RF and microwave applications represent one of the fastest-growing segments of the high performance electronics market, where ongoing innovation is critical. Manufacturers compete intensively to meet market needs with reduced cost, size, weight and many other performance criteria demands. Under this scenario, transmission lines based on metamaterial concepts can be considered a very interesting alternative to the conventional transmission lines. They are more compact (compatible with planar manufacturing processes) and present higher degrees of design flexibility. Furthermore, metamaterial transmission lines can also provide many other unique properties not achievable with ordinary transmission lines, such as dispersion or impedance engineering. Nevertheless, the impact in the industry is still not relevant, mostly due to the complexity of the related synthesis and design procedures. These procedures are mainly based on the engineer’s experience, with the help of costly full-wave electromagnetic (EM) simulators and parameter extraction methods. The aim of this thesis is to contribute to simplify and speed up the synthesis and design procedures of artificial transmission lines. In particular, the lines obtained by periodically loading a conventional transmission line with electrically small resonators, such as split ring resonators (SSRs) or its complementary particle (CSRR). The design procedure is automated by using Space Mapping techniques. In contrast to other alternative methods, real synthesis is found from the circuit schematic (that provides a given target response) and without need of human intervention. Some efforts to make the method practical and useful have been carried out. Given a certain target response, it is determined whether it can be physically implemented with a chosen technology, and hence proceeding next to find the synthesis, or not. For this purpose, a two-step Aggressive Space Mapping approach is successfully proposed. In contrast to other methods, the real synthesis is found from certain target circuit values (corresponding to the equivalent circuit model that characterizes the structure to be synthesized). Different efforts have been carried out in order to implement a useful and practical method. Some of them were focused to determine if, given certain circuit parameters (which determine the target response) and certain given technology specifications (permittivity and height of the substrate, technology limits), that response is physically realizable (convergence region). This technique was successfully formulated and it is known as “Two-Step Aggressive Space Mapping Approach”. In this work, the latest improvements made till date, from the synthesis of basic unit cells until different applications and kinds of metamaterial-based circuits, are presented. The results are promising and prove the validity of the method, as well as its potential application to other basic cells and more complex designs. The general knowledge gained from these cases of study can be considered a good base for a coming implementation in commercial software tools, which can help to improve its competitiveness in markets, and also contribute to a more general use of this technology. / Rodríguez Pérez, AM. (2014). Synthesis of Planar Microwave Circuits based on Metamaterial Concepts through Aggressive Space Mapping [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48465

Le travail de cette thèse est en rapport avec les métamatériaux et ses applications. Tout d’abord, un état de l’art est dressé en présentant leur évolution depuis leur apparition en 19ème siècle jusqu’au nos jours. Les notions sur les milieux chirale, bi-anisotrope, cristaux photoniques et quelques applications dans ces milieux sont données. Ensuite, nous présentons les équations classiques de Maxwell dans les milieux complexes. L’effet bi-anisotrope dans les métamatériaux est ensuite validé par l’extraction des paramètres caractéristiques du matériau main gauche (LHM). La validation a été faite en utilisant deux types différents du résonateur avec inclusion (SRR). Les métamatériaux sont également étudiés comme des cristaux photoniques quand les dimensions utilisées sont de l’ordre de la longueur d’onde correspondant.De plus, les résonateurs SRR et multi-SRR sont analysés du point de vue analytique et électromagnétique afin d’extraire leur fréquence de résonance. Par conséquent, ces composants peuvent être introduits dans différents types de conception; La surface conductrice magnétique artificielle (AMC) illustre un cas explicite et efficace de ces derniers. Une antenne dipôle, placée sur cette surface à la place d’un plan de masse conventionnel, a été étudiée comme une application des métamatériaux. Les résultats relatifs sur la directivité, le gain et le coefficient de réflexion montrent une nette amélioration. Une antenne multi-bandes, comme une autre application des métamatériaux, a également été conçue et simulée. Le résonateur SRR est inséré dans l’antenne de départ afin de créer une autre résonance, et par conséquent une autre bande est ainsi créée. / The work in this thesis deals with metamaterials, its components and applications. A historical overview about these materials, features and researches in the domain are presented. Chiral media, binaisotropic materials and photonic crystals are also studied in order to visualize physics behind metamaterials.Electromagnetic properties in complex media are widely investigated. Starting from Maxwell’s equations, bi-anisotropic materials and their