Presented in this thesis are the following experimental and theoretical investigations carried out on the three-layer electromagnetically coupled (EMC) circular microstrip antennas and their arrays. 1.Three-Layer EMC Circular Microstrip Antenna A three-layer EMC circular microstrip antenna consists of a probe-fed circular microstrip patch having two parasitically excited circular microstrip patches (without ground planes) stacked above it, with air gaps in between successive substrates. In the "inverted" configuration, the parasitic patches are on the lower (nearer to the driven substrate) surface of the substrate. An exhaustive experimental study of the resonant frequencies, input impedance, impedance bandwidth and radiation characteristics of this antenna, has been carried out for both the "normal" and the "inverted" configurations. Based on this experimental study, the design and optimisation of the antenna have been discussed and experimentally tested. In the S-band, it is found that an impedance bandwidth as high as 20 percent coupled with good patterns, high gain and low cross-polarisation levels, have been obtained. 2.Three-Layer EMC Circular Microstrip Antenna Arrays Experimental work has also been carried out on linear arrays of three-layer EMC circular microstrip antennas. The design of a linear array both in the E- and H- planes, of the three-layer microstrip antennas in their "normal" as well as "inverted" configurations, has been discussed and realisation carried out. Impedance bandwidths of the arrays have been experimentally found to be the same as that of the three-layer antenna element High gain and good pattern shape with sidelobes as well as cross-polarisation levels better than -20 dB through a scan angle of 40°, have been realised. A study of the mutual coupling between two-layer as well as three-layer EMC circular patch elements has also been carried out for the useful range of interelement spacings. 3.Theoretical Analysis of Resonant Frequencies of Multilayer Patch Structures Theoretical investigations have been carried out on the resonance properties of single-layer and multilayer EMC patch structures employing the full-wave analysis based on spectral domain immittance approach. The impedance Green's functions for all these structures have been derived from the combination of equivalent transverse transmission lines concept Galerkin's method is employed in the spectral (Hankel) transform domain where two sets of disk current expansions are used for obtaining die characteristic equation. By solving the characteristic equation, the resonant frequencies are obtained for various values of the parameters of the layered antenna.

This thesis presents solutions and studies related to the design of wideband antennas for wireless handheld terminal applications. A method of electrically shortening the terminal chassis length to obtain resonance at high frequencies has been proposed and evaluated, thereby increasing the antennas impedance bandwidth. No significant effect on the lower frequency band in a dual-band antenna prototype has been observed, making the method suitable for multi-band applications. The chassis has further been utilized as a zero-thickness 0.9 - 2.7 GHz high efficiency antenna by inserting a notch in the chassis center, and a feasibility study for typical phones has been performed. Additionally, the effect of talk position on the chassis wave-mode has been investigated, where the standard equivalent circuit model for terminal antennas has been modified to include the presence of the users head. The model has been used to explain measured and simulated effects concerning frequency detuning, efficiency reduction and bandwidth enhancements when the terminal is placed in talk position. The use of a hands-free earpiece cord is currently mandatory for FM radio reception as the cord is utilized as antenna. However, there is currently a market driven demand for removing the cord requirement since many modern phones are equipped with speakers and Bluetooth headsets. In this thesis, an active ferrite loop antenna is proposed as an internal replacement/complement with a performance of -23 dB (G/T degradation) compared to a full-size lossless dipole in urban environments. Also, a modification to the cord is suggested for DVB H reception. Complex matching networks have been investigated to increase the bandwidth of dual band PIFA antennas, and a printed dual band dipole has been integrated with a modified Marchand balun for dual resonance at two separate frequency bands, thus covering the commercial cellular bands 824-960 and 1710-2170 MHz with a single antenna.

