This research investigates the realization of parametric amplification in superconducting circuits and structures where nonlinearity is provided by Josephson junction (JJ) elements. We aim to develop a systematic analysis over JJ-based devices toward design of novel traveling-wave Josephson parametric amplifiers (TW-JPA). Chapters of this thesis fall into three categories: lumped JPA, superconducting periodic structures and discrete Josephson transmission lines (DJTL). The unbiased Josephson junction (JJ) is a nonlinear element suitable for parametric amplification through a four-photon process. Two circuit topologies are introduced to capture the unique property of the JJ in order to efficiently mix signal, pump and idler signals for the purpose of signal amplification. Closed-form expressions are derived for gain characteristics, bandwidth determination, noise properties and impedance for this kind of parametric power amplifier. The concept of negative resistance in the gain formulation is observed. A design process is also introduced to find the regimes of operation for gain achievement. Two regimes of operation, oscillation and amplification, are highlighted and distinguished in the result section. Optimization of the circuits to enhance the bandwidth is also carried out. Moving toward TW-JPA, the second part is devoted to modelling the linear wave propagation in a periodic superconducting structure. We derive closed-form equations for dispersion and s-parameters of infinite and finite periodic structures, respectively. Band gap formation is highlighted and its potential applications in the design of passive filters and resonators are discussed. The superconducting structures are fabricated using YBCO and measured, illustrating a good correlation with the numerical results. A novel superconducting Transmission Line (TL), which is periodically loaded by Josephson junctions (JJ) and assisted by open stubs, is proposed as a platform to realize a traveling-wave parametric device. Using the TL model, this structure is modeled by a system of nonlinear partial differential equations (PDE) with a driving source and mixed-boundary conditions at the input and output terminals, respectively. This model successfully emulates parametric and nonlinear microwave propagation when long-wave approximation is applicable. The influence of dispersion to sustain three non-degenerate phased-locked waves through the TL is highlighted. A rigorous and robust Finite Difference Time Domain (FDTD) solver based on the explicit Lax-Wendroff and implicit Crank-Nicolson schemes has been developed to investigate the device responses under various excitations. Linearization of the wave equation, under small-amplitude assumption, dispersion and impedance analysis is performed to explore more aspects of the device for the purpose of efficient design of a traveling-wave parametric amplifier. Knowing all microwave characteristics and identifying different regimes of operation, which include impedance properties, cut-off propagation, dispersive behaviour and shock-wave formation, we exploit perturbation theory accompanied by the method of multiple scale to derive the three nonlinear coupled amplitude equations to describe the parametric interaction. A graphical technique is suggested to find three waves on the dispersion diagram satisfying the phase-matching conditions. Both cases of perfect phase-matching and slight mismatching are addressed in this work. The incorporation of two numerical techniques, spectral method in space and multistep Adams-Bashforth in time domain, is employed to monitor the unilateral gain, superior stability and bandwidth of this structure. Two types of functionality, mixing and amplification, with their requirements are described. These properties make this structure desirable for applications ranging from superconducting optoelectronics to dispersive readout of superconducting qubits where high sensitivity and ultra-low noise operation is required.

