The rise of connected devices and the internet of things has increased the need for systems capable of transmitting high frequency signals wirelessly. An important part of these systems are the filters. Filters remove signals within unwanted frequency ranges. These filters can be implemented using e.g. periodic structures. In this article, we present a design for such a filter that aims to have a stopband between 3-6 [GHz] using square complementary split ring resonators (CSRR) on a substrate integrated waveguide (SIW). The design is based on a dimensional parametric study. An alternative design based on circular CSRR's is also presented and discussed. The design is validated using a commercially available software and a novel method simulating higher order of modes (HOM). The novel simulation method is shown to be advantageous due to its ability to evaluate the attenuation coefficient of a periodic filter. Additionally, a quadratic CSRR structure was shown to have a larger stopband and a similar attenuation coefficient when compared to circular CSRR structure when applied on a SIW. Furthermore, an impedance matching structure for the both CSRR filters were designed and both filters were simulated. / Förekomsten av uppkopplade enheter och användandet av sakernas internet har ökat behovet av system som kan sända högfrekventa signaler trådlöst. En viktig del av dessa system är filter, som eliminerar signaler inom oönskade frekvensband. Dessa filter kan implementeras med periodiska strukturer. I denna rapport presenterar vi en design för ett sådant filter med ett stoppband mellan 3-6 [GHz] som använder sig av kvadratiska "complementary split ring resonators" (CSRR) på en "substrate integrated waveguide" (SIW). Designen är baserad på en geometrisk parametrisk studie. En alternativ design som använder sig av cirkulära CSSRs presenteras och diskuteras. Den föreslagna designen valideras med en kommersiellt tillgänglig och en egenframställd metod vid namn "higher order of modes" (HOM) metoden. Den egenframställda simulationsmetoden visas vara fördelaktig då den är kapabel att evaluera filtrets attenuationskoefficient. Utöver detta visas att en design baserad på kvadratiska CSRRs vara fördelaktig då den genererar ett större stoppband och liknande attenuationskoefficient jämfört med den cirkulära CSSR designen vid tillämpning på en SIW. Fortsättningsvis presenteras en matchande struktur för båda filter varpå båda kompletta filter simuleras. / Kandidatexjobb i elektroteknik 2022, KTH, Stockholm

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The main topic of the thesis are inverse scattering problems of electromagnetic waves from periodic structures. We study first the direct problem and its numerical resolution using volume integral equation methods with a focus on the case of strongly singular integral operators and discontinuous coefficients. In a second investigation of the direct problem we study conditions on the material parameters under which well-posedness is ensured for all positive wave numbers. Such conditions exclude the existence of guided waves. The considered inverse scattering problem is related to shape identification. To treat this class of inverse problems, we investigate the so-called Factorization method as a tool to identify periodic patterns from measured scattered waves. In this thesis, these measurements are always related to plane incident waves. The outline of the thesis is the following: The first chapter is the introduction where we give the state of the art and new results of the topics studied in the thesis. The main content consists of five chapters, divided into two parts. The first part deals with the scalar case where the TM electromagnetic polarization is considered. In the second chapter we present the volume integral equation method with new results on Garding inequalities, convergence theory and numerical validation. The third chapter is devoted to the analysis of the Factorization method for the inverse scalar problem as well as some numerical experiments. The second part is dedicated to the study of 3-D Maxwell's equations. The fourth and fifth chapters are respectively generalizations of the results of the second and third ones to the case of Maxwell's equations. The sixth chapter contains the analysis of uniqueness conditions for the direct scattering problem, that is, absence of guided modes.

