Contribution to the design of waveguide-fed compound-slot arrays by means of equivalent circuit modelling

Los arrays de ranuras son sistemas de antennas conocidos desde los años 40, principalmente destinados a formar parte de sistemas rádar de navíos de combate y grandes estaciones terrenas donde el tamaño y el peso no eran altamente restrictivos. Con el paso de los años y debido sobre todo a importantes avances en materiales y métodos de fabricación, el rango de aplicaciones de este tipo de sistemas radiantes creció en gran medida. Desde nuevas tecnologías biomédicas, sistemas anticolisión en automóviles y navegación en aviones, enlaces de comunicaciones de alta tasa binaria y corta distancia e incluso sistemas embarcados en satélites para la transmisión de señal de televisión. Dentro de esta familia de antennas, existen dos grupos que destacan por ser los más utilizados: las antennas de placas paralelas con las ranuras distribuidas de forma circular o espiral y las agrupaciones de arrays lineales construidos sobre guia de onda. Continuando con las tareas de investigación desarrolladas durante los últimos años en el Instituto de Tecnología de Tokyo y en el Grupo de Radiación de la Universidad Politécnica de Madrid, la totalidad de esta tesis se centra en este último grupo, aunque como se verá se separa en gran medida de las técnicas de diseño y metodologías convencionales. Los arrays de ranuras rectas y paralelas al eje de la guía rectangular que las alimenta son, sin ninguna duda, los modelos más empleados debido a la fiabilidad que presentan a altas frecuencias, su capacidad para gestionar grandes cantidades de potencia y la sencillez de su diseño y fabricación. Sin embargo, también presentan desventajas como estrecho ancho de banda en pérdidas de retorno y rápida degradación del diagrama de radiación con la frecuencia. Éstas son debidas a la naturaleza resonante de sus elementos radiantes: al perder la resonancia, el sistema global se desajusta y sus prestaciones degeneran. En arrays bidimensionales de slots rectos, el campo eléctrico queda polarizado sobre el plano transversal a las ranuras, correspondiéndose con el plano de altos lóbulos secundarios. Esta tesis tiene como objetivo el desarrollo de un método sistemático de diseño de arrays de ranuras inclinadas y desplazadas del centro (en lo sucesivo “ranuras compuestas”), definido en 1971 como uno de los desafíos a superar dentro del mundo del diseño de antennas. La técnica empleada se basa en el Método de los Momentos, la Teoría de Circuitos y la Teoría de Conexión Aleatoria de Matrices de Dispersión. Al tratarse de un método circuital, la primera parte de la tesis se corresponde con el estudio de la aplicabilidad de las redes equivalentes fundamentales, su capacidad para recrear fenómenos físicos de la ranura, las limitaciones y ventajas que presentan para caracterizar las diferentes configuraciones de slot compuesto. Se profundiza en las diferencias entre las redes en T y en ! y se condiciona la selección de una u otra dependiendo del tipo de elemento radiante. Una vez seleccionado el tipo de red a emplear en el diseño del sistema, se ha desarrollado un algoritmo de cascadeo progresivo desde el puerto alimentador hacia el cortocircuito que termina el modelo. Este algoritmo es independiente del número de elementos, la frecuencia central de funcionamiento, del ángulo de inclinación de las ranuras y de la red equivalente seleccionada (en T o en !). Se basa en definir el diseño del array como un Problema de Satisfacción de Condiciones (en inglés, Constraint Satisfaction Problem) que se resuelve por un método de Búsqueda en Retroceso (Backtracking algorithm). Como resultado devuelve un circuito equivalente del array completo adaptado a su entrada y cuyos elementos consumen una potencia acorde a una distribución de amplitud dada para el array. En toda agrupación de antennas, el acoplo mutuo entre elementos a través del campo radiado representa uno de los principales problemas para el ingeniero y sus efectos perjudican a las prestaciones globales del sistema, tanto en adaptación como en capacidad de radiación. El empleo de circuito equivalente se descartó por la dificultad que suponía la caracterización de estos efectos y su inclusión en la etapa de diseño. En esta tesis doctoral el acoplo también se ha modelado como una red equivalente cuyos elementos son transformadores ideales y admitancias, conectada al conjunto de redes equivalentes que representa el array. Al comparar los resultados estimados en términos de pérdidas de retorno y radiación con aquellos obtenidos a partir de programas comerciales populares como CST Microwave Studio se confirma la validez del método aquí propuesto, el primer método de diseño sistemático de arrays de ranuras compuestos alimentados por guía de onda rectangular. Al tratarse de ranuras no resonantes, el ancho de banda en pérdidas de retorno es mucho mas amplio que el que presentan arrays de slots rectos. Para arrays bidimensionales, el ángulo de inclinación puede ajustarse de manera que el campo quede polarizado en los planos de bajos lóbulos secundarios. Además de simulaciones se han diseñado, construido y medido dos prototipos centrados en la frecuencia de 12GHz, de seis y diez elementos. Las