On the geometry and the coupling schemes of broadband dielectric resonator antennas

Transcription

1 Research Collection Doctoral Thesis On the geometry and the coupling schemes of broadband dielectric resonator antennas Author(s): Almpanis, Georgios Publication Date: 29 Permanent Link: Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library

2 DISS. ETH No ON THE GEOMETRY AND THE COUPLING SCHEMES OF BROADBAND DIELECTRIC RESONATOR ANTENNAS A dissertation submitted to the SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH for the degree of Doctor of Sciences presented by GEORGIOS ALMPANIS D. Eng, National Technical University of Athens, Greece M. Sc, University of Central Florida, USA born May 19, 1979 citizen of Greece accepted on the recommendation of Prof. Dr. C. Hafner, examiner Prof. Dr. C. Fumeaux, co-examiner Dr. M. Mattes, co-examiner 29

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4 DISS. ETH No ON THE GEOMETRY AND THE COUPLING SCHEMES OF BROADBAND DIELECTRIC RESONATOR ANTENNAS A dissertation submitted to the SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH for the degree of Doctor of Sciences presented by GEORGIOS ALMPANIS D. Eng, National Technical University of Athens, Greece M. Sc, University of Central Florida, USA born May 19, 1979 citizen of Greece accepted on the recommendation of Prof. Dr. C. Hafner, examiner Prof. Dr. C. Fumeaux, co-examiner Dr. M. Mattes, co-examiner 29

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6 Acknowledgments First and foremost I would like to express my gratitude to my supervisor Prof. Rüdiger Vahldieck for his support and guidance throughout my dissertation. He gave me the freedom to choose my research topics and he created the environment where I could concentrate on my research without being disturbed by various financial and administrative issues. Despite his at times busy schedule, he was always available when I was in need of his scientific intuition and insights. I am most grateful to him for giving me the opportunity to work under his supervision and for offering me the moral and scientific support to achieve my academic goals. Many thanks to Prof. Christian Hafner for accepting to be my referee and for reading and commenting on my thesis. His instructive comments contributed greatly to the qualitative improvement of the manuscript. I would like to thank Prof. Christophe Fumeaux from the University of Adelaide, Australia for his invaluable scientific and moral support. I owe much of the success of this work to him, since he believed in the potential of the project and he provided me with his large experience and expertise. With his continuous encouragement, his resourcefulness, his calm and carefully evaluating manner he supported me in every step of my dissertation and he taught me things that go beyond science itself. Finally, I am grateful to Dr. Michael Mattes from the Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland for being my co-examiner and for reviewing my thesis. His support in the final steps of my PhD is very much appreciated. I am greatly indebted to the administration and support staff of my institute for creating the ideal conditions for me in order to focus on my work. I would like to thank Barbara Schuhbeck-Wagner and Susanne Oxe for their invaluable help regarding administrative issues, Ray Ballisti and Aldo Rossi for the IT support and Claudio Maccio and Martin Lanz for their help in the fabrication of the various devices. I would like to most particularly thank Hansruedi Benedickter for his great scientific skills and insights as well as for the countless hours we spent together measuring the various devices.

7 6 ACKNOWLEDGMENTS My work at ETH became a very rewarding and also fun experience thanks to my colleagues at the institute. Our numerous discussions on electromagnetics and other engineering-related issues enhanced my knowledge in the fields and helped me evolve personally and scientifically. In addition to that, our social gatherings, our excursions in the Swiss countryside and our exhausting sport sessions in the Polyterasse made my years in the institute unforgettable. Outside of ETH, I would like to express my gratitude to all the people close to me for their love, patience and support. First and foremost my parents Dimitris and Danai and my sister Nadia, without whom I wouldn t have become the person that I am now. I would like to thank my good friends Yorgos Papagrigorakis and Tania Zachaki for being there for me whenever I needed them, my aunt Kety for her moral support and my cousin Nana for the parcels she has been sending me from my home country all these years. In addition, I would like to thank all these people who have, in their way, constantly given me initiatives to strive for my personal and professional improvement: Oliver, Christina, my friends from the NTUA and so many others. Finally, I would like to thank my high-school mathematics professor Mrs. Saliaraki, who was the first one to inspire me to study engineering. Zurich, February 19 th 29

8 To my parents Dimitris and Danai and my sister Nadia

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10 Abstract The high demand for faster and more reliable services in several applications of modern communications increases the requirements for a large data transmission capacity and hence a wide operational bandwidth. In addition to that, mobile communications set some strict specifications concerning the size, the weight and the efficiency of the RF front-ends, which are responsible for the transformation of the base-band signal to a radiated electromagnetic wave and vice versa. The element of the RF front-end that mainly determines the size and the efficiency of the unit is its antenna. As a result, compact and low-weight antennas exhibiting a wide operational bandwidth and a high radiation efficiency are attractive candidates for a large number of practical applications in the communications area. Dielectric Resonator Antennas (DRAs) are open resonating structures made out of high-permittivity low-loss dielectric materials. They are characterized by a high radiation efficiency, a compact size and a wide operational bandwidth as compared to the other resonating antennas. In addition to that, their excited modes, their resonance frequencies and their radiation characteristics are determined by their geometry, their dielectric constant and their coupling mechanism. This great versatility of the DRAs in terms of their shape and feeding scheme in combination with their other advantageous inherent properties make them suitable candidates for many commercial applications. This thesis will introduce these structures and will examine their excited modes, their resonance frequencies and their far-field characteristics. More specifically, the operational properties of the canonical Dielectric Resonator Antennas (DRAs) (sphere, cylinder, parallelepiped) will be investigated and the achieved performance enhancement through the proper design of their coupling schemes will be described. In addition to that, the operation of the non-canonical DRAs will be examined and compared to that of the canonical geometries. The properties of the different inverted and non-inverted structures of non-canonical shapes will be demonstrated and therefore, the performance improvement obtained through the trani

11 ii ABSTRACT sition from a canonical to a non-canonical geometry will be emphasized. Finally, the effect of the electrical properties (permittivity, permeability) of the resonator on the operational characteristics of the DRA will be discussed and the possibility for a well-controlled multi-band operation and/or a wide impedance bandwidth of the DRA will be examined. In all these investigations, an attempt will be made to look into the underlying processes that affect the performance of the DRAs and hence, to provide the readers with qualified information about their design and optimization procedures. Various DRA configurations for different types of applications will be discussed. For most of them, the analytical and/or the numerical results will be compared with measurements of fabricated prototypes, in order to experimentally validate the good operation of the described devices.

12 Zusammenfassung Die hohe Nachfrage nach schnelleren und zuverlässigeren Dienstleistungen in verschiedenen Anwendungen der modernen Kommunikation erhöht die Anforderungen für eine grosse Datenübertragungskapazität und damit für eine hohe Betriebsbandbreite. Zusätzlich setzt die mobile Kommunikation einige strenge Spezifikationen in Bezug auf die Grösse, das Gewicht und die Effizienz der RF Front-Ends, die verantwortlich dafür sind, das Baseband Signal zu einer ausgestrahlten elektromagnetischen Welle und umgekehrt zu transformieren. Meist ist die Antenne das grössen- und leistungsbestimmende Element des RF Front-Ends. Deshalb sind die kompakten, leichten, von hoher Betriebsbandbreite und grosser Strahlungsleistungsfähigkeit charakterisierten Antennen geeignet für viele praktische Anwendungen im Gebiet der Kommunikation. Dielektrische Resonatorantennen (DRAs) sind offene Resonanzkörper aus dielektrischen Materialien mit hoher Dielektrizitätszahl und niedrigen Verlusten. Sie haben eine hohe Strahlungsleistungsfähigkeit, ein kleines Gewicht und eine kleine Grösse. Gegenüber anderen Resonanzantennen haben die DRAs auch eine höhere Betriebsbandbreite. Ihre angeregten Moden, Resonanzfrequenzen und Strahlungseigenschaften sind durch ihre Gestaltung, Dielektrizitätszahl und Kupplungsmechanismen bestimmt. Diese grosse Vielseitigkeit der DRAs in Bezug auf ihre Form und Anspeisung in Kombination mit ihren anderen vorteilhaften Eigenschaften, machen sie attraktiv für viele kommerzielle Anwendungen. In dieser Dissertation werden die DRAs eingeführt und gleichzeitig werden die angeregten Moden, Resonanzfrequenzen und Fernfeldeigenschaften der DRAs untersucht. Die Eigenschaften der kanonischen DRAs (Kugel, Zylinder, Parallelepiped) werden ausführlich untersucht, und die erreichte Leistungsverbesserung durch das angemessene Design ihrer Anspeisung wird diskutiert. Die Operation der nichtkanonischen DRAs wird zusätzlich untersucht und mit der Operation der kanonischen Strukturen verglichen. Die Eigenschaften der verschiedenen invertierten und nichtinvertierten DRAs von nichtkanonischen Formen werden aufgezeigt. Folglich wird die erhaltene Leistungsverbesserung durch den Übergang iii

13 iv ZUSAMMENFASSUNG von einer kanonischen zu einer nichtkanonischen Form gezeigt. Die Wirkung der elektrischen Eigenschaften (Permittivität, Permeabilität)des Resonators auf die Eigenschaften der DRAs wird besprochen. Schliesslich wird die Möglichkeit für eine leicht kontrollierbare Multiband Operation sowie eine hohe Bandbreite der DRAs untersucht. In allen diesen Untersuchungen wird versucht jene grundlegenden Prozesse zu erforschen, die die Leistung der DRAs beeinflussen. Damit werden die Leser mit der qualifizierten Information über das Design und Optimierungsverfahren der DRAs versorgt. Verschiedene DRA-Konfigurationen für verschiedene Anwendungen werden beschrieben. In den meisten Fällen werden die analytischen und/oder numerischen Ergebnisse mit Messungen der fabrizierten Prototype verglichen, um die Funktion der beschriebenen DRAs experimentell zu validieren.

14 Contents 1 Introduction Motivation Comparison of the DRAwith the MSA Theoretical Considerations Experimental Comparison in the Ka band Objective of the Dissertation Overview of the Dissertation Canonical DRAs Introduction The Hemispherical DRA The TE 111 mode of the HDRA The Q-factor of TE 111 mode The Rectangular DRA Resonance Frequency and Near Fields Radiation Q-factor The Cylindrical DRA The TM 1δ mode The HEM 11δ mode CouplingmethodstoDRAs Themicrostripline The coaxial probe Theco-planarslotloop Theaperture Aperture coupled Canonical DRAs Dual mode aperture coupled CDRA The double bowtie aperture coupled DRA Offset cross-slot coupled CDRA Conclusion Broadband DRA Geometries 55 v

15 vi CONTENTS 3.1 Introduction The Bandwidth of the RDRA The high-profile RDRA Thedouble-slabDRA The semi-trapezoidal DRA The pyramidal DRA Conclusion Inverted DRA Geometries Introduction Theeffectoftheairgap The trapezoidal DRA The resonance frequency of the trapezoidal DRA The high-profile inverted trapezoidal DRA The inverted truncated conical DRA Conclusion Appendix Advanced DRA Configurations Introduction Theprobe-fedbridgeDRA Advanced multi-band probe-fed BDRAs Theaperture-fedBDRA Advanced multi-band aperture-fed BDRAs The Magneto-Dielectric Resonator Antennas The inherent bandwidth of the BDRAs The coupling to the MDRAs Conclusion Conclusion Discussion FutureWork Bibliography 153 List of Publications 159 Curriculum Vitae 163

16 List of Figures 1.1 Configuration of the microstrip antenna and of the DRA Return loss of the cylindrical DRAand the circular disk MSA Radiation efficiency of the DRAand the MSA Canonical DRAs HDRAgeometry Field distribution of the TE 111 mode DRAmodel Normalized resonance frequency of the TE111 z mode Field distribution of the TE111 z mode CDRAgeometry Field distribution of the TM 1δ mode Field distribution of the HEM 11δ mode Microstrip coupling for the excitation of the HEM 11δ mode of the CDRA Coaxial probe coupling for the excitation of the TE 111 modeofthehdra Co-planar loop coupling for the excitation of the TE 11δ modeoftherdra Aperture coupling for the excitation of the TM 1δ mode of the CDRA Configuration of the aperture coupled CDRA Configuration of the aperture antenna with an infinite suband superstrate of heights t and h respectively Resonance frequencies vs. slot length L s for r =15.5mm Return loss for DRAradii r =12mmandr =13mm Radiation patterns for the E- and H-planes at f =5.2GHz and 6.3GHz The configuration of the double bowtie aperture coupled DRA vii

17 viii LIST OF FIGURES 2.2 Schematic of the structure with the bowtie shaped apertures between a sub- and a superstrate Schematic of the double bowtie aperture coupled CDRA Measured and simulated (HFSS) return loss of the CDRAas a function of frequency Input impedance vs. frequency Radiation patterns for the E- and H-planes at frequencies f =5.2GHz, 6.25 GHz and 6.7GHz Schematic of the double bowtie aperture coupled RDRA Measured and simulated (HFSS) return loss of the RDRAas a function of frequency Radiation patterns for the E- and H-planes at 5.15 GHz, 6.5 GHz and 6.95GHz Schematic of the cross-slot-coupled DRA Measured and simulated (HFSS) return loss as a function offrequency Measured and simulated ARin the broadside direction as a function of frequency Measured radiation patterns in the x z and y z planes Simulated 3 db ARbandwidth and angle θ cp vs. the distance between the two aperture centers Probe-fed RDRA % Bandwidth of the probe-fed RDRAas a function of its aspect ratios Configuration of the probe-fed high-profile RDRA Electric field configuration of the TE 111 and the TE 113 modes Return loss and input impedance of the high-profile RDRA Radiation patterns of the high-profile probe-fed RDRA Return loss vs. frequency for different values of the resonator height h Configuration of the probe-fed double-slab DRA Resonance frequencies of the double-slab DRAfor different dimensions of slab Simulated (HFSS) return loss for a double-slab DRA E-field distribution of the resonant modes of the doubleslab DRA Radiation patterns of the double-slab DRA

18 LIST OF FIGURES ix 3.13 % Bandwidth of the double-slab DRAand of an effective RDRAversus the resonators dielectric permittivity Fabricated prototype of a double-slab DRA Return loss of the double-slab DRAof Fig Radiation patterns of the double-slab DRA Configuration of the probe-fed semi-trapezoidal DRA Transition from the double-slab to the semi-trapezoidal DRA Return loss of the semi-trapezoidal DRAshown in the inset Effect of the height h 2 and the length a 2 on the return loss of the semi-trapezoidal DRA Measured radiation patterns of the semi-trapezoidal DRA Transition from the rectangular to the pyramidal DRA Configuration of the probe-fed pyramidal DRA Simulated fractional bandwidth of the pyramidal DRA vs. its height h Simulated 15 db cross-pol beamwidth of the pyramidal DRA vs. its height h Return loss and broadside gain of the probe-fed pyramidal DRA Measured radiation patterns of the probe-fed pyramidal DRA Field distributions of the TE 111 mode in a regular and in an inverted DRAgeometry Configuration of a probe-fed and an aperture-fed DRA Simulated (HFSS) return loss and input impedance of the probe-fed RDRAof Fig. 4.2 (a) for different values of the air gap thickness d Simulated % bandwidth of the probe-fed RDRAas a function of the air gap thickness d Simulated return loss and input impedance of the aperturefed CDRAfor different values of the air gap thickness d Configuration of the probe-fed trapezoidal DRA Resonance frequency and % bandwidth of various trapezoidal DRAgeometries Asymmetry in the E-plane versus Δx at the frequency of excitation of the lowest-order mode

19 x LIST OF FIGURES 4.9 Measured return loss and input impedance for the rectangular and the trapezoidal DRAs Measured broadside gain vs. frequency for the rectangular and the trapezoidal DRAs Measured radiation patterns of the rectangular and the trapezoidal DRAsin the E- and H-planes at 7.4GHz Simulated % bandwidth and relative size of the rectangular and the trapezoidal DRAsvs. their permittivity for a fixed operation at 7.4GHz Geometrical configurations of an inverted trapezoid and an inverted symmetrical pyramid Resonance frequencies of the inverted trapezoid and the inverted symmetrical pyramid for different values of Δx Enforcement of the magnetic wall condition at the inclined surfaces of the pyramid, at a height h r Resonance frequencies computed by the proposed semianalytical method as well as the commercial code (HFSS) High-profile inverted trapezoidal probe-fed DRA Simulated and measured return loss of the trapezoidal DRA shown in Fig Mechanically stable high-profile inverted trapezoidal probefed DRA Simulated and measured return loss and input impedance for the trapezoidal DRAof Fig Measured broadside gain vs. frequency of the trapezoidal DRA Measured radiation patterns in the E- and H-planes for the trapezoidal DRAof Fig Geometrical configuration and fabricated prototype of the inverted truncated conical DRA Simulated (CST) return loss of the truncated conical DRA for different shapes of the dielectric resonator and for different diameters of the metallic hat Simulated and measured return loss and input impedance of the inverted truncated conical DRAfor free-space operation Measured free-space radiation patterns for the co- (E θ )and cross-polarization (E φ )

20 LIST OF FIGURES xi 4.27 Simulated and measured return loss of the inverted truncated conical DRAfor on-body operation Amplitude of S 21 and phase of the transfer function of the inverted truncated conical DRAfor free-space and on-body operation Time-domain response of a pair of inverted truncated annular conical DRAsfor transmission in free-space Time-domain response of a pair of inverted truncated annular conical DRAsfor on-body transmission Transient response of the inverted truncated conical DRA Configuration of a bridge DRAand a RDRA Return loss of the BDRAand the RDRA E-field distribution and radiation patterns of the resonant modeofthebdra Geometrical configuration, return loss and radiation patterns of an advanced BDRA Radiation patterns (at the resonance frequency) of the BDRAfor different values of its dielectric permittivity Geometrical configuration and return loss of a probe-fed double-bridgedra Resonance frequencies of the two lowest-order BDRAmodes for different values of a 2 and h Radiation patterns of the double-bdrawith a 2 /a 1 =.4, h 2 /h 1 =.4 at the frequencies 3.87 GHz and 5.14 GHz Geometrical configuration of a probe-fed BDRAcoupled with a RDRA Return loss of the BDRAconfiguration of Fig Radiation patterns of the BDRAconfiguration of Fig Geometrical configuration of an aperture-fed BDRA Fabricated prototype and return loss of the configuration of Fig Measured radiation patterns of the aperture-fed BDRA Fabricated prototype and return loss of the dual-mode BDRAconfiguration Return loss of the dual-mode aperture-fed BDRAfor different values of w p

21 xii LIST OF FIGURES 5.17 Measured radiation patterns of the dual-mode aperture-fed BDRAof Fig (a) Geometrical configuration of the dual-band double-bdra Fabricated prototype and return loss of the dual-band double-bdra Measured radiation patterns of the dual-band double-bdra Fractional bandwidth and resonance frequency of a probefed MDRA Geometrical configuration of a probe-fed BDRAcoupled withamdra Simulated return loss of the configuration of Fig for different values of ε r2 and μ r Comparison of the fractional bandwidth of the MDRAand the DRAmode Geometrical configuration and fractional bandwidth of a probe-fed BDRAcoupled with a RDRA

22 List of Tables 1.1 Commercially available dielectric materials Dimensions of the antenna configurations of Fig Comparison of the resonance frequencies of various DRAs found though simulation, the proposed (semi-analytical) method and measurement xiii

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24 List of Acronyms and Abbreviations Antenna Theory DRA... Dielectric Resonator Antenna MDRA... Magneto-Dielectric Resonator Antenna RDRA... Rectangular Dielectric Resonator Antenna CDRA... Cylindrical Dielectric Resonator Antenna HDRA... Hemispherical Dielectric Resonator Antenna BDRA... Bridge-shaped DRA VSWR... Voltage Standing-Wave Ratio AR... Axial Ratio LP... Linearly Polarized CP... Circularly Polarized LHCP... Left Handed Circular Polarization RHCP... Right Handed Circular Polarization PLF... Polarization Loss Factor UWB... Ultra-Wideband RPF... Radiation Power Factor xv

25 xvi LIST OF ACRONYMS Electromagnetics and Numerical Methods BAN... Body Area Networks EM... electromagnetic FEM... Finite Element Method FDTD... Finite-Difference Time-Domain FVTD... Finite-Volume Time-Domain MoM...Method of Moments FIT... Finite Integration Technique DWM... Dielectric Waveguide Model HFSS... High Frequency Structure Simulator RF... Radio Frequency CPW... Coplanar Waveguide E... Electric H... Magnetic PEC Perfect Electric Conductor PMC Perfect Magnetic Conductor TE... Transverse Electric TM... Transverse Magnetic FWHM... Full Width at Half Maximum VSWR... Voltage Standing Wave Ratio

26 1 Introduction 1.1 Motivation Since the early 197s dielectric resonators of very high permittivity (relative dielectric constant of the order 1 3) were used as resonant cavities for different active and passive microwave components including filters, oscillators, amplifiers and tuners [1]. Van Bladel was the first to examine the properties of these resonators; his work focused on the classification of the excited modes as well as on the investigation of the fields distributions [2], [3]. This examination was made under the hypothesis that the structures are strictly energy storage devices. For cavities, however, that are not enclosed by metallic walls, electromagnetic fields can also be detected beyond the geometrical boundaries of the resonator. When the dielectric permittivity is very high, the radiation loss is negligible and the unloaded Q factor of the resonator is mainly limited by the dielectric losses (Q u =1/ tan(δ) 1, 2, ). On the other hand, the decrease of the dielectric permittivity value results in an increase of the amount of energy lost in the form of radiation and hence in a degradation of the resonator s operation as a cavity. Long et al. demonstrated in 1983 that dielectric resonators made of low permittivity materials (8 ε r 2) and placed in open environments exhibit small radiation Q-factors if excited in their lower-order modes [4]. The high radiation losses of these resonators make them particularly useful as radiating elements, especially in high-frequency applications where ohmic losses are a serious problem for the conventional metallic antennas. Apart from their low dissipation loss and the subsequent high radiation efficiency, DRAs offer many other attractive features, such as good mechanical and temperature stability, compatibility with MIC s, low mutual coupling in array configurations and most importantly, a small size and weight due to the scaling of the DRA dimensions with the permittivity according to the relation λ / ε r,withλ being the free-space wavelength. Moreover, the DRAs versatility in terms of their shape and feeding mechanism allows for the efficient control of the excited modes and 1

27 2 1 INTRODUCTION Supplier Product type Permittivity Countis Laboratories Magnesium, calcium, silicon, and titanium oxides Emerson & Cuming Eccostock R Morgan Electro Ceramics D-Series Murata Electronics B-, E-, F-, M-, U- Series PFC Inc. Aluminum and Berylium Oxides Rogers Corporation RO/laminate R, RT/duroid R,TMM R SCI Engineered Materials Inc. Trans-Tech Lanthanum Aluminates and Aluminum Oxides Magnesium-aluminum and magnesiumcalcium titanates Table 1.1: Commercially available dielectric materials. thus of the input impedance, the bandwidth, the polarization and the radiation patterns. Different DRA modes can be excited through various feeding techniques using conventional transmission lines, while the DRA shape and permittivity can be varied in order to accommodate different design requirements. The most common dielectric resonator ge-

28 1.2 COMPARISONOFTHEDRAWITHTHEMSA 3 ometries are canonical shapes such as the parallelepiped, the cylinder and the sphere/hemisphere, but depending on the application, various noncanonical shapes may also be encountered. Concerning now the electric properties of the dielectric resonators, a large number of suppliers worldwide provide linear, non-dispersive, low-loss materials demonstrating a wide range of dielectric permittivity values. Table 1.1 lists some of these suppliers as a demonstration for the great variety of materials available. One of the most important challenges in the design of an antenna is its bandwidth response. Modern communications set the bandwidth requirements very high and the antenna technology needs to keep up with them. DRAs are inherently more wideband than other resonant antennas like for example the microstrip antennas, since they are volumetric sources that can more effectively fill the radian sphere (4π/3(λ /2π) 3 ). Hence, DRAs exhibit a higher Radiation Power Factor (RPF), or in other words, a lower Q-factor than microstrip antennas. Since, however, DRAs are resonant structures, they are, in principle, narrowband. Even for a DRA of a low dielectric permittivity ε r = 1, the bandwidth response does not exceed 1 15%, which is not always enough for many commercial applications. The DRA bandwidth can be increased through the reduction of the dielectric permittivity according to the relation BW ( ε r ) p,withp being a function of the DRA geometry as well as of the excited mode [5]. A reduction of ε r will result, however, in an increase of the DRA dimensions, which is also highly undesirable in most of the commercial applications. This trade-off between the DRA bandwidth and size makes the design and the optimization of the DRA a challenging process. Moreover, the DRA designer might have to face additional challenges arising from the requirements for well-behaved Linearly Polarized (LP) or Circularly Polarized (CP) operation with stable patterns and good polarization purity. It is then clear that the thorough investigation of the DRA operation is crucial towards the improvement of its properties and the subsequent enhancement of its practical applicability. 1.2 Comparison of the DRA with the microstrip antenna The microstrip antenna (MSA) is undeniably the most extensively used antenna for low-gain microwave and millimeter-wave applications [6]. It consists of a metallic patch on top of a grounded substrate and it is coupled

29 4 1 INTRODUCTION through a coaxial probe or an aperture. The large popularity of MSAs is caused by their low profile, their compatibility with MIC designs and their mechanical robustness. In addition, MSAs are comformable to planar and nonplanar surfaces and they are inexpensive to fabricate using modern printed-circuit techniques. In comparison, DRAs involve a more complex and costly fabrication process, since the dielectric material is relatively expensive to acquire and its machining cannot easily be made in an automatic way. Hence, DRAs might not be entirely suitable for applications where the fabrication cost is the main criterion. On the other hand, DRAs have a clear advantage over MSAs in applications where a high antenna efficiency and/or a wide impedance bandwidth is required. These attractive features of the DRAs will be the subject of investigation in this section. At the beginning, a general comparison in terms of radiation efficiency and impedance bandwidth will be made for both, DRA and MSA. Afterwards, the performance in the millimeter-wave range of a cylindrical DRA and of a circular-disc MSA will be compared experimentally, as a means to further highlight the operational advantages of DRAs Theoretical Considerations Before we start with the comparison between the DRA and the MSA, a few important terms need to be clarified [7]. First, the dielectric Q-factor Q d and the conductor Q-factor Q c are defined as following: Q d = ωw (1.1) P d Q c = ωw (1.2) P c where ω is the angular resonance frequency, W is the stored electromagnetic energy and P d, P c is the power lost in the dielectric and in the conductor, respectively. A more detailed discussion on these terms goes beyond the scope of this section - more information on the Q-factor of an antenna will be provided in the next chapter. Using the above equations, it turns out that the ratio between the lost

30 1.2 COMPARISONOFTHEDRAWITHTHEMSA 5 power and the radiated power P r is computed by: P d = Q r P r Q d (1.3) P c = Q r P r Q c (1.4) where Q r = ωw/p r is the radiation Q-factor. The DRA has primarily dielectric losses and for a dielectric resonator made of a good quality material (tan(δ) < ) its dielectric Q-factor is Q d > 5. Moreover, the radiation Q-factor of the fundamental DRA mode (for a dielectric permittivity of around 1) is found by literature to be Q r 1 [5]. As far as the microstrip antenna is concerned, typical values of the conductor Q-factor in the microwave range are Q c > 3, while its radiation Q-factor is Q r 3. Based on the equations (1.3) and (1.4) as well as the aforementioned values of the antennas Q-factors, it is clear that the DRAs exhibit a higher radiation efficiency than microstrip antennas, since their losses are much lower: P d 1 = =.2% P r 5 (1.5) P c = 3 = 1% P r 3 (1.6) Continuing with the comparison between the DRA and the MSA, their fractional impedance bandwidth can be computed from their Q-factor through the relation: BW = 1 Q % (1.7) for which, a Voltage Standing Wave Ratio (VSWR) of 2 is assumed. According to this relation the DRA bandwidth can be roughly estimated as BW DRA 1%, while in the case of the MSA the bandwidth is BW microstrip 2%. Hence, the DRA outperforms the MSA in terms of the bandwidth response.