Η υπερθερμία αποτελεί μια επικουρική μέθοδο θεραπείας του καρκίνου και η βιοϊατρική έρευνα τις τελευταίες δεκαετίες, με σκοπό την εκμετάλλευση και την ανάδειξη των ιδιοτήτων της μεθόδου, στοχεύει στην εφαρμογή της στην κλινική πράξη. Μια προσπάθεια με παρόμοιο σκοπό γίνεται τα τελευταία χρόνια στο Εργαστήριο Μικροκυμάτων και Οπτικών Ινών (ΕΜΟΙ) της σχολής Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών (ΗΜΜΥ) του Εθνικού Μετσόβιου Πολυτεχνείου, όπου έχει σχεδιαστεί και κατασκευαστεί ένα μικροκυματικό σύστημα υπερθερμίας. Το προτεινόμενο σύστημα ενσωματώθηκε σε ένα τρισδιάστατο σύστημα παθητικής μικροκυματικής ραδιομετρικής απεικόνισης (ΜiRaIS), το οποίο παρέχει τη δυνατότητα παρακολούθησης των μεταβολών της θερμοκρασίας και της αγωγιμότητας της υπό εξέταση περιοχής σε πραγματικό χρόνο και μελετήθηκε και κατασκευάστηκε στα πλαίσια παλαιότερης διδακτορικής διατριβής στο ίδιο εργαστήριο της σχολής ΗΜΜΥ. Στην παρούσα διδακτορική διατριβή γίνεται η θεωρητική και πειραματική μελέτη του προτεινόμενου συστήματος υπερθερμίας. Η αρχή λειτουργίας του συστήματος είναι όμοια με εκείνη του MiRaIS και βασίζεται στη χρήση μιας ελλειψοειδούς αγώγιμης κοιλότητας για εστίαση της ακτινοβολίας επιλεκτικά στους ιστούς που χρήζουν θεραπείας. Ο ανακλαστήρας για εστίαση που κατασκευάστηκε και χρησιμοποιήθηκε στην πειραματική διαδικασία, βελτιώνει την εργονομία του συστήματος, διατηρώντας παράλληλα της ιδιότητες εστίασης του πρωτότυπου ελλειψοειδούς. Στα πλαίσια της παρούσας διατριβής πραγματοποιήθηκε αρχικά η θεωρητική μελέτη και μοντελοποίηση της διάταξης με σκοπό την εξακρίβωση των ιδιοτήτων εστίασης του συστήματος και στη συνέχεια επιχειρήθηκε η βελτίωση των ιδιοτήτων αυτών με χρήση διατάξεων διηελκτρικών υλικών, καθώς και πειραματικές μετρήσεις του συνολικού συστήματος υπερθερμίας-μικροκυματικής ραδιομετρίας. Η θεωρητική ηλεκτρομαγνητική μελέτη του συστήματος έγινε με τη χρήση ενός εμπορικά διαθέσιμου υπολογιστικού πακέτου προσομοίωσης (XFdtd, Remcom Inc.), το οποίο χρησιμοποιεί τη μέθοδο των πεπερασμένων διαφορών στο πεδίο του χρόνου για την επίλυση ηλεκτρομαγνητικών προβλημάτων. Ερευνώνται τρεις διατάξεις διηλεκτρικών υλικών με σκοπό τη βελτίωση των ιδιοτήτων εστίασης του συστήματος, οι οποίες επικεντρώνονται στη μελέτη του βάθους διείσδυσης της ακτινοβολίας και της χωρικής διακριτικής ικανότητας. Τα υλικά τοποθετούνται είτε στο εσωτερικό του ελλειψοειδούς είτε γύρω από το μοντέλο κεφαλιού ως στρώματα προσαρμογής, με σκοπό την επίτευξη βηματικής αλλαγής της διηλεκτρικής σταθεράς στη διεπιφάνεια αέρα-μοντέλο ανθρώπινου κεφαλιού. Τα αποτελέσματα καταδεικνύουν τα πλεονεκτήματα από τη χρήση των διηλεκτρικών υλικών, καθώς παρουσιάζεται βελτίωση και στις δυο παραμέτρους των ιδιοτήτων εστίασης, ανάλογα με τη διάταξη που χρησιμοποιείται, τη θέση του μοντέλου κεφαλιού στο εσωτερικό του συστήματος και τη συχνότητα λειτουργίας. Για τη διενέργεια των πειραμάτων, η πειραματική διάταξη τοποθετήθηκε σε ανηχοϊκό θάλαμο, ο οποίος εξασφαλίζει την απομόνωσή της από τον περιβάλλοντα χώρο. Στις πειραματικές διαδικασίες που ακολουθήθηκαν, χρησιμοποιήθηκαν ομοιώματα, τα οποία στη φάση της υπερθερμίας υπέδειξαν τις περιοχές εστίασης της ενέργειας για την εκάστοτε συχνότητα ακτινοβολίας, ενώ στη φάση της μικροκυματικής ραδιομετρίας βοήθησαν στη μελέτη της θερμοκρασιακής διακριτικής ικανότητας του συστήματος. Η μέθοδος της μικροκυματικής ραδιομετρίας χρησιμοποιήθηκε για την παρακολούθηση των μεταβολών της θερμοκρασίας της ακτινοβολούμενης περιοχής κατά τη διάρκεια των συνεδριών της υπερθερμίας. Επίσης, κατά τη διάρκεια των πειραμάτων πραγματοποιήθηκαν μετρήσεις με στρώματα προσαρμογής από διηλεκτρικά υλικά, τα οποία τοποθετήθηκαν γύρω από το αντικείμενο ενδιαφέροντος και βοήθησαν στην πληρέστερη κατανόηση της επίδρασης της παρουσίας τους στις ιδιότητες εστίασης του συστήματος και στην επιβεβαίωση των αντίστοιχων θεωρητικών αποτελεσμάτων. / The application of hyperthermia process has been widely used in clinical research and efforts are being made for its implementation in clinical practice, as many researchers have used this method as an adjunct treatment procedure for cancer. During the past two decades, a great deal of research has been carried out, with the aim of developing effective techniques for hyperthermia treatment, primarily using RF, microwave and ultrasound energy. A similar effort is carried out in the Laboratory of Microwaves and Fiber Optics (MFOL), School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), where a proposed hyperthermia system has been designed and constructed. A system for deep brain hyperthermia treatment, designed to also provide passive measurements