medidas de pérdidas de retorno y diagrama de radiación revelan excelentes resultados, certificando la bondad del método genuino Method of Moments - Forward Matching Procedure desarrollado a lo largo de esta tésis. Abstract The slot antenna arrays are well known systems from the decade of 40s, mainly intended to be part of radar systems of large warships and terrestrial stations where size and weight were not highly restrictive. Over the years, mainly due to significant advances in materials and manufacturing methods, the range of applications of this type of radiating systems grew significantly. From new biomedical technologies, collision avoidance systems in cars and aircraft navigation, short communication links with high bit transfer rate and even embedded systems in satellites for television broadcast. Within this family of antennas, two groups stand out as being the most frequent in the literature: parallel plate antennas with slots placed in a circular or spiral distribution and clusters of waveguide linear arrays. To continue the vast research work carried out during the last decades in the Tokyo Institute of Technology and in the Radiation Group at the Universidad Politécnica de Madrid, this thesis focuses on the latter group, although it represents a technique that drastically breaks with traditional design methodologies. The arrays of slots straight and parallel to the axis of the feeding rectangular waveguide are without a doubt the most used models because of the reliability that they present at high frequencies, its ability to handle large amounts of power and their simplicity of design and manufacturing. However, there also exist disadvantages as narrow bandwidth in return loss and rapid degradation of the radiation pattern with frequency. These are due to the resonant nature of radiating elements: away from the resonance status, the overall system performance and radiation pattern diminish. For two-dimensional arrays of straight slots, the electric field is polarized transverse to the radiators, corresponding to the plane of high side-lobe level. This thesis aims to develop a systematic method of designing arrays of angled and displaced slots (hereinafter "compound slots"), defined in 1971 as one of the challenges to overcome in the world of antenna design. The used technique is based on the Method of Moments, Circuit Theory and the Theory of Scattering Matrices Connection. Being a circuitry-based method, the first part of this dissertation corresponds to the study of the applicability of the basic equivalent networks, their ability to recreate the slot physical phenomena, their limitations and advantages presented to characterize different compound slot configurations. It delves into the differences of T and ! and determines the selection of the most suitable one depending on the type of radiating element. Once the type of network to be used in the system design is selected, a progressive algorithm called Forward Matching Procedure has been developed to connect the proper equivalent networks from the feeder port to shorted ending. This algorithm is independent of the number of elements, the central operating frequency, the angle of inclination of the slots and selected equivalent network (T or ! networks). It is based on the definition of the array design as a Constraint Satisfaction Problem, solved by means of a Backtracking Algorithm. As a result, the method returns an equivalent circuit of the whole array which is matched at its input port and whose elements consume a power according to a given amplitude distribution for the array. In any group of antennas, the mutual coupling between elements through the radiated field represents one of the biggest problems that the engineer faces and its effects are detrimental to the overall performance of the system, both in radiation capabilities and return loss. The employment of an equivalent circuit for the array design was discarded by some authors because of the difficulty involved in the characterization of the coupling effects and their inclusion in the design stage. In this thesis the coupling has also been modeled as an equivalent network whose elements are ideal transformers and admittances connected to the set of equivalent networks that represent the antennas of the array. By comparing the estimated results in terms of return loss and radiation with those obtained from popular commercial software as CST Microwave Studio, the validity of the proposed method is fully confirmed, representing the first method of systematic design of compound-slot arrays fed by rectangular waveguide. Since these slots do not work under the resonant status, the bandwidth in return loss is much wider than the longitudinal-slot arrays. For the case of two-dimensional arrays, the angle of inclination can be adjusted so that the field is polarized at the low side-lobe level plane. Besides the performed full-wave simulations two prototypes of six and ten elements for the X-band have been designed, built and measured, revealing excellent results and agreement with the expected results. These facts certify that the genuine technique Method of Moments - Matching Forward Procedure developed along this thesis is valid and trustable.

