High performance multilayer Substrate Integrated Waveguide (SIW) technics for low-cost millimeter-wave circuits

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High performance multilayer Substrate Integrated Waveguide (SIW) technics for low-cost millimeter-wave

circuits

Frederic Parment

To cite this version:

Frederic Parment. High performance multilayer Substrate Integrated Waveguide (SIW) technics for low-cost millimeter-wave circuits. Optics / Photonic. Université Grenoble Alpes, 2016. English.

�NNT : 2016GREAT077�. �tel-01505416�

THÈSE

Pour obtenir le grade de

DOCTEUR DE LA COMMUNAUTE UNIVERSITE GRENOBLE ALPES

Spécialité : OPTIQUE ET RADIOFREQUENCES

Arrêté ministériel : 25 Mai 2016

Présentée par

Frédéric PARMENT

Thèse dirigée par Pr Tan Phu VUONG, Codirigée par Pr Ke WU

Co-encadrée par M Anthony GHIOTTO Co-encadrée par M Jean-Marc DUCHAMP

préparée au sein du Laboratoire IMEP-LaHC de l’Institut National Polytechnique de Grenoble,

dans l'École Doctorale Electronique, Electrotechnique, Automatique, et Traitement du Signal.

Guides d’onde Intégrés au Substrat (SIW) multicouches à haute performance pour des circuits millimétriques à faible coût

Thèse soutenue publiquement le 04 Novembre 2016, devant le jury composé de :

Monsieur Eric RIUS

Professeur à l’Université de Bretagne Occidentale, Président Monsieur Hervé AUBERT

Professeur à l’Institut National Polytechnique de Toulouse, Rapporteur Monsieur Jean-Louis CAZAUX

Responsable Innovation à Thales Alenia Space de Toulouse, Rapporteur Monsieur Maurizio BOZZI

Professeur à l’Université de Pavie, Membre Monsieur Ke WU

Professeur à l’Ecole Polytechnique de Montréal, Membre Monsieur Anthony GHIOTTO

Maître de conférences à l’Institut Polytechnique de Bordeaux, Membre Monsieur Jean-Marc DUCHAMP

Maître de conférences à l’Université Joseph Fourier, Membre Monsieur Tan Phu VUONG

Professeur à l’Institut Polytechnique de Grenoble, Membre Monsieur Ludovic CARPENTIER

Ingénieur de recherche au CNES de Toulouse, Membre Invité Monsieur Pierre MONTEIL

Responsable Business Unit à COBHAM de Bordeaux, Membre Invité Monsieur Laurent PETIT

Responsable Projet Recherche et Technologie à Radiall Voreppe, Membre Invité

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La théorie, c'est quand on sait tout et que rien ne fonctionne. La pratique, c'est quand tout fonctionne et que personne ne sait pourquoi. Ici, nous avons réuni théorie et pratique : Rien ne fonctionne... et personne ne sait pourquoi !

Albert Einstein

A ma famille et mes proches…

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ACKNOWLEDGEMENT

I would like to express my sincere gratitude to my supervisor, Pr Tan Phu VUONG, and my co-supervisors Pr Ke WU, Mr Anthony GHIOTTO and Mr Jean-Marc DUCHAMP for their help, guidelines and support, that contributed to the excellent research work presented in this thesis manuscript. I would like to particularly thank Anthony for his unwavering support, valuable advices, and unfailing commitment in my research project and beyond.

I would like to also express my thanks to the engineers and technicians that offered a strong support, together with valuable assistance and advices, during my experimental validations, including Mr Nicolas CORRAO from the IMEP-LaHC research center, Ms Magali DE MATOS and Ms Isabelle FAVRE from the IMS research center, and Mr Traian ANTONESCU, Mr Jules GAUTHIER, Mr Steeve DUBE, Mr Jean-Sebastien DECARIE and Mr Maxime THIBAULT from the POLY-GRAMES research center.

I would like to express my recognition to the administrative staff, inluding Isabelle, Joëlle, Valérie, Annaïck, Brigitte, Dahlila, Fabienne from Grenoble, and Rachel from the POLY-GRAMES for their support. They have helped me a lot during my PhD on the different admisnitrative aspects.

I would like to thank my colleges and friends, including Zyad, Matthieu, Aline, Hamza, Ayssar, Isaac, Vipin, Furat, An-Thu, Vladimir, Vlad, and others from the IMEP-LaHC, Jaber and Kuangda from the POLY-GRAMES, and Tifenn, Alexandre, and others from the IMS. I would also like to thank my supportive friends, Alexis and Alexandre.

Finally, I would like to express a deep sense of gratitude to my parents, Michèle and Jean-Michel, and my brother, Nicolas. You helped me all along my studies. You have supported me so that I could give my best. The last but not least, I would like to take the opportunity to express my love to my girlfriend, Lucile, who supported me the most, during the good and the bad days.

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TABLE OF CONTENTS

ACKNOWLEDGEMENT 5

TABLE OF CONTENTS 7

LIST OF ACRONYMS AND ABBREVIATIONS 9

SYNTHESE EN FRANÇAIS 11

CHAPTER I: INTRODUCTION 19

CHAPTER II: STATE-OF-THE-ART ON ELECTROMAGNETIC TRANSMISSION LINES 25

CHAPTER III: THE AIR-FILLED SIW TECHNOLOGY 65

CHAPTER IV: AIR-FILLED SIW FEEDING NETWORK ELEMENTS 101

CHAPTER V: AIR-FILLED SIW FILTERS AND ANTENNAS 147

CHAPTER VI: CONCLUSION AND PERSPECTIVES 183

ANNEX 1: COMPLETE ELLIPTIC INTEGRAL OF THE FIRST KIND 187

ANNEX 2: CALCULATION TO OBTAIN EQUATION (1.2) OF THE

CHAPTER III 189

LIST OF PUBLICATIONS, AWARDS AND PUBLICATIONS 191

ABSTRACT 195

RESUME 195

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LIST OF ACRONYMS AND ABBREVIATIONS

AFSIW Air-Filled Substrate Integrated Waveguide ALTSA Antipodal Linear Tapered Slot Antenna

APHC Average Power Handling Capability (W or dBm) 𝐵⃗ Magnetic induction (T)

BW Bandwidth (GHz)

c Light velocity (m/s)

CBCPW Conductor-Backed Coplanar Waveguide CMOS Complementary Metal Oxide Semi-conductor

CPW Coplanar Waveguide

𝐷⃗⃗ Electric induction (C/m²)

DFSIW Dielectric-Filled Substrate Integrated Waveguide

DUT Device Under Test

𝐸⃗ Electric field (V/m)

E0 Dielectric strength (MV/m) EBG Electromagnetic BandGap

EM Electromagnetic

f Frequency (Hz)

fc Cut-off frequency (Hz) FR-4 Flame Resistant 4

h Height of the structure (m) 𝐻⃗⃗ Magnetic field (A/m) HPBW Half Power Beamwidth (°)

IoT Internet Of Thing 𝑗 Current density (A/m²)

k Wave number (rad/m)

k0 Free-space Wave number (rad/m) Kc Cut-off wave number (rad/m)

LTCC Low Temperature Co-fired Ceramics

MHMIC Miniature Hybrid Microwave Integrated Circuit PCB Printed Circuit Board

PIM Passive InterModulation

PPHC Peak Power Handling Capability (W or dBm) q Electronic charge (C)

RADAR RAdio Detection And Ranging

RMS Root Mean Square

RWG Rectangular Waveguide

SIC Substrate Integrated Circuit

SINRD Substrate Integrated Non-Radiating Dielectric Waveguide SIS Substrate Integrated System