<p>This thesis presents solutions and studies related to the design of wideband antennas for wireless handheld terminal applications. A method of electrically shortening the terminal chassis length to obtain resonance at high frequencies has been proposed and evaluated, thereby increasing the antennas impedance bandwidth. No significant effect on the lower frequency band in a dual-band antenna prototype has been observed, making the method suitable for multi-band applications. The chassis has further been utilized as a zero-thickness 0.9 - 2.7 GHz high efficiency antenna by inserting a notch in the chassis center, and a feasibility study for typical phones has been performed. Additionally, the effect of talk position on the chassis wave-mode has been investigated, where the standard equivalent circuit model for terminal antennas has been modified to include the presence of the users head. The model has been used to explain measured and simulated effects concerning frequency detuning, efficiency reduction and bandwidth enhancements when the terminal is placed in talk position.</p><p>The use of a hands-free earpiece cord is currently mandatory for FM radio reception as the cord is utilized as antenna. However, there is currently a market driven demand for removing the cord requirement since many modern phones are equipped with speakers and Bluetooth headsets. In this thesis, an active ferrite loop antenna is proposed as an internal replacement/complement with a performance of -23 dB (G/T degradation) compared to a full-size lossless dipole in urban environments. Also, a modification to the cord is suggested for DVB H reception.</p><p>Complex matching networks have been investigated to increase the bandwidth of dual band PIFA antennas, and a printed dual band dipole has been integrated with a modified Marchand balun for dual resonance at two separate frequency bands, thus covering the commercial cellular bands 824-960 and 1710-2170 MHz with a single antenna.</p>

In this study we tried to design a microstrip antenna, to get a suitable radiation pattern for a LEO satellite. Our aim is to get a radiation pattern that has a maximum power which is not in the broadside direction to the antenna surface / instead broadside radiation has a relatively lower power density. Maximum power radiation is desired to be at about 30 &ndash / 50 degrees angle beyond the normal to the antenna surface. We desire circularly polarized radiation. We used two concentric antennas / one is a circular patch at the center and the other is an annular ring which is used at the outer region. By using Ansoft Ensemble 8.0 software, we design an antenna which has a resonance frequency at 8.2 GHz. Using the result of the program we design the real antenna. The measurement results are compared with the simulation results.

Method of Moments (MoM)/Green&rsquo / s function formulation is developed for the analysis of electromagnetic radiation from planar rectangular microstrip antennas with different feeding techniques. Investigated structures are microstrip line fed patch antenna, proximity coupled patch antenna and slot coupled patch antenna. For all these structures equivalent problems are defined. Then, integral equations where currents are the unknowns are obtained from boundary conditions and by using spectral domain representation of Green&rsquo / s functions. Finally, MoM is applied to convert these integral equations to a system of linear equations. Currents on the conducting surfaces as well as equivalent magnetic currents on the apertures are modeled as a sum of piecewise sinusoidal subdomain basis functions with unknown coefficients which are calculated by solving the system of linear equations. Based on the formulations provided in this study, a Fortran code is developed. Numerical results calculated by using the code are presented in the form of patch and line currents and input impedances. Presented results are in good agreement with the results given in the literature.

Wideband and dual band stacked microstrip patch antennas are investigated for the new wideband and dual band applications in the area of telecommunications. In this thesis, aperture-coupled stacked patch antennas are used to increase the bandwidth of the microstrip patch antenna. By this technique, antennas with 51% bandwidth at 6.1 GHz and 43% bandwidth at 8 GHz satisfying S11&lt / -15 dB are designed, manufactured and measured. A dual-band aperture coupled stacked microstrip patch antenna operating at 1.8 GHz with 3.8% bandwidth and at 2.4 GHz with 1.6% bandwidth is designed, produced and measured for mobile phone and WLAN applications. In addition, an aperture coupled stacked microstrip patch antenna which operates at PCS frequencies in 1.7-1.95 GHz band is designed. Dual and circularly polarized stacked aperture coupled microstrip patch antennas are also investigated. A triple band dual polarized aperture coupled stacked microstrip patch antenna is designed to operate at 900 MHz, at 1.21 GHZ and at 2.15 GHz. Mutual coupling between aperture coupled stacked microstrip patch antennas are examined and compared with the coupling of aperture coupled microstrip patch antennas