3D hp-adaptive finite element simulations of a magic-T electromagnetic waveguide structure

This paper employs a 3D hp self-adaptive grid-refinement finite element strategy for the solution of a particular electromagnetic waveguide structure known as Magic-T. This structure is utilized as a power divider/combiner in communication systems as well as in other applications. It often incorporates dielectrics, metallic screws, round corners, and so on, which may facilitate its construction or improve its design, but significantly difficult its modeling when employing semi-analytical techniques. The hp-adaptive finite element method enables accurate modeling of a Magic-T structure even in the presence of these undesired materials/geometries. Numerical results demonstrate the suitability of the hp-adaptive method for modeling a Magic-T rectangular waveguide structure, delivering errors below 0.5% with a limited number of unknowns. Solutions of waveguide problems delivered by the self-adaptive hp-FEM are comparable to those obtained with semi-analytical techniques such as the Mode Matching method, for problems where the latest methods can be applied. At the same time, the hp-adaptive FEM enables accurate modeling of more complex waveguide structures.

A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities

We propose the use of a highly-accurate three-dimensional (3D) fully automatic hp-adaptive finite element method (FEM) for the characterization of rectangular waveguide discontinuities. These discontinuities are either the unavoidable result of mechanical/electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems. The proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi-analytical methods. It supports anisotropic refinements on irregular meshes with hanging nodes, and isoparametric elements. It makes use of hexahedral elements compatible with high-order H(curl)H(curl) discretizations. The 3D hp-adaptive FEM is applied for the first time to solve a wide range of 3D waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed.

High-accuracy adaptive simulations of a Petri dish exposed to electromagnetic radiation

This paper analyses numerically the electric field distribution of a liquid contained in a Petri dish when exposed to electromagnetic waves excited in a rectangular waveguide. Solutions exhibit high-gradients due to the presence of the dielectric liquid contained in the dish. Furthermore, electromagnetic fields within the dielectric have a dramatically lower value than on the remaining part of the domain, which difficults its simulation. Additionally, various singularities of different intensity appear along the boundary of the Petri dish. To properly reproduce and numerically study those effects, we employ a highly-accurate hp-adaptive finite element method. Results of this study demonstrate that the electric field generated within the circular Petri dish is non-homogeneous, and thus, a better shape, size, or location of the dish is needed to achieve an equally distributed radiation enabling the uniform growth of cell cultives.

UV laser-induced high resolution cleaving of Si wafers for micro-nano devices and polymeric waveguide characterization

In this work we propose a method for cleaving silicon-based photonic chips by using a laser based micromachining system, consisting of a ND:YVO4laser emitting at 355 nm in nanosecond pulse regime and a micropositioning system. The laser makes grooved marks placed at the desired locations and directions where cleaves have to be initiated, and after several processing steps, a crack appears and propagate along the crystallographic planes of the silicon wafer. This allows cleavage of the chips automatically and with high positioning accuracy, and provides polished vertical facets with better quality than the obtained with other cleaving process, which eases the optical characterization of photonic devices. This method has been found to be particularly useful when cleaving small-sized chips, where manual cleaving is hard to perform; and also for polymeric waveguides, whose facets get damaged or even destroyed with polishing or manual cleaving processing. Influence of length of the grooved line and speed of processing is studied for a variety of silicon chips. An application for cleaving and characterizing sol–gel waveguides is presented. The total amount of light coupled is higher than when using any other procedure.