This thesis reports on an experimental study of slow viscoelastic flow through models of fibrous porous media. The models were square arrays of parallel cylinders, with solid volume fractions or ‘solidities’ of 2.5%, 5.0%, and 10%. An initial study using a Newtonian fluid provided a baseline for comparison with results for two Boger fluids, so that the effects of fluid elasticity could be determined. Boger fluids are elastic fluids that have near constant viscosities and can be used in experiments without having to account for shear-thinning effects. The experimental approach involved measurements of pressure loss through the three arrays and interior velocity measurements using particle image velocimetry (PIV). For the Newtonian flows, pressure loss measurements were in good agreement with the analytical predictions of Sangani and Acrivos (1982). PIV measurements showed velocity profiles which were symmetrical and independent of flow rate. Pressure loss measurements for the Boger fluid flows revealed that the onset of elastic effects occurred at a Deborah number of approximately 0.5, for both fluids and the three arrays. Flow resistance data collapsed for the two Boger fluids, and increased with solidity. For all three models, the flow resistance increased monotonically with Deborah number, reaching values up to four times the Newtonian resistance for the 10% model. PIV measurements showed that the transverse velocity profiles for the Newtonian and Boger fluids were the same at Deborah numbers below the elastic onset. Above onset, the profiles became skewed. The skewness, like the flow resistance, was observed to increase with both Deborah number and solidity. In the wake regions between cylinders in a column, periodic flow structures formed in the spanwise direction. The structures were staggered from column to column, consistent with the skewing. As either Deborah number or solidity increased, the flow structures became increasingly three-dimensional, and the stagger became more symmetric. An analysis of fluid stresses reveals that the elastic flow resistance is attributed to additional normal stresses caused by shearing, and not by extension.

This thesis reports on an experimental study of slow viscoelastic flow through models of fibrous porous media. The models were square arrays of parallel cylinders, with solid volume fractions or ‘solidities’ of 2.5%, 5.0%, and 10%. An initial study using a Newtonian fluid provided a baseline for comparison with results for two Boger fluids, so that the effects of fluid elasticity could be determined. Boger fluids are elastic fluids that have near constant viscosities and can be used in experiments without having to account for shear-thinning effects. The experimental approach involved measurements of pressure loss through the three arrays and interior velocity measurements using particle image velocimetry (PIV). For the Newtonian flows, pressure loss measurements were in good agreement with the analytical predictions of Sangani and Acrivos (1982). PIV measurements showed velocity profiles which were symmetrical and independent of flow rate. Pressure loss measurements for the Boger fluid flows revealed that the onset of elastic effects occurred at a Deborah number of approximately 0.5, for both fluids and the three arrays. Flow resistance data collapsed for the two Boger fluids, and increased with solidity. For all three models, the flow resistance increased monotonically with Deborah number, reaching values up to four times the Newtonian resistance for the 10% model. PIV measurements showed that the transverse velocity profiles for the Newtonian and Boger fluids were the same at Deborah numbers below the elastic onset. Above onset, the profiles became skewed. The skewness, like the flow resistance, was observed to increase with both Deborah number and solidity. In the wake regions between cylinders in a column, periodic flow structures formed in the spanwise direction. The structures were staggered from column to column, consistent with the skewing. As either Deborah number or solidity increased, the flow structures became increasingly three-dimensional, and the stagger became more symmetric. An analysis of fluid stresses reveals that the elastic flow resistance is attributed to additional normal stresses caused by shearing, and not by extension.

A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. The current research focuses on wave propagation in nonlinear periodic structures to explore tunability in filtering properties such as bandgaps, cut-off frequencies and response directionality. The first part of the research documents amplitude-dependent dispersion properties of weakly nonlinear periodic media through a general perturbation approach. The perturbation approach allows closed-form estimation of the effects of weak nonlinearities on wave propagation. Variation in bandstructure and bandgaps lead to tunable filtering and directional behavior. The latter is due to anisotropy in nonlinear interaction that generates low response regions, or "dead zones," within the structure.The general perturbation approach developed has also been applied to evaluate dispersion in a complex nonlinear periodic structure which is discretized using Finite Elements. The second part of the research focuses on wave dispersion in strongly nonlinear periodic structures which includes pre-compressed granular media as an example. Plane wave dispersion is studied through the harmonic balance method and it is shown that the cut-off frequencies and bandgaps vary significantly with wave amplitude. Acoustic wave beaming phenomenon is also observed in pre-compressed two-dimensional hexagonally packed granular media. Numerical simulations of wave propagation in finite lattices also demonstrated amplitude-dependent bandstructures and directional behavior so far observed.