of temperature and/or conductivity variations inside the human body, is presented in the present PhD thesis. The proposed system comprises both therapeutic and diagnostic modules, operating in a totally contactless way, based on the use of an ellipsoidal beamformer to achieve focusing on the areas under treatment and monitoring. The radiometry monitoring module, the Three Dimensional Passive Microwave Radiometry Imaging System (MiRaIS), has been studied, designed and constructed in the framework of a previous PhD thesis in the same laboratory of MFOL. In the present thesis, the proposed system is theoretically and experimentally studied. The operation principal is based on the use of an ellipsoidal conductive wall cavity for focusing the emitted radiation on the tissues that should accept treatment. The ellipsoidal cavity, which was constructed and used in the experimentation procedure, is newly developed and improves the system’s ergonomics retaining at the same time the focusing properties of the prototype system. In the framework of the present work, theoretical modeling and experimentation of the proposed system is carried out in order to examine and improve its focusing attributes. In the theoretical study, three setups are investigated for the improvement of the system’s focusing properties (e.g. penetration depth of the electromagnetic field, spatial sensitivity) using dielectric materials. The research is carried out with the use of a commercially available software tool, XFdtd (Remcom Inc.). The materials are placed inside the ellipsoidal or used as matching layers around the head model for the achievement of a stepped change of the refraction index on the air-human head model interface. The results revealed the possible advantages of using matching dielectric materials, as improvement on the focusing properties of the system is clearly observed, depending on the setup used, the position of the head model inside the system and the operating frequency. The experiments were performed inside an anechoic chamber providing maximum accuracy by avoiding all possible EMC/EMI issues. Along with the hyperthermia experiments, the implementation of the microwave radiometry process was also tested with the proposed system. Microwave radiometry could provide the temperature monitoring of the radiated area during the hyperthermia sessions. In the experimental procedures water phantoms were used, which during hyperthermia indicated the energy absorbing areas at the irradiation frequency, while during microwave radiometry revealed the system’s temperature sensitivity. Also, measurements were conducted using dielectric matching layers, placed around the medium of interest, in order to fully understand the effect of those materials on the system’s focusing properties as well as to confirm the respective theoretical results. Taking into consideration the present study and the advantage of the non invasive character of the proposed brain hyperthermia system, it is concluded that further research is required in order to explore its potentials at becoming a part of the standard treatment protocol of brain malignancy in the future.

Ces travaux de recherche portent sur la problématique CEM (Compatibilité Electromagnétique) en électronique de puissance. Cette étude s'intéresse particulièrement à la modélisation HF (haute fréquence) des convertisseurs d'énergie dans le but d'étudier la propagation des perturbations conduites vers le réseau avec ou sans l’utilisation du RSIL (Réseau Stabilisateur d'Impédance de Ligne). Une première partie présente les outils de modélisation des sources de perturbation dans les convertisseurs statiques.La seconde partie est consacrée à la modélisation HF d'un système d'entraînement à vitesse variable. L'onduleur de tension triphasé est représenté par trois générateurs équivalents afin de reconstituer le découpage des tensions de sortie. Un modèle HF du câble blindé de 4 conducteurs tenant compte de la dissymétrie est ensuite proposé. Les résultats de simulation ont été validés par des relevés expérimentaux. La comparaison montre qu'il est possible de modéliser correctement le comportement HF du dispositif jusqu'à 20MHz.Une troisième partie porte sur la propagation des perturbations conduites vers le réseau sans RSIL. Il a fallu pour cela déterminer et modéliser l'impédance du réseau. L'influence du pont redresseur à diodes sur la propagation des perturbations de mode commun a ensuite été étudiée. Les résultats de simulation montrent que l'impact de ces perturbations sur la tension réseau est prépondérant lorsque le pont redresseur est à