[pt] Células de medição (MCs) são amplamente utilizadas na engenharia de micro-ondas para a caracterização eletromagnética dos materiais. Neste trabalho, apresentamos uma formulação baseada na técnica de casamento de modos (MMT) para a caracterização eletromagnética de MCs para materiais anisotrópicos uniaxiais. Apresentamos e validamos uma técnica para modelagem de MCs com uma e duas portas por meio da de matrizes de espalhamento generalizadas (GSMs) extraídas do MMT. Uma vez que as soluções fechadas (isto é, não numéricas) são usadas para calcular as integrais de acoplamento das GSMs, a presente abordagem é uma alternativa computacionalmente eficiente para modelar MCs quando comparada às técnicas usuais de força bruta numérica (tais como soluções baseadas em elementos, volumes, ou diferenças finitas). Um algoritmo de inversão também é apresentado para recuperar os parâmetros constitutivos de meios complexos (materiais com perdas e anisotrópicos). Diferentemente da maioria dos trabalhos que utilizam métodos semi-analíticos, a novidade do presente método consiste em considerar MCs com seção transversal grande frente ao comprimento de onda, em vários modos podem ser progagantes. Apresentamos uma série de resultados numéricos que mostram que a técnica de inversão apresentada neste estudo pode recuperar adequadamente os parâmetros constitutivos de um material de amostra, uma vez que os parâmetros de espalhamento da MC são conhecidos. / [en] Measurement cells (MCs) are widely used in microwave engineering for the electromagnetic characterization of materials. In this work, we present a mode-matching technique (MMT) formulation for the electromagnetic characterization of MCs for uniaxial anisotropic materials. We present and validate a technique for modeling MCs with one- and two-ports via generalized scattering matrices (GSMs) extracted from the MMT. Since closed-form solutions are used for computing the coupling integrals of the GSMs, the present approach is a computationally-efficient alternative to modeling MCs when compared to usual brutal-force techniques (such as finite-elements, finitevolumes, and finite-difference solutions). An inverse algorithm is also presented to retrieve the constitutive parameters of complex media (lossy and anisotropic materials). Differently from the majority of the works using semi-analytical methods, the novelty of the present method rely on considering overmoded MCs. We present a series of numerical results that show that the inversion technique presented herein can properly retrieve the constitutive parameters of a sample material once the MC scattering parameters are known.

In this work, waveguides with simultaneous negative dielectric permittivity and magnetic permeability, otherwise known as left-handed waveguides, are investigated. An approach of formulating and solving an eigenvalue problem with finite element method resulting in the dispersion relation of the waveguides is adopted in the analysis. Detailed methodology of one-dimensional scalar and two-dimensional vector finite element formulation for the analysis of grounded slab and arbitrary shaped waveguides is presented. Based on the analysis, for waveguides with conventional media, excellent agreement of results is observed between the finite element approach and the traditional approach. The method is then applied to analyze left-handed waveguides and anomalous dispersion of modes is found. The discontinuity structure of a left-handed waveguide sandwiched between two conventional dielectric slab waveguides is analyzed using mode matching technique and the results are discussed based on the inherent nature of the materials. The scattering characteristics of a parallel plate waveguide partially filled with left-handed and conventional media are also analyzed using finite element method with eigenfunction expansion technique.