Submitted by Lara Oliveira (lara@ufersa.edu.br) on 2017-07-14T18:14:07Z No. of bitstreams: 1 JonasRSS_DISSERT.pdf: 2555775 bytes, checksum: 1cffc3792b8fe12b4067e7bc74ee127d (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-18T15:08:15Z (GMT) No. of bitstreams: 1 JonasRSS_DISSERT.pdf: 2555775 bytes, checksum: 1cffc3792b8fe12b4067e7bc74ee127d (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-18T15:11:33Z (GMT) No. of bitstreams: 1 JonasRSS_DISSERT.pdf: 2555775 bytes, checksum: 1cffc3792b8fe12b4067e7bc74ee127d (MD5) / Made available in DSpace on 2017-07-18T15:11:41Z (GMT). No. of bitstreams: 1 JonasRSS_DISSERT.pdf: 2555775 bytes, checksum: 1cffc3792b8fe12b4067e7bc74ee127d (MD5) Previous issue date: 2016-12-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The antennas in nano-metric scales are part of a line of research that has been gaining strength in recent years, being the target of numerous studies and publications in several universities in Brazil and around the world. Nano antennas are characterized as a promising new branch in the development of devices capable of being applied in different areas, in addition to communication. Occupying a prominent place in the new era of technologies, the nano antennas, here restricted only to dipole and microstrip, generate enormous expectations about this new revolution, not only between researchers, but also in a part of society. Currently, wireless communications require that radiator devices have wide bandwidth and miniaturization for mobile devices, so this dissertation discusses the potential application of antennas for communications in the frequency range in Terahertz. At these frequencies, there are numerous restrictions on the propagation of signals, so high performance antenna are necessary to allow communication with reduced losses. The purpose of this work is to study some configurations and types of antennas, such as microstrip antenna and dipole antenna, with application in the subterahertz frequency, which can be used, for example, in internal networks, medicine, photovoltaic power generation, spectroscopy, near-field microscopy and high quality images. Some configurations of antennas with various materials for communications in the frequency range will be presented to verify the feasibility of the use of nano dipole antennas and miniaturized microstrip antennas in this type of application. The methodology adopted suggests the comparison of the simulated results, through the software Ansoft HFSS ® and CST Microwave Studio ®, with the results of other published works / As antenas em escalas nanométrica fazem parte de uma linha de pesquisa que vem aumentando nos últimos anos, sendo alvo de inúmeros estudos e publicações. As nanoantenas caracterizam-se como um novo e promissor ramo no desenvolvimento de dispositivos capazes de ser aplicados em diferentes áreas, além da comunicação. Ocupando lugar de destaque na nova era das tecnologias, as nanoantenas, aqui restritas somente as de dipolo e microfita, geram enorme expectativas. Atualmente as comunicações sem fio requer que os dispositivos radiadores possuam uma ampla largura de banda e miniaturização para dispositivos móveis, assim, essa dissertação discute a aplicação potencial de antenas para comunicações na faixa de frequência em Terahertz. Nessas frequências existem inúmeras restrições na propagação de sinais, então antenas com alto rendimento são necessárias para permitir comunicação com perdas reduzidas. A proposta desse trabalho é estudar algumas configurações e tipos de antenas, tais como de antena de microfita e antena dipolo, com aplicação na faixa de frequência em subterahertz, que podem ser utilizadas, por exemplo, nas redes internas, medicina, na geração de energia fotovoltaica, espectroscopia, microscopia de campo próximo e obtenção de imagens de alta qualidade. Serão apresentadas algumas configurações de antenas e com diversos materiais para comunicações na faixa de frequência em questão, para verificar a viabilidade do uso de nanoantenas de dipolo e de antenas de microfita miniaturizadas neste tipo de aplicação. A metodologia adotada sugere a comparação dos resultados simulados, através dos softwares Ansoft HFSS ® e CST Microwave Studio ®, com os resultados de outros trabalhos publicados / 2017-07-14

