This research is the array processing help wireless communication techniques to increase the signal accuracy. This technique has an important part of prevalent applications. The wireless communication system, radar, and sonar. Beamforming is one of methods in array processing that filters signals based on their capture time at each element in an array of antennas spatially. Numerous studies in adaptive array processing have been proposed in the last several decades, which are divided in two parts. The first one related to non-adaptive beamforming techniques and the next one related to digitally adaptive Beamforming methods. The trade-off between computational complexity and performance make them different. In this thesis, we concentrate on the expansion of array processing algorithms in both non-adaptive and adaptive ones with application of beamforming in 4G mobile antenna and radar systems. The conventional and generalized side-lobe canceller (GSC) structures beamforming algorithms were employed with a phase array antenna that changed the phase of arrivals in array antenna with common phased array structure antennas. An eight-element uniform linear array (ULA), consisting of di-pole antennas, represented as the antenna array. An anechoic chamber measures the operation of beamforming algorithms performance. An extended modified Kaiser weighting function is proposed to make a semi-adaptive structure in phased array beamforming. This technique is extended to low complexity functions like hyperbolic cosine and exponential functions. Furthermore, these algorithms are used in GSC beamforming. The side-lobe levels were so lower than other algorithms in conventional beamforming around -10 dB. On the other hand, a uniform linear arrays for smart antenna purposes designed to utilize in implementing and testing the proposed algorithms. In this thesis, performance of smart antenna with rectangular aperture coupled microstrip linear array which experimental investigations carried out for obtaining X-band operation of rectangular microstrip antenna by using aperture coupled feeding technique. Frequency range set at approximately 8.6 to 10.9 GHz, by incorporating frequency range of the antenna resonates for single wideband with an impedance bandwidth of 23%. The enhancement of impedance bandwidth and gain does not affect the nature of broadside radiation characteristics. This thesis describes the design, operation, and realization of the beamforming such as Sidelobe level (SLL) control and null forming array antenna are examined with the prototype. An antenna radiation pattern beam maximum can be simultaneously placed towards the intended user or Signal of interest (SOl), and, ideally nulls can be positioned towards directions of interfering signals or signals not of interest (SNOIs). Finally, we focused on the adaptive digitally algorithms in compact antenna that faces with mutual coupling. The variable step-size normalized lease mean square (VS-NLMS) algorithm is implemented in beamforming. This algorithm utilizes continuous adaptation. The weights are attuned that the final weight vector to the most satisfied result. The gradient vector can be achieved by iterative beamforming algorithm from the available data. This algorithm is compared with LMS, NLMS, VSS-NLMS algorithms, it is determined that the VSS-NLMS algorithm is better performance to other algorithms. Finally, we introduced novel adaptive IP-NNLMS beamformer. This beamformer reaches to faster convergence and lower error floor than the previous adaptive beamformers even at low SNRs in presence of mutual coupling. The experimental results verified the simulation results that the proposed technique has better performance than other algorithms in various situations. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

Este trabalho apresenta um estudo da técnica da Reflectometria no Domínio do Tempo - TDR, para qualificação de álcool combustível. Há grande interesse na qualificação de combustíveis pois a adulteração é uma prática comum no Brasil e tem implicações nocivas no funcionamento do motor, causa maior poluição ambiental e evasão fiscal. O presente estudo foi focado em etanol adulterado com água, utilizando uma sonda comercial e sondas desenvolvidas neste trabalho, tendo sido dividido em três etapas: a primeira etapa consistiu em confirmar a viabilidade da técnica TDR para o tema proposto utilizando o sensor comercial de umidade de solo VG400 da Vegetronix, enquanto que o segundo passo tratou da simulação de sondas dos tipos bifilar, microstrip, coaxial e helicoidal em simulador tridimensional de eletromagnetismo, visando a escolha e otimização do tipo de sonda a ser usada para a qualificação do combustível. O terceiro e último passo consistiu na fabricação das sondas simuladas escolhidas e na realização de ensaios utilizando amostras de etanol com variadas proporções de água. Este estudo mostrou que a sonda helicoidal, que é uma proposta original deste trabalho, apresentou maior sensibilidade entre os modelos escolhidos, mostrando uma variação de resposta entre as amostras de etanol e água puros 12,5% maior que a sonda bifilar, que é a segunda sonda mais sensível dentre as estudadas. / This work presents a study of the Time-Domain Reflectometry - TDR technique for ethanol fuel qualification. There is a great interest in fuel qualification since adulteration is a common practice, which brings harmful consequences to the vehicle motor functioning, besides causing higher environmental pollution and tax evasion. The present study is focused on the qualification of ethanol adulterated with water, by using a commercial probe and probes developed in this work. It was divided in three steps: the first step has confirmed the viability of the technique for the proposed theme using a commercial sensor Vegetronix VG400 for soil moisture analysis. The second step was the simulation of bifilar, microstrip, coaxial and helical probe geometries using a 3D eletromagnectics software, leading to the optimization of the probe for fuel qualification. The last step was the fabrication of the simulated probes and the test of their performance into alcohol adulterated with various proportions of water. This study showed that the helical probe, an original proposal of this work, presented higher sensibility among the chosen models. Its response variation between pure alcohol and pure water was 12.5% greater than the bifilar probe, which was the second most sensitive sensor among the studied geometries.