Electromagnetic analysis of periodic structures under a waveguide viewpoint

The fundamental objective of this Ph. D. dissertation is to demonstrate that, under particular circumstances which cover most of the structures with practical interest, periodic structures can be understood and analyzed by means of closed waveguide theories and techniques. To that aim, in the first place a transversely periodic cylindrical structure is considered and the wave equation, under a combination of perfectly conducting and periodic boundary conditions, is studied. This theoretical study runs parallel to the classic analysis of perfectly conducting closed waveguides. Under the light shed by the aforementioned study it is clear that, under certain very common periodicity conditions, transversely periodic cylindrical structures share a lot of properties with closed waveguides. Particularly, they can be characterized by a complete set of TEM, TE and TM modes. As a result, this Ph. D. dissertation introduces the transversely periodic waveguide concept. Once the analogies between the modes of a transversely periodic waveguide and the ones of a closed waveguide have been established, a generalization of a well-known closed waveguide characterization method, the generalized Transverse Resonance Technique, is developed for the obtention of transversely periodic modes. At this point, all the necessary elements for the consideration of discontinuities between two different transversely periodic waveguides are at our disposal. The analysis of this type of discontinuities will be carried out by means of another well known closed waveguide method, the Mode Matching technique. This Ph. D. dissertation contains a sufficient number of examples, including the analysis of a wire-medium slab, a cross-shaped patches periodic surface and a parallel plate waveguide with a textured surface, that demonstrate that the Transverse Resonance Technique - Mode Matching hybrid is highly precise, efficient and versatile. Thus, the initial statement: ”periodic structures can be understood and analyzed by means of closed waveguide theories and techniques”, will be corroborated. Finally, this Ph. D. dissertation contains an adaptation of the aforementioned generalized Transverse Resonance Technique by means of which the analysis of laterally open periodic waveguides, such as the well known Substrate Integrated Waveguides, can be carried out without any approximation. The analysis of this type of structures has suscitated a lot of interest in the recent past and the previous analysis techniques proposed always resorted to some kind of fictitious wall to close the structure. vii Resumen El principal objetivo de esta tesis doctoral es demostrar que, bajo ciertas circunstancias que se cumplen para la gran mayoría de estructuras con interés práctico, las estructuras periódicas se pueden analizar y entender con conceptos y técnicas propias de las guías de onda cerradas. Para ello, en un primer lugar se considera una estructura cilíndrical transversalmente periódica y se estudia la ecuación de onda bajo una combinación de condiciones de contorno periódicas y de conductor perfecto. Este estudio teórico y de caracter general, sigue el análisis clásico de las guías de onda cerradas por conductor eléctrico perfecto. A la luz de los resultados queda claro que, bajo ciertas condiciones de periodicidad (muy comunes en la práctica) las estructuras cilíndricas transversalmente periódicas guardan multitud de analogías con las guías de onda cerradas. En particular, pueden ser descritas mediante un conjunto completo de modos TEM, TE y TM. Por ello, ésta tesis introduce el concepto de guía de onda transversalmente periódica. Una vez establecidas las similitudes entre las soluciones de la ecuación de onda, bajo una combinación de condiciones de contorno periódicas y de conductor perfecto, y los modos de guías de onda cerradas, se lleva a cabo, con éxito, la adaptación de un conocido método de caracterización de guías de onda cerradas, la técnica de la Resonancia Transversal Generalizada, para la obtención de los modos de guías transversalmente periódicas. En este punto, se tienen todos los elementos necesarios para considerar discontinuidades entre guías de onda transversalmente periódicas. El analisis de este tipo de discontinuidades se llevará a cabo mediante otro conocido método de análisis de estructuras cerradas, el Ajuste Modal. Esta tesis muestra multitud de ejemplos, como por ejemplo el análisis de un wire-medium slab, una superficie de parches con forma de cruz o una guía de placas paralelas donde una de dichas placas tiene cierta textura, en los que se demuestra que el método híbrido formado por la Resonancia Transversal Generalizada y el Ajuste Modal, es tremendamente preciso, eficiente y versátil y confirmará la validez de el enunciado inicial: ”las estructuras periódicas se pueden analizar y entender con conceptos y técnicas propias de las guías de onda cerradas” Para terminar, esta tésis doctoral incluye también una modificación de la técnica de la Resonancia Transversal Generalizada mediante la cual es posible abordar el análisis de estructuras periódica abiertas en los laterales, como por ejemplo las famosas guías de onda integradas en sustrato, sin ninguna aproximación. El análisis de este tipo de estructuras ha despertado mucho interés en los últimos años y las técnicas de análisis propuestas hasta ix el momento acostumbran a recurrir a algún tipo de pared ficticia para simular el carácter abierto de la estructura.

Propagation Mechanism modeling in the Near-Region of Arbitrary Cross-Sectional Tunnels.

Along with the increase of the use of working frequencies in advanced radio communication systems, the near-region inside tunnels lengthens considerably and even occupies the whole propagation cell or the entire length of some short tunnels. This paper analytically models the propagation mechanisms and their dividing point in the near-region of arbitrary cross-sectional tunnels for the first time. To begin with, the propagation losses owing to the free space mechanism and the multimode waveguide mechanism are modeled, respectively. Then, by conjunctively employing the propagation theory and the three-dimensional solid geometry, the paper presents a general model for the dividing point between two propagation mechanisms. It is worthy to mention that this model can be applied in arbitrary cross-sectional tunnels. Furthermore, the general dividing point model is specified in rectangular, circular, and arched tunnels, respectively. Five groups of measurements are used to justify the model in different tunnels at different frequencies. Finally, in order to facilitate the use of the model, simplified analytical solutions for the dividing point in five specific application situations are derived. The results in this paper could help deepen the insight into the propagation mechanisms in tunnels.