31 6 1 INTRODUCTION z z w m l m l t r PEC h s x w t w m w t y PECl m l t1 x l t2 h s r h d y (a) (b) Figure 1.1: Geometrical configuration of the antennas under investigation. (a) Microstrip antenna. (b) DRA Experimental Comparison in the Ka band The operational advantage of the DRAs in terms of their radiation efficiency becomes more prominent in the millimeter-wave range, where the ohmic losses of the MSAs are much higher. To demonstrate that, two comparable antenna configurations were examined [8]: the circular-disc MSA shown in Fig. 1.1 (a) and the cylindrical DRA of Fig. 1.1 (b). For a direct comparison, the two antennas were chosen to have similar feeding networks and they were designed to operate at the same frequency f = 35 GHz in the Ka band. The analysis of the two antennas was made using ANSOFT HFSS R. For an operation at around f = 35 GHz, the dimensions of the two antenna configurations are summarized in Table 1.2. It can be observed that the two antennas are similar; the radii of the circular patch and of the dielectric cylinder are very close to each other, while their feeding networks are of the same type. A standard quarter-wave transformer [9] was used to match the input impedance of the antennas to the 5 Ω microstrip line. The sole difference was the width of the transformer in the two cases. The quarter-wave transformer used for the MSA was narrower than the microstrip line, since the input impedance of the circular disc was higher than 5 Ω. In contrast to that, the width of the transformer in the case of the DRA was larger than that of the microstrip line due to its low input impedance. Fig. 1.2 illustrates the simulated and measured return loss of the two antenna configurations. A very good agreement between the numerical and the measured results is observed. Moreover, the clear advantage

32 1.2 COMPARISONOFTHEDRAWITHTHEMSA 7 Parameter MSA DRA w m [mm] w t [mm] l m [mm] l t [mm] l t1 [mm] - 1. l t2 [mm] -.55 h s [mm] h d [mm] r [mm] ε r,dra - 1 ε r,substrate Table 1.2: Dimensions of the antenna configurations of Fig of the DRA in terms of its bandwidth response is demonstrated. The fractional bandwidth (S 11 < 1 db) of the DRA exceeds 15%, whereas in the case of the MSA it only reaches 2.6%. Next, the radiation efficiency of the two antennas was compared by using the directivity/gain method (D/G) and the Wheeler cap method. In both cases, the losses due to the test setup and the feeding schemes were determined and taken into account for calibration purposes. The D/G method is the most straightforward method for calculating the radiation efficiency η of an antenna. The directivity D and the gain

33 8 1 INTRODUCTION Return Loss [db] simulated MSA measured MSA simulated DRA measured DRA frequency [GHz] Figure 1.2: Return loss of the cylindrical DRA and the circular disk MSA. G of the antenna can easily be computed through the radiation pattern measurements and then the radiation efficiency can be calculated from the relation: η = P rad P in = G cp+xp D cp+xp (1.8) where P rad and P in is the power radiated from the antenna and the power delivered to the antenna terminals respectively, while the subscript cp+xp refers to the total gain/directivity for both, co- and cross-polarization. In case the polarization purity is very high (above 3 db), the crosspolarization can be neglected. In any other case the cross-polarized patterns must be considered for the accurate calculation of the radiation efficiency. Apart from that, the sampling interval of the radiation pattern measurements is another critical factor in the determination of the antenna s directivity and gain. The smaller the sampling interval is, the higher the precision of the calculated efficiency is. Since, however, the small sampling interval results also in a very large number of measurements that have to be made and processed, an examination of the measurements convergence needs always to be made. More information on this matter is provided in [8]. The Wheeler cap method is another very simple technique for measuring the radiation efficiency of an antenna [1]. For an antenna mounted on a ground plane and coupled through a suitable feeding scheme, its unloaded

34 1.2 COMPARISONOFTHEDRAWITHTHEMSA 9 Q-factor Q rcd can be expressed by: 1 = P rad + P cd = (1.9) Q rcd ωw Q rad Q cd where P rad and P cd denote the radiated power and the power lost in the dielectric and the conductors, respectively. When a metallic cap is placed on top of the antenna so that it covers it completely, the antenna is prevented from radiating. In that case, the unloaded Q-factor of the resonator is equal to Q cd, which is computed by: 1 Q cd = P cd ωw (1.1) Finally, the radiation efficiency of the antenna can be determined from equations (1.9) and (1.11) according to: P rad η = =1 Q rcd (1.11) P rad + P cd Q cd The main drawback of the standard Wheeler cap method is that the metallic cap has to be made small enough to prevent any resonances within the cavity. This problem is exacerbated in the millimeter-wave range, where the fabrication of a suitably small metallic box is cumbersome. For that reason, instead of the standard Wheeler cap method, the modified Wheeler cap method [11] is applied here, in which the effect of the cap resonances can be effectively canceled. The calculated radiation efficiency of the MSA and the DRA is plotted versus frequency in Fig. 1.3 (a) and (b) for both, the D/G and the Wheeler cap methods. In the D/G method, the co- and the cross-polarized patterns are sampled with an elevation interval of 2 and an azimuth interval of 5, while in the Wheeler cap method the metallic cap is a cube of dimensions 3 mm 3 mm 5 mm. For reference purposes, Fig. 1.3 includes also the simulated results, which were computed by mimicking the experimental Wheeler cap setup. The simulated results for the D/G method are not shown, since they are in very close agreement with those from the Wheeler cap method. It is observed in the figure that the radiation efficiency of the MSA is around 8% in the band between 34.7GHzand 35.7 GHz. The agreement between the simulations, the Wheeler cap method and the D/G method

35 1 1 INTRODUCTION efficiency efficiency frequency [GHz] frequency [GHz] (a) (b).7 simulation D/G.6 Wheeler cap Figure 1.3: Radiation efficiency of the two antennas. (b) Cylindrical DRA. (a) Circular-disc MSA. is very good. In the case of the DRA, a radiation efficiency of up to 95% is measured at 35.5 GHz. Moreover, the efficiency never becomes lower than 88% within the entire operational band of the DRA. The agreement between the simulations and the Wheeler cap method is acceptable - the large oscillations of the efficiency measured with the D/G method reflect the higher uncertainty and lower repeatability of the method. In any case it is clear that the radiation efficiency of the DRA is much higher than of the MSA. If the results of this study are compared with the measured efficiency of MSAs and DRAs in the lower GHz range (around 9 95% for both) [12], [13], it can be concluded that the increase of the operation frequency leads to a rapid decrease of the MSA s efficiency, but does not severely affect the efficiency of the DRA. 1.3 Objective of the Dissertation DRAs are attractive candidates for many types of applications due to their inherent merits of high radiation efficiency, small size and wide bandwidth. Especially in the millimeter-wave range, where the losses from the imperfect conductors become substantial, the DRAs are much more suitable than any metallic antennas in applications requiring a high radiation effi-

36 1.3 OBJECTIVE OF THE DISSERTATION 11 ciency. Moreover, the ever increasing need in modern communications for low-profile antennas having more than 1% fractional bandwidth demonstrates the value of the DRAs as compared to other resonating antennas. Despite the many advantages of DRAs and although they have been discovered since the mid 8 s, they have only received broad attention in the last 1 years. The reasons were that first, the fabrication cost was too high in comparison with the metallic antennas and second, the availability of dielectric materials having a low permittivity (ε r =8 2) and low dielectric losses was very small. Things changed in the last years through the progress of material sciences, leading to the development of a wide range of inexpensive dielectric materials with very good properties. This prompted the antenna engineers worldwide to show more interest in this type of antennas. However, in spite of more than 1 years of ongoing research, the field of DRAs is still largely unexplored due to the large number of dielectric resonator shapes as well as coupling schemes that can be employed. In this thesis, the focus is on the investigation of the DRA properties as well as the design and analysis of various antenna configurations exhibiting enhanced performance. In order to comprehend the operation and the radiation characteristics of the DRAs, we will start with the analytical and numerical examination of the canonical dielectric resonator shapes (sphere, parallelepiped, cylinder). This will provide an insight on the properties of the DRA modes, and, most importantly, it will demonstrate the correlation between DRA shape and performance. The geometry of the dielectric resonator in combination with the type and position of the coupling scheme does not only determine the excited modes and their subsequent radiation characteristics, but it can also lead to an enhanced antenna performance in terms of bandwidth, gain and polarization. This is possible through the thorough examination and understanding of the underlying processes, which are initiated by the geometrical modification of a DRA and result in the changing of its operation. The aim of this thesis is to explain these processes and to provide the readers with qualified information about how to improve the radiation characteristics of DRAs, while keeping the rest of their properties stable. Examples of DRA configurations for various types of applications will be discussed. In all cases, the main focus will be on the design procedure and not just the description of the antenna s geometrical configuration. In that way, the design principles can easily be applied beyond the particular cases

37 12 1 INTRODUCTION presented and adapted to satisfy similar specifications at any possible operation frequency. 1.4 Overview of the Dissertation The next five chapters of this dissertation are outlined below: Chapter 2 presents the basic theory of DRAs. The operation and the properties of the canonical dielectric resonators will be examined, their modes will be classified and models for the determination of their resonance frequencies and radiation Q-factors will be developed. Next, some of the most commonly-used feeding schemes will be discussed and the coupling mechanisms to the various DRA modes will be described. Finally, the concept of the partial independence of the slot modes from the dielectric resonator modes in aperture-fed DRAs will be introduced. This is a new, very exciting operational concept for the DRAs, since it can be easily employed in various DRA configurations in order to improve their bandwidth response. A few representative examples of successfully exploiting this concept will be provided in the last sections of the chapter. Chapter 3 gives an overview of non-canonical DRAs, whose shapes can be regarded as geometrical variations of the canonical parallelepiped. If designed properly, these structures can exhibit bandwidths of more than 6 per cent as well as very well-behaved radiation properties. Because of the great practical value of these novel devices, their wideband nature will be discussed in detail and their operation will be compared to that of the rectangular DRAs. Design guidelines and parameter curves will be provided for the generalization of the DRAs design procedure. In Chapter 4, techniques will be introduced for the reduction of the DRAs Q-factor. The effect of the air gap in between the dielectric resonator and the feeding scheme will be described and the performance of various inverted resonator shapes will be investigated. The concept of inverted DRA geometries relies on the reduction of the fields confinement within the resonator in order to enhance the impedance bandwidth. This very simple and subtle operational concept is also very powerful: it can dramatically improve the performance of a DRA without complicating its operation. A few examples of wideband inverted DRAs will be demonstrated. Among these, a Ultra-Wideband (UWB) DRA exhibiting a 5% impedance bandwidth and good signal dispersion properties will

38 1.4 OVERVIEW OF THE DISSERTATION 13 be discussed in the last section of the chapter. Chapter 5 presents the operational characteristics of the bridge DRAs. Bridge DRAs are attractive candidates for various applications, since they can exhibit a wideband or a multi-mode operation and they can integrate the electronics of the front end within their volume. Thus, several antenna-packaging related problems can easily be circumvented. In the last section of this chapter the use of magneto-dielectric materials (ε r,μ r 1) towards the further enhancements of the DRA properties will be discussed. Examples of well-operating MDRAs (Magneto-Dielectric Resonator Antennas) will be demonstrated. Finally, Chapter 6 summarizes the most important results of this dissertation and provides directions for possible future work.

39 14

40 2 The Canonical Dielectric Resonator Antennas 2.1 Introduction As mentioned in the previous chapter, one of the most attractive features of the DRA is its versatility in terms of shape and feeding mechanism. The DRA shape and size can be varied, depending on the specified resonance frequency, the type of the excited modes and the desired impedance bandwidth and radiation characteristics [14], [15]. The canonical DRA geometries, including the hemisphere (referred to as Hemispherical Dielectric Resonator Antenna (HDRA)), the parallelepiped (Rectangular Dielectric Resonator Antenna (RDRA)) and the cylinder (Cylindrical Dielectric Resonator Antenna (CDRA)), are particularly common, since they are simple to fabricate and their resonance frequencies and radiation Q-factors can be accurately determined through closed-form expressions [14]. It is interesting to underline here that for these geometries and for a given resonance frequency and dielectric permittivity, the RDRA has two degrees of freedom, since two of its three dimensions can be chosen independently. In contrast, the CDRA has one degree of freedom and the HDRA none. Fig. 2.1 illustrates these DRA geometries, fed by some commonly used coupling schemes, such as the microstrip line, the coaxial probe and the slot. This chapter will focus primarily on the examination of the canonical DRA geometries. The main reason for investigating them first, is that a rigorous classification of the DRA modes (as of the Transverse Electric (TE), Transverse Magnetic (TM) or hybrid type) already exists for these simple shapes. Besides that, the canonical shapes are the building blocks for all other advanced DRAs geometries. Consequently, in order to understand how these geometries operate and in which way they can contribute to a better antenna performance, it is crucial that the characteristics of canonical DRA structures are fully analyzed first. To start with the DRA analysis, various models will be employed in order to predict the resonance frequency and the radiation Q-factor of the DRA modes. In addition to that, the near fields and the radiation 15

41 16 2 CANONICAL DRAS PEC PEC PEC (a) (b) (c) Figure 2.1: Canonical DRAs. (a) HDRA coupled through a microstrip line. (b) RDRA coupled through a coaxial probe. (c) CDRA coupled through a slot. characteristics of the DRAs fundamental modes will be described. Subsequently, various commonly used feeding schemes will be discussed and methods to increase the impedance bandwidth in the cases of LP or CP operation will be highlighted. Within this context, there will be an extensive discussion about the excitation of the fundamental DRA modes in the RDRA and the CDRA through slot coupling and the independence, to a first order approximation, of those modes from the slot resonance. This important operational concept of the DRAs will be used to design wideband antennas with stable radiation characteristics. Examples of LP and CP DRAs will be demonstrated to show the strength and the generality of the method. 2.2 The Hemispherical Dielectric Resonator Antenna The HDRA is particularly popular for theoretical analysis due to its simple geometry. In fact, the isolated sphere is the sole geometry for which an analytical closed-form solution is possible; to that end the Maxwell equations are resolved by taking into account the boundary conditions at the interface in combination with zero energy at infinity and by using the spherical coordinates (ρ, θ, φ). The HDRA can support both, transverse electric TE nmr and transverse magnetic TM nmr modes, where the indices n, m and r denote the order of the variation of the fields in the elevation, azimuth and radial directions, respectively. For given values of n and r, boththete nmr and the TM nmr modes have the same resonant frequencies [5] for any value of m n. Moreover, each of the TE nmr or TM nmr modes can have an azimuthal variation of either the cos(mφ) orthesin(mφ) type. This degeneracy of

42 2.2 THE HEMISPHERICAL DRA 17 z z x PEC y l a PEC y (a) (b) Figure 2.2: HDRA geometry. (a) General view. (b) Side view. the HDRA modes is a limiting factor for many practical applications and hence, the HDRA is less commonly used compared to the other canonical DRA shapes. From the different HDRA low-order modes that are practically encountered, the TE 111,theTE 11 and the TM 11 are the most common. The TE 111 mode radiates like a horizontal magnetic dipole, while the other two radiate like an axial magnetic and an axial electric dipole respectively. Depending on the application requirements, any of the three modes can be excited by means of a suitable coupling scheme The TE 111 mode of the HDRA The analysis for the fundamental TE 111 mode of the HDRA, is representative of a procedure that can be applied to any other hemispherical resonator mode [16]. Because of that and for the sake of brevity, only this HDRA mode will be investigated here. The configuration of a HDRA placed on a groundplane of infinite lateral dimensions is illustrated in Fig A coaxial probe of length l is used to excite the TE 111 mode in the dielectric hemisphere. The field distribution of this HDRA mode is depicted in Fig According to the image theory, such a DRA geometry is equivalent to a dielectric sphere in free space, fed by a probe of total length 2l. Forthis sphere and at frequencies around the TE 111 mode resonance, the E-field Green s function for the z-directed component is given by [17]:

43 18 2 CANONICAL DRAS G TE111 = 3k sin(θ)sin(θ )cos(φ φ ) 8πω εr r [Φ(kr )Ψ(kr)+α TE Ĵ 1 (kr )Ĵ1(kr )] (2.1) with Φ(kr) = Ψ(kr) = Ĵ 1 (kr ), r > r Ĥ (2) 1 (kr ), r < r (2.2) Ĥ (2) 1 (kr), r > r Ĵ 1 (kr), r < r (2.3) α TE = 1 Δ [Ĥ(2) 1 (ka)ĥ (2) 1 (k a) ε r Ĥ (2) 1 (ka)ĥ(2) 1 (k a)](2.4) TE Δ TE = Ĵ1(ka)Ĥ (2) 1 (k a) ε r Ĵ 1(ka)Ĥ(2) 1 (k a) (2.5) where k = ω μ ε, k = k εr are the wavenumbers in free space and inside the dielectric, ω is the angular frequency and Ĵ1(x), Ĥ (2) 1 (x) are the first-order spherical Bessel function of the first kind and spherical Hankel function of the second type, respectively. Moreover, r(r, θ, φ) and r (r,θ,φ ) represent the vector location of the observation point and the source point, respectively, while the prime on the Bessel and Hankel functions denote the derivative with respect to the argument. In the above formulation, the fields are assumed to vary harmonically as e jωt. Starting now from equation (2.1), the z-directed electric field E z can be found from: E z ( r) = G TE111 ( r, r )J z (z )ds (2.6) where J z (z )=J sin(k(l z )), l z l (2.7) is the surface current on the coaxial probe. The input impedance Z in of the HDRA excited at its TE 111 mode is finally estimated according to the

44 2.2 THE HEMISPHERICAL DRA 19 z E H PEC y y (a) x (b) Figure 2.3: Field distribution of the TE 111 mode. (a) DRA fields E y and E z at x =. (b) DRA fields H x and H y at z =. relation: Z in = 1 2Iz 2() E z ( r)j z (z)ds (2.8) Based now on the above equation, the resonance frequency of the TE 111 mode of the dielectric hemisphere can be determined by setting the imaginary part of the input impedance to zero. It is important to underline here that since the fields outside the resonator are of the radiative type [16], the resonance frequency is complex: ω = ω jω (2.9) This indicates that these modes are leaky modes, which is of course self-evident, since the HDRA is radiating. The real part of equation (2.9) is the resonance frequency of the TE 111 mode, while the imaginary part will be used in order to determine the radiation Q-factor of the resonant mode The Q-factor of TE 111 mode The Q-factor is a very important antenna parameter, since it provides a measure of the antenna s impedance bandwidth. More specifically, the total unloaded Q-factor (Q u ) is connected with the bandwidth BW and the maximum acceptable VSWR S through the relation: BW = S 1 Q u S (2.1)

45 2 2 CANONICAL DRAS It is therefore obvious that for a well-operating, wideband antenna, the Q-factor needs to be as low as possible. This can also be deduced from the definition of the Q-factor: 1 = P tot Q u ωw = P rad + P cd = (2.11) ωw Q rad Q cd where ω is the operating angular frequency, W is the time averaged energy stored in the resonator and P rad and P cd denote, respectively, the radiated power and the power lost in the dielectric and the imperfect conductors. Hence, for an antenna with negligible dielectric and conductor loss compared to its radiated power (1/Q cd 1/Q rad ), the total unloaded Q-factor is related to the radiation Q-factor by the following relation: Q u Q rad = P rad ωw (2.12) and then, a low Q-factor corresponds to larger radiated power. For the TE 111 mode of the dielectric hemisphere, the radiation Q-factor can be determined in a straightforward manner by using equation (2.9). According to [18], the Q-factor can then be found through: stored energy Q u =2π radiated energy per cycle = ω 2ω (2.13) 2.3 The Rectangular Dielectric Resonator Antenna The RDRA offers certain practical advantages compared to the CDRA and the HDRA. First, as mentioned before, the RDRA has two independent shape parameters as degrees of freedom to achieve a pre-specified resonance frequency for a given value of the dielectric permittivity. As a second advantage, the mode degeneracy problem can be avoided in the case of the dielectric parallelepiped through proper selection of the resonator s dimensions [5]. It should be underlined here that, in contrast, mode degeneracy always exists in the case of the HDRA as well as for the hybrid modes of the CDRA [1]. The mode degeneracy is a limiting factor for the antenna operation, since it contributes to large crosspolarization which degrades the co-polarized gain. The final advantage of the RDRA involves the design flexibility for bandwidth optimization.

46 2.3 THE RECTANGULAR DRA 21 Numerous studies in the past have demonstrated the dependence of the impedance bandwidth on the aspect ratios of the dielectric resonator [5]. Since the RDRA has two independent aspect ratios (height/length and width/length) for any given resonance frequency and dielectric permittivity, the dielectric parallelepiped is more flexible in terms of bandwidth control. The analysis of the operation of RDRAs is a complex electromagnetic field problem. Since no analytical closed-form solution is possible, numerical techniques such as the Finite Element Method (FEM), the Finite- Difference Time-Domain (FDTD) and the Method of Moments (MoM) are employed in order to compute the resonance frequency, the input impedance and the far fields of the RDRA. These techniques are, however, time-consuming and memory intensive and therefore, several simple models have been developed instead, to estimate the resonance frequency, the Q-factor and the fields of the RDRA. The Dielectric Waveguide Model (DWM) was proposed by Marcatili in 1969, in order to determine the guided wavelength in dielectric waveguides with rectangular cross-section [19]. The dielectric waveguide is illustrated in Fig. 2.4(a) having a width w and a height h. The fields are propagating along the z-direction and they are assumed to vary sinusoidally within the waveguide, while they decay exponentially outside of it. If the dielectric waveguide is then truncated along the z-direction, an isolated RDRA of length a,widthw and height h is formed. This is shown in Fig. 2.4(b). The final structure is illustrated in Fig. 2.4(c), with the RDRA being placed on a groundplane and having a height h/2, as explained from image theory. To proceed with the RDRA analysis, Van Bladel s general classification of the modes for DRAs of arbitrary shapes is used [2], [3]. According to Van Bladel, modes of a dielectric resonator of very high permittivity can be of a confined or nonconfined type. For both types of modes, the component of the electric field intensity, which is normal to the interface between the dielectric resonator and the air, should vanish: E ˆn = (2.14) with E being the electric field intensity and ˆn the vector normal to the interface. The above equation is one of the conditions satisfied at the magnetic wall. The second magnetic wall condition, i.e., ˆn H = (2.15)

47 22 2 CANONICAL DRAS y y y a a x w x w h h/2 z z z w h (a) (b) (c) x PEC Figure 2.4: DRA model. (a) Dielectric waveguide. (b) Isolated RDRA. (c) RDRA on a groundplane. where H is the magnetic field intensity is not necessarily satisfied at the dielectric resonator surfaces. The confined modes of the dielectric resonator satisfy both (2.14) and (2.15) and they can only be supported by dielectric bodies of revolution such as the sphere (hemisphere) and the cylinder. The nonconfined modes satisfy only (2.14) and are supported by any arbitrary dielectric resonator shape. Since the RDRA is not a body of revolution, it can only support nonconfined modes Resonance Frequency and Near Fields Fundamental electromagnetic fields theory suggests that the modes of a dielectric waveguide can be of the TE type, of the TM type or hybrid. Marcatilli demonstrated that the existence of TM modes for dielectric waveguides of rectangular cross-section is doubtful, since they do not satisfy the condition (2.14) [19]. Therefore, for the ongoing analysis of the RDRA modes, only the TE mnl modes will be discussed, with the indices m, n and l denoting the order of variation along the x, y and z directions of the Cartesian coordinate system, respectively. Assuming a TE z mode, the electric vector potential is given by the equation F = ψ ê z (2.16) where ψ is a scalar wave function given by ψ = C cos(k x x)cos(k y y)cos(k z z) (2.17)

48 2.3 THE RECTANGULAR DRA 23 provided that the modes are symmetric around x, y and z. Then, the field components inside the dielectric resonator are [18]: E x = Ck y cos(k x x)sin(k y y)cos(k z z) (2.18) E y = Ck x sin(k x x)cos(k y y)cos(k z z) (2.19) E z = (2.2) H x = C k x k z jωμ sin(k xx)cos(k y y)sin(k z z) (2.21) H y = C k y k z jωμ cos(k xx)sin(k y y)sin(k z z) (2.22) H z = C k2 x + k2 y jωμ cos(k xx)cos(k y y)cos(k z z) (2.23) where k x, k y and k z are the wavenumbers along the x, y and z directions, ω is the angular frequency, μ is the permeability and C is an arbitrary constant. Enforcing the magnetic wall condition (2.14) at the surfaces of the resonator x = w/2 and y = h/2, the wavenumbers k x and k y are found to be: k x = mπ w k y = nπ h (2.24) (2.25) Next, the Marcatili s approximation [19] is used, in order to find an expression for the wavenumber k z. The tangential components of the field at z = ±a/2 are matched with an external field, which decays exponentially as it propagates normally from these surfaces. The components of this external field are given by: E x = Dk y cos(k x x)sin(k y y) e βz (2.26) E y = Dk x sin(k x x)cos(k y y) e βz (2.27) H x = D k x β jωμ sin(k x x)cos(k y y) e βz (2.28) H y = D k y β jωμ cos(k x x)sin(k y y) e βz (2.29) where β = kx 2 + k2 y k2 and D is a constant. k denotes the freespace wavenumber corresponding to the frequency f (k = 2π λ = 2πf c, c