Este trabalho de pesquisa apresenta uma nova abordagem para calibrar uma sonda helicoidal TDR, usada para medir o teor de umidade do solo. Foi empregada uma aproximação tomando em consideração a interpretação física dos valores de constantes dielétricas. As equações de calibração foram determinadas mediante um modelo dielétrico misto, quais relacionam a constante dielétrica da mistura multifase com a constante dielétrica e frações de volumes dessas componentes. Ensaios realizados em laboratório permitirem o desenvolvimento de duas equações de calibração para a avaliação de teor de umidade volumétrico e gravimétrico dos solos. A calibração foi executada com medições de constante dielétrica em diferentes líquidos e solos, usando uma sonda convencional TDR e a sonda helicoidal TDR. As leituras realizadas com as duas sondas foram depois comparadas. O modelo dielétrico das duas fases permitiu descrever a contribuição dos materiais dielétricos do corpo da sonda helicoidal e os materiais investigados. Mostrou-se que o conhecimento das características físicas e geométricas da sonda TDR usada nos ensaios é de crucial para garantir a qualidade das constantes dielétricas lidas, e conseqüentemente a determinação do teor de umidade in situ. / The objective of this work was to calibrate a coiled TDR probe used to measure the water content of soil. It was used an approach that takes into account a physical interpretation of the values of the dielectric constants. The calibration equations were determined by means of a mixed dielectric model, which relates the dielectric constant of a multi-phase mixture with the dielectric constants and volume fractions of its components. Tests carried out in the laboratory allowed development of two calibration equations for the assessment of the volumetric and gravimetric soil water content. Calibration was performed with measurements of dielectric constants in different liquids and soils, using a conventional TDR probe and a coiled TDR. The readings performed with the two probes were then compared. The dielectric model of two phases permitted describing the contribution of the dielectric material of the body of the probe coil and the materials investigated. It has been shown that knowledge of the physical and geometrical characteristics of the TDR probe used in the tests is crucial for the quality of the dielectric constant readings, and consequently the determination of water content in situ.

"This thesis presents an implementation of the Finite Difference Time Domain (FDTD) method on a massively parallel computer system, for the analysis of electromagnetic phenomenon. In addition, the implementation of an efficient mesh generator is also presented. For this research we selected the MasPar system, as it is a relatively low cost, reliable, high performance computer system. In this thesis we are primarily concerned with the selection of an efficient algorithm for each of the programs written for our selected application, and devising clever ways to make the best use of the MasPar system. This thesis has a large emphasis on examining the application performance."

