Sobre la solución del problema de la radiación electromagnética

En la presente Tesis Doctoral se propone una posible solución al problema de la radiación electromagnética. Este es un problema científico estudiado desde hace mucho tiempo y que hasta el presente no se ha podido resolver de manera exacta. Aquí se redefine nuevamente el problema y se plantea el mismo partiendo un modelo de radiador formado por dos placas planas circulares paralelas, que por sus reducidas dimensiones eléctricas, se considerará para el estudio como un dipolo simétrico corto. Se obtienen las soluciones de las ecuaciones de Maxwell para la radiación electromagnética emitida por dicho sistema y se propone lo que sería el principio de formación de las ondas electromagnéticas. Con ayuda de este se ofrece una posible interpretación de las soluciones obtenidas. Luego a dicho sistema se le realizan correcciones en sus dimensiones a fin de ajustar las soluciones obtenidas al caso real de un dipolo simétrico de media onda. Además se analiza de una manera sencilla la naturaleza material del campo electromagnético y su estructura, lo que hace posible proponer una manera original de comprender las ecuaciones de Maxwell. Finalmente se propone un modelo sencillo mediante el cual se puede demostrar la Ley de Planck para la distribución espectral de la energía electromagnética radiada por los cuerpos calientes, pero desde las soluciones de las ecuaciones de Maxwell para la radiación de las antenas. Con esto podría ser aceptado que la solución del problema de la radiación electromagnética es única tanto para las antenas como para los cuerpos calientes en la naturaleza. ABSTRACT In this PhD thesis a possible solution to the problem of electromagnetic radiation is proposed. This is a scientific problem which has been studied for a long time and to this day has still not exactly been solved. The problem is redefined here again and it is stated using a model formed by two flat parallel circular plates as the radiator system, which due to its reduced electrical dimensions will be considered for the study as a short symmetrical dipole. The solutions of the Maxwell equations for emitted electromagnetic radiation are obtained by said system, and that which could be the principle formation of electromagnetic waves is proposed. Using this principle, a possible interpretation of the solutions obtained is presented. Then the system will perform corrections in size to adjust the solutions obtained to the real case of a symmetrical half-wave dipole. The material nature of the electromagnetic field and its structure is also analyzed in a simple way, making it possible to present an original way to understand the Maxwell equations. Finally, a simple model which can be used to prove Planck's law of spectral distribution of the electromagnetic energy radiated by hot bodies is proposed, but parting from the solutions of the Maxwell equations for the antennas radiation. With this it could be accepted that the solution to the problem of electromagnetic radiation is unique to both antennas and hot bodies on nature.

Contribución al análisis eficiente y a la mejora de prestaciones de antenas reflectarray

