Generalized Principle of Pattern Multiplication and Its Applications 9789811935589, 9789811935596

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Modern Antenna

Junping Geng · Chaofan Ren · Kun Wang · Erwei Liu · Jing Zhang

Generalized Principle of Pattern Multiplication and Its Applications

Modern Antenna Editors-in-Chief Junping Geng, Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China Jiadong Xu, School of Electronics and Information, Northwestern Polytechnical University, Xi’an, Shaanxi, China Series Editors Yijun Feng, School of Electronic Science and Engineering, Nanjing University, Nanjing, Jiangsu, China Xiaoxing Yin, School of Information Science and Engineering, Southeast University, Nanjing, Jiangsu, China Gaobiao Xiao, Electronic Engineering Department, Shanghai Jiao Tong University, Shanghai, China Anxue Zhang, Institute of Electromagnetic and Information Technology, Xi’an Jiaotong University, Xi’an, Shaanxi, China Zengrui Li, Communication University of China, Beijing, China Kaixue Ma , School of Microelectronics, Tianjin University, Tianjin, China Xiuping Li, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China Yanhui Liu, School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China Shiwei Dong, National Key Laboratory of Science and Technology on Space Microwave, China Academy of Space Technology (Xi’an), Xi’an, Shaanxi, China Mingchun Tang, College of Microelectronics and Communication Engineering, Chongqing University, Chongqing, China Qi Wu, School of Electronics and Information Engineering, Beihang University, Beijing, China

The modern antenna book series mainly covers the related antenna theories and technologies proposed and studied in recent years to solve the bottleneck problems faced by antennas, including binary coded antenna optimization method, artificial surface plasmon antenna, complex mirror current equivalent principle and low profile antenna, generalized pattern product principle and generalized antenna array, cross dielectric transmission antenna, metamaterial antenna, as well as new antenna technology and development. This series not only presents the important progress of modern antenna technology from different aspects, but also describes new theoretical methods, which can be used in modern and future wireless communication, radar detection, internet of things, wireless sensor networks and other systems. The purpose of the modern antenna book series is to introduce new antenna concepts, new antenna theories, new antenna technologies and methods in recent years to antenna researchers and engineers for their study and reference. Each book in this series is thematic. It gives a comprehensive overview of the research methods and applications of a certain type of antenna, and specifically expounds the latest research progress and design methods. As a collection, the series provides valuable resources to a wide audience in academia, the engineering research community, industry and anyone else who are looking to expand their knowledge of antenna methods. In addition, modern antenna series is also open. More antenna researchers are welcome to publish their new research results in this series.

Junping Geng · Chaofan Ren · Kun Wang · Erwei Liu · Jing Zhang

Generalized Principle of Pattern Multiplication and Its Applications

Junping Geng Department of Electronic Engineering Shanghai Jiao Tong University Shanghai, China

Chaofan Ren Department of Electronic Engineering Shanghai Jiao Tong University Shanghai, China

Kun Wang Department of Electronic Engineering Shanghai Jiao Tong University Shanghai, China

Erwei Liu Department of Electronic Engineering Shanghai Jiao Tong University Shanghai, China

Jing Zhang Department of Electronic Engineering Shanghai Jiao Tong University Shanghai, China

Modern Antenna ISBN 978-981-19-3558-9 ISBN 978-981-19-3559-6 (eBook) https://doi.org/10.1007/978-981-19-3559-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Foreword

Phased array antennas are easy to achieve beam control and fast scanning, and have a wide range of applications in radar, communications and other fields. As people’s requirements for radar and communication detection and transmission continue increasing, correspondingly, higher requirements are placed on the performance of phased arrays. High-gain wide-angle scanning is a key performance bottleneck that urgently needs to be broken for phased arrays. The fixed element pattern in the traditional phased array has little or no contribution to the large-angle scanning beam gain. When the beam points to large angle, the equivalent spacing between the array elements becomes smaller and the coupling between the array elements increases, which limits the scanning range of the array. In order to broaden the scanning range of the array, a wide-beam antenna unit is usually applied to the array. However, the wide-beam antenna unit has the disadvantage of low gain, which have to sacrifice part of the array gain to achieve the wide-angle coverage. In another side, the cost of the phased array is very high, and it limits its application in many sides too. This book studies the high gain and wide-angle scanning array, and it presents the improvement and revolutionary to phase array from the new theory, new antenna and new array. The main results are as follows: 1.

2.

This book firstly proposed the generalized element factor (GEF), which means the pattern of a little aperture can be excited by several different independent modes. And the difference between these modes controls the radiation performance of the aperture, even the scanning properties of the small aperture. Then, the generalized principle of the pattern multiplication (GPPM) is proposed based on the generalized element factor. Then the array based on GPPM can simultaneously achieve high gain and wide-angle scanning, which is proved theoretically, and it greatly improves array performance. This book designs a dual-port phase mode antenna element. The element’s operating mode changes as the phase difference between the two ports changes, the pattern changes meanwhile. The simulated power flow distribution and pattern also verify multi-mode characteristics of the antenna. The experimental results are basically consistent with the simulation. The proposed phase mode antenna

v

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Foreword

3.

is used as an example of the generalized element factor (GEF) in the generalized pattern multiplication. On this basis, the phase mode antenna element is expanded into a 1*4 one-dimensional array to expand the scanning range. Experimental test results show that the antenna array achieves can scan −78°−78° and −70°−70° at 2.3 GHz and 2.4 GHz, respectively. This book designs a dual-port phase mode SSPPs antenna, which can scan in 3D free space. And further extend the SSPPs antenna to two kinds of 1D arrays with four elements, both of them perform 3D scanning with high gain and large range. It informs that the 1D array based on phase mode antenna and GPPM can realize 3D scanning, and it has good promotion to future radar and wireless communication.

Shanghai, China

Junping Geng

Acknowledgments The author would like to thank Prof. Ronghong Jin for his useful discussion. The author also would like to thank Lei Wang, Haobo Wu, Xuxu Cheng, Silei Yang, Jingzheng Lu, Weinan Gao, Da Su, Yangzhou Zhang, Rui Zhao, Xudong Tang, Ao Zhang, Haotian Li and Guolin Tong for their support and assistance during the manuscript preparation.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Concept and Connotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The New Development to Phased Array . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Large Angle Scanning Array—Wide Beam Unit . . . . . . . . . . 1.3.2 Large Angle Scanning Array–Tightly Coupled Array . . . . . . 1.3.3 Expand Scanning Angle of Array Based on Decoupling and Mutual Coupling Calibration of Array Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Ultra-Wide Angle Scanning Array Antenna Combined with Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.5 The Large Angle Scanning Array by Combining Electric Scanning with Mechanical Scanning . . . . . . . . . . . . . 1.3.6 Pattern Reconfigurable Antenna to Expand Array Scanning Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.7 Multi-Mode Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Development Trend and Problems of Phased Array . . . . . . . . . . . . . . 1.4.1 Development Trend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Development Problems of Phased Array . . . . . . . . . . . . . . . . . 1.5 Content Arrangement of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 5 5 6

13

2 The Basic Principle of Phased Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Antenna Electric Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Return Loss and Work Band of Antenna . . . . . . . . . . . . . . . . . 2.1.2 Input Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 The Parameters of Antenna Patterns . . . . . . . . . . . . . . . . . . . . 2.1.4 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.6 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Uniform Linear Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33 33 33 34 35 38 39 40 40

9

16 18 20 24 24 25 26 27

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2.3 Principle of Pattern Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Principle of Pattern Multiplication . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Ideal Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Wide Angle Scanning Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Millimeter Wave Array Based on Digital Coded Metamaterial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Wide Angle Scanning Array Based on the HIS . . . . . . . . . . . 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46 46 48 50

3 The Generalized Principle of Pattern Multiplication . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Phase Mode Element and the Generalized Element Factor . . . . . . . . 3.2.1 Ideal Phase Mode Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Generalized Element Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Phase Mode Element Array and the Generalized Principle of Pattern Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Generalized Array Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Generalized Principle of Pattern Multiplication . . . . . . . . . . . 3.3.3 Extended Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Comparison Among the Array Consist of Different Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Connotation and Boundary of the Generalized Principle of Pattern Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Connotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83 83 84 84 86

4 The Phased-Mode Slots Aperture Unit and Its Array . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Phase Mode Element Based on the Two Slots Aperture . . . . . . . . . . 4.2.1 Element Model [13, 14, 22] . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Element Electromagnetic Model . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Element Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Extended 1D Array with 0.7λ Elements Spacing [14, 22] . . . . . . . . . 4.3.1 Array Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Array Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Improved Compacted PMA [14, 22] . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Geometry Structure of the Improved Phase Mode Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 The EM Characteristics of the Improved Compacted Phase Mode Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Key Parameter Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 S Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95 95 96 96 100 101 106 107 107 112

50 64 81 82

88 88 90 91 92 93 93 93 93 93

112 112 115 116

Contents

4.4.5 Radiation Performances Varying with Phase Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Improved Compacted PMA Array with Smaller Elements Spacing 0.4λ [14, 22] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Configuration of the Array with ICPMA Based on GPPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Performances of the Array with ICPMA Based on GPPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Phased-Mode SSPPs Antenna and Its 1D Array to Scan in 3D Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Phase Mode SSPPs Antenna Element . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Element Electromagnetic Model . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Element Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Extended 1D Array: 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Array Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Array Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Extended 1D Array: 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Array Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Array Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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117 119 120 121 122 125 126 129 129 131 131 131 136 139 141 143 145 145 145 147 149

About the Authors

Dr. Junping Geng received his B.E degree in plastic working of metals, M.S. degree in corrosion and protection of equipment and Ph.D. degree in circuit and system from the Northwestern Polytechnic University, Xian, China, in 1996, 1999 and 2003, respectively. From 2003 to 2005, he was a Postdoctoral Researcher with Shanghai Jiao Tong University, Shanghai, China. In April 2005, he joined the faculty of the Electronic Engineering Department, Shanghai Jiao Tong University. He was promoted to an associated professor in 2008, and he is now a doctoral supervisor. From 2010 to 2011, he was a visiting scholar with the Institute Electrical and Computer Engineering, University of Arizona, AZ, USA. He is a committee member of Antenna Society of Chinese Institute of Electronics. And he has been the Senior member of IEEE in 2017, and he also is the editorin-chief of the Modern Antenna book series (Springer). Besides, he is among the editorial board of Nano Material, Journal of Antennas, and ever was among the editorial board of International Journal of Antenna and Propagation and International Journal of Aerospace Engineering. He has served as session chairs or member of Technology Program Committee (TPC) for more than 30 international conferences. He is mainly engaged in the teaching and research work on the fields covering antenna, array and electromagnetic theory, wireless communications, nanotechnology, etc. In 2015, he received the best paper award in IEEE MAPE 2015. In 2013, he was awarded the third rank xi

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About the Authors

of Shanghai Award for Natural Sciences. In 2010, he received the best paper award in IEEE iWAT2010. In 2008, he won the second prize of Chinese National Technology Innovation Awards as the third co-author. In 2007, he won the first prize of Technology Innovation Awards of the Ministry of Education as the fourth coauthor. In 2009, he won the second prize of “Hengshan Liangci” Excellent Paper. He won the Shanghai Jiao Tong University excellent annual assessment in 2007, 2014, 2016, 2017 and 2018, respectively, and he also won the third prize for excellent teachers in 2008, excellent in the appointment period 2014–2016 in Shanghai Jiao Tong University too. He won the third prize of postdoctoral award fund in 2006. So far he had published over 380 papers at home and abroad, more than 130 of them in international journals. He has applied over 150 invention patents, and 98 of them have been granted. Also, he has published four monographs of Omnidirectional Slots Antenna (Supported by “National science and technology academic works publishing fund in 2021”), Spoof Surface Plasmon Polarizations Antenna, Antenna Optimization and Design Based on Binary Coding, Smart Antenna in Wireless Communication and one textbook of Introduction to Computational Electromagnetism (Supported by Shanghai “Peak Plateau” discipline construction plan) and provided chapters for three books. He has been in charge of or involved in over 40 projects including National Natural Science Foundation of China, the State Key Program of National Natural Science, 173, 973, 863, Innovation group and Shanghai Research Projects.

About the Authors

xiii

Chaofan Ren received the B.S. degree in information engineering from Shanghai Jiao Tong University, Shanghai, China, in 2016, where he is currently pursuing the Ph.D. degree in electromagnetic and microwave technology. His current research interests include low-profile directional UWB antennas, low-profile omnidirectional antennas and phase mode SSPPs antennas.

Kun Wang received the B.S. degree in electronic and information engineering from the Hi-Tech College of Xi’an University of Technology, Xi’an, China, in 2012, and the M.S. degree in Electronic and Communication Engineering from Shanghai Jiao Tong University, Shanghai, China, in 2017, respectively, where he is currently pursuing the Ph.D. degree in electromagnetic and microwave technology with Shanghai Jiao Tong University, Shanghai, China. His current research interests include microstrip antennas, reconfigurable antennas and millimeter wave antennas. Erwei Liu received the B.S. degree in communication engineering from Harbin Institute of Technology, Weihai, China, in 2018, and the M.S. degree in electronic and communication engineering from Shanghai Jiao Tong University, Shanghai, China, in 2021, respectively. His current research interests include shared-aperture antennas and wide-angle scanning array.

xiv

About the Authors

Jing Zhang received the B.S. degree in communication engineering from Wuhan University, Hubei, China, in 2019, and she is currently pursuing the M.S. degree in electronic and communication engineering from Shanghai Jiao Tong University, Shanghai, China. Her current research interests include microstrip antenna, SSPPs antennas and array.