49 24 2 CANONICAL DRAS being the speed of light in vacuum c = 1 ε μ ). After a mode matching procedure is applied, the following transcendental equation is obtained for the wavenumber k z : ( ) kz a k z tan = (ε r 1)k 2 2 k2 z (2.3) where ε r is the relative dielectric permittivity of the dielectric resonator. Finally, the resonance frequency of the TEmn1 z mode of the RDRA, for given dimensions a, w, h and dielectric permittivity ε r, can be estimated by solving the separation equation k 2 x + k 2 y + k 2 z = ε r k 2 (2.31) after having substituted the expressions for k x, k y and k z from (2.24), (2.25) and (2.3) respectively. Based on the above equations, the normalized resonance frequency of the fundamental TE111 z mode of the RDRA is plotted in Fig. 2.5 versus its aspect ratio a/h, for different values of the aspect ratio w/h. The normalized frequency is defined as: F = 2πwf ε r (2.32) c The curves illustrated in Fig. 2.5 are quite general. The resonance frequency f of the TE111 z mode can be easily found by using this plot, provided that the aspect ratios and the dielectric permittivity of the RDRA are already given. The TE111 z mode of the RDRA is of particular interest to us, since it is the lowest-order mode and, as it will be shown next, it has the lowest Q-factor. The field distribution of the TE111 z mode inside the dielectric resonator is depicted in Fig It can be observed that the fields are similar to those from a slot-directed magnetic dipole and therefore, the far-field characteristics are also expected to be the same Radiation Q-factor To derive an expression for the radiation Q-factor of the RDRA, its total stored energy W and radiated power P rad must be determined. We assume that the RDRA is made of a high quality dielectric material with very low

50 2.3 THE RECTANGULAR DRA F 8.5h = h w =2h ah / Figure 2.5: Normalized resonance frequency of the TE z 111 mode. y E PEC x z H (a) x (b) Figure 2.6: Field distribution of the TE z 111 mode. (a) DRA fields E x and E y at z =. (b) DRA fields H x and H z at y =. tan(δ) and therefore, the dielectric losses are negligible. Since the fields inside the resonator are known [5], the total stored energy can be easily found by integration of the power density. Moreover, the radiated power can be computed using the standard relation for the power radiated by a magnetic dipole of moment p m [2]. The final expressions for the total stored energy W and the radiated power P rad are [2]: W = ε ε r awh 32 ( 1+ sin(k ) za) (k 2 x k z a + ) k2 y (2.33) P rad = 1k 4 jω8ε (ε r 1) k x k y k z sin(k z a/2) 2 (2.34)

51 26 2 CANONICAL DRAS By using equation (2.12) in conjunction with equations (2.33) and (2.34), an expression for the radiation Q-factor of the RDRA as a function of its dimensions and its permittivity can be obtained. It also turns out that Q rad ε 3/2 r (2.35) The proportionality between the radiation Q-factor Q rad and the dielectric permittivity ε r is to be expected. As the dielectric permittivity increases, the fields become more and more confined inside the resonator and consequently, the radiated power becomes smaller. Hence, Q rad increases, or, in other words, the impedance bandwidth decreases. 2.4 The Cylindrical Dielectric Resonator Antenna The CDRA is the most widely used DRA in practical applications, since it is much easier and cheaper to fabricate compared to the RDRA and the HDRA and at the same time it provides more design parameters for the control of the bandwidth and the resonance frequency than the dielectric hemisphere. A typical configuration for a CDRA is illustrated in Fig. 2.7, where a simple dielectric cylinder of height h, radius a and dielectric permittivity ε r is residing on a groundplane of infinite lateral dimensions. This geometry is equivalent to an isolated cylinder of permittivity ε r, radius a and height 2h, as explained by image theory. The modes that can be supported by a dielectric body of revolution like the cylinder are of three types: the transverse electric TE npm,the transverse magnetic TM npm,andthehybridmodeshem npm. Here, the indices n, p and m denote the number of full-period field variations in the azimuth, in the radial direction and in the z direction respectively. From the aforementioned modes, the HEM 11δ (radiating like a horizontal magnetic dipole), the TE 1δ (radiating like a vertical magnetic monopole) and the TM 1δ (radiating like a vertical electric monopole) are the most common, since they are of the lowest order and they also have the lowest radiation Q-factors. In this nomenclature for the CDRA modes, the index δ denotes the fact that the dielectric resonator is shorter than one-half wavelength. This can be explained from the fact that the DRA is an open radiating structure and thus the fields are not entirely confined within the dielectric volume.

52 2.4 THE CYLINDRICAL DRA 27 z h y a y PEC x (a) PEC x (b) Figure 2.7: CDRA geometry. (a) General view. (b) Top view. For the analysis of the dielectric cylinders, the DWM in combination with the magnetic wall model can be employed in order to find some firstorder solutions for the resonance frequencies, the near-field distributions and the radiation patterns [4], [21]. Alternatively, surface integral equations can be used to formulate such problems [22]. The MoM is then employed to reduce the integral equations to a system of matrix equation of the type: [Z][I] =[V ] (2.36) where [Z] is a square matrix that represents the impedance and admittance submatrices, [I] is a column vector containing the electric and magnetic surface current coefficients to be determined and [V ] is the generalized voltage vector comprising the excitation from the coupling scheme. Since the DRA natural frequencies are the frequencies for which the system can sustain a response without any excitation, they can be allocated by searching for values of s = σ+jω, for which the determinant vanishes: det[z] = (2.37) Finally, the resonance frequency and the radiation Q-factor of the excited CDRA mode can be determined from equations (2.38) and (2.39) respectively: f = ω 2π Q = ω 2σ (2.38) (2.39) Based on the above analysis, a number of empirical expressions has been developed for the resonance frequency and the radiation Q-factor

53 28 2 CANONICAL DRAS z E H PEC y y (a) x (b) Figure 2.8: Field distribution of the TM 1δ mode. (a) DRA fields E y and E z at x =. (b) DRA fields H x and H y at z =. of various CDRA modes. These expressions are very simple to use and they have a quite high degree of accuracy. In the following sections, such empirical expressions will be given for the TM 1δ and the HEM 11δ modes of the dielectric cylinder. More expressions for other CDRA modes can be found in literature [14] The TM 1δ mode As mentioned before, the TM 1δ mode radiates like a vertical electric monopole (Fig. 2.8) and hence, it exhibits monopole-like radiation patterns (with a null in the broadside) and E θ polarization. The resonance frequency and the radiation Q-factor of this CDRA mode can be found from the following equations [5]: k a =.8945( x e x )/ε.45 r (2.4) Q = 1.9 x( x e 3.67x ) (2.41) where x = a/2h and the resonance frequency can be determined according to the relation f res (GHz) = 3k a/(2πa(cm)) The HEM 11δ mode The HEM 11δ mode is the fundamental mode of the dielectric cylinder. It radiates like a horizontal magnetic dipole (Fig. 2.9), exhibiting broadside radiation patterns, low cross-polarization and the largest possible

54 2.5 COUPLING METHODS TO DRAS 29 z E H y PEC y (a) x (b) Figure 2.9: Field distribution of the HEM 11δ mode. (a) DRA fields E y and E z at x =. (b) DRA fields H x and H y at z =. bandwidth (lowest radiation Q-factor) for the cylindrical geometry. The resonance frequency and the radiation Q-factor of the HEM 11δ mode can be determined through the equations [5]: k a = ( x x x x 4 )/ε.42 r (2.42) Q = xε 1.2 r ( e 2.8x(1.8x) ) (2.43) where, again, x = a/2h and f res (GHz) = 3k a/(2πa(cm)). 2.5 Coupling methods to DRAs A crucial part in the design of every practical DRA is the selection of a suitable energy coupling scheme. The type of the coupling scheme and its location with respect to the antenna can affect decidedly its performance in terms of impedance bandwidth, radiation patterns and polarization. In other words, the antenna feed can determine the amount of energy coupled as well as the type of the excited modes and subsequently the DRA radiation characteristics. It is thus apparent that a careful examination of the different coupling methods is necessary towards the objective of optimized DRA performance. According to the fundamental electromagnetic theory and the Lorentz Theorem of Reciprocity [23], the amount of coupling, k, between the (electric or magnetic) source and the fields inside the DRA can be determined

55 3 2 CANONICAL DRAS according to: k k ( E J e )dv or (2.44) ( H J m )dv (2.45) where E, H are the vectors for the electric and magnetic field intensity and J e, Jm are the electric and magnetic currents, respectively. It should be mentioned that the magnetic current is a fictitious quantity that is considered, essentially, as an analogy to the electric current. The above equations state that in order to achieve strong coupling between an electric (magnetic) current source and the DRA, the source should be placed in the vicinity of the strongest electric (magnetic) fields of the DRA mode. It is thus clear that a good understanding of the field distributions of the DRA modes is crucial, before a suitable feeding scheme is chosen. The following sections will review four of the most common feeding schemes for the DRAs: the microstrip line, the coaxial probe, the coplanar loop and the rectangular aperture. For the latter, an extensive investigation will be made about the independence, to a first order approximation of the DRA resonances from the aperture resonances. Then, examples will be provided, where this operational concept is successfully exploited to enhance the DRA bandwidth The microstrip line One of the simplest methods to couple energy to a DRA is through proximity coupling from a microstrip line. As illustrated in Fig. 2.1, the microstrip coupling excites the magnetic fields inside the DRA and produces a horizontal magnetic dipole mode. The degree of coupling depends on the distance of the DRA from the microstrip line as well as its dielectric permittivity [24]. The main disadvantage of this coupling scheme is the spurious radiation due to the microstrip line. This translates into instable radiation patterns and low polarization purity.

56 2.5 COUPLING METHODS TO DRAS 31 z microstrip line PEC E-field H-field y x y (a) (b) Figure 2.1: Microstrip coupling for the excitation of the HEM 11δ mode of the CDRA. (a) Side view. (b) Top view. z probe PEC y y (a) E-field H-field x (b) PEC Figure 2.11: Coaxial probe coupling for the excitation of the TE 111 mode of the HDRA. (a) Side view. (b) Top view The coaxial probe The coaxial probe is an extensively used feeding scheme, since its coupling mechanism is very straightforward and the fabrication cost low. In order to achieve maximum coupling, the probe should be placed at a position, where the electric field intensity is at a maximum, as indicated by equation (2.44) and shown in Fig for the case of the TE 111 mode of the HDRA. The degree of coupling can be further enhanced by varying the probe height and by placing it either outside, or inside the dielectric resonator.

57 32 2 CANONICAL DRAS z PEC PEC y y (a) E-field H-field x (b) co-planar circular slot Figure 2.12: Co-planar loop coupling for the excitation of the TE 11δ the RDRA. (a) Side view. (b) Top view. mode of The co-planar slot loop The co-planar slot loop has a coupling mechanism that is in principle similar to that of the coaxial probe, but at the same time it has one important difference from it. Since it is a planar structure printed on the groundplane where the DRA is placed, it does not require any drilling of holes inside the dielectric resonator, like in the case when the probe is located inside the dielectric resonator. As a result, the interference with the field distribution of the excited modes is small and the fabrication complexity low. The degree of coupling to the DRA can vary, depending on the relative position of the loop with respect to the dielectric resonator. The coupling mechanism of the co-planar loop is demonstrated in Fig for the case of the fundamental TE 11δ mode of the RDRA The aperture The aperture coupling is an inductive type of coupling; it behaves like a horizontal magnetic dipole that excites the magnetic fields inside the dielectric resonator. A typical configuration of an aperture fed DRA is illustrated in Fig The aperture is etched in the groundplane of an open-ended microstrip line, which serves as the feeding scheme for the dielectric resonator. Since the groundplane is located in between the DRA and the microstrip line, the feed does not interfere with the antenna and therefore spurious radiation is avoided. Other advantages of the aper-

58 2.6 APERTURE COUPLED CANONICAL DRAS 33 PEC slot z y PEC y microstrip line E-field H-field (a) x (b) Figure 2.13: Aperture coupling for the excitation of the TM 1δ CDRA. (a) Side view. (b) Top view. mode of the ture coupling include the easy implementation at higher frequencies, the simplicity in coupling to DRAs arrays as well as the number of different ways to enhance the coupling mechanism to the DRA. The microstrip stub length, the aperture shape and size as well as its relative position with respect to the DRA are some of the parameters that can be varied to provide efficient coupling. Finally, an important advantage of the aperture coupling is the previously mentioned possibility to enhance the impedance bandwidth of the antenna by combining the DRA resonances with the aperture resonances. This is going to be the topic of the next section. 2.6 Aperture coupled Canonical DRAs The enhancement of the matching bandwidth while maintaining the antenna s size has always been a topic of great interest for the antenna community. Chu s research on the relationship between the antenna s impedance bandwidth and its size set some fundamental limitations to the achievable bandwidth [25]. These limitations do not however directly apply to multi-resonant structures. This is often encountered in filter design, where a large number of high-q resonators can be used for the increase of the filter s operational bandwidth. Based on the above and since the dielectric resonator and the aperture are both resonant structures, the DRA s bandwidth can be significantly

59 34 2 CANONICAL DRAS enhanced through the merging of these resonances. In addition, both the aperture mode and the fundamental mode of all canonical DRAs have similar radiation properties and hence the final DRA structure exhibits stable radiation patterns and high polarization purity within the entire spectrum Dual mode aperture coupled CDRA Standard CDRA design As a practical demonstration to what was mentioned previously, the aperture-coupled CDRA of Fig is considered. In this configuration, the dielectric cylinder of dielectric permittivity ε rd =1.2, height h = 4.5 mm and radius r is centered on top of a rectangular aperture in a finite ground plane of dimensions 12mm 12mm. The aperture, with length L s and width W s =.5mm, is etched in the groundplane of an open-ended microstrip line. The microstrip line of width W m =2.4mm is a 5 Ω line printed on a Duroid R substrate of permittivity ε rs =2.2 and thickness t =.7874 mm. Finally, the stub length P = 4mm of the microstrip line under the aperture is designed to ensure impedance matching. With reference to Fig. 2.14, the parameters that determine the resonance frequency of the aperture are primarily the permittivity of the sub- and superstrate (DRA), ε rs and ε rd respectively, as well as the aperture s length L s. From the other side, the DRA modes occur at frequencies determined by the dielectric permittivity and the dimensions r, h of the dielectric resonator, according to the equations (2.4), (2.42). By tuning these parameters, an increased bandwidth for the proposed antenna can be obtained, provided that the aperture and DRA modes are designed to be offset. To ensure stable radiation characteristics within the spectrum, the fundamental HEM 11δ mode of the CDRA is excited. In that case, both the aperture and the DRA mode radiate as horizontal magnetic dipoles. Variation of the aperture length - Identification of the modes To demonstrate the independence, to a first-order approximation, between the aperture and the DRA mode, simulations are carried out, in

60 2.6 APERTURE COUPLED CANONICAL DRAS 35 z h y W m r W s L s t PEC W m x rs PEC rd P (a) (b) Figure 2.14: Configuration of the aperture coupled CDRA. (a) General view. (b) Top view. z y h t x rd rs W m Figure 2.15: Configuration of the aperture antenna with an infinite sub- and superstrate of heights t and h respectively. which the aperture length L s varies from 7 mm to 11 mm, while the radius of the cylinder is fixed at 15.5 mm and the rest of the antenna specifications remain as before. These simulations focus on two aspects. First, the aperture mode in the configuration of Fig is investigated. There, the aperture is sandwiched between the substrate of dielectric permittivity ε rs =2.2 and height t =.7874 mm and a superstrate of permittivity ε rd =1.2 and height h =4.5 mm. This investigation is time-efficiently conducted by means of the commercial software tool ANSOFT Designer R,

61 36 2 CANONICAL DRAS which employs the MoM and assumes infinite lateral dimensions for the sub- and superstrate. Second, the resonances of the slot and the DRA are investigated using ANSOFT HFSS R (FEM), which can accurately analyze the finalized structure of finite dimensions. From the two resonances observed, one is affected by the variation of the slot length, whereas the other is not. In Fig. 2.16, the resonance frequencies of the antenna structure with respect to the aperture length are illustrated. For the given dimensions of the dielectric disc, the HEM 11δ mode is expected to occur at 5.2 GHz according to (2.42), as indicated by the arrow. As the slot length L s is increased, the resonance frequency of the aperture mode drops and above a certain value of the aperture length (L s 7.8mm),the HEM 11δ mode starts getting excited. For an aperture length of 8.5mm, the aperture and the DRA modes coincide. As the aperture length increases further, the DRA mode retains its expected resonance frequency. Comparison between results by HFSS (DRA on top of the aperture) and Designer (infinite superstrate) proves the initial assumption, that the only mode affected significantly by the aperturelengthisanaperturemode. Variation of the DRA radius - Verification of the design principle To experimentally verify the above results, an antenna prototype was manufactured according to the geometrical configuration described before. The aperture length was set to 8.5 mm and multiple dielectric discs were fabricated with radii r ranging from 12 mm to 14 mm. Height and permittivity remained fixed. As indicated in Fig. 2.16, the use of a dielectric disc of radius r =15.5 mm would result in both, the aperture and the DRA mode resonating at the same frequency (5.2 GHz). By using discs of different radii, the two modes are gradually offset and therefore a wider impedance bandwidth can be achieved. The simulated and measured return loss of this antenna for disc radii of 12 mm and 13 mm is shown in Fig By comparing the two graphs, it is apparent that the increase of the disc radius results in the decrease of the resonance frequency of the dielectric resonator mode (the resonance at the higher frequency), whereas the aperture resonance remains unaffected. For the case of the 13 mm radius disc, a bandwidth of 27% is achieved experimentally. Finally, for the disc of radius r = 12 mm, the radiation patterns are illustrated at frequencies 5.2 GHz and 6.3 GHz. The measured and simu-

62 2.6 APERTURE COUPLED CANONICAL DRAS 37 Frequency [G H z] HFSS slot mode HFSS HEM 11 mode DESIGNER slot mode length of the slot Ls [mm] Figure 2.16: Resonance frequencies vs. slot length L s for r =15.5 mm. Return Loss [db] r =12mm Return Loss [db] r =13mm -25 measurement -25 measurement simulation (HFSS) simulation (HFSS) frequency [GHz] frequency [GHz] Figure 2.17: Return loss for DRA radii r =12mmandr = 13 mm. -15 lated radiation patterns are depicted in Fig for the E-plane (φ = ) and H-plane (φ =9 ). At the lower frequency, the slot is at resonance, whereas at the higher frequency the HEM 11δ mode occurs. As expected, the radiation patterns at both frequencies resemble the ones of a horizontal magnetic dipole. For both resonances, the maximum gain observed is around 5 dbi.

63 38 2 CANONICAL DRAS f = 5.2 GHz f = 6.3 GHz E-plane 15 measured simulated H-plane 15 Figure 2.18: Radiation patterns for the E- and H-planes at 5.2GHz and 6.3GHz The double bowtie aperture coupled DRA It was demonstrated before that the aperture and the DRA resonances are, to a first order approximation, independent from each other. Hence, enhanced performance can be achieved by designing the aperture and the dielectric resonator to be resonant at nearby frequencies. In that way, a very wide operational bandwidth can be obtained, provided that the excited modes are overlapping and chosen in such a way so as to exhibit similar radiation characteristics. This operational concept of the aperture coupled DRAs can be further used in geometries, where the dielectric resonator is coupled through a feed comprising more than one apertures. Such a DRA configuration is depicted in Fig There, a microstrip line couples energy to a dielectric resonator of rectangular or circular cross-section through two

64 2.6 APERTURE COUPLED CANONICAL DRAS 39 (a) (b) Figure 2.19: The configuration of the double bowtie aperture coupled DRA. (a) RDRA (b) CDRA parallel bowtie shaped apertures. As a result, three horizontal-magneticdipole type modes can be excited: the fundamental mode of the dielectric resonator and two modes from the bowtie apertures. The design procedure of the double bowtie aperture coupled DRA can be separated into three simple steps. In the first step, the two bowtie shaped apertures are designed to be resonant at nearby frequencies f 1 and f 2. To that end, the structure depicted in Fig. 2.2 is simulated assuming a flat dielectric superstrate (permittivity ε rd and height h) situatedon top of the apertures and infinitely extended in the x y direction. This assumption of infinite dimensions allows the computationally efficient use of the Ansoft Designer R. The bowtie apertures with lengths L s1, L s2 and widths W s1, W s2 are etched into the groundplane of a microstrip line, which is a 5 Ω line of width W m. The distances P 1 and P 2 from the centers of the two slots to the open end of the microstrip line are chosen to ensure good impedance matching. With reference to Fig. 2.2, the parameters that determine the resonance frequency of the bowtie shaped apertures are primarily the permittivity of the sub- and superstrate ε rs and ε rd respectively, as well as the aperture lengths L s1 and L s2. The widths W s1 and W s2 (or the flare angles of the bowties) are used as matching parameters for the two apertures, as well as to further increase their bandwidth [26]. It should be underlined here that the two parallel apertures are capacitively coupled to each other. This affects not only the resonance frequencies, but also the radiation properties of the apertures and it should thus be taken into

65 4 2 CANONICAL DRAS y z W m L s1 W s1 W s2 L s2 x h t superstrate substrate rd rs P 2 P 1 (a) (b) Figure 2.2: Schematic of the structure with the bowtie shaped apertures between a sub- and a superstrate. (a) Front view. (b) Side view. consideration in the design. The second step of the procedure involves the design of the dielectric resonator. Its permittivity ε rd and height h are taken to be the same as that of the dielectric superstrate, while the rest of its dimensions (radius for the cylinder, length and width for the parallelepiped) are tuned in order to obtain a resonance at a frequency f 3, which is nearby, but larger than the frequencies f 1 and f 2. In the third step, the coupling scheme from the first step is combined with the dielectric resonator designed in the second step. To do so, the coupling scheme of Fig. 2.2 is kept unchanged, while the lateral dimensions of the substrate are made finite. Moreover, the superstrate is replaced by the dielectric resonator whose dimensions and permittivity were determined during the second step. The final structure is fine-tuned for the further enhancement of its impedance bandwidth and radiation properties. This tuning involves primarily the stub lengths P 1 and P 2, the flare angles of the bowties as well as the position of the dielectric resonator center relative to the center line of the feeding microstrip. It should be emphasized here that the parameters tuning can also help producing more symmetrical radiation patterns. The asymmetry is caused by the scheme of the two parallel apertures steering the beam at an angle different from the broadside direction. To obtain symmetrical radiation, two approaches

66 2.6 APERTURE COUPLED CANONICAL DRAS 41 are followed. In the first approach, the distance between the two apertures is made very small, so that the phase shift between the two apertures is also minor. The second approach involves shifting the dielectric resonator center along the line connecting the apertures centers. This technique affects both the matching and the direction of maximum radiation. So, it becomes apparent that the dielectric resonator does not only serve as a loading to increase the front-to-back ratio, but it also helps forming the radiation patterns of the resonant apertures. Ansoft HFSS R was used for the simulations in this step. The double bowtie aperture coupled CDRA As a first practical example of the design procedure described before, a double bowtie aperture coupled CDRA operating in the 5.GHz 6.5GHz range is illustrated in Fig The dielectric resonator is made from Rogers TMM R 1i laminate with dielectric permittivity ε rd =9.8, height h =4.5mm and radius r = 12 mm. The dielectric cylinder lies on top of the two bowtie shaped apertures, which have dimensions L s1 =7.9mm, L s2 =6mm,W s1 =.58 mm, W s2 =2.2mm, and their width at the center is W c1 = W c2 =.3mm. The center of the cylinder is placed at a position P = 3.1mm from the open end of the microstrip line. The width of the microstrip line is W m = 2.4 mm and its open end is at distances P 1 =4.1mm and P 2 =2.7mm from the aperture centers. Finally, the Duroid R substrate s permittivity is ε rd =2.2, its thickness is t =.7874 mm and its dimensions are 1 mm 1 mm. With the objective of comparing the numerical results from HFSS with measurements, an antenna prototype was fabricated accordingto the specifications given above. The measured and simulated return loss of the DRA is illustrated in Figure An impedance bandwidth of 33 per cent is measured, which is a very satisfying result for a structure with a single dielectric disc. The discrepancy between the simulated and the measured results is most probably caused by the air gap between the ground plane and the dielectric resonator [27] as well as other fabrication tolerances. It should be noted here that the numerical results of HFSS were validated using the full-wave analysis tool CST R employing the Finite Integration Technique. To further illustrate the excitation of the three modes in the described

67 42 2 CANONICAL DRAS y W m L s1 W s1 W s2 L s2 x h t rd rs z r P P 1 P 2 (a) (b) Figure 2.21: Schematic of the double bowtie aperture coupled CDRA. (a) Front view. (b) Side view. Return Loss [db] measurement simulation frequency [GHz] Figure 2.22: Measured and simulated (HFSS) return loss of the CDRA as a function of frequency. geometry, the simulated real and imaginary parts of the DRA input impedance are depicted in Fig (a). The two aperture modes are excited at 5.6GHz and 6.5 GHz, while the fundamental HEM 11δ mode of the dielectric cylinder is resonant at 6.75GHz. This statement can be further substantiated by comparing the input impedance plot of Fig (a) with the one illustrated in Fig (b). This last plot shows the input

68 2.6 APERTURE COUPLED CANONICAL DRAS 43 Impedance [Ohm] real real imaginary imaginary frequency [GHz] frequency [GHz] (a) Impedance [Ohm] Figure 2.23: Input impedance vs. frequency. (a) Double bowtie aperture scheme with the CDRA on top. (b) Double bowtie aperture scheme sandwiched between an infinite sub- and superstrate. 1 5 (b) impedance of the double bowtie aperture scheme sandwiched between the infinite sub- and superstrates (Fig. 2.2). There, the infinite superstrate serves as a dielectric loading and it does not, as expected, excite any dielectric resonator modes. Consequently, only the aperture modes are resonant. Fig (b) demonstrates the validity of the aforementioned hypothesis, since only two resonances are observed: one at 5.65 GHz and one at 6.7 GHz. The comparison between Fig (a) and 2.23 (b) associates the third mode (indicated by the local maximum of the input resistance) in Fig (a) with the dielectric resonator mode. It is worth mentioning here that the replacement of the superstrate by the dielectric resonator shifts slightly the resonant aperture modes to lower frequencies, due to the lowering of the effective permittivity ε eff. The measured radiation patterns (parallel and cross polarization) are depicted in Fig at frequencies 5.2GHz,6.25 GHz and 6.7 GHz. As expected, the polarization remains reasonably pure for a wide elevation angle range and the gain in the broadside direction is stable at around 3.5 dbi. In addition, the shift of directivity to an offbroadside angle, caused by the slot array, has been canceled through the tuning procedure described before.