El diseño de una antena reflectarray bajo la aproximación de periodicidad local requiere la determinación de la matriz de scattering de estructuras multicapa con metalizaciones periódicas para un gran número de geometrías diferentes. Por lo tanto, a la hora de diseñar antenas reflectarray en tiempos de CPU razonables, se necesitan herramientas númericas rápidas y precisas para el análisis de las estructuras periódicas multicapa. En esta tesis se aplica la versión Galerkin del Método de los Momentos (MDM) en el dominio espectral al análisis de las estructuras periódicas multicapa necesarias para el diseño de antenas reflectarray basadas en parches apilados o en dipolos paralelos coplanares. Desgraciadamente, la aplicación de este método numérico involucra el cálculo de series dobles infinitas, y mientras que algunas series convergen muy rápidamente, otras lo hacen muy lentamente. Para aliviar este problema, en esta tesis se propone un novedoso MDM espectral-espacial para el análisis de las estructuras periódicas multicapa, en el cual las series rápidamente convergente se calculan en el dominio espectral, y las series lentamente convergentes se calculan en el dominio espacial mediante una versión mejorada de la formulación de ecuaciones integrales de potenciales mixtos (EIPM) del MDM. Esta versión mejorada se basa en la interpolación eficiente de las funciones de Green multicapa periódicas, y en el cálculo eficiente de las integrales singulares que conducen a los elementos de la matriz del MDM. El novedoso método híbrido espectral-espacial y el tradicional MDM en el dominio espectral se han comparado en el caso de los elementos reflectarray basado en parches apilados. Las simulaciones numéricas han demostrado que el tiempo de CPU requerido por el MDM híbrido es alrededor de unas 60 veces más rápido que el requerido por el tradicional MDM en el dominio espectral para una precisión de dos cifras significativas. El uso combinado de elementos reflectarray con parches apilados y técnicas de optimización de banda ancha ha hecho posible diseñar antenas reflectarray de transmisiónrecepción (Tx-Rx) y polarización dual para aplicaciones de espacio con requisitos muy restrictivos. Desgraciadamente, el nivel de aislamiento entre las polarizaciones ortogonales en antenas DBS (típicamente 30 dB) es demasiado exigente para ser conseguido con las antenas basadas en parches apilados. Además, el uso de elementos reflectarray con parches apilados conlleva procesos de fabricación complejos y costosos. En esta tesis se investigan varias configuraciones de elementos reflectarray basadas en conjuntos de dipolos paralelos con el fin de superar los inconvenientes que presenta el elemento basado en parches apilados. Primeramente, se propone un elemento consistente en dos conjuntos apilados ortogonales de tres dipolos paralelos para aplicaciones de polarización dual. Se ha diseñado, fabricado y medido una antena basada en este elemento, y los resultados obtenidos para la antena indican que tiene unas altas prestaciones en términos de ancho de banda, pérdidas, eficiencia y discriminación contrapolar, además de requerir un proceso de fabricación mucho más sencillo que el de las antenas basadas en tres parches apilados. Desgraciadamente, el elemento basado en dos conjuntos ortogonales de tres dipolos paralelos no proporciona suficientes grados de libertad para diseñar antenas reflectarray de transmisión-recepción (Tx-Rx) de polarización dual para aplicaciones de espacio por medio de técnicas de optimización de banda ancha. Por este motivo, en la tesis se propone un nuevo elemento reflectarray que proporciona los grados de libertad suficientes para cada polarización. El nuevo elemento consiste en dos conjuntos ortogonales de cuatro dipolos paralelos. Cada conjunto contiene tres dipolos coplanares y un dipolo apilado. Para poder acomodar los dos conjuntos de dipolos en una sola celda de la antena reflectarray, el conjunto de dipolos de una polarización está desplazado medio período con respecto al conjunto de dipolos de la otra polarización. Este hecho permite usar solamente dos niveles de metalización para cada elemento de la antena, lo cual simplifica el proceso de fabricación como en el caso del elemento basados en dos conjuntos de tres dipolos paralelos coplanares. Una antena de doble polarización y doble banda (Tx-Rx) basada en el nuevo elemento ha sido diseñada, fabricada y medida. La antena muestra muy buenas presentaciones en las dos bandas de frecuencia con muy bajos niveles de polarización cruzada. Simulaciones numéricas presentadas en la tesis muestran que estos bajos de niveles de polarización cruzada se pueden reducir todavía más si se llevan a cabo pequeñas rotaciones de los dos conjuntos de dipolos asociados a cada polarización. ABSTRACT The design of a reflectarray antenna under the local periodicity assumption requires the determination of the scattering matrix of a multilayered structure with periodic metallizations for quite a large number of different geometries. Therefore, in order to design reflectarray antennas within reasonable CPU times, fast and accurate numerical tools for the analysis of the periodic multilayered structures are required. In this thesis the Galerkin’s version of the Method of Moments (MoM) in the spectral domain is applied to the analysis of the periodic multilayered structures involved in the design of reflectarray antennas made of either stacked patches or coplanar parallel dipoles. Unfortunately, this numerical approach involves the computation of double infinite summations, and whereas some of these summations converge very fast, some others converge very slowly. In order to alleviate this problem, in the thesis a novel hybrid MoM spectral-spatial domain approach is proposed for the analysis of the periodic multilayered structures. In the novel approach, whereas the fast convergent summations are computed in the spectral domain, the slowly convergent summations are computed by means of an enhanced Mixed Potential Integral Equation (MPIE) formulation of the MoM in the spatial domain. This enhanced formulation is based on the efficient interpolation of the multilayered periodic Green’s functions, and on the efficient computation of the singular integrals leading to the MoM matrix entries. The novel hybrid spectral-spatial MoM code and the standard spectral domain MoM code have both been compared in the case of reflectarray elements based on multilayered stacked patches. Numerical simulations have shown that the CPU time required by the hybrid MoM is around 60 times smaller than that required by the standard spectral MoM for an accuracy of two significant figures. The combined use of reflectarray elements based on stacked patches and wideband optimization techniques has made it possible to design dual polarization transmit-receive (Tx-Rx) reflectarrays for space applications with stringent requirements. Unfortunately, the required level of isolation between orthogonal polarizations in DBS antennas (typically 30 dB) is hard to achieve with the configuration of stacked patches. Moreover, the use of reflectarrays based on stacked patches leads to a complex and expensive manufacturing process. In this thesis, we investigate several configurations of reflectarray elements based on sets of parallel dipoles that try to overcome the drawbacks introduced by the element based on stacked patches. First, an element based on two stacked orthogonal sets of three coplanar parallel dipoles is proposed for dual polarization applications. An antenna made of this element has been designed, manufactured and measured, and the results obtained show that the antenna presents a high performance in terms of bandwidth, losses, efficiency and cross-polarization discrimination, while the manufacturing process is cheaper and simpler than that of the antennas made of stacked patches. Unfortunately, the element based on two sets of three coplanar parallel dipoles does not provide enough degrees of freedom to design dual-polarization transmit-receive (Tx-Rx) reflectarray antennas for space applications by means of wideband optimization techniques. For this reason, in the thesis a new reflectarray element is proposed which does provide enough degrees of freedom for each polarization. This new element consists of two orthogonal sets of four parallel dipoles, each set containing three coplanar dipoles and one stacked dipole. In order to accommodate the two sets of dipoles in each reflectarray cell, the set of dipoles for one polarization is shifted half a period from the set of dipoles for the other polarization. This also makes it possible to use only two levels of metallization for the reflectarray element, which simplifies the manufacturing process as in the case of the reflectarray element based on two sets of three parallel dipoles. A dual polarization dual-band (Tx-Rx) reflectarray antenna based on the new element has been designed, manufactured and measured. The antenna shows a very good performance in both Tx and Rx frequency bands with very low levels of cross-polarization. Numerical simulations carried out in the thesis have shown that the low levels of cross-polarization can be even made smaller by means of small rotations of the two sets of dipoles associated to each polarization.

