A existência de ondas gravitacionais foi confirmada indiretamente pela observação astronômica de pulsares binários. Detectores de ondas gravitacionais tem sido desenvolvidos desde o trabalho pioneiro de Weber nos anos 60. Esforços estão sendo realizados no sentido de aumentar a sensibilidade dos detectores e realizar uma detecção direta, que ainda não foi confirmada. O Grupo GRAVITON está aperfeiçoando e melhorando a sensibilidade de um detector de ondas gravitacionais que se encontra no Laboratório de Estado Sólido e Baixas Temperaturas do Instituto de Física da Universidade de São Paulo (LESBT/IFUSP), na cidade de São Paulo com apoio da FAPESP (processo 2006/56041-3). Esse detector, denominado MARIO SCHENBERG, é composto por uma massa ressonante esférica de CuAl(6%) com 65 cm de diâmetro, com aproximadamente 1150 kg, que deverá atingir a sensibilidade h ~ 10-22 em uma banda passante de 50 Hz, em torno de 3200 Hz, quando estiver operando a temperaturas da ordem de 0,05 K. Atualmente o detector já tem toda a sua infraestrutura criogênica montada e testada para resfriamentos a 4 K e toda a suspensão da esfera bem como todo o sistema de filtragem mecânica construídos e montados. Já foram realizadas as primeiras corridas comissionadas em 2006, 2007 e 2008, quando foram realizados vários diagnósticos sobre o sistema e desde então vem sendo desenvolvidos os transdutores para colocar o detector novamente em operação com melhor sensibilidade. Paralelamente, foram realizadas melhorias no próprio detector em razão dos diagnósticos realizados. O trabalho aqui apresentado está associado ao projeto acima. O autor desenvolveu atividades associadas à construção e desenvolvimentos do detector, que podem ser divididas em três partes principais: na parte mecânica, foi desenvolvido, instalado e testado um novo sistema de isolamento vibracional da suspensão da esfera; na parte criogênica foram feitas novas conexões térmicas, cálculos de gastos de hélio líquido e feitos desenvolvimentos para o funcionamento do refrigerador por diluição; e na parte eletrônica foi feita a instalação da eletrônica responsável pela transdução do sinal, além do desenvolvimento de um novo par de antenas de microfita. / The existence of gravitational waves has been confirmed indirectly by astronomical observation of binary pulsars. Gravitational wave detectors have been developed since the pioneering work of Weber in the 60s. Efforts are being made to increase the sensitivity of the detectors and perform a direct detection, wich has not been confirmed yet. The GRAVITON Group is enhancing and improving the sensitivity of a gravitational wave detector which is at the Laboratório de Estado Sólido e Baixas Temperaturas of the Instituto de Física of the Universidade de São Paulo (LESBT / IFUSP), in São Paulo city and is supported by FAPESP (processo 2006/56041-3). This detector, called MARIO SCHENBERG, consists of a spherical resonant mass of CuAl (6%) with 65 cm in diameter, and approximately 1150 kg, which should reach the sensitivity of h ~ 10-22 in a bandwidth of 50 Hz around 3200 Hz, when operating at temperatures of 0.05 K. Currently the detector already has all its infrastructure assembled and tested for cryogenic cooling down to 4 K and the whole suspension of the sphere as well as all mechanical isolation system constructed and assembled. Commissioning runs have already been done in 2006, 2007 and 2008, when several diagnoses on the system were performed and since then there have been many developments on the transducers to put back the detector into operation with improved sensitivity. At the same time, improvements have been made within the detector itself due to the diagnoses. The work presented here is associated with the above project. The author has developed activities and developments associated with the detector construction, which can be divided into three main parts: the mechanical part, in which a new system of vibration isolation was designed for the sphere suspension, installed and tested; the cryogenic part, in which new connections and thermal calculations of liquid helium boil-off rate were made as well as other developments for the operation of a dilution refrigerator; and the electronic part, in which the installation of the electronic signal responsable for the transduction was made, besides the development of a new pair of micro-strip antenna.