A grande maioria da população mundial está crescentemente exposta à radiação eletromagnética proveniente de fontes que muitas vezes estão localizadas nas proximidades do corpo. A radiação eletromagnética é considerada um agente possivelmente cancerígeno para as pessoas, classificação 2B indicada pela Organização Mundial da Saúde-OMS (WHO/IARC, 2011). Devido às preocupações em relação aos riscos associados a esta exposição existem normas que recomendam os valores máximos de exposição permitidos (ICNIRP, 1998; FCC, 2001). A correta avaliação das doses de radiação é, portanto, relevante. Este trabalho tem a finalidade de avaliar o impacto dos resultados do cálculo da dose da Taxa de Absorção Específica (SAR) em usuários expostos a radiação por tablets operando na faixa de radiocomunicações Wi-fi. Os três modelos existentes de cabeça humana utilizados serão um manequim homogêneo SAM phantom e dois modelos de cabeça realistas heterogêneos: um adulto masculino e uma criança masculina. Será também utilizado nas simulações um modelo masculino de criança que foi desenvolvido através de imagens de tomografia computadorizada (TC) pelo processo de segmentação feito no software AMIRA. Será utilizado um modelo genérico de tablet. Os parâmetros dosimétricos usados para simulação da SAR serão computados pelo software SEMCAD X que é baseado no Método das Diferenças Finitas no Domínio do Tempo (FDTD). Será criado também um código do Método FDTD através do software MATLAB que servirá para a escolha dos parâmetros do SEMCAD X. A distância entre o tablet e os modelos de cabeças varia de 50 mm a 300 mm. Os resultados da SAR serão comparados com os limites de exposição recomendados pelas normas internacionais. Também serão simuladas diferentes posições da antena no tablet. Da análise dos resultados foi constatado que os valores de SAR são muito baixos e todos os resultados ficaram dentro dos limites do psSAR recomendados pela FCC de 1,6 W/kg em cada 1 g de tecido e de 2 W/kg em cada 10 g de tecido estabelecidos pela ICNIRP. Comparando os valores de SAR do modelo SAM com o modelo DUKE, o modelo SAM se mostra conservador, porém quando a comparação é feita com as crianças o SAM deixa de ser conservador. / The vast majority of the world population is increasingly exposed to electromagnetic radiation from sources which are often located near to the body. Electromagnetic radiation is considered a possible carcinogen for people, classification 2B indicated by the World Health Organization-WHO (WHO/IARC, 2011). Due to concerns regarding the risks associated with this exposition there are regulations suggesting maximum allowed exposure values (ICNIRP, 1998; FCC, 2001). The correct evaluation of radiation doses is therefore relevant. This work aims to assess the impact of the results of the calculation of Specific Absorption Rate dose (SAR) in users exposed to radiation from tablets operating in the Wi-fi band. The three existing models of human head used are a homogeneous dummy SAM phantom and two heterogeneous realistic head models: a male adult and a male child. It will also be used in the simulations a male child model which was developed from computed tomography (CT) imaging using the AMIRA software for the segmentation process. A generic model of tablet is used. Dosimetric parameters used for simulation of the SAR are computed using the SEMCAD X software which is based on the Finite Difference Method in Time Domain (FDTD). A FDTD code was developed using the MATLAB software in order to help to choose the input SEMCAD X parameters. The distances between the tablet and the head of the models varies from 50 mm to 300 mm. SAR results are compared with the exposure limits recommended by international standards. Different antenna positions on the tablet are simulated too. Examining the results it was found that the SAR values are very low and all results are within the psSAR limits recommended by FCC (1,6 W/kg averaged over 1 g of tissue) and by ICNIRP (2 W/kg in 10 g of tissue). Comparing the SAR in the SAM model with the SAR in the DUKE model, the SAM model shows to be conservative. However, when compared with the children, the SAM is not conservative.

La complexification de la modélisation multi-physique conduit d’une part à devoir simuler des systèmes d’équations différentielles ordinaires et d’équations différentielles algébriques de plus en plus grands en nombre d’inconnues et sur des temps de simulation longs. D’autre part l’évolution des architectures de calcul parallèle nécessite d’autres voies de parallélisation que la décomposition de système en sous-systèmes. Dans ce travail, nous proposons de concevoir des méthodes de décomposition de domaine pour la résolution d’EDO en temps. Nous reformulons le problème à valeur initiale en un problème aux valeurs frontières sur l’intervalle de temps symétrisé, sous l’hypothèse de réversibilité du flot. Nous développons deux méthodes, la première apparentée à une méthode de complément de Schur, la seconde basée sur une méthode de type Schwarz dont nous montrons la convergence pouvant être accélérée par la méthode d’Aitken dans le cadre linéaire. Afin d’accélérer la convergence de cette dernière dans le cadre non-linéaire, nous introduisons les techniques d’extrapolation et d’accélération de la convergence des suites non-linéaires. Nous montrons les avantages et les limites de ces techniques. Les résultats obtenus nous conduisent à développer l’accélération de la méthode de type Schwarz par une méthode de Newton. Enfin nous nous intéressons à l’étude de conditions de raccord non-linéaires adaptées à la décomposition de domaine de problèmes non-linéaires. Nous nous servons du formalisme hamiltonien à ports, issu du domaine de l’automatique, pour déduire les conditions de raccord dans le cadre l’équation de Saint-Venant et de l’équation de la chaleur non-linéaire. Après une étude analytique de la convergence