Análisis de reflectores en MatLab

Sabor, Software de Análisis de BOcinas y Reflectores, es una herramienta didáctica la cual es utilizada en los laboratorios de la escuela para realizar prácticas de la asignatura Antenas y Compatibilidad Electromagnética, esta herramienta da a los alumnos una visión gráfica de lo que se enseña en clase de teoría de lo que son los campos en las aperturas de los reflectores. El proyector pretende sustituir al primer Sabor , ya que se queda obsoleto debido al sistema operativo, ya que funciona solo para Windows XP y con ordenadores de 32 bits, y también realizar mejoras y corregir errores de la versión anterior. El proyecto se ha desarrollado en Matlab que es un software matemático con grandes ventajas en cuanto a cálculo, desarrollo gráfico, y a la creación de nuevos algoritmos en su propio lenguaje y además está disponible para las plataformas Unix, Windows, Mac OSX y GNU/Linux. El objetivo del proyecto ha sido implementar, al igual que las versiones anteriores, cinco tipos de reflectores, como son: Parabólico, Offset, Cassegrain y los dos Dobles Offset, Cassegrain y Gregorian, y han sido analizados con un alimentador ideal ,cos-q, y por último los resultados obtenidos se han comparado con las versiones anteriores de Sabor, como son Sabor 3.0 y el primer Sabor. El proyecto consta de partes muy bien diferencias como son :  La interpretación correctas de las formulas que se han utilizado para la realización de este proyecto ,dichas formulas han sido las dadas por el proyecto fin de carrera titulado Sabor3.0 de Francisco Egea Castejón.  GUIDE, the graphical user interface development environment, con el que se creó: GUI, graphical user interface, que es la parte de Matlab dedicada a crear interfaces de usuario , herramienta utilizada para crear nuestras distintas ventanas dedicadas para la obtención de datos para analizar los distintos reflectores y para mostrar por pantalla los distintos resultados.  Programación Orientada a Objetos de Matlab y sus distintas propiedades como son la herencia lo cual es muy útil para ocupar menos memoria ya que con un único método podemos realizar distintos cálculos con los distintos reflectores, objetos, solo cambiando las propiedades de cada objeto  Y por último ha sido la realización de validación de los resultados con la ayuda de las versiones anteriores de Sabor, que están detallados en el capítulo 5 y la unión con bocinas del proyecto fin de carrera Análisis de Bocinas en Matlab de Javier Montero. Por otra parte tenemos las mejoras realizadas a las antiguas versiones como son: realización de registros que el usuario puede guardar y cargar con las distintas variables, también se ha realizado un fichero .txt en el que consta la amplitud del campo con su respectiva theta para que el usuario pueda visualizarlo en cualquier plataforma gráfica de datos como por ejemplo exel. ABSTRACT. Sabor, Software de Análisis de BOcinas y Reflectores, is a teaching tool, which is used to do laboratory practice in the subject of Antennas y Compatibilidad Electromagnética, this tool gives students a graphic view of the knowledge that are given in theory class in regard to aperture field of reflectors. This project intend to replace the first Sabor, because it is outdated, due to the operating system, because Sabor works only with Widows XP and computer with 32 bits, and to make improves and correct errors that were detected in the last version of Sabor too. This project has been carried out in Matlab, which is a mathematical software with high-level language for numerical computation, visualization and application development, and furthermore it is available to different platforms such as Unix, Windows ,Mac OSX and GNU/Linux This project has focused on implementing, the same as last versions, five kind of reflectors, such as : Parabolic, Offset, Cassegrain and two offset dual reflector Cassegrain y Gregorian ,and these were analysed with a cos-q ideal feed, and finally the results were checked with the versions of Sabor, as well as Sabor 3.0 and the first Sabor. This project consist of four parts:  The correct interpretation of the formulas , which were used to do this project, from the final project Sabor3.0 by Francisco Egea Castejón.  GUIDE, the graphical user interface development environment, tool that was used to create : GUI, graphical user interface, part of Matlab dedicated to create user interface.  Object Oriented Programming of Matlab and different properties like inheritance, that is very useful for saving memory space because with only one method we can analyse different kind of reflectors, object, only change the properties of the object.  At finally, the results were contrasted with the results from the previous versions and the link reflectors with horns from the final project Análisis de Bocinas en Matlab by Javier Montero. On the other hand, we have the improvements such as: registers and .txt file. The registers are used by user to save and load different variables and .txt file is useful because it allows to the user plotting in different platforms for example exel.