Abbreviations

A-CLPSO CP DGS DOA EBG EM Espar FBR GA GAF Gbps GEF GPPM HIS HPBW ICPMA LHCP MIMO MOM PMA RCS RHCP RMIM SLL SPPs SSPPs TCDAs THAAD TSA ULA UWA

Adaptive comprehensive learning particle swarm optimizer Circularly polarized Defected ground structure Direction of arrive Electromagnetic band gap Electromagnetic Electronically steerable parallel array antenna Front-to-back ratio Generalized array Generalized element factor Gigabit-per-second Generalized element factor Generalized principle of pattern multiplication High impedance surface Half power beam width Improved and compacted phase mode antenna Left-hand polarization Multi-input and multi-output Method of moment Phase mode antenna Radar cross section Right-hand polarization Receiving mutual impedance method Sidelobe level Surface plasmon polaritons Spoof surface plasmon polaritons Tightly coupled dipole arrays Terminal High Altitude Area Defense Tapered slot line antenna Uniform linear array Ultra-wide angle xv

List of Figures

Fig. 1.1

Fig. 1.2

Fig. 1.3 Fig. 2.1 Fig. 2.2 Fig. 2.3 Fig. 2.4 Fig. 2.5 Fig. 2.6 Fig. 2.7 Fig. 2.8 Fig. 2.9 Fig. 2.10 Fig. 2.11 Fig. 2.12 Fig. 2.13 Fig. 2.14

Fig. 2.15 Fig. 2.16

Printed wide slot array, a element structure, b 8 elements array. Figure reproduced with permission from Ref. [7], © 2014 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Element structure and it’s scanning pattern, phi2-phi1 = Δ∅aΔ∅ = 0°,θ = 0° bΔ∅ = 46°, θ = 30° cΔ∅ = 120°, θ = 50° dΔ∅ = 180°, θ = 59° e element structure. Figure reproduced with permission from Ref. [96], © 2020 IEEE . . . . . Dual port SSPPs antenna. Figure reproduced with permission from Ref. [97], © 2021 IEEE . . . . . . . . . . . . . . . Transmission line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normalized pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Antenna directional pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uniform linear array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common array antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1D linear array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two element pattern with various interval distance and excitation amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The pattern when d ≥ λ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-dimensional antenna array . . . . . . . . . . . . . . . . . . . . . . . . . . . The pattern of the two-dimensional array . . . . . . . . . . . . . . . . . . . N element antenna array with arbitrary arrangement . . . . . . . . . . Element factor of the ideal omnidirectional element . . . . . . . . . . 1 × 8 linear array with interval distance 0.5λ . . . . . . . . . . . . . . . . Array beam pointing to 0°, 30° and 60° for the linear array of eight ideal omnidirectional element with half-wavelength interspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Element factor of the half wavelength dipole . . . . . . . . . . . . . . . . Array beam pointing to 0°, 30°, 60° and 72° based on the half wave length dipole element . . . . . . . . . . . . . . . . . . . . .

7

23 23 34 36 36 41 42 43 44 45 45 46 47 48 48

49 49 50

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Fig. 2.17

Fig. 2.18

Fig. 2.19

Fig. 2.20

Fig. 2.21 Fig. 2.22

Fig. 2.23

Fig. 2.24

Fig. 2.25

Fig. 2.26

Fig. 2.27

List of Figures

The structure construction process (the digits being used for the grid setting in current Fig are shown in bold): a Step1; b Step 2. When setting the third grid around A which is already a grid of “1” (it is named B but it has been set to “1” in the initialization), the third digit is reversed and the next setting starts on it; c Step 3; d Step 4; e Step 2, 3 in the second circulation. f Step 4 in the second circulation and then it is ready for the third circulation. Figure reproduced with permission from Ref. [17], © 2009 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration of proposed antenna. a 3-D view of proposed antenna. b exploded view showing individual layers c Driven patch. d Parasitic patch. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . . . . . . . . . . . Binary codification of grid and its represent state (“0” represents substrate and “1” represents copper, “black” represents substrate and “yellow” represents copper). a Driven patch printed on substrate 1. b Parasitic patch printed on substrate 2. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The surface current distribution on the driven patch and parasitic patch for port 1 at 25 GHz a driven patch b parasitic patch. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated surface current phase distribution of the proposed antenna for port 1 at 25 GHz [18] . . . . . . . . . . . . . . . . . . . . . . . . . Simulated polarization of proposed antenna a Abs b Axial ratio c +45° polarization d -45° polarization. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . Simulated return loss and isolation of Ant 1 and Ant 2. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated radiation pattern of Ant 1 and Ant 2 for port 1 in x-o-z plane at 25 GHz. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . . . . . . . . . . . Simulated radiation pattern of Ant 1 and Ant 2. a The view of different layers b measurement environment. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . Measured and simulated S-parameters of proposed antenna. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measured and simulated realized gain of proposed antenna. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Figures

Fig. 2.28

Fig. 2.29

Fig. 2.30

Fig. 2.31

Fig. 2.32 Fig. 2.33

Fig. 2.34 Fig. 2.35 Fig. 2.36

Fig. 2.37

Fig. 2.38

Fig. 2.39 Fig. 2.40 Fig. 2.41

Fig. 2.42 Fig. 2.43 Fig. 2.44

Measured and simulated realized gain of proposed antenna for port 1. a 24 GHz b 27.5 GHz c 30 GHz. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . The model of antenna array. a The simulated model b The measured model. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated and measured beam scanning of wide-angle scanning array. a 24 GHz b 27.5 GHz c 30 GHz. Figure reproduced with permission from Ref. [18], © 2019 IEEE . . . . . Configuration of the low-profile dual-polarized antenna element: a Three-dimensional view of the antenna. b Detailed drawing of the antenna. Figure reproduced with permission from Ref. [23], © 2019 IEEE . . . . . . . . . . . . . . . Configuration of the unit cell of the HIS: a Simulated model. b Exploded view of the structure [24] . . . . . . . . . . . . . . . . Effects of different parameters on the reflection phase of the HIS: a Dimension of the unit. b Height of the substrate. c Gap between the metal patch [24] . . . . . . . . . . Dispersion diagram of the HIS [24] . . . . . . . . . . . . . . . . . . . . . . . . Configuration of the a conventional and b proposed HIS-based antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparisons of the simulation results on the conventional and proposed HIS: a Reflection phase. b Dispersion diagram. Figure reproduced with permission from Ref. [23], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparisons of the simulation results on the dual-polarized antenna based on conventional and proposed HIS: a Input impedance. b S-parameters [24] . . . . . . . . . . . . . . . . . . . . . . . . . . . S-parameters of different stages of the proposed antenna. Figure reproduced with permission from Ref. [23], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a Prototype of the proposed antenna. b Measurement environment of the antenna [24] . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated and measured S-parameters of the antenna [24] . . . . . Simulated and measured radiation patterns of the antenna. a E-plane at 2.2 GHz. b H-plane at 2.2 GHz. c E-plane at 2.5 GHz. d H-plane at 2.5 GHz. e E-plane at 2.8 GHz. f H-plane at 2.8 GHz [24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated and measured gains of the antenna. Figure reproduced with permission from Ref. [23], © 2019 IEEE . . . . . Top view of a HIS of the array. b Array [24] . . . . . . . . . . . . . . . . Simulated electric field distribution of the antenna element at a 2.1 GHz. b 2.2 GHz. c 2.3 GHz. d 2.5 GHz. e 2.6 GHz. f 2.7 GHz [24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Fig. 2.45

Fig. 2.46

Fig. 2.47 Fig. 2.48

Fig. 2.49

Fig. 2.50

Fig. 2.51

Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 3.4 Fig. 3.5 Fig. 3.6 Fig. 3.7 Fig. 3.8 Fig. 3.9 Fig. 4.1 Fig. 4.2 Fig. 4.3

Fig. 4.4

List of Figures

Simulated electric field distribution in y–o-z plane when the x-polarization of the element 4 is excited at a 2.0 GHz. b 2.1 GHz. c 2.2 GHz. d 2.3 GHz [24] . . . . . . . . . . . . . . . . Simulated electric field distribution in x-o-z plane when the y-polarization of the element 4 is excited at a 2.0 GHz. b 2.1 GHz. c 2.2 GHz. d 2.3 GHz [24] . . . . . . . . . . . . . . . . Simulated reflection phase of the proposed HIS with different incident angle [24] . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated electric field distribution in y-o-z plane when the x-polarization of the element 4 is excited at a 2.5 GHz. b 2.6 GHz. c 2.7 GHz. d 2.8 GHz [24] . . . . . . . . . . . . . . . . Simulated electric field distribution in x-o-z plane when the y-polarization of the element 4 is excited at a 2.5 GHz. b 2.6 GHz. c 2.7 GHz. d 2.8 GHz [24] . . . . . . . . . . . . . . . . a View of the array and measurement system. b View of the measurement environment. Figure reproduced with permission from Ref. [23], © 2019 IEEE . . . . . . . . . . . . . . . Simulated and measured beam scanning performance of the array at 2.5 GHz in a y-polarization and b x-polarization. Figure reproduced with permission from Ref. [23], © 2019 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GEF element pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of the phase mode antenna . . . . . . . . . . . . . . . . . . . . . . . Radiation patterns of the SSPPs antenna in the odd mode at 7.4, 7.7, 8.0 and 8.3 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation patterns of the SSPPs antenna in the even mode at 7.4, 7.7, 8.0 and 8.3 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arbitrary N element array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 × 8 linear array with interval distance 0.5λ . . . . . . . . . . . . . . . . GEF element pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Array constitute of GEF element . . . . . . . . . . . . . . . . . . . . . . . . . . Gain variation of the array constitute of three types of element while scanning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Antenna structure a 3-D dimensional schematic diagram, b front view, c back view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase mode antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated electric field distributions in x-o-y plane varies with the phase difference Δ∅ between the two ports. a port1 excited separately, b port2 excited separately, cΔ∅ = 0°, dΔ∅= 45°, eΔ∅ = 90◦ ,fΔ∅ = 120°, gΔ∅ = 180° . . . . . Simulated power flow distribution in x-o-z plane varies with the phase difference Δ∅ between the two ports, a port1 excited separately, b port2 excited separately, cΔ∅ = 0◦ ,dΔ∅ = 45◦ ,eΔ∅ = 90◦ ,fΔ∅ = 120◦ ,gΔ∅ = 180◦ . . . . . .

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List of Figures

Fig. 4.5

Fig. 4.6 Fig. 4.7 Fig. 4.8 Fig. 4.9

Fig. 4.10

Fig. 4.11

Fig. 4.12

Fig. 4.13

Fig. 4.14

Fig. 4.15

Fig. 4.16 Fig. 4.17

Simulated pattern in x-o-z plane varies with the phase difference Δ∅ between the two ports of the proposed antenna, a port1 excited separately, b port2 excited separately, cΔ∅ = 0◦ ,dΔ∅ = 45◦ ,eΔ∅ = 90◦ ,fΔ∅ = 120◦ ,gΔ∅ = 180◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fabricated prototype of the proposed antenna . . . . . . . . . . . . . . . . Comparison of the simulated and measured S-Parameters of the proposed multi-mode phase antenna . . . . . . . . . . . . . . . . . . The configuration of the phase-mode antenna with phase difference Δ∅ between dual ports . . . . . . . . . . . . . . . . . . . . . . . . . Measured and simulated pattern in x-o-z plane changes with the phase difference Δ∅ between the two ports at f = 2.3 GHz. a port1 excited separately, bΔ∅ = 0°, cΔ∅ = 45°, dΔ∅ = 90°, eΔ∅ = 120°, fΔ∅ = 180° . . . . . . . . . . . . . . . . Measured and simulated pattern in x-o-z plane changes with the phase difference Δ∅ between the two ports at f = 2.4 GHz. a port1 excited separately, bΔ∅ = 0°, cΔ∅ = 45°, dΔ∅ = 90°, eΔ∅ = 120°, fΔ∅ = 180° . . . . . . . . . . . . . . . . Measured and simulated patterns in x-o-z plane changes with the phase difference Δ∅ between the two ports at f = 2.5 GHz. a port1 excited separately, bΔ∅ = 0°, cΔ∅ = 45°, dΔ∅ = 90°, eΔ∅ = 120°, fΔ∅ = 180° . . . . . . . . . . . . . . . . Compare the measured gains with varied phase difference Δ∅ and the simulated gains, the measured direction of the lobe and the simulated direction of the lobe of the PMA at f = 2.4 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration of array by MPA based on GPPM, a array structure with uniform space distance da, and b the configuration principle of the array with phase shifters . . . . . Structure of the 1 × 4 array. a Front view and b side view of array, c phased array by PMA with phase shifters and feed net work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The measured scanning patterns of the array based on the PMA element at a 2.3 GHz, c 2.4 GHz and e 2.5 GHz, and the simulated scanning patterns of the array based on the PMA element at b 2.3 GHz, d 2.4 GHz and f 2.5 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compare the simulated and the measured gains varying with scanning angle at 2.3, 2.4 and 2.5 GHz . . . . . . . . . . . . . . . . . Antenna geometry. a Three-dimensional (3-D) view of the proposed improved compacted phase mode antenna. b Top view of the proposed improved compacted phase mode antenna. c Back view of the proposed improved compacted phase mode antenna . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Fig. 4.18 Fig. 4.19

