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Experimental evaluation of the measurement results based on FSM (Frequency Shift Method) concept in the non-conventional FOP (Fall-of-Potential) measuring scheme, for different angles between the test conductors, is presented in this paper. As it is well known, the optimal angle between the test conductors is θ = 90°. However, in practice, most often because of the physical obstacles in the surround substation, this condition cannot be provided. We have experimentally determined that the angle between the test conductors must be less than 60° relative to the optimal angle θ. In that case the corresponding measurement error is less than 3%.

The condition of thesubstationgrounding grid is vital for the safety of the people. Inadequate grounding may cause failures in majorsubstation's equipment, as well as in control, metering and telecommunication equipment. Therefore, it is necessary to clearly identify damaged elements on grounding grid. This paper presents an approach to test the integrity of the grounding grid in a general framework of IEEE Std. 81-2012. More precisely, in order to locate damaged grounding riser(s) and/or grounding grid conductor(s), this paper is focused on novel unambiguous criteria for post-processing of raw-data collected from the measurements. In order to avoid the effect of power frequency interference on the measurement, we use DC test current of 100A. The field test is described and discussed in details. The outcome of field test clearly shows the validity and feasibility of the proposed approach.

When designing an electric motor drive for a conversion of bicycle to an electric vehicle it is obligatory to determine the required power of the electric motor and the energy of a battery pack. By using a classical method, drive requirements can be established with speed and torque measurement on the drive wheel of the vehicle using a torque meter. The given traction profile is used for the design of the drive. This paper describes the method for estimation of power and required energy of vehicle only by means of global positioning system (GPS). When selecting a GPS device, it is necessary to take the resolution of the device and accuracy of vehicle speed and altitude into account. Using the measured track (speed and altitude profile) and the drag model of the vehicle it is possible to calculate both power that the vehicle develops, and energy consumed for a certain distance. The GPS device measurements, selection of electric drive, bicycle electrification and analysis of processed KTM Knoxville electric bicycle is presented.

Power cables and application of various power electronic devices, such as voltage source converters play very important role in the transmission and converting green energy. In these systems high frequency harmonics of voltages and currents appear, stressing additionally the insulation of the cables and their joints and terminations. The analysis of basic kinds of electric stress grading in the cable termination has been particularly made in high frequency range. Possible insulation failure can occur because of lower breakdown strength of dielectric material under HF voltage and appearance of hot-spot due to distortion of electric field distribution amid resonance. The Hybrid boundary element method (HBEM) can be successfully applied for analysis of such structures. Combined with theoretical analysis, it is possible to calculate right position of hot-spots because of the existence of a harmonics. The practical solution is application of geometric stress grading method, which is not susceptible in HF range. The total losses effects in HF range generate more intensive heat dissipation. The distribution of the thermal field in cable accessories was also determined. The experiments show a good agreement with the numerical results.

A new numerical procedure for optimization of the coaxial ring conductor’s system for electrostatic shielding is developed in the paper. The optimization of functional, consisting of electrostatic energy density and system of equations that is derived from the equipotential character of conductor’s system, is used. By minimizing this functional, the system of nonlinear equations is obtained and then numerically solved. The energy density is defined in the points along the axis of the system. A few numerical examples are given.

Measuring of above ground permanent connections electrical resistance may be a difficult task to achieve, when the high-voltage power facility is in normal operating condition. In order to improve the susceptibility to the power frequency interference in the measurements, we present a measurement approach, which utilizes the DC test current of 100 A through the grounding grid connections to structures or equipment. The main advantage of the proposed approach is reflected in the fact that we create an algorithm for detection of above ground permanent connection with high value of electrical resistance. The criteria for evaluation of poor connection are empirically derived. Field test results justify and validate the proposed approach., ISBN 978-86-7877-027-2

The measurements which are related to the high-voltage substation grounding system are inevitably affected by electromagnetic interference caused by power frequency and its harmonics. In order to avoid the problem due to interferers, traditional measurements are based on heavy test current injection. In most cases this approach is impractical. In this paper, we evaluate experimentally an effective method for eliminating the effect of interference at power frequency. This approach based on test signal at three frequencies, is slightly different from the power frequency. For that matter, there are two problems: 1. How to choose adequate set of test frequencies, and 2. How to determine optimal intensity of the test current. In this paper, we solve the mentioned problems based on the results of extensive field test measurements at substations 110/X kV, 220/X kV and 400/X kV. We show that the set of suitable test frequencies are: 40 Hz, 60 Hz and 75 Hz. Also shown is a method for finding the optimal intensity of the test current.