New methods for the synthesis of radiation patterns of coupled antenna arrays = Nuevos métodos de síntesis de diagramas de radiación de agrupaciones de antenas acopladas

El principal objetivo de esta tesis es el desarrollo de métodos de síntesis de diagramas de radiación de agrupaciones de antenas, en donde se realiza una caracterización electromagnética rigurosa de los elementos radiantes y de los acoplos mutuos existentes. Esta caracterización no se realiza habitualmente en la gran mayoría de métodos de síntesis encontrados en la literatura, debido fundamentalmente a dos razones. Por un lado, se considera que el diagrama de radiación de un array de antenas se puede aproximar con el factor de array que únicamente tiene en cuenta la posición de los elementos y las excitaciones aplicadas a los mismos. Sin embargo, como se mostrará en esta tesis, en múltiples ocasiones un riguroso análisis de los elementos radiantes y del acoplo mutuo entre ellos es importante ya que los resultados obtenidos pueden ser notablemente diferentes. Por otro lado, no es sencillo combinar un método de análisis electromagnético con un proceso de síntesis de diagramas de radiación. Los métodos de análisis de agrupaciones de antenas suelen ser costosos computacionalmente, ya que son estructuras grandes en términos de longitudes de onda. Generalmente, un diseño de un problema electromagnético suele comprender varios análisis de la estructura, dependiendo de las variaciones de las características, lo que hace este proceso muy costoso. Dos métodos se utilizan en esta tesis para el análisis de los arrays acoplados. Ambos están basados en el método de los elementos finitos, la descomposición de dominio y el análisis modal para analizar la estructura radiante y han sido desarrollados en el grupo de investigación donde se engloba esta tesis. El primero de ellos es una técnica de análisis de arrays finitos basado en la aproximación de array infinito. Su uso es indicado para arrays planos de grandes dimensiones con elementos equiespaciados. El segundo caracteriza el array y el acoplo mutuo entre elementos a partir de una expansión en modos esféricos del campo radiado por cada uno de los elementos. Este método calcula los acoplos entre los diferentes elementos del array usando las propiedades de traslación y rotación de los modos esféricos. Es capaz de analizar agrupaciones de elementos distribuidos de forma arbitraria. Ambas técnicas utilizan una formulación matricial que caracteriza de forma rigurosa el campo radiado por el array. Esto las hace muy apropiadas para su posterior uso en una herramienta de diseño, como los métodos de síntesis desarrollados en esta tesis. Los resultados obtenidos por estas técnicas de síntesis, que incluyen métodos rigurosos de análisis, son consecuentemente más precisos. La síntesis de arrays consiste en modificar uno o varios parámetros de las agrupaciones de antenas buscando unas determinadas especificaciones de las características de radiación. Los parámetros utilizados como variables de optimización pueden ser varios. Los más utilizados son las excitaciones aplicadas a los elementos, pero también es posible modificar otros parámetros de diseño como son las posiciones de los elementos o las rotaciones de estos. Los objetivos de las síntesis pueden ser dirigir el haz o haces en una determinada dirección o conformar el haz con formas arbitrarias. Además, es posible minimizar el nivel de los lóbulos secundarios o del rizado en las regiones deseadas, imponer nulos que evitan posibles interferencias o reducir el nivel de la componente contrapolar. El método para el análisis de arrays finitos basado en la aproximación de array infinito considera un array finito como un array infinito con un número finito de elementos excitados. Los elementos no excitados están físicamente presentes y pueden presentar tres diferentes terminaciones, corto-circuito, circuito abierto y adaptados. Cada una de estas terminaciones simulará mejor el entorno real en el que el array se encuentre. Este método de análisis se integra en la tesis con dos métodos diferentes de síntesis de diagramas de radiación. En el primero de ellos se presenta un método basado en programación lineal en donde es posible dirigir el haz o haces, en la dirección deseada, además de ejercer un control sobre los lóbulos secundarios o imponer nulos. Este método es muy eficiente y obtiene soluciones óptimas. El mismo método de análisis es también aplicado a un método de conformación de haz, en donde un problema originalmente no convexo (y de difícil solución) es transformado en un problema convexo imponiendo restricciones de simetría, resolviendo de este modo eficientemente un problema complejo. Con este método es posible diseñar diagramas de radiación con haces de forma arbitraria, ejerciendo un control en el rizado del lóbulo principal, así como en el nivel de los lóbulos secundarios. El método de análisis de arrays basado en la expansión en modos esféricos se integra en la tesis con tres técnicas de síntesis de diagramas de radiación. Se propone inicialmente una síntesis de conformación del haz basado en el método de la recuperación de fase resuelta de forma iterativa mediante métodos convexos, en donde relajando las restricciones del problema original se consiguen unas soluciones cercanas a las óptimas de manera eficiente. Dos métodos de síntesis se han propuesto, donde las variables de optimización son las posiciones y las rotaciones de los elementos respectivamente. Se define una función de coste basada en la intensidad de radiación, la cual es minimizada de forma iterativa con el método del gradiente. Ambos métodos reducen el nivel de los lóbulos secundarios minimizando una función de coste. El gradiente de la función de coste es obtenido en términos de la variable de optimización en cada método. Esta función de coste está formada por la expresión rigurosa de la intensidad de radiación y por una función de peso definida por el usuario para imponer prioridades sobre las diferentes regiones de radiación, si así se desea. Por último, se presenta un método en el cual, mediante técnicas de programación entera, se buscan las fases discretas que generan un diagrama de radiación lo más cercano posible al deseado. Con este método se obtienen