69 44 2 CANONICAL DRAS E-plane H-plane f = 5.2 GHz f = 6.25 GHz co-pol cross-pol f = 6.7 GHz Figure 2.24: Radiation patterns for the E- and H-planes at frequencies 5.2GHz, 6.25 GHz and 6.7GHz. The double bowtie aperture coupled RDRA The validity and repeatability of the proposed design procedure for different dielectric resonator shapes is demonstrated further through its application to the design of a double bowtie aperture coupled RDRA. For the same frequency range of operation as in the CDRA case, the geometrical configuration of the substrate and of the coupling scheme remains the same as before. The sole difference is obviously the dielectric resonator, which is now a parallelepiped made from Rogers TMM 1i laminate of dielectric permittivity ε rd =9.8and dimensions a = d = 2.5mm and h =4.5mm. To obtain better matching as well as more symmetrical radiation patterns, the dielectric parallelepiped is centered at a distance P =3.6mm from the open end of the microstrip line, and displaced by distance Δy =1.2mmfrom the microstrip s center line. The geometrical configuration of the double bowtie aperture coupled RDRA

70 2.6 APERTURE COUPLED CANONICAL DRAS 45 d y W m a y P L s1 P 1 P 2 L s2 x h t rd rs z (a) (b) Figure 2.25: Schematic of the double bowtie aperture coupled RDRA. (a) Front view. (b) Side view. Return Loss [db] -1-2 measurement theory frequency [GHz] Figure 2.26: Measured and simulated (HFSS) return loss of the RDRA as a function of frequency. is depicted in Fig A prototype was fabricated and measured, so that a comparison with the numerical results could be made. The plot of the DRA return loss versus frequency is illustrated in Fig The measured impedance bandwidth exceeds 37 per cent and reasonable agreement is obtained be-

71 46 2 CANONICAL DRAS E-plane H-plane f=5. 15 GHz f = 6.5 GHz f=6. 95 GHz co-pol cross-pol Figure 2.27: Radiation patterns for the E- and H-planes at frequencies 5.15 GHz, 6.5 GHz and 6.95 GHz. 9 tween simulation and experiment. The radiation patterns (parallel and cross polarization) are shown in Fig at frequencies 5.15 GHz, 6.5GHz and 6.95 GHz. Just like in the cylindrical configuration, stable radiation patterns are achieved. It is worth mentioning here that if a rectangular (not a square) dielectric resonator had been used (a d in Fig. 2.25), the polarization purity would have been improved. This is due to the fact that the TE111 x mode would be resonant at a different frequency compared to the TE y 111 mode and therefore the polarization at the frequency of the mode would not be distorted by the orthogonal resonant mode. TE y Offset cross-slot coupled CDRA As a final demonstration of an aperture coupled DRA, a circularly polarized CDRA will be discussed, exhibiting a wide 3 db Axial Ratio (AR) bandwidth and well behaved radiation patterns.

72 2.6 APERTURE COUPLED CANONICAL DRAS 47 y P W m x L s1 y W s2 W s1 x h t rd rs z r L s2 PEC P 1 P 2 (a) (b) Figure 2.28: Schematic of the cross-slot-coupled DRA. Inset: Centered design from [28] (a) Front view. (b) Side view. CP antennas are particularly advantageous in applications for longdistance communications, where the depolarization effect is strong and therefore the Polarization Loss Factor (PLF) can significantly deteriorate the signal to noise ratio (SNR) of the receiver. The CP operation for DRAs has been extensively studied within the antenna community; in most of the cases, however, the proposed geometries were difficult to fabricate and their 3 db AR bandwidth did not exceed 3%. In [28], a DRA geometry was proposed, in which good CP operation was accomplished by using two crossed slots of unequal lengths, to couple energy from a microstrip line to a cylindrical dielectric resonator. Both slots were angled at 45 with respect to the feeding microstrip line and their centers were at the same position, centered underneath the dielectric cylinder, as depicted in the inset of Fig Their lengths were unequal, so that two neardegenerate orthogonal modes of equal amplitude and 9 phase difference were excited at frequencies close to that of the fundamental HEM 11δ mode of the CDRA. The resulting 3 db AR bandwidth was 3.91 per cent. The operation of the CP CDRA described before can be further enhanced, if the partial independency of the aperture modes and the dielectric resonator mode is considered. For the DRA configuration shown in Fig. 2.28, the two apertures are resonant at frequencies, which depend on their lengths as well as the dielectric permittivity of the substrate and of the dielectric resonator (serving as superstrate). The 9 angle crossing of

73 48 2 CANONICAL DRAS the apertures prevents the coupling between the two excited orthogonal modes. Consequently, the investigation for each aperture resonance may be conducted separately. CP operation is obtained when the two modes have equal amplitudes and ±9 phase difference (for right-handed or lefthanded circular polarization). The amplitude of the orthogonal modes is affected by the matching of each aperture and consequently also by the stub length P. Therefore, excitation by two crossed slots may provide CP operation over a significantly expanded bandwidth, provided the following requirements are satisfied. First, the length of one aperture must be adequately larger than the other, in order to excite two orthogonal modes at offset frequencies. Second, different stub lengths must be chosen for the two apertures, so that better matching can be ensured and thus near-degenerate modes will be excited. To start with the DRA design procedure, for a CP operation around the center frequency f cp the following steps are followed. First, the longer of the two slots is designed to be resonant at a frequency f 1 = f cp f, while the shorter one at a frequency f 2 = f cp + f,wheref f f cp. To that end, the two slots are designed and optimized separately from one another. Each slot forms an angle of 45 with respect to the microstrip line and is sandwiched between the substrate and a superstrate of the same height h and permittivity ε rd as of the dielectric resonator. Infinite lateral dimensions are assumed, so that the resonances resulting from the finite dimensions of the structure are avoided. The numerical analysis is performed by means of ANSOFT DESIGNER R,whichcan efficiently estimate the slot lengths L s1, L s2 and the stub lengths P 1, P 2 for best matching at the desired frequencies. After the two crossed slots have been individually analyzed, they are put together in the same structure, retaining the same stub lengths and angles ±45 with respect to the microstrip line. As expected, the performance of the crossed-slots scheme is almost identical to the superposition of the performances of the two separate slots, due to absence of coupling between them. In the second step, the superstrate is replaced by a cylinder of the same height and permittivity, while the crossed-slots geometry is kept unchanged. Additionally, the lateral substrate dimensions are made finite. The simulations are now performed with ANSOFT HFSS R to accommodate the finite lateral dimensions. The radius of the dielectric cylinder is initially chosen such that its fundamental HEM 11δ mode is resonant at the frequency f cp. However, in order to obtain optimum CP operation, its

74 2.6 APERTURE COUPLED CANONICAL DRAS 49 Return Loss [db] measurement simulation frequency [GHz] Figure 2.29: Measured and simulated (HFSS) return loss. radius might need to be altered slightly. Further fine-tuning might still be necessary, in order to enhance the CP bandwidth without deteriorating the return loss (S 11 ) levels or the radiation patterns. This optimization involves primarily the stub lengths and the position of the disc center relative to the center line of the feeding microstrip. For a CP DRA operating at 5.7 GHz, the aforementioned procedure results in the configuration illustrated in Fig The dielectric cylinder is made from Rogers TMM 1i laminate, with dielectric permittivity ε rd = 9.8, height h =5.1mmand radius r =15.2mm. Its center is located on top of the longer slot (centered). Both slots are etched in the finite ground plane of a carrier substrate (ε rs =2.2 andthicknesst =.78 mm) with lateral dimensions 12 mm 12 mm. The slots have dimensions L s1 =11.4mm, L s2 =8.9mm and W s1 = W s2 =.3mm, while the stub lengths P 1 =4.2mm and P 2 =4.7mm ensure good impedance matching for the slots. Finally, the substrate carries on the opposite side a 5 Ω microstrip line of width W m =2.4mm, which forms angles ±45 with the two apertures. In order to provide experimental validation for the design procedure described before, an antenna prototype was manufactured and measured. Fig illustrates the plots of the measured and simulated return loss of the cross-slot coupled DRA versus frequency. The wide impedance bandwidth obtained is due to the aperture and the dielectric disc resonances. More specifically, the two apertures are resonant at about 4.4GHz

75 5 2 CANONICAL DRAS Axial Ratio [db] 6 3 measurement simulation frequency [GHz] Figure 2.3: Measured and simulated AR in the broadside direction as a function of frequency. and 5.9 GHz, while the HEM 11δ mode resonance occurs at 5.25 GHz. To demonstrate the spectrum where good CP operation is obtained, the measured and simulated axial ratio in the broadside direction (z axis) is shown in Fig The measured and simulated CP bandwidth, as determined from the 3 db AR, is found to be around 4.7% and 6.3% respectively. The radiation patterns of the DRA under investigation were extracted at the frequency of its lowest AR f =5.75 GHz. The patterns are depicted in Fig in the two orthogonal planes x z (φ = )andy z (φ =9 ). It is observed that the DRA is left-handed circularly polarized, which is expected since L s1 >L s2. Moreover, the polarization purity is good, and the beamwidth of good CP operation ( 15 db cross-polarization levels) is at least 12 in both planes. Finally, the measured CP gain in the broadside direction is approximately 3.5 dbi. It was mentioned before that the choice of different stub lengths (P 1 P 2 ) for the two apertures contributes decidedly to the further enhancement of the CP bandwidth. This effect was investigated in more detail and the results are demonstrated in Fig There, the 3 db AR fractional bandwidth (with respect to the center frequency f cp )ofthedrais plotted against the asymmetry of the cross-slot coupling scheme (defined as the stub lengths difference P 2 P 1 )fortwodifferentslotlengthratios L s1 /L s2. Additionally, the same graph illustrates the effect of the scheme

76 2.6 APERTURE COUPLED CANONICAL DRAS = o LHCP 21 RHCP =9 18 o Figure 2.31: Measured radiation patterns in the x z and y z planes at f = 5.75 GHz. asymmetry P 2 P 1 on the off-broadside angle θ cp, for which good CP operation (at the frequency f cp ) is actually obtained. As observed in the plots, up until a certain value of P 2 P 1, the CP bandwidth becomes broader as the asymmetry increases. At the same time, however, the angle θ cp drops. It is therefore apparent that a trade-off needs to be made between the bandwidth and the CP beamwidth of the designed CP DRA. In the case of our manufactured prototype (L s1 /L s2 =1.28) and for an asymmetry P 2 P 1 of.5 mm, the simulated CP bandwidth is 6.3% and the angle θ cp is around 11. If the ratio of the longer to the shorter slot length becomes larger, the CP bandwidth can further increase, provided that the stub lengths are correspondingly adjusted. This is evident through the second set of curves in Fig There, the aperture lengths ratio L s1 /L s2 is It is observed that in this case, when the stub lengths P 1 and P 2 are equal, no 3 db AR bandwidth can be obtained. As the two slot centers are moved apart, the CP bandwidth increases and for an asymmetry value of about 1.2 mm, the bandwidth becomes maximum. It should be emphasized here that the maximum obtained CP bandwidth for L s1 /L s2 =1.43 is larger than that for L s1 /L s2 =1.28. This bandwidth enhancement comes along with a drop in the angle θ cp of good CP operation due to the larger design asymmetry. To experimentally validate the above results, a second CP DRA was manufactured. Its cross-slot coupling scheme had dimensions L s1 =11.7mm, L s2 =8.2mm and P 1 =3.1mm, P 2 =4.3mm, while the rest of its geometrical configuration was the same as of the first DRA. A 6.8% broadside CP bandwidth

77 52 2 CANONICAL DRAS % CP Bandwidth CP BW } L/L s1 s2 = 1.28 Angle cp CP BW Angle } L/L s1 s2 = 1.43 cp angle cp P 2 - P 1 [mm] 2 Figure 2.32: Simulated 3 db AR bandwidth and angle θ cp vs. the distance between the two aperture centers, for two different ratios of aperture lengths. P 1 =4.2mm for L s1/l s2 =1.28, P 1 =3.1mm for L s1/l s2 =1.43. was found, whereas the angle θ cp was measured to be less than Conclusion Dielectric resonators of canonical shapes are fundamental in the DRA theory, since their operational properties can be easily predicted through analytical or simplified but yet sufficiently accurate models. A rigorous classification of the canonical DRA modes already exists, while closedform expressions for their resonance frequencies and radiation Q-factors have been developed and their near-field distributions have been demonstrated. Therefore, the design of a canonical-shaped dielectric resonator coupled in a certain mode through a suitable feeding scheme is a very simple and straightforward procedure. In addition, the in-depth understanding of the radiation properties of the canonical DRAs can lead to the development of non-canonical shapes with enhanced operational characteristics in terms of their impedance bandwidth, their gain and polarization. The non-canonical geometries cannot be handled in an analytical manner and hence the optimization process can be significantly facilitated

78 2.7 CONCLUSION 53 through their consideration as deviations from canonical shapes. In that way, their excited modes and their subsequent radiation properties can, to a certain extent, be predicted. Apart from the shape itself of the dielectric resonator, the role of the energy coupling scheme is not to be underestimated. The type and the location of the coupling scheme with respect to the dielectric resonator not only determines the excited DRA mode and thus the antenna radiation characteristics, but it can also dramatically affect its bandwidth. More specifically, the aperture coupled dielectric resonator may exhibit a significantly enhanced impedance bandwidth through the merging of the resonant DRA modes together with the aperture resonances. These two important DRA operational concepts, i.e. the deviation from a canonical to a non-canonical shape for enhanced performance and the modes-merging technique for the bandwidth enhancement will be employed extensively in the following chapters.

79 54

80 3 Broadband Dielectric Resonator Antenna Geometries 3.1 Introduction Resonant antennas, like for instance the DRAs and the MSAs, are radiating elements that inherently have a much more limited bandwidth compared to frequency independent antennas [6]. The reason is that the input impedance of resonant antennas changes rapidly with frequency and hence good matching can be achieved only for a narrow spectrum around the resonance frequency. In the case of DRAs, the impedance bandwidth suffers additionally from its strong dependency on the dielectric permittivity of the resonator. As the permittivity increases, the radiation Q-factor of the excited DRA modes increases and subsequently the impedance bandwidth becomes narrower. To improve the DRAs bandwidth response, several of the bandwidth enhancement techniques of the microstrip antennas can be employed. These techniques can be classified in three main categories. First, an external matching network like a quarter-wave transformer or a matching stub can be utilized. This technique is conceptually simple, but it increases the fabrication complexity and it can potentially degrade the antenna efficiency and gain through the rise of the insertion loss. Second, the bandwidth of a resonating antenna can be enhanced through the merging of multiple resonances. This technique was already introduced in the previous chapter, where the resonances of the feeding apertures were combined together with those from the canonical DRA. The modes-merging technique is not, however, limited to that. It is possible to excite multiple higher-order DRA modes at nearby frequencies, exhibiting the same polarization and radiation patterns. Then, a wide impedance bandwidth can be obtained, even when a simple non-resonant coupling scheme, like a coaxial probe, is used. This investigation will be the main focus of the current chapter. The third bandwidth enhancement technique involves decreasing the radiation Q-factor of the excited DRA modes through the insertion of air gaps or through geometrical modifications of the resonator. 55

81 56 3 BROADBAND DRA GEOMETRIES This leads to a smaller confinement of the fields inside the dielectric resonator and consequently to a wider bandwidth. A detailed investigation on this subject will be conducted in the next chapter. The excitation of multiple modes inside the dielectric resonator has several advantages compared to the combination of the DRA and the coupling scheme resonances. First, the realization of a resonant feed can create space-conservation problems in the device and it might also preclude some of the DRA configurations from being used in an array environment. Second, a resonant feed might degrade the antenna s good operation. For instance, some aperture-coupled DRAs suffer from the considerable backradiation, while a probe-fed dielectric resonator, in which the monopole is also resonant, is prone to instable radiation patterns or low polarization purity. From another side, the excitation of multiple dielectric resonator modes is conceptually more straightforward and the determination of the resonators dimensions can be simply done through the closed-form expressions developed for the canonical DRAs. Even when non-canonical DRAs are used, these expressions can still be deployed to roughly determine starting dimensions. Afterwards, numerical analysis and/or design curves can be used to determine an optimal geometrical configuration. This chapter will present different broadband dielectric resonator geometries that range from canonical shapes of various aspect ratios to noncanonical shapes utilizing the modes-merging technique. The first section will investigate the impedance bandwidth of a simple probe-fed RDRA for different aspect ratios (length/height) and (width/height). It will be demonstrated that the impedance bandwidth of a DRA depends strongly on these aspect ratios and hence its bandwidth response can vary substantially even for the same excited mode at the same frequency. In the second section of the chapter the high-profile RDRA [29] will be discussed. There, the fundamental TE 111 mode of the dielectric parallelepiped is combined with the higher-order TE 113 mode to provide an improved bandwidth response. The third section will investigate the double-slab DRA, which consists of two parallel rectangular slabs attached to each other. It will be demonstrated that degenerate modes appear for large values of the dielectric permittivity, while for lower permittivity values the double-slab geometry can provide a larger bandwidth compared to the canonical-shaped RDRAs. The double-slab geometry will be used as a starting point for DRA shapes deviating from the simple parallelepiped. These advanced DRAs will be investigated in the final sections of this chapter.

82 3.2 THE BANDWIDTH OF THE RDRA 57 z x y w l p a h PEC Figure 3.1: Probe-fed RDRA. 3.2 Bandwidth enhancement for the probe-fed RDRA A typical configuration of a probe-fed RDRA is illustrated in Fig A dielectric parallelepiped of dimensions a, w, h and permittivity ε rd is mounted on a ground plane of finite lateral dimensions. The dielectric resonator is coupled in its fundamental TE 111 mode through the center conductor of an SMA connector protruding out of a small hole in the metallic plane. The probe has a length l p and is attached to one of the resonator s surfaces, as shown in the figure. The resonance frequency and the radiation Q-factor of the RDRA can be determined according to the dielectric waveguide model presented in the previous chapter. It has been shown that for a specified resonance frequency and permittivity of the dielectric resonator, two out of the three parallelepiped s dimensions can be chosen independently. This design flexibility is particularly advantageous for two main reasons. First, many applications often require that the dielectric resonator s profile is as low as possible. In the case of the dielectric parallelepiped it is possible to predetermine its height and width and then calculate the necessary length for a resonance at the desired frequency. As a second reason, the DRA impedance bandwidth is significantly affected by the relative dimensions of the dielectric resonator. The rectangular shape provides two independent aspect ratios (length/height and width/height) and thus a significant degree of control over the RDRA bandwidth is possible. To demonstrate that, the simulated bandwidth of a probe-fed RDRA is plotted for different aspect ratios (a/h) and(w/h) in Fig The dielectric resonator is excited in its fundamental TE 111 mode at the (randomly selected) frequency f =3GHz.

83 58 3 BROADBAND DRA GEOMETRIES % Bandwidth w =.5h = h w =2h w =3h ah / Figure 3.2: % Bandwidth of the probe-fed RDRA as a function of the aspect ratios a/h and w/h. It can be observed in the figure that the % bandwidth of the RDRA is strongly dependent on the aspect ratios. For example, the impedance bandwidth of the dielectric cube (a = h = w) is approximately 11%, whereas for the case of the parallelepiped with relative dimensions a = 4h =4w it exceeds 16%. It is also interesting to note that for all aspect ratios w/h the impedance bandwidth is high when a<h. As the ratio a/h increases, the bandwidth drops and after a certain value of a/h the bandwidth starts increasing again. The simulated results presented here are in agreement with the theoretical curves shown in [5]. These curves were determined for isolated DRAs at a resonance frequency f = 5 GHz. The agreement between the plots serves as an indication for the generality of the dependence between bandwidth and aspect ratios. 3.3 The high-profile RDRA In principle, the RDRA optimization in terms of its aspect ratios cannot result in a very wide impedance bandwidth. To that end, the optimization of the parallelepiped s dimensions can be combined with the merging of multiple dielectric resonator modes at nearby frequencies. One simple way to employ the modes-merging technique is by coupling to a dielectric parallelepiped, whose height h is much larger than its width

84 3.3 THE HIGH-PROFILE RDRA 59 z h x y l p w a PEC Figure 3.3: Configuration of the probe-fed high-profile RDRA. w and its length a. This method was introduced in [29] and it is revisited here in order to better illustrate its operational principles. As demonstrated in that study, the fundamental TE 111 and the higher-order TE 113 modes of the RDRA are finally excited at adjacent frequencies. The separation between the two modes depends on the relative dimensions of the resonator and therefore it is possible to obtain a wideband RDRA even when a simple feeding scheme like the coaxial probe is used. The configuration of a typical probe-fed high-profile RDRA is shown in Fig The dielectric parallelepiped of permittivity ε rd is mounted on a groundplane of finite lateral dimensions and is fed through a probe of length l p. The reason for exciting both the TE 111 and the TE 113 modesisthat they exhibit similar broadside radiation patterns and polarization, as deduced from their E-field configuration shown in Fig. 3.4 (a) and (b) respectively. Moreover, the H-field inside the DRA is very strong around the groundplane for these two modes and hence both modes can be sufficiently excited, provided the coaxial probe has a length: l p λ g /4 where (3.1) λ g = λ (εrd +1)/2 (3.2) with λ being the free-space wavelength. This is because the strip current is maximum around the feed point for this probe length and thus the coupling is also maximum. In needs to be emphasized here that the TE 112

85 6 3 BROADBAND DRA GEOMETRIES z E z E x x (a) (b) Figure 3.4: Electric field configuration of (a) the TE 111 mode and (b) the TE 113 mode for a dielectric parallelepiped in free space. mode is not excited in the configuration of Fig. 3.3 because of the presence of the groundplane. According to the above considerations as well as the closed-form expressions (2.24), (2.25), (2.3) and (2.31) of the previous chapter, a probe-fed RDRA was designed for operation between 5 GHz and 6 GHz. The dimensions of the parallelepiped were determined as a =14mm,w =7.5mm and h = 23 mm, while its dielectric permittivity was ε rd =9.8. A probe length l p =8.5mmwas selected, so that best matching would be achieved. The return loss of the probe-fed high-profile RDRA is plotted against frequency in Fig. 3.5 (a). Two resonances at 4.6GHz and at 6.GHz can be observed, resulting in an impedance bandwidth of more than 36 per cent. These two resonances correspond to the excitations of the TE 111 and the TE 113 modes, as demonstrated in the plot of the RDRA s input impedance versus frequency in Fig. 3.5 (b). To ensure that the excited modes are the TE 111 and the TE 113 and that good operation is obtained in the 4.5 GHz 6. GHz spectrum, the radiation patterns of the RDRA were calculated. Fig. 3.6 shows the patterns in the E- and H- planes at frequencies 4.6GHz and 6.GHz. It can be observed that both modes exhibit similar broadside radiation patterns, with the H- plane patterns being perfectly symmetrical and the E-plane patterns slightly asymmetrical due to the asymmetrical feeding

86 3.3 THE HIGH-PROFILE RDRA 61 Return Loss [db] -1-2 Input Impedance [Ohm] frequency [GHz] frequency [GHz] (a) 5 imaginary real Figure 3.5: (a) Simulated (HFSS) return loss and (b) input impedance of the probe-fed high-profile RDRA E-plane H-plane f= 4.6 GHz (b) co-pol cross-pol f= 6. GHz Figure 3.6: Radiation patterns of the high-profile probe-fed RDRA in the E- and H- planes for co- and cross-polarization

87 62 3 BROADBAND DRA GEOMETRIES Return Loss [db] -1-2 h = 17mm h = 2mm h = 23mm h = 26mm { TE frequency [GHz] TE Figure 3.7: Return loss vs. frequency for different values of the height h. scheme used in the configuration. In addition, the cross-polarization level of the higher-order TE 113 mode is, as expected, higher than that of the fundamental mode, with the effect being more distinct in the H-plane. As a last note to the described geometry, it was mentioned before that the separation of the TE 111 and the TE 113 modes on the frequency axis depends on the relative dimensions of the parallelepiped. More specifically, provided that the dielectric resonator height is much larger than its width and length, the TE 111 and the TE 113 modes are excited at nearby frequencies. This effect is demonstrated in Fig. 3.7, where the return loss of the RDRA is plotted against frequency for different values of the parallelepiped height h. It can be observed that for low values of h the TE 111 and the TE 113 modes are resonant at frequencies, which are far apart from each other. As the height increases, the resonance frequency of the TE 111 mode decreases slowly, whereas for the TE 113 mode it drops rapidly. Finally, for a certain height of the parallelepiped (h = 23 mm) the two resonances become adjacent, resulting in a wide matching bandwidth. 3.4 The double-slab DRA Towards the objective of bandwidth enhancement while retaining stable and well-behaved radiation characteristics, the use of non-canonical dielectric resonators can be considered an attractive alternative. A very

88 3.4 THE DOUBLE-SLAB DRA 63 z z PEC h 1 a 1 x w 1 w 2 h 2 a 2 y y l p PEC (a) (b) Figure 3.8: Configuration of the probe-fed double-slab DRA. (a) Front view. (b) Back view. simple non-canonical shape that can be regarded as a geometrical variation of the well-known parallelepiped is the double-slab structure shown in Fig It consists of two parallel dielectric slabs attached to each other and fed through a coaxial probe of length l p. The taller slab has a length a 1,widthw 1 and height h 1, while the shorter one has dimensions a 2, w 2 and h 2. Both slabs have the same dielectric permittivity ε rd. The operation of the double-slab DRA is characterized by properties not observed in the case of the canonical parallelepiped. One very important property is the excitation of modes with similar characteristics in dielectric resonators made of high permittivity materials. These modes are resonant at slightly offset frequencies and they exhibit similar near field distributions and radiation patterns. To demonstrate this, the double-slab DRA of Fig. 3.8 is considered. When a 1 = a 2 and h 1 = h 2 the double-slab shape turns into a simple RDRA (shown in Fig. 3.1) of length a = a 1 = a 2, height h = h 1 = h 2 and width w = w 1 + w 2. For this RDRA, the fundamental TE 111 mode is resonant at a frequency f 1, which is determined from the DWM presented in the previous chapter. As the lengths a 1, a 2 and the heights h 1, h 2 start varying, two resonances start appearing in the vicinity of f 1. This effect is illustrated in Fig. 3.9 for a randomly chosen RDRA of dimensions a =8mm,h = 11 mm, w = 1 mm and dielectric permittivity ε rd = 4. This structure is resonant at the frequency f 1 =3.63 GHz. Assuming that the dielectric parallelepiped consists of two parallel slabs of dimensions a 1 = a 2 = 8 mm, h 1 = h 2 =11mmand w 1 = w 2 = w/2 = 5 mm, we examine the resonant modes when slab #1