The measurement of grounding system impedance of an energized substation is usually required. Consequently, the power system frequency interference and harmonic frequencies may adversely affect the measurement. In order to improve the signal-to-interference ratio, we can increase the intensity of the test current or the test current frequency should be slightly differ-ent from the power system frequency. In the latter case, so called Frequency Shift Method (FSM), the intensity of test current may be relatively low. In this paper, we empirically examine the suffi-cient intensity of the test current. The corresponding field test in the 220/110/10 kV substation is described

The measurement of grounding system impedance may be affected by power system frequency interference and its harmonics. The Shifted Frequency Method (SFM) is potentially insensitive to the electromagnetic interference. In this paper, we evaluate this method in the hydroelectric power plant for two different load conditions of the connected overhead power lines. Presented field tests results further validate and justify the SFM method.

There is an interest for generating uniform magnetic field for various purposes in practice, especially for biomagnetic purposes. The aim of this paper will be obtaining optimal system for generating uniform field in given space. For that purposes in this paper, system of Helmholtz’s coils will be analysed using analytical approach, FEM simulation for numerical verification and genetic algorithm for optimization of dimensions. The system of coils and rectangular contours will be also analysed and its characteristics will be compared with Helmholtz’s coils system features.

Having in mind that the process of fragmentation of International Public Law (IPL) has enabled the formation of numerous legal regimes, it is necessary to understand and analyze the relationship between two legal orders - IPL as a general legal regime and European Union (EU) Law as a specialized legal regime in such a broader context. Although preconditions for deciphering the relationship between these two legal orders were created with the creation of community law, the focus of research for decades was the crystallization of the internal relationship between the newly created community law and national legal orders. Only in recent years has there been a growing interest in deciphering the external relationship of EU Law to IPL. Given that IPL does not provide an answer to the question of relations with other legal orders, nor does it impose a method of incorporating its own norms, the answer to the basic research question concerning the relation between IPL and EU Law must be sought in EU Law. Although the EU, just as other international legal subjects, is obliged to respect IPL, it has the freedom to develop the relation to IPL on its own terms and merits. Therefore, after confirming that IPL and EU Law represent complete and comparable legal orders, the dissertation is conceptually the conceptual framework of the dissertation is based on research through the prism of basic institutes of each legal order: subjects, formal sources and responsibilities as reference indicators of the relation between the two said legal orders. Chapter II makes a comparison of legal subjects in the legal orders under consideration. In the trinity of subjects of law, both within IPL and EU Law, there is a certain similarity in terms of subjects, but also a great variance. Therefore, a true comparison can be made only in terms of States, which are the undisputed, original and full subjects of both legal orders. However, it may be noted that the degree of freedom in accordance with the concept of full sovereignty is higher in the domain of IPL than in EU Law, where the concept of sovereignty was reconceptualized into shared sovereignty. Additionally, the law-making power of States is significantly reduced within EU Law, due to the obligation of loyal cooperation between Member States, whose scope is not always discernible. In contrast, when concluding international treaties in IPL, States are only limited by imperative norms. Given that IO as subjects IPL cannot be compared with EU institutions, there was a need for reconceptualization of compared subjects. The EU, as a specific IO, was compared to typical governmental IOs, which ultimately revealed its many specific features. The different status of individuals is one of the basic demarcation lines between IPL and EU Law. Having in mind that their subjectivity is only in statu nascendi in certain areas, the status of individuals as legal subjects in IPL is disputable. On the other hand, in this segment, EU Law has moved away from the logic of the general IPL, having granted individuals the status of the legal subjects. However, after a deeper analysis, such a clear distinction is blurred as it is substatially diminished. It follows that the subjectivity of individuals in EU Law is at a higher stage of development than the subjectivity in IPL, not only in terms of granted subjective rights but also in terms of their established procedural capacity. Chapter III examines the relation between IPL and EU Law through the prism of formal sources, primarily international treaties, international customary law and general legal principles. For a long time, the qualification of the relation of EU Law to IPL in legal doctrine was based solely on the analysis of the relation of EU Law to a group of international agreements of economic nature, subsequently extending such an inductive conclusion to the entire general IPL, which later proved to be incorrect. Although one of the proclaimed goals of the EU is "strict observance and the development of international law", a deeper analysis of CJEU case-law actually shows that EU Law has developed ways to avoid the use of international treaties and customary law within it through various judicial techniques and principles. Having in mind that the reception of international treaties and customary law in EU Law alone cannot achieve their full effect, the issue of their incorporation is only the first of two key issues. The true attitude towards the formally proclaimed goal of strict observance of IPL is perceived at the level of the effect of international legal norms, originating either from treaties or international customary law. The established strict and inadequate test of direct effect in the narrow sense prevents the direct effect of international provisions, for which reason legal doctrine offers a solution in the form of redesigning and/or extending