de la DDM associée à ces conditions de transmission, nous proposons et étudions une formulation de Lagrangien augmenté sous l’hypothèse de séparabilité de la contrainte. / Complexification of multi-physics modeling leads to have to simulate systems of ordinary differential equations and algebraic differential equations with increasingly large numbers of unknowns and over large times of simulation. In addition the evolution of parallel computing architectures requires other ways of parallelization than the decomposition of system in subsystems. In this work, we propose to design domain decomposition methods in time for the resolution of EDO. We reformulate the initial value problem in a boundary values problem on the symmetrized time interval, under the assumption of reversibility of the flow. We develop two methods, the first connected with a Schur complement method, the second based on a Schwarz type method for which we show convergence, being able to be accelerated by the Aitken method within the linear framework. In order to accelerate the convergence of the latter within the non-linear framework, we introduce the techniques of extrapolation and of acceleration of the convergence of non-linear sequences. We show the advantages and the limits of these techniques. The obtained results lead us to develop the acceleration of the method of the type Schwarz by a Newton method. Finally we investigate non-linear matching conditions adapted to the domain decomposition of nonlinear problems. We make use of the port-Hamiltonian formalism, resulting from the control field, to deduce the matching conditions in the framework of the shallow-water equation and the non-linear heat equation. After an analytical study of the convergence of the DDM associated with these conditions of transmission, we propose and study a formulation of augmented Lagrangian under the assumption of separability of the constraint.

L’objectif de ma thèse est d’étendre les modèles électromagnétiques existants à l’Institut Fresnel pour les fréquences optiques vers le domaine des fréquences térahertz (THz), pour mieux comprendre les phénomènes physiques mis en jeu lors d’interaction onde-matière. Cette compréhension permettrait d’améliorer l’analyse des images THz acquises et de mieux définir les configurations des systèmes optiques utilisés. Ce travail est réalisé en comparant les résultats issus de la modélisation avec ceux provenant d’expériences menées par imagerie THz au sein de l’entreprise Terahertz Waves Technologies. Dans le futur, la modélisation pourrait devenir un outil prédictif pour la caractérisation de matériaux dans le domaine THz.Les ondes THz se situent entre l’infrarouge lointain et les micro-ondes dans le spectre électromagnétique allant de 0.01 mm à 3 mm (ou 100 GHz à 30 THz). Ces ondes bénéficient des avantages des ondes optiques et des micro-ondes dépendant des longueurs d’ondes utilisées. L’imagerie THz présente un fort potentiel pour la caractérisation de la matière, car ces ondes peuvent pénétrer beaucoup de matériaux qui sont opaques dans le visible et dans l’infrarouge. La détection de défauts, les délaminations, la présence d’humidité, etc…, sont un exemple des problématiques qui peuvent être investiguées grâce au rayonnement THz.Dans un premier temps, j’ai pu simuler la réponse optique d’échantillons polymères plans homogènes et isotropes avec de bons accords entre le calcul et la mesure. Ces résultats ont permis de réaliser de premières modélisations d’images en adéquation avec l’imagerie THz. L’étude est ensuite élargie aux matériaux anisotropes qui existent dans l’environnement industriel actuel ainsi qu’aux objets de forme cylindrique. Les modèles développés considèrent l’indice de réfraction complexe d’un échantillon et son épaisseur, c’est pourquoi un chapitre est dévolu à la méthode d’estimation de ces paramètres à partir de mesures issues de spectroscopie THz dans le domaine temporel mise en œuvre. / The aim of my thesis is to extend the electromagnetic models already existing at the Institut Fresnel for the optical frequencies towards the terahertz (THz) range, to have a better knowledge of the physical phenomena involved in THz light-matter interactions. This understanding would allow to improve the analysis of the THz images acquired and to have a better definition of the optical systems configurations that we use. To achieve this work, we compare the results coming from the model with those from the experiments led by THz imaging by Terahertz Waves Technologies. In the future, the modelling could become a predictive tool for the characterization of materials in the THz domain.THz waves are located between far infrared and microwaves in the electromagnetic spectrum going from 0.01 mm to 3 mm (or 100 GHz to 30 THz). These waves benefit from advantages of the optical waves and from microwaves depending on used frequencies. THz imaging presents a high potential one for the characterization on the material, because these waves can penetrate a lot of materials which are opaque in the visible and the infrared lights. Detection of defects, delaminations, the presence of humidity, etc…, are examples of the problems which can be investigated with THz light.At first, I was able to model the optical response of planar, homogenous, isotropic and polymeric samples with good agreements between the calculation and the measurement. These results allowed to realize first modellings of images which are consistent with THz imaging. Therefore, the study is enlarged to anisotropic materials which exist in the current industrial environment as well as the objects of full cylindrical shape. The developed models consider the complex refractive index of a sample and its thickness, that is why a chapter is devoted to the method of estimation of these parameters from measurements coming from THz Time-Domain Spectrocopy signals which was implemented.