SISW Substrate Integrated Slab Waveguide SIW Substrate Integrated Waveguide tanδ Loss tangent

TE Transverse Electric

TEM Tranverse Electric Magnetic

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TM Transverse Magnetic

TRL Thru-Reflect-Line

VNA Vector Network Analyzer W Width of the structure (m)

WR Waveguide, Rectangular

αg Losses constant (Np/m) βg Phase constant (rad/m)

𝛤 Propagation constant (m^-1)

δ Skin depth (m)

ε Permittivity (F/m)

ε0 Vacuum permittivity (F/m) εr Relative permittivity

η Wave impedance (Ω)

λ Wavelength (m)

μ Permeability (H/m)

μ0 Vacuum permeability (H/m) μr Relative permeability

ρ Volume density charge (C/m³)

σ Conductivity (S/m)

ω Angular frequency (rad/s)

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SYNTHESE EN FRANÇAIS

L’émergence de nouvelles applications qui requièrent le développement de nouvelles technologies opérant aux fréquences millimétriques et au-delà, entre 30 et 300 GHz, est principalement due à l’augmentation ininterrompue des données et à l’accroissement insatiable de la demande en bande-passante. Le manque de canal libre dans les bandes radiofréquences et micro-ondes y contribue et force l’industrie à développer de nouveaux systèmes opérant en plus haute fréquence. Parmi ces nouvelles applications, l’Internet-des- Objets, les radars pour des systèmes types avioniques ou automobiles, les constellations de pico- et nanosatellites [1], l’imagerie médicale et sécuritaire, etc… sont un des nombreux marchés ciblés [2]. Les ondes millimétriques peuvent fournir beaucoup d’avantages pour ces futurs systèmes parmi lesquels de larges bandes passantes, une pénétration accrue dans la fumée ou le brouillard, un vaste spectre peu utilisé et bien d’autres.

Un autre point qui est tout aussi important pour l’industrie est la densité d’intégration.

En effet, une haute densité d’intégration permet de réduire les coûts par la production de masse, avec un emballage petit et léger facilitant l’adoption des produits. C’est dans le début des années 1950 que la première ligne de transmission planaire, appelée microruban, a été développée. Aujourd’hui, cette même ligne est devenue la ligne de transmission la plus populaire et utilisée jusqu’à 30 GHz. Elle combine une structure simple, bien décrite théoriquement avec des modèles implémentés dans la plupart des logiciels de conception, et elle peut être produite à prix bon marché par l’utilisation de procédés de fabrication issus des circuits imprimés. Cependant, au-delà de 30 GHz, les lignes de transmission en guides d’onde coplanaires sont préférées aux lignes microrubans, car à ces fréquences, ces dernières ont besoin de substrat fin pour éviter l’excitation de mode d’ordre supérieur, pour éviter aussi de subir des courants de fuite, qui augmentent les pertes par radiation, et elles deviennent aussi plus difficiles à fabriquer du fait dela réduction de la longueur d’onde qui requièrent une

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tolérance de fabrication accrue, notamment sur les vias par exemple. Néanmoins, la contribution sur les performances induites par la rugosité de surfaces et celle de l’effet de peaux de la ligne conductrice augmente avec la fréquence. Par conséquent, ces circonstances, prises dans leur ensemble, génèrent une haute densité de courants s’écoulant au travers d’une fine région sous la surface métallique du conducteur, et les pertes s’en retrouvent d’autant augmentées [3]-[4]. Ce problème devient bien plus important dès lors que la forme des bords de la ligne conductrice n’est plus rectangulaire. Bien que le récent développement de substrat faibles pertes ait largement réduit les pertes, celles qui sont liées au conducteur deviennent prédominantes aux fréquences millimétriques et au-delà. Enfin, la tenue en puissance pour ce genre de lignes de transmission est un problème pour les applications à forte puissance. Pour toutes ces raisons, la technologie en guide d’onde rectangulaire est encore très utilisée en haute fréquence parce qu’elle surpasse en performance toutes les lignes standards. Très coûteux à produire, lourds et difficiles à interconnecter ou à intégrer avec d’autres technologies, les inconvénients du guide d’onde rectangulaire restent un challenge à résoudre encore aujourd’hui.

Pour combler le fossé entre le guide d’onde rectangulaire et les lignes de transmission planaires, une nouvelle génération de circuits planaires a vu le jour au début des années 2000, c’est-à-dire les Circuits Intégrés au Substrat (CIS) [5]. Cette nouvelle famille de lignes de transmission a reçu une attention particulière depuis plus de dix ans. Les CISs combinent les avantages des technologies sur circuits imprimés avec celle du guide d’onde : un poids léger, une structure compacte, blindée par nature, bon marché et facile a interconnecté avec des technologies traditionnelles. Cette technologie peut se décliner en plusieurs topologies : le Guide d’onde Intégré au Substrat (SIW) [6] en Fig. 1(a), le Guide d’onde Intégré au Substrat à Barreau Diélectrique (SISW) [7] en Fig. 1(b), et le Guide d’onde Diélectrique Intégré au Substrat Non-Radiatif (SINRD) [8] en Fig. 1(c) comme exemples non exhaustifs. Beaucoup

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d’entre eux ont été réalisés en utilisant différentes techniques de fabrication comme les circuits imprimés (PCB), les circuits micro-ondes intégrés hybrides miniatures (MHMIC), les céramiques cocuites à basse température (LTCC) ou bien les technologies sur silicium comme le CMOS [9].

(a) (b)

(c)

Figure 1 : Illustration du SIW (a), SISW (b), et SINRD (c).

Le SIW est devenu le plus populaire et la topologie la plus utilisée de la famille des CISs. Il hérite principalement ses propriétés du guide d’onde rectangulaire, et il est facile à fabriquer, car il n’a besoin que de deux rangés de vias métalisés. C’est pourquoi il est aussi facile à concevoir qu’à fabriquer. Du PCB au CMOS en passant par le LTCC, le SIW est compatible avec beaucoup de processus de fabrication. De quelques gigahertz à une centaine de gigahertz, son spectre d’application est large et varié : applications spatiales, radar automobile, ou application de sûreté comme les scanners et ainsi de suite. Le SIW bénéficie d’un grand potentiel. Néanmoins, le SIW est une ligne de transmission utilisant du substrat et souffre des pertes induites par le diélectrique, qui augmentent à haute fréquence, et diminue sa tenue en puissance. Cette limitation réduit grandement la performance d’une telle technologie, et donc son champ d’application.

Plan de masse du dessus Substrat

diélectrique Via métallisé

Trou d’air

Substrat diélectrique

Plaque de métal du dessus

Plaque de métal du dessous Trou d’air

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Figure 2 : Comparaison des propriétés entre une ligne de transmission standard en circuit imprimé, un guide d’onde rectangulaire, un SIW et un SIW creux.

Après une brève introduction dans le Chapitre I, le contexte actuel de cette thèse est bien plus détaillé dans le Chapitre II. Cette partie présente de façon chronologique les différentes lignes de transmission électromagnétiques en partant des équations de Maxwell, des guides d’onde métalliques rectangulaires jusqu’aux lignes planaires et les structures dites SIW. Une comparaison entre ces lignes en termes de performance mais aussi sur les procédés de fabrication est faite, ceci afin de mieux comprendre quelle est le positionememnt de la technologie SIW creux au milieu des technologies existantes.