this principle. Therefore, the Court of Justice should de lege ferenda build a different test concerning the application of the principle of direct effect in a so-called broader or external sense, in order to enable greater observance, application and effect of international legal norms within the EU legal system. This would also facilitate their better integration, which is only perfunctory and formal for the time being. The relation between the general IPL and EU Law may also be observed by comparing the general legal principles of IPL and the general legal principles of EU Law. Having in mind their specific dichotomy, practice reveals that they are used as a means of both dividing and approximating these legal orders. Finally, in Chapter IV, after analyzing the regimes of responsibility in IPL and EU Law, research results revealed certain similarities as well as numerous differences. In principle, the comparison of responsibility in these legal orders is complex due to thier hybrid and multifaceted character. In IPL, the hybrid character of responsibility is reflected in the pervading elements of private and public law, as well as in the possibility of pursuing state responsibility in cases involving both illegal and legal acts. Unlike most internal legal systems (including EU Law), the basic criterion of division in IPL is the illegality of an act. What both IPL and EU Law have in common is a shifting focus from the narrow issue of violation of law and its reparation to a broader context. In this sense, both legal orders tend to achieve a dual goal. In addition to ensuring the protection of the subjective rights of the injured party, which is achieved through compensation as one of the fundamental principles of law, they also strive to achieve a higher goal which is embodied in the proper functioning of the entire legal order. The regime of responsibility in EU Law is also multi-hybrid, given that it is a specific mixture of private and public law segments, and that it recognizes responsibility for both illegal and legal acts. The discernible hybridity of EU Law has another distinctive dimension in relation to IPL, bearing in mind that EU Law drew inspiration not only from IPL but also from national legal orders. Thus, the element distinguishing EU law from IPL constitutes an element of similarity with national orders; it is reflected in instituting a clear classification into contractual and non-contractual liability. Hence, the basic focus and the basic criteria for classifiaction of responsibilities are different in the two legal systems. Nevertheless, IPL has had a significant impact on EU Law in the field of accountability, given that the concept of accountability of states in IPL has served as a direct inspiration for the birth of a parallel concept within EU Law. Although it is quite delicate and complex to compare two hybrid sets of responsibility regimes stemming from IPL and EU Law, it is prima facie observed that the concept and regulation of responsibility in general IPL is at a much lower level than in EU Law. We may observe hesitancy even in the stance of the International Law Commission, which should be the flagship of codification. In contrast, in EU Law, this task is resolutely performed by the Court of Justice. The analysis of relevant indicators shows that the qualification of the formely existing monistic relationship between EU Law and IPL has changed. Therefore, although it is logical to conclude that their relation is dualistic, such a statement is not entirely true. It would be too harsh and incorrect to claim that there has been a clear-cut shift from monism to dualism, or from an open to a closed relationship with the IPL. Considering the need for a nuanced understanding of the approach of the Court of Justice to IPL, such simple and one-sided attributes are not recommended. In effect, the constitutional architecture of the EU legal order and the insistence on its external autonomy must constantly find a delicate balance between the formal respect for international law as one of the proclaimed goals of the EU and the demand to defend the autonomy and integrity of its own legal order. It is concluded that the internally built autonomy of the EU legal order (in relation to national legal orders) had to be confirmed on the external level (in relation to IPL). Accordingly, the so-called external autonomy implies that EU Law does not rely entirely on the rules and logic of IPL. Therefore, the dual nature of EU Law and its hybridity play a key role in determining its relation to IPL. Although it is part of the system of general international law, EU Law as a self-contained legal regime is characterized by the hybridity of basic legal institutes, and it is a mixture of rules of IPL and the peculiarities of its legal order. The relation of EU Law to IPL was primarily shaped by the Court of Justice, which played a key role as a quasi-constitutional court, preserving and nurturing the autonomy of the EU legal order in relation to IPL, while concurrently taking into account the obligation to respect IPL in principle. However, having in mind that proclamations and practice are often different, the dissertation critically analyzed the proclaimed general attitude of respecting IPL by considering the method of reception and the effect of its norms within EU Law, with the aim of deciphering the true relationship between these legal orders. In practice, the observance of IPL appears in its negative form, as avoidance of application. In other words, there are numerous legal technics and legal arguments that essentially aim to avoid international obligations without raising the subsequent question of responsibility. Through the work of its judicial bodies, EU Law has created an array of legal instruments which are manifested as a specific combination of doctrines, application tests, legal principles and methods of interpretation by means of which EU Law defends its basic values and basic principles as an expression of identity and autonomy from the rules established in another order - the international legal order. By combining the tests of direct effect, methods of transformation, standards on the seriousness of damage, exclusive jurisdiction of the Court of Justice, the duty of loyal cooperation, as well as frequent transformations of international legal norms into internal law, EU Law has strongly diverged from IPL. Therefore, dualistic pluralism would be the most suitable theoretical framework that could most accurately explain such a nuanced, complex and dynamic relation.