l'état bloqué. Les résultats expérimentaux ont permis de valider cette étude. Ce travail se termine par une étude préliminaire sur l'association de deux convertisseurs connectés localement à une même source d'énergie / These research works focus on EMC (Electromagnetic Compatibility) in power electronics systems. Specifically, the study focuses on HF (high frequency) modeling of the power converters in order to study the conducted emissions toward the power grids with or without the use of an LISN (Line Impedance Stabilisation Network). The first part presents the modeling tools of the electromagnetic emissions sources in power converters.The second part describes the HF modeling method of an adjustable speed drive (ASD) that will be used to estimate the conducted emissions. In a first part, a behavioural model of PWM inverter is proposed as an EMI noise source. Then, a model of the shielded 4-wire energy cable that taking into account of the dissymmetry structure is proposed and validated in the frequency domain for two different lengths. The comparison of measurement and simulation results of conducted emissions (with LISN) shows the good compromise between the simulation duration and accuracy of the results.A third part is dedicated to the propagation of conducted emissions toward the power grid without using a LISN. The first stage consists in proposing a model impedance of the network impedance. The influence of the bridge rectifier diodes on the propagation paths of common mode disturbances has been studied in the second step. The simulation results show that the impact of these disturbances on the network voltage is more important when the bridge rectifier is normally off-state. The experimental results have validated this study. This work concludes with a preliminary study on the association of two converters connected locally to a single energy source

Cette thèse traite de la résolution du problème direct de propagation d'un champ élastodynamique rayonné par une source dans un milieu stratifié anisotrope. Le contexte applicatif visé est le contrôle non destructif par ondes ultrasonores guidées de plaques de matériaux composites. Aux basses fréquences, ces matériaux sont assimilables à des milieux homogènes, anisotropes et dissipatifs. Deux approches causales sont étudiées et mises en oeuvre pour résoudre l'équation d'onde, et leur intérêt vis-à-vis de la méthode modale harmonique - la plus couramment employée dans ce domaine applicatif - est discuté. L'une des méthodes est modale et est formulée directement dans le domaine temporel. Elle permet de traiter facilement l'anisotropie, y compris en 3D, mais souffre des écueils classiques concernant le régime non-établi ou le cas du guide ouvert. L'autre approche est une formulation dans le domaine de Laplace de la méthode dite par ondes partielles. Elle présente l'intérêt d'être extrêmement polyvalente tout en conduisant à des coûts numériques tout à fait raisonnables. Dans un second temps, la possibilité d'exploiter ces deux méthodes pour résoudre des problèmes de diffraction par des défauts est étudiée. Une approche par éléments finis de frontière basée sur la méthode par ondes partielles est considérée. Elle permet de traiter efficacement le cas de défauts plans. L'extension à des défauts plus généraux est brièvement discutée. / This work adresses the direct problem of the propagation of an elastodynamic field radiated by a source in an anisotropic layered medium. Applications concern non destructive evaluation of composite plates by ultrasonic guided waves. In the lower frequencies, these materials can be modeled as homogeneous, anisotropic and dissipative media. Two causal approaches are studied and developped to solve the wave equation, and their interest is discussed regarding to the widely used harmonic modal method. One of these methods is modal, and is formulated directly in the time domain. It allows to deal easily with anisotropy, even in 3D ; however it also suffers classical shortcomings such as the high cost of the unestablished regime or the difficulty to deal with open waveguides. The other method is a formulation of the so-called partial-waves method in the Laplace domain. Its attractiveness relies in its versatility and in the fact that computational costs can be very acceptable. In a second time, we consider using both methods to solve problems of diffraction by defects. A boundary element method based on the partial-waves approach is developped and leads to solve very efficiently the case of a planar defect. The possibility of treating more general defects is briefly discussed.