Ainsi, dans le Chapitre III, cette nouvelle topologie de CIS est présentée dont le nom est SIW creux. Elle consiste en une ligne de transmission réalisée grâce aux techniques des circuits imprimés multicouches avec une partie à l’intérieur en air faite par un micro-usinage laser. L’objectif d’une telle structure est de diminuer drastiquement la contribution des pertes diélectriques en remplaçant le substrat par de l’air. Les rangés de vias sont maintenues afin d’obtenir une structure complète SIW, avec aucune propagation du mode TM. La structure finale est présentée au Chapitre III avec une analyse théorique des pertes et de la tenue en puissance qui est comparée aux résultats de simulation et expérimentaux. Une comparaison des performances est donnée à la Fig. 2 entre le guide d’onde rectangulaire, le SIW, une ligne

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planaire standard en PCB et le SIW creux. Il est à noter qu’une réduction de 75% des pertes comparé à une ligne SIW utilisant le même substrat a été observée lors des mesures des niveaux de pertes. Ceci a conduit à une augmentation de la tenue en puissance moyenne.

Enfin, pour interconnecter cette technologie avec celle qui est en SIW, une transition a été conçue et mesurée ainsi que des topologies de coudes. Cette transition a été conçue de façon large bande afin de pouvoir l’utiliser pour interconnecter n’importe quel composant en SIW creux avec le SIW. Pour des raisons liées à la mesure, un kit de calibration Thru-Reflect-Line a été créé en SIW creux pour dé-embeder toutes transitions se trouvant entre le dispositif à mesurer et l’analyseur de réseau.

Ensuite, plusieurs circuits passifs ont été conçus et implémentés en utilisant le SIW creux. Dans le Chapitre IV, des éléments basiques souvent utilisés dans des réseaux d’alimentation sont démontrés. Un diviseur de puissance utilisant une jonction en T et un coupleur de Riblet ont été réalisé. Une diminution des pertes a été observée. Deux coupleurs directionnels, un de type Moreno et un autre de type deux trous sont détaillés. Enfin, un déphaseur à double paroi diélectrique en SIW creux est présenté avec une analyse théorique, suivie par des résultats de simulations et de mesures. Basé sur ce composant, un déphaseur large bande compensé en SIW creux est décrit et mesuré. La compensation a été réalisée en utilisant la variation croissante de la phase avec la fréquence pour le déphaseur à double paroi diélectrique et la variation décroissante de la phase avec la fréquence pour un SIW creux élargie. Ainsi, les deux variations se companse l’une l’autre. Un déphasage de 43° ± 6° est démontré sur toute la bande Ka.

Pour finir, des filtres et antennes basés sur le SIW creux sont présentés. Dans la première partie du chapitre V, deux filtres passe-bande ont été réalisés en SIW creux. D’une part, un filtre d’ordre trois utilisant des ponts inductifs a été conçu et comparé à sa version en SIW. Une amélioration du facteur de qualité d’un facteur 4 environ dans le cas du dispositif

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en SIW creux est à noter. D’autre part, un filtre d’ordre quatre multicouche à cavités verticalement empilées est présenté. C’est le premier dispositif dans cette technologie utilisant pleinement la possiblité de monter verticalement et donc de réduire l’empreinte d’un composant passif tel qu’un filtre. Dans la seconde partie de ce chapitre, deux antennes en SIW creux sont testées. D’abord, une antenne à fentes en SIW creux avec 4 ouvertures rectangulaires est démontrée et comparée avec sa version en SIW. Ensuite, une antenne de type ALTSA est créée en SIW creux en utilisant le processus multicouche des circuits imprimés. Les performances de cette antenne sont également comparées à sa version SIW.

Dans les deux cas, une augmentation du gain est observé ainsi qu’une amélioration de l’efficacité de radiation.

Finalement, le Chapitre VI conclut ce manuscrit. Le travail de recherche présenté dans ce manuscrit de thèse a fait l’objet de nombreuses publications incluant 5 revues internationales (4 publiées et 1 soumise), 6 conférences internationales, 6 conférences nationales et 4 communications.

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References:

[1] P. Christopher, "Millimeter wave advantages for satellite communications," Military Communications Conference, 1983. MILCOM 1983. IEEE, Washington, DC, USA, pp. 555-562.C, 2010.

[2] D. R. Vizard, “Millimeter-wave applications: from satellite communications to security systems,” Microwave Journal, Euro-Global Edition, vol. 49, no. 7, pp. 22–36, Jul. 2006.

[3] K. Wu, "Towards the development of terahertz substrate integrated circuit technology," Silicon Monolithic Integrated Circuits in RF Systems (SiRF), 2010 Topical Meeting on, New Orleans, LA, pp. 116-119, 2010.

[4] M. Bozzi, A. Georgiadis and K. Wu, "Review of substrate-integrated waveguide circuits and antennas," in IET Microwaves, Antennas & Propagation, vol. 5, no. 8, pp.

909-920, June 6, 2011.

[5] Ke Wu, D. Deslandes and Y. Cassivi, "The substrate integrated circuits - a new concept for high-frequency electronics and optoelectronics," Telecommunications in Modern Satellite, Cable and Broadcasting Service, 2003. TELSIKS 2003. 6th International Conference on, pp. P-III-P-X vol.1, 2003.

[6] M. Bozzi, F. Xu, D. Deslandes and K. Wu, "Modeling and design considerations for substrate integrated waveguide circuits and components," Telecommunications in Modern Satellite, Cable and Broadcasting Services, 2007. TELSIKS 2007. 8th International Conference on, Nis, pp. P-VII-P-XVI, 2007.

[7] D. Deslandes, M. Bozzi, P. Arcioni and Ke Wu, "Substrate integrated slab waveguide (SISW) for wideband microwave applications," Microwave Symposium Digest, 2003 IEEE MTT-S International, Philadelphia, PA, USA, vol.2, pp. 1103-1106, 2003.

[8] P. Mondal and K. Wu, "A leaky-wave antenna in substrate integrated non-radiative dielectric (SINRD) waveguide with controllable scanning rate," in IEEE Transactions on Antennas and Propagation, vol. 61, no. 4, pp. 2294-2297, April 2013.

[9] K. Wu, "Substrate integrated circuits (SICs) for GHz and THz electronics and photonics: Current status and future outlook," German Microwave Conference Digest of Papers, Berlin, pp. 292-295, 2010.

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CHAPTER I:

INTRODUCTION

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The emerging applications require the development of new technologies especially at millimeter-waves and beyond (30 GHz to 300 GHz). This is mainly due to the increase of data and hence the growth of bandwidth. The lack of free channel in the radiofrequency and microwave bands forces the industries to develop new systems at higher frequency. Among these new applications, Internet-Of-Things, automotive and aircraft radar systems, pico- and nano-satellite constellations [1] and communications, medical and safety imaging like scanners are one of the targeted markets as described in [2]. Millimeter-waves can provide various advantages for those future systems among which broad bandwidth, the penetration through smog or fog, the large unused frequency spectrum and so on.

Another point which is critical for industries is the density of integration. A high- density reduces cost, allows mass-producible, small and lightweight packaging for commercial products. This is during the beginning of the 1950’s that the first planar transmission line, called microstrip, was developed. Nowadays, microstrip is the most used and popular transmission line up to 30 GHz. It combines a simple structure, theoretically well-analyzed with models implemented into software and it can be produced at a low-cost owing to the Printed Circuit Board manufacturing process. However, beyond 30 GHz, Coplanar Waveguide (CPW) transmission lines are preferred because microstrip lines need thin substrate to avoid higher order modes excitation, undergo leakage currents that raise the radiation loss and, are more difficult to fabricate due to the reduction of the wavelength that requires high precision fabrication tolerances, like vias for example. Nevertheless, the contribution of the surface roughness and the skin effect on the performance of the stripline rises with the frequency. As consequences, both circumstances generate high current density flowing through a thin region below the metallic surface of the conductor and the losses are significantly raised [3]-[4]. This issue is even worse for planar transmission lines in general when the shape of the conductor strip edges is not rectangular. Even if the recent development

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of low-loss dielectric has largely reduced the losses, the conductor losses are predominant in millimeter-waves and beyond. Finally, the power handling is also an issue for high power applications. For these reasons, the Rectangular Waveguide (RWG) technology is still preferred at high frequency because it surpasses performances from all standard transmission lines. However, such structure is too expensive, heavy and difficult to integrate or interconnect.