La dynamique d’une structure peut être vue aussi bien en termes de modes (ondes stationnaires) qu’en termes d’ondes élastiques libres. Les approches modales sont largement utilisées en mécanique et de nombreuses techniques de réduction de modèles (Model Order Reduction - MOR) ont été développées dans ce cadre. Quant à la dynamique des structures périodiques, les approches propagatives sont majoritairement utilisées, où la périodicité est exploitée en utilisant la théorie de Bloch. Pour les structures périodiques complexes, plusieurs techniques MOR sur la base d’onde ont été proposées dans la littérature. Dans ce travail, une approche couplée propagative et modale a été développée pour étudier la propagation des ondes dans les structures périodiques. Cette approche commence par la description modale d’une cellule unitaire (échelle mésoscopique) en utilisant la synthèse modale (Component Mode Synthesis - CMS). Par la suite, la méthode propagative - Wave Finite Element Method (WFEM) est appliquée sur la structure (échelle macroscopique). Cette méthode est nommée “CWFEM” pour CondensedWave Finite Element Method. Elle combine les avantages de la CMS et WFEM. La CMS permet d’analyser le comportement local d’en extraire une base réduite. La WFEM exploite la périodicité de la structure d’en extraire les paramètres de propagation. Ainsi, l’analyse de la propagation des ondes dans la structure à l’échelle macroscopique peut être réalisée en prenant en compte l’échelle mésoscopique. L’efficacité de la CWFEM est illustrée par de nombreuse applications aux structures périodiques monodimensionnelle (1D) et bidimensionnelle (2D). Le critère de réduction optimale assurant la convergence est discuté. Les caractéristiques de propagation dans les structures périodiques sont identifiées: bande passante, bande interdite, la directivité marquée (wave beaming effects), courbe de dispersion, band structure, surface des lenteurs... Ces propriétés peuvent répondre au besoin de conception des barrières vibroacoustiques, pièges à ondes. La CWFEM est ensuite appliquée pour étudier la propagation des ondes dans des plaques perforées et plaques raidies. Une méthode d’homogénéisation pour déterminer le modèle équivalent de la plaque perforée est proposée. Les comportements à haute fréquence tels que la directivité marquée sont également prédits par CWFEM. Trois modèles de plaques avec perforations différentes sont étudiées dans ce travail. Une validation expérimentale est effectuée sur deux plaques. Pour la plaque raidie, l’influence des modes internes sur la propagation globale est discutée. La densité modale est estimée, en moyenne et haute fréquences, pour une plaque raidie finie, où une bonne corrélation est obtenue en comparant les résultats à l’issue des analyses modales. / Structural dynamics can be described in terms of structural modes as well as elastic wave motions. The mode-based methods are widely applied in mechanical engineering and numerous model order reduction (MOR) techniques have been developed. When it comes to the study of periodic structures, wave description is mostly adopted where periodicity is fully exploited based on the Bloch theory. For complex periodic structures, several MOR techniques conducted on wave basis have been proposed in the literature. In this work, a wave and modal coupled approach is developed to study the wave propagation in periodic structures. The approach begins with the modal description of a unit cell (mesoscopic scale) using Component Mode Synthesis (CMS). Subsequently, the wave-based method -Wave Finite Element Method (WFEM) is applied to the structure (macroscopic scale). The method is referred as “CWFEM” for Condensed Wave Finite Element Method. It combines the advantages of CMS and WFEM. CMS enables to analyse the local behaviour of the unit cell using a reduced modal basis. On the other hand, WFEM exploits fully the periodic propriety of the structure and extracts directly the propagation parameters. Thus the analysis of the wave propagation in the macroscopic scale waveguides can be carried out considering the mesoscopic scale behaviour. The effectiveness of CWFEM is illustrated via several one-dimensional (1D) periodic structures and two-dimensional (2D) periodic structures. The criterion of the optimal reduction to ensure the convergence is discussed. Typical wave propagation characteristics in periodic structures are identified, such as pass bands, stop bands, wave beaming effects, dispersion relation, band structure and slowness surfaces...Their proprieties can be applied as vibroacoustics barriers, wave filters. CWFEM is subsequently applied to study wave propagation characteristics in perforated plates and stiffened plate. A homogenization method to find the equivalent model of perforated plate is proposed. The high frequency behaviours such as wave beaming effect are also predicted by CWFEM. Three plate models with different perforations are studied. Experimental validation is conducted on two plates. For the stiffened plate, the influence of internal modes on propagation is discussed. The modal density in the mid- and high- frequency range is estimated for a finite stiffened plate, where good correlation is obtained compared to the mode count from modal analysis.