The designs of various feeding networks for microstrip antennas have been investigated in this dissertation. In the active microstrip antenna designs, an amplifier-type microstrip antenna integrates a two- port amplifier circuitry to the various passive antennas through a 50£[ inset microstrip feed line which can function in broadband operation¡ACP operation and dual-frequency operation. As for the broadband circularly polarized microstrip antenna with a dual-perpendicular feed design, antenna with a dual-perpendicular feed which was formed by a Wilkinson power divider with a quarter-wavelength section of microstrip line for providing equal splitting of the input power and 90¢X phase difference to the two feed points has been presented. The broadband CP bandwidth can be achieved due to the good isolation between the two output lines of the feed network. In the microstrip antennas with CPW feed designs, we first proposed a microstrip antenna with three-dimensional CPW feed. A separate feed substrate is used which can provide a large-area space for the layout of complicated microwave circuitry. In addition, the feed substrate can also be oriented to the patch substrate with various angles, resulting in more flexibility in the proposed three-dimensional feed design. Finally, we proposed a design with two slot lines located at both sides of the coupling slot which can lengthen the excited patch surface current path, thus the resonant frequency is reduced and an antenna size reduction up to 40% has been obtained.

The Method of Moments (MoM) has been used extensively to solve electromagnetic problems. Its popularity is largely attributed to its adaptability to structures with various shapes and success in predicting the equivalent induced currents accurately. However, due to its dense matrix, especially for large structures, the MoM suffers from long matrix solution time and large storage requirement. In this thesis it is shown that use of wavelet basis functions result in a MoM matrix which is sparser than the one obtained by using traditional basis functions. A new wavelet system, different from the ones found in literature, is proposed. Stabilized Bi-Conjugate Gradient Method which is an iterative matrix solution method is utilized to solve the resulting sparse matrix equation. Both a one-dimensional problem with a microstrip line example and a two-dimensional problem with a rectangular patch antenna example are studied and the results are compared.

This thesis presents the design, fabrication, and measurement of tunable frequency microstrip antennas using RF MEMS (Microelectromechanical Systems) technology. The integration of RF MEMS components with radiators enable to implement tunable systems due to the adjustable characteristics of RF MEMS components. In the frame of this thesis, different types of structures have been investigated and designed. The first structure consists of a microstrip patch antenna which is loaded with a microstrip stub whose length is controlled by RF MEMS switches. In the other structure, the length of a microstrip patch antenna is changed by connecting a metal plate using RF MEMS switches. The third structure is composed of a microstrip patch antenna and a microstrip stub on which RF MEMS variable capacitors are placed periodically to control the resonant frequency. In order to maintain an easier integration with RF MEMS capacitors, another structure consisting of a microstrip patch antenna and a coplanar waveguide (CPW) stub which is loaded with variable RF MEMS capacitors is designed. The final structure is a dual frequency CPW-fed rectangular slot antenna whose resonant frequencies are shifted by RF MEMS variable capacitors placed on a short circuited stub inserted inwards the antenna. The fabrication of CPW-fed rectangular slot antenna is completed in the MEMS fabrication facilities of METU using RF MEMS process based on electroforming on glass substrate. The measurement results show that RF MEMS components might be a proper solution to obtain tunable frequency antenna structures.

