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Dual Polarized Geodesic Lens

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Dual Polarized Geodesic Lens DEGREE PROJECT IN TECHNOLOGY, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020 Dual Polarized Geodesic Lens Freysteinn Viðar Viðarsson KTH ROYAL INSTITUTE OF TECHNOLOGY ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Authors Freysteinn Viðar Viðarsson Information and Communication Technology KTH Royal Institute of Technology Place for Project Göteborg, Sweden Stockholm, Sweden Examiner Oscar Quevedo-Teruel Supervisor Astrid Algaba Brazalez (Ericsson) Martin Johansson (Ericsson) Lars Manholm (Ericsson) Oskar Zetterström (KTH) Nelson J. G. Fonseca (ESA) ii Abstract Gradient-index (GRIN) lens antennas, such as the Luneburg lens, posses attractive electromagnetic properties. The smooth change in refractive index ensures no internal reflections and the focusing of the electromagnetic waves results in a directive antenna. The main challenge of the design of a GRIN lens is acquiring the required refractive index. Two dimensional dielectric lenses can be realized using 3 dimensional homogeneous surfaces eliminating the challenge of discritizating the continuous change in refractive index. These type of lenses are commonly referred to as geodesic lenses. In this thesis a dual polarized geodesic lens antenna is presented. The antenna consists of two metal plates that form a parallel plate waveguide (PPW) section which is deformed to mimic the behaviour of a Luneburg lens. The antenna operates in the Ka band and polarizer unit cells are employed to alter the polarization state of the antenna. The polarizers are placed in a circular configuration in the flare of the antenna to maintain a compact design and good scanning range. Eleven waveguide feeds are used with 10° separation resulting in a scanning range of ±50° in the azimuth plane. The final design is a lens antenna with a center frequency of 28 GHz and 20 % bandwidth. Simulations of the design show reflection coefficients below -15 dB and crosstalk below -17 dB. The total efficiency at 28 GHz is 90 % and above 85 % for the full frequency band. iii Sammanfattning Lutningsindex-linsantenner (GRIN), till exempel Luneburg-linsen, har attraktiva elektromagnetiska egenskaper. Den jämna förändringen i brytningsindexet garanterar att inga interna reflektioner inträffar och fokuset av de elektromagnetiska vågorna resulterar i en direkt antenn. Den största utmaningen att utforma en GRIN-lins är att bestämma de brytningsindexen som behövs. Plana linser kan man förverkliga med användning av tredimensionella homogena ytor som eliminerar utmaningen att diskretisera den kontinuerliga förändringen i brytningsindex. Denna typ av lins kallas geodetisk lins. I detta examensarbete är en dubbelpolariserad geodetisk linsantenn designad. Antennen består av två metallplattor som bildar en parallell platt vågledare som är deformerad för att efterlikna beteendet hos en Luneburg-lins. Antennen fungerar i Ka- bandet och har polarisator enhetsceller för att ändra antennens polarisationstillstånd. Polarisatorerna placeras i en cirkulär konfiguration i antennen för att bibehålla en kompakt design och ett bra skanningsområde. Elva vågledare används med 10° separation vilket resulterar i ett skanningsområde på ±50° i azimutplanet. Den slutliga designen är en linsantenn med en mittfrekvens på 28 GHz och 20 % bandbredd. Simuleringar av designen visar reflektionskoefficienter under -15 dB och crosstalk under -17 dB. Den totala effektiviteten vid 28 GHz är 90 % och över 85 % för hela frekvensbandet. iv Acknowledgements The work of this thesis was done in the spring semester of 2020 at Ericsson Research in Gothenburg. I would like to thank my supervisor at Ericsson Astrid Algaba Brazalez, Lars Manholm, and Martin Johansson. They made me feel welcome at Ericsson and always had helpful suggestions. Sincere gratitude to my supervisor at KTH, Oskar Zetterström, and my examiner Oscar Quevedo-Teruel for their encouragement, technical support and help with the manufacturing process. Many thanks to Nelson J.G Fonseca from ESA for his invaluable inputs and contagious enthusiasm. Lastly thanks to my friends and family who are always there for me. Göteborg, September 2020 Freysteinn Viðar Viðarsson v Contents 1 Introduction 1 1.1 Background .................................. 1 1.2 Luneburg Lens ................................ 2 1.3 Geodesic Lenses ............................... 3 1.4 Prior Art .................................... 5 1.5 Industry Demand ............................... 7 1.6 Design Specifications ............................ 7 1.7 Thesis Outline ................................ 8 2 Theory 9 2.1 Geodesic Surfaces .............................. 9 2.2 Polarization .................................. 12 2.2.1 Linear Polarization .......................... 