Cette thèse doctorale aborde divers aspects méthodologiques de l’analyse de levés électromagnétiques aéroportés en domaine temporel (TDEM) pour une interprétation détaillée à finalités géologique et hydrogéologique. Ce travail s’est appuyé sur un levé réalisé dans la région de Courtenay (Nord-Est de la région Centre) caractérisée par un plateau de craie karstifié (karst des Trois Fontaines) recouvert par des argiles d’altération et des alluvions. Tout d’abord, une méthode de filtrage des données TDEM utilisant la Décomposition en Valeurs Singulières (SVD) a été développée. L’adaptation rigoureuse de cette technique aux mesures TDEM a permis de séparer avec succès les bruits, qui ont pu être cartographiés, et le « signal géologique », diminuant grandement le temps nécessaire à leur traitement. De plus, la méthode s’est avérée efficace pour obtenir, rapidement, des informations géologiques préliminaires sur la zone. Ensuite, une analyse croisée entre le modèle de résistivité obtenu en inversant les données filtrées et les forages disponibles a été effectuée. Celle-ci a mené à une amélioration de la connaissance géologique et hydrogéologique de la zone. Une figure d’ondulation, séparant deux dépôts de craie, et le réseau de failles en subsurface ont pu être imagés, apportant un cadre géologique au karst des Trois Fontaines. Enfin, une nouvelle méthode combinant l’information aux forages et les pentes issues du modèle de résistivité EM a permis d’obtenir un modèle d‟une précision inégalée du toit de la craie. L’ensemble de ces travaux fournit un cadre solide pour de futures études géo-environnementales utilisant des données TDEM aéroportées, et ce, même en zone anthropisée. / This PhD thesis addresses various methodological aspects of the analysis of airborne Time Domain ElectroMagnetic (TDEM) surveys for a detailed interpretation in geological and hydrogeological purposes. This work was based on a survey conducted in the region of Courtenay (north-east of the Région Centre, France) characterized by a plateau of karstified chalk (karst des Trois Fontaines) covered by weathering clays and alluvium. First, a TDEM data filtering method using the Singular Value Decomposition (SVD) was developed. The rigorous adaptation of this technique to TDEM data has successfully separated the noise, which was mapped, and the “geological signal”, greatly reducing the time required for processing. Furthermore, the method has proved to be effective to obtain quick preliminary geological information on the area. Then, a cross analysis between the resistivity model obtained by inverting the filtered data and the available boreholes was conducted. This has led to the improvement of the geological and hydrogeological knowledge of the area. An undulating feature, separating two chalk deposits, and a fault network were imaged in subsurface, providing a geological framework for the Trois Fontaines karst. Finally, a new 3D modelling method combining the information at boreholes and the slopes derived from the EM resistivity model yielded an accurate model of the top of the chalk. All of this work provides a solid framework for future geo-environmental studies using airborne TDEM data, even in anthropized area.