Les communications futures pour les applications civiles et militaires utilisent des signaux modulés complexes large bande qui seront émis à travers des amplificateurs de puissance multivoie de type DOHERTY qui devront avoir des performances en puissance, rendement, OBO et largeur de bande qui constituent aujourd’hui un véritable défi à relever. Pour ce faire les concepteurs ont besoin d’outils de caractérisation temporelle permettant la mesure normalisées et l’optimisation des tensions et courants aux accès des dispositifs non linéaires sous pointes ou connectorisés. Ce travail de thèse a permis de mettre en œuvre cet outil de caractérisation temporelle qui a été utilisé pour répondre à des besoins spécifiques pour la modélisation de transistor, pour l’optimisation de leur fonctionnement en termes de stabilité impulsion à impulsion, pour la recherche des conditions optimales de leur fonctionnement dans un amplificateur de type Doherty. Pour cette mise en œuvre une modélisation mathématique des échantillonneurs a été réalisée pour évaluer leurs performances et choisir le mieux adapté à la mesure temporelle RF. Des procédures d’étalonnages rigoureuses ont été développées pour obtenir simultanément des formes d’ondes temporelles calibrées à spectre très large (Basse fréquences jusqu’aux Hyperfréquences). / The future communications for civil and military applications will use complex wideband modulated signals to be transmitted through multi-channel DOHERTY power amplifiers which should have high performance in terms of power, efficiency, OBO, and bandwidth. In order to meet these stringent requirements, designers need time-domain characterization tools for calibrated measurements and for optimizing voltages and currents at both ports of non-linear connectorized or on-wafer devices. This work successfully implements time-domain characterization tools used to meet specific needs for transistor modeling, to optimize their operation in terms of pulse to pulse stability, and to search optimal conditions of their operation modes in a Doherty power amplifier. For this implementation, mathematical modeling is performed to evaluate sampler’s performances in terms of time-domain sampling efficiency in order to choose the best suited sampling architecture for RF time-domain measurements. Rigorous calibration procedures have been developed to obtain simultaneously full time-domain calibrated waveforms (from low Frequencies to Microwave frequencies).

[pt] Com a crescente demanda por maior capacidade na transmissão de dados, uma solução tem sido estudada para transmissão de rádio sobre fibra combinando múltiplos canais de dados sobre a portadora óptica na rede de acesso baseada em multiplexação por sub-portadoras. Ademais, essa rede de acesso é comumente ramificada na forma de uma rede óptica passiva. Monitoramento desses enlaces em fibra é, então, cada vez mais importante. A tecnologia atual de reflectometria óptica no domínio do tempo utilizada para monitoramento opera em um comprimento de onda óptico separado e possui ampla largura de banda de detecção, tornando-se relativamente cara. A busca por uma alternativa de monitoramento de alta precisão e baixo custo é de suma importância para a oferta de transmissão com garantia de qualidade de serviço. Neste trabalho, o uso de multiplexação por sub-portadoras é explorado, incorporando uma técnica de monitoramento de varredura de tom de baixa frequência na transmissão de dados. Um modelo matemático para a resposta em frequência do enlace foi derivado e a localização e a intensidade de uma falha são estimadas através da comparação com a amplitude e a fase detectadas da luz retroespalhadaa medida em que é feita uma varredura de frequência do sinal de monitoramento, aplicando-se um algoritmo de minimos quadrados. O modelo proposto considera que a medida do enlace antes da ocorrência de uma falha é conhecida. Uma única falha nova pode então ser detectada com precisão e sua posição e intensidade são estimadas da maneira descrita. / [en] With ever growing demand for higher capacity in data transmission, a solution has been proposed for analog Radio over Fiber transmission, combining several data channels over the optical carrier in the access network using Sub-Carrier Multiplexing (SCM). Furthermore, this access network is often branched in the form of a passive optical network (PON). Monitoring such fiber links is thus increasingly important. Current optical time domain reflectometry (OTDR) technology used for monitoring operates at a separate optical wavelength and has wide bandwidth detection, making it relatively costly. The pursuit of a low cost, high precision monitoring alternative is of paramount importance for cost effective quality of service (QoS) improvement. In this work employment of SCM for data multiplexing is exploited embedding a low frequency tone sweep monitoring technique into data transmission. A mathematical model for the frequency response of the link was derived and the fault location and intensity is estimated through comparison with acquired amplitude and phase of the backscattered light for the varying frequency by applying a simple least mean squared (LMS) algorithm. The modeling suggested requires that measurement of the link prior to the occurrence of a fault is known. A single new fault can then be accurately detected and its position and intensity estimated in the way described.