Fig. 4.20 Fig. 4.21 Fig. 4.22

Fig. 4.23 Fig. 4.24

Fig. 4.25

Fig. 4.26

Fig. 4.27 Fig. 4.28

Fig. 4.29 Fig. 5.1

Fig. 5.2

Fig. 5.3

List of Figures

The configuration of the phase mode antenna with phase difference Δ∅ between dual ports . . . . . . . . . . . . . . . . . . . . . . . . . Simulated pattern in x-o-z plane varies with the phase difference Δ∅ between the two ports of the proposed antenna, a port1 excited separately, b port2 excited separately, c Δ∅ = 0°, d Δ∅ = 45°, e Δ∅ = 90°, f Δ∅ = 120°, g Δ∅ = 180° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effect of L 5 on |S11 | performance . . . . . . . . . . . . . . . . . . . . . . . . . Effect of h on gain and lobe directions of the multi-mode antenna with phase difference Δ∅ . . . . . . . . . . . . . . . . . . . . . . . . . The improved compacted phase mode antenna (ICPMA), a fabricated prototype of the ICPMA; b the configuration of the ICPMA with phase difference Δ∅ between dual ports . . . Comparison of the simulated and measured S-parameters of the proposed improved phase mode antenna . . . . . . . . . . . . . . Measured and simulated pattern in x-o-z plane changes with the phase difference Δ∅ between the two ports at f = 2.0 GHz. a port1 excited separately, b Δ∅ = 0°, c Δ∅ = 60°, d Δ∅ = 90°, e Δ∅ = 130°, f Δ∅ = 180° . . . . . . . . . . . . . . . Compare the measured gains with varied phase difference Δ∅ and the simulated gains, the measured direction of the lobe and the simulated direction of the lobe of the improved compacted PMA at f = 2.0 GHz . . . . . . . . . . . . Configuration of array by ICMPA based on GPPM, a array structure with uniform space distance da, and b the configuration principle of the array with phase shifters . . . . . Structure of the 1 × 4 array with improved compacted phase mode antenna. a Front view and b side view of array . . . . The measured scanning patterns of the array based on the PMA element at a 2.0 GHz, c 2.1 GHz, and the simulated scanning patterns of the array based on the PMA element at b 2.0 GHz, d 2.1 GHz . . . . . . . . . . . . . . . Compare the simulated and the measured gains varying with scanning angle at 2 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration of the SSPPs antenna with phased-mode. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of the SSPPs antenna with phased-mode. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current distributions in the SSPPs structure a odd mode, b even mode. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Figures

Fig. 5.4

Fig. 5.5

Fig. 5.6

Fig. 5.7 Fig. 5.8 Fig. 5.9

Fig. 5.10

Fig. 5.11

Fig. 5.12

Fig. 5.13

Fig. 5.14

Simulated E x component varies with the phase difference between the two ports of the proposed antenna. aΔϕ = 0◦ ,bΔϕ = 60◦ ,cΔϕ = 90◦ ,dΔϕ = 135◦ ,eΔϕ = 180◦ ,f only port1 excited, g only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . Simulated power flow varies with the phase difference between the two ports of the proposed antenna. a Top view of the proposed antenna, bΔϕ = 0◦ ,cΔϕ = 60◦ ,dΔϕ = 90◦ ,eΔϕ = 135◦ ,fΔϕ = 180◦ ,g only port1 excited, h only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . Simulated 3D pattern varies with the phase difference between the two ports of the proposed antenna. aΔϕ = 0◦ ,bΔϕ = 60◦ ,cΔϕ = 90◦ ,dΔϕ = 135◦ ,eΔϕ = 180◦ ,f only port1 excited, g only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . Fabricated prototype of the proposed antenna. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . The simulated and measured S-parameters. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . The simulated and measured gains varying with phase difference at 5.2 GHz. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated patterns in (Φ,θ ) coordinate space varies with the phase difference between the two ports of the proposed antenna. aΔϕ = 0◦ bΔϕ = 60◦ cΔϕ = 90◦ dΔϕ = 135◦ eΔϕ = 180◦ f only port1 excited g only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measured patterns in (Φ,θ ) coordinate space varies with the phase difference between the two ports of the proposed antenna. aΔϕ = 0◦ bΔϕ = 60◦ cΔϕ = 90◦ dΔϕ = 135◦ eΔϕ = 180◦ f only port1 excited g only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration of array by generalized principle of pattern multiplication. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration of array 1 based on the proposed antenna. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration of array 2 based on the proposed antenna a fabricated prototype, b simulated prototype. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . .

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Fig. 5.15

Fig. 5.16

Fig. 5.17

Fig. 5.18

Fig. 5.19

Fig. 5.20

Fig. 5.21

List of Figures

Four-element linear array with phase shifters and feeding network. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measured pattern of array 2 scanning along θ -direction. a (Φm , θm ) = (0°, 0°) at Δϕ = 180◦ and τ = 0◦ ; b (Φm , θm ) = (0°, 20°) at Δϕ = 180° and τ = -100°; c (Φm , θm ) = (0°, 40°) at Δϕ = 150° and τ = 170°; d (Φm , θm ) = (0°, 60°) at Δϕ = 100° and τ = 100°; e (Φm , θm ) = ( 0°, 73°) at Δϕ = 120° and τ = 50°. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . Simulated pattern of array 2 scanning along θ -direction. a (Φm , θm ) = (0°, 0°) at Δϕ = 180◦ and τ = 0◦ ; b (Φm , θm ) = (0°, 20°) at Δϕ = 180° and τ = -100°; c (Φm , θm ) = (0°, 40°) at Δϕ = 150° and τ = 170°; d (Φm , θm ) = (0°, 60°) at Δϕ = 100° and τ = 100°; e (Φm , θm ) = (0°, 73°) at Δϕ = 120° and τ = 50°. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . Measured pattern of array 2 scanning along Φ-direction. a (Φm , θm ) = (90°, 50°) at Δϕ = 100◦ and τ = 0◦ ; b (Φm , θm ) = (100°, 50°) at Δϕ = 60° and τ = 50°; c (Φm , θm ) = (110°, 50°) at Δϕ = 90° and τ = 90°; d (Φm , θm ) = (120°, 50°) at Δϕ = 0° and τ = 120°; e (Φm , θm ) = (140°, 50°) at Δϕ = 0° and τ = 170°. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . Simulated pattern of array 2 scanning along Φ-direction. a (Φm , θm ) = (90°, 50°) at Δϕ = 100◦ and τ = 0◦ ; b (Φm , θm ) = (100°, 50°) at Δϕ = 60° and τ = 50°; c (Φm , θm ) = (110°, 50°) at Δϕ = 90° and τ = 90°; d (Φm , θm ) = (120°, 50°) at Δϕ = 0° and τ = 120°; e (Φm , θm ) = (140°, 50°) at Δϕ = 0° and τ = 170°. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . Configuration of array 3 based on the proposed antenna. a Fabricated prototype, b simulated prototype. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . Measured pattern of array 3 scanning along θ -angle. a (Φm , θm ) = (90°, 90°) at Δϕ = 0◦ and τ = 50◦ ; b (Φm , θm ) = (90°, 70°) at Δϕ = 0° and τ = 70°; c (Φm , θm ) = (90°, 50°) at Δϕ = 0° and τ = 100°; d (Φm , θm ) = (90°, 30°) at Δϕ = 180° and τ = 160°; e (Φm , θm ) = (90°, 10°) at Δϕ = 180° and τ = 250°; f (Φm , θm ) = (90°, 0°) at Δϕ = 180° and τ = 0° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Figures

Fig. 5.22

Fig. 5.23

Simulated pattern of array 3 scanning along θ -angle. a (Φm , θm ) = (90°, 90°) at Δϕ = 0 ◦ and τ = 50◦ ; b (Φm , θm ) = (90°, 70°) at Δϕ = 0° and τ = 70°; c (Φm , θm ) = (90°, 50°) at Δϕ = 0° and τ = 100°; d (Φm , θm ) = (90°, 30°) at Δϕ = 180° and τ = 160°; e (Φm , θm ) = (90°, 10°) at Δϕ = 180° and τ = 250°; f (Φm , θm ) = (90°, 0°) at Δϕ = 180° and τ = 0°. Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . . Measured and simulated pattern of Array 3 scanning along Φ-angle. Measured results: a (Φm , θm ) = (90°, 50°) at Δϕ = 120◦ and τ = 140◦ ; b (Φm , θm ) = (90°, 70°) at Δϕ = 60◦ and τ = 100◦ ; and c (Φm , θm ) = (90°, 90°) at Δϕ = 0◦ and τ = 50◦ ; simulated results: d (Φm , θm ) = (90°, 50°) at Δϕ = 120◦ and τ = 140◦ ; e (Φm , θm ) = (90°, 70°) at Δϕ = 60◦ and τ = 100◦ ; and f (Φm , θm ) = (90°, 90°) at Δϕ = 0◦ and τ = 50◦ . Figure reproduced with permission from Ref. [32], © 2021 IEEE . . . . . . . . . . . . . . .

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List of Tables

Table 2.1 Table 2.2 Table 2.3 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 4.5 Table 4.6 Table 4.7 Table 4.8 Table 4.9

Table 4.10 Table 4.11 Table 4.12 Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5

Optimized geometric parameters of the proposed antenna . . . . Comparisons between the proposed antenna and other models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimensions of the HIS-based low-profile dual-polarized antenna element (unit: mm) [23] . . . . . . . . . . . . . . . . . . . . . . . . . Parameters of the proposed phase-mode antenna . . . . . . . . . . . . Optimized parameters of the proposed antenna . . . . . . . . . . . . . Main lobe direction and the gain of the proposed phase-mode antenna in different modes . . . . . . . . . . . . . . . . . . . Optimized combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimized phase difference combination of Δ∅ and α . . . . . . . Comparison with other phased array . . . . . . . . . . . . . . . . . . . . . . Parameters of the proposed phase mode antenna . . . . . . . . . . . . Optimized parameters of the proposed antenna . . . . . . . . . . . . . Main lobe direction and the gain of the proposed improved compacted multimode antenna in different mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimized combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimized phase difference combination of Δ∅ AND ζ . . . . . Comparison with other reported phased array . . . . . . . . . . . . . . Comparison with other reported SSPPs antenna and phase-mode antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The scanning capability of the antenna element controlled by phase difference Δϕ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimized phase difference combination of Δϕ and τ when array 2 scanning along θ -direction . . . . . . . . . . . . . . . . . . Optimized phase difference combination of Δϕ and τ when array 2 scanning along ϕ-direction . . . . . . . . . . . . . . . . . . Optimized phase difference combination of Δϕ and τ when array 3 scanning along θ -direction . . . . . . . . . . . . . . . . . .

55 63 67 97 102 107 108 108 111 113 116

119 121 121 124 138 140 142 142 145

xxvii

xxviii

Table 5.6 Table 5.7

List of Tables

Optimized phase difference combination of Δϕ and τ when array 3 scanning along ϕ-direction . . . . . . . . . . . . . . . . . . Comparison with other reported phased array . . . . . . . . . . . . . .

145 148

Chapter 1

Introduction

Abstract This chapter introduces the key concepts of this book, and described the background to study the generalized principle of pattern multiplication. Then the new developments of the phased array were reviewed. The development trend and problems of phased array are summarized, which are just what we proposed the generalized principle of pattern multiplication to solve in this book.

1.1 Concept and Connotation (1)

Phase mod antenna, (PMA)

The radiation of the antenna aperture is essentially the sum (or integral) of the radiated electrical field outside the aperture of current distribution. The standing current distribution on the aperture is also called the mode, and each mode corresponds to an electromagnetic radiation pattern. If a single antenna aperture is excited by multiple current distribution modes (J1, J2, J3…), the far fieldΣ is just the vectors sum of the N E n . In addition, to these electrical field in far field region of each current mode, n=1 current distributions (J1, J2, J3…) being excited in the antenna aperture, if their initial phases are different, they can be described as (J1(ϕ10 ), J2(ϕ20 ), J3(ϕ30 ) . . .). For a given set of phases (ϕ10 , ϕ20 , ϕ30 . . .), the antenna unit aperture has a determined far-field pattern corresponding to it. If ( the initial phase ) corresponding to each current mode in the aperture changes, i.e. ϕ1j , ϕ2j , ϕ3j . . . , a new sequence, the antenna element aperture has a new far-field pattern corresponding to it. So, the antenna aperture is the phase mode antenna. Besides the far field of the aperture varies with the phases of these modes, the polarization or other characters of the aperture may change with the phases of these modes. (2)

Generalized element factor (GEF)

For a multi-port phase mode antenna element, when the element is expanded to an array, the normalized pattern of the element is called generalized element factor. As mentioned above, the generalized element factor is determined by the pattern of the mixed current distribution excited by the excitation signals from multiple ports and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 J. Geng et al., Generalized Principle of Pattern Multiplication and Its Applications, Modern Antenna, https://doi.org/10.1007/978-981-19-3559-6_1

1

2

1 Introduction

their initial phases. When the phase difference of the excitation signals between these ports are changed, the far-field radiation characteristics (beam direction, polarization, etc.) of the antenna unit aperture will change accordingly. When the phase difference of each mode changes slowly and uniformly, it is a steady-state generalized element factor. When the phase differences of each mode changes with time, the generalized element factor is called time-varying generalized element factor. ( ( ( ) )) f e = f e φ, θ, φem ϕ1 (t), ϕ2 (t), . . . ϕ p (t) , θem ϕ1 (t), ϕ2 (t), . . . , ϕ p (t)

(1.1)

where φ is the azimuth, and θ is the angle( with Z axis, (φem , θem) ) is the main lobe direction when the excitation phases are ϕ1 (t), ϕ2 (t), . . . ϕ p (t) to all ports (1, 2, …, p) of this element aperture. (3)

Generalized array factor (GAF)

For array extended by the multi-port phase mode antenna element, the phase difference between each phase mode antenna element can be given, which is similar to the array factor of traditional array. The array factor of phase mode antenna array can be regarded as the normalized pattern synthesized by the array of omnidirectional elements. When the phase difference between each phase mode antenna element changes with time, the array factor is time-varying generalized array factor. Because the phase mode antenna units work with multi-mode aperture, the phase difference between antenna units is only the phase difference between the geometric centers of the corresponding aperture units, not necessarily the phase difference between the corresponding mode phase centers of each aperture. f a = f a (φ, θ, φam (τ1 (t), τ2 (t), . . . τn (t)), θam (τ1 (t), τ2 (t), . . . , τn (t)))

(1.2)

where φ is the azimuth, and θ is the angle with Z axis, (φam , θam ) is the main lobe direction when the excitation phases are (τ1 (t), τ2 (t), . . . τn (t)) to all ports (1, 2, …, n) of every element aperture. (4)

Generalized principle of pattern multiplication (GPPM).

