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The aim of this PhD thesis is to present the results determined in research on influence of certain metal medical implants in head and neck surgery on the distribution of penetrating electromagnetic field and the amount of absorbed energy within certain biological tissues due to exposure to RF radiation from mobile phones. Within the research, several 3D numerical models in high resolution, were created. A 3D numerical model of the human head has been developed which, in terms of dimensions, morphology and tissue composition, corresponds to the characteristics of an adult's head, sufficiently to enable obtaining reliable results by applying appropriate numerical procedures. In addition, based on available 3D images of surgical interventions, 3D numerical models of individual metal medical implants have been created. As a source of electromagnetic radiation, a modern smartphone with appropriate antennas for 3G and 4G mobile network have been used. Accordingly, calculations and analyzes were performed for the frequencies 1800 MHz and 2600 MHz, which correspond to the carrier frequencies of the mentioned mobile networks. The paper presents the results for the electric field distribution and the amount of absorbed electromagnetic energy of a mobile phone inside the user head model in the presence of the following metal medical implants: - Titanium plate for the reconstruction of a major skull defect; - Titanium dynamic mesh for the reconstruction of minor skull defects; - Titanium plate and screws used in jaw traumatology; - Dental implants and - Fixed denture. In order to determine the degree of influence of these metal medical implants on the electric field distribution and the amount of absorbed energy of the electromagnetic wave, within the biological tissues of the mobile phone users, a comparative analysis of the user head model with and without metal medical implants has been performed. During the analysis, the same mobile phone electromagnetic radiation exposure conditions were assumed for both models. A comprehensive analysis of the obtained results, related to the spatial distribution of electric field intensity and absorbed electromagnetic energy, concluded that the presence of metal medical implants affects the change in the value of electric field intensity and SAR, within biological tissues with installed implants.

In this PhD thesis two-channel QMF IIR filter banks have been discussed. As a part of this research, direct synthesis of a new IIR filter class, as a lowpass protoype function which satisfies condition for complementary decomposition, has been proposed. Since attenuation characteristic of the new filter class lies in the area between the Butterworth’s and the Elliptic’s attenuation characteristics of the same order, new class has been referred to as Transitional Butter-Elliptic filters. Transfer function of the the lowpass prototype function was separated into two allpass filters by complementary decomposition. Then, lowpass and highpass filters, as power symmetric filter pair, are obtained using those allpass filters. The main advantage of complementary IIR filters based on parallel connection of two allpass filters, is its smaller sensitivity to digital word length change compared to standard filters and low-cost implementation since the same hardware is used for the lowpass and the highpass transfer function. Within the analysis of the new filter class, transfer functions of the odd order with one, two, three and four extremal values of attenuation characteristics in the passband and in the stopband, has been discussed. All types of Transitional filters have been compared with the Butterworth’s and the Elliptic’s filters of the same order. It is shown that in comparison with Butterworth filter, the Transitional filter has better selectivity but lower selectivity than Elliptic filter. However, the proposed new filter class has pure imaginary poles and accuracy in complementary decomposition is at very high level, which the Elliptic filter cannot achieve. Also, the practical realization of the new filter class is easier than for the Elliptic filter since the new class has conjugate-complex zeros on the unit circle and one multiple zero at z = −1. Further, poles and zeros of the Elliptic filter are accumulated near the passband edge and the distance between them decreases as the filter order increases. This requires a very long digital word length for high-order filter realization. The new class filter has approximately equidistant arrangement of poles so it can be realized with shorter digital word length than it is required for the Elliptic filter realization. For Transitional filters class with one extremum of multiplicity L in the passband and in the stopband, closed-form expression for the transfer function coefficients has been obtained. Application of these kind of filters is significant since for sample rate conversion the lowestcomplexity filter is required. With appropriate selection of filters in analysis and synthesis section, the conditions for ii removing the aliasing effects are fulfilled. Magnitude distortions in IIR filter bank can also be completely eliminated and therefore output signal of the QMF bank has only phase distortion. In order to obtain nearly perfect reconstruction of the output signal, the allpass equalizer has been proposed for group delay compensation. Also, effect of the equalizer order on the accuracy of signal reconstruction has been analyzed.