A precisão e acurácia dos métodos mais utilizados atualmente de processamento de dados de espectroscopia por Ressonância Magnética (MRS), baseados na Transformada de Fourier (FT), requerem supressão apropriada (o que está longe de ser trivial) e aquisições longas para a obtenção de alta resolução espectral. Além disso, a FT tem dificuldades quando faltam dados no domínio de tempo, como, por exemplo, pela redução do tempo de aquisição, e consequente número de pontos adquiridos. Isto pode ocorrer, também, por artefatos na aquisição ou, ainda, seja pela exclusão intencional dos primeiros pontos do sinal para a eliminação de ressonâncias largas que estão distorcendo a linha de base no domínio da frequência. Neste estudo, propomos a utilização do Método de Diagonalização na Base de Krylov (KBDM) como uma alternativa a FT para algumas de suas limitações. O método ajusta sinais de experimentos de Free Induction Decay (FID) por uma soma de funções harmônicas complexas, amortecidas exponencialmente, permitindo uma fácil manipulação dos seus parâmetros de caracterização. O KBDM é numericamente mais efetivo para análise de sinais truncados e tem diversos recursos que possibilitam remover picos de forma mais eficiente, como por exemplo, o pico residual da água. Além disso, foi introduzida a possibilidade de quantificação de dados de MRS com o método. Para avaliar a sensibilidade, eficiência e reprodutibilidade do método para quantificar e analisar sinais truncados, foi proposto fazer simulações de espectros clínicos e experimentos em phantoms que representassem o ambiente metabólico do cérebro, para MRS de próton de diferentes níveis de ruídos e para pequenas variações do N-acetil aspartato (NAA). Com estes estudos pôde se comprovar a viabilidade do método para processar dados de MRS e verificar seu potencial na complementação das técnicas atualmente empregadas, especialmente quando uma resolução espectral e temporal maior que o limite imposto pela Relação de Incerteza do formalismo de Fourier é necessária. Além disso, uma desejável facilidade de manipulação de picos específicos (por exemplo, exclusão e quantificação) é proporcionada pelo método. Como perspectivas animadoras deste trabalho esperamos a introdução do KBDM como uma técnica eficiente e coadjuvante ao Imageamento de Ressonância Magnética funcional (fMRI), auxiliando estudos de funções cerebrais, em sequências de MRS para identificar uma rápida variação das linhas associadas as atividades metabólicas dos cérebros. / The precision and accuracy of the most widely used methods to perform Magnetic Resonance Spectroscopy (MRS) data processing based on the Fourier Transform (FT), require appropriate suppression (which is far from trivial) and long acquisitions to obtain high spectral resolution. Furthermore, FT poses difficulty when there are missing data in the time domain. This occurs because of reduction of the acquisition time and consequently also in the number of acquired points, or because of artifacts during acquisition, or even intentional exclusion of the first signal points for the elimination of broad resonances that are producing the distorted baseline in the frequency domain. In this study, we propose the use of the Krylov Basis Diagonalization Method (KBDM) formalism as an alternative to some of FT limitations. The method adjusts signals of Free Induction Decay (FID) experiments with a sum of complex harmonic functions, exponentially damped, allowing easy manipulation of its characterization parameters. The KBDM is numerically more effective for truncated signal analysis and has several features that make it possible to remove peaks more efficiently, such as the residual water peak. Moreover, we introduced the possibility of quantification of MRS data with the described method. To evaluate the sensitivity, efficiency and reproducibility of the method for quantifying and analyzing truncated signals, and through the clinical spectra simulations and experiments in phantoms that would represent the brain metabolic environment, we proposed to perform proton MRS at different noise levels and with small variations of N- acetyl aspartate (NAA) metabolite. These studies allowed to prove the feasibility of the method to process MRS data and verified its potential in complementing techniques currently employed, especially when a greater temporal and spectral resolution is required, more than the limit imposed by the Uncertainty Relation of FT formalism. Furthermore, it is also a desirable effortless tool of handling specific peaks (e.g., exclusion and quantification). Exciting prospects from this work include the introduction of KBDM as an efficient and adjuvant technique to functional Magnetic Resonance Imaging (fMRI), for studying the brain functions, in MRS sequence to identify rapid variation in spectroscopic lines associated to metabolic activities in the brain.