Submitted by Lara Oliveira (lara@ufersa.edu.br) on 2017-05-24T22:06:39Z No. of bitstreams: 1 AnamariaSM_DISSERT.pdf: 10659120 bytes, checksum: 007308f84bbdb900c2823d1a72b2f4a4 (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-05-26T11:53:10Z (GMT) No. of bitstreams: 1 AnamariaSM_DISSERT.pdf: 10659120 bytes, checksum: 007308f84bbdb900c2823d1a72b2f4a4 (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-05-26T11:54:09Z (GMT) No. of bitstreams: 1 AnamariaSM_DISSERT.pdf: 10659120 bytes, checksum: 007308f84bbdb900c2823d1a72b2f4a4 (MD5) / Made available in DSpace on 2017-05-26T11:54:39Z (GMT). No. of bitstreams: 1 AnamariaSM_DISSERT.pdf: 10659120 bytes, checksum: 007308f84bbdb900c2823d1a72b2f4a4 (MD5) Previous issue date: 2016-05-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Communication systems it has excelled in the development, social, economic and cultural society. Every time there are new technologies seeking to offer the fastest, easy and reliable access to various communications services. In this context, the microstrip antennas stand out by having compact size and reduced cost. However, it presents some limitations related to narrow bandwidth and low gain. A significant advance to minimize these losses came to the use of structures EBG (Electromagnetic Band Gap) and PBG (Photonic Band Gap) in the components of the antennas. This paper proposes the study and analysis of the behavior of microstrip antennas properties designed with EBG/PBG structures in the substrate and the ground plane. So that the structures are arranged just under the patch and are developed with variations in radius, cylinder height and positioning in the ground plane. For the resonance frequency 5.85 GHz, and substrates of different permittivity. In computer modeling was used ANSYS HFFS® software. After analyzing the simulated results seven devices were built, through a vector network analyzer, the measurements of the main parameters were performed. Ultimately simulation are compared and measured values, so that the results presented in most configurations a concord in the pattern of graphics, although the frequency displacement. Also noted that antennas with the EBG/PBG structures presented multiband, enabling the application specific frequency bands as well as, an increase in the value of total gain, bandwidth and reduction of surface currents / Os sistemas de comunicação assumiram papéis fundamentais para o desenvolvimento, social, econômico e cultural na sociedade. A cada momento, surgem novas tecnologias procurando oferecer o acesso mais rápido, fácil e confiável aos diversos serviços de comunicações. Nesse contexto, as antenas de microfita se destacam por possuírem características como, tamanho compacto e custo reduzido. No entanto, apresentam algumas limitações relacionadas a largura de banda estreita e ganho reduzido. Um avanço significativo para minimizar essas perdas, proveio com a utilização de estruturas de bandas proibidas (EBG – Eletromagnetic Band Gap e PBG – Photonic Band Gap) nos componentes das antenas. Este trabalho propõe o estudo e análise do comportamento das propriedades de antenas de microfita projetadas com configurações de estruturas EBG/PBG no substrato e no plano de terra. De modo que as estruturas estão arranjadas apenas sob o patch e, são desenvolvidas com variações no raio, altura do cilindro e posicionamento no plano de terra. Para a frequência de ressonância de 5,85 GHz, e substratos de diferentes permissividades. Na modelagem computacional foi utilizado o software ANSYS HFFS®, e com a análise dos resultados simulados foram fabricados sete dispositivos, onde através de um analisador de redes vetoriais, foram realizadas as medições dos principais parâmetros. Por fim são comparados os valores simulados e medidos, de modo que que os resultados apresentaram na maioria das configurações uma concordância no padrão de seus gráficos, apesar dos deslocamentos de frequência. Também foi observado que as antenas com as estruturas EBG/PBG apresentaram comportamento de multibandas, possibilitando a aplicação em faixas de frequências específicas, assim como, ocorreu um aumento nos valores de ganho total, largura de banda e a redução das correntes de superfície / 2017-05-24