(a) (b)

(c)

Figure 1: Pictures of SIW (a) [6], SISW (b) [7], and SINRD (c) [8].

To bridge the gap between RWG and planar transmission line, a new generation of planar circuits have been introduced during the beginning 2000’s, namely the Substrate Integrated Circuits (SIC) [5]. This new family of transmission line has received a particular attention since the past decade. SICs combine advantages from both previous technologies: a light weight, a compact and low-cost structure that is easy to interconnect with traditional technologies and is self-shielded. SICs can be declined in several topologies: Substrate Integrated Waveguide (SIW) [6] Fig. 1(a), Substrate Integrated Slab Waveguide (SISW) [7]

Fig. 1(b), and Substrate Integrated Non-Radiating Dielectric Waveguide (SINRD) [8]

Fig. 1(c) as a list of non-exhaustive examples. Many of them have been realized using

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different fabrication techniques like PCB, MHMIC, LTCC or CMOS [9]. SIW became the most popular and used topology from the SICs family. It inherits largely its properties from the RWG, and it is easy to fabricate as it requires mainly two rows of matalized via-holes. In addition, SIW is compatible with different manufacturing techniques including PCB, CMOS, LTCC, for example. From few GHz to a few hundred of GHz, its spectrum of applications is large and various, including space and radar applications. SIW benefits from a great potential.

Nevertheless, SIW is a substrate-based transmission line and suffers from dielectric losses, which increase at high frequency and decrease the power handling capability. This limitation reduces the performance of such technology, and hence its applications.

In this context, which is more detailed in Chapter II, a new topology of SIC, namely Air-Filled SIW (AFSIW), is presented in this thesis. It consists of a multilayer printed circuit board transmission line with a laser micromached air-cut. The aim of such structure is to drastically reduce the dielectric loss contribution by removing the dielectric and replacing it by air. The rows of vias are maintained to obtain a complete SIW structure, without TM modes propagation. The structure with a theoretical analysis of losses and power handling capability compared to the simulated and the measured results are presented in Chapter III. A comparison of performances between the standard planar transmission line, RWG, SIW, and AFSIW is shown in Fig. 2. To interconnect this technology with existing SIW, a transition is introduced and bend topologies are studied. For measurement purposes, an AFSIW Thru- Reflect-Line calibration kit has been designed to de-embed all necessary transitions between the device under test (DUT) and the Vector Network Analyzer (VNA).

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Figure 2: Comparison of standard transmission line, RWG, SIW and AFSIW properties.

Then, several passive circuits have been designed and implemented using this AFSIW technology. In Chapter IV, basic elements often found in feeding networks are explored. A power divider using a T-junction, together with Riblet, Moreno and two-hole couplers are demonstrated. Then, a double dielectric slab-loaded AFSIW phase shifter is introduced with analytical, simulated and measured results. Based on this component, a broadband compensated AFSIW phase shifter is proposed.

Finally, passive resonating and radiating circuits have been explored by the implementation of AFSIW filters and antennas. In the first part of the Chapter V, two passband filters are experimented using AFSIW technology. On the one hand, a third order AFSIW filter using inductive posts compared to its SIW counterpart is realized, and on the other hand, a fourth order multilayer vertically stacked cavitie AFSIW filter is presented. In the second part, two AFSIW antennas are introduced. An AFSIW slot antenna with four apertures is demonstrated and compared to its SIW counterpart. Then, an AFSIW Antipodal Linear Tapered Slot Antenna (ALTSA) is designed based on AFSIW technology. This antenna is also compared to its SIW version. At the end, Chapter VI concludes this thesis and presents some perpestives.

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The research work, introduced in this manuscript, has been published in 5 international journals (4 published and 1 submitted), 6 international conferences, 6 national conferences and 4 communications.

References:

[1] P. Christopher, "Millimeter wave advantages for satellite communications," Military Communications Conference, 1983. MILCOM 1983. IEEE, Washington, DC, USA, pp. 555-562.C, 1983.

[2] D. R. Vizard, “Millimeter-wave applications: from satellite communications to security systems,” Microwave Journal, Euro-Global Edition, vol. 49, no. 7, pp.22–36, Jul. 2006.

[3] K. Wu, "Towards the development of terahertz substrate integrated circuit technology," Silicon Monolithic Integrated Circuits in RF Systems (SiRF), 2010 Topical Meeting on, New Orleans, LA, pp. 116-119, 2010.

[4] M. Bozzi, A. Georgiadis and K. Wu, "Review of substrate-integrated waveguide circuits and antennas," in IET Microwaves, Antennas & Propagation, vol. 5, no. 8, pp.

909-920, June 6, 2011.

[5] Ke Wu, D. Deslandes and Y. Cassivi, "The substrate integrated circuits - a new concept for high-frequency electronics and optoelectronics," Telecommunications in Modern Satellite, Cable and Broadcasting Service, 2003. TELSIKS 2003. 6th International Conference on, pp. P-III-P-X, vol.1, 2003.

[6] M. Bozzi, F. Xu, D. Deslandes and K. Wu, "Modeling and design considerations for substrate integrated waveguide circuits and components," Telecommunications in Modern Satellite, Cable and Broadcasting Services, 2007. TELSIKS 2007. 8th International Conference on, Nis, pp. P-VII-P-XVI, 2007.

[7] D. Deslandes, M. Bozzi, P. Arcioni and Ke Wu, "Substrate integrated slab waveguide (SISW) for wideband microwave applications," Microwave Symposium Digest, 2003 IEEE MTT-S International, Philadelphia, PA, USA, pp. 1103-1106, vol.2, 2003.

[8] P. Mondal and K. Wu, "A leaky-wave antenna in substrate integrated non-radiative dielectric (SINRD) waveguide with controllable scanning rate," in IEEE Transactions on Antennas and Propagation, vol. 61, no. 4, pp. 2294-2297, April 2013.

[9] K. Wu, "Substrate integrated circuits (SICs) for GHz and THz electronics and photonics: Current status and future outlook," German Microwave Conference Digest of Papers, Berlin, pp. 292-295, 2010.