The multi-port phase mode antenna element is expanded into a uniform array. When the multi-mode phase mode antenna elements work synchronously, the far field of the array is the vector superposition of the far field of all the elements. Finally, the pattern of the array is the product of the generalized element factor and the generalized array factor, which is the generalized pattern product principle, f = f e · f a . In the generalized principle of pattern multiplication, both the generalized element factor and the generalized array factor can control the beam characteristics, and the product of the two factors can control the beam characteristics of the array together. (5)

Generalized array (GA)

When the multi-port phase mode antenna element is expanded into an array, the radiation characteristics of the antenna element aperture can be controlled by the

1.2 Background

3

phase difference and amplitude of multiple excitation ports of the element, and the radiation characteristics of the array can also be controlled by the layout of the array and the overall phase difference of different element aperture. Such array is called generalized array.

1.2 Background Since its birth, phased array antenna has been widely used for its flexible beam scanning characteristics. In the past half century, with the progress of signal processing and semiconductor material technology, the performance and application range of phased array antenna have been greatly improved. Phased array antenna has been well promoted and applied in land-based, space-based, sea based and space-based systems. At the same time, it also promotes the rapid development of radar, wireless communication and deep space exploration. But phased array antenna also has its inherent defects. In traditional array, the antenna elements work in a single mode, the aperture efficiency is limited, the element pattern is fixed, the element contributes to the scanning gain in a limited angle, and the contribution to other angles is very small or almost zero. When scanning at large angle, the coupling between elements has a great influence, so that the array can only scan effectively within ±45° of the normal direction of the main radiation surface. These have become the bottleneck for the further development of many detection systems. The current international environment is not peaceful, and the competition among countries in advanced military equipment is increasingly fierce, which puts forward higher performance requirements for phased array antenna of radar and communication. For example, in the field of aerospace, the limited search airspace means that the ground air defense radar can not quickly warn the fatal strike from some areas. For the space-based exploration system, the limited exploration airspace is not conducive to the comprehensive collection of signals from space or ground. The intersection and docking technology of high-speed spacecraft and space station has always been regarded as a barrier of space development. In order to achieve a wide range of target acquisition, the angle coverage of microwave radar is required to be very wide. But at present, the international system has not exceeded the ±60° scanning angle. For example, the scanning range of the third generation of microwave intersection radar used by American space flight aircraft has reached 360° × 120°. With the increase of the range of the long-range guidance section in the followup space engineering intersection and docking mission, the scanning angle of the intersection radar must be larger, which puts forward higher requirements for the ultra-wide angle scanning ability of the antenna. Low earth orbit remote sensing satellite can only establish satellite ground data transmission link when the satellite goes over the top to transmit a large amount of remote sensing data to the ground station, so the larger the scanning angle of the planar phased array antenna on the satellite, the longer the data transmission time and the larger the data transmission

4

1 Introduction

capacity, and the less the number of ground stations is required; on the other hand, in order to increase the field of view of the remote sensor, the attitude of the satellite platform should be adjusted frequently It will also make the planar phased array antenna of the data transmission system deflect, which also puts forward higher requirements for the ultra-wide angle scanning ability of the planar phased array antenna. In addition, with the increase of space garbage and debris, the risk factor of spacecraft in space increases rapidly. The spacecraft needs to be able to detect the surrounding space debris from all angles, and the antenna array on the spacecraft also needs to be able to quickly achieve ultra-wide angle beam scanning. At present, the stratospheric airship platforms developed by many countries are in urgent need of ultra-wide angle scanning/switching array antenna due to the drastic changes of stratospheric airflow and flight attitude. Phased array radar with large scanning angle plays an important role in air defense weapon, measurement and control system, electronic reconnaissance and countermeasure system. It can find targets in a large range of airspace and provide fast and accurate information for search, detection, recognition, acquisition and tracking. Obviously, whether it is radar system, electronic countermeasure system or communication system, in order to expand its target search range, improve its survivability and combat capability, it is urgent to achieve higher gain and high gain large angle scanning in the limited aperture, expand the beam scanning range of phased array to quasi hemispherical or full hemispherical (±90°) space, and at the same time, it is also necessary to be able to anti-interference. With the increase of beam scanning angle, the equivalent spacing between adjacent elements decreases, the coupling increases, the equivalent aperture decreases, the scanning beam widens, and the antenna gain decreases sharply, which makes the typical beam scanning range of planar phased array within (±45°). Although there are many researching attempts in expanding the scanning angle range of planar phased array antenna, the main improvements are some technologies, which can expand the scanning angle to about ±60°, or have good scanning characteristics in a certain local angle range, and the cost is very high. Non planar antenna technology is also used to increase the scanning angle range, but the increase of antenna array profile height is difficult to adapt to the surface conformal installation of high-speed moving carrier. Therefore, it is difficult to improve the performance of phased array in gain, scanning angle and anti-interference at the same time under the existing phased array system. It is urgent to find the reason of limited performance improvement of phased array in theory, explore new system and method in principle, and systematically study and solve the problem of Limited performance of phased array combined with new theory and technology. It is also one of the hot spots and difficulties in the current academic and engineering applications, which has very important academic significance and engineering application value.

1.3 The New Development to Phased Array

5

1.3 The New Development to Phased Array The main reasons for the limited beam scanning range of planar antenna array include the following two aspects: on the one hand, the beam width of the antenna element itself is limited in the limited space angle range (generally ±45o in the positive direction of the element), so that the energy radiation of the array can’t be radiated to the whole space area, but can only be limited in a certain range. On the other hand, due to the mutual coupling between the antenna elements, when the array scans to a large angle in space, the effective spacing of the elements decreases, the coupling between the elements increases rapidly, and the radiation efficiency of the array decreases rapidly, resulting in the decrease of radiation gain, the broadening of beam, the total reflection or storage of energy, and the blind spot of scanning. At present, researchers at home and abroad have made a lot of explorations and attempts to expand the beam scanning range of planar phased array.

1.3.1 Large Angle Scanning Array—Wide Beam Unit The actual antenna element doesn’t radiate omni-directionally. If the influence of the floor is considered, the beam of the antenna element will be narrower. The beam width of the antenna unit essentially determines the beam scanning range of the array. Therefore, the wide beam antenna unit is helpful to realize the wide angle scanning phased array. At the same time, the planar phased array antenna can’t achieve large-scale scanning due to the mutual coupling effect between the elements, which deteriorate the pattern of the elements and the impedance matching. For the planar phased array composed of ordinary microstrip patch, the optimal scanning range is only within ±45°, which limits the spatial search area of the planar phased array antenna. The improved phased array antenna based on the wide beam antenna element can complete two-dimensional large angle scanning. This kind of wide beam makes the radiation energy of the element itself cover the space area as much as possible, so that the phased array antenna can complete the large angle energy coverage. The types of elements with large angle scanning potential include slot antenna (linear conical slot, exponential conical slot, etc.), dipole antenna (coaxial dipole, printed microstrip dipole, etc.), spiral antenna (planar spiral, four arm spiral antenna, etc.) and wide beam microstrip antenna, etc. It should be emphasized that the radiation pattern of dipole antenna is always omnidirectional on H plane, while the radiation beam width on E plane is only about 60°. This kind of beam characteristic is more suitable for two-dimensional phased array antenna element with one side wide beam and the other side narrow beam. In addition, the spiral antenna can achieve broadband and circular polarization. It should also be emphasized that the wide beam microstrip antenna also has the advantages of low profile, easy integration and conformal.

6

1 Introduction

In reference [1], a new type of double-layer tapered slot line antenna (TSA) element and it’s combined phased array antenna are introduced. The antenna element works in X-band and is fed by coplanar waveguide. The results of literature shows that the TSA element with end fire characteristic has a very wide beam width, and the beam width of E-plane and H-plane is more than 120°. In reference [2], the resonant microstrip meander line antenna is used as the element, and the 3 dB beam width of the antenna element exceeds 130°. The planar phased array with this element can achieve the main beam scanning range of ±60°. In reference [3], J. A. Kasemodel et al. realized wide beam radiation pattern by using the tightly coupled dipole, and constructed a 8 × 8 microstrip array based on this antenna element, realizing the beam scanning range of ±70° in E plane and ±60° in H plane. In reference [4], S. E. V. Lavan et al. designed a wide beam crossed L-shaped dipole element working in Xband and Ku band. The 7 × 7 planar array achieved wide angle scanning performance of 60° in X-band and 50° in Ku band. However, the antenna array with wide beam element still can’t overcome the problems of gain reduction caused by the wide beam element and the increased mutual coupling between elements at large angle which result from the decrease of equivalent element interval distance. Although the tightly coupled antenna broadens the beam by coupling, the radiation efficiency of the array is not high. In the 1980s, due to the maturing of electronic computers, VLSI, solid-state power devices, phase shifters suitable for various band, and the substantial reduction of cost, as well as the continuous development of digital beamforming, adaptive theory and technology, low sidelobe technology and intelligent theory and technology, the onedimensional and two-dimensional phased array radars are becoming more and more cost-effective, so the 1980s is the era that phased array radar in the world achieves great development. Advanced countries have developed a variety of tactical phased array radars for different purposes, and China is no exception. By 1993, phased array radar was not only widely used in military land, sea, air and space, but also extended from military to civil fields [5, 6].

1.3.2 Large Angle Scanning Array–Tightly Coupled Array Shanghai Jiao tong University has designed a printed wide slot antenna with back cavity [7, 8], which has wide beam characteristics and is suitable for large angle scanning. The antenna adopts inverted π feed structure, which is composed of three tuning branches. The parasitic impedance caused by coaxial transmission probe feed is compensated by adjusting the size of the branches, and the impedance bandwidth of the antenna is broadened by the branches at both ends. When the height between the metal back cavity and the slot is one fourth, the input impedance of the slot matches the impedance of the microstrip line, and the antenna element achieves the maximum radiation gain. The side wall of the metal cavity is concave, the directional radiation pattern is formed by the antenna element, and the E-plane pattern in the

1.3 The New Development to Phased Array Fig. 1.1 Printed wide slot array, a element structure, b 8 elements array. Figure reproduced with permission from Ref. [7], © 2014 IEEE

7

Metal

Feed

Grooved back cavity

CPW

Coaxial wire

(a)

(b)

whole working frequency band has a wide beam. The 3 dB beam width in the E-plane is 122°, and the 3 dB beam width in the H-plane is 88° (Fig. 1.1). In reference [9], Chengdu University of Electronic Science and technology has designed a wide-angle scanning phased array based on the pattern reconfigurable antenna elements which use the artificial electromagnetic materials. The pattern reconfigurable antenna element is composed of parallel parasitic arrays with compact spacing between the dipoles. By loading PIN diodes on the parasitic dipoles, two switchable states are realized, and the main beam direction points to the left and right sides respectively. When the array scans to different spatial positions (y < 0 and y > 0), the beam of the pattern reconfigurable antenna unit points to the left and right-side area respectively. Finally, the scanning range of the main beam is ±88°, which greatly expands the scanning range of the traditional planar phased array. Reference [9] also proposes a linear array based on high impedance surface printed circuit board. The array achieves a beam scanning range of ±85°. In the whole scanning space, the sidelobe level of the array is kept within −10 dB, and the gain fluctuation is about 3 dB. At the same time, the application of artificial electromagnetic materials and pattern reconfiguration technology in phased array can break through the problem of narrow beam scanning range of planar phased array. However, the scanning beam obtained by this method is still wide and the gain

8

1 Introduction

fluctuation is large, and the problem of increased coupling owing to the equivalent interval distance reduction when scanning to the large angle cannot be avoided. In reference [10], domestic scholars have effectively reduced the mutual coupling between array elements by means of polarization diversity, but they can’t completely eliminate the influence of mutual coupling on the received signal, so there are still some errors in the later signal processing. In reference [11], domestic scholars have effectively suppressed the coupling effect between antenna elements by using symmetrical U-shaped DGS structure in microstrip array antenna elements. However, this method is mainly effective for antenna operates in single frequency, but it is still a difficult problem for mutual coupling calibration for elements operating in dual band or multi band, which needs further study. In reference [12], domestic scholars have designed two kinds of uniform electromagnetic band gap structures to cover the two working bands of the antenna respectively, and then cascade the two structures and load them between the two slot antenna elements. Simulation analysis and experimental results show that the cascaded EBG structure can effectively suppress surface waves and reduce mutual coupling in both frequency bands. The EBG structure can effectively reduce the coupling between the elements of the array antenna. However, when applied in the actual processing, the inherent periodic structure of the structure is complex, which often makes the processing difficult. In addition, this method needs to design different resonant elements, and the design cost is high. In reference [13], domestic scholars have designed a MIMO antenna which uses broadband T-shaped neutral line to increase isolation. The antenna consists of a broadband T-shaped neutral line printed on the front of the substrate. The T-shaped neutral line has three branches. The structure of branch 1 and branch 2 are the same, and they are respectively connected with antenna element 1 and antenna element 2 to form coupling path 1. Branch 3 is connected with the system floor, and branch 1 or branch 2 and branch 3 form coupling path 2. Simulation results show that good isolation is achieved. The advantage of this method is that it does not occupy space in structure, and the disadvantage is that it absorbs part of the energy of the radiation element, and the radiation efficiency is low. It only decreases the coupling between the elements in a narrow working frequency band, and designs different coupling branches for different antennas, so it is not universal. In reference [14], domestic scholars proposed a decoupling network design method based on power integrity analysis, that is, by designing a reasonable decoupling network, the impedance of power distribution network is controlled below the target impedance in frequency domain, so that the power noise can meet the requirements of noise tolerance and achieve the purpose of decoupling. The main defect of this method is that the frontend decoupling network is loaded between the antenna feed port and the active device, which introduces large channel insertion loss and sacrifices the efficiency of the antenna. In addition, although this method can be analyzed independently from the antenna element to a certain extent, it has certain versatility, but the network size is large in structure, which can’t meet the needs of miniaturization, so its application is limited. In reference [15], domestic scholars have also proposed a uniform circular array direction finding antenna receiving mutual impedance test and mutual coupling

1.3 The New Development to Phased Array

9

compensation system. According to the receiving mutual impedance theory, the receiving mutual impedance matrix of uniform circular array is established. Then, mutual coupling compensation is carried out on the direction-finding terminal processor in the working frequency point when the direction-finding equipment works, so as to make the direction-finding equipment output more accurate. Both open circuit voltage method and receiving mutual impedance method have inherent disadvantages. For the actual array, the radiation pattern is greatly affected by the scattering of the array structure; the stronger the scattering of the structure, the greater the difference between the algorithm weighted pattern and the actual pattern. Because the line antenna is a kind of antenna with the least scattering effect, the open circuit voltage method and the receiving mutual impedance method are more suitable for the array composed of line antennas. There are few researches on the mutual coupling calibration of planar antennas such as microstrip antennas by these two methods.