13 2.2.2 Circular Polarization ......................... 13 2.3 Co-Polarization and Cross-Polarization .................. 14 3 Lens Design 15 3.1 The ”Water Drop” Lens ........................... 15 3.2 Flare ...................................... 16 3.3 Feeding .................................... 17 3.4 Lens Layout and Results .......................... 19 3.5 Modifying the Lens Profile .......................... 22 3.5.1 The Modified Water Drop Lens ................... 25 4 Polarizer 29 4.1 Polarizer Unit Cell .............................. 29 4.2 Floquet Study ................................. 31 4.3 Integrating Lens and Polarizer ....................... 32 vi CONTENTS 5 Manufacturing and Adjustments 37 5.1 Polarizer ................................... 37 5.2 Stepped Horn ................................. 38 5.3 Feeding Network ............................... 39 6 Results 42 6.1 S-Parameters ................................. 42 6.2 Far Field Scanning Results ......................... 43 6.3 Losses .................................... 44 7 Future Work and Sustainability 48 7.1 Conslusion and Future work ........................ 48 7.2 Words on Sustainability ........................... 49 vii List of Figures 1.2.1 An illustration of how a Luneburg lens transforms a point source at its periphery to a plane wave on the opposite side of excitation. 3 1.2.2 Plot showing how the refractive index inside a Luneburg lens varies from the lens center. ................................ 4 1.3.1 An illustration how the folding idea can be implemented as proposed by Kunz [11] ................................... 5 2.1.1 (a) Refractive index distribution of the flat Luneburg lens. (b) The profile of the Rinehart-Luneburg lens. ................... 10 2.1.2 Illustration of a light beam bending when travelling between two different mediums where n2 > n1 ...................... 12 2.2.1 Propagating EM wave with linear polarization . 13 2.2.2Propagating EM wave with circular polarization . 14 3.1.1 Surface profile of the water drop lens with an aperture width of 107 mm. Blue dashed line shows the medium profile and the red lines the PPW implementation. Electric field distribution in the lens is included in the inset. ..................................... 16 3.2.1 Reflection coefficient of the flare. The flare has a length Lf = 14.5 mm and height Hf = 12 mm ........................... 17 3.3.1 Dimensions from data sheet of a WR28 [32] . 18 3.3.2The horn has 3 steps to transit from the height of the waveguide to the height of the lens. .............................. 18 3.3.3Cross-section of stepped horn showing relevant design dimensions. 18 3.3.4Reflection coefficients of transition from feed to lens profile. The inset shows how the model was simulated. ................... 19 3.4.1 (a) Top view of the bottom plate of the lens (b) Cross Section of the lens 20 3.4.2S-parameters when feeding port 6 ..................... 21 3.4.3Far field results when feeding port 6 .................... 21 viii LIST OF FIGURES 3.5.1 Strip of the lens profile with PMC boundaries in x-direction . 22 3.5.2An illustration of how lens profile is modified. Blue line shows the original profile and the red curve shows the profile after being modified 23 3.5.3Reflection coefficients of the lens strip with varied chamfering on the 1st bend ...................................... 23 3.5.4Reflection coefficients of the lens strip with varied chamfering on the 2nd bend ................................... 24 3.5.5 Reflection coefficients of the original lens strip and the lens strip with chamfer1 = 0.5 mm and chamfer2 = 0.35 mm . 24 3.5.6Comparison Between S-parameters of original lens profile and modified (a) Reflection Coefficients (b) Selected Crosstalk . 26 3.5.7 S-parameters of modified lens when feeding port 6 . 27 3.5.8S-parameters of modified lens when feeding port 1 . 27 3.5.9Electric field at 28 GHz on the lens (a) Port 1 being fed - Bottom plate (b) Port 6 being fed - Bottom plate (c) Port 1 being fed - Top plate (d) Port 6 being fed - Bottom plate ....................... 28 3.5.10Farfield results of the modified water drop lens. 28 4.0.1 General view of the polarizer functionality . 30 4.1.1 Polarizer unit cell .............................. 30 4.1.2 3-Layered polarizer configuration ..................... 31 4.2.1 Polarizer in CST with unit cell boundary conditions . 32 4.2.2Visualisation of the TE(0,0) and TM(0,0) modes of the Floquet ports . 32 4.3.1 Transmittivity of TM and TE waves with varying rotation on the last polarizer. ................................... 33 4.3.2Reflection coefficients of the integrated aperture . 33 4.3.3Selected crosstalk of integrated aperture . 34 4.3.4Far field results for port 1 and port 6 at 25.2, 28 and 30.8 GHz . 35 4.3.5Normalized radiation pattern of the lens with a flare
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