diseños que minimizan el coste de fabricación. En cada uno de las diferentes técnicas propuestas en la tesis, se presentan resultados con elementos reales que muestran las capacidades y posibilidades que los métodos ofrecen. Se comparan los resultados con otros métodos disponibles en la literatura. Se muestra la importancia de tener en cuenta los diagramas de los elementos reales y los acoplos mutuos en el proceso de síntesis y se comparan los resultados obtenidos con herramientas de software comerciales. ABSTRACT The main objective of this thesis is the development of optimization methods for the radiation pattern synthesis of array antennas in which a rigorous electromagnetic characterization of the radiators and the mutual coupling between them is performed. The electromagnetic characterization is usually overlooked in most of the available synthesis methods in the literature, this is mainly due to two reasons. On the one hand, it is argued that the radiation pattern of an array is mainly influenced by the array factor and that the mutual coupling plays a minor role. As it is shown in this thesis, the mutual coupling and the rigorous characterization of the array antenna influences significantly in the array performance and its computation leads to differences in the results obtained. On the other hand, it is difficult to introduce an analysis procedure into a synthesis technique. The analysis of array antennas is generally expensive computationally as the structure to analyze is large in terms of wavelengths. A synthesis method requires to carry out a large number of analysis, this makes the synthesis problem very expensive computationally or intractable in some cases. Two methods have been used in this thesis for the analysis of coupled antenna arrays, both of them have been developed in the research group in which this thesis is involved. They are based on the finite element method (FEM), the domain decomposition and the modal analysis. The first one obtains a finite array characterization with the results obtained from the infinite array approach. It is specially indicated for the analysis of large arrays with equispaced elements. The second one characterizes the array elements and the mutual coupling between them with a spherical wave expansion of the radiated field by each element. The mutual coupling is computed using the properties of translation and rotation of spherical waves. This method is able to analyze arrays with elements placed on an arbitrary distribution. Both techniques provide a matrix formulation that makes them very suitable for being integrated in synthesis techniques, the results obtained from these synthesis methods will be very accurate. The array synthesis stands for the modification of one or several array parameters looking for some desired specifications of the radiation pattern. The array parameters used as optimization variables are usually the excitation weights applied to the array elements, but some other array characteristics can be used as well, such as the array elements positions or rotations. The desired specifications may be to steer the beam towards any specific direction or to generate shaped beams with arbitrary geometry. Further characteristics can be handled as well, such as minimize the side lobe level in some other radiating regions, to minimize the ripple of the shaped beam, to take control over the cross-polar component or to impose nulls on the radiation pattern to avoid possible interferences from specific directions. The analysis method based on the infinite array approach considers an infinite array with a finite number of excited elements. The infinite non-excited elements are physically present and may have three different terminations, short-circuit, open circuit and match terminated. Each of this terminations is a better simulation for the real environment of the array. This method is used in this thesis for the development of two synthesis methods. In the first one, a multi-objective radiation pattern synthesis is presented, in which it is possible to steer the beam or beams in desired directions, minimizing the side lobe level and with the possibility of imposing nulls in the radiation pattern. This method is very efficient and obtains optimal solutions as it is based on convex programming. The same analysis method is used in a shaped beam technique in which an originally non-convex problem is transformed into a convex one applying symmetry restrictions, thus solving a complex problem in an efficient way. This method allows the synthesis of shaped beam radiation patterns controlling the ripple in the mainlobe and the side lobe level. The analysis method based on the spherical wave expansion is applied for different synthesis techniques of the radiation pattern of coupled arrays. A shaped beam synthesis is presented, in which a convex formulation is proposed based on the phase retrieval method. In this technique, an originally non-convex problem is solved using a relaxation and solving a convex problems iteratively. Two methods are proposed based on the gradient method. A cost function is defined involving the radiation intensity of the coupled array and a weighting function that provides more degrees of freedom to the designer. The gradient of the cost function is computed with respect to the positions in one of them and the rotations of the elements in the second one. The elements are moved or rotated iteratively following the results of the gradient. A highly non-convex problem is solved very efficiently, obtaining very good results that are dependent on the starting point. Finally, an optimization method is presented where discrete digital phases are synthesized providing a radiation pattern as close as possible to the desired one. The problem is solved using linear integer programming procedures obtaining array designs that greatly reduce the fabrication costs. Results are provided for every method showing the capabilities that the above mentioned methods offer. The results obtained are compared with available methods in the literature. The importance of introducing a rigorous analysis into the synthesis method is emphasized and the results obtained are compared with a commercial software, showing good agreement.