Cílem této práce je popsat současný stav v oblasti mikrovlnných komponent na bázi textilu a poté také autorův příspěvek k výzkumu. V tomto studijním oboru je třeba řešit mnoho problémů, a proto jsou stanoveny velmi konkrétní cíle, které by měly tvořit kompletní komunikační systém, který by byl snadno integrovatelný do čalounění uvnitř letadla nebo jiného vozidla. První kapitola je zaměřena na použití relativně nízkofrekvenčních obvodů v pásmu UHF a vysokofrekvenční sklízení energie. Po simulacích následují praktická měření. Další kapitola charakterizuje nové 3D pletené textilie a jejich vysokofrekveční vlastnosti a modelování na velmi vysokých frekvencích, které jsou žádoucí pro užití jako komunikační kanály. S prakticky ověřeným a numericky popsaným textilním substrátem pro použití v pásmu SHF je představena nový vlnovod integrovaný do textilu na bázi tisknutelného umělého magnetického vodiče s praktickou metodikou návrhu. Po ověření byl vlnovod použit pro základní dělič výkonu, dvě různé antény a dva typy senzorů. Všechny návrhy byly vyrobeny a testovány s uspokojivými výsledky.

In this thesis, we analyze the electromagnetic wave propagation in waveguidestructuresexhibiting periodical geometry, including glide symmetry. The analysisis performed using a mode matching technique which correlates the different modecoefficients from separate but, connected regions in the structure. This technique isused to obtain the dispersion diagrams for two one-dimensional periodic structures:a glide-symmetric corrugated metasurface and a coaxial line loaded with periodicholes. The mode matching formulation is presented in Cartesian and cylindricalcoordinate system for the former and the later, respectively. The mode matchingresults are compared to simulated results obtained from the Eigenmode Solver inCST Microwave Studio and are found to agree very well. / I detta examensarbete, analyseras elektromagnetisk v°agutbredning i periodiskav°agledarstrukturer som uppvisar glid symmetri. Analysen genomf¨ordes genom enmod matchnings-teknik som korrelerar de olika mod-koefficienterna fr°an separeraderegioner i strukturen med varandra. Denna teknik anv¨ands f¨or att ta framdispersionsrelationen f¨or tv°a endimensionella periodiska strukturer: en glid symmetriskkorrugerad meta-yta och en koaxial ledare belagd med periodiskt urgr¨opdah°aligheter. Mod matchnings-formuleringen presenteras i Kartesiska och cylindriskakoordinatsystem respektive f¨or de ovan n¨amnda fallen. Mod matchnings-resultatenj¨amf¨ors med data-simulerade resultat erh°allna fr°an CST Microwave Studio och de¨overenst¨ammer v¨al med varandra.

Wireless sensors are used widely for condition monitoring in electric machines. The metal enclosure of an electric motor restricts the signal from sensors to radiate outside. The signal from the metal cavity needs to be guided to the only opening in the enclosure, through a narrow gap between the stator and the rotating rotor. Gap waveguide technology is proposed as a solution by texturing the stator surface with electromagnetic band gap (EBG) structures. Arrays of periodic holey structures are used to realize the metasurface waveguide. Two Bravais lattice structures – square and hexagonal, are explored for guiding waves along a desired path in a parallel plate waveguide. Simulations are carried out to study the influence of various dimensions of the unit cells. A waveguide with hexagonal hole-type unitcell is designed and manufactured for experimental verification. The possibility of extending the same technology to cylindrical surface is confirmed by simulations. / Trådlösa sensorer används allmänt för tillståndsövervakning i elektriska maskiner. Metallhöljet hos en elektrisk motor begränsar signalen från sensorerna från att stråla utåt. Signalen från metallhåligheten behöver styras till den enda öppningen i höljet, genom ett smalt mellanrum mellan statorn och den roterande rotorn. Gap-vågledarteknik föreslås som en lösning genom att strukturera statorytan med elektromagnetiska bandgap-strukturer (EBG). Arrayer av periodiskt håliga strukturer används för att realisera metayt-vågledare. Två Bravais gitterkonstruktioner –kvadratiska och sexkantiga, undersöks för styrning av vågor längs en önskad väg i en parallellplattvågledare. Simuleringar utförs för att studera påverkan av olika dimensioner hos enhetscellerna. En vågledare med hexagonal håltypsenhetscell är konstruerad och tillverkad för experimentell verifiering. Möjligheten att utvidga samma teknik till cylindrisk yta bekräftas genom simuleringar.