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.

U disertaciji je predložen i razvijen metod procene izloženosti zaširokopojasna merenja nivoa električnog polja visokih frekvencija.Metod je baziran na određivanju granica izloženosti, kao i njihovomprilagođenju spektralnom sadržaju polja na mernoj lokaciji. Verifi-kacija razvijenog metoda je obavljena analizom rezultata eksperimen-talnih merenja u realnim uslovima., One new exposure assessment approach for broadband measurements of thehigh-frequency electric field strength is proposed and developed in the thesis.The approach is based on the determination of the upper and lowerexposure boundaries, as well as their adaptation to the specral content of thefield at the measurement location. The verification of the developedapproach was performed by analyzing the results of experimentalmeasurements in real conditions.

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.

The area of freedom, security and justice was established by the EU constituent treaties and it was set as a special objective of the European integration. This area has undergone dynamic stages of institutional and normative development to become an integral part of the EU today. It would be difficult to imagine the existence of the EU without it. Historical development of the Union showed that protection of the basic citizens‘ values is not possible without clearly defined policies and joint cooperation of the Member States in the area of internal affairs and judiciary. Sensitivity of this cooperation stems from transferring national responsibilities to supranational level in the areas that are the core of every state‘s sovereignty. Use of legal force apparatus and criminal law jurisdiction have been until recently a national issue, and the Member States have been keeping this area from breakthrough of international or, in the case of EU, deeper mutual cooperation at any cost. The area of freedom, security and justice consists of three areas. The European area of freedom and free movement of people has been created by the Single Market. In addition to the advantages for the Union‘s citizens and citizens of third countries, the Single Market has enabled expansion and transfer of criminal activity in the area without internal borders. The European area of security entails police cooperation of the Member States on preserving security within the area of freedom and free movement of people. The cooperation in this area is the basis for efficient joint preventive and repressive action on fighting crime, especially serious crime with cross-border dimension. The European area of justice consists of elements of criminal law and civil law cooperation of the Member States. Joint definitions of criminal offences and sanctions, mutual recognition of verdicts and guaranteeing the rights of suspects or accused in a criminal procedure are crucial issues of the cooperation that has led gradually to supranational norms of the EU criminal law.

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.