Gaussian Beam Microwave Antennas in Quasi-Optical Systems for Wireless Power Transmission

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Gaussian Beam Microwave Antennas in Quasi-Optical Systems for Wireless Power Transmission Faculty of Sciences and Technology Department of Physics Gaussian Beam Microwave Antennas in Quasi-optical Systems for Wireless Power Transmission Ricardo Andr´eMendes Pereira Dissertation submitted for the degree of Master of Physics Engineering September, 2017 Gaussian Beam Microwave Antennas in Quasi-optical Systems for Wireless Power Transmission Dissertation submitted for the Master's degree in Physics Engineering in the specialisation of Instrumen- tation, in the Physics Department of the Faculty of Sci- ences and Technology of the University of Coimbra. Supervisors: Prof. Nuno Borges Carvalho, University of Aveiro, Institute of Telecommunica- tions; Prof. Jos´ePinto da Cunha, University of Coimbra, Physics Department. Ricardo Andr´eMendes Pereira Coimbra, September 2017 Work done in collaboration with: Acknowledgements Depois de estes longos e calorosos anos na Universidade de Coimbra, ´echegada a al- tura da despedida, poss´ıvel apenas gra¸cas`aquelesque me rodeiam. Houve momentos altos e baixos, mas o que importa ´eque tudo passou e ficam as mem´oriasde tempos espetaculares. No entanto, o fim desta etapa marca muito mais do que o fim da vida de estudante universit´ario.Quero, portanto, aproveitar para fazer chegar uma palavra de carinho aos meus mais queridos. Em primeiro lugar, a todos os meus professores, um grande abra¸coe beijinho! (Nany, o que seria da minha matem´atica sem ti!). Em especial para esta disserta¸c~ao,n~aopodia deixar de real¸caros meus orientadores. Prof. Nuno Borges Carvalho, pela disponi- bilidade em acolher e confiar em mim para este projeto. Prof. Jos´ePinto da Cunha n~aosabe como apreciei as tardes (e por vezes noites) passadas a discutir f´ısica. Ainda neste assunto, agrade¸coao pessoal do IT Aveiro pela ajuda que todos prestaram, em particular ao Daniel Belo pela ajuda na orienta¸c~aono IT desde os almo¸cosao CST. Aos t´ecnicosque tanto me facilitarem o acesso `asferramentas necess´ariaspara avan¸car cada etapa e em especial ao Hugo Mostardinha um agradecimento pela preciosa ajuda, mesmo em alturas de afli¸c~ao,e pela contacto com a empresa Famaval. A estes ´ultimos, todo o sucesso do mundo, garanto que os espelhos ser~aousados ´unicae exclusivamente para aquilo a que foram desenhados. A todos os meus amigos, n~aome vou alongar, um enorme abra¸co.Acabou a fase ermita, prometo! Dr. Joaquim Mira, um abra¸coespecial por me incutir o valor do trabalho desde a tenra idade. E, como n~aopodia deixar de ser, o melhor para o fim. Meus pais, obrigado por todo o amor, apoio e dedica¸c~aoque sempre demonstraram, por vezes bem sei que a muito a custo (n~ao´ef´acil),e Vasco e Francisco, por me trazerem `aterra e simplesmente estarem sempre l´a. Finalmente, Patr´ıcia. Es´ bem capaz de ter sofrido mais do que toda a gente com este trabalho, talvez at´emais do que eu, mas apesar disso sempre me apoiaste. Por isso agrade¸co-tedo fundo do meu cora¸c~ao. Que aproveitemos para estar juntos. Obrigado por tudo. Beij~aoenorme fofinha! i iii Resumo Atrav´esde ferramentas quasi-´oticas,a an´alisede um sistema composto por dois refletores parab´olicosfoi feita com o objetivo de transferir energia sem fios, usando micro-ondas (`afrequ^enciade 5.8 GHz). Primeiramente desenvolveram-se scripts com duas principais finalidades: visualizar a frente de onda dos feixes gaussianos para diferentes modos de propaga¸c~ao,tanto em coordenadas retangulares como em cil´ındricase a propaga¸c~aode feixe gaussiano atrav´es de um sistema (composto por refletores ou lentes). Depois de se efetuar este estudo, recorreu-se a uma an´alisete´orica com o intuito de permitir a prototipagem do sistema usando o m´ınimopar^ametrosposs´ıvel. Foi poss´ıvel simplificar a an´aliseatrav´esda utiliza¸c~aodo princ´ıpioda reciprocidade, ao igualar os dois espelhos e as antenas (emissora e recetora). Conseguiu-se chegar a um conjunto de equa¸c~oesque cumprem o objetivo. De seguida concretizou-se o sistema com base nos resultados anteriores por forma a efetuar experi^enciaslaboratoriais, com vista na valida¸c~aoda teoria. A antena escolhida para emissor e recetor de radia¸c~aoforam s~aodo tipo corneta circular de superf´ıcie plana, uma vez que estas oferecem uma maior aproxima¸c~aoda radia¸c~aoemitida a um feixe gaussiano, juntamente com uma relativa facilidade de constru¸c~ao.Ap´oso desenho e simula¸c~aoda antena, juntamente com o guia de ondas e o conetor SMA que a alimenta, utilizando um software CAD, CST Studio Suite, prosseguiu-se `asua constru¸c~ao.Tal foi feito numa impressora 3D, em 4 partes, seguido da colagem de fita de cobre como material condutor da antena. Foi necess´arioencomendar conetores