The grounding system has an important role to maintain safe and reliable operation of highvoltage (HV) power facility (usually substation). The main task of a grounding system is to discharge maximum ground fault current expected into the soil, without exceeding safety limits for touch and step voltages within the substation and the surrounding area. It is desirable that the substation grounding provides a near zero resistance to remote earth. The prevailing practice is to install a grounding grid of horizontal ground electrodes (buried bare copper conductors) supplemented by a number of vertical ground rods connected to the grid, and by a number of equipment grounding mats and interconnecting cables. The grounding grid provides a common ground for the electrical equipment and for all metallic structures at the substation. It also limits the surface potential gradient. Grounding is traditionally modeled as a pure resistance. This is a good approximation at low frequencies, but as the frequency gets higher, inductance starts to play an important role. National and international standards give detailed guidelines for grounding system design, as well as for testing, under power frequency conditions, but only limited recommendations for high frequency and transient conditions are available. The main performance metrics of the grounding system are: grounding grid integrity, grounding system impedance, and touch and step voltage. The performance metrics should be periodically tested. The goal is to perform the test when the substation is in-service (to avoid interruption of service and costly downtime). Due to conductive interference in the grounding system (usually several amperes, up to about 15 A), caused by power frequency, its harmonics and background noise, the active HV substation is an extremely challenging environment for the measurement on grounding system. This is further compounded by the impact of very low impedance of the grounding system (typically less than 0.5 Ω). Essential data to calculate safety risks in advance is often not available. Measurements are therefore an essential supplement to the theory. Unlike the theoretical approaches, empirical approaches are not widely available in the literature due to the arduous work involved, the difficulty to obtain permissions, and safety restrictions. There is a continual interest in scientific community and standardization bodies to improve the measurement of performance metrics of the grounding system. The drawbacks of actual measurement methods are related to less or more subjectivity and requirements for high level of test current (up to 100 A AC and up to 300 A DC). In this thesis, in order to avoid mentioning drawbacks, we elaborated and experimentally verified the efficient methods. The overall contribution of this thesis is the substantial enhancement of the grounding system measurement by eliminating the current restrictions found in the IEEE standards 80 and 81, respectively. The original works, that constitute the core of this thesis, have been published in referring publications. This thesis is divided into three parts. Part I includes Chapters 2 and 3. Part II includes Chapters 4 to 7. Part III contains Chapter 8. Part I gives an extensive review of published literature related to the analytical and simulation investigations of earth electrode systems. Part I also analyzes the existing methods for measurement performance metrics of the grounding system. Critical review of the constraints inherent in existing methods was given. Part II includes original contributions of the thesis: new method for measurement of grounding grid integrity (Ch.4); an effective method (so called FSM) for eliminating the effect of conductive interference at power frequency (Ch. 5); new method for grounding system impedance measurement (so called FOP-FSM) (Ch.6); new method for measurement of touch and step voltage (so called FEM-FSM) (Ch.7). Our experiment-driven verification approach of the proposed measurement methods is based on totally 49 power facilities (voltage range: 110 kV, 220 kV and 400 kV) in Serbia. Part III gives an extensive review of thesis results. Part III also proposes and elaborates directions for further automation of the proposed measurement methods.

In this dissertation, the development and incorporation of numerical model of metamaterials into the Transmission Line-Matrix (TLM) mesh is presented. The Drude model is used to describe the frequency-dependent metamaterial properties and the bilinear Z-transform is applied to transfer this dependence in the discrete time-domain. Consequently, the numerical procedure for incorporation of the numerical model of metamaterials into the TLM mesh is obtained.

Analysis of microwave transmission lines is the main subject of research in the world for more than six decades. Since the day of stripline invention, back in 1949, and its modifications that followed in the forthcoming years, an "army" of scientists was trying to analyze it, simplify it and design new structures. These structures, due to their characteristics, have found wide application in microwave integrated circuits, for microwave filters and antennas design, delay lines, directional couplers, etc. Various numerical and analytical methods such as: the variational method, the method of moments, the boundary element method, the conformal mapping, the moving perfect electric wall method, the equivalent electrodes method etc. can be applied with more or less accuracy to the microwave transmission lines analysis. The aim of this doctoral dissertation is quasi TEM analysis of microwave transmission lines using the hybrid boundary method (HBEM). This method, developed at the Department of Theoretical Electrical Engineering in the Faculty of Electronic Engineering of Niš, is based on the equivalent electrodes methods and the point-matching method for the potential of the perfect electric conductor electrodes and for normal component of the electric field at the boundary surface between any two dielectric layers. Until now, it was applied to multilayered electromagnetic problems, grounding systems, electromagnetic field determination in the vicinity of cable terminations as well as magnetic field and force calculations of permanent magnets. In order to expand the field of method’s application, it is, for the first time, applied for the microwave transmission lines analysis. Single and coupled, shielded and open microwave transmission lines with homogeneous, isotropic single-layer and multilayer dielectrics were analysed in the examples presented. Structures with the ground planes of infinite width, but also the real cases – geometry with ground planes of finite width, the finite metallization thickness and substrate width, are also shown in this dissertation. The hybrid boundary element method has been proved to be a very simple, powerful and accurate procedure for microwave transmission lines analysis. The obtained system of linear equations is always well-conditioned, as the system matrix always has the greatest elements on the main diagonal. Quite good convergence for the desired parameters is achieved for only 700-1500 unknowns (equivalent electrodes). For the most examples, the convergence of results, calculation time, equipotential contours and distribution of polarized charges per unit length along boundary surfaces are shown in the tables and graphically. In order to validate the characteristic parameters results, obtained by the hybrid boundary element method, all the results will be compared to those obtained by software FEMM and FlexPDE as well as the results already reported in the literature. These results were shown in tables and graphically. The relative error for the characteristic impedance is less than 0.5 % in regards to the results obtained using the FEMM with few thousands elements and the uniform meshing technique. The computation time is even several times shorter than in the case of the analysis using the FEMM and FlexPDE. The real challenge for the author was to apply the hybrid boundary element method for analysis of microstrip transmission lines with Tellegen material (non-reciprocal bi-isotropic media). Unlike a wide range of literature that deals with the analysis of microwave transmission lines with isotropic dielectric, bi-isotropic media, due to their complexity, are not so common subject of research. The hybrid boundary element method was successfully applied for the analysis of such structures. Applying the hybrid boundary element method it is possible to analyze quickly, easily and sufficiently accurate the complex configuration of microwave transmission lines with isotropic and bi-isotropic substrate. In that way this dissertation represents a small contribution to the history of the development of methods for the analysis of microwave lines long more than 60 years.

Permanent magnets are increasingly being used as a result of the wider adoption of electrical devices and gadgets. There is a constant need for their optimization and size reduction, leading to new mathematical methods for their field calculation. The quality of electrical devices that contain permanent magnets is dependent on the magnetic material they are made of, their magnetization, and their size. Many different methods for permanent magnet field calculation are available, aiming towards the simplest and fastest analysis of magnetic structures in relation to different parameters. In most cases, analytical methods for permanent magnet field calculation based on the distribution of magnetic charges or Ampere's microscopic currents are limited to block and cylindrical structures. In order to overcome drawbacks of analytical and numerical methods, this theisis presents two additional, semi-numerical approaches.