89 64 3 BROADBAND DRA GEOMETRIES Frequency [G Hz] 4 f RDRA 12 3 h1= h2=11mm h1=11mm, h2=7mm a 2 [mm] Figure 3.9: Resonance frequencies of the double-slab DRA for different values of the dimensions a 2 and h 2 of slab 2. (a 1, h 1, w 1 ) stays as it is, while the dimensions of slab #2 are changing. It is then observed that as the length a 2 of the second slab is increasing, the single TE 111 mode resonance is split into two resonances at offset frequencies. The separation of these modes depends on the length a 2 as well as the height h 2 of slab #2. To demonstrate the repeatability of the previously obtained results, the same investigation as before is repeated for different heights of the two slabs: h 1 =11mm,h 2 = 7 mm (Fig. 3.9). Again, for a 1 = a 2 =8mmone resonant mode is observed but as a 2 starts increasing, a second resonant mode appears at a higher frequency. To further examine these modes, the case when a 2 = 1.5mm and h 2 = 7 mm is randomly selected. The return loss of the double-slab DRA with the aforementioned specifications is illustrated in Fig It can be observed in the figure that two modes are resonant: one at the frequency f =3.42GHz and the second at f =3.61 GHz. At these two frequencies, the E-field distributions (on the x y plane) and the radiation patterns of the double-slab DRA are examined, and the results are schematically shown in Fig and Fig respectively. As observed in the figures, the two resonant modes exhibit similar field distributions and similar radiation patterns. It must be mentioned here that the modes are denoted as hybrid TE 111 modes due to their strong E y component arising from

90 3.4 THE DOUBLE-SLAB DRA 65 Return Loss [db] frequency [GHz] Figure 3.1: Simulated (HFSS) return loss for a double-slab DRA with dimensions a 1 = 8 mm, a 2 =1.5 mm, h 1 = 11 mm, h 2 = 7 mm, w 1 = w 2 =5mm and permittivity ε rd = 4. x x y y (a) (b) Figure 3.11: Schematic representation of the E-field distribution (top view) for the resonant modes of the double-slab DRA. (a) First resonance at f = 3.42 GHz. (b) Second resonance at f =3.61 GHz. the asymmetry of the structure and resulting in high cross-polarization levels. It was mentioned before that modes of similar characteristics can only be observed when the dielectric permittivity contrast between the resonator and the air is large. For lower values of the dielectric permittivity

91 66 3 BROADBAND DRA GEOMETRIES E-plane f= 3.42 GHz H-plane f= 3.61 GHz Figure 3.12: Radiation patterns of the double-slab DRA at the frequencies 3.42 GHz and 3.61 GHz. % Bandwidth double-slab DRA effective RDRA dielectric permittivity r Figure 3.13: % Bandwidth of the double-slab DRA and of an effective RDRA versus the dielectric permittivity of the resonators. this effect is no longer identifiable; instead, a single hybrid TE 111 mode is resonant, which exhibits a wider impedance bandwidth compared to the canonical RDRA. To demonstrate that, the % bandwidth of a DRA with dimensions a 1 = 8 mm, a 2 =1.5mm, h 1 =11mm,h 2 =7mm and w 1 = w 2 = 5 mm is compared to a canonical RDRA (called effective RDRA) that is operating at the same frequency as the double-slab resonator. Both DRAs have the same dielectric permittivity and similar aspect ratios. Fig summarizes the results for values of the dielectric permittivity ranging from ε r =1toε r = 2. It can be observed that the

92 3.4 THE DOUBLE-SLAB DRA 67 Figure 3.14: Fabricated prototype of a double-slab DRA. impedance bandwidth of the double-slab resonator is always larger than that of the dielectric parallelepiped. This is not unexpected; the noncanonical and asymmetrical shape of the double-slab DRA contributes to the smaller confinement of the fields within the dielectric resonator and hence to a lower radiation Q-factor compared to the canonical RDRA. This bandwidth improvement comes nevertheless along with a drawback: the polarization purity is lower due to the asymmetrical geometry, giving rise to hybrid modes (with non-negligible transverse electric field components). This aspect will be discussed in detail at the end of this section. As a demonstration for a well-operating double-slab DRA, the geometry depicted in Fig will be discussed. The DRA consists of a double-slab dielectric resonator mounted on a groundplane of dimensions 12 mm 1 mm. It is coupled through a coaxial probe of diameter 1.21 mm and length l p = 9.6 mm determined according to (3.1). The taller slab of the resonator has a length a 1 =17mm,awidthw 1 =3.5mm and a height h 1 = 25 mm, while the shorter one has dimensions a 2 =1mm, w 2 =3.5mmandh 2 = 2 mm. The resonator is made from Rogers TMM 1i laminate of dielectric permittivity ε rd =9.8 and ideally, it should be fabricated as one continuous structure. If this is not mechanically possible, two separate slabs can be cut and stuck together with dielectric glue, so that any air gaps will be prevented. The return loss of the double-slab DRA described above is illustrated in Fig. 3.15, exhibiting very good agreement between the simulated and the

93 68 3 BROADBAND DRA GEOMETRIES measured results. It can be observed that three modes are resonant; the first at 4.75 GHz, the second at 5.5GHzandthethird at6.5 GHz. These modes correspond to the TE 111, the TE 113 and a higher-order hybrid mode arising from the double-slab geometry. The resulting impedance bandwidth exceeds 47 per cent. A brief comparison between the bandwidth response of the double-slab DRA and that of the high-profile RDRA described in Section 3.3 shows that the double-slab geometry exhibits a better performance. It should be emphasized here that both resonators have similar dimensions and they are made from the same dielectric material. The main drawback of the double-slab DRA compared to the highprofile RDRA are the higher cross-polarization levels due to its asymmetrical and non-canonical shape. To demonstrate that, the measured radiation patterns of the double-slab DRA are depicted in Fig at the frequencies 4.75 GHz, 5.5GHzand6.5 GHz. It is found that the patterns are broadside within the entire operational bandwidth, with their symmetry in the E-plane deteriorating slightly at the higher frequencies. The ripples around the broadside direction are caused by the diffraction from the finite-sized groundplane. The cross polarization is found to be around 3 dbi for the lower frequencies and at 15 dbi for the higher. The degradation of the polarization purity at high frequencies is due to the strong transverse E-field component of the hybrid mode and is caused by the resonator shape in combination with the relative position of the feed. 3.5 The semi-trapezoidal DRA The investigation of the double-slab dielectric resonator in the previous section demonstrated the possibility of enhancing the DRA performance by employing non-canonical geometries. The double-slab geometry was the first to be examined due to its straightforward progression from the parallelepiped. Since, however, the fabrication complexity and cost of the double-slab DRA is high, the investigation of similar, yet simpler geometries is very useful. Based on these considerations, the semi-trapezoidal dielectric resonator of Fig can be considered as a good alternative to the double-slab geometry. The semi-trapezoidal DRA consists of a dielectric resonator with dimensions h 1, h 2, a 1, a 2, w and dielectric permittivity

94 3.5 THE SEMI-TRAPEZOIDAL DRA 69 Return Loss [db] measured simulated frequency [GHz] Figure 3.15: Return loss of the double-slab DRA of Fig E-plane H-plane f= 4.75 GHz f = 5.5 GHz f=6. 5 GHz co-pol cross-pol Figure 3.16: Measured radiation patterns in the E- and H-planes of the doubleslab DRA of Fig

95 7 3 BROADBAND DRA GEOMETRIES z z a 1 w/2 w/2 PEC h 1 x a 2 h 2 y y l p w w/2 PEC (a) (b) Figure 3.17: Configuration of the probe-fed semi-trapezoidal DRA. (a) Front view. (b) Back view. z z y y PEC x PEC x (a) (b) Figure 3.18: Transition from the double-slab to the semi-trapezoidal DRA. (a) Original geometry. (b) Transition to the new geometry. ε rd, which is excited by the center conductor of an SMA connector. The probe is situated in the middle of the wider back side of the dielectric resonator, and its length l p is numerically estimated so that best matching is obtained. The evolution from the double-slab to the semi-trapezoidal geometry is depicted in Fig It can be observed that the abrupt transitions in the double-slab shape are avoided by the fictitious addition of an infinite number of intermediate slabs in between the slabs of the initial structure. As a result, the emerging geometry is simpler and cheaper to fabricate. In addition, the semi-trapezoidal shape is a continuous version of the double-slab shape and at the same time a generalized version of the canonical parallelepiped. Hence, its performance can be more easily predicted through the comparison with the performance of the parallelepiped.

96 3.5 THE SEMI-TRAPEZOIDAL DRA 71 For an operation of the DRA between 5 GHz and 1 GHz, the semitrapezoidal dielectric resonator is found to have the following specifications: permittivity ε rd =9.8, heights h 1 =16mm,h 2 = 11 mm, width w = 24 mm and lengths a 1 = 7.5mm, a 2 = 6 mm. The resonator is mounted on a groundplane of dimensions 14 mm 1 mm and is coupled through a coaxial probe of length l p = 6 mm. According to this configuration an antenna prototype was fabricated and measured, so that the numerical results (from ANSOFT HFSS R ) could be validated. The calculated and measured return loss is depicted in Fig. 3.19, where a reasonable agreement between theory and experiment is observed. The measured impedance bandwidth ( S 11 < 1 db) is around 62% and it covers the spectrum between 5.5 GHz and 1 GHz. The wideband performance of the DRA is the result of the excitation of multiple low-order modes within the dielectric volume. This is possible through the dielectric resonator shape in combination with the relative position of the coaxial feed, that facilitate the excitation of multiple modes. To demonstrate that and to highlight the differences between the performance of the semitrapezoidal and of the rectangular shape, these two DRA geometries will be compared next. As it was mentioned before, the parallelepiped can be considered a special case of the more general trapezoidal shape. More specifically, provided that the semi-trapezoid s dimensions are chosen so that h 1 = h 2 and a 1 = a 2, a canonical parallelepiped emerges. Since the Dielectric Waveguide Model can adequately characterize the performance of the RDRA, but it cannot predict that of the semi-trapezoidal DRA, the dielectric parallelepiped is used as a starting point in the antenna design process. In the next step, the resonator s geometry is modified towards the semitrapezoidal shape, so that the performance advantages of the trapezoidal shape are incorporated in the final structure. It becomes, thus, important to investigate how and under which conditions the deviation from the canonical rectangular geometry can lead to a better DRA performance. Let us take for example the case of a semi-trapezoidal DRA of permittivity ε rd =9.8, whose operation covers a band above 6 GHz. Starting with a RDRA of the same permittivity, the DWM dictates the dimensions of the dielectric parallelepiped for an operation at 6 GHz: h = h 1 = h 2 =16mm, a = a 1 = a 2 =7.6mm andw = 24 mm. Based on this geometrical configuration, the effect of the height h 2 and the length a 2 on the return loss of the DRA is investigated. The results of this investigation are summarized

97 72 3 BROADBAND DRA GEOMETRIES Return Loss [db] measured simulated frequency [GHz] Figure 3.19: Return loss of the semi-trapezoidal DRA shown in the inset. in Fig. 3.2 (a) and (b), where the return loss of the semi-trapezoidal DRA is plotted versus frequency for different values of h 2 and a 2. With reference to Fig. 3.2 (a), the good operation of the canonical RDRA around the 6 GHz band is demonstrated with the black solid line. The variation of the height h 2 of the semi-trapezoidal DRA does not significantly affect its operational band; it has, nevertheless, an influence on the matching of the antenna as well as on the excited modes at higher frequencies. In contrast with the height h 2, the length a 2 has a more dramatic effect on the DRA performance. This can be clearly observed in Fig. 3.2 (b). The variation of a 2 results in a larger number of low-order modes being sufficiently excited and hence in a wider impedance bandwidth. To sum up, for a DRA operation in a pre-specified band, the first step of the design process involves designing a dielectric parallelepiped according to the closed form expressions provided by DWM. Then, the resonator shape can get modified towards a semi-trapezoid through the variation of its length a 2 and height h 2. This will lead to a significant enhancement of its matching bandwidth. This procedure was used in the case of the probefed semi-trapezoidal DRA depicted in the inset of Fig. 3.19, resulting in an operational band ranging from 5.5 GHz to approximately 1.3 GHz. There, the fundamental TE 111 and the higher-order TE 113 modes are excited at around 6 GHz and 7.5 GHz, respectively. The undesired TE 121 mode is also resonant in the lower frequency domain, but the trapezoidal shape of the dielectric resonator in combination with the relative location

98 3.5 THE SEMI-TRAPEZOIDAL DRA 73 Return Loss [db] -1 parallelepiped -1 a 2 =7.6mm -2 h 2 =1mm -2 h 2 =6mm h 2 =11mm h 2 =16mm frequency [GHz] (a) h 2 =16mm parallelepiped a 2=3mm =1.5mm a2=4.5mm a2=6mm a2=7.5mm a frequency [GHz] Figure 3.2: Effect of (a) the height h 2 and (b) the length a 2 on the return loss of the semi-trapezoidal DRA. The rest of the dimensions stay fixed. (b) of the feeding probe results in the minimization of its influence on the antenna performance. This will be demonstrated in the following section. In the spectrum between 7.5 GHz and 1.3 GHz, higher-order modes of the type TE 1mn (m, n>1) appear. These resonant modes contribute to the wide impedance bandwidth of the DRA, but at the same time they degrade its polarization purity due to their non-negligible E x components. The measured radiation patterns of the semi-trapezoidal DRA are illustrated in Fig at frequencies 6.5 GHz, 8. GHz and 9.5 GHz. It is observed that the patterns are broadside within the entire DRA operational bandwidth, while the cross polarization remains within acceptable limits (below 15 db) for an angle of at least θ = ±4 from the broadside (z axis or θ = ). As the frequency increases, the polarization purity decreases and the patterns become less symmetrical. This degradation of the DRA s radiation characteristics is caused by the asymmetrical shape of the resonator in combination with the excitation of higher-order modes with strong transverse electric field components. A way to cope with this problem will be the subject of investigation in the following section.

99 74 3 BROADBAND DRA GEOMETRIES E-plane H-plane f= 6.5 GHz f = 8. GHz f= 9.5 GHz co-pol cross-pol Figure 3.21: Measured radiation patterns of the semi-trapezoidal DRA. 3.6 The pyramidal DRA To alleviate the problems of the asymmetrical patterns and the high crosspolarization of the semi-trapezoidal DRA, the symmetric pyramidal geometry is introduced. The pyramidal shape can be derived from the rectangular - the main difference is that the height of the pyramid is not uniform along the x axis. The transition from the rectangular to the symmetric pyramidal shape is shown in Fig. 3.22: the pyramidal geometry emerges when two identical dielectric slabs of triangular cross-section are removed from the upper edges of the parallelepiped. The rest of the pyramid s dimensions remain the same as of the canonical parallelepiped. The geometrical configuration of the probe-fed pyramidal DRA is shown in Fig (a). The dielectric resonator has a uniform length a, heights h 1 and h 2 and widths w 1 and w 2. It is made out of a dielectric material of permittivity ε rd and it is coupled through a coaxial probe of length l p placed in the middle of its widest face, as shown in the figure.

100 3.6 THE PYRAMIDAL DRA 75 z x Figure 3.22: Transition from the rectangular to the pyramidal DRA. Similarly to the case of the semi-trapezoidal DRA, the symmetric pyramidal DRA can be considered as a variation of the parallelepiped. Therefore, the DRA design process should start with the determination of the parallelepiped s dimensions for an operation at a specified frequency and afterwards, the modification towards the pyramidal shape should take place. The advantages of the pyramidal shape compared to the parallelepiped are illustrated in the plots of Fig and Fig. 3.25, where the effect of the height h 1 on the impedance bandwidth and the 15 db cross-pol beamwidth of the DRA is demonstrated. The 15dB crosspol beamwidth is defined here as the full angle θ (in degrees) for which the cross-polarization level is below 15 db at the frequency of excitation of the lowest-order mode. For the numerical investigations conducted here, a pyramidal dielectric resonator of dimensions h 2 =16mm, a = 9 mm, w 1 =35mmandw 2 = 7 mm and of dielectric permittivity ε rd =9.8 is used. The resonator is mounted on a groundplane of dimensions 14 mm 1 mm and is fed through a probe of length l p =8.4mm, chosen so that good impedance matching is obtained. All simulations are performed using ANSOFT HFSS R. A careful observation of the plots shown in Fig and Fig provides valuable insight into the operation of the dielectric pyramid and into its advantages compared to the simple parallelepiped. When the pyramid height h 1 is equal to its height h 2 (i.e. h 1 = h 2 =16mm),the canonical rectangular shape emerges. For this DRA geometry the simulated impedance bandwidth is 42 per cent, while its 15 db cross-pol beamwidth is approximately 32 (θ = ±16). In the case of the pyramidal DRA (h 1 <h 2 ), both, the impedance bandwidth and the 15 db beamwidth are significantly affected by the height h 1. It can be observed that for h 1 being between 7 mm and 13 mm the impedance bandwidth exceeds 48 per cent, whereas for h 1 being between 2 mm and 8 mm the

101 76 3 BROADBAND DRA GEOMETRIES z w 2 x h 1 y h 2 l p w 1 a (a) (b) Figure 3.23: (a) Configuration of the probe-fed pyramidal DRA. (b) Fabricated prototype. % Impedance Bandwidth height [mm] Figure 3.24: Simulated (HFSS) fractional bandwidth of the pyramidal DRA vs. its height h 1. h 1 15 db beamwidth is at least 55. In any case it is clear that the pyramidal shape is more advantageous than the parallelepiped, since the height h 1 can be used as an additional degree of freedom for the DRA bandwidth enhancement as well as for the improvement of its polarization purity. To find an optimal value of h 1 that results in the largest possible bandwidth and beamwidth, a simple graphical procedure is used. In the plots of Fig and Fig the shadowed regions indicate the values of h 1, for which the impedance bandwidth and the 15 db beamwidth are close to maximum. The overlap of these regions provides the optimum value

102 3.6 THE PYRAMIDAL DRA 77 Beamwidth [degrees] height [mm] h 1 Figure 3.25: Simulated (HFSS) 15 db cross-pol beamwidth of the pyramidal DRA vs. its height h 1. of h 1 which, in this case, is found to be h 1 = 8 mm. For this value of the height h 1 and for the rest of the pyramid dimensions being as specified before, the antenna prototype shown in Fig (b) was fabricated and measured. Fig (a) illustrates the resulting measured return loss of the pyramidal DRA, which is plotted together with the simulated results for comparison purpose. A good agreement between numerical results and experiment is achieved. The frequency shift of the resonances is in the order of less than 3 per cent and it can be attributed to fabrication tolerances as well as the imprecise knowledge of the dielectric permittivity of the resonator. The measured 1 db bandwidth exceeds 48 per cent. To demonstrate the good operation of the pyramidal DRA within its operational band, Fig (b) illustrates the antenna s broadside gain as a function of frequency. The variation of the gain is due on the one hand to the diffraction from the finite-sized groundplane and on the other hand to the different gain of the various high-order DRA modes excited inside the dielectric resonator. This effect is common for antennas employing the modes merging technique for bandwidth enhancement. The measured radiation patterns of the pyramidal DRA are depicted in Fig at the frequencies 4.5GHz, 5.2GHz and 6.7GHz. The small asymmetry in the E-plane of the patterns is caused by the asymmetric feeding through the coaxial probe, which was chosen due to its simplicity.

103 78 3 BROADBAND DRA GEOMETRIES Return Loss [db] simulated measured frequency [GHz] (a) Gain [dbi] frequency [GHz] (b) Figure 3.26: (a) Simulated (HFSS) and measured return loss and (b) measured broadside gain of the probe-fed pyramidal DRA. The cross-polarization is always below 2 db for an angle of more than θ = ±45 from broadside (z axis). Finally, in the H-plane the patterns are, as expected, perfectly symmetric and the cross-polarization remains below 15 db for a beamwidth of at least Conclusion The excitation of multiple modes inside the dielectric resonator is a very powerful tool in the hands of antenna engineers, since the DRA bandwidth can be significantly enhanced without degrading in parallel the radiation patterns or the polarization purity. The price that has to be paid for this improvement is usually an increase in the cost and the fabrication complexity of the dielectric resonator. In the case of the high-profile RDRA, where the fundamental TE 111 and the higher-order TE 113 modes are excited at adjacent frequencies, the dielectric resonator shape is a simple parallelepiped. However, its height is much larger than its width and length, resulting in a high-profile and thus, a relatively fragile and unstable structure that is not suitable for many applications. Non-canonical DRAs deserve special attention, since they can be mechanically stable and at the same time they can outperform every canon-

104 3.7 CONCLUSION 79 E-plane H-plane f = 4.5 GHz f = 5.2 GHz f = 6.7 GHz co-pol cross-pol Figure 3.27: Measured radiation patterns of the probe-fed pyramidal DRA. ical DRA in terms of bandwidth. This is the result of the excitation of multiple modes at offset frequencies in combination with the larger number of degrees of freedom provided by non-canonical shapes, so that a good impedance matching can be achieved. Moreover, there is a strong indication that the non-canonical shape causes a decrease in the radiation Q-factor of the excited modes, which results in the further enhancement of the DRA impedance bandwidth. Finally, an important advantage of the non-canonical dielectric resonator is that its shape together with the type and the position of its feed result in a selective excitation of modes. As a result, only modes exhibiting similar radiation characteristics can be selected and therefore the radiation patterns and the polarization can be well-behaved within the entire operational bandwidth of the DRA. The main disadvantages of the non-canonical geometries include their higher fabrication complexity as well as the difficulty in predicting their performance. This is due to the lack of exact or even approximate analytical models, to help quickly estimate the resonance frequency, the Q-

105 8 3 BROADBAND DRA GEOMETRIES factor and the far-field characteristics of their excited modes. Some noncanonical shapes can, however, be consideredasdeviationsorextensions of canonical geometries and hence, their performance can be roughly determined according to their canonical counterparts. It thus becomes clear that the good understanding of the canonical DRAs performance is not only necessary for their own good operation, but also for the prediction of the radiation characteristics of more advanced DRA geometries. Apart from the improvement of the DRA s bandwidth response, it is interesting to investigate whether the use of non-canonical shapes can meet the challenges of a good UWB performance as well as of a wellcontrolled multi-band operation without any increase in the total antenna volume. Attempts to solve such problems will be demonstrated in the following chapters.

106 4 Inverted Dielectric Resonator Antenna Geometries 4.1 Introduction A common technique for the bandwidth enhancement of DRAs is the decrease of their inherent Q-factor. This results in a smaller confinement of the fields inside the dielectric resonator and thus in a reduced amount of stored energy inside the antenna. Towards the objective of lowering the Q-factor of a DRA, the reduction of its dielectric permittivity is the most straightforward solution. This technique is not, however, optimal as it has a few important drawbacks. First, the decrease of the resonator s permittivity leads to an increase in its size and weight, which is undesirable in most commercial applications. Moreover, the reduction of the dielectric permittivity results in the deterioration of the coupling to the resonator and subsequently in the degradation of the antenna performance. For example, in the case of probe-coupling to a dielectric resonator of low permittivity, the probe height needs to be large in order to provide sufficient coupling. This leads, however, to spurious radiation, which deteriorates the radiation patterns and the polarization purity of the antenna. A way to lower the Q-factor of a DRA without changing its permittivity is by modifying the dielectric resonator shape. A properly designed and optimized resonator can result in an increase of the amount of energy that is radiated, compared to the energy that is stored in the antenna s near fields. Fig. 4.1 illustrates such a dielectric resonator geometry, in which the main body of the resonator is positioned upside down. As shown in the figure, the fields inside such inverted DRA geometries are less confined within the resonator volume as compared to the fields inside the RDRA. Hence, the Q-factor of inverted DRAs is lower and their impedance bandwidth is wider [3]. The evolution towards the inverted DRA geometries started from the notched dielectric resonators presented in [15]. These structures consisted of simple canonical resonators, which were having holes (notches) inside their volume. The holes resulted in the reduction of the Q-factor of the 81

107 82 4 INVERTED DRA GEOMETRIES PEC PEC Electric field Magnetic field (a) (b) Figure 4.1: Field distributions of the TE 111 mode. (a) Rectangular DRA. (b) Inverted DRA geometry. excited DRA modes and hence in a wider impedance bandwidth than that of the solid DRAs. Apart from the case of the notched geometries, air gaps in general can improve the bandwidth response of DRAs. More specifically, the introduction of a small air gap in between the feed and the dielectric resonator can lead to a bandwidth enhancement for the DRA, as well as to a small shift of its resonance frequency and input impedance [27]. A detailed investigation of the effect of the air gap on the performance of a probe-fed and an aperture-fed DRA will be conducted in the first section of the current chapter. The rest of this chapter is organized as following: in the second section, the inverted trapezoidal DRA will be presented and compared to the RDRA. The trapezoid is one of the simplest shapes emerging from the parallelepiped that can be formed as an inverted structure. Moreover, the trapezoidal shape can be regarded as a starting point for many advanced inverted geometries employing the operational and design concepts of the previous chapters. An example of such an inverted DRA geometry will be given in the last section of this chapter. There, an inverted truncated conical DRA will be discussed, exhibiting a wide impedance bandwidth and good signal dispersion characteristics. Finally, in the appendix of this chapter, the model of a UWB antenna system will be described and quality measures for the characterization of its dispersion properties will be provided.

108 4.2 THE EFFECT OF THE AIR GAP 83 d a r l p PEC h h Slot Microstrip Line d (a) (b) Figure 4.2: Geometrical configuration of canonical DRAs featuring an air gap between the coupling scheme and the dielectric resonator. (a) Probe-fed RDRA. (b) Aperture-fed CDRA. 4.2 The effect of the air gap in probe- and aperture-fed DRAs For the investigation of the effect of the air gap on the DRA performance two of the most common DRA configurations will be considered: the probe-fed RDRA shown in Fig. 4.2 (a) and the aperture-fed CDRA of Fig. 4.2 (b). The properties and the geometrical configuration of both DRAs have been described extensively in previous chapters. Starting with the RDRA, a dielectric parallelepiped of dimensions a = 13 mm, w = 1mm, h = 1.4 mm and permittivity ε rd = 1.2 isassumed, which is excited in its fundamental TE 111 mode at the frequency f = 5 GHz. When this dielectric resonator is coupled through a coaxial probe, the electromagnetic field boundary conditions require that the electric field lines are normal to the surface of the probe. Besides, it is well known in the electromagnetic theory that the normal component of the electric field is discontinuous on the boundary between two media of different permittivities. It can thus be predicted that the introduction of a thin air gap (ε r = 1) in between the probe and the dielectric resonator will have a significant effect on the resonance frequency and the input impedance of the DRA. In addition, since the effective permittivity of the DRA decreases through the introduction of the air gap, its impedance bandwidth is expected to increase. To demonstrate these effects, the return loss and the input impedance of the previously described RDRA are

109 84 4 INVERTED DRA GEOMETRIES Return Loss [db] Input Impedance [ ] d = 5. mm d =.5 mm d =.1 mm real imaginary frequency [GHz] frequency [GHz] Figure 4.3: Simulated (HFSS) return loss and input impedance of the probe-fed RDRA of Fig. 4.2 (a) for different values of the air gap thickness d. numerically estimated for different values of the air gap thickness d. The results of this investigation are summarized in Fig It is observed that the increase of the air gap thickness results in an increase in the resonance frequency of the DRA as well as a decrease of its input impedance. Moreover, for a certain value of the air gap thickness d the DRA s bandwidth response shows an improvement compared to the case when the probe and the dielectric resonator are attached to each other (d = ). As the thickness d increases further, the impedance bandwidth deteriorates dramatically due to the increasingly capacitative character of the probe, which can no longer couple efficiently to the DRA. This decoupling between the feed and the dielectric resonator is also evident from the flattening of the reactance curves. The dependency of the DRA fractional bandwidth (S 11 < 1 db) on the air gap thickness d is graphically represented in Fig In the case of the aperture-fed CDRA, the dielectric cylinder of height h = 6.5 mm, radius r = 8 mm and permittivity ε rd =1.2 isexcited in its fundamental HEM 11δ mode at the frequency f =5.1GHz. The aperture has a length L a =9mmandawidthW a =.5mm, while the microstrip line has a width W m =2.4mm and a stub length P =11mm. Similarly to before, the operation of the aperture-fed CDRA was analyzed for different values of the air gap thickness h. The resulting curves of the

110 4.2 THE EFFECT OF THE AIR GAP 85 % Bandwidth d [mm] Figure 4.4: Simulated % bandwidth of the probe-fed RDRA as a function of the air gap thickness d. Return Loss [db] Input Impedance [ ] d = 5 5. mm d =.4 mm d =.8 mm real imaginary frequency [GHz] frequency [GHz] Figure 4.5: Simulated (HFSS) return loss and input impedance of the aperturefed CDRA for different values of the air gap thickness d. return loss and the input impedance versus frequency are illustrated in Fig. 4.5, exhibiting similar trends as for the probe-fed RDRA. The sole difference is that the increase of the air gap thickness h results here in an increasingly inductive character of the coupling scheme. In both cases however, a deterioration of the DRA bandwidth is observed for an increase of the air gap thickness h above a certain value.