1.3.3 Expand Scanning Angle of Array Based on Decoupling and Mutual Coupling Calibration of Array Antenna The traditional array antenna is mainly used in the military field at first. Finding the target and determining the direction of the enemy signal are the primary task in electronic warfare. Beamforming is also the application of traditional array antenna in radar system, which can scan in the space area based on the phase shifter. In the previous research work, people seldom consider the realization of antenna array itself, but think that each antenna element is ideal and does not interfere with each other. With the development of demand, the application of traditional array antenna is also facing new challenges, such as the compactness and concealment of structure, the timeliness and accuracy of information processing. Due to the requirements of miniaturization and modularization of modern equipment, the antenna element is becoming more and more miniaturized, and the array is becoming more and more compact. The mutual coupling between the array antenna elements have become an important factor that can’t be ignored. Due to the coupling effect, the spatial and surface fields of the coupled element are no longer the same as those of the isolated element. Some other parameters, such as current distribution, radiation power, radiation impedance and input impedance are different from the isolated element. In recent years, owing on the influence of mutual coupling between antenna elements in the array, the research on mutual coupling characteristics and the method of realizing mutual coupling calibration has become the research hotspot of many scholars at home and abroad, which aims at improving the performance of the array. There are two kinds of decoupling and mutual coupling compensation methods for array antennas.

10

1.3.3.1

1 Introduction

Restraining Coupling/Decoupling Method on Structure

The first method of mutual coupling calibration is to optimize the antenna design. This kind of method is mainly applied to the decoupling calibration of each element in MIMO system and to increase the isolation between units. The purpose of reducing coupling and increasing isolation is achieved mainly by spatial, polarization and pattern diversity. Many scholars have studied the influence of diversity on mutual coupling, such as adjusting the position of antenna unit, polarization mode and beam pointing angle to reduce mutual coupling. The purpose of reducing mutual coupling is achieved by polarization diversity of different array elements [16–22]. Defected ground structure (DGS) affects the current distribution on the microstrip line floor by opening a certain shape of gap, which will change the inductance and capacitance characteristics of the transmission line. It can be equivalent to an LC resonant circuit. Because of this characteristic, DGS is widely used in the design of filters and antennas to suppress harmonics, suppress cross polarization level of patch antennas, and increase mutual isolation between array elements [23–26]. This method mainly concentrates on the designs of structure, such as the length, position, number of gaps and so on. Periodic resonant structure can reduce the mutual coupling between array elements by adding resonant elements or periodic structure between array elements. Electromagnetic band gap (EBG) structure has the characteristics of high impedance surface and surface wave suppression, which is a common structure for mutual coupling suppression. This structure is composed of a group of metal structures which are raised or suspended on a plane metal plate, and has periodic array structure. In the EBG structure, the adjacent metals are equivalent to capacitors, and the connected metals are equivalent to inductors, which can be equivalent to resonant LC circuits. This makes it impossible for the current to flow from the metal surface and achieves high electromagnetic impedance characteristics. This characteristic makes EBG structure widely used in microstrip array antenna to reduce the coupling between elements. The stub loaded and neutral line loading technology can increase the isolation between antennas and reduce mutual coupling by adding coupling branches on the floor between antenna elements [27–29]. According to the superposition principle of the electric field, the coupling effect between the antenna elements and the influence of the loaded coupling branches are superimposed to realize the purpose of counteracting the mutual coupling between the elements. The purpose of decoupling is achieved by adding additional coupling paths to achieve current neutralization or phase cancellation. Matching network suppresses coupling, which reduces mutual coupling between array elements by designing decoupling network. The coupling between elements is regarded as circuit parameters, and the elements of front-end network are designed by matrix operation to counteract the coupling. The existing decoupling network design can be roughly divided into two categories: one is lumped element decoupling network [30], the other is microstrip line decoupling network [31].

1.3 The New Development to Phased Array

11

In 2004, Chung et al. used DGS structure to increase the isolation between dual polarized planar microstrip antennas and reduce the interaction [24]. The DGS structure is added to the common microstrip feeder. The results show that the coupling of the antenna element is restrained and the isolation is greatly improved compared with that of the common microstrip feeding mode. In 2003, Yang et al. Applied a mushroom shaped EBG structure to microstrip array antenna to reduce mutual coupling between elements [32]. In reference [28], a U-shaped microstrip line is loaded between two microstrip patch antennas. The structure of the loading branch is simple, and the decoupling effect can basically meet the requirements of antenna design. In 2008, Chen et al. Designed a decoupling matching network for strong mutual coupling antenna [30]. The decoupled matching network is composed of transmission lines and lumped elements. The measurement results show that the design of the network can greatly improve the isolation of antenna ports. In references [18, 19], polarization diversity is realized by two microstrip antennas with one corner removed, triangular radiation elements with slots and two UWB antennas. In reference [21], through the mode of electric dipole excited by a bent monopole antenna placed at one end and the mode of magnetic dipole excited by a coupling ring placed at the other end, because the two radiation modes are nearly vertical, the inductive coupling effect between the elements of the antenna is reduced, and the isolation between the elements of the antenna array is increased finally. The test results show that the coupling effect between the two elements is improved and the isolation can reach to −30 dB.

1.3.3.2

Decoupling Analysis and Calibration

Electromagnetic analysis method is an earlier method to analyze and study mutual coupling calibration. Gupta, an American scholar, studied the influence of mutual coupling effect on adaptive array as early as 1983, and proposed the open circuit voltage method based on circuit analysis. The open circuit voltage method uses the open circuit voltage to replace the decoupling voltage of the array, and solves the coupling matrix through the open circuit voltage method, so as to realize the mutual coupling calibration of the array [33]. This method has been applied in DOA estimation, adaptive beamforming and other aspects, and achieved good calibration results [34, 35]. However, in the experiment, when the antenna terminal is connected with a large load, a more ideal mutual coupling calibration effect can be obtained, but it leads to a serious mismatch for antenna elements. In addition, in the open circuit voltage method, the array is in the transmitting state, and the mutual coupling calibration effect for the receiving state is limited. In 2002, Singapore scholar H. T. Hui proposed the receiving mutual impedance method (RMIM) [4]. The concept of receiving mutual impedance is defined by array in receiving state. Compared with the open circuit voltage method, this method is more consistent with the state of the receiving array, so the mutual coupling matrix obtained by this method has a better effect in mutual coupling calibration, which

12

1 Introduction

is mainly reflected in the deeper null in the anti-interference algorithm and higher direction- finding accuracy in direction finding [37]. There is a certain coupling relationship between array antenna elements, and the coupling matrix is mutual coupling matrix. If accurate mutual coupling matrix information is obtained, it means mutual coupling calibration or compensation can be realized. Solving mutual coupling matrix to realize mutual coupling calibration is one of the common methods in modern times. There are two kinds of methods to solve the coupling matrix: the first is to calculate the voltage/current received by the array antenna from the perspective of electromagnetic analysis; the second is based on the array signal processing, which is often combined with the direction of arrival estimation and realizes the mutual coupling matrix through iterative and joint estimation The solution of the problem is given. The full wave method is a kind of method based on the method of moment (MOM) to solve the array mutual coupling matrix. This kind of method analyzes the relationship between the actual voltage of the port and the MOM voltage through the method of moments [38]. According to the measured voltage/current of the actual array, the coefficients of the undetermined equations are solved by the mutual coupling matrix coefficients. Compared with the open circuit voltage method, this method has smaller angle estimation error in DOA estimation. However, in practice, it is necessary to assume the current distribution, or to know the direction of the incident electric field, or to solve the minimum norm solution of the underdetermined equations. Because this assumption is not completely consistent with the actual array situation, the calibration effect of this method is not very ideal. In reference [39], Liu Yuan, a domestic scholar, proposed a compensation method for mutual coupling between array elements. The mutual coupling matrix of the array is obtained by approximating the actual measured pattern in an ideal array model without mutual coupling. This method avoids the problem that mutual impedance of antenna array is difficult to measure accurately, and eliminates the influence of mutual coupling on array synthesis. However, in practical application, this method has the same limitation as the receiving mutual impedance method, that is, the mutual coupling calibration effect for line antenna array is better, and the mutual coupling calibration for microstrip antenna is not ideal. The reason is: for the wire antenna array, because its element pattern is omnidirectional in a certain direction, it is similar to the ideal current source, and its response to different incoming wave directions is consistent. However, for the microstrip antenna, because of its non-Omni directivity, the response of the antenna to different directions is different, so the mutual coupling matrix is different. Generally speaking, the first method of coupling matrix can clearly describe the electromagnetic characteristics of the array. In practical application, the coupling matrix obtained in advance is used in the array signal processing algorithm to obtain the required information. So this kind of method is also called offline methods. However, the above method is more suitable for wire antenna array, so there are obvious limitations in the adaptability of array calibration. The second kind of coupling matrix method is array signal processing method, which does not need to calibrate the source or know the mutual coupling parameters of the array in advance [40]. This kind of method does not need to know the mutual

1.3 The New Development to Phased Array

13

coupling matrix of the array in advance, so it is also called online methods, blind calibrations methods and self-calibration methods. Its advantage is that it can realize self-calibration according to the electromagnetic environment. The existing methods are based on one assumption: the coupling matrix of array is symmetric Toeplitz structure, so the main research object of this kind of methods is regular array such as linear array and circular array. Using the symmetric Toeplitz structure characteristics of the coupling matrix of linear array and circular array, the coupling matrix is solved. In this assumption, for the linear array, the electromagnetic environment of the element on the edge is not exactly the same as that of the element in the array, so this assumption has some problems in the linear array. In addition, this kind of method is mainly based on the symmetric Toeplitz structure of mutual coupling matrix. The coupling suppression method can improve the radiation efficiency and gain of the array, but the current coupling suppression measures are often aimed at a certain working state of the array, especially the working mode of the side fire array. When the scanning angle increases to a large angle, the equivalent spacing between the elements has changed, and the coupling state has also changed, so the coupling suppression measures of the original state may not be effective. In addition, the decoupling method based on signal processing, mainly in baseband processing, is often used as a correction and compensation method after system integration. This method needs special RF channel, digital channel and baseband module, the system is complex and expensive.