25

CHAPTER II: STATE- OF-THE-ART ON

ELECTROMAGNETIC TRANSMISSION

LINES

26

TABLE OF CONTENTS

TABLE OF CONTENTS ... 26 LIST OF FIGURES ... 27 LIST OF TABLES ... 28 1. ELECTROMAGNETIC RADIATION ... 29 1.1. FREE SPACE PROPAGATION ... 30 1.2. GUIDED WAVES [2] ... 33 2. TRANSMISSION LINES ... 35 2.1. METALLIC WAVEGUIDES ... 35 2.2. PLANAR TRANSMISSION LINES ... 40 2.2.1. Stripline ... 40 2.2.2. Microstrip Line ... 43 2.2.3. Coplanar Waveguide ... 45 2.2.4. Slow-Wave Transmission Line ... 48 2.2.5. Discussion ... 49 2.3. SUBSTRATE INTEGRATED WAVEGUIDE ... 50 2.3.1. Historical Background ... 50 2.3.2. SIW Structure and Performance ... 52 2.3.3. SIW Topologies ... 55 2.3.4. SIW Circuits ... 57 3. CONCLUSION ... 59 REFERENCES ... 61

27

LIST OF FIGURES

FIGURE 1:ELECTROMAGNETIC SPECTRUM [1]. ... 29 FIGURE 2:ILLUSTRATION OF THE FREE SPACE MODEL. ... 31 FIGURE 3:A PLANAR SECTION FROM A UNIFORM RECTILINEAR TRANSMISSION SYSTEM. ... 34 FIGURE 4:PICTURE OF KA-BAND RECTANGULAR WAVEGUIDE COMPONENTS [2]. ... 36 FIGURE 5:GEOMETRY OF RECTANGULAR WAVEGUIDE. ... 37 FIGURE 6:RECTANGULAR WAVEGUIDE LOSSES [7]. ... 39 FIGURE 7:(A)AVERAGE POWER HANDLING CAPABILITY (APHC) AND (B)PEAK POWER

HANDLING CAPABILITY (PPHC) FOR STANDARD RECTANGULAR WAVEGUIDES [8]. ... 39 FIGURE 8:EVOLUTION OF THE FLAT-STRIP LINE: FROM (A)COAXIAL LINE,(B)SQUARE LINE,(C)

RECTANGULAR LINE TO (D) FLAT-STRIP TRANSMISSION LINE [9]. ... 40 FIGURE 9:(A)STRIPLINE PROPOSED BY AIRBORNE INSTRUMENTS LABORATORY AND (B) THE

TRI-PLATE LINE PROPOSED BY SAUNDERS ASSOCIATES INC.[9]. ... 41 FIGURE 10:(A)GEOMETRY OF A STRIPLINE AND (B) A DESCRIPTION OF ITS ELECTRIC AND

MAGNETIC FIELD [2]. ... 41 FIGURE 11:(A)GEOMETRY OF A MICROSTRIP LINE AND (B) A DESCRIPTION OF ITS ELECTRIC AND

MAGNETIC FIELD FOR THE FUNDAMENTAL MODE [2]. ... 43 FIGURE 12:GEOMETRY OF A CPW WITH A FINITE THICKNESS SUBSTRATE [17]. ... 45 FIGURE 13:GEOMETRY OF A CBCPW WITH A FINITE THICKNESS SUBSTRATE [17]. ... 47 FIGURE 14:GEOMETRY OF (A) A SLOW WAVE CPW[27] AND (B) A SLOW WAVE MICROSTRIP

[28]. ... 48 FIGURE 15:EVOLUTION OF COMPUTER POWER [43]. ... 52 FIGURE 16:EVOLUTION OF PUBLISHED PAPERS ON SIW EXTRACTED FROM IEEEXPLORE

WEBSITE. ... 52 FIGURE 17:(A)SIW GEOMETRY [46] AND (B)SIW CROSS-SECTION VIEW WITH THE

FUNDAMENTAL TE10MODE ELECTRICAL FIELD REPRESENTATION. ... 53 FIGURE 18:DIFFERENT TOPOLOGIES OF SIW:(A)SIFW,(B)HF-SIW,(C)SISW, AND (D)RSIW

[54]. ... 56 FIGURE 19:(A)3-D VIEW AND (B) CROSS SECTION VIEW OF THE SW-SIW[56]. ... 57 FIGURE 20:SEVERAL TOPOLOGIES OF FILTER:(A)FILTER WITH ASYMMETRIC INDUCTIVE POSTS,

(B)FILTER WITH SYMMETRIC INDUCTIVE POSTS,(C)FILTER WITH CIRCULAR CAVITIES, AND

(D)FILTER WITH RECTANGULAR CAVITIES AND CROSS-COUPLING [54]. ... 58 FIGURE 21:(A)BLOCK DIAGRAM AND (B) PICTURE OF THE 4X4BUTLER MATRIX [59]. ... 58 FIGURE 22:TOPOLOGIES OF ANTENNAS:(A)ALTSA,(B) HORN ANTENNA,(C) LEAKY WAVE

ANTENNA, AND (D) ANTENNA NETWORK. ... 59 FIGURE 23:COMPARISON OF INSERTION LOSS, COST AND SIZE OF DIFFERENT RESONATOR

TECHNOLOGIES [70]. ... 60

28

LIST OF TABLES

TABLE I:ELECTROMAGNETIC EQUATIONS OF THE TE AND TM MODES IN RECTANGULAR

WAVEGUIDE [2]. ... 37 TABLE II:TRANSMISSION LINES PERFORMANCE COMPARISON. ... 60

29

1. ELECTROMAGNETIC RADIATION

Electromagnetic Radiation (EMR) consists mainly of electromagnetic waves which can be split up into transverse electric and magnetic fields propagating at the speed of light through vacuum. These waves are characterized by the frequency or the wavelength of their oscillations constituting the electromagnetic spectrum as depicted in Fig. 1.

Figure 1: Electromagnetic Spectrum [1].

The physical optics theory appeared during the 17^th century with the research work from Christiaan Huygens. His research is mainly focused on the law of reflection and refraction to predict wave behavior. Then, Augustin Fresnel kept up to work on the optical domain and developed the concept of wavelength and interference.

In the middle of 19^th century, James Clerk Maxwell has summarized the electromagnetic laws developed by Gauss, Ampere, Faraday, and others, and introduced the Maxwell’s equations given by (1.1) to (1.5). He succeeded to foresee the existence of electromagnetic waves and demonstrated that the light is an electromagnetic wave. These equations consist of a set of partial differential equations which describe how electric and

30

magnetic fields are generated and altered by each other, or by charges and currents at a macroscopic level.

Maxwell

Gauss 𝑑𝑖𝑣 𝐸⃗ = 𝜌

𝜀₀ (1.1)

𝑑𝑖𝑣 𝐵⃗ = 0 (1.2)

Maxwell

Faraday 𝑟𝑜𝑡⃗⃗⃗⃗⃗⃗ 𝐸⃗ = −𝜕𝐵⃗

𝜕𝑡 (1.3)

Maxwell

Ampere 𝑟𝑜𝑡⃗⃗⃗⃗⃗⃗ 𝐵⃗ = 𝜇₀𝑗 + 𝜇₀𝜀₀𝜕𝐸⃗

𝜕𝑡 (1.4)

Lorentz 𝐹⃗⃗⃗ = 𝑞(𝐸⃗ + 𝑣 ∗ 𝐵⃗ ) _𝐿 (1.5)

Later on, Heinrich Hertz, Alexander Popov, Edouard Branly and Nikola Tesla began to develop and study theories and applications using the shortwave radio. Guglielmo Marconi was the first to manage to transfer a message from Great Britain to Canada over the Atlantic Ocean using a wireless telegraph in 1901. From this moment, the development of applications based on electromagnetic waves increased faster and faster.

1.1. Free Space Propagation

The propagation inside a wireless channel such as air, space or sea water can be modeled as the electromagnetic waves undergo many effects including reflection, diffraction and scattering due to the presence of obstacles in the channel. These phenomena can lead to increase propagation losses and have to be taken into account for designing a system (transmitter, receiver or transceiver) with a link budget analysis.