111 86 4 INVERTED DRA GEOMETRIES z PEC x w a 1 y a 2 l p h Figure 4.6: Configuration of the probe-fed trapezoidal DRA. 4.3 The trapezoidal DRA As it was discussed in the introduction of this chapter, the reduction of a DRA s Q-factor through the use of an inverted dielectric resonator can lead to the improvement of its bandwidth response. The trapezoid can be considered a generalization of the canonical parallelepiped and it can be formed in either an inverted or in a non-inverted shape. Because of that and since the inverted trapezoid can be used as a building block for other inverted geometries, it is instructive to investigate its operation and properties before we proceed to more complex structures. The probe-fed RDRA has already been investigated in a previous chapter. If operated in its fundamental TE 111 mode, the RDRA exhibits an impedance bandwidth of about 1-15 per cent (for a permittivity of about 1), high efficiency, low cross-polarization and broadside radiation patterns. The resonance frequency of the TE 111 mode can be determined according to the closed-form expressions (2.24), (2.25), (2.3) and (2.31) deduced from the DWM. A careful consideration of the trapezoidal DRA geometry (Fig. 4.6) leads to the observation that the depicted trapezoid is a generalization of the rectangular parallelepiped. In other words, provided that the height h and the width w of the trapezoid are constant, the trapezoid becomes a rectangular parallelepiped, if its lengths a 1 and a 2 are chosen to be equal. To compare the operation of the rectangular and the trapezoidal DRAs when excited in their lowest order mode, these geometries are investigated numerically and experimentally. The numerical analysis is performed using the full-wave analysis tool ANSOFT HFSS R. Fig. 4.6 illustrates the configuration of the considered DRAs, which are probe-fed trapezoids of

112 4.3 THE TRAPEZOIDAL DRA 87 a a + x a a - x ( x=) x [mm] [GHz] f %BW a + x a a - x Figure 4.7: Simulated (HFSS) resonance frequency and % bandwidth of various trapezoidal DRA geometries. dielectric permittivity ε rd = 1, height h =7.6mm and width w = 6 mm. The lengths a 1 and a 2 are varied according to the relations a 1 = a +Δx and a 2 = a Δx, wherea = 9 mm. In all those geometries the total volume of the dielectric remains unchanged. The results of the numerical analysis are summarized in Fig. 4.7, where the resonance frequency (zero-crossing of the input reactance) and the fractional bandwidth (S 11 < 1 db) of the DRA are provided for different values of Δx. It can be observed that an increase of Δx from 1 to 3 (in other words, the shift from the regular trapezoidal shape to the rectangular parallelepiped and then to the inverted trapezoidal shape) results in a monotonous increase of the resonance frequency and of the fractional bandwidth of the TE 111 mode. In conclusion, the inverted

113 88 4 INVERTED DRA GEOMETRIES trapezoid (Δx >) exhibits a significantly wider bandwidth compared to the parallelepiped (Δx = ) and the regular trapezoid (Δx < ). This is not unexpected; as it has been explained before, the field lines inside the inverted trapezoids are less confined than in the rectangular and the regular trapezoidal DRAs. Hence, the Q factors of the inverted trapezoidal DRAs are lower and their bandwidth is wider. The bandwidth enhancement brought by the inverted trapezoidal resonators comes along with a few practical limitations. First, the inverted trapezoidal DRAs are electrically smaller than the RDRAs. This means that the trapezoidal structures need to become larger in size, in order to be resonant at the same frequency as the dielectric parallelepiped. The second limitation of the inverted trapezoidal DRAs involves the symmetry of their radiation patterns in the E-plane, which deteriorates as the trapezoidal shape becomes more asymmetrical. To demonstrate this, Fig. 4.8 illustrates the asymmetry of the radiation patterns in the E-plane as a function of Δx at the frequency of excitation of the lowest-order mode. The dimensions a, w and h of the trapezoid are the same as before. The asymmetry of the radiation patterns in the E-plane is defined as the ratio (expressed in db) of the DRA s gain at the elevation angles +θ and θ from broadside, with θ ranging from 1 to 7. It is worth mentioning here that the H-plane patterns are not affected by the trapezoidal shape, since the width of the trapezoid remains constant. Hence, the patterns in the H-plane remain symmetrical within the entire operational spectrum. As observed in Fig. 4.8, the asymmetry of the E-plane patterns increases with Δx. The more the dielectric resonator shape deviates from the canonical parallelepiped, the more asymmetrical the patterns become, especially at elevation angles above 6. It needs to be underlined here that even in the case of the RDRA (Δx = ), a small asymmetry of approximately.5db 1.5dB is encountered, although perfectly symmetrical patterns in both planes should theoretically be expected. This is caused by the asymmetry introduced by the probe feeding. A different coupling scheme like for example an aperture would yield more symmetrical patterns. In this investigation, however, the probe was chosen mainly because of its simplicity. It is now clear that the lengths a 1 and a 2 cannot be arbitrarily chosen, without also taking into consideration the asymmetry of the radiation patterns. However, the tradeoff between the bandwidth and the patterns symmetry is not dramatic. Even a small deviation from the

114 4.3 THE TRAPEZOIDAL DRA 89 Asymmetry [db] =1 o =2 o =3 o =4 o =5 o =6 o =7 o x [mm] Figure 4.8: Asymmetry in the E-plane as a function of Δx at the frequency of excitation of the lowest-order mode. rectangular to the inverted trapezoidal shape can lead to a substantial increase in the impedance bandwidth, without significantly deteriorating the radiation characteristics of the antenna. As a demonstration of that fact, a trapezoid with dielectric permittivity ε rd = 1 and dimensions a 1 = a +Δx =9+2.5 =11.5mm, a 2 = aδx =92.5 =6.5mm, h =7.6mm, w = 6 mm is chosen. According to Fig. 4.7, this trapezoid is resonant at 8.19 GHz in its lowest order mode. In order to obtain operation at 7.52 GHz, where the RDRA (Δx = ) is also resonant, a number of different approaches can be used. The approach of increasing the permittivity of the dielectric resonator is not suitable, since the higher ε rd would result in a higher radiation Q-factor and therefore in a smaller bandwidth. The increase of just one of the dimensions of the dielectric resonator is also not eligible due to the change of the aspect ratios of the trapezoid. Such a change could detrimentally affect the DRA bandwidth, as it was shown in the previous chapter. The most suitable approach is to scale the trapezoid, so that it resonates at the desired frequency, while the rest of the antenna characteristics remain unaltered. The finalized trapezoidal DRA has a dielectric constant of ε rd = 1 and dimensions a 1 =12.7mm, a 2 =7.2mm, h =8.4mm and w =6.6mm. For these specifications, a prototype was manufactured and compared to the RDRA of dimensions a 1 = a 2 = a = 9 mm, h =7.6mm and w = 6 mm. Fig. 4.9 depicts the measured return loss and the input impedance of

115 9 4 INVERTED DRA GEOMETRIES Return Loss [db] 8 Input Impedance [ ] real rectangle trapezoid imaginary frequency [GHz] frequency [GHz] Figure 4.9: Measured return loss and input impedance for the rectangular and the trapezoidal DRAs. the two DRAs versus frequency. Both antennas are resonant at approximately 7.4 GHz (defined through the zero-crossing of the input reactance), indicating a 1.6 per cent error from the numerically expected resonance frequency of 7.52 GHz. The RDRA exhibits a measured impedance bandwidth of approximately 11.9 per cent, which is almost half the bandwidth of 22 per cent obtained by the trapezoidal DRA (19 per cent was expected from the simulations). The bandwidth enhancement for the trapezoidal DRA does not come along with a significant change in the operation of its lowest order mode, compared to the RDRA. To demonstrate that, the measured broadside gain of both DRAs as well as their measured radiation patterns at 7.4 GHz (E- and H- planes) are illustrated in Fig. 4.1 and 4.11 respectively. It can be observed that the DRAs broadside gain differs by less than.3 db in the frequency range between 7 GHz and 8.5GHz. In addition, their patterns at the frequency of excitation of their lowest order mode (7.4 GHz) indicate an identical horizontal-magnetic-dipole-like operation. The sole difference is that the E-plane patterns of the trapezoidal DRA exhibit an asymmetry, which nevertheless does not exceed 2 3dB, even at large elevation angles. Based on the above considerations it becomes clear that the lowest-order mode of the trapezoidal DRA has very similar characteristics with the TE 111 mode of the RDRA. Since, however, the lowest-order trapezoidal

116 4.3 THE TRAPEZOIDAL DRA 91 Gain [dbi] rectangle trapezoid frequency [GHz] Figure 4.1: Measured broadside gain vs. frequency for the rectangular and the trapezoidal DRAs E-plane H-plane rectangular DRA trapezoidal DRA Figure 4.11: Measured radiation patterns of the rectangular and the trapezoidal DRAs in the E- and H-planes at 7.4GHz. mode does not abide by the transcendental equations characterizing the TE 111 mode, it will be called pseudo-te 111 mode. To illustrate the generality of using an inverted trapezoid instead of a parallelepiped in order to obtain a wider bandwidth, a numerical investigation is carried out for DRAs of various dielectric constants. The objective is to make the DRA electrically smaller by increasing its dielectric permittivity. Since this will result in the decrease of the DRA s impedance bandwidth, it is interesting to compare the performance of the trapezoidal

117 92 4 INVERTED DRA GEOMETRIES % Bandwidth % Bandwidth for rectangle % Bandwidth for trapezoid % Trapezoidal volume relative to the RDRA volume with = dielectric permittivity rd Figure 4.12: Simulated (HFSS) % bandwidth and relative size of the rectangular and the trapezoidal DRAs vs. their dielectric permittivity for a fixed operation at 7.4 GHz. rd % Relative Volume and the rectangular DRAs while the permittivity changes. The results of this investigation are summarized in Fig. 4.12, where the fractional bandwidth of the two DRAs is plotted versus their permittivity for a fixed operation at 7.4 GHz. The dimensions of the rectangular and the trapezoidal DRAs are a rec = s 9 mm, h rec = s 7.6 mm, w rec = s 6mm and a 1,trap = s 12.7mm, a 2,trap = s 7.2mm, h trap = s 8.4mm, w trap = s 6.6 mm respectively. The constant s is a scaling factor denoting the decrease in the DRA dimensions when the permittivity is increasing beyond the reference value of ε rd = 1. Fig includes the plot of the relative trapezoidal DRA volume compared to the volume of the original RDRA. This relative volume is plotted as a function of the dielectric constant for an operation at 7.4GHz. It is observed in the graph that the increase of the dielectric permittivity leads to a reduction of the impedance bandwidth for both, the rectangular and the trapezoidal DRAs. Despite this decrease, for all values of the permittivity the acquired bandwidth for the inverted trapezoid is at least 1.5 times larger than for the parallelepiped. As an example, the RDRA of permittivity ε rd = 1 and dimensions a = 9 mm, h =7.6mm, w =6mm exhibits an impedance bandwidth of 11.4 per cent, whereas the trapezoid of the same permittivity as before and dimensions a 1 =12.7mm, a 2 = 7.2mm, h = 8.4mm, w = 6.6mm (1.33 times bigger in volume than

118 4.3 THE TRAPEZOIDAL DRA 93 the parallelepiped) is by almost 7 per cent more wideband at the same frequency of operation. It is interesting to observe here that the same bandwidth as of the RDRA can be obtained with a trapezoidal DRA of permittivity ε rd = 17, whose volume is just 72 per cent of the volume of the RDRA. It is thus obvious that for a certain frequency of operation and a predetermined required impedance bandwidth, size reduction can be achieved through the trapezoidal shape The resonance frequency of the trapezoidal DRA It was mentioned in a previous chapter that analytical expressions for the resonance frequencies of the DRA modes are only possible in the case of the dielectric sphere/hemisphere. For the rest of the canonical DRAs like the cylinder and the parallelepiped, approximate expressions based on the DWM can be developed. In the case of the trapezoidal DRA, the non-canonical geometry of the dielectric resonator makes the task of finding its resonance frequencies even more cumbersome. If, however, we take into consideration that the trapezoid is a generalized version of the canonical parallelepiped, a properly modified DWM can be employed towards that end. In the current section the basic steps of this method will be described and the validity of its results will be investigated. To start with, it needs to be mentioned that similarly to the RDRA, the analysis of the trapezoidal DRA will concentrate on the TE mnl modes, with the indices m, n and l denoting the order of variation along the x, y and z directions of the cartesian coordinate system, respectively. To find a suitable wave function ψ for the determination of the electric vector potential for these modes, the dielectric resonator shape needs to be considered. Here, the dielectric resonator has the form of a non-symmetric trapezoid, which makes the task of finding the wave function quite complicated. This task can get, however, simplified through the observation that the inverted trapezoid of Fig (a) and the inverted symmetric pyramid of Fig (b) are operating in a very similar manner. To demonstrate that, eigenmode analysis is performed for these two geometries. Their dimensions are a = 9 mm, h =7.6mm, w =6mmandtheir permittivity is ε rd = 1. The results of the eigenmode analysis are summarized in Fig. 4.14, where the resonance frequency of the lowest-order mode of both structures is computed for different values of Δx. It must

119 94 4 INVERTED DRA GEOMETRIES z z a+ x a+ x h a h a PEC a - x (a) x PEC a - x (b) x Figure 4.13: Geometrical configurations of (a) an inverted trapezoid and (b) an inverted symmetrical pyramid. f [G z] res H trapezoid pyramid x [mm] Figure 4.14: Resonance frequencies of the inverted trapezoid and the inverted symmetrical pyramid for different values of Δx. be emphasized here that the height and the volume of the two structures is the same for every value of Δx. It is observed in the figure that the resonance frequencies of the two geometries are very close to each other for small values of Δx. As Δx increases, the disagreement between the resonance frequencies increases, but it still never exceeds 2 3per cent. Because of that and since the fields configuration inside these structures is very similar to the configuration of the TE 111 mode, it can be safely concluded that for small values of Δx

120 4.3 THE TRAPEZOIDAL DRA 95 the inverted trapezoid and the inverted symmetrical pyramid operate in a similar way. As a result, instead of looking into the inverted trapezoidal geometry, the much simpler symmetrical pyramidal DRA of Fig (b) can be analyzed for the determination of the resonant modes. The wave function ψ of the symmetrical pyramid can be approximately defined according to the relation: ψ C cos(k x x)cos(k y y)cos(k z z) (4.1) Then, assuming a TE y mode, the electric field components inside the dielectric resonator are estimated as [18]: E x = Ck z cos(k x x)cos(k y y)sin(k z z) (4.2) E y = (4.3) E z = Ck x sin(k x x)cos(k y y)cos(k z z) (4.4) where k x, k y and k z are the wavenumbers along the x, y and z directions and C is an arbitrary constant. Enforcing the magnetic wall condition E n =atthesurface z = h of the dielectric resonator, the wavenumber k z is found to be: k z = nπ (4.5) 2h For the determination of the wavenumber k y, the Marcatili s approximation [19] is used. The procedure is identical to the case of the RDRA. It finally comes out that: ( ) ky w k y tan = (ε r 1)k 2 2 k2 y (4.6) where ε r is the permittivity of the dielectric resonator and k is the freespace wavenumber corresponding to the frequency f: k = 2π = 2πf (4.7) λ c with c being the speed of light in vacuum. Next, the enforcement of the magnetic wall condition on the inclined surfaces of the symmetric pyramid and more specifically at an arbitrary height z = h r results in the following expression: E n r = (4.8)

121 96 4 INVERTED DRA GEOMETRIES z x a 1 =a+ x a r n r h r PEC a 2 =a- x x Figure 4.15: Enforcement of the magnetic wall condition at the inclined surfaces of the pyramid, at a height h r. where n r is the normal vector on the inclined surface of the resonator at the height h r (Fig. 4.15). Assuming that the TE y 111 mode is resonant, equation (4.8) can be rewritten as: sin(φ) E x +cos(φ) E z = C tan(φ) k z cos(k x a r )cos(k y y)sin(k z h r )= Ck x sin(k x a r )cos(k y y)cos(k z h r ) tan(φ) π ( π ) 2h tan 2h h r = k x tan(k x a r ) h π ( π ) Δx 2h tan 2h h r = k x tan(k x a r ) π ( π ) 2Δx tan 2h h r = k x tan(k x a r ) (4.9) where a r is computed according to: a r = a h 1 tan(φ) = a h 1 Δx (4.1) h Finally, the resonance frequency of the TE y 111 (m = n = l =1)mode can be estimated by solving the separation equation k 2 x + k2 y + k2 z = ε r k 2 (4.11) after having substituted the expressions for k x, k y and k z from (4.9), (4.6) and (4.5) respectively.

122 4.3 THE TRAPEZOIDAL DRA 97 f [G z] res H 9 8 semi-analyt. hr=.47h semi-analyt. hr=.5h semi-analyt. hr=.53h semi-analyt. hr=.56h semi-analyt. hr=.59h numerical x [mm] Figure 4.16: Resonance frequencies computed by the proposed semi-analytical method as well as the commercial code (HFSS). It can be observed from (4.9) that the estimated value of the resonance frequency varies for different values of h r. In other words, depending on the height h r where the magnetic wall condition is enforced, the above set of equations gives a different result for the resonance frequency of the TE y 111 mode. To investigate how strongly the height h r and the resonance frequency are correlated, an investigation is conducted with trapezoidal DRAs having a Δx ranging between 2 and 3. The results of this investigation are summarized in Fig. 4.16, showing the estimated values of the DRA s resonance frequency for different values of h r and comparing them with the results of the simulation. It is observed that for values of the height h r in between.47h and.59h, the simulated results show a similar trend as the results of the proposed approach. The best agreement is obtained when h r =.56h. To demonstrate the validity and the repeatability of the proposed semianalytical method, a number of different trapezoidal DRAs were numerically analyzed and the results of the simulations were compared with the results of the method. The resonance frequency was initially calculated at a large number of heights h r and then the arithmetic average of the calculated values was estimated. The results are shown in Table 4.1, exhibiting a good agreement between the numerical simulations, the proposed semianalytical method and the measurements. It needs to be emphasized here that this method cannot always determine the resonance frequency of the

123 98 4 INVERTED DRA GEOMETRIES antenna dimensions resonance frequency f numer. f analyt. f meas. a 1 =6.5mm, a 2 =11.5mm, w = 6 mm, h = 7.6 mm, ε rd =1 a 1 =6.7mm, a 2 =13.2mm, w = 6.6mm, h = 8.4mm, ε rd =1 a 1 =7.6mm, a 2 =13.6mm, w = 6 mm, h = 7.6 mm, ε rd =1 a 1 = 1mm, a 2 = 16mm, w = 3mm, h = 16.1mm, ε rd =1 a 1 = 6 mm, a 2 =13mm,w = 5 mm, h =12mm,ε rd =1 a 1 = 7 mm, a 2 =1mm,w = 4 mm, h =12mm,ε rd = Table 4.1: Comparison of the resonance frequencies of various DRAs found though simulation, the proposed (semi-analytical) method and measurement. various trapezoids very accurately, due to the number of simplifications that have to be made. The method can provide, however, a good starting point for the design of the trapezoidal DRAs at predetermined frequencies. Afterwards, the exact geometrical configuration of the trapezoids can be determined by means of numerical analysis.

124 4.3 THE TRAPEZOIDAL DRA The high-profile inverted trapezoidal DRA The use of the inverted trapezoidal shape has been demonstrated to be more advantageous than the parallelepiped on the criterion of the impedance bandwidth. In fact, for a suitable choice of the lengths a 1 and a 2 (Fig. 4.6) of the trapezoid, the bandwidth can reach and even exceed 3 per cent. This bandwidth improvement is, however, combined with an asymmetry in the E-plane patterns, which deteriorates further as the length a 1 becomes much larger than a 2. One way to obtain a wide bandwidth for an inverted trapezoidal DRA without degrading the rest of its radiation properties is by combining the resonance of its fundamental mode with that of a higher-order mode. This technique was demonstrated in the previous chapter for the case of a high-profile RDRA. In a similar manner, the fundamental TE 111 and the higher-order TE 113 modes of the trapezoidal DRA can be excited at nearby frequencies, provided that its height h is much larger than its length a and width w. Based on this design concept, two different implementations for wideband trapezoidal DRAs were developed. The first implementation is illustrated in Fig. 4.17, showing a simple trapezoidal DRA of dielectric permittivity ε rd1 = 1 and dimensions a 1 = 7 mm, a 2 =1mm,w =4mm and h = 12 mm. The dielectric resonator is fed through the center conductor of an SMA connector, which is protruding out of a small hole in a metallic plate of dimensions 14 mm 12 mm. The probe is situated in the middle of the narrow side of the dielectric resonator and it has a length l p =6.mm, optimized for best matching. The dependence of the matching on the probe length l p is shown in Fig. 4.18, where the return loss of the trapezoidal DRA is plotted against frequency for various values of l p. It is observed that for a probe length l p =6.mm the 1 db impedance bandwidth becomes approximately 59 per cent. The measured return loss in this case is in good agreement with the simulation. A mechanically more stable implementation of the trapezoidal DRA is depicted in Fig The dielectric resonator consists of two parts; a trapezoid of dielectric permittivity ε rd1 = 1 and dimensions a 1 = 7 mm, a 2 = 1 mm, w = 4mm and h = 12 mm and a plate of triangular cross-section with a permittivity ε rd2 = 2.2 and length a 3 = 3 mm, width w = 4 mm and height h = 12 mm that complements the rectangular shape. The dielectric resonator is coupled through a coaxial probe

125 1 4 INVERTED DRA GEOMETRIES w a 1 z PEC x rd1 h y a 2 l p (a) (b) Figure 4.17: High-profile inverted trapezoidal probe-fed DRA. (a) Geometrical configuration. (b) Fabricated prototype. Return Loss [db] frequency [GHz] simulated l p =5mm simulated l p =6mm simulated l p = 7mm measured l p =6mm Figure 4.18: Simulated (for different probe lengths) and measured (for best matching) return loss of the trapezoidal DRA of Fig of length l p =6.2mmand is residing on a groundplane of dimensions 14 mm 12 mm. The most important advantage of this new implementation is that the DRA is more rigid, since instead of a trapezoid, there is a rectangular parallelepiped now residing on the groundplane. This mechanical improvement does not come along with a cancelation of the wide bandwidth connected to the inverted trapezoidal shape. The reason is that the triangular section is made out of a low-permittivity material. As a result, the DRAs of Fig and 4.19 operate in very similar ways. Because of that and for the sake of brevity, we will from now on concentrate

126 4.3 THE TRAPEZOIDAL DRA 11 w a 1 z PEC rd1 x h rd2 a y 3 a 2 l p (a) (b) Figure 4.19: Mechanically stable high-profile inverted trapezoidal probe-fed DRA. (a) Geometrical configuration. (b) Fabricated prototype. on the DRA configuration depicted in Fig A prototype of the mechanically stable trapezoidal DRA has been fabricated and measured. The plots of the return loss and the input impedance versus frequency are illustrated in Fig. 4.2, exhibiting an acceptable agreement between numerical and experimental results. The small discrepancy observed is most probably due to fabrication tolerances and the large standard deviation in the dielectric constant of the trapezoid (ε rd1 1 ±.2). In addition, the discrepancy at the frequencies above 12 GHz in the input impedance curves is caused by the low adaptive frequency set in the FEM solver (frequency-domain solver) for the accurate analysis of the structure at the lower frequencies. Fig. 4.2 displays, in addition to HFSS simulations, a numerical analysis performed with an inhouse developed Finite-Volume Time-Domain (FVTD) solver [31]. The FVTD method combines an explicit time-stepping with a tetrahedral discretization. The agreement between the results from the two very different computational methods (time-domain vs. frequency-domain, different in-cell approximations, different tetrahedral meshes) is striking and dissimilarities are only observed at high frequencies. This confirms that the small discrepancy between simulations and measured results can most likely be attributed to fabrication tolerances. As observed from the input impedance curves, the trapezoidal DRA reaches a bandwidth of 62 per cent (6.8GHz 13 GHz) through the excitation of three modes at nearby frequencies: the TE y 111,theTEy 113 and a higher-order mode. The first two modes were intentionally excited,

127 12 4 INVERTED DRA GEOMETRIES Return Loss [db] Input Impedance [ ] 1 real imaginary -3 FEM results FVTD results -4 Measurement frequency [GHz] frequency [GHz] Figure 4.2: Simulated and measured return loss and input impedance for the trapezoidal DRA of Fig since they exhibit similar radiation characteristics and they consequently contribute to a wide operational bandwidth with stable patterns and polarization. To determine whether the DRA operation is also stable for the third mode, the broadside gain of the DRA was measured as a function of frequency. The results are shown in Fig In the frequency range between 6.8GHz and 9.5GHz the TE y 111 mode is dominant, resulting in broadside operation with a gain of around 3 dbi. At 1 GHz the TE y 113 mode is excited; this leads to a broadside gain of 4 6 dbi. Finally, the excitation of the third mode at approximately 12 GHz results in the rapid decrease of the broadside gain. Since well-behaved broadside DRA operation is desired, operation up to only 12.2 GHz is considered. Finally, the DRA operational bandwidth is estimated to be around 57 per cent, within which stable broadside patterns and good polarization purity is attained. The radiation patterns of the trapezoidal DRA of Fig are depicted in Fig at frequencies 8.GHz and1.5 GHz. The radiation is broadside within the entire operational bandwidth and the cross-polarization remains below 15 db for a wide range of elevation angles θ. The minor ripples at around θ = in the E-plane are the result of diffraction effects due to the finite size of the groundplane. Finally, the H-plane patterns are, as expected, perfectly symmetrical for all frequencies, whereas the E- plane patterns become less symmetrical with increasing frequency. This

128 4.4 THE INVERTED TRUNCATED CONICAL DRA 13 Gain [dbi] operational bandwidth frequency [GHz] Figure 4.21: Measured broadside gain vs. frequency of the trapezoidal DRA. asymmetry can be kept, however, within acceptable limits when considering the design procedure presented before. To further account for the gain drop above 12.2 GHz, Fig illustrates the radiation patterns of the trapezoidal DRA at the frequency 12.3 GHz. It is observed that the patterns of this mode are characterized by an increased asymmetry in the E-plane due to the trapezoidal shape, higher levels of cross-polarization and some ripples at around θ 6. The broadside gain of this third mode is lower than of the TE y 113 mode and it decreases further as the frequency increases. This is most probably due to the further deterioration of the E-plane patterns symmetry and the increase of the cross-polarization at higher frequencies. 4.4 The inverted truncated conical DRA An example of a well-operating DRA, whose geometry can be considered as a progression from the inverted trapezoidal shape, will be the subject of investigation in this section. This DRA is intended for a specific Body Area Networks (BAN) application, which sets some strict specifications concerning the antenna s operational bandwidth and signal dispersion properties. In order to thoroughly examine the performance of this DRA, its operation in both, the frequency- and the time-domain will be examined.