Submitted by Lara Oliveira (lara@ufersa.edu.br) on 2017-07-18T21:43:56Z No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-25T14:46:31Z (GMT) No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2017-07-25T14:46:56Z (GMT) No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) / Made available in DSpace on 2017-07-25T14:47:21Z (GMT). No. of bitstreams: 1 ThiagoELM_DISSERT.pdf: 3255456 bytes, checksum: 6ce3964b5242ccf305c4e0f3d94ee65e (MD5) Previous issue date: 2013-11-22 / The microstrip antennas are in constant evidence in current research due to its numerous advantages. Fractal geometry proposed by Mandelbrot(1975 ) combined with the performance and convenience of planar structures are an excellent combination used in the design of antennas in order to reduce the dimensions and enhance its bandwidth, and allows the emergence of best bands frequency by virtue of ownership of high -similarity. Compared with the conventional microstrip antennas, patch antennas with fractal type substrates have lower resonance frequency, enabling the manufacture of even more compact antennas. The aim of this work consists of the design of patch antennas with dielectric substrates organized almost periodic basis through the use of fractal geometry sequence Cantor applied to a circular patch antenna fed by microstrip line, designed for a resonant frequency of 10 GHz. Analysis of this microstrip antenna is made in various types of dielectric substrates by simulation through software commercial Ansoft HFSS - Designer, used for accurate analysis of the electromagnetic behavior of the antennas by the finite element method by presenting results from resonant frequency and radiation pattern, making comparisons with other results in the literature. This dissertation also presents a bibliographic study on theories of antennas while also addressing about fractal geometry, emphasizing its characteristics and properties as well as its applicability. This paper also presents a study of almost periodic structures and their mathematical formalism considered throughout this work / As antenas de microfita estão em constante evidência nas pesquisas atuais, devido às suas inúmeras vantagens. A geometria fractal proposta por Mandelbrot (1975) aliada ao bom desempenho e comodidade das estruturas planares são uma excelente combinação utilizada no projeto de antenas com o intuito de reduzir suas dimensões e realçar sua largura de banda, além de permitir o surgimento de melhores bandas de frequência em consequência da propriedade da alto-similaridade. Em comparação com as antenas em microfita convencionais, as antenas tipo patch com substratos fractais apresentam frequência de ressonância inferiores, possibilitando a fabricação de antenas ainda mais compactas. O objetivo desse trabalho consiste no projeto de antenas patch com substrato dielétrico organizado de forma quase periódica por meio da utilização da geometria fractal da sequência de Cantor aplicada a uma antena de patch circular alimentada por linha de microfita, projetada para uma frequência ressonância de 10 GHz. É feita análise dessa antena de microfita em vários tipos de substratos dielétricos por simulação através do software comercial Ansoft Designer-HFSS, usado para análise precisa do comportamento eletromagnético das antenas através do método dos elementos finitos apresentando resultados de frequência de ressonância, diagrama de radiação, carta de Smith e de campos elétricos e magnéticos fazendo-se comparações com outros resultados obtidos na literatura. Esta dissertação ainda apresenta um estudo bibliográfico em teorias de antenas, abordando também a respeito da geometria fractal, dando ênfase a suas características e propriedades como também a sua aplicabilidade. Este trabalho ainda apresenta um estudo sobre as estruturas quase periódicas e seu formalismo matemático / 2017-07-18

Submitted by Vanessa Christiane (referencia@ufersa.edu.br) on 2018-04-25T19:00:54Z No. of bitstreams: 1 ThomasTOP_DISSERT.pdf: 5209914 bytes, checksum: dc0480e3c31cf33dad2055a2722ab763 (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2018-06-18T16:53:46Z (GMT) No. of bitstreams: 1 ThomasTOP_DISSERT.pdf: 5209914 bytes, checksum: dc0480e3c31cf33dad2055a2722ab763 (MD5) / Approved for entry into archive by Vanessa Christiane (referencia@ufersa.edu.br) on 2018-06-18T17:02:42Z (GMT) No. of bitstreams: 1 ThomasTOP_DISSERT.pdf: 5209914 bytes, checksum: dc0480e3c31cf33dad2055a2722ab763 (MD5) / Made available in DSpace on 2018-06-18T17:02:51Z (GMT). No. of bitstreams: 1 ThomasTOP_DISSERT.pdf: 5209914 bytes, checksum: dc0480e3c31cf33dad2055a2722ab763 (MD5) Previous issue date: 2018-02-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In wireless communications, there is a growing need for more compact and portable systems. In this context, research related to the development of antennas has intensified in recent years, especially those related to microstrip antennas, since these have unique properties as well as several applications. In this work, two different antenna configurations were designed, an array of microstrip antennas for the transmitting device and a single element with an omnidirectional pattern for the receiver, according to the needs of the application. The antennas are designed by the Transmission Line Theory according to the frequency of radio operation and the electrical and physical properties of