1.3.4 Ultra-Wide Angle Scanning Array Antenna Combined with Metamaterials A long time ago, the special propagation characteristics of electromagnetic wave in gradient index media have attracted people’s attention [41]. According to Snell’s law, when electromagnetic wave propagates in gradient index medium, its propagation direction will produce corresponding deflection. The mirage phenomenon in the atmosphere, such as the shape change of the sun at sunrise and sunset, is caused by the gradient refractive index caused by the non-uniform distribution of air in the atmosphere. Since the nineteenth century, the gradient index effect and its application have been deeply studied in the field of electromagnetism. The gradient index devices represented by Maxwell fisheye lens, Lomber lens and gradient index fiber emerge in endlessly. In recent years, artificial electromagnetic materials, known as “metamaterials”, have attracted extensive attention of researchers. Comparing to natural materials, the values of electromagnetic constitutive parameters (permittivity, permeability, conductivity, etc.) of metamaterial composed of periodic man-made microstructure units are more flexible [42, 43]. Metamaterial can be used to realize the accurate design of GRIN devices, and realize the novel electromagnetic functions that traditional materials can’t achieve. Metamaterial technology can break through the

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1 Introduction

bottleneck and short board of traditional microwave technology, and realize engineering design in microwave devices and microwave antennas. At present, metamaterial technology has been successfully used in antenna gain enhancement, sidelobe suppression and antenna cross section reduction. Since Pendry and Smith first proposed structural electromagnetic metamaterials, many other microstructures of metamaterials have been proposed [44–54]. Brien et al. Proposed a nanoscale symmetric ring structure photonic crystal working in the infrared band, which has the effect similar to SRR structure [44]; based on the research of saadoum et al., Huang fu, Jiang tao, et al. Designed a kind of Ω type metamaterial [45]. He placed two Ω shaped metal lines with opposite opening direction on both sides of PCB symmetrically by rotating 180° and placed three Ω structure units longitudinally along Z axis. The electric field direction of the incident wave is parallel to the two linear arms of the thin metal wire of the Ω structure, which makes the structure produce electric plasma resonance and realize negative permittivity; the magnetic field of the incident wave passes through the circular part surrounded by the thin metal wire of the Ω structure vertically, which makes the Ω structure produce magnetic plasma resonance and realize negative permeability. Compared with the Smith structure, the metamaterial of this structure makes full use of the coupling effect between the two metal structures in the element, and the Smith structure produces negative permittivity and negative permeability characteristics by the two parts respectively. In 2005, Grzegorczyk and other researchers constructed metamaterials with symmetric ring structure [46]. Its unit structure consists of two open loops of the same size symmetrically placed in x, y and z directions. There are two ring structures and one rod structure in each periodic unit. Compared with some asymmetric metamaterials, symmetric ring metamaterials can overcome the chiral effect caused by the asymmetry of two metal open rings. Most of the metamaterials studied at first only show left-handed electromagnetic properties in a certain passband. Metamaterials with multi-band and wideband double negative characteristics are one of the key research directions in the future. In order to realize multi-band, metamaterial units are usually designed as the combination of metal rings of different sizes and shapes, so that metamaterials have multiple resonance bands with double negative characteristics, so as to realize the left-handed characteristics of multi-band. If multi-band is connected with each other, then broadband left-handed materials can be realized. Multi-band and broadband left-handed materials have important applications in some fields, such as multi-band filters, wavelength division multiplexers, couplers and so on. Chen et al. Used the derivative structure of S-type resonator to realize multi pass band left-handed material [52]. It is composed of two S-type resonant rings with different sizes, which can produce negative refraction in two different frequency bands. Generally speaking, for a specific left-handed structure, a small unit corresponds to a specific left-handed bandwidth. Therefore, n different small units correspond to n different left-handed bandwidths. Usually, the broadband left-handed material unit is composed of complex small split rings. For example, in the metamaterial structure [53], two split rectangular metal rings act as magnetic resonators, and the

1.3 The New Development to Phased Array

15

copper strip in the middle acts as electric resonators. The electric resonator provides negative permittivity and the magnetic resonator provides negative permeability. By adjusting the geometry size of the two resonators, their negative resonant frequencies can overlap, thus realizing the left-handed characteristic. This method is also suitable for terahertz band [49, 50]. In order to achieve isotropy, Wang et al. Designed a broadband three-dimensional metamaterial structure composed of isotropic hexahedron [55] in 2009. Each side of the cube is etched with a Jerusalem cross shaped metal pattern. The simulation results show that the left-handed frequency band of this kind of metamaterial is between 5.75 and 9.0 GHz, and the left-handed bandwidth is approximately independent of the polarization direction and incident angle of the incident wave, so it can be approximately considered that the three-dimensional metamaterial is isotropic. In order to make metamaterials fully isotropic, Gong et al. Proposed a geometric model of ball rod shape [56]. Through research, the author found that this geometric structure has negative refraction characteristics in a specific visible light frequency range. Due to the high symmetry of the model, the model has isotropic electromagnetic characteristics, which is more suitable for practical application. Although the above metamaterials have excellent properties, their basic properties are not adjustable, which limits the application of metamaterials. Nowadays, tunable metamaterials have become a research hotspot. Tunable metamaterial means that the interaction between incident wave and metamaterial can be controlled artificially, and the transmission, reflection and absorption of electromagnetic wave can be adjusted according to the need. Generally, tunable metamaterials can be divided into two categories: one is to change the effective electromagnetic characteristics of metamaterials by changing the nonlinear characteristics of resonators [57, 58] or dielectric substrates [59, 60]; the other is based on structural combination methods, such as changing the arrangement of cells [61], reconstructing the structural elements of metamaterials [62], rotating elements [48], or bending metamaterials [49] And so on. There are two ways to realize the adjustable metamaterial: one is the adjustment of electric device. From the knowledge of electrodynamics, we know that when an electron is stationary or moving slowly, an electric field will be generated around it. The characteristic of electrostatic force is that the force between two charged bodies is inversely proportional to the square of their distance. At the micro scale, this is a huge advantage, because the distance between charged objects is very small (down to a few microns), resulting in a large electrostatic force between charged objects. Therefore, electrostatic force can be widely used as a micro mechanical actuator, and it is also suitable for tunable metamaterials in the operating frequency range of GHz and THz [50]. Recently, it has been reported that silicon micromachining structure can be used to control the relative position of the metamaterial structure unit [47], which can make the metamaterial unit change from one geometry to another. Different from some nonlinear elements, the micromachined reconfigurable metamaterial element shows only one resonant frequency shift due to external excitation. The reconstructed metamaterial element can be transformed from one geometry to another. For example, the shape of the metamaterial studied by Zhu et al. Can vary between “[]” and “I” [47].

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1 Introduction

This kind of reconstructed metamaterial can suppress the existing resonant modes in the new resonant mode, so as to achieve the purpose of adjusting the electromagnetic characteristics in a large range. The experimental results show that the permeability of the adjustable metamaterial can vary from −0.26 to +0.29. Another way is thermomechanical adjustment. In reference [51], a kind of metamaterial whose working frequency band is adjusted within THz by thermomechanical method. Each unit is composed of an inclined silicon nitride wafer with 400 nm thickness and two bi-material cantilevers connected with SRR on silicon nitride substrate. When the THz wave is perpendicular to the SRR surface with no tilt angle, the metamaterial does not produce resonance response. With the increase of temperature, the cantilever bends upward, and the magnetic field penetrates through the SRR to cause magnetic resonance. This research result can be used in devices or thermal detectors that need to dynamically adjust the negative refractive index. We can also use photo thermomechanical technology to realize tunable metamaterials. In the infrared band, in order to make the metamaterials continuously adjustable in a wide range, the reconfigurable photonic metamaterials based on nano metal dielectric films provide a way to realize the thermomechanical tunability of photons. Reference [52] presents a schematic diagram of photonic metamaterial reconstruction using bent substrate. When the substrate is heated and cooled, it bends upward and downward, so that the light can be controlled. At present, the buckyball technology used to expand the scanning angle will increase the profile of the antenna, which is not suitable for conformal installation of planar array antenna. The general metamaterials used to improve the performance of antenna array are mainly passive metamaterials with fixed structure, whose dispersion performance is fixed. Correspondingly, they can’t adapt to the improvement of antenna performance when the array beam scanning to different angles, and may have the opposite effect. Although the current reconfigurable metamaterials can adjust the dispersion characteristics of metamaterials, it is still in the preliminary research stage, and the adjustable mode and range are limited.

1.3.5 The Large Angle Scanning Array by Combining Electric Scanning with Mechanical Scanning In engineering, the combination of mechanical scanning and electrical scanning is often used to expand the scanning angle of the antenna, which can almost scan to any angle. For example, the terminal High Altitude Area Defense (THAAD) of the U.S. military is a land-based theater anti-missile system under the U.S. missile defense agency and the U.S. Army. THAAD’s standard radar configuration is an an/tpy-2 X-band solid active multifunctional phased array radar, which is one of the most powerful land-based mobile anti-missile detection radars in the world. The radar has a long warning range and takes into account both strategy and tactics. The antenna array covers an area of 9.2 square meters and is equipped with 30,464

1.3 The New Development to Phased Array

17

antenna elements. The azimuth mechanical rotation range is −178° ~ +178°, and the pitch mechanical rotation range is 0° ~ 90°. however, the electric scanning range, pitch angle and azimuth of the antenna are 0o ~ 50°. Obviously, the combination of mechanical scanning and electrical scanning is more suitable for independent rotatable radar, which requires additional mechanical rotation system and does not require high scanning time. For those conformal large angle scanning arrays on the surface of high-speed moving carrier, it is difficult to meet the requirements. Metamaterial technology can break through the bottleneck and short board of traditional microwave technology, and has been applied in the engineering design of microwave devices and antennas. At present, metamaterial technology has been successfully used in antenna gain enhancement, sidelobe suppression and antenna cross section reduction. The 54th Research Institute of China Electronics Technology Group Corporation has proposed a horn shaped phased array antenna loaded with metamaterial cladding to expand the beam scanning range of the antenna [63]. When the beam of the phased array antenna is scanned to 30 degrees, the grating lobe appears, which limits the scanning range of the beam. The super material cladding structure can modulate the field distribution of the bell mouth surface, make the phase distribution of the radiation mouth surface more precise, and significantly suppress the grid lobe level, thus expanding the beam scanning range of the antenna. The scanning range of the phased array antenna loaded with the metamaterial is extended by 15°. Two kinds of metamaterials with slightly different refractive index are loaded on the interface of each antenna element of phased array, which can adjust the phase distribution of the whole array, reduce the grating lobe level and expand the scanning angle range. The directivity of the phased array antenna becomes worse when scanning at a large angle because of the large phase step. The phased array loaded with metamaterial coating can refine the phase of the radiation interface and change the phase more smoothly, which means that the radiation direction of the antenna is more concentrated and the gain is increased accordingly. Compared with the empty horn phased array without loaded metamaterial, the loaded metamaterial can effectively improve the gain of the antenna and reduce the sidelobe of the antenna, especially in large angle scanning. In the aspect of two-dimensional hypersurface, many people have done a lot of research in China. Professor Feng Yi jun’s team of School of electronics of Nanjing University has integrated active elements into the design of electromagnetic super surface, proposed the design scheme of active Huygens super surface, and successfully designed and developed a reconfigurable active Huygens super lens, which realizes the functions of microwave signal focusing at any focus position, any multi focus focusing and fast scanning of dynamic focus [64]. Shanghai Jiao tong University has also obtained ultra-wideband ultra-surface through two-dimensional discrete grid optimization, and combined it with ultra-wideband antenna to obtain stable pattern and high gain [65]. Xi’an University of Electronic Science and technology, Tsinghua University, University of Electronic Science and technology, Southeast University, Xi’an Jiao tong University and many other teams have also made good exploration and Research on metamaterials.

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1 Introduction

1.3.6 Pattern Reconfigurable Antenna to Expand Array Scanning Angle Reconfigurable antenna technology is a new technology proposed at the end of last century. It adjusts the working parameters of the antenna by electromagnetic, mechanical or other means, so that one antenna has the function of multiple antennas. When these multiple antennas work in space in turn, it is equivalent to broadening the scanning angle of the array. The scanning array element is commonly used as a pattern reconfigurable antenna. By changing the effective radiation part or array form of the antenna, the radiation pattern of the antenna can be changed timely while keeping the working frequency unchanged. The antenna can meet the needs of satellite communication, automobile and various radars. Frequency and pattern reconfigurable antenna is the combination of frequency and pattern reconfigurable antenna function, that is, it can reconstruct radiation pattern in ultra-wide frequency band, which is also the most complex part and ultimate goal of reconfigurable antenna research. At present, due to the late start of this technology, there is no antenna with good performance of frequency and pattern reconfiguration at the same time, but there are some valuable research results [66, 67], For example, “self-organizing antenna” proposed by C.M. Coleman is the classic representative of reconfigurable antenna with frequency and pattern. “Self-organizing” refers to that when the environment around the antenna changes [68], the feedback signal will be transmitted to the microprocessor to control the switch between the template elements of the antenna, so that the electrical structure of the antenna can change dynamically. In the design process, the genetic algorithm optimization technology is used to make the antenna scan in the maximum radiation direction on the plane where the metal mesh is located. The scanning lobe is wide, but the gain of the antenna is low. The pattern reconfigurable antenna often uses electrically controllable switching or tuning to the parasitic dipole of the antenna with both driving and parasitic dipoles. By changing the coupling between the driving and parasitic dipoles, that is, when the effective source current of the driving oscillator changes, the induced current generated on the parasitic dipole has a certain phase difference with it, so as to realize the reconfiguration of the radiation beam, which is consistent with that of the antenna The reflector and the director of the traditional Yagi antenna absorb the energy radiated by the driving oscillator and radiate out to form a similar directivity. Roger F. Harrington proposed an earlier espar antenna structure [69, 70]. Espar (electronically steerable parallel array antenna) antenna is an electronically controlled passive array antenna. The antenna is a circular array composed of seven half wave symmetrical dipole antennas, and its radiation characteristics depend on the impedance loading of the six parasitic dipoles in the periphery and the feeding of the middle driving dipole; when the reactance value of the parasitic oscillator changes, the beam aligned with different target directions can be reconstructed. In addition, the effects of different