129 14 4 INVERTED DRA GEOMETRIES E-plane H-plane f= 8. GHz f = 1.5 GHz f= 12.3 GHz co-pol cross-pol Figure 4.22: Measured radiation patterns in the E- and H-planes for the trapezoidal DRA of Fig at 8.GHz, 1.5GHz and 12.3GHz. Antenna designs exhibiting good UWB properties in BAN applications can be quite challenging due to the lossy, dispersive propagation environment (human skin). Moreover, the requirements for large bandwidth, stable radiation patterns and low antenna size and profile are not easily met with most of the commercially available antennas. In our case, the antenna is intended for a BAN application for the intensive-care unit in hospitals. For this application the antenna should meet the following specifications. First, it should have a low profile and it should be mounted on a groundplane that is as small as possible. The antenna should operate in the 3.4 GHz to 5. GHz frequency band exhibiting omnidirectional patterns and stable operation, independent of the environment (human body or free-space). Finally, the antenna operation should be characterized by good UWB properties. This type of operation requires a wide impedance bandwidth and a low signal dispersion. Short pulses should be radiated with a temporal extent that is not significantly larger than that of the in-

130 4.4 THE INVERTED TRUNCATED CONICAL DRA 15 cross-sectional view d c s a 1 rd h d i a 2 top view r g PEC (a) (b) Figure 4.23: The inverted truncated conical DRA. (a) Geometrical configuration. (b) Fabricated prototype. put signal. In addition, the ringing and chirp effect on these pulses should be reduced to a minimum [32]. An antenna that could be considered as a potential candidate for this application is the inverted truncated conical DRA shown in Fig (a). For the analysis of this antenna, two commercial full-wave analysis tools were used: ANSOFT HFSS R employing FEM in the frequency domain and CST R Microwave Studio using Finite Integration Technique (FIT) in the time-domain. The use of two numerical tools based on different methods allows cross-checking the accuracy of the simulations and therefore provides a reliable reference point before the fabrication of a prototype. The DRA configuration of Fig (a) consists of an inverted truncated annular conical dielectric resonator of height h =12.5mm, radii a 1 = 19.5mm, a 2 =16.5 mm and dielectric permittivity ε rd =9.8 residing on a groundplane of radius r g = 3 mm. The dimensions of the dielectric

131 16 4 INVERTED DRA GEOMETRIES resonator have been determined according to the following procedure. First, the simple annular ring-shaped dielectric resonator (a 1 = a 2 = a) is considered [33]. For this geometry, its radius a is computed according to the empirical relation: a = b/.3 (4.12) where b is the radius of the hole in the center and hence, it is equal to the sum of the probe radius r i = d i /2 and the spacing s between the outer radius of the probe and the inner surface of the dielectric resonator: b = r i + s = d i /2+s (4.13) Then, the height h of the annular ring is determined from the solution of the TM 1δ mode design formula obtained from [5]: h = 2 (2πfop ) 2 ( ) ε rd π c a 1 (4.14) where f op is the frequency of operation of the DRA. In the second step, the annular ring is transformed into the inverted conical shape, since the latter geometry provides a lower Q-factor and thus a wider bandwidth for the DRA. The resonance frequency of the DRA is not significantly affected by this transformation, under the conditions that the total volume stays the same and that the lengths a 1 and a 2 are not much different from a. To demonstrate the bandwidth enhancement through the inverted conical dielectric resonator, Fig (a) illustrates the return loss of three truncated conical DRAs of the same total volume. It is observed that the inverted conical DRA (a 1 =19.5mm, a 2 =16.5mm) exhibits a wider impedance bandwidth than the annular ring (a 1 = a 2 =18.mm) and the non-inverted conical DRA (a 1 =16.5mm, a 2 =19.5mm). It is worth mentioning here that a comparison of various types of conical DRAs was also made in [34] highlighting the advantages of the inverted conical shape. However, the excited DRA modes in [34] and the resulting radiation characteristics were different from the ones in the configuration presented here. In the present case, the DRA is excited in its TM 1δ mode through the center conductor of an SMA connector (diameter d i =1.28 mm) situated in the center of the dielectric resonator. The distance from the outer radius

132 4.4 THE INVERTED TRUNCATED CONICAL DRA 17 Return Loss [db] Return Loss [db] a1 = 16.5 mm, a2 = 19.5 mm a1 = 18. mm, a2 = 18. mm a = 19.5 mm, a = 16.5 mm frequency [GHz] (a) h = 12.5 mm d c =3mm r =2mm rd = no cap d c =3mm dc =5mm h = 12.5 mm a 1 = 19.5 mm a 2 = 16.5 mm r =2mm rd = frequency [GHz] Figure 4.24: Simulated (CST) return loss of the truncated conical DRA. (a) Different resonator shapes. (b) Different diameters of the metallic hat. (b) of the probe to the inner surface of the dielectric resonator is chosen to be different from zero (s = 2 mm), as a means to further enhance the DRA bandwidth. Finally, the probe is capacitively loaded with a metallic hat [35], so that its height can be reduced to the height of the dielectric resonator. Hence, the DRA profile is not distorted by the presence of the center pin. The effect of the metallic hat on the response (return loss) of the DRA is shown in Fig (b). A brief comparison between the DRA under investigation and the one shown in [33] demonstrates several functional and conceptual differences. One obvious difference is that in the present DRA there is no pin extending beyond the height of the dielectric resonator. Instead, a metallic cap is placed on top of the probe in order to maintain its electrical length after the reduction of its mechanical length. Therefore, a good operation can still be obtained for a DRA of a much lower profile. A further difference to [33] is that the center conductor of the SMA connector is only used to excite the dielectric resonator mode in the proposed configuration, whereas in [33] it is used both as a feeding and a resonant radiating element. The resulting 3 : 1 bandwidth is obtained by coupling to multiple modes at nearby frequencies. In the context of UWB operation, the excitation of multiple resonant modes creates rapid changes of the phase over

133 18 4 INVERTED DRA GEOMETRIES -1 Return Loss [db] Input Impedance [ ] 1 real imaginary HFSS -5 CST HFSS -4 Measurement Measurement frequency [GHz] frequency [GHz] (a) Figure 4.25: Simulated and measured (a) return loss and (b) input impedance of the inverted truncated conical DRA for free-space operation. (b) frequency and look angle, contributing thus to signal dispersion. From here it follows that the modes-merging technique is not entirely appropriate for pulsed operation. In the DRA configuration presented here, the sole excited mode is the TM 1δ and the large bandwidth is obtained through the inverted shape of the dielectric resonator. Thus, by setting the resonance frequency of the TM 1δ mode just below the band of interest (3.4 GHz 5. GHz), it is possible to obtain a nearly linear phase above resonance. Frequency-domain results In order to validate the simulation results, the antenna prototype of Fig (b) was fabricated and measured. The return loss and the input impedance of the DRA in free-space are plotted versus frequency in Fig. 4.25, exhibiting a good agreement between numerical and experimental results. The impedance bandwidth (S 11 < 1 db) covers a frequency range between 3 GHz and 5 GHz, with the TM 1δ mode being resonant at 3.3 GHz. The good operation of the DRA in the aforementioned band is also evident through its measured radiation patterns (co- and cross polarization), which are depicted in Fig at frequencies 3. GHz, 4. GHz

134 4.4 THE INVERTED TRUNCATED CONICAL DRA E E GHz 4. GHz GHz Figure 4.26: Measured free-space radiation patterns for the co- (E θ ) and crosspolarization (E φ )at3.ghz, 4.GHz and 5.GHz. and 5. GHz. It can be observed that the monopole-like patterns are reasonably stable within the entire spectrum, while the cross polarization remains always below 15 db. To investigate the effect of the human body on the DRA performance, the antenna geometry was simulated using a simplified model for the human tissue (see inset of Fig. 4.27). The tissue was modeled as a stack of three layers: a skin layer of thickness h s = 1 mm, a layer of fat with thickness h f = 5 mm and finally a muscle layer of h m = 5 mm. The dispersive characteristics of these three layers were determined according to [36]. The model was simulated with CST and the results were compared to measurements performed with the DRA placed on different parts of the human body (arm, leg and chest). The results are illustrated in Fig. 4.27, showing good agreement between simulations and measurements. From Fig and Fig it is obvious that the effect of the tissue on the DRA performance is not that significant, at least not with the chosen size of groundplane and frequency range.

135 11 4 INVERTED DRA GEOMETRIES Return Loss [db] Measurement 1 (arm) Measurement 2 (leg) Measurement 3 (chest) CST h s h f h m skin fat muscle frequency [GHz] Figure 4.27: Simulated and measured return loss of the inverted truncated conical DRA for on-body operation. In order to examine the dispersive properties of the DRA, measurements were performed in both, the frequency- and the time-domain. Considering the frequency-domain results first, the transmission coefficient S 21 was measured in the frequency range between 3 GHz and 5 GHz for two identical inverted truncated conical DRAs placed parallel to each other at a distance of l = 16 cm. A proper calibration was performed for the elimination of the dispersive effects from the connecting cables. The amplitude of S 21 versus frequency is illustrated in Fig for both, free-space and on-body transmission. It can be observed that, as expected, the path attenuation is higher in the presence of the human skin. The small instabilities in the S 21 curve for on-body operation (compared to the more stable free-space curve) can be attributed to propagation effects on the human body. Next, the DRA transfer function was extracted from the S 21 measurements by using a procedure that will be presented in the Appendix. The phase of the transfer function for free-space and on-body operation is depicted in Fig for an electrical delay of 1 ns. It is clear that the phase characteristics exhibit a nearly linear dependency on frequency between 3.4 GHz and 5 GHz. This linearity results in a virtually constant group delay over the entire frequency domain, a crucial condition for good pulsed operation.

136 4.4 THE INVERTED TRUNCATED CONICAL DRA 111 Transmission [db] in free-space on-body frequency [GHz] Figure 4.28: Amplitude of S 21 and phase of the transfer function of the inverted truncated conical DRA for free-space and on-body operation. l Phase [rad] Time-domain measurements For the time-domain measurements, a modulated Gaussian pulse with spectral content between 3.4 GHz and 5 GHz (defined at 3 db level) was applied to the input of the transmitting antenna. The impulse generator consisted of a cascade of a fast triangular pulse generator and a low-pass as well as a high-pass filter. Fig illustrates the normalized input voltage signal at the terminals of the transmitting antenna and the received voltage signal for free-space transmission. The received signal is normalized to the amplitude of the transmitted signal for ease of comparison. The two identical antennas were placed parallel to each other at a distance l = 16 cm, as illustrated in the inset of Fig The measurements demonstrate that the received pulse has a duration of about 1.42 ns at 1% of amplitude level, as opposed to the duration of 1.25 ns of the transmitted pulse. This temporal extension of the transmitted waveform can be considered acceptable for the intended application. Besides, other typical problems of dispersive antennas such as ringing or chirp effects are not distinguished here. For the case of on-body operation the input and the received waveforms are shown in Fig There, the received signal is scaled with the same normalization factor as the received signal for transmission in freespace. The comparison of Fig. 4.3 with Fig leads to the observation

137 112 4 INVERTED DRA GEOMETRIES Normalized Amplitude TX Impulse (Normalized) RX Impulse (Normalized) l time [nsec] Figure 4.29: Time-domain response of a pair of inverted truncated annular conical DRAs for transmission in free-space. Normalized Amplitude TX Impulse (Normalized) RX Impulse (Scaled) l time [nsec] Figure 4.3: Time-domain response of a pair of inverted truncated annular conical DRAs for on-body transmission. that the two received waveforms have a very similar shape; their main difference is the smaller amplitude of the received waveform for on-body operation due to the increased attenuation from the skin. No further deterioration of the transmitted waveform was detectable in the frequency range considered. As a final quality measure for the characterization of the DRA s disper-

138 4.5 CONCLUSION 113 Normalized transient response envelope time [nsec] Figure 4.31: Transient response of the inverted truncated conical DRA. sive character, the transient response was extracted from the antenna s transfer function through an inverse discrete Fourier transformation (see Appendix). The shape of the transient response in combination with its peak value p and the Full Width at Half Maximum (FWHM) are critical parameters for the characterization of the antenna s UWB properties. The results of our investigation are illustrated in Fig The peak value p of the transient response is found to be around.4 m/ns, while its Full Width at Half Maximum (FWHM) is approximately 39 ps. These values affirm the good operation of the DRA in the frequency spectrum between 3.4 GHz and 5 GHz. In addition, these values are comparable or better than those of typical UWB antennas like the spiral and the log-periodic antenna [37]. In this section a number of models and quality measures were employed for the examination of the dispersive properties of the inverted conical DRA. A thorough description and characterization of these models will be provided in the Appendix. 4.5 Conclusion The reduction of the Q-factor of a DRA through the proper modification of the dielectric resonator geometry is a very useful operational and design concept in the DRA theory. If this concept is then combined with the

139 114 4 INVERTED DRA GEOMETRIES modes-merging technique introduced in the previous chapters, the DRA s bandwidth response will be significantly improved. As a demonstration for that, a probe-fed inverted trapezoidal DRA was investigated in this chapter, exhibiting an impedance bandwidth of more than 6 per cent and stable patterns as well as a good polarization purity. This was possible through the excitation of the TE 111 and the TE 113 modes at nearby frequencies. It needs to be emphasized here that a bandwidth of more than 1 per cent could theoretically be obtained with a more asymmetrical inverted trapezoid. However, this would also lead to an increase in the asymmetry of the patterns in the E-plane, which is not desirable in some applications. In other applications like for example in indoor communications, the shape of the radiation patterns is not a very crucial parameter. Hence, it would be realistic to employ there some very asymmetrical trapezoids in order to further enhance the impedance bandwidth. What needs to be kept in mind is that in any case, the geometrical modification of a canonical dielectric resonator towards an inverted shape can have a beneficial effect on the DRA performance, without necessarily degrading the antenna operation or increasing the fabrication complexity. Based on the above observation, a inverted conical DRA was demonstrated in the last section of the chapter, exhibiting a wide impedance bandwidth and stable radiation characteristics. In this device, just one dielectric resonator mode was excited and as a result, the phase of the DRA s transfer function was linear and its group delay was constant across frequency. These operational characteristics translate into a good UWB operation of the DRA, as characterized through its signal dispersion properties in combination with its percentage bandwidth. The significance of this result is not to be overseen; the DRA is the sole resonating antenna that exhibits such a performance, while the typical UWB antennas are not comparable with DRAs in terms of their size or their type of operation.

140 Appendix The linear time invariant (LTI) system model Let s assume that an antenna is operating in its receiving mode and it is terminated with its real and frequency-independent characteristic port impedance Z c. A plane wave with polarized field strength spectrum E i is incident on the antenna from the angle (θ i, φ i ). Then, the received voltage spectrum U r,i at the terminating load of the antenna is given by: U r,i (ω, θ i,φ i ) Zc = H n (ω, θ i,φ i ) E i (ω, θ i,φ i ) Z (4.15) where H n is the normalized antenna height and Z = μ ε = 12π Ωis the characteristic free space impedance. In the time domain, the above equation is translated into the convolution of the antenna s transient response h n (t, θ, φ) with the polarized field strength e i (t, θ, φ): u r,i (t) Zc = h n (t, θ i,φ i ) e i(t, θ i,φ i ) Z (4.16) = 1 Z ( h n,copol (t, θ i,φ i ) e i,copol (t, θ i,φ i ) + h n,xpol (t, θ i,φ i ) e i,xpol (t, θ i,φ i )) From the other side, the radiated electric field E t of a transmitting antenna at a distance r and angle (θ t, φ t ) in the far-field region is computed according to the relation: E t (ω, r, θ t,φ t ) = 1 ( Z r exp jω r ) A n (ω, θ t,φ t ) U t(ω) (4.17) c Zc where U t (ω) is the voltage at the antenna terminals and A n is the polarized transmit factor in the frequency domain. The above equation is expressed 115

141 116 Appendix in the time domain as following: e t (t, r, θ t,φ t ) = 1 ( Z r δ t r ) a n (t, θ t,φ t ) u t(t) (4.18) c Zc It is interesting ) to note here that the convolution with the Dirac function δ (t rc represents the time retardation of the signal traveling with the light speed c = 1 μ ε to the distance r where the electric field is measured. Next, the reciprocity theorem [6] is applied in order to yield a connection between the antenna height H n (receiving mode) and the transmit factor A n (transmitting mode). Finally, the radiation equations (4.17) and (4.18) can be rewritten as: E t (ω, r, θ t,φ t ) = Z e t (t, r, θ t,φ t ) Z = 1 r δ ( t r c ) ) 1 exp ( jω rc jωh 2πrc n (ω, θ t,φ t ) U t(ω) (4.19) Zc 1 2πc t h n (t, θ t,φ t ) u t(t) (4.2) Zc For a wireless link consisting of a transmitting and a receiving antenna placed in their mutual far field, the received signal voltage at the antenna terminals can be estimated from the previous equations. It is finally found that: U r,2 (ω) = Z c,2 Z c,1 Hn,2 (ω, θ i,φ i ) exp( jω r 12/c ) 2πr 12 c (4.21) jωh n,1 (ω, θ t,φ t )U t,1 (ω) Z c,2 u r,2 (t) = 1 hn,2 (t, θ i,φ i ) δ(t r 12 ) (4.22) Z c,1 2πr 12 c c h n,1 (t, θ t,φ t ) t u t,1(t) where 1, 2 refer to the transmitting and the receiving antennas respectively. Based on the above equations, the transfer function H n and the transient response h n (t) of an antenna can be calculated. More specifically,

142 Appendix 117 the transmission coefficient S 21 between a reference antenna (e.g. a horn antenna with a known transfer function H n,ref ) and the investigated antenna can be measured by using a vector network analyzer. A proper calibration has to be made first, so that the dispersive effects from the connecting cables are eliminated. Then, according to equation (4.22) and by assuming that Z C1 = Z C2 =5Ω,wehave: S 21 (ω) = U r,2 = (4.23) U t,1 r12/c e jω = H n,ref (ω)h n (ω)jω 2πr 12 c and thus the transfer function H n of the antenna can be estimated, since all the other quantities in the relation are known. Finally, the complex analytical transient response h + n can be obtained through the inverse discrete Fourier transformation of the transfer function: N 1 h + 1 n (k Δt) = H n + N Δt (n Δf) ej(2π/n)kn (4.24) n= where Δt and Δf are the time and frequency resolutions respectively. Quality measures In general, antenna properties like the input impedance, the efficiency, the gain, the effective area and the radiation patterns are useful but not sufficient to fully characterize the UWB antenna performance [32]. To do that, the most decisive criterion is the signal dispersion of the antenna. The signal dispersion corresponds to the stretching out of the UWB signal waveform or, alternatively, to the variation of the received waveform with respect to the look angle. This is due to the shifting of the antenna s phase center as a function of frequency. To characterize the signal dispersion of an antenna several quality measures must be used, which examine its transient radiation behavior in both, the frequency- and the time-domain. In the frequency domain, the ability of the antenna to effectively transmit and receive power can be examined through its effective gain pattern G eff : G eff = ω2 πc 2 H n (ω, θ, φ) 2 (4.25)

143 118 Appendix Moreover, the antenna s transfer function H n (ω) = H n (ω) e jϕ(ω) provides a very straightforward measure for the characterization of the signal dispersion. The group delay τ g (ω) denotes the delay of a portion of spectral energy at frequency ω due to its transmission in free space. The group delay is defined as the derivative of the phase of the transfer function with respect to frequency: τ g (ω) = dϕ(ω) (4.26) dω As expected, in the case of a non-dispersive antenna the group delay is constant across frequency. In the time-domain, the quality measures of the antenna s UWB performance are connected to its real-valued transient response h n (t): h n (t) =Re{h + n (t)} (4.27) The transient response of a non-dispersive antenna should be identical to the Dirac function, so that the received waveform would not be distorted but only transferred in time compared to the initial one. Because of that, the most common time-domain quality measures examine the shape of the transient response. The first two quality measures, namely the peak value p(θ, φ) of the antenna s transient response: p(θ, φ) =max h + n (t, θ, φ) (4.28) and the full width at half maximum (FWHM) of the magnitude of its envelope: w.5 (θ, φ) =t 1 h + n (t 1,θ,φ) =p/2 t 2 t2<t 1, h + n (t 2,θ,φ) =p/2 (4.29) examine how similar the transient response is to the Dirac function. In the same manner, the duration of the ringing τ r,a denotes the time taken until the envelope of the transient response has fallen below a certain value a with respect to its maximum value. The ringing duration is computed by: τ r,a (θ, φ) =t a h + n (t a,θ,φ) =ap(θ,φ) t p tp<t a, h + n (t p,θ,φ) =ap(θ,φ) (4.3) It is self-evident that in a non-dispersive antenna the peak value p(θ, φ) should be as big as possible, while the FWHM and the ringing duration τ r,a as small as possible.

144 5 Advanced Dielectric Resonator Antenna Configurations 5.1 Introduction One of the most important features of the DRAs, which is affecting decisively their character and their radiation properties, is their inherent ability to effectively fill the radian sphere 4π/3(λ/2π) 3 [1]. Volumetric sources like DRAs radiate throughout their entire volume and hence they exhibit a much higher radiation power factor (RPF) compared to the linear and surface radiators. The RPF factor quantifies the amount of energy radiated from the antenna, which, in the case of the DRAs, is considerably larger than the energy stored in their near fields. Thus, the radiation Q-factor of the DRAs is smaller and their impedance bandwidth is larger than that of the typical resonant antennas. Since these operational advantages of the DRAs are connected with their volumetric nature, it is clear that the geometry and the electrical properties of the dielectric resonator volume are crucial factors for the determination and the improvement of the antenna s radiation characteristics. The strong relation between the dielectric resonator volume and its operational properties has already been demonstrated in previous chapters. The dependency of the resonant frequency and the impedance bandwidth of the DRA on its dimensions and dielectric permittivity has been extensively studied. In addition, the effect of the dielectric resonator geometry on the type and the properties of the excited DRA modes has been investigated and various analytical as well as empirical models have been developed in order to accurately predict the DRA performance. Finally, a number of different geometrical modifications have been suggested for the dielectric resonator shape and their effect on the DRA operational characteristics has been examined. In this chapter, the correlation between the typical features of the dielectric resonator and its operational properties will be investigated using a totally different approach. The electrical properties of the resonator like its permittivity ε r and permeability μ r have a far more significant role in 119

145 12 5 ADVANCED DRA CONFIGURATIONS the DRA operation compared to what has been described in the previous chapters. To start with, the type of modes excited within the dielectric resonator volume depends less on the resonator geometry itself and more on the shape of the interface between the high permittivity material and the surrounding medium (air). In other words, two dielectric structures of different overall geometries, whose shells (defined by the interface between the dielectric and the air) are of identical shapes, are likely to support similar modes. This finding can lead to a new family of DRAs with very attractive properties and straightforward design procedures. Another important development that is connected with the electrical properties of the resonator is the introduction of the magneto-dielectric materials. This opens new perspectives in the design of the DRAs, since the operational advantages of the dielectric resonators can be combined with some of the attractive features of the magnetic materials. More specifically, the use of materials having both permittivity and permeability values larger than one results in a significant enhancement of the DRA bandwidth as well as in an increase of the antenna s inductive coupling. As a result, the Magneto-Dielectric Resonator Antenna (MDRA) exhibits improved operational characteristics, as compared to a DRA of high dielectric constant ε r and permeability μ r =1. The current chapter is organized as following: in the first part, the bridge DRAs will be introduced. A comparison between their operation and the operation of the canonical RDRAs will be performed through numerical analysis. Afterwards, a number of advanced bridge DRA configurations will be demonstrated that exhibit an easily-controlled dual-mode operation as well as well-behaved radiation characteristics. Experimental validation of the proposed concepts will be provided through prototyping and measurement of the most attractive designs. The second part of the chapter will provide a short introduction on MDRAs. This type of antennas is still largely unexplored, mainly due to the lack of high-quality low-loss magneto-dielectric materials in the microwave regime. Since, however, the operational advantages of the MDRAs are of high importance and they bear the promise of significant performance improvement, their theoretical investigation is crucial for the demonstration of these materials potential as well as for the more complete description of the DRAs is this dissertation.