Design and demonstration of an electronically scanned reflectarray antenna at 100 GHz using multiresonant cells based on liquid crystals

The design, fabrication and measured results are presented for a reconfigurable reflectarray antenna based on liquid crystals (LC) which operates above 100 GHz. The antenna has been designed to provide beam scanning capabilities over a wide angular range, a large bandwidth and reduced Side-Lobe Level. Measured radiation patterns are in good agreement with simulations, and show that the antenna generates an electronically steerable beam in one plane over an angular range of 55º in the frequency band from 96 to 104 GHz. The Side Lobes Level is lower than -13 dB for all the scan angles and -18 dB is obtained over 16% of the scan range. The measured performance is significantly better than previously published results for this class of electronically tunable antenna, and moreover verifies the accuracy of the proposed procedure for LC modeling and antenna design.

A Transportable Reflectarray Antenna for Satellite Ku-band Emergency Communications

The design of a Ku-band reconfigurable reflectarray antenna for emergency satellite communications is presented. Bidirectional high data rate satellite links are needed in emergency conditions where other telecommunication infrastructures are not available. In order to operate in this type of scenario, an antenna should be deployable, transportable, and easily repointable. The need of an automatic and fast satellite location and pointing system leads to a completely electronic reconfigurable antenna. The operative bandwidth is from 10.7 to 12.5 GHz for reception and from 14 up to 14.5 GHz for transmission (30% of relative bandwidth). The selected antenna architecture is based on a dual reflectarray system comprising a passive subreflectarray and an active main reflectarray made of reconfigurable 1-bit elementary cells based on PIN diodes.

Design of broadband transmitarray unit cells with comparative study of different numbers of layers

A generalized methodology to design low-profile transmitarray (TA) antennas made of several stacked layers with nonresonant printed phasing elements is presented. A study of the unit cell bandwidth, phase-shift range and tolerances has been conducted considering different numbers of layers. A structure with three metalized layers with capacitive and inductive elements enabling a phase range of nearly 360° and low insertion loss is introduced. A study of the four-layer structure shows improvement in the performance of the unit cells in terms of bandwidth from 2% to more than 20% and a complete phase coverage. Implementations on a flexible substrate of TAs with progressive phase shift operating at 19 GHz are used for validation.