The reflection effect occurs when electromagnetic waves strike an object, such as the ground, buildings or walls, which have a larger size than the wavelength of the propagating waves. Furthermore, if the radio wave falls on a propagating medium having different electrical properties, part of the energy is transmitted and part of it is reflected back. The diffraction consists of a phenomena occurring when a travelling wave interacts with a surface having sharp irregularities. This happens in the case of skyscrapers and creates a shadowed

31

region where the received energy decreases as the user moves deeper. The Huygens’ principle can explain the diffraction effect and describes the field in the shadow region as a sum of multiple secondary sources producing a new wave front in direction of the receiver. Contrary to the reflection effect, the scattering manifests itself when the obstacle on the propagating channel is smaller than the wavelength of the waves. These various phenomena can lead to a multipath loss effect, increasing or decreasing the received power and must be included in the propagation equation.

In general case, antennas are used for transmitting signals and imply that the free space equations are mainly developed inside the far-field region, also called Fraunhofer region, where the propagating waves behave as plane waves and the power decays inversely with distance. Hence, this distance, df, is usually depicted as in (1.6) and depends on the largest dimension, D, of the antenna [2].

𝑑_𝑓= 2𝐷²

𝜆 (1.6)

The most well-known equation which models the free space propagation is the Friis equation given in (1.7) for two antennas in direct sight without obstacles [2] as shown in Fig. 2.

Figure 2: Illustration of the free space model.

𝑃_𝑟(𝑑) = 𝑃_𝑡𝐺_𝑡𝐺_𝑟𝜆²

(4𝜋)²𝑑²𝐿 (1.7)

where Pt is the transmitted power, Pr(d) is the received power, Gr and Gt are the receiver and transmitter antenna gain respectively, d is the distance between the antennas, ηrad is the

d

Antenna Receiver Antenna

Transmitter

G_tP_t G_rP_r

λ

32

radiation efficiency, and L is the coefficient taking into account all the perturbing effects. It has to be notified that the gain is related to the effective aperture, Ae, which depends on the physical size of each antenna as described in (1.8) [2].

𝐺 = 𝜂_𝑟𝑎𝑑4𝜋𝐴_𝑒

𝜆² (1.8)

Hence, it is also easy to represent the attenuation suffered by the propagating signal through a wireless channel. It is given by the difference of the transmitted and received power, called Path Loss, PL, and it is expressed in (1.9) [2].

𝑃𝐿(𝑑𝐵) = 10𝑙𝑜𝑔₁₀(𝑃_𝑡

𝑃_𝑟) (1.9)

To go further, some researchers had tried to find a better equation than this from Friis to match specific applications. Longley-Rice model, Durkin’s model, Okumura’s model, and Hata’s model are the most used for outdoor propagation model. As an example, Okumura’s model [3] is mainly used inside urban area from 100 MHz to 1900 MHz for a distance between 1 km and 100 km. This model has been essentially developed for mobile telecommunication. It is based on an empirical formula obtained from numerous measurements of signal attenuation between base stations to mobile phones. The empirical path-loss equation of Okumura is given by (1.10) [3] at a distance d.

𝑃𝐿_𝑑𝐵(𝑑) = 𝐿_{(𝑓𝑐,𝑑)}+ 𝐴_𝑚𝑢

(𝑓𝑐,𝑑)− 𝐺(ℎ_𝑡) − 𝐺(ℎ_𝑟) − 𝐺_{𝐴𝑅𝐸𝐴} (1.10) where L_(fc,d) is the free space path loss at a distance d and a carrier frequency fc, A_mu(fc,d) is the median attenuation in addition to free space path loss, G(ht) and G(hr) are the base station and mobile antenna gain, and GAREA is the gain changing with the environment. A_mu(fc,d) and GAREA are determined by the experiments. G(ht) and G(hr) are defined as follow:

𝐺(ℎ_𝑡) = 20𝑙𝑜𝑔₁₀( ℎ_𝑡

200) , 30 𝑚 < ℎ_𝑡 < 1000 𝑚 (1.11) 𝐺(ℎ_𝑟) = 10𝑙𝑜𝑔₁₀(ℎ_𝑟

3), ℎ_𝑟 ≤ 3 𝑚 (1.12)

33 𝐺(ℎ_𝑟) = 20𝑙𝑜𝑔₁₀(ℎ_𝑟

3) , 3 𝑚 < ℎ_𝑟 < 10 𝑚 (1.13) hr and ht are the height of the base station antenna and the mobile phone antenna respectively. This model has a derivation of 10-14 dB compared to empirical path loss and the path loss extracted from measurement.

Furthermore, contrary to Okumura’s model, it also exists indoor propagation models to take into account the specific environment related to the interior arrangement of our buildings.

For example, the covered distances are smaller than outside and the composition of each wall influences the propagation channel. When the control of the propagating waves is required by the application and the shape of the channel, it is necessary to model the behavior of signals by solving the Maxwell’s equations.

1.2. Guided Waves [2]

In the case of harmonic conditions, it is assumed that the material used as propagation channel is isotropic, linear and homogeneous. Hence, the dielectric losses and the magnetic losses are defined as depicted in equations (1.14) and (1.15). Therefore, the Maxwell’s equations become as in (1.16).

𝐷⃗⃗ = 𝜀𝐸⃗ (1.14)

𝐵⃗ = 𝜇𝐸⃗ (1.15)

Maxwell’s equations

𝑑𝑖𝑣 𝐷⃗⃗ = 0

(1.16) 𝑑𝑖𝑣 𝐵⃗ = 0

𝑟𝑜𝑡⃗⃗⃗⃗⃗⃗ 𝐸⃗ = −𝑗𝜔𝜇𝐻⃗⃗

𝑟𝑜𝑡⃗⃗⃗⃗⃗⃗ 𝐻⃗⃗ = 𝑗𝜔𝜀𝐸⃗

Based on (1.16), the wave’s equations for the electric and magnetic field can be extracted from [2] and are given in (1.17) and (1.18).

∆𝐸⃗ + 𝜔²𝜇𝜀𝐸⃗ = 0⃗ (1.17)

∆𝐻⃗⃗ + 𝜔²𝜇𝜀𝐻⃗⃗ = 0⃗ (1.18)

34

In the case of guided waves inside uniform rectilinear transmission system, as depicted in Fig. 3, the wave’s equations can be applied and solved. For that, it is assumed that a planar section of the propagation material is uniform and the propagation is along z-axis in a Cartesian coordinate system. The other axis (x, y) are used for the transverse fields. Thus, by studying the wave’s equations in this material, the dispersion equation can be written as in (1.19) [4].

Figure 3: A planar section from a uniform rectilinear transmission system.

𝐾_𝑐² = 𝛤²+ 𝜔²𝜇𝜀 with 𝛤 = 𝛼_𝑔+ 𝑗𝛽_𝑔 (1.19) Γ is the propagation constant and is the same inside all the planar section, even if there is more than one material because of the continuity equations. Then, the general equations of propagation can be defined as the relation between the transverse and lengthwise components of the electromagnetic field and are defined in (1.20) and (1.21) [4].

𝐾_𝑐²𝑒⃗⃗⃗ = 𝑗𝜔𝜇(𝑛⃗ ⋀𝑔𝑟𝑎𝑑_𝜏 ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ (ℎ_𝑧)) − (±) 𝛤𝑔𝑟𝑎𝑑⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ (𝑒_𝑧) (1.20) 𝐾_𝑐²ℎ⃗⃗⃗⃗ = −𝑗𝜔𝜀(𝑛⃗ ⋀𝑔𝑟𝑎𝑑_𝜏 ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ (𝑒_𝑧)) − (±) 𝛤𝑔𝑟𝑎𝑑⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ (ℎ_𝑧) (1.21) Based on the previous conditions and on the equations (1.20) and (1.21), only three main modes can exist and propagate in such propagation channel. Transverse Magnetic (TM) and Transverse Electric (TE) mode are characterized by the fact that there is no propagation of the magnetic and electric lengthwise field respectively. They are depicted in (1.22) and (1.23) where ZTM and ZTE are the impedance wave of each mode [2].