SMA espec´ıficos,procedendo- se de seguida `amedi¸c~aodos par^ametrosprincipais da antena. Tendo concluindo que os resultados foram positivos, procedeu-se `aconstru¸c~aoda segunda antena. Por outro lado, foi poss´ıvel obter dois espelhos parab´olicos,juntamente com os suportes necess´arios, atrav´esda empresa Famaval. Finalmente, utilizando um gerador de sinal e um analisador de espetro, efetuou-se uma experi^enciapreliminar de transfer^enciade energia de uma antena para a outra. Os resul- tados n~aoforam satisfat´otiospelo que existe de efetuar um varrimento dos par^ametros mais completo. A dificuldade de alinhamento dos diferentes componentes do sistema ´e apontado como o principal fator pela principal perda de efici^encia. Este estudo apresenta m´etodos de an´aliseque possibilitam rapidamente prototipar sis- temas de transfer^enciade energia por microondas, compostos por dois componentes que permitem a aplica¸c~aodo princ´ıpioda reciprocidade. v Abstract Using the quasi-optical formalism a double parabolic reflector system was analysed in order to achieve Wireless Power Transfer, using Microwaves (at the frequency of 5.8 GHz). Firstly, scripts were developed with two main goals: the visualisation of the gaussian beam wave fronts for different modes of propagation, in both rectangular and cylindrical coordinates, and the propagation of gaussian beams throughout a system (composed of either mirrors or lenses). After this analysis a theoretical approach is made to arrive at a way to quickly prototype the system, using the minimum parameters possible. The use of the reciprocity principle to simplify this analysis can be done by simply making both reflectors and antennas (emitting and receiving) equal. A set of equations were derived, which serve this purpose. A system set-up based on the results obtained was made with the objective of setting up a lab experiment, so as to validate the theory. The chosen antenna for the emitter and receiver was a smooth surface conical antenna for having the radiation pattern best approximated to that of a gaussian beam while remaining relatively easy to build. After designing and simulating the antenna, as well as the waveguide and the SMA connector which feed it, in a CAD software, CST Studio Suite, the antenna was built. It was done on a 3D printer, in 4 parts, followed by the gluing of copper tape as the antenna's conducting material. It was necessary to order the specific SMA connectors for this antenna. After their arrival, the main parameters of the antenna were measured with positive results. Because of it, the second antenna was built and measured in the same way. On the other hand, it was possible to obtained the parabolic reflectors, along with the necessary supports, from the company Famaval. Finally, using a signal generator and a spectrum analyser, a preliminary experiment of power transfer from one antenna to other was performed. The results were not satisfactory, for which a more thorough parameter sweep is necessary. The difficulty in aligning the different system's components is pointed as the main factor for the major efficiency loss. In this study one can find analysis tools that allow for fast prototyping of systems for power transfer through microwaves, made up of two components that respect the reciprocity principle. Contents Acknowledgements i Resumo iii Abstract v List of Figures ix List of Tables xi Listings xiii 1 Introduction 1 1.1 Background and Motivation . .1 1.2 History and State-of-the-art . .2 1.3 Structure . .3 2 Electromagnetism 5 2.1 Particles and Electric Charges . .5 2.2 Maxwell's Equations . .6 2.2.1 Gauss's Electric Law . .6 2.2.2 Amp`ere'sLaw and Maxwell's Correction . .7 2.2.3 Faraday's Law . .8 2.2.4 Gauss's Magnetic Law . .9 2.2.5 Continuity Equation and Lorentz Force Law . .9 2.2.6 Summary . .9 2.3 Electromagnetic Radiation . 11 2.3.1 Electromagnetic Spectrum and Why Microwaves . 11 3 Quasi-Optics 13 3.1 Gaussian Beam Formalism . 13 3.1.1 Paraxial Approximation . 14 3.1.2 Beam Parameters . 15 3.1.3 Near and Far Field Regions . 18 3.2 Higher Order Modes . 19 3.2.1 Higher Order Modes in Cylindrical Coordinates . 19 3.2.2 Higher Order Modes in Rectangular Coordinates . 20 3.3 Beam Transformation . 21 3.3.1 Rays, Matrices and the Complex Beam Parameter . 22 vii viii CONTENTS 4 Graphical Representation Scripts 25 4.1 Initialisation . 25 4.2 Wave Front . 26 4.3 Beam Propagation and Transformation . 28 4.3.1 Cell Array . 28 4.3.2 Arrays for Storing Quantity Values . 29 4.3.3 Main Loop . 30 5 Double Reflector Quasi-optical System Analysis and Results 33 5.1 Maximum Distance Between Mirrors . 36 5.2 Focal Length . 37 5.3 Beam in the Far-Field (Region 1, where L d2 =z )............ 38 ≈ in c 5.4 Beam in the Near-Field (Region 2, where L z ).............. 39 ≈ c 5.5 Paraxial Limit .
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