A source reconstruction technique for planar arrays of wide slots

A method to reconstruct the excitation coefficients of wide-slot arrays from near-field data is presented. The plane wave spectrum (PWS) is used for reconstruction, and the shape of the field distribution on a wide slot is considered in the calculation of the PWS. The proposed algorithm is validated through the reconstruction of the excitation coefficients of a wide-slot array with element failures from the simulated nearfield data. The element failures are clearly located by the proposed algorithm

Quantisation of the bosonic string

In this work we review the basic principles of the theory of the relativistic bosonic string through the study of the action functionals of Nambu-Goto and Polyakov and the techniques required for their canonical, light-cone, and path-integral quantisation. For this purpose, we briefly review the main properties of the gauge symmetries and conformal field theory involved in the techniques studied.

Resonant elements contactless coupled to bolometric micro-stripes

One of the main technical difficulties in the fabrication of optical antennas working as light detectors is the proper design and manufacture of auxiliary elements as load lines and signal extraction structures. These elements need to be quite small to reach the location of the antennas and should have a minimal effect on the response of the device. Unfortunately this is not an easy task and signal extraction lines resonate along with the antenna producing a complex signal that usually masks the one given by the antenna. In order to decouple the resonance from the transduction we present in this contribution a parametric analysis of the response of a bolometric stripe that is surrounded by resonant dipoles with different geometries and orientations. We have checked that these elements should provide a signal proportional to the polarization state of the incoming light.

Desenvolvimento e otimização de antenas Vivaldi antipodais para aplicações a altas frequências.

Esta tese propõe a síntese e o estudo de uma nova técnica de cavidades de borda aplicada a antenas Vivaldi, com o intuito de melhorar suas características de diretividade. Embora as antenas do tipo Vivaldi possuam características diretivas, elas produzem radiações laterais indesejáveis, o que se reflete nos elevados índices de lóbulos laterais devido a correntes superficiais que fluem ao longo das bordas metalizadas nas laterais da antena. Estas correntes são a origem das radiações laterais que vêm sendo mitigadas pela aplicação de cavidades ressonantes, triangulares ou retangulares, que aprisionam tais correntes e, consequentemente, atenuam os lóbulos laterais, sem o incremento do lóbulo principal, uma vez que toda a energia dos lóbulos laterais é apenas confinada nos ressonadores e por isso literalmente perdida. Ao contrário desses esforços, este trabalho propõe cavidades radiantes tanto na forma de abertura exponencial, como na forma do fractais de Koch, que funcionam como radiadores auxiliares (antenas auxiliares), canalizando as correntes de borda e aproveitando-as para aumentar os níveis do lóbulo principal, mitigando os níveis de lóbulo lateral. A síntese desta nova técnica foi implementada em uma antena Vivaldi antipodal com características de baixa diretividade, como qualquer antena Vivaldi, o que foi corrigido e a aplicação da técnica de cavidades radiantes deu origem a duas novas antenas Vivaldis efetivamente diretivas. Os resultados foram obtidos através de simulações do modelo numérico no CST Microwave Studio e confirmados com medidas de laboratório, o que evidenciou a melhora das características de diretividade da antena pela aplicação da nova técnica de cavidades radiantes.

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.

On the development of advanced techniques for mixed-elastohydrodynamic lubrification modelling of journal and sliding bearing systems.