the substrates used. The results were obtained through simulations in the ANSYS HFSS® software, and the best results were used to fabricate the devices in order to validate the simulations performed. The results of the simulations reached the characteristics of the application, as the return losses of both antennas were in accordance with the frequency band of the application in the band ISM in 2.4 GHz, with respect to the behavior of the radiation, the antenna proposed to the transmitter had a gain of 6.1 dB, approximately three times greater than the commonly used dipole / monopole antenna. The experimental result of the loss of return was shown to be in agreement with the simulated standard, in spite of the frequency displacement, both antennas constructed were suitable for application in the radio control of the UAV, having the microstrip array 7.5 MHz of bandwidth in the band of application and the simple element proposed to the 58.5 MHz receiver. The antennas were then implemented in the radiofrequency system and a range test was performed in order to verify the communication of the devices, presenting satisfactory results. Thus, a flight is performed via software for visual inspection of transmission lines, aiming the collection of images for analysis / Em comunicações sem fio, existe uma crescente necessidade por sistemas mais compactos e portáteis. Nesse contexto, as pesquisas relacionadas ao desenvolvimento de antenas têm se intensificado nos últimos anos, em especial, as relacionadas às antenas de microfita, visto que estas possuem propriedades singulares, bem como diversas aplicações. Neste trabalho foram projetadas duas configurações distintas de antenas, um arranjo de antenas de microfita para o dispositivo transmissor e um elemento simples com padrão omnidirecional para o receptor, de acordo com as necessidades da aplicação. As antenas são projetadas pela Teoria da Linha de Transmissão de acordo com a frequência de operação do rádio e as propriedades elétricas e físicas dos substratos utilizados. Os resultados foram obtidos através de simulações no software ANSYS HFSS®, e os melhores resultados foram utilizados para fabricação dos dispositivos a fim de validar as simulações realizadas. Os resultados das simulações atingiram as características da aplicação, pois as perdas de retorno de ambas antenas apresentaram conformidade com a faixa de frequências da aplicação na banda ISM em 2,4 GHz, no que diz respeito ao comportamento da radiação, a antena proposta ao transmissor teve ganho de 6,1 dB, aproximadamente três vezes maior do que a antena dipolo/monopolo comumente utilizada. O resultado experimental do coeficiente de reflexão se mostrou concordante com o padrão simulado, apesar do deslocamento de frequência, ambas antenas construídas se adequaram para aplicação no rádio controle do VANT, tendo o arranjo de microfita 7,5 MHz de largura de banda na faixa de aplicação e o elemento simples proposto ao receptor 58,5 MHz. Em seguida, as antenas foram implementadas no sistema de radiofrequência e foi realizado um teste de alcance a fim de averiguar a comunicação dos dispositivos, apresentando resultados satisfatórios. Desse modo, um voo foi realizado para inspeção visual de linhas de transmissão, visando a coleta de imagens para análise / 2018-04-25

Made available in DSpace on 2014-06-11T19:24:38Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-10-14Bitstream added on 2014-06-13T18:20:52Z : No. of bitstreams: 1 brinhole_er_me_bauru.pdf: 2082084 bytes, checksum: e9da8790c90b7d67f56ee24ea0858f1c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Cefet - Cornelio Procopio / Neste trabalho, apresenta-se o desenvolvimento de uma metodologia utilizando redes neurais artificiais, para auxiliar na determinação da freqüência de ressonância no projeto de antenas tipo microfita de equipamentos móveis, tanto para antenas retangulares como para antenas triangulares. Compararam-se modelos deterministas e modelos empíricos baseados em Redes Neurais Artificiais (RNA) da literatura pesquisada com os modelos apresentados neste trabalho. Apresentam-se modelos empíricos baseados em RNAs tipo Perceptron Multicamadas (PMC). Os modelos propostos também são capazes de serem integrados em um ambiente CAD (Computed Aided Design) para projetar antenas tipo microfita de equipamentos móveis. / This work presents the development of models that can be used in the design of microstrip antennas for mobile communications. The antennas can be triangular or rectangular. The presented models are compared with deterministic and empirical models based on artificial neural networks (ANN) presented in the literature. The models are based on Perceptron Multilayer (PML). The models can be embedded in CAD systems, in order to design microstrip antennas for mobile communications.