Le bruit tonal d’interaction rotor-stator, généré par l’impact des sillages issus des pales d’un rotorsur la grille d’aubes d’un stator redresseur, contribue de manière déterminante au bruit d’origineaérodynamique des turbomachines axiales carénées, qui équipent une large part des systèmes de propulsionaéronautique et de conditionnement d’air. La prédiction du bruit par l’utilisation de simulationsnumériques demeure onéreuse, notamment dans les premières phases de conception lorsque de nombreusesconfigurations doivent être testées. Dans cette optique, l’approche analytique choisie dans cettethèse apporte une alternative tout à fait appropriée. Les modèles analytiques basés sur une fonctionde réponse aéroacoustique de profil isolé ne permettent pas de reproduire l’effet de grille engendrépar le nombre important d’aubes de stator. Inversement, de fortes approximations sont nécessairespour décliner les fonctions de réponse de grilles d’aubes existantes dans des configurations tridimensionnelles.Le formalisme proposé, basé sur la méthode de raccordement modal, permet d’introduiresimplement l’effet de grille dans une géométrie annulaire d’étage rotor-stator. Un modèle de réponse degrille rectilinéaire bidimensionnel est tout d’abord présenté pour la transmission d’ondes acoustiques àtravers le stator ainsi que pour la génération de bruit par l’impact de rafales hydrodynamiques. Dansce cadre, une analyse linéaire et non visqueuse est considérée, pour laquelle les modes acoustique ettourbillonnaire d’un gaz sont couplés par le biais des frontières rigides. Les perturbations de vitessesliées aux sillages sont modélisées comme des rafales convectées. Leur impact sur la grille de statorgénère des ondes acoustiques se propageant en amont, en aval ainsi que dans les espaces inter-aubesdu stator, vu comme un réseau périodique de guides d’ondes. Les sections de bords d’attaque et defuite des aubes sont considérées comme des interfaces sur lesquelles la continuité des fluctuations depression, de vitesse axiale et de vorticité est vérifiée. Un système d’équations est ainsi obtenu, puisrésolu par des projections sur les bases modales du conduit et des inversions matricielles. Le champacoustique rayonné est ainsi déterminé uniformément dans tout le domaine. Les résultats issus de cesmodélisations sont comparés à ceux des fonctions de réponse de grilles d’aubes rectilinéaires issues dela littérature, montrant un très bon accord avec les modèles basés sur la technique de Wiener-Hopf. Leformalisme est par la suite étendu aux grilles annulaires par l’ajout de fonctions de Bessel comme fonctionsde forme radiale exprimant les effets tridimensionnels. Finalement, une procédure est présentéepour rendre compte de l’hétérogénéité des aubes de stator, caractéristique des nouvelles architecturesde turbomachines. Cette méthodologie est basée sur l’emploi conjoint du principe du dipôle de bordd’attaque et de la fonction de réponse aéracoustique de la grille de stator à l’aide de la technique deraccordement modal. Le principe de dipôle de bord identifie le chargement instationnaire des aubesinduit par l’impact de rafales hydrodynamiques, calculé par le formalisme d’Amiet, avec la trace duchamp de pression acoustique produit par un dipôle placé au voisinage du bord de l’aube. Les prédictionsissues de ce modèle, appliqué dans un cadre bidimensionnel, sont ensuite comparées à des mesuresobtenues pendant la campagne d’essais du projet SEMAFOR. / The rotor-stator wake-interaction tonal noise, generated by the impingement of rotor wakes onoutlet guide vanes, plays a crucial role in the aerodynamic noise of axial-flow ducted fan stages. Thelatter are widely used in most aeronautic propulsion and air-conditioning systems. The noise predictionby means of numerical simulations remains expensive, especially at the preliminary design stage whennumerous configurations must be tested. In this respect, the analytical approach chosen in this thesisprovides a well suited alternative. The analytical modeling based on an isolated-airfoil response functioncan not reproduce the cascade effect introduced by the large number of stator vanes. Conversely, drasticapproximations are required to extend the current cascade response functions to three-dimensionalconfigurations. The proposed modeling based on the mode-matching technique simply introduces thecascade effect in an annular rotor-stator stage. A rectilinear cascade response function is firstly presentedto account for the acoustic transmission through the stator along with the wake-interaction noise.In this context, a linearized and non-viscous analysis is carried out, in which the acoustic and vorticalmodes of a gas are coupled at rigid physical boundaries. The velocity perturbations issued from thewakes are written as a sum of convected gusts. Their impingement on the cascade of vanes generatesacoustic waves propagating upstream, downstream of the cascade, as well as inside the inter-vane channelsof the stator, seen as a periodic array of bifurcated waveguides. The duct cross sections at theleading-edge and the trailing-edge of the vanes are seen as interfaces on which the continuity of thefluctuating pressure, axial velocity and vorticity is fulfilled. A system of linear equations is obtained,then solved by means of modal projections and matrix inversions. The acoustic field is then uniformlycalculated in the whole domain. Comparisons with rectilinear cascade response functions show a verygood agreement with predictions based on the Wiener-Hopf technique. The configuration of an annularcascade is addressed by introducing the Bessel functions as radial shape functions, expressing threedimensionaleffects. Finally, a procedure is presented to account for the heterogeneity of the statorvanes, typical of modern fan architectures. This approach is based on the combinaison of the leadingedgedipole principle and the cascade response function derived from the mode-matching technique.The edge-dipole principle identifies Amiet’s solution for the unsteady loading and the radiation of adipole approached very close to the edge of a half plane. The predictions provided by this modeling,applied in a two-dimensional configuration, are finaly compared to measurements performed in the testcampaign of the SEMAFOR project.