The present thesis is focused on the development of a thorough mathematical modelling and computational solution framework aimed at the numerical simulation of journal and sliding bearing systems operating under a wide range of lubrication regimes (mixed, elastohydrodynamic and full film lubrication regimes) and working conditions (static, quasi-static and transient conditions). The fluid flow effects have been considered in terms of the Isothermal Generalized Equation of the Mechanics of the Viscous Thin Films (Reynolds equation), along with the massconserving p-Ø Elrod-Adams cavitation model that accordingly ensures the so-called JFO complementary boundary conditions for fluid film rupture. The variation of the lubricant rheological properties due to the viscous-pressure (Barus and Roelands equations), viscous-shear-thinning (Eyring and Carreau-Yasuda equations) and density-pressure (Dowson-Higginson equation) relationships have also been taken into account in the overall modelling. Generic models have been derived for the aforementioned bearing components in order to enable their applications in general multibody dynamic systems (MDS), and by including the effects of angular misalignments, superficial geometric defects (form/waviness deviations, EHL deformations, etc.) and axial motion. The bearing exibility (conformal EHL) has been incorporated by means of FEM model reduction (or condensation) techniques. The macroscopic in fluence of the mixedlubrication phenomena have been included into the modelling by the stochastic Patir and Cheng average ow model and the Greenwood-Williamson/Greenwood-Tripp formulations for rough contacts. Furthermore, a deterministic mixed-lubrication model with inter-asperity cavitation has also been proposed for full-scale simulations in the microscopic (roughness) level. According to the extensive mathematical modelling background established, three significant contributions have been accomplished. Firstly, a general numerical solution for the Reynolds lubrication equation with the mass-conserving p - Ø cavitation model has been developed based on the hybridtype Element-Based Finite Volume Method (EbFVM). This new solution scheme allows solving lubrication problems with complex geometries to be discretized by unstructured grids. The numerical method was validated in agreement with several example cases from the literature, and further used in numerical experiments to explore its exibility in coping with irregular meshes for reducing the number of nodes required in the solution of textured sliding bearings. Secondly, novel robust partitioned techniques, namely: Fixed Point Gauss-Seidel Method (PGMF), Point Gauss-Seidel Method with Aitken Acceleration (PGMA) and Interface Quasi-Newton Method with Inverse Jacobian from Least-Squares approximation (IQN-ILS), commonly adopted for solving uid-structure interaction problems have been introduced in the context of tribological simulations, particularly for the coupled calculation of dynamic conformal EHL contacts. The performance of such partitioned methods was evaluated according to simulations of dynamically loaded connecting-rod big-end bearings of both heavy-duty and high-speed engines. Finally, the proposed deterministic mixed-lubrication modelling was applied to investigate the in fluence of the cylinder liner wear after a 100h dynamometer engine test on the hydrodynamic pressure generation and friction of Twin-Land Oil Control Rings.

Identification of geostationary satellites using polarization data from unresolved images

In order to protect critical military and commercial space assets, the United States Space Surveillance Network must have the ability to positively identify and characterize all space objects. Unfortunately, positive identification and characterization of space objects is a manual and labor intensive process today since even large telescopes cannot provide resolved images of most space objects. Since resolved images of geosynchronous satellites are not technically feasible with current technology, another method of distinguishing space objects was explored that exploits the polarization signature from unresolved images. The objective of this study was to collect and analyze visible-spectrum polarization data from unresolved images of geosynchronous satellites taken over various solar phase angles. Different collection geometries were used to evaluate the polarization contribution of solar arrays, thermal control materials, antennas, and the satellite bus as the solar phase angle changed. Since materials on space objects age due to the space environment, it was postulated that their polarization signature may change enough to allow discrimination of identical satellites launched at different times. The instrumentation used in this experiment was a United States Air Force Academy (USAFA) Department of Physics system that consists of a 20-inch Ritchey-Chrétien telescope and a dual focal plane optical train fed with a polarizing beam splitter. A rigorous calibration of the system was performed that included corrections for pixel bias, dark current, and response. Additionally, the two channel polarimeter was calibrated by experimentally determining the Mueller matrix for the system and relating image intensity at the two cameras to Stokes parameters S0 and S1. After the system calibration, polarization data was collected during three nights on eight geosynchronous satellites built by various manufacturers and launched several years apart. Three pairs of the eight satellites were identical buses to determine if identical buses could be correctly differentiated. When Stokes parameters were plotted against time and solar phase angle, the data indicates that there were distinguishing features in S0 (total intensity) and S1 (linear polarization) that may lead to positive identification or classification of each satellite.

South America, 1807 (Image 2 of 7) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Colombia Prima or South America : in which it has been attempted to delineate the extent of our knowledge of that continent, extracted chiefly from the original manuscript maps of ... Pinto, likewise fom those of João Joaquin da Rocha, João da Costa Ferreira ... Francisco Manuel Sobreviela &c. and from the most authentic edited accounts of those countries, digested & constructed by ... Louis Stanislas D'Arcy Delarochette. It was published by William Faden geographer to His Majesty and to His Royal Highness the Prince of Wales in June 4th, 1807. Scale [ca. 1:3,000,000]. This layer is image 2 of 7 total images of the eight sheet map, representing the northern portion of the map.The image inside the map neatline is georeferenced to the surface of the earth and fit to the South America Lambert Conformal Conic projected coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, roads, territorial boundaries, shoreline features, mines, tribes, and more. Relief shown by hachures. Includes notes.This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection. These maps typically portray both natural and manmade features. The selection represents a range of originators, ground condition dates, scales, and map purposes.