TM mode ℎ⃗⃗⃗⃗ = −_𝜏 1

𝑍_𝑇𝑀(𝑒⃗⃗⃗ ⋀(±𝑛⃗ )) with 𝑍_{𝜏 𝑇𝑀} = 𝛤

𝑗𝜔𝜀 (1.22)

0

z y

µ ε x Planar section

35

∆𝑒_𝑧+ 𝐾_𝑐²𝑒_𝑧 = 0

TE mode

𝑒_𝜏

⃗⃗⃗ = 𝑍_𝑇𝐸(ℎ⃗⃗⃗⃗ ⋀𝑛⃗ ) with 𝑍_{𝜏 𝑇𝐸} = 𝑗𝜔𝜇

±𝛤 (1.23)

∆ℎ_𝑧+ 𝐾_𝑐²ℎ_𝑧= 0

The third main mode is the Transverse Electric Magnetic (TEM) mode, which means that there is any propagation of lengthwise electromagnetic fields. Hence, the general equations of propagation (1.20) and (1.21) cannot be used. It is required to combine equations (1.16) and the general expression of the electric (1.24) and the magnetic field (1.25) [4].

𝐸⃗ = (𝑒⃗⃗⃗ + 𝑛⃗ . 𝑒_{𝜏 𝑧})𝑒^±𝛤𝑧 (1.24) 𝐻⃗⃗ = (ℎ⃗⃗⃗⃗ + 𝑛⃗ . ℎ_{𝜏 𝑧})𝑒^±𝛤𝑧 (1.25) As a result, the dispersion equation for the TEM mode is obtained in (1.26) and the transverse electric and magnetic fields are given in (1.27) and (1.28) respectively [4].

𝛤² = −𝜔²µ_𝑐𝜀_𝑐𝑎 (1.26)

𝑒_𝜏

⃗⃗⃗ = 𝑍_𝑇𝐸𝑀(ℎ⃗⃗⃗⃗ ^𝑛⃗ ) with 𝑍_{𝜏 𝑇𝐸𝑀} = 𝑗𝜔µ_𝑐

±𝛤 (1.27)

ℎ_𝜏

⃗⃗⃗⃗ = − 1

𝑍_𝑇𝐸𝑀(𝑒⃗⃗⃗ ^𝑛⃗ ) with 𝑍_{𝜏 𝑇𝐸𝑀} = ±𝛤

𝑗𝜔𝜀_𝑐𝑎 (1.28)

Now, it is easier to describe and predict the behavior of classical transmission line.

Using TE, TM and TEM mode, the main characteristics of each transmission line can be found. And finally, it allows scientists to design them and understand such structures.

2. TRANSMISSION LINES

2.1. Metallic Waveguides

The first wave guiding structure has been tested in 1894 based on the theory of Joseph John Thomson generalized by Lord Rayleigh [5]. He solved the boundary value problem of electromagnetic waves propagating in an arbitrary shaped waveguide. He has shown that the waves can travel with specific modes known as TE or TM modes, and a combination from them called hybrid mode. The cut-off wavelength was introduced to determine the section of a

36

hollow tube and the frequency below which waves could no longer propagate. Therefore, it became possible to develop passive devices, as shown in Fig. 4, or systems using these technologies and transmit an electromagnetic signal from one point to another while controlling the direction of propagation.

Figure 4: Picture of Ka-band rectangular waveguide components [2].

There are different topologies of waveguide such as the dielectric-loaded waveguide, the circular or ridge waveguide [6] and the well-known rectangular metallic waveguide as depicted in Fig. 5. The behavior of the last one is very well-described by solving the equations (1.22) and (1.23) for the TM and TE mode respectively while the boundary conditions have to be applied. Then, the propagation equations of the electric and magnetic fields in each mode are obtained as described in [2]. The equations of each mode inside such waveguide are summed up in Table 1.

37

Figure 5: Geometry of rectangular waveguide.

Value TEmn mode TMmn mode

k 𝜔√µ𝜀 𝜔√µ𝜀

kc √(𝑚𝜋

𝑎 )

2

+ (𝑛𝜋 𝑏 )

2 √(𝑚𝜋

𝑎 )

2

+ (𝑛𝜋 𝑏 )

2

fc

𝑐

2𝜋√𝜀_𝑐𝑎√(𝑚𝜋 𝑎 )

2

+ (𝑛𝜋 𝑏 )

2 𝑐

2𝜋√𝜀_𝑐𝑎√(𝑚𝜋 𝑎 )

2

+ (𝑛𝜋 𝑏 )

2

β √𝑘²− 𝑘_𝑐² √𝑘²− 𝑘_𝑐²

λc

2𝜋 𝑘_𝑐

2𝜋 𝑘_𝑐 λg

2𝜋 𝛽

2𝜋 𝛽 νp

𝜔 𝛽

𝜔 𝛽

Ez 0 𝐸₀sin (𝑚𝜋𝑥

𝑎 )sin (𝑚𝜋𝑦 𝑏 )

Hz 𝐻₀cos(𝑚𝜋𝑥

𝑎 )𝑐𝑜𝑠 (𝑚𝜋𝑦

𝑏 ) 0

Ex

𝑗𝜔µ_𝑐𝜋𝑛

𝑘_𝑐²𝑏 𝐻₀cos(𝑚𝜋𝑥

𝑎 )𝑠𝑖𝑛 (𝑚𝜋𝑦

𝑏 )𝑒^{−𝑗𝛽𝑧} −𝑗𝛽𝜋𝑚

𝑘_𝑐²𝑎 𝐸₀cos(𝑚𝜋𝑥

𝑎 )𝑠𝑖𝑛 (𝑚𝜋𝑦 𝑏 )𝑒^{−𝑗𝛽𝑧} Hx

𝑗𝛽𝜋𝑚

𝑘_𝑐²𝑎 𝐻₀sin(𝑚𝜋𝑥

𝑎 )𝑐𝑜𝑠 (𝑚𝜋𝑦

𝑏 )𝑒^{−𝑗𝛽𝑧} 𝑗𝜔𝜀_𝑐𝑎𝜋𝑛

𝑘_𝑐²𝑏 𝐻₀sin(𝑚𝜋𝑥

𝑎 )𝑐𝑜𝑠 (𝑚𝜋𝑦 𝑏 )𝑒^{−𝑗𝛽𝑧} Ey −𝑗𝜔µ_𝑐𝜋𝑚

𝑘_𝑐²𝑎 𝐻₀sin(𝑚𝜋𝑥

𝑎 )𝑐𝑜𝑠 (𝑚𝜋𝑦

𝑏 )𝑒^{−𝑗𝛽𝑧} −𝑗𝛽𝜋𝑛

𝑘_𝑐²𝑏 𝐸₀sin(𝑚𝜋𝑥

𝑎 )𝑐𝑜𝑠(𝑚𝜋𝑦 𝑏 )𝑒^{−𝑗𝛽𝑧} Hy

𝑗𝛽𝜋𝑛

𝑘_𝑐²𝑏 𝐻₀cos(𝑚𝜋𝑥

𝑎 )𝑠𝑖𝑛 (𝑚𝜋𝑦

𝑏 )𝑒^{−𝑗𝛽𝑧} −𝑗𝜔𝜀_𝑐𝑎𝜋𝑚

𝑘_𝑐²𝑎 𝐸₀cos(𝑚𝜋𝑥

𝑎 )𝑠𝑖𝑛 (𝑚𝜋𝑦 𝑏 )𝑒^{−𝑗𝛽𝑧}

Z 𝑍_𝑇𝐸 = 𝑘𝜂

𝛽 𝑍_𝑇𝐸 = 𝛽𝜂

𝑘

Table I: Electromagnetic equations of the TE and TM modes in rectangular waveguide [2].