146 5.2 THE PROBE-FED BRIDGE DRA 121 z z PEC x y t w l p a h PEC x y w 2 a 2 h 2 l p2 (a) (b) Figure 5.1: Geometrical configuration of (a) a probe-fed bridge DRA and (b) a probe-fed RDRA. 5.2 The probe-fed bridge DRA A typical configuration for a probe-fed Bridge-shaped DRA (BDRA) is illustrated in Fig. 5.1 (a). It consists of a bridge-shaped dielectric resonator of permittivity ε r, which has a length a, awidthw, aheighth and a uniform thickness t. The bridge is coupled through a coaxial cable of length l p and it is mounted on top of a ground plane of finite lateral dimensions. The coaxial probe was selected as the feeding scheme of the BDRA mainly due to its operational and design simplicity. A careful observation of the BDRA of Fig. 5.1 (a) leads to the conclusion that the bridge-shaped resonator may be regarded as a hollow dielectric parallelepiped. Because of that, it is interesting to compare the operation of the BDRA with the operation of a canonical RDRA of the same dimensions and coupling mechanism. For this comparison to be possible, the dielectric permittivity of the parallelepiped must be chosen to be much lower than that of the bridge. The reason for that is that the hollow parallelepiped can be regarded as a dielectric parallelepiped of permittivity ε r1 = 1 embedded within a bridge-shaped dielectric structure of permittivity ε r,b >> ε r1. So, the hollow parallelepiped is equivalent to a canonical parallelepiped of effective permittivity ε r,ef f,forwhich ε r1 <ε r,ef f << ε r,b. Based on the above considerations, the BDRA of Fig. 5.1 (a) is compared to the canonical RDRA shown in Fig. 5.1 (b). Both structures have the same, randomly selected dimensions: a = a 2 =2mm,w = w 2 =12mmandh = h 2 = 16 mm. Moreover, the thickness of the bridgeshaped resonator is t = 1 mm and its dielectric permittivity is ε r,b = 4.

147 122 5 ADVANCED DRA CONFIGURATIONS Return Loss [db] bridge DRA RDRA frequency [GHz] Figure 5.2: Simulated (HFSS) return loss of the BDRA and the RDRA of Fig. 5.1 (a) and Fig. 5.1 (b) respectively. On the other hand, the permittivity of the dielectric parallelepiped is set to ε r2 = ε r,ef f =8.6, chosen so that its resonance frequency is the same as that of the bridge DRA. Finally, both antennas are residing on identical ground planes of dimensions 12 mm 1 mm and they are fed through coaxial probes of length l p =9.4mm. The comparison of the two DRA geometries is performed by means of the commercial full-wave analysis software ANSOFT HFSS R. The simulated return loss of the two DRA configurations of Fig. 5.1 (a) and (b) is illustrated in Fig It is observed that both antennas are resonant at the same frequency f =3.63GHz with the impedance bandwidth of the BDRA being larger than that of the RDRA (15.5 % versus 12.1%). This bandwidth enhancement is most probably caused by the hollow shape of the BDRA, which is resulting in the smaller confinement of the antenna s near fields as compared to the canonical parallelepiped. This effect, which is encountered often with the notched and inverted DRA geometries [15], [3], was discussed in detail in the previous chapter. Fig. 5.3 (a) and (b) illustrate the schematic E-field distribution and the simulated radiation patterns of the BDRA s lowest-order mode, which is resonant at the frequency f = 3.63 GHz. It can be observed that this mode exhibits identical radiation characteristics with those of the fundamental TE 111 mode of the canonical RDRA, as observed from the RDRA s radiation patterns shown in Fig. 5.3 (c). Hence, it can be safely suggested

148 5.2 THE PROBE-FED BRIDGE DRA co-pol -1-2 cross-pol co-pol -1-2 cross-pol E-plane E-plane 21 H-plane H-plane (a) (b) (c) Figure 5.3: (a) E-field distribution and (b) radiation patterns of the resonant mode of the BDRA. (c) Radiation patterns of the RDRA of Fig. 5.1 (b). that these two modes are the same and, as a result, the excitation of the fundamental DRA mode in these structures is primarily determined by the shape of the interface between the high-permittivity material and its surrounding medium (air). To verify that, let us look into the alternative BDRA geometry of Fig. 5.4 (a). This configuration consists of the bridgeshaped dielectric resonator of Fig. 5.1 (a), supported by a cross-shaped dielectric structure of the same width w s as the bridge. The exact configuration of this structure is specified by the dimensions h s =7mmand l s = 12 mm, which were randomly chosen. The dielectric permittivity of the crossed slabs is set to ε r,s = 8, much smaller than the permittivity ε r,b = 4 of the bridge. The return loss and the radiation patterns of the BDRA structure of Fig. 5.4 (a) are illustrated in Fig. 5.4 (b) and (c) respectively. The structure is resonant at the frequency f =3.39 GHz, which is lower than the resonance frequency of the original BDRA, as demonstrated in the same plot for comparison purposes. The reason for this frequency shift is that the crossed slabs of permittivity ε r,s >ε r,air = 1 lead to an increase in the effective permittivity of the BDRA of Fig. 5.4 (a) as compared to that of the original geometry. In other words, if the BDRA configuration of Fig. 5.4 (a) was replaced by its equivalent canonical RDRA, the dielectric permittivity of the latter would be larger than the effective permittivity of the original BDRA. Apart from the observed shift in the resonance frequency, the BDRA structure of Fig. 5.4 (a) exhibits similar radiation characteristics with the original geometry. As a demonstration for that, Fig. 5.4 (c) shows the ra-

149 124 5 ADVANCED DRA CONFIGURATIONS r,b l s h s r,s Return Loss [db] -1-2 simple advanced frequency [GHz] co-pol -1 cross-pol -2 (a) (b) (c) E-plane H-plane Figure 5.4: (a) Geometrical configuration of an advanced BDRA. (b) Simulated (HFSS) return loss of the advanced BDRA as compared to the return loss of the BDRA of Fig. 5.1 (a). (c) Radiation patterns at f =3.39 GHz. diation patterns of the investigated structure at frequency f = 3.39 GHz. It can be observed that the two BDRA geometries exhibit similar patterns in both, the E- and the H-plane. In addition to that, the E-field distribution of the excited BDRA mode is almost identical to that illustrated in Fig. 5.3 (a) for the case of the simple dielectric bridge. Based on all the above, it can be concluded that the shape of the high-permittivity resonator determines the type and the properties of the excited mode(s), whereas any other low-permittivity components affect almost exclusively the frequency, at which this mode is resonant. In order to complete our description of the bridge-shaped resonators, the effect of their dielectric permittivity value on the BDRA radiation characteristics will have to be examined. As it was mentioned before, a BDRA excited in its lowest-order mode exhibits similar radiation properties with those of the canonical RDRA. Therefore, the BDRA and the RDRA can be considered equivalent structures, with the effective permittivity of the dielectric parallelepiped ranging between the permittivity of the bridge and that of the surrounding medium. The exact value of the effective permittivity depends primarily on the permittivity of the chosen material as well as the thickness of the dielectric bridge. As an example, a very thin bridge-shaped resonator made of a relatively low-permittivity material will have a low effective permittivity. This might result in a decrease of the antenna s coupling efficiency and consequently, in a degra-

150 5.2 THE PROBE-FED BRIDGE DRA r,b = GHz E-plane co-pol 18 H-plane co-pol r,b =2 E-plane cross-pol 4.84 GHz H-plane cross-pol r,b =3 4.5 GHz r,b = GHz Figure 5.5: Radiation patterns (at the resonance frequency) of the BDRA for different values of its dielectric permittivity ε r,b. dation of its overall performance. This effect is demonstrated in Fig. 5.5, where the radiation patterns of the BDRA of Fig. 5.1 (a) are plotted for different values of its dielectric permittivity ε r,b. It can be observed that for low values of the permittivity (ε r,b = 1) the effective permittivity of the structure is very low, resulting therefore in a very weak coupling to the dielectric resonator and consequently in the radiation from the feeding probe being dominant. Hence, the patterns exhibit monopole-like radiation characteristics and the dielectric bridge serves merely as a dielectric loading to the probe. As the permittivity ε r,b increases, the DRA resonance frequency drops, and at the same time the coupling to the dielectric resonator becomes stronger. Hence, the TE 111 mode is more efficiently excited. This is demonstrated in Fig. 5.5 for the cases ε r,b =3, 4, where it can be observed that the co-polarized patterns are broadside.

151 126 5 ADVANCED DRA CONFIGURATIONS Advanced multi-band probe-fed BDRAs It was shown in the previous section that the high-permittivity contrast at the interface between the dielectric resonator and its surrounding medium defines the type and the properties of the excited mode(s). Based on this concept, the geometrical configuration of the bridge-shaped DRA was investigated and its operation was compared to that of the RDRA. The BDRA is an attractive candidate for many commercial applications, since it can help overcoming several antenna-packaging related problems. As an example, some of the components in a RF front-end can be placed in the empty space within the bridge volume, so that they are protected from various mechanical and/or climatic conditions. In addition to that, the dielectric bridge may incorporate other radiating elements in order to improve the antenna s bandwidth response or to obtain well-controlled multi-mode operation. A few representative examples of well-operating dual-mode BDRA configurations will be the subject of discussion in this section. The probe-fed double-bdra The geometrical configuration of the probe-fed double-bdra is illustrated in Fig. 5.6 (a). It consists of a double-bridge-shaped resonator of lengths a 1, a 2,heightsh 1, h 2,widthw 1 = w 2 = w and uniform thickness t, which is made of a dielectric material of permittivity ε r,b. The resonator is fed by a coaxial probe of length l p and it is mounted on top of a ground plane with lateral dimensions 12 mm 1 mm. To investigate the operation of the double-bdra, the dimensions of the larger bridge are fixed to a 1 =2mm,h 1 =16mm,t =1mmand w = 6 mm, while the dimensions a 2 and h 2 of the smaller bridge vary. The permittivity of the dielectric structure is ε r,b =4andthelengthof the feeding probe is set to l p =9mm,sothatbestmatchingisachieved. Fig. 5.6 (b) illustrates the simulated return loss of the double-bdra for the cases when a 2 = h 2 = mm, when a 2 /a 1 =.4, h 2 /h 1 =.4 and finally when a 2 /a 1 =.6, h 2 /h 1 =.6. The results of the numerical investigation are summarized in Fig. 5.7, where the plots of the resonance frequencies of the two lowest-order BDRA are provided for different values of the dimensions a 2 and h 2. All simulations were performed by using HFSS.

152 5.2 THE PROBE-FED BRIDGE DRA 127 t a 1 a 2 h 2 h 1 Return Loss [db] -1 a2 =mm, h2 =mm a 2 / a1 = h2/ h1 =.4 a2/ a1 = h2/ h1 =.6 l p PEC (a) frequency [GHz] (b) Figure 5.6: (a) Geometrical configuration of a probe-fed double-bridge DRA. (b) Simulated (HFSS) return loss of the double-bdra for a 1 = 2 mm, h 1 = 16 mm and w 1 = w 2 = 6 mm. Resonance frequency [G H z] second mode first mode resonant path a / a = h / h Figure 5.7: Resonance frequencies of the two lowest-order BDRA modes for different values of the ratios a 2/a 1 and h 2/h 1 (a 2/a 1 = h 2/h 1). The dimensions a 1 and h 1 stay fixed to 2 mm and 16 mm respectively. When a 2 = h 2 = mm the structure of Fig. 5.6 (a) is reduced to a simple bridge-shaped DRA having a similar configuration as the one shown in Fig. 5.1 (a). The BDRA exhibits a single resonance at f =

153 128 5 ADVANCED DRA CONFIGURATIONS 3.87 GHz which corresponds to the excitation of the TE 111 mode. As the dimensions of a 2 and h 2 increase, a second resonant mode appears at a higher frequency. For small values of a 2 and h 2 (usually a 2 <.5 a 1 and h 2 <.5 h 1 ) the resonance frequency of the second mode is affected almost exclusively by the size of the smaller bridge. Consequently, the increase of a 2 and h 2 results in the decrease of the resonance frequency of the second mode. As the dimensions a 2 and h 2 increase beyond the values a 2 =.5a 1 and h 2 =.5h 1 respectively, the resonance frequency of the second mode starts increasing. This is because a new resonant path comprising the upper and left parts of the double-bridge structure is now created, and the increase of a 2 and h 2 leads to the decrease of this paths length. It is important to underline here that the variation of the dimensions a 2 and h 2 does not significantly affect the resonance frequency of the lowest-order mode. Based on this observation, a dual-mode double-bdra operating at the predetermined frequencies f 1 and f 2 (f 1 <f 2 ) can easily be obtained, if, first, the larger bridge is designed to be resonant at the frequency f 1 and, afterwards, the dimensions of the smaller bridge are suitably varied until a resonance at the frequency f 2 is achieved. It is self-evident that the ratios a 1 /a 2 and h 1 /h 2 do not need to be equal in the final design; they were only chosen equal in the previous investigation for simplicity reasons. To demonstrate the good operation of the double-bdra, its radiation patterns are plotted in Fig. 5.8 for the case that a 2 /a 1 = h 2 /h 1 =.4 and the rest of its dimensions remain as specified before. It can be observed that the patterns are broadside at both frequencies 3.87 GHz and 5.14 GHz, at which the structure is resonant. Concerning the crosspolarization of the structure, it is very low in the E-plane and quite substantial in the H-plane. The poor polarization purity in the H-plane is due to the feeding probe; it will be shown later that other coupling schemes like for example the aperture lead to a high polarization purity in both planes. The probe-fed BDRA coupled with a RDRA A second example of a well-operating dual-mode BDRA configuration is illustrated in Fig It consists of a simple probe-fed BDRA of dimensions a 1, h 1, w 1, t and dielectric permittivity ε r,b, which incorporates

154 5.2 THE PROBE-FED BRIDGE DRA GHz E-plane co-pol H-plane co-pol E-plane cross-pol H-plane cross-pol GHz Figure 5.8: Radiation patterns of the double-bdra with a 2/a 1 = h 2/h 1 =.4 at the frequencies 3.87 GHz and 5.14 GHz. l p PEC t x a 1 a2 r,s h 2 h1 PEC w 2 y r,b w 1 x (a) (b) Figure 5.9: Geometrical configuration of a probe-fed BDRA coupled with a RDRA. (a) Side view. (b) Top view. a dielectric slab of dimensions a 2, h 2, w 2 and permittivity ε r,s.theslab is coupled inductively with the dielectric bridge and hence, its position with respect to the bridge will have a significant effect on the amount of coupling to its excited mode(s). It must be mentioned here that since the slab can be designed to be resonant at a chosen frequency, dual-mode operation can easily be obtained for this configuration by designing the two radiating elements at different frequencies. In that case, both resonant modes are of the TE 111 type and therefore well-behaved broadside radiation patterns will be obtained. For the analysis of the dual-mode BDRA of Fig. 5.9 let us assume a dielectric bridge with the dimensions a 1 =2mm,w 1 =6mm,h 1 =16mm, t = 1 mm and the permittivity ε r,b = 4. This BDRA configuration is identical to the structure of Fig. 5.6 (a) (a 2 = h 2 = ), which was investi-

155 13 5 ADVANCED DRA CONFIGURATIONS gated previously. The BDRA is resonant at the frequency f =3.87 GHz and it exhibits broadside radiation patterns, when excited in its fundamental TE 111 mode. Concerning now the RDRA, let us assume a dielectric parallelepiped of dimensions a 2 =1mm,h 2 =1mm,w 2 =6mmand permittivity ε r,s = 1. The parallelepiped is positioned symmetrically with respect to the x axis, at a distance Δx + t from the feeding probe, as illustrated in Fig The return loss of the BDRA configuration of Fig. 5.9 is illustrated in Fig. 5.1 for different values of the distance Δx between the dielectric bridge and the slab. It is observed that the variation of Δx results in an appreciable change of the coupling to the RDRA mode. On the other hand, the matching of the BDRA mode and the resonance frequencies of the two excited modes remain largely unaffected. Apart from the change in the matching of the second mode, the separation Δx of the two radiating elements affects also the radiation patterns of the second mode (RDRA). This is demonstrated in Fig. 5.11, where the radiation patterns of the BDRA configuration of Fig. 5.9 are plotted at frequency f =5.8 GHz for three different values of Δx. It can be observed that for small values of Δx the patterns are symmetric around the broadside (θ = ). As the distance between the slab and the dielectric bridge (and consequently, also the feeding probe) increases, the patterns become increasingly asymmetric in the E-plane. This effect is expected: the coaxial probe provides asymmetric coupling in the configuration of Fig. 5.9 and the increase of the distance between the probe and the slab makes this asymmetry even more pronounced. As a result, the radiation patterns in the E-plane become asymmetric with respect to the z axis (θ = ). It must be mentioned here that the radiation patterns of the BDRA mode remain always broadside and symmetric, while the cross-polarization in the H-plane is quite large for both resonant modes due to the presence of the probe. 5.3 The aperture-fed BDRA One way to deal with the asymmetrical radiation patterns and the low polarization purity of the above configurations is by replacing the coaxial probe with another coupling scheme that features high symmetry and low cross-polarization levels. A possible candidate is the aperture-coupling

156 5.3 THE APERTURE-FED BDRA 131 Return Loss [db] -1-2 x =1mm -3 x =4mm x =7mm frequency [GHz] Figure 5.1: Simulated (HFSS) return loss of the BDRA of Fig x=1 mm x=4 mm E-plane co-pol H-plane co-pol E-plane cross-pol H-plane cross-pol 24 x=7 mm Figure 5.11: Radiation patterns of the BDRA configuration of Fig. 5.9 at the frequency f =5.8 GHz for Δx = 1 mm, Δx =4mmandΔx = 7 mm. scheme that was discussed in Chapter 2. Coupling to the radiating element is achieved through an aperture that is etched in the ground plane of an open-ended microstrip line. In that way, the groundplane keeps the radiating element separated from the microstrip line and therefore the spurious radiation from the latter is avoided. A typical configuration of an aperture-fed BDRA is shown in Fig A bridge-shaped dielectric resonator of dimensions a 1, h 1, w 1, t and permittivity ε r,b is fed through an aperture of length l s and width w s that is

157 132 5 ADVANCED DRA CONFIGURATIONS a 1 h 1 PEC t a p r,b PEC w 1 w p l s w s w m h p P r,p y x (a) (b) Figure 5.12: Geometrical configuration of an aperture-fed BDRA. (a) General view. (b) Top view. etched on a groundplane of finite lateral dimensions. The microstrip line is a 5 Ω transmission line of width w m featuring a stub length P,chosen so that best matching is obtained. Finally, as a means of improving the coupling between the aperture and the dielectric bridge, a thin slab of dimensions a p, h p, w p and permittivity ε r,p is symmetrically positioned on top of the aperture. The DRA geometry shown in Fig is similar to the configuration presented in [38]. There, a notched RDRA of low dielectric permittivity was coupled inductively through a rectangular slot. The operational concept of this structure relied on the reduction of the RDRA s Q-factor through the introduction of a notch inside its volume. Therefore, the DRA bandwidth was enhanced, while the rest of the DRA s radiation characteristics were not significantly affected. The basic drawbacks of the notched low-permittivity DRAs were that first, the introduction of the notch resulted in the increase of the DRA s resonance frequency and second, the notch had to be small enough so that the patterns and the polarization would not be distorted. This prevented the introduction of any other radiating elements inside the resonator s empty space and hence, dual- or multi-mode operation was not easy to obtain. Besides, the introduction of a second radiating element could affect the DRA operation due to the significant amount of coupling between the two elements. The reason for that was the small confinement of the fields in the DRA volume resulting from the low value of the permittivity of the dielectric resonator. As opposed to the several limitations in the performance of the notched

158 5.3 THE APERTURE-FED BDRA 133 (a) Return Loss [db] -1-2 Simulation Measurement frequency [GHz] (b) Figure 5.13: (a) Fabricated prototype of the aperture-fed BDRA. (b) Simulated (HFSS) and measured return loss co-pol cross-pol 9 E-plane H-plane Figure 5.14: Measured radiation patterns of the aperture-fed BDRA. DRAs, the operational characteristics of the high-permittivity aperturefed BDRAs are particularly attractive. To investigate the properties of the aperture-fed BDRA, HFSS simulations were performed for a BDRA configuration featuring the following specifications: a 1 =2mm,h 1 = 16 mm, w 1 = 8 mm, t = 1 mm, ε r,b = 4, l s = 15mm, w s = 2 mm, w m =2.4mm, P =3.6mm, a p = 8 mm, h p =1mmw p =15mm. An antenna prototype was fabricated in order to experimentally validate the numerical results. The fabricated prototype is depicted in Fig (a). The plot of the BDRA s return loss versus frequency is illustrated in Fig (b), showing a good agreement between simulation and mea-

159 134 5 ADVANCED DRA CONFIGURATIONS surement. The structure is resonant at the frequency f = 3.8 GHz and its measured impedance bandwidth exceeds 11 per cent. Finally, the radiation patterns of the aperture-fed BDRA are illustrated in Fig at its resonance frequency. It can be observed that the patterns are broadside and symmetric along the z-axis (θ = ). Moreover, the polarization purity is very good (above 2 dbi) in both, the E- and the H-planes. Because of the low cross-polarization, the co-polarized gain has increased by around 4 db with respect to the gain of the probe-fed configuration of Fig. 5.1 (a). It is thus clear that the aperture-coupling scheme is more suitable for the feeding of the BDRAs as compared to the coaxial probe Advanced multi-band aperture-fed BDRAs Similarly to the case of the probe-fed BDRAs, some dual-mode aperture fed BDRA configurations will be investigated next. The BDRA coupled with a RDRA The first dual-mode BDRA that will be examined here has a similar geometrical configuration as the one depicted in Fig The main difference is that the dielectric slab of dimensions a p, h p, w p and permittivity ε r,p is not just used for the improvement of the matching between the aperture feed and the dielectric bridge, but it also serves as a radiating element. Hence, a dual-mode operation is obtained from the combination of the resonances of the high-permittivity bridge-shaped resonator and the dielectric slab. For the experimental validation of the simulations the antenna prototype of Fig (a) was fabricated. In that configuration, the dielectric bridge was the same as in the previously examined device, while the dielectric slab had dimensions a p =13.5mm, h p =13.5mm, w p =33mm and permittivity ε r,p = 1. The coupling scheme comprised an aperture of length l s = 19 mm and width w s = 4 mm, which was etched on the groundplane of a microstrip line of width w m =2.4mm. Finally, a stub length of P =6.8mm was used to ensure good impedance matching. Fig (b) illustrates the simulated and measured return loss of the device under investigation. It is observed that the device operates (S 11 < 1 db) around the frequencies 3.5GHz and 5.5 GHz that correspond to the frequencies of excitation of the BDRA mode and the RDRA mode

160 5.3 THE APERTURE-FED BDRA 135 (a) Return Loss [db] Simulation Measurement frequency [GHz] (b) Figure 5.15: (a) Fabricated prototype of the aperture-fed BDRA coupled to a RDRA. (b) Simulated (HFSS) and measured return loss. respectively. To verify the excitation of these two modes, the width w p of the dielectric slab was varied and its effect on the return loss of the device was examined. The results of this numerical study are summarized in Fig. 5.16, where the return loss of the dual-mode BDRA is illustrated for values of w p ranging between 9.5mmand13.5mm. The other dimensions of the BDRA remained the same. It can be observed in the figure that the variation of the width w p of the dielectric slab has a significant effect on the resonance frequency of the second mode (at the higher frequency). In contrast, the effect on the resonance frequency of the first resonant mode is much smaller. Hence, it can be concluded that the first resonance corresponds to the BDRA mode while the second one to the RDRA mode. The same conclusions are also drawn if one parameter of the bridge-shaped resonator is changed. In that case, there is a significant effect on the first resonance and a much weaker influence on the second one. It is interesting to note here that despite the fact that the two bridgeshaped resonators of Fig (a) and Fig (a) are identical, they are resonant at somewhat different frequencies (f =3.8 GHz and f = 3.5 GHz respectively). This is caused by the presence of the large dielectric slab in the second configuration, which contributes to the increase of the effective permittivity of the BDRA configuration and thus to the decrease

161 136 5 ADVANCED DRA CONFIGURATIONS Return Loss [db] w p =9.5 mm w p =11.5 mm w p =13.5 mm frequency [GHz] Figure 5.16: Simulated (HFSS) return loss of the dual-mode aperture-fed BDRA of Fig for different values of the slab width w p GHz E-plane co-pol H-plane co-pol E-plane cross-pol H-plane cross-pol GHz Figure 5.17: Measured radiation patterns of the dual-mode aperture-fed BDRA of Fig of the BDRA s resonance frequency. The radiation patterns of the dual-mode BDRA of Fig (a) are illustrated in Fig at the frequencies 3.5 GHz and 5.5 GHz. Broadside and symmetric radiation patterns are obtained at both frequencies, with the cross-polarization in both planes being quite low (below 15 dbi). The double-bdra To demonstrate the great design versatility provided by the high permittivity bridge-shaped resonator, the dual-band double-bdra of Fig. 5.18

162 5.3 THE APERTURE-FED BDRA 137 y t a 1 a 2 t h p h 2 h1 PEC w m w p w s l s w 2 P w 1 x a p (a) (b) Figure 5.18: Geometrical configuration of the dual-band double-bdra. (a) Side view. (b) Top view. will be described next. The double-bdra geometry consists of two dielectric bridges of dimensions a 1 =2mm,h 1 = 16 mm, w 1 =8mmand a 2 =1.5mm, h 2 =9.2mm, w 2 = 11 mm respectively, which are designed to operate at the same frequencies as those in the configuration described in the previous section. These two resonators have a uniform thickness t = 1 mm as well as the same dielectric permittivity ε r,b = 4. The feeding scheme comprises an aperture of length l s = 17 mm and width w s = 4 mm, while the microstrip line has a width w m =2.4mmandastub length P = 1 mm. Finally, a dielectric slab with dimensions a p = 7 mm, h p =1mm,w p = 25 mm and permittivity ε r,p =1isusedtoincrease the coupling between the aperture and the two bridge-shaped resonators. The fabricated prototype of the dual-band double-bdra is depicted in Fig (a). Fig (b) illustrates the plots of the simulated and measured return loss of the device as a function of frequency. It can be observed that a good agreement between the numerical and the experimental results has been achieved. In addition, a dual-band operation at the frequencies 3.5GHz and 5.5 GHz has been obtained for the device. To demonstrate the good operation of the double-bdra at these two frequencies, its measured radiation patterns in the E- and H-plane are shown in Fig It is observed that, as expected, the patterns are broadside and symmetric, while the polarization purity is within acceptable limits. As a final note for the aperture-fed BDRAs presented in the last sections, the operational principles of the dual-band BDRA can also be extended for the case of multi-band operation. For instance, a triple

163 138 5 ADVANCED DRA CONFIGURATIONS (a) Return Loss [db] Simulation Measurement frequency [GHz] (b) Figure 5.19: (a) Fabricated prototype of the dual-band double-bdra. (b) Simulated (HFSS) and measured return loss GHz E-plane co-pol H-plane co-pol E-plane cross-pol H-plane cross-pol GHz Figure 5.2: Measured radiation patterns of the dual-band double-bdra. BDRAs or a double-bdras coupled with a RDRA are bound to exhibit a reasonably well-behaved triple-band operation or also a wide impedance bandwidth through the merging of the three excited modes. The main limitation of this principle is associated with the fact that the increase in the number of radiating elements leads to an increase in the mutual coupling between the elements. However, even if such a problem is difficult to be handled analytically, the various numerical techniques that are nowadays available can help optimizing such structures for an operation at predetermined frequencies.