Made available in DSpace on 2014-12-17T14:54:59Z (GMT). No. of bitstreams: 1 ElderECO_TESE_Capa_ate_pag86.pdf: 3877192 bytes, checksum: d9b068e5eaa76a69d5a1fa1f245dbc5d (MD5) Previous issue date: 2011-09-02 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The search for ever smaller device and without loss of performance has been increasingly investigated by researchers involving applied electromagnetics. Antennas using ceramics materials with a high dielectric constant, whether acting as a substract element of patch radiating or as the radiant element are in evidence in current research, that due to the numerous advantages offered, such as: low profile, ability to reduce the its dimensions when compared to other devices, high efficiency of ratiation, suitability the microwave range and/or millimeter wave, low temperature coefficient and low cost. The reason for this high efficiency is that the dielectric losses of ceramics are very low when compared to commercially materials sold used in printed circuit boards, such as fiberglass and phenolite. These characteristics make ceramic devices suitable for operation in the microwave band. Combining the design of patch antennas and/or dielectric resonator antenna (DRA) to certain materials and the method of synthesis of these powders in the manufacture of devices, it s possible choose a material with a dielectric constant appropriate for the design of an antenna with the desired size. The main aim of this work is the design of patch antennas and DRA antennas on synthesis of ceramic powders (synthesis by combustion and polymeric precursors - Pe- chini method) nanostructured with applications in the microwave band. The conventional method of mix oxides was also used to obtain nanometric powders for the preparation of tablets and dielectric resonators. The devices manufactured and studied on high dielectric constant materials make them good candidates to have their small size compared to other devices operating at the same frequency band. The structures analyzed are excited by three different techniques: i) microstrip line, ii) aperture coupling and iii) inductive coupling. The efficiency of these techniques have been investigated experimentally and compared with simulations by Ansoft HFSS, used in the accurate analysis of the electromagnetic behavior of antennas over the finite element method (FEM). In this thesis a literature study on the theory of microstrip antennas and DRA antenna is performed. The same study is performed about the materials and methods of synthesis of ceramic powders, which are used in the manufacture of tablets and dielectric cylinders that make up the devices investigated. The dielectric media which were used to support the analysis of the DRA and/or patch antennas are analyzed using accurate simulations using the finite difference time domain (FDTD) based on the relative electrical permittivity (er) and loss tangent of these means (tand). This work also presents a study on artificial neural networks, showing the network architecture used and their characteristics, as well as the training algorithms that were used in training and modeling some parameters associated with the devices investigated / A busca por dispositivos cada vez menores e sem perda de desempenho vem sendo cada dia mais investigada pelos pesquisadores da ?rea envolvendo eletromagnetismo apli- cado. Antenas utilizando materiais cer?micos com uma alta constante diel?trica, sejam elas atuando como substrato do elemento patch radiante ou como sendo o pr?prio ele- mento radiante est?o em evid?ncia nas pesquisas atuais, isso devido ?s in?meras vantagens que apresentam, tais como: baixo perfil, capacidade de redu??o de suas dimens?es (quando comparado a outros dispositivos), alta efici?ncia de radia??o, adequabilidade a faixa de micro-ondas e/ou ondas milim?tricas, baixo coeficiente de temperatura e baixo custo. A raz?o para essa alta efici?ncia ? que as perdas diel?tricas das cer?micas s?o muito baixas, quando comparadas ?s dos materiais comercialmente usados em placas de circuito impresso, tais como: fibra de vidro e fenolite. Essas caracter?sticas tornam os dispositivos cer?micos adequados para operar na faixa de micro-ondas. Aliando o projeto de antenas patch e/ou antenas ressoadoras diel?tricas (DRA) ao uso de certos materiais e ao m?todo de s?ntese desses p?s na fabrica??o dos dispositivos, ? poss?vel escolher um material com uma determinada constante diel?trica para o projeto de uma antena com o tamanho desejado. O objetivo principal deste trabalho consiste no projeto de antenas patches e antenas DRA sob s?ntese de p?s cer?micos (s?ntese por combust?o e por precursores polim?ricos - m?todo Pechini) nanoestruturados para aplica??es na faixa de micro-ondas. O m?todo convencional de mistura de ?xidos tamb?m foi utilizado na obten??o de p?s nanom?tricos para a confec??o das pastilhas e ressoadores diel?tricos. Os dispositivos fabricados e estudados sobre materiais de alta constante diel?trica os tornam bons candidatos ? fabrica??o de dispositivos e circuitos de dimens?es reduzidas quando comparado aos outros dispositivos tradicionais operando na mesma faixa de