Ce travail de cette thèse propose une conception et une réalisation d’un banc intégré de caractérisation temporelle des dispositifs RF non-linéaires conçu avec des récepteurs de type THA. Ce banc est une version miniaturisée, moins onéreuse et à performances comparables d’un banc similaire « éclaté » et développé au sein d’XLIM. Le banc intégré développé dans ce travail est entièrement étalonné. Il est versatile vis-à-vis des techniques de sous échantillonnage mis en œuvre pour mesurer des signaux RF sur des temps d’acquisition très différents (<50 µs ou < quelques ms). La technique CIS est utilisée pour l’acquisition périodiques de signaux RF périodiques de durée courtes. La technique DQD est utilisée pour l’acquisition périodiques ou apériodique de signaux RF périodiques ou apériodiques. Cet outil a été utilisé pour extraire, à partir des formes d’ondes temporelles mesurées à leurs accès, plusieurs paramètres caractéristiques (AM/AM- AM/PM, EVM) d’amplificateurs GaN de gamme 10 à 50 W soumis à des excitations simples ou à des signaux modulés. Ce manuscrit décrit aussi la mise en œuvre le développement, parallèlement au travail précédent, d’une plateforme de laboratoire de travaux pratiques à distance pour le projet européen TEMPUS EOLES. / This work proposes the design and the realization of a 4-channel integrated and calibrated time-domain characterization system for the characterization of non-linear microwave devices. This integrated measurement system uses THA based receivers. This is a miniaturized, less expensive and comparable version of a similar laboratory available tool developed within XLIM. The integrated instrument developed in this work is fully calibrated. It is versatile with respect to sub-sampling techniques used to measure RF signals over very different acquisition times (<50 µs or < few ms). The CIS technique is used for the periodic acquisition of periodic short duration RF signals. The DQD technique is used for the periodic or aperiodic acquisition of periodic or aperiodic RF signals. This tool was used to extract, from the measured time-domain waveforms at their ports, several characteristic parameters (AM/AM-AM/PM, EVM) of GaN amplifiers operating in the 10 to 50 W range and excited with simple or modulated signals. This manuscript also describes the implementation, and the development, performed along with the previous work, of a laboratory platform for remote practical works in the context of the European project TEMPUS EOLES.

Les travaux de cette thèse concerne l’étude d’une méthode élément finis d’ordre spatial élevé que l’on peut assimilé à une extension du schéma de Yee. On parle alors de méthode différences finies d’ordre élevé. Après avoir donné, dans un premier chapitre, un historique non exhaustif des principales méthodes utilisées pour résoudre les équations de Maxwell dans le cadre de problèmes de CEM et montré l’ intérêt de disposer d’un solveur de type "différences finies d’ ordre élevé", nous présentons dans un deuxième chapitre le principe de la méthode. Nous donnons pour cela les caractéristiques du schéma spatial et temporel en précisant les conditions de stabilité de la méthode. En outre, dans une étude purement numérique, nous étudions la convergence du schéma. On se focalise ensuite sur la possibilité d’utiliser des ordres spatiaux variable par cellules dans chaque direction de l’espace. Des comparaisons avec le schéma de Yee et un schéma de Galerkin Discontinu particulier sont ensuite effectuées pour montrer les gains en coûts calcul et mémoire et donc l’intérêt de notre approche par rapport aux deux autres. Dans un troisième chapitre, nous nous intéressons à l’étude de modèles physiques indispensable au traitement d’un problème de CEM. Pour cela, nous nous focalisons particulièrement sur un modèle de fil mince oblique, des modèles de matériaux volumiques et minces et enfin sur la prise en compte de sol parfaitement métallique dans une agression de type onde plane. Chaque modèle est détaillé et validé par comparaison avec des solutions analytiques ou résultant de la littérature, sur des exemples canoniques. Le quatrième chapitre est dédié à une technique d’hybridation entre notre méthode et une approche Galerkin Discontinu en vue de traiter des géométries possédant des courbures. Nous donnons pour cela une stratégie d’hybridation basée sur l’échange de flux qui garantie au niveau continue la conservation d’une énergie. Nous présentons ensuite quelques exemples montrant la validité de notre approche dans une stratégie multi-domaines/multi-méthodes que nous précisons. Enfin le dernier chapitre de cette thèse concerne l’exploitation de notre méthode sur des cas industriels en comparaisons avec d’autres méthodes ou des résultats expérimentaux. / This thesis is about the study of a high spatial finite element method whichcan be assimilated at an extension of the Yee schema. In the next, this method is also called high order finite difference method. In the first chapter, we give a non exhaustive recall of the major methods used to treat EMC problems and we show the necessity to have this kind of schema to simulate efficiently some EMC configurations. In the second chapter, the principle of the numerical method is presented and a stability condition is given. A numerical study analysis of the schema convergence is also done. Next, we show the interest to have the possibility to use local spatial order by cell in each direction of the computational domain. Some canonic examples are given to show the advantages interms of CPU time and memory storage of the method by comparison with Yee’s scheme and DG approach. In the third chapter, we define and validate on several examples,some physical models as thin wire, materials and perfectly metallic ground in presence of a plane wave, to have the possibility to treat EMC problems. The fourth chapter is about a hybridization strategy between our high order FDTD method and a DG schema.We focalize our study on a hybrid method which provides an energy conservation of the continuous problem. A numerical example is given to validate the method. Finally, in the last chapter, we present some simulations on industrial problems to show the possibility of the method to treat realistic EMC problems.