Neste trabalho é desenvolvida uma metodologia baseada na aplicação do método dos momentos conjugado à aproximação por diferenças finitas, para análise no domínio do tempo da distribuição de correntes transitórias em meios condutores. O procedimento computacional permite que sejam considerados sistemas de condutores longos, com seção transversal genérica, discretizados em elementos filiformes. Assim, a equação integral que descreve o problema é substituída por uma representação matricial. No caso de meios não homogêneos, o método dos elementos finitos é usado para a obtenção da matriz que permite a solução do problema. Como o método proposto baseia-se na solução passo a passo no tempo, é interessante, para maior eficiência computacional, que as matrizes tenham sua dimensão reduzida, o que pode ser realizado por meio da Transformada Discreta Wavelet, como investigado no trabalho. Também é feita uma análise da estabilidade do procedimento computacional, para verificação das condições de aplicabilidade do mesmo. A validação do procedimento desenvolvido é feita a partir da comparação dos resultados obtidos para problemas com solução já conhecida por meio de medições ou por outros métodos de resolução. São apresentados resultados da aplicação do método proposto a alguns casos de interesse prático, na área de Compatibilidade Eletromagnética, destacando-se a análise do efeito de blindagem e o estudo de crosstalk em um sistema multicondutor. O procedimento desenvolvido ainda pode ser aprimorado com a utilização de elementos com formas mais gerais do que a filiforme proposta, permitindo sua extensão a problemas tridimensionais. Também pode ser estudado o pré-condicionamento da matriz a ser reduzida pela aplicação da Transformada Wavelet, a fim de permitir um melhor desempenho do processo computacional. / In this work, a methodology is developed, based on the application of the moment method associated to a finite difference approximation, for time domain analysis of transient current distribution in conducting media. The computational procedure allows that long conductors with any cross section can be considered, approximated by filamentary elements. Thus, the integral equation that describes the problem is substituted by a matrix representation. In the case of non homogeneous regions, the finite element method is used to obtain the matrix that allows the solution of the problem. As the proposed method works in a time step by step scheme, it is interesting, for increased computational efficiency, to reduce the size of the involved matrices. This can be done by application of the Discrete Wavelet Transform, as investigated in this work. An analysis of the numerical stability of the computational procedure is also done, aiming to establish its applicability conditions. Validation of the numerical procedure developed is done by comparing the results obtained for problems whose solution is known by measurement or by another method. Some problems of practical interest in Electromagnetic Compatibility were solved and the results are presented, concerning particularly shielding effects and multi conductor crosstalk. The developed procedure can be improved employing elements with more general shapes, besides the filamentary ones, allowing the consideration of three dimensional systems. Also, pre conditioning of the matrices before application of the Wavelet Transform can be studied, for a better performance of the method.

This thesis is a combination of the development of numerical models regarding transient simulation of transmission lines and their advantages associated with fault location methods. The transmission line models presented in this work are in time-domain, which is a new approach considering traditional methods as being the phasor and traveling wave techniques. The use of phasors for this purpose has some technical difficulties: the presence of a damped DC component, greater influence of the fault impedance and metrological equipment layout. This work deals with single-phase AC and mono polar DC transmission lines. The proposed transmission line model has three main differentials compared to the traditional Bergeron model: full distribution of linear resistance; full distribution of leakage conductance; and just one recurrence of historical values. The first point is critical for evaluation of the exponential component of transient short circuit currents. The second point refers to the inclusion of the corona effect in the transmission line modeling. The single recurrence indicated in the third topic is given by the complete resolution of the telegrapher\'s equations, so there is no need of serial composition to improve waveform accuracy. The principle of fault location method is calculating the absolute difference between fault voltages seen by the transmission line ends. This technique guarantees a lower influence of the fault impedance and its electrical parameters. / Esta dissertação é uma combinação do desenvolvimento de modelos numéricos para simulação de transitórios eletromagnéticos em linhas de transmissão e suas benesses associadas à localização de faltas. Os modelos de linha de transmissão aqui apresentados estão no domínio do tempo, o que descaracteriza a abordagem tradicional de localização de faltas como técnicas fasoriais e ondas viajantes. A utilização de fasores para esse propósito admite algumas dificuldades técnicas: presença da componente DC amortecida, maior influência da impedância de falta e disposição dos equipamentos metrológicos. Abordam-se linhas de transmissão de sistemas alternado monofásico e contínuo monopolar. A modelagem proposta possui três principais diferenciais frente ao modelo de Bergeron: plena distribuição da resistência linear; plena distribuição da condutância transversal; e apenas uma recorrência a valores históricos. O primeiro ponto é fundamental para avaliação da componente exponencialmente amortecida das correntes transitórias de curto circuito. O segundo ponto se refere à inclusão do efeito corona no modelamento. A recorrência unitária apontada no terceiro tópico apresenta a vantagem de não ser necessária a composição em série do modelo para aprimorar a qualidade das formas de onda. O princípio de localização de faltas se dá pelo cálculo da diferença absoluta entre as tensões instantâneas de falta vistas pelos terminais da linha. Essa técnica garante uma menor influência de impedância de falta e dos parâmetros elétricos.