frequ?ncia. As estruturas analisadas s?o excitadas por tr?s diferentes t?cnicas: i) linha de microfita, ii) acoplamento por abertura e iii) acoplamento indutivo. A efici?ncia dessas t?cnicas de alimenta??o s?o investigadas experimentalmente e comparada com simula??es realizadas pelo Ansoft HFSS, utilizado na an?lise precisa do comportamento eletromagn?tico das antenas atrav?s do m?todo dos elementos finitos (FEM). Nesta tese um estudo bibliogr?fico sobre teoria de antenas de microfita e antenas DRA ? realizado. O mesmo estudo ? realizado a respeito dos materiais e dos m?todos de s?ntese dos p?s cer?micos que s?o utilizados na fabri- ca??o das pastilhas e dos cil?ndros diel?tricos que compor?o os dispositivos investigados. Os meios diel?tricos os quais serviram de suporte na an?lise das antenas patch e/ou DRA s?o analisados atrav?s de simula??es precisas utilizando o m?todo das diferen?as finitas no dom?nio do tempo (FDTD) com base na permissividade el?trica relativa (er) e tangente de perda desses meios (tand). Este trabalho ainda apresenta um estudo em redes neurais artificiais, evidenciando a arquitetura de rede utilizada e suas caracter?sticas, bem como os algoritmos de treinamento que foram usados no treinamento e na modelagem de alguns par?metros associados aos dispositivos investigados

Made available in DSpace on 2014-12-17T14:55:10Z (GMT). No. of bitstreams: 1 ElderECO.pdf: 2183610 bytes, checksum: d02ab6a3abf8c0cd3e77eadf92d529a0 (MD5) Previous issue date: 2008-12-03 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The microstrip antennas are in constant evidence in current researches due to several advantages that it presents. Fractal geometry coupled with good performance and convenience of the planar structures are an excellent combination for design and analysis of structures with ever smaller features and multi-resonant and broadband. This geometry has been applied in such patch microstrip antennas to reduce its size and highlight its multi-band behavior. Compared with the conventional microstrip antennas, the quasifractal patch antennas have lower frequencies of resonance, enabling the manufacture of more compact antennas. The aim of this work is the design of quasi-fractal patch antennas through the use of Koch and Minkowski fractal curves applied to radiating and nonradiating antenna s edges of conventional rectangular patch fed by microstrip inset-fed line, initially designed for the frequency of 2.45 GHz. The inset-fed technique is investigated for the impedance matching of fractal antennas, which are fed through lines of microstrip. The efficiency of this technique is investigated experimentally and compared with simulations carried out by commercial software Ansoft Designer used for precise analysis of the electromagnetic behavior of antennas by the method of moments and the neural model proposed. In this dissertation a study of literature on theory of microstrip antennas is done, the same study is performed on the fractal geometry, giving more emphasis to its various forms, techniques for generation of fractals and its applicability. This work also presents a study on artificial neural networks, showing the types/architecture of networks used and their characteristics as well as the training algorithms that were used for their implementation. The equations of settings of the parameters for networks used in this study were derived from the gradient method. It will also be carried out research with emphasis on miniaturization of the proposed new structures, showing how an antenna designed with contours fractals is capable of a miniaturized antenna conventional rectangular patch. The study also consists of a modeling through artificial neural networks of the various parameters of the electromagnetic near-fractal antennas. The presented results demonstrate the excellent capacity of modeling techniques for neural microstrip antennas and all algorithms used in this work in achieving the proposed models were implemented in commercial software simulation of Matlab 7. In order to validate the results, several prototypes of antennas were built, measured on a vector network analyzer and simulated in software for comparison / As antenas de microfita est?o em constante evid?ncia nas pesquisas atuais, isso devido ?s in?meras vantagens que apresentam. A geometria fractal aliada ao bom desempenho e comodidade das estruturas planares s?o uma excelente combina??o para projetos e an?lise de estruturas cada vez menores e com caracter?sticas multi-ressonantes e banda larga. Essa geometria tem sido aplicada em antenas tipo patch em microfita para reduzir o seu tamanho e evidenciar o seu comportamento multi-banda. Em compara??o com as antenas em microfita convencionais, as antenas patch quase-fractais apresentam freq??ncias de resson?ncia inferiores, possibilitando a fabrica??o de antenas ainda mais compactas. O