1.3 The New Development to Phased Array

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distances between the parasitic and driving dipoles on the radiation characteristics of the antenna are also studied. Literature [71] and literature [56] respectively describe two kinds of antenna structures, which are the feed structure of the antenna or the RF device loaded with slots on the floor to realize the reconfiguration of the antenna. Markus Berg et al. Designed a frequency reconfigurable slot ring antenna [72], which can change the resonant frequency of the antenna by changing the length of the microstrip feeder. That is, the RF PIN diode switch is loaded on the microstrip feeder, and the switching off and on can switch the resonant frequency of the antenna from 1.63 GHz to 2.34 GHz, with a frequency change rate of 43%. In addition, the relative bandwidth of the antenna is 8.5% and 11.5% when the pin diode switch is off and on, respectively. The simulation and experimental results verify the effectiveness and reliability of the new frequency reconfigurable antenna. Symeon Nikolaou et al. Designed an annular slot antenna with reconfigurable frequency and pattern [73]. The radiation part of the annular slot antenna is printed on the front of the PCB, and the DC bias part is printed on the back of the PCB. By controlling the small voltage in the reverse bias circuit of the antenna the resonant frequency of the antenna can be switched between 5.2 GHz and 6.4 GHz by using the pin switch diode, and the resonant frequency of the antenna without any bias is 5.8 GHz. The antenna can realize three kinds of frequency reconstruction; the antenna pattern can be reconstructed by controlling the state of the large pin switch diode which is short circuited inside and outside the annular slot on the front of the antenna. Taking the pattern reconfigurable antenna as the basic element of phased array antenna is a new method to extend the scanning range of phased array. The multifunction of reconfigurable antenna makes one antenna realize the function of multiple antennas, so the use of reconfigurable antenna can reduce the size of the system, reduce the weight and improve the electromagnetic compatibility [71, 72, 74]. Therefore, the combination of directional reconfigurable technology and phased array can add a degree of freedom to the phased array adjustment. In addition to the amplitude and phase adjustment of the conventional phased array, the cell structure can also be adjusted. By reconstructing the radiation state, the microstrip antenna element can achieve several different states with different main beam direction, which is equivalent to enlarging the beam width of the antenna. In reference [75], an eight-element linear array is designed by taking the quasi Yagi reconfigurable antenna unit with three beam states as the basic element of the phased array. By using the weighted sparse array technology, the scanning range of H-plane main beam can reach ±60°, and its 3 dB beam width coverage can reach ±68°. In reference [76], the feed network of the subarray composed of three microstrip antenna elements is reconstructed to achieve three different beam radiation States, and the main beam scanning in the corresponding space of the phased array is carried out in each beam state of the subarray. The array composed of four microstrip antenna subarrays achieves the Ka band ±75° beam scanning range. In addition to using pin switch diodes to reconstruct several independent radiation patterns, the pattern reconfigurable array loaded with

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1 Introduction

varactor diodes can also achieve wide-angle scanning performance with low gain fluctuation [77]. However, the current reconfigurable antenna pattern reconstruction state is only a few simple, and can’t control the small step scanning reconstruction of the pattern precisely, the continuity is poor, and the beam width and gain fluctuate greatly in the scanning process, so it is still unable to fundamentally solve the problems of beam broadening and gain reduction. China’s national high technology research program (863) and National Natural Science Foundation of China have also funded research on reconfigurable antenna projects, such as “Research on electromagnetic theory and key technologies of reconfigurable antenna”, “compact reconfigurable planar antenna for mobile terminals”, etc., and have achieved certain valuable research results [78]. In the late 1970s, China also developed a two-dimensional phased array radar for detecting long-range missiles launched by other countries and satellites in outer space [79]. Because the development cost of phased array radar was very high at that time, it was more economical for tactical radar to use other systems as equipment. Therefore, at that time, the main purpose of the international community was to master the phased array system and related technology, and few troops were equipped with phased array radar.

1.3.7 Multi-Mode Antenna The antenna radiates through the current or magnetic current on the surface of the antenna, and different surface current or magnetic current distributions are called different modes. By stimulating the multi-mode of the antenna, the antenna pattern can be adjusted, thereby improving the performance of the antenna, expanding the application scenarios of the antenna, and facilitating the realization of a wide-angle scanning array. In 2020, Bin-Feng Sun, Xiao Ding, You-Feng Cheng, and Wei Sha et al. realized the design of wide-beam antenna unit by combining two antenna modes in one antenna aperture [80], and then applied it to 8 × In the two-dimensional array of 8, a scan effect of ±65° is achieved. The antenna unit is composed of a central circular patch and four surrounding rectangular patches. The circular patch generates the TM11 mode (normal direction), and the parasitic patch generates the zero-order mode (end-fire direction). Both modes are excited at the same time to make the antenna it has a wide beam width of 156 degrees in two orthogonal planes. In 2017, Behrouz Babakhani and Satish Kumar Sharma designed a three-mode circular patch antenna [81], which can generate two independently controllable zero points in the upper half of the free space. The central patch produces TM11 mode (normal direction), and the two short-circuit loop patches produce TM21 mode and TM31 mode respectively. Each mode is excited separately. By controlling the excitation amplitude of each mode, the antenna pattern and Zero position.

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In 2019, Hong-Wei Yu, Yong-Chang Jiao, Dan-Yang Li, and Zi-Bin Weng designed a reconfigurable microstrip patch antenna with wide-angle coverage [82]. The antenna can work in two modes: TM30 mode and TM40 mode. The main beam direction of TM30 mode is {0°, ±37°}, and the main beam direction of TM40 mode is {±17°, ± 58°}. By controlling the excitation amplitude between the two modes, the half-power beam width of the antenna is −68°−73°. In 2005, Satish K. Sharma and others studied a multi-mode microstrip patch antenna, which realized the conversion of TM11 and TM21 radiation modes by adjusting the amplitude and phase of the feed. After that, they formed a 1 × 8 linear array. The research results showed that the phase center of the array can be moved by controlling the amplitude and phase of the unit, that is, mode conversion. In the end, the scanning angle of the antenna can reach 24° [83]. In 2012, Tuan Q. Tran proposed a multi-mode antenna. By controlling the amplitude and phase of multiple input ports, different working modes (TM11, TM21, TM31) of the circular patch are excited. The main beam direction of the pattern of different working modes is different. When the scanning angle changes, you can increase the scanning angle by switching between different modes [84]. In 2013, Xiao Ding proposed a reconfigurable antenna. Three different working modes are realized by loading slits and pin diodes on three patches and feeder networks. The pattern generated by these three working modes can cover the upper half plane, which is equivalent to expanding the beam width. The final 1 × 4 antenna array can achieve ±75° large-angle beam scanning [85]. In 2013, H.-Y. Huang, B.-Z. Wang, X. Ding and W. Shao proposed a small antenna design, the antenna can provide two different radiation directional pattern, which is caused by the excitation of two different modes. According to the state of the Pin diode, the antenna works in normal patch mode (TM11) or unipolar patch mode [86]. In 2014, M. Zou, J. Pan, L. Zuo and Z. Nie proposed a simple rectangular microstrip antenna with an omnidirectional cone beam pattern. The high-order TM02 and TM20 modes are excited by the two probes in phase and with the same amplitude to produce an omnidirectional mode [87]. In 2016, D. Manteuffel designed a four-port multimode antenna that can generate four different radiation patterns. When different ports are excited, it corresponds to a radiation pattern. The combined effect of these radiation patterns can achieve the effect of a wide beam. Using this antenna unit can increase the scanning angle [88]. In 2016, Marek Klemes, Halim Boutayeb and Fayez Hyjazie designed a beam control system [89], which can control the axial beam of any large circular array. The system includes 3 variable phase shifters and a certain number of mixers. By combining two low-order phase modes with a difference of one order, the deflection angle of the main beam is controlled accordingly to realize the large-angle scanning of the antenna array. In 2017, X. Ding, YF Cheng, W. Shao and BZ Wang proposed a microstrip patch antenna [90]. The TM01 and TM20 resonance modes on the patch are excited and Switch to generate spatially complementary radiation beams. By combining these beams, the formed phased array shows excellent wide-angle scanning performance with gain fluctuations less than ±0.75 dB.

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1 Introduction

In 2017, Y. F. Cheng, X. Ding, W. Shao, M. X. Yu and B.-Z. Wang proposed a pattern reconfigurable antenna [91]. The scanning of the antenna can be reconstructed by combining modes that work in two symmetrical modes in two subspaces. The phased array can scan its beam from −81° to +81° in the E-plane, and the gain fluctuation is less than 3 dB. In 2018, Z. Jiang designed a reconfigurable antenna. The antenna generates 3 working modes through two diodes, forming 3 different beam pointing patterns covering the hemisphere, which is equivalent to a wide beam antenna. The antenna array can achieve ±70° beam scanning, and the gain roll-off is less than 3 dB [92]. In 2018, Igor Syrytsin, Shuai Zhang and others proposed a four-mode end-fire planar phased antenna array with a large scanning angle and a very small gap, as shown in Fig. 13a, with a −10 dB bandwidth of 8.2 GHz, the −6 dB bandwidth is 10.8 GHz, the gap is 1.2 mm, and the scanning angle can reach about 140°. The array unit has different radiation patterns in different modes. As shown in Fig. 13b, the wide bandwidth and wide scan angle are obtained by combining the four modes. Because the array unit has a wide embedded radiation pattern, the linear array composed of it can achieve a wide scanning angle [93]. In 2018, Cheng Y F et al. designed a multi-mode antenna with two sub-units based on the SIW cavity-backed antenna. By adjusting the feed phase difference of the two sub-units, unit beam deflection can be realized. The one-dimensional array designed by this unit can achieve ±75° 3 dB beam scanning, but the number of phase shifters in this feeding method has doubled, so this design method can achieve large-angle scanning, but the array antenna The cost is greatly increased [94]. In 2019, Guo-Feng Gao; Xiao Ding; You-Feng Cheng; Wei Shao proposed a novel multi-mode patch antenna [95], which can interactively excite a slotted antenna The TM10/TM01 mode of the square patch and the TM21 mode of the other round patch. By switching and combining excitation modes, broad beam radiation with the same electric field polarization is generated in the x-o-z and y-o-z planes. It was then applied to a 64-element phased array to achieve dual-polarization wide-angle scanning on two planes. Simulation and measurement results show that the phased array can support main beam scanning in the range of −64° to +64°, and 3 dB coverage of −78° to 78° in each scanning plane. In 2020, the team of Geng Junping from Shanghai Jiao tong University proposed a multi-mode antenna as shown in Fig. 1.2 [96]. The antenna has two ports. When the phases between the two ports are different, the beam directions of the element pattern are different, so as to realize the scanning of the element pattern. Different from the traditional reconfigurable antenna, this antenna can realize the continuous changed pattern. It has a broader application prospect in the large-angle scanning of the array. In recent years, the team of Geng Junping from Shanghai Jiaotong University has used SSPPs technology to design a variety of phase-mode antenna units for array scanning [97]. The team students proposed a phase mode spatial scanning SSPPs antenna with dual-port feed, as shown in Fig. 1.3. The antenna consists of two trapezoidal monopoles, four loaded circular patches, a symmetrical SSPPs transmission line and two diamond modulation structures. By changing the phase difference

1.3 The New Development to Phased Array

23

Fig. 1.2 Element structure and it’s scanning pattern, phi2-phi1 = Δ∅ a Δ∅ = 0°,θ = 0° b Δ∅ = 46°, θ = 30° c Δ∅ = 120°, θ = 50° d Δ∅ = 180°, θ = 59° e element structure. Figure reproduced with permission from Ref. [96], © 2020 IEEE

L1

Fig. 1.3 Dual port SSPPs antenna. Figure reproduced with permission from Ref. [97], © 2021 IEEE

W1

a

d

h

p

Z

Lm

X port1

port2

between the two feed ports, the odd and even modes and mixed modes of SSPPs are generated, and beam scanning in the wide three-dimensional space range of 4.4–5.8 GHz frequency band is realized.

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1 Introduction

1.4 Development Trend and Problems of Phased Array 1.4.1 Development Trend With the increasing demand of civil and military applications for ultra-wide angle scanning array, it has become an important trend and goal of ultra-wide angle scanning array to expand the scanning angle of the array and even realize the whole hemisphere beam scanning. Secondly, continuous and stable ultra-wide angle beam scanning is also the performance guarantee of array application. At present, the main technology is to expand the scanning angle, but the beam is very wide, even the sidelobe is very large, and the main beam is seriously deformed, so it is difficult to achieve linear small step quasi continuous scanning. Thirdly, the systematic analysis and characterization of UWA scanning array model is the basis of solving the development of UWA scanning array. At present, many people explore the possible expansion methods from different angles. From the perspective of the principle of array pattern product, they actually improve the element factor, array factor, narrow beam system of spatial filtering and so on. In essence, array scanning is the continuous broadcast of infinitely many beam functions. The array meeting the requirements of ultra-wide angle scanning is actually the extremum of the functional problem in this beam space. Fourth, it is urgent to explore new technical principles and design methods to expand the scanning angle of the array. At present, there are three main methods to extend the beam scanning angle of phased array, one is to change the pattern of array elements, the other is to reduce the energy coupling between array elements, and the third is to combine metamaterials. Many methods have been proposed to reduce mutual coupling, such as enlarging the spacing between antenna elements, loading DGS structure [98, 99], EBG structure [100, 101], left-handed material structure [102–104], etc. these methods reduce mutual coupling in a sense, but also bring a lot of negative effects, such as increasing the size, introducing larger grating lobe, causing strong backward radiation, etc. Therefore, changing the radiation pattern characteristics of antenna element is another solution. The reconfigurable antenna with multiple patterns is favored by researchers at home and abroad. It increases the freedom of antenna design. When the antenna element is composed of phased array, it can not only control the phase between the array element, but also control each antenna element’s pattern. This can greatly expand the scanning range and reduce the grating lobe of scanning pattern. In addition, the tightly coupled array has good radiation characteristics at large scanning angle, which challenges the coupling mechanism of the array from another direction. It is necessary to reveal the coupling mechanism thoroughly.