[pt] Neste presente trabalho, o Método do Casamento de Modos é aplicado na análise e no projeto de estruturas coaxiais. A estrutura de excitação é um dos pontos críticos do projeto de antenas do tipo discone quando se pretende explorar suas características de banda larga. Seções não uniformes de guias de ondas coaxiais são usualmente utilizadas como elementos dessa estrutura de excitação sendo, eventualmente, necessária a inclusão de anéis dielétricos para garantir a rigidez mecânica da antena. Devido a essas não uniformidades encontradas nas dimensões e no meio dielétrico desse dispositivo de microondas, métodos numéricos serão utilizados na predição do seu comportamento eletromagnético. O correto dimensionamento desses anéis e das descontinuidades de guias de onda coaxiais que compõe a estrutura de alimentação, permite estabelecer um compromisso entre minimização das perdas, alargamento da banda passante e rigidez mecânica. Associados ao Método do Casamento de Modos serão utilizados algoritmos de otimização que farão o ajuste das dimensões dessas seções de guias de onda coaxiais não uniformes, visando à minimização da perda de retorno e o aumento da banda de operação da antena. Finalmente, será feito o estudo de algumas estruturas de excitação, onde serão otimizados seus desempenhos para a perda de retorno. / [en] In this present work, the Mode Matching technique is applied in the analysis and project of coaxial structures. The feed junction is one of the critical points of the project of discone antennas when broadband performance is expected. Usually, these junctions are composed of nonuniform sections of coaxial waveguide and, to guarantee the necessary mechanical rigidity of the structure, some sections are filled with dielectric material. The project of these feed junctions requires a compromise between frequency band, compact structure, minimal losses, and mechanical rigidity. Due to the discontinuities, numerical methods are used to predict the electromagnetic behavior. Here, Mode Matching technique associated with an optimization algorithm is employed in the adjustment of the dimensions of the coaxial waveguide sections, seeking the minimization of the return loss and the enlargement of the antenna bandwidth. Several types of junctions are explored and their performance is compared.

[pt] Neste trabalho são analisadas junções entre guias coaxiais não homogêneos com perdas. A expansão modal dos campos eletromagnéticos em um guia coaxial com duas camadas radiais é detalhadamente deduzida, e posteriormente a formulação é generalizada para guias com multicamadas radiais. As constantes de propagação para guias com perdas são determinadas pelo método do winding number, garantindo que todos os autovalores possam ser encontrados. O método do casamento de modos é aplicado na análise e projeto de estruturas coaxiais. A formulação é aplicada na otimização de estruturas de acoplamento e cornetas radiantes com carregamento dielétrico não homogêneo. O preenchimento não homogêneo é empregado nas estruturas radiantes a fim de minimizar a perda de retorno, e principalmente controlar e melhorar o formato do diagrama de radiação para operação em banda larga. Adicionalmente, a formulação é utilizada para analisar a propagação eletromagnética em sistemas de telemetria sem fio para poços de petróleo. / [en] In this work, we analyzed junctions between coaxial waveguides heterogeneously filled with lossy dielectrics. The modal expansion of the electromagnetic fields in a coaxial waveguide with two radial layers is derived in detail, and afterward the formulation is generalized for a multilayer waveguide. The propagation constants for lossy waveguides are determined through the method of winding number, ensuring that all eigenvalues can be found. The mode matching technique is applied in the analysis and design of coaxial structures. The formulation is applied in the optimization of coupling structures and radiating horns with heterogeneous dielectric loading. The heterogeneous filling is used in radiating structures in order to reduce the return loss, and especially to control and improve the shape of the radiation pattern for broadband operation. Additionally, the formulation is used to analyze the electromagnetic propagation in wireless telemetry systems for oil wells.