre o tema do trabalho. O próximo item, visando a sistematizar o projeto da antena, é a caracterização da antena de formato E, obtida ao variar seus parâmetros e verificar o desempenho por meio da análise do comportamento das freqüências que compõem a largura de banda. O trabalho prossegue com simulações numéricas e medidas da largura de banda, do ganho, dos níveis de polarização e da eficiência da antena. A tese é concluída com observações sobre o analisado e sugestões para prosseguimento e aperfeiçoamento das investigações técnicas realizadas. / The optimization of wideband E-format microstrip antenna employing the Finite Difference Time Domain (FDTD) method is shown in this work. This developed software is used to optimize different design parameters and characteristics of the antenna, such the dimensions, the bandwidth, the input impedance and the polarization. Firstly, an introduction considering the main issues related to wireless communications and antennas is done. Then, a review of the wideband antennas theory and conventional methods to the antenna analysis, with emphasis on the FDTD method, are described. The following topic is a parametric study, where the antenna parameters are being changed and performance variations are considered. Next, simulations using the FDTD method and measurements are compared and the relevant characteristics are optimized, e.g., in terms of dimensions, bandwidth, input impedance, gain, efficiency and polarization. Finally, the main contributions and conclusion of this thesis are described and some suggestions for further works are presented.

The finite difference time domain (FDTD) method is commonly used for numerical simulations of the electromagnetic wave propagation in time domain. The FDTD method is easy to implement and the computational results are highly relevant to the analytical solution, so that the FDTD method is applied to variety application problems. However, the computational efficiency of the FDTD method is constrained by the upper limit of the temporal discretisation. The Courant Friedrich Lewy (CFL) stability condition limits the time step for the computation of the FDTD method, so that if the spatial discretisation of the computation is set to be small in order to obtain high accurate results, the size of the temporal discretisation need to be satisfy the CFL stability condition. The locally one dimensional FDTD (LOD-FDTD) method is unconditionally stable. The time step and the spatial step can be independently chosen for the computation of the LOD-FDTD method. The arithmetic operations of the LOD-FDTD method is fewer than that of the other implicit FDTD method, such as the Crank Nicolson FDTD (CN-FDTD) method and the alternating direction implicit FDTD (ADI-FDTD) method. Although the implementation of the LOD-FDTD method is simpler than that of the ADI-FDTD method,the numerical error in the computational results of the LOD-FDTD method is equivalent to that in the computational results of the ADI-FDTD method. In this thesis, a new three dimensional (3D) frequency dependent (FD) LOD-FDTD method is proposed. The one pole Debye model is incorporated into the 3D-FD-LOD-FDTD method in order to deal with practical applications. The proposed method is implemented in Fortran 90 and parallelised with OpenMP. A simulation model of the human phantom is developed in the 3D-FD-LOD-FDTD method with fine structures and frequency dependent dielectric properties of the human tissues, and numerical simulation of electromagnetic wave propagation inside the human head is shown.