Cette thèse développe des estimations d’erreur a posteriori et critères d’arrêt pour les méthodes de décomposition de domaine avec des conditions de transmission de Robin optimisées entre les interfaces. Différents problèmes sont considérés: l’équation de Darcy stationnaire puis l’équation de la chaleur, discrétisées par les éléments finis mixtes avec un schéma de Galerkin discontinu de plus bas degré en temps pour le second cas. Pour l’équation de la chaleur, une méthode de décomposition de domaine globale en temps, avec mêmes ou différents pas de temps entre les différents sous domaines, est utilisée. Ce travail est finalement étendu à un modèle diphasique en utilisant une méthode de volumes finis centrés par maille en espace. Pour chaque modèle, un problème d’interface est résolu itérativement, où chaque itération nécessite la résolution d’un problème local dans chaque sous-domaine, et les informations sont ensuite transmises aux sous-domaines voisins. Pour les modèles instationnaires, les problèmes locaux dans les sous-domaines sont instationnaires et les données sont transmises par l’interface espace-temps. L’objectif de ce travail est, pour chaque modèle, de borner l’erreur entre la solution exacte et la solution approchée à chaque itération de l’algorithme de décomposition de domaine. Différentes composantes d’erreur en jeu de la méthode sont identifiées, dont celle de l’algorithme de décomposition de domaine, de façon à définir un critère d’arrêt efficace pour cette méthode. En particulier, pour l’équation de Darcy stationnaire, on bornera l’erreur par un estimateur de décomposition de domaine ainsi qu’un estimateur de discrétisation en espace. On ajoutera à la borne de l’erreur un estimateur de discrétisation en temps pour l’équation de la chaleur et pour le modèle diphasique. L’estimation a posteriori répose sur des techniques de reconstructions de pressions et de flux conformes respectivement dans les espaces H1 et H(div) et sur la résolution de problèmes locaux de Neumann dans des bandes autour des interfaces de chaque sous-domaine pour les flux. Ainsi, des critères pour arrêter les itérations de l’algorithme itératif de décomposition de domaine sont développés. Des simulations numériques pour des problèmes académiques ainsi qu’un problème plus réaliste basé sur des données industrielles sont présentées pour illustrer l’efficacité de ces techniques. En particulier, différents pas de temps entre les sous-domaines sont considérés pour cet exemple. / This work contributes to the developpement of a posteriori error estimates and stopping criteria for domain decomposition methods with optimized Robin transmission conditions on the interface between subdomains. We study several problems. First, we tackle the steady diffusion equation using the mixed finite element subdomain discretization. Then the heat equation using the mixed finite element method in space and the discontinuous Galerkin scheme of lowest order in time is investigated. For the heat equation, a global-in-time domain decomposition method is used for both conforming and nonconforming time grids allowing for different time steps in different subdomains. This work is then extended to a two-phase flow model using a finite volume scheme in space. For each model, the multidomain formulation can be rewritten as an interface problem which is solved iteratively. Here at each iteration, local subdomain problems are solved, and information is then transferred to the neighboring subdomains. For unsteady problems, the subdomain problems are time-dependent and information is transferred via a space-time interface. The aim of this work is to bound the error between the exact solution and the approximate solution at each iteration of the domain decomposition algorithm. Different error components, such as the domain decomposition error, are identified in order to define efficient stopping criteria for the domain decomposition algorithm. More precisely, for the steady diffusion problem, the error of the domain decomposition method and that of the discretization in space are estimated separately. In addition, the time error for the unsteady problems is identified. Our a posteriori estimates are based on the reconstruction techniques for pressures and fluxes respectively in the spaces H1 and H(div). For the fluxes, local Neumann problems in bands arround the interfaces extracted from the subdomains are solved. Consequently, an effective criterion to stop the domain decomposition iterations is developed. Numerical experiments, both academic and more realistic with industrial data, are shown to illustrate the efficiency of these techniques. In particular, different time steps in different subdomains for the industrial example are used.