0

z y

µ ε x b

a

38

This structure presents different loss mechanisms that impact the performance of such waveguide. First, the dielectric loss is mainly due to the dissipation of the electromagnetic energy inside the dielectric material. It can be explained by the fact that the molecules are naturally polarized and when an electric field is applied, it changes this polarization. As the electric field alternatively changes its polarization, it switches the polarization of the molecules constituting the dielectric material. As a result, a dissipation of the energy appears and molecules evacuate this energy by heat. It becomes obvious that this phenomenon depends also on the frequency. The metallic walls create the second loss mechanism. Each metallic material is mainly composed of atomic ions. When a current created by the magnetic field go through a metallic surface, collisions between electrons and atoms are generated. The created energy is evacuated by heating the conductor and leads to the conductor loss. These losses can be described by (1.29) and (1.30) for the dielectric and ohmic loss respectively for a rectangular waveguide as depicted in [2]. Hence, the total loss can be extracted and is illustrated in Fig. 6 [7] based on previous equations for different standard rectangular waveguide.

Another important property of the rectangular waveguide is the power handling. This results in different phenomenon that can limit the maximum transmitted power. For example, it exists the corona and multipaction effect¹ which take place generally for space and airspace applications. Here, the study is mainly focused on the average and peak power handling. The first one concerns the continuous power and the second one describes the maximum power that a wave-guiding structure can reach during a short time. Fig. 7 illustrates both of these parameters for several standard waveguides [8].

It can be concluded from Fig. 6 that rectangular waveguide is a high power and low loss transmission line. In addition, it is a bulky structure. However, it is necessary to use a precise

1The multipactor effect is a phenomenon in radio frequency waveguides, where, under certain conditions, secondary electron emission in resonance with an alternating electric field leads to exponential electron multiplication.

39

mechanical machining process to fabricate waveguide made of brass or aluminum and then, it results in a high cost and heavy device.

𝛼_𝑑 = 𝑘²𝑡𝑎𝑛𝛿

2𝛽 (1.29)

𝛼_𝑐 = 𝑅_𝑠

𝑎³𝑏𝛽𝑘𝜂(2𝑏𝜋² + 𝑎³𝑘²) 𝑤𝑖𝑡ℎ 𝑅_𝑠 = √𝜔𝜇_𝑐

2𝜎 (1.30)

Figure 6: Rectangular waveguide losses [7].

(a) (b)

Figure 7: (a) Average Power Handling Capability (APHC) and (b) Peak Power Handling Capability (PPHC) for standard rectangular waveguides [8].

40

2.2. Planar Transmission Lines

According to [9], the first planar transmission line appeared during the Second World War. It has been introduced by V. H. Rumsey and H. W. Jamieson. They have been applied to an antenna system and power feeding network. It consisted in a flat-strip coaxial transmission line. Its evolution is described in Fig. 8 and the work was reported at an IRE meeting and in subsequent articles [10]-[13]. After several years, during the 1950’s, the first planar circuit based on microwave printed-circuit technique have been realized mainly through several expanded research and development program. Several companies or laboratories decided to involve in this promising technology.

Figure 8: Evolution of the flat-strip line: from (a) Coaxial line, (b) Square line, (c) Rectangular Line to (d) flat-strip transmission line [9].

2.2.1. Stripline

Two different laboratories originally proposed the first stripline. The two proposed version are similar as illustrated in Fig. 9. The first one, shown in Fig. 9(a), consists in strip conductor inserted between two dielectric materials and enclosed by two conducting plates.

The second one, as described in Fig. 9(b), was made using a dielectric plate enclosed by two strip conductors and two conducting plates are suspended on top and bottom of the structure, also known as tri-plate line.

41

(a) (b)

Figure 9: (a) Stripline proposed by Airborne Instruments Laboratory and (b) the tri-plate line proposed by Saunders Associates Inc. [9].

The actual version of the stripline used as a transmission line is described in Fig. 10(a) with its electromagnetic field in Fig. 10(b). A thin conductor strip of W width is buried and centered inside a wide dielectric material. Two ground planes are added at a distance b/2 from the strip conductor and cover the entire dielectric region.

(a) (b)

Figure 10: (a) Geometry of a stripline and (b) a description of its electric and magnetic field [2].

The stripline can propagate TEM modes due to its structure and it is also the most used in this case. The characteristic impedance, given by (1.31) can be extracted from the TEM mode equations (1.26) to (1.28) and a computational fitting as described in [2].

𝑍₀ =30𝜋

√𝜀𝑟

𝑏

𝑊_𝑒+ 0.441𝑏 (1.31)

42 𝑊_𝑒

𝑏 = 𝑊

𝑏 − { 0 𝑓𝑜𝑟 𝑊 𝑏⁄ > 0.35 (0.35 −𝑊

𝑏)

2

𝑓𝑜𝑟 𝑊 𝑏⁄ < 0.35 (1.32) where We is the effective width of the strip conductor as depicted in (1.32). There are two cases for the calculation of the effective width due to fringing effect. For narrow strip conductor, the fringing effect impacts the electromagnetic behavior of such transmission line and is estimated for a W/b ratio lower than 0.35. For reasons related to stripline design, a version derived from the equations (1.31) and (1.32) is given in (1.33). This relation is referenced to the same 0.35 limit as in (1.32) but it is expressed in terms of impedance 120Ω.

𝑊 𝑏 =

{

30𝜋 𝑍₀√𝜀𝑟

− 0.441 𝑓𝑜𝑟 √𝜀_𝑟 𝑍₀ < 120𝛺

0.85 − √0.6 − 30𝜋 𝑍₀√𝜀𝑟

− 0.441 𝑓𝑜𝑟 √𝜀_𝑟𝑍₀> 120𝛺

(1.33)

The losses from a stripline are generated mainly by the conductor and dielectric losses.

The dielectric loss inherits largely from the TE or TM mode as described in (1.29). In the case of TEM, the cut-off wave number is cancelled, and therefore, the propagation constant becomes equal to the wave number which leads to (1.34). Concerning the ohmic loss, if t represents the thickness of the central conductor strip, it can be found by the perturbation method or Wheeler’s incremental inductance rule as in [2]. This results in the equation (1.35).

𝛼_𝑑 =𝑘𝑡𝑎𝑛𝛿

2 (1.34)

𝛼_𝑐 = {

2.7 ∗ 10⁻³𝑅_𝑠𝜀_𝑟𝑍₀

30𝜋(𝑏 − 𝑡) 𝐴 𝑓𝑜𝑟 √𝜀_𝑟𝑍₀ < 120𝛺 0.16𝑅_𝑠

𝑍₀𝑏 𝐵 𝑓𝑜𝑟 √𝜀_𝑟𝑍₀ > 120𝛺

(1.35)

with

𝐴 = 1 + 2𝑊 𝑏 − 𝑡+1

𝜋 𝑏 + 𝑡

𝑏 − 𝑡ln (2𝑏 − 𝑡

𝑡 ) (1.36)

𝐵 = 1 + 𝑏

0.5𝑊 + 0.7𝑡(0.5 +0.414𝑡

𝑊 + 1

2𝜋𝑙𝑛 (4𝜋𝑊

𝑡 )) (1.37)