Made available in DSpace on 2014-12-17T14:55:45Z (GMT). No. of bitstreams: 1 JannaynaDB_DISSERT.pdf: 1591261 bytes, checksum: c15fb1758e21a5e052a25aed22b0a0db (MD5) Previous issue date: 2010-08-13 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / This paper proposes a method based on the theory of electromagnetic waves reflected to evaluate the behavior of these waves and the level of attenuation caused in bone tissue. For this, it was proposed the construction of two antennas in microstrip structure with resonance frequency at 2.44 GHz The problem becomes relevant because of the diseases osteometabolic reach a large portion of the population, men and women. With this method, the signal is classified into two groups: tissue mass with bony tissues with normal or low bone mass. For this, techniques of feature extraction (Wavelet Transform) and pattern recognition (KNN and ANN) were used. The tests were performed on bovine bone and tissue with chemicals, the methodology and results are described in the work / Este trabalho prop?e um m?todo baseado na teoria das ondas eletromagn?ticas refletidas para avaliar o comportamento dessas ondas e o n?vel de atenua??o provocada no tecido ?sseo. Para isto, foi proposta a confec??o de duas antenas em estrutura de microfita com freq??ncia de resson?ncia em 2.44 GHz. O problema torna-se relevante pelo fato das doen?as Osteometab?licas atingirem uma grande parcela da popula??o, entre homens e mulheres. Com esse m?todo, classifica-se os sinais em dois grupos: tecido com massa ossea normal ou tecidos com baixa massa ?ssea. Para isto, t?cnicas de extra??o de caracter?sticas (Transformada Wavelet) e de reconhecimento de padr?es (KNN e RNA) foram usados. Os testes foram realizados em tecido osso bovino e com elementos qu?micos, a metodologia aplicada e resultados obtidos s?o descritos no trabalho

Made available in DSpace on 2014-12-17T14:55:53Z (GMT). No. of bitstreams: 1 MarinaldoPSN_DISSERT.pdf: 999347 bytes, checksum: 61ef641028185e656504321954690c18 (MD5) Previous issue date: 2011-11-25 / Universidade Federal do Rio Grande do Norte / This work presents a theoretical and numerical analysis for the radiation characteristics of rectangular microstrip antenna using metamaterial substrate. The full wave analysis is performed in the Fourier transform domain through the application of the Transverse Transmission Line - TTL method. 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. The general equations for the electromagnetic fields of the antenna are developed using the Transverse Transmission Line - TTL method. Imposing the boundary conditions, the dyadic Green s function components are obtained relating the surface current density components at the plane of the patch to the electric field tangential components. Then, Galerkin s method is used to obtain a system of matrix equations, whose solution gives the antenna resonant frequency. From this modeling, it is possible to obtain numerical results for the resonant frequency and return loss for different configurations and substrates / Esta disserta??o de Mestrado apresenta uma an?lise te?rica e num?ricocomputacional, das caracter?sticas ressonantes de uma antena de microfita com patch retangular utilizando substrato metamaterial. A an?lise utiliza o formalismo de onda completa atrav?s da aplica??o do m?todo da Linha de Transmiss?o Transversa - LTT, no dom?nio da transformada de Fourier. ? realizado um estudo acerca da teoria dos metamateriais com o intuito de obter seus par?metros construtivos, os mesmos s?o caracterizados atrav?s de tensores permissividade e permeabilidade. As equa??es gerais para os campos eletromagn?ticos da antena s?o desenvolvidas aplicando o m?todo da Linha de Transmiss?o Transversa - LTT. A imposi??o das condi??es de contorno adequada ? estrutura permite determinar as fun??es di?dicas de Green, relacionando as componentes da densidade de corrente no patch com as componentes tangenciais do campo el?trico. O m?todo de Galerkin ? ent?o usado para obter a equa??o matricial, cuja solu??o n?o trivial fornece a freq??ncia de resson?ncia da antena. A partir da modelagem ? poss?vel obter resultados para a freq??ncia de resson?ncia em diferentes configura??es de antenas e substratos, al?m da perda de retorno