effect are deeply analyzed whereas two types of Split Ring Resonator (SRR) are treated to determine constitutive parameters of Left Handed Materials (LHM). The metamaterials are also studied as photonic crystals since the effective medium approach is not applicable when the dimensions of the inclusions tend to the operating wavelength.Moreover, SRRs and Multi SRRs are synthesized analytically and electromagnetically in order to extract their resonant frequencies. Consequently, these components could be introduced in any design; Artificial Magnetic Conductor (AMC) surface is an efficient case. Thus, a low profile antenna positioned over such surface is examined as an application of metamaterials. The results of directivity, gain and reflection coefficient are of great importance and affirm the employing of metamaterials in such applications. A dual band PCB antenna, as another application of metamaterials, is designed and simulated. The SRR element studied in the previous chapters is used as the trap which inserted in the arm of the antenna in order to create another resonance, and consequently another band is created.

Artificial magnetic materials (AMMs) are a type of metamaterials which are engineered to exhibit desirable magnetic properties not found in nature. AMMs are realized by embedding electrically small metallic resonators aligned in parallel planes in a host dielectric medium. In the presence of a magnetic field, an electric current is induced on the inclusions leading to the emergence of an enhanced magnetic response inside the medium at the resonance frequency of the inclusions. AMMs with negative permeability are used to develop single negative, or double negative metamaterials. AMMs with enhanced positive permeability are used to provide magneto-dielectric materials at microwave or optical frequencies where the natural magnetic materials fail to work efficiently. Artificial magnetic materials have proliferating applications in microwave and optical frequency region. Such applications include inversely refracting the light beam, invisibility cloaking, ultra miniaturizing and frequency bandwidth enhancing low profile antennas, planar superlensing, super-sensitive sensing, decoupling proximal high profile antennas, and enhancing solar cells efficiency, among others. AMMs have unique enabling features that allow for these important applications. Fundamental limitations on the performance of artificial magnetic materials have been derived. The first limitation which depends on the generic model of permeability functions expresses that the frequency dispersion in an AMM is limited by the desired operational bandwidth. The other constraints are derived based on the geometrical limitations of inclusions. These limitations are calculated based on a circuit model. Therefore, a formulation for permeability and magnetic susceptibility of the media based on a circuit model is developed. The formulation is in terms of a geometrical parameter that represents the geometrical characteristics of the inclusions such as area, perimeter and curvature, and a physical parameter that represents the physical, structural and fabrication characteristics of the medium. The effect of the newly introduced parameters on the effective permeability of the medium and the magnetic loss tangent are studied. In addition, the constraints and relations are used to methodically design artificial magnetic material meeting specific operational requirements. A novel design methodology based on an introduced analytical formulation for artificial magnetic material with desired properties is implemented. The synthesis methodology is performed in an iterative four-step algorithm. In the first step, the feasibility of the design is tested to meet the fundamental constraints. In consecutive steps, the geometrical and physical factors which are attributed to the area and perimeter of the inclusion are synthesized and calculated. An updated range of the inclusion's area and perimeter is obtained through consecutive iterations. Finally, the outcome of the iterative procedure is checked for geometrical realizability. The strategy behind the design methodology is generic and can be applied to any adopted circuit based model for AMMs. Several generic geometries are introduced to realize any combination of geometrically realizable area and perimeter (s,l) pairs. A realizable geometry is referred to a contour that satisfies Dido's inequality. The generic geometries introduced here can be used to fabricate feasible AMMs. The novel generic geometries not only can be used to enhance magnetic properties, but also they can be configured to provide specific permeability with desired dispersion function over a certain frequency bandwidth with a maximum magnetic loss tangent. The proposed generic geometries are parametric contours with uncorrelated perimeter and area function. Geometries are configured by tuning parameters in order to possess specified perimeter and surface area. The produced contour is considered as the inclusion's shape. The inclusions are accordingly termed Rose curve resonators (RCRs), Corrugated rectangular resonators (CRRs) and Sine oval resonators (SORs). Moreover, the detailed characteristics of the RCR are studied. The RCRs are used as complementary resonators in design of the ground plane in a microstrip stop-band filter, and as the substrate in design of a miniaturized patch antenna. The performance of new designs is compared with the counterpart devices, and the advantages are discussed.