Circuital model for the spherical geodesic waveguide perfect drain

The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering.

Analysis of Super Imaging Properties of Spherical Geodesic Waveguide Using COMSOL Multyphisics

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit using materials of negative dielectric and magnetic constants. Recently, two devices with positive refraction, the Maxwell Fish Eye lens (MFE) (Leonhardt et al 2000) and the Spherical Geodesic Waveguide (SGW)(Minano et all 2011) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Moreover, recent analysis of the SGW with defined object and image surfaces, which are both conical sections of the sphere, has shown that the system transmits images bellow diffraction limit. The key assumption is the use of a perfectly absorbing receptor called perfect drain. This receptor is capable to absorb all the radiation without reflection or scattering. Here, it is presented the COMSOL analysis of the SGW using a perfect drain that absorbs perfectly two modes. The design procedure for PD capable to absorb k modes is proposed, as well.

COMSOL Multyphisics Super Resolution Analysis of a Spherical Geodesic Waveguide Suitable for Manufacturing

Recently it has been proved theoretically (Miñano et al, 2011) that the super-resolution up to ?/500 can be achieved using an ideal metallic Spherical Geodesic Waveguide (SGW). This SGW is a theoretical design, in which the conductive walls are considered to be lossless conductors with zero thickness. In this paper, we study some key parameters that might influence the super resolution properties reported in (Miñano et al, 2011), such as losses, metal type, the thickness of conductive walls and the deformation from perfect sphere. We implement a realistic SGW in COMSOL multiphysics and analyze its super-resolution properties. The realistic model is designed in accordance with the manufacturing requirements and technological limitations.

Super resolution using a modified Spherical Geodesic Waveguide suitable for manufacturing

The previous publications (Miñano et al, 2011) have shown that using a Spherical Geodesic Waveguide (SGW), it can be achieved the super-resolution up to ? /500 close to a set of discrete frequencies. These frequencies are directly connected with the well-known Schumann resonance frequencies of spherical symmetric systems. However, the Spherical Geodesic Waveguide (SGW) has been presented as an ideal system, in which the technological obstacles or manufacturing feasibility and their influence on final results were not taken into account. In order to prove the concept of superresolution experimentally, the Spherical Geodesic Waveguide is modified according to the manufacturing requirements and technological limitations. Each manufacturing process imposes some imperfections which can affect the experimental results. Here, we analyze the influence of the manufacturing limitations on the super-resolution properties of the SGW. Beside the theoretical work, herein, there has been presented the experimental results, as well.

Perfect imaging analysis of the spherical geodesic waveguide

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to ?/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.

Rectangular room dimensions estimation using narrowband signal and sectorized antennas

A system for estimation of unknown rectangular room dimensions based on two radio transceivers, both capable of full duplex operations, is presented. The approach is based on CIR measurements taken at the same place where the signal is transmitted (generated), commonly known as self- to-self CIR. Another novelty is the receiver antenna design which consists of eight sectorized antennas with 45° aperture in the horizontal plane, whose total coverage corresponds to the isotropic one. The dimensions of a rectangular room are reconstructed directly from radio impulse responses by extracting the information regarding features like round trip time, received signal strength and reverberation time. Using radar approach the estimation of walls and corners positions are derived. Additionally, the analysis of the absorption coefficient of the test environment is conducted and a typical coefficient for office room with furniture is proposed. Its accuracy is confirmed through the results of volume estimation. Tests using measured data were performed, and the simulation results confirm the feasibility of the approach.

Self-positioning and mapping of rectangular rooms with sectorized narrowband antennas

A system for simultaneous 2D estimation of rectangular room and transceiver localization is proposed. The system is based on two radio transceivers, both capable of full duplex operations (simultaneous transmission and reception). This property enables measurements of channel impulse response (CIR) at the same place the signal is transmitted (generated), commonly known as self-to-self CIR. Another novelty of the proposed system is the spatial CIR discrimination that is possible with the receiver antenna design which consists of eight sectorized antennas with 45° aperture in the horizontal plane and total coverage equal to the isotropic one. The dimensions of a rectangular room are reconstructed directly from spatial radio impulse responses by extracting the information regarding round trip time (RTT). Using radar approach estimation of walls and corners positions is derived. Tests using measured data were performed, and the simulation results confirm the feasibility of the approach.

Extreme super-resolution using the spherical geodesic waveguide

Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 superresolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ/500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.