objetivo desse trabalho consiste no projeto de antenas patches quase-fractal por meio da utiliza??o de curvas fractais de Koch e Minkowski aplicado ?s margens radiante e n?o-radiante de uma antena inset-fed patch retangular convencional alimentada por linha de microfita com reentr?ncias, inicialmente projetada para a freq??ncia de 2,45 GHz a ser observada. A t?cnica inset-fed ? investigada para o casamento de imped?ncias das antenas fractais, que s?o alimentadas atrav?s de linhas de microfita com reentr?ncias. A efici?ncia dessa t?cnica ? investigada experimentalmente e comparada com simula??es realizadas pelo software comercial Ansoft Designer, usado para a an?lise precisa do comportamento eletromagn?tico das antenas atrav?s do m?todo dos momentos e pelo modelo neural proposto. Nessa disserta??o um estudo bibliogr?fico em teoria de antenas de microfita ? realizado, o mesmo estudo ? realizado a respeito da geometria fractal, dando ?nfase a suas mais diversas formas, t?cnicas de gera??o desses fractais bem como sua aplicabilidade. Este trabalho ainda apresenta um estudo em redes neurais artificiais, evidenciando os tipos/arquitetura de redes utilizadas e suas caracter?sticas, bem como os algoritmos de treinamento que foram utilizados para sua implementa??o. As equa??es dos ajustes dos par?metros para as redes utilizadas nesse trabalho foram deduzidas a partir do m?todo do gradiente. Tamb?m ser? realizada uma investiga??o com ?nfase na miniaturiza??o dessas novas estruturas propostas, indicando o quanto uma antena projetada com contornos fractais ? capaz de miniaturizar uma antena patch retangular convencional. O estudo tamb?m consiste de uma modelagem por meio de redes neurais artificiais dos mais diversos par?metros eletromagn?ticos das antenas quase-fractais. Os resultados apresentados demonstram a excelente capacidade das t?cnicas neurais para modelagem de antenas de microfita, e todos os algoritmos utilizados nesse trabalho na obten??o dos modelos propostos foram implementados no software comercial de simula??o Matlab 7. Com a finalidade de validar os resultados obtidos, v?rios prot?tipos de antenas foram constru?dos, medidos em um analisador de rede vetorial e simulados em software para compara??o

Made available in DSpace on 2014-12-17T14:55:12Z (GMT). No. of bitstreams: 1 ManoelBLA.pdf: 2395577 bytes, checksum: 6394225c6ebbbdad59d4fa162aa97882 (MD5) Previous issue date: 2008-11-19 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This paper presents a theoretical and numerical analysis of the parameters of a rectangular microstrip antenna with metamaterial substrate. The metamaterial (MTM) theory was applied along with Transverse Transmission Line (LTT) method to characterize substrate quantities and obtain the general equations of the electromagnetic fields. A study on metamaterial theory was conducted to obtain the constructive parameters, which were characterized through permittivity and permeability tensors to arrive at a set of electromagnetic equations. Electromagnetic principes are used to obtained parameters such as complex resonance frequency, bandwidth and radiation pattern were then obtained. Different metamaterial and antenna configurations were simulated to miniaturize them physically and increase their bandwidth, the results of which are shown through graphics. The theoretical computational analysis of this work proved to be accurate when compared to other studies, and may be used for other metamaterial devices. Conclusions and suggestions for future work are also proposed / Este trabalho apresenta a an?lise te?rica e num?rica dos par?metros de uma antena de microfita tipo patch retangular sobre substrato metamaterial. Para isso, ? aplicada a teoria de metamateriais - MTM, em conjunto com o m?todo da Linha de Transmiss?o Transversa - LTT, para a caracteriza??o das grandezas do substrato e obten??o das equa??es gerais dos campos eletromagn?ticos. ? realizado um estudo acerca da teoria de metamateriais com o intuito de obter seus par?metros construtivos, os mesmos s?o caracterizados atrav?s de tensores permissividade e permeabilidade. Essa teoria ? aplicada ao m?todo da Linha de Transmiss?o Transversa chegando-se ?s equa??es gerais para os campos eletromagn?ticos da antena. Em seguida s?o utilizados princ?pios da teoria eletromagn?tica para obter-se caracter?sticas como: freq??ncia de resson?ncia complexa, diagramas de radia??o e largura de banda. S?o simulados diferentes configura??es de metamateriais e antenas com o intuito de miniaturizar as dimens?es f?sicas e aumentar a largura de banda das mesmas, os resultados s?o apresentados atrav?s de gr?ficos. A an?lise te?rica computacional deste trabalho se mostra precisa, em compara??o a outros, podendo ser empregado em dispositivos que utilizem metamateriais como substratos. Ao final s?o apresentadas conclus?es e sugest?es para trabalhos futuros