Artificial magnetic materials (AMMs) are a type of metamaterials which are engineered to exhibit desirable magnetic properties not found in nature. AMMs are realized by embedding electrically small metallic resonators aligned in parallel planes in a host dielectric medium. In the presence of a magnetic field, an electric current is induced on the inclusions leading to the emergence of an enhanced magnetic response inside the medium at the resonance frequency of the inclusions. AMMs with negative permeability are used to develop single negative, or double negative metamaterials. AMMs with enhanced positive permeability are used to provide magneto-dielectric materials at microwave or optical frequencies where the natural magnetic materials fail to work efficiently. Artificial magnetic materials have proliferating applications in microwave and optical frequency region. Such applications include inversely refracting the light beam, invisibility cloaking, ultra miniaturizing and frequency bandwidth enhancing low profile antennas, planar superlensing, super-sensitive sensing, decoupling proximal high profile antennas, and enhancing solar cells efficiency, among others. AMMs have unique enabling features that allow for these important applications. Fundamental limitations on the performance of artificial magnetic materials have been derived. The first limitation which depends on the generic model of permeability functions expresses that the frequency dispersion in an AMM is limited by the desired operational bandwidth. The other constraints are derived based on the geometrical limitations of inclusions. These limitations are calculated based on a circuit model. Therefore, a formulation for permeability and magnetic susceptibility of the media based on a circuit model is developed. The formulation is in terms of a geometrical parameter that represents the geometrical characteristics of the inclusions such as area, perimeter and curvature, and a physical parameter that represents the physical, structural and fabrication characteristics of the medium. The effect of the newly introduced parameters on the effective permeability of the medium and the magnetic loss tangent are studied. In addition, the constraints and relations are used to methodically design artificial magnetic material meeting specific operational requirements. A novel design methodology based on an introduced analytical formulation for artificial magnetic material with desired properties is implemented. The synthesis methodology is performed in an iterative four-step algorithm. In the first step, the feasibility of the design is tested to meet the fundamental constraints. In consecutive steps, the geometrical and physical factors which are attributed to the area and perimeter of the inclusion are synthesized and calculated. An updated range of the inclusion's area and perimeter is obtained through consecutive iterations. Finally, the outcome of the iterative procedure is checked for geometrical realizability. The strategy behind the design methodology is generic and can be applied to any adopted circuit based model for AMMs. Several generic geometries are introduced to realize any combination of geometrically realizable area and perimeter (s,l) pairs. A realizable geometry is referred to a contour that satisfies Dido's inequality. The generic geometries introduced here can be used to fabricate feasible AMMs. The novel generic geometries not only can be used to enhance magnetic properties, but also they can be configured to provide specific permeability with desired dispersion function over a certain frequency bandwidth with a maximum magnetic loss tangent. The proposed generic geometries are parametric contours with uncorrelated perimeter and area function. Geometries are configured by tuning parameters in order to possess specified perimeter and surface area. The produced contour is considered as the inclusion's shape. The inclusions are accordingly termed Rose curve resonators (RCRs), Corrugated rectangular resonators (CRRs) and Sine oval resonators (SORs). Moreover, the detailed characteristics of the RCR are studied. The RCRs are used as complementary resonators in design of the ground plane in a microstrip stop-band filter, and as the substrate in design of a miniaturized patch antenna. The performance of new designs is compared with the counterpart devices, and the advantages are discussed.