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1.4.2 Development Problems of Phased Array Obviously, with the development of electromagnetic theory and antenna technology, many new technologies are used to improve the performance of array antenna and expand the scanning angle of array antenna. At the same time, with the development of radar and wireless communication technology and the expansion of application fields, the expectation of ultra-wide angle scanning array is higher and higher. However, there are still many problems restricting the research and application of ultra-wide angle scanning array. (1) (2)

(3)

(4)

(5)

The mechanical scanning speed is slow, the structure is complex, and it is not suitable for conformal high-speed carrier surface. In the array antenna, the ideal omni-directional antenna element does not exist, and the actual antenna element pattern will be greatly distorted. At this time, the ideal pattern product principle will produce great errors. It is urgent to study the requirements of ultra-wide angle scanning array for antenna pattern from the basic principle. For the common low profile microstrip antenna array, even if the array element spacing is very large, when the beam is pointing to a low pitch angle, the equivalent array element spacing becomes smaller, the equivalent aperture size of the array decreases, the corresponding coupling effect increases, and the radiation efficiency decreases. This is also the main reason for the decrease of gain when the array antenna scans at a large angle. At present, there is no good method and mechanism on the fundamental solution. Due to the layout of the antenna, in addition to the distance, the parallel or vertical relationship, current density distribution and so on all affect the coupling, especially the strong coupling impedance between local current elements may be the main factor. These need to start from the basic model of the array antenna, research and build the mathematical model of ultra-wide angle scanning, especially the table of array performance changes during beam scanning there is no relationship between them. In addition, the radiation characteristics of tightly coupled array can be improved when scanning at a large angle, which challenges us to understand the coupling from another angle. We need to deeply and completely reveal the coupling mechanism. For the end fire antenna, such as log periodic folded slot antenna, although the main beam meets the requirements of large angle radiation, due to the special current distribution and specific phase difference, it does not have the beam scanning ability of wide angle range, so it needs to be combined with other forms of antenna to realize large range scanning. Reconfigurable antenna technology has a good effect on the scan angle expansion of array antenna, but the current reconfigurable technology can only achieve a limited number of States, limited by the device, it is difficult to achieve continuous pattern reconstruction. At the same time, due to the introduction

26

(6)

1 Introduction

of additional devices, especially the active switch and other nonlinear devices, it may interfere with the electromagnetic signal and reduce the g/T value and signal-to-noise ratio. Similarly, it is also necessary to study the requirements and constraint boundary of reconfigurable antenna elements for ultra-wide angle scanning array from the basic relationship between array antenna and electromagnetic, especially the relationship between the mathematical model of continuously adjustable spatial filtering and array scanning. Metamaterial antenna can change the scanning performance of the antenna, but the current baki sphere technology to expand the scanning angle will increase the profile of the antenna, which is not suitable for conformal installation of planar array antenna. However, the flexible performance changes of metamaterials provide a great degree of freedom for the performance expansion of array scanning. It is worth starting from the basic principle of metamaterials and combining with the working principle of scanning array to build a new mathematical model for systematic research.

1.5 Content Arrangement of the Book The content of this book mainly includes the following aspects: The first chapter describes the relevant application background and significance of the antennas in this book, introduces the research status and latest development of phased array antennas at home and abroad, and briefly introduces the main work of this article. The second chapter first introduces the important parameters that need to be used in the antenna design, then introduces the related theory of phased array, and finally designs two wide-angle scanning arrays. The third chapter proposed the generalized element factor, and the generalized principle of the pattern multiplication is proposed based on the generalized element factor. The fourth chapter first proposes the phase mode antennas whose pattern can change with the phase difference between the two ports. The simulated power flow distribution and pattern also verify the phase mode of the antenna unit, the experimental results are basically consistent with the simulation. Then the proposed phase mode antenna was applied into a 1 × 4 one-dimensional array as one example of generalized element factor (GEF). Experimental test results show that the antenna array achieves wide-angle scanning characteristics of −78°−78° and −70°−70° at 2.3 GHz and 2.4 GHz, respectively. The fifth chapter designs a dual-port phase mode SSPPs antenna, which can scan in 3D free space.

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27

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73. Berg M, Komulainen M, Salonen E, Jantunen H (2006) Frequency reconfigurable MicrostripFed annular slot antenna, First European conference on antennas and propagation, EuCAP 74. Nikolaou S, Bairavasubramanian R, Lugo C, Carrasquillo I, Thompson DC, Ponchak GE, Papapolymerou J, Tentzeris MM (2006) Pattern and frequency reconfigurable annular slot antenna using PIN diodes. IEEE Trans Antennas Propag 54(2):439–448 75. Mak ACK, Rowell CR, Murch RD et al (2007) Reconfigurable multiband antenna designs for wireless communication devices[J]. IEEE Trans. on Antennas Propagat 55(7):1919–1928 76. Bai YY, Xiao SQ, Tang MC et al (2011) Wide-angle scanning phased array with pattern reconfigurable elements [J]. IEEE Trans Antennas Propag 59(11):4071–4076 77. Ding X, Wang B-Z, He G-Q (2011) Research on a millimeter-wave phased array with wideangle scanning performance [J]. IEEE Trans Antennas Propag 61(10):5319–5324 78. Xiao S, Zheng C, Li M et al (2015) Varactor-loaded pattern reconfigurable array for wide-angle scanning with low gain fluctuation [J]. IEEE Trans Antennas Propag 63(5):2364–2369 79. Yang X (2006) Research on microstrip reconfigurable antenna, Ph.D thesis. University of Electronic Science and technology 80. Xu Z (2008) Research on broadband wide angle active phased array antenna unit, Ph.D dissertation. Xi’an University of Electronic Science and technology 81. Sun B, Ding X, Cheng Y, Shao W (2020) 2-D wide-angle scanning phased array with hybrid patch mode technique. IEEE Antennas Wirel Propag Lett 19(4):700–704 82. Babakhani B, Sharma SK (2017) Dual null steering and limited beam peak steering using triple-mode circular microstrip patch antenna. IEEE Trans Antennas Propag 65(8):3838–3848 83. Yu H, Jiao Y, Li D, Weng Z (2019) A TM30-/TM40-mode pattern-reconfigurable microstrip patch antenna for wide beam coverage. IEEE Trans Antennas Propag 67(11):7121–7126 84. Sharma SK, Shafai L, Balaji B, Damini A, Haslam G (2005) Investigations on multimode microstrip patch antenna and phased arrays providing multiphase centres. 2005 IEEE antennas and propagation society international symposium, vol 1A. Washington, DC, pp 326–329 85. Tran TQ, Sharma SK (2012) Radiation characteristics of a multimode concentric circular microstrip patch antenna by controlling amplitude and phase of modes [J]. IEEE Trans Antennas Propag 60(3):1601–1605 86. Ding X, Wang BZ, He GQ (2013) Research on a millimeter-wave phased array with wide-angle scanning performance [J]. IEEE Trans Antennas Propag 61(10):5319–5324 87. Huang H-Y, Wang B-Z, Ding X, Shao W (2013) A pattern-reconfigurable antenna based on TM 10 and TM 02 modes of rectangular patch. Appl Comput Electromagn Soc J 28(2):693–700 88. Zou M, Pan J, Zuo L, Nie Z (2014) Omnidirectional rectangular microstrip antenna operating at TM 02 and TM 20 modes for mobile applications. Electron Lett 50(24):1790–1792 89. Manteuffel D, Martens R (2016) Compact multimode multielement antenna for indoor UWB massive MIMO. IEEE Trans Antennas Propag 64(7):2689–2697 90. Klemes M, Boutayeb H, Hyjazie F (2016) Minimal-hardware 2-D steering of arbitrarily large circular arrays (combining axial patterns of phase-modes). 2016 IEEE international symposium on phased array systems and technology (PAST). Waltham, MA, pp 1–8 91. Ding X, Cheng YF, Shao W, Wang BZ (2017) A wide-angle scanning phased array with microstrip patch mode reconfiguration technique. IEEE Trans Antennas Propag 65(9):4548– 4555 92. Cheng YF, Ding X, Shao W, Yu MX, Wang B-Z (2017) A novel wide-angel scanning phased array based on dual-mode pattern reconfigurable elements. IEEE Antennas Wirel Propag Lett 16:396–399 93. Jiang Z, Xiao S, Li Y (2018) A wide-angle time-domain electronically scanned array based on energy-pattern- reconfigurable elements. IEEE Antennas Wirel Propag Lett 17(9):1598–1602. https://doi.org/10.1109/LAWP.2018.2856844 94. Syrytsin I, Zhang S, Pedersen GF, Morris AS (2018) Compact quad-mode planar phased array with wideband for 5G mobile terminals. IEEE Trans Antennas Propag 66(9):4648–4657 95. Cheng Y, Ding X, Shao W, Wang B (2018) Dual-band wide-angle scanning phased array composed of SIW-cavity backed elements. IEEE Trans Antennas Propag 66(5):2678–2683

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Chapter 2

The Basic Principle of Phased Array

Abstract This chapter introduces the basic principle of phased array and some key characters. The traditional principle of pattern multiplication is the foundation of the phased array, in which the array factor is the key to beam scan. People try to widen the beam width of the antenna to realize the wide angle scanning array, and our two examples are given.

2.1 Antenna Electric Parameters Antenna is the equipment to transmit or receive electromagnetic wave. It has become an indispensable part of civil defense system, such as wireless communication, radar, navigation, remote sensing, telemetry, radio astronomy and electronic warfare.

2.1.1 Return Loss and Work Band of Antenna Return loss |S11 |: The antenna can be regarded as a load connected at the end of the transmission line, and the return loss is the reflection coefficient at the port where the transmission line feeds the signal, which represents the comprehensive index of the impedance matching between the transmission line (port) and the antenna [1–3]. Work band: Usually, it is the frequency band with |S11 | < −10 dB. In Engineering, it is the frequency band with |S11 | < −15 dB. To the mobile, it is the frequency band with |S11 | < −6 dB.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 J. Geng et al., Generalized Principle of Pattern Multiplication and Its Applications, Modern Antenna, https://doi.org/10.1007/978-981-19-3559-6_2

33

34

2 The Basic Principle of Phased Array

2.1.2 Input Impedance The characteristic impedance in the transmission line (Fig. 2.1): Zc =

U + (z) U − (z) = − I + (z) I − (z)

(2.1)

The ratio of complex voltage to complex current at any point of the transmission line is defined as the input impedance at that point: Z in (z) =

U (z) I (z)

(2.2)

Let z′ replace z:   U z ′ = Ul cos βz ′ + j Il Z c sin βz ′

(2.3)

  Ul I z ′ = Il cos βz ′ + j sin βz ′ Zc

(2.4)

  Z l + j Z c tan βz ′ Z in z ′ = Z c Z c + j Z l tan βz ′

(2.5)

The voltage reflect coefficient: U − (z) U + (z)    ′ 1 +  z′ 1+ Z in z = Z c = Zc ′ 1− 1 − (z ) U (z) =

z′ = 0 → Zl = Z c l =

Fig. 2.1 Transmission line

1+ 1−

Zl − Zc Zl + Zc

(2.6)

(2.7) (2.8) (2.9)

2.1 Antenna Electric Parameters

35

Explanation: When Z l = Z c , l = 0: there is no reflection at the load side. When Z l /= Z c , l /= 0: the impedance of the wave source is not equal to the characteristic impedance, it will be reflected again. Generally, the characteristic impedance of transmission line is 50 Ω or 75 Ω. The characteristic impedance of the antenna connector is also 50 Ω or 75 Ω. If the antenna has no heat loss, the equivalent load of the antenna in the circuit is the radiation resistance of the antenna. For the resonant antenna, when the antenna operates at the resonant frequency, the external radiation performance of the antenna is the strongest, that is, the radiation resistance is at the minimum value, the imaginary part of the input impedance is zero, and the input impedance phase is zero. This is consistent with conjugate matching. The frequency point with smaller return loss |S11 | is that the transmission line or feed port matches or nearly matches the equivalent load impedance of the antenna, which is not consistent with the frequency point of antenna resonance, so the radiation efficiency of the antenna is not high at this time, and return loss |S11 | is a comprehensive index.

2.1.3 The Parameters of Antenna Patterns The antenna is mainly used for far field radiation/reception. The main characteristic parameters of the antenna are: main lobe width, side lobe level, front to back ratio, directivity coefficient, efficiency, gain, equivalent height, polarization, input impedance, etc. In spherical coordinates, the far-field radiation from the antenna to the field point is only a function of the angles θ and Φ, which is the pattern function |f (θ, φ)|. In general, the function that normalizes the pattern function with respect to its maximum value is called the normalized pattern function, denoted as |f(θ, φ)|.   | f (θ, φ)| = |F(θ, φ)|/ F(θ, φ)max 

(2.10)

The pattern drawn according to the normalized pattern function is called the normalized pattern of the antenna. Obviously, the E-plane and H-plane patterns of the current element shown in the figure below are also normalized patterns (because the maximum value in the maximum radiation direction is 1). Although the antenna pattern can describe the radiation energy in different directions, the concept of specific quantity is not clear enough, so some other characteristic parameters are used to describe the directivity of the antenna (Figs. 2.2 and 2.3). (1)

Main lobe width: when the E-plane and H-plane patterns of an antenna have the shape of multiple lobes as shown in the figure above, the lobe in the maximum radiation direction of the antenna is usually called the main lobe, and the

36

2 The Basic Principle of Phased Array

(a) E- plane

(b) H-plane

Fig. 2.2 Normalized pattern

Fig. 2.3 Antenna directional pattern

(2)

remaining lobes are called the side lobe (or side lobe) and the back lobe (or tail lobe). Take two points on both sides of the main lobe where the radiation power (field strength) is equal to 1/2 of the radiation power in the direction of the maximum value (1/2 of the field strength). The angle between these two points is called the half power point angle of the main lobe, which is recorded as (2θ0.5 ) E,H or (2θ−3d B ) E,H , or half power beamwidth (or more simply, main lobe width). The angle between the two rays is called the width of the zero point of the main lobe, which is recorded as 2θ0 . Sidelobe level: the actual antenna pattern often has several sidelobes. The side lobe value close to the main lobe value is called the first side lobe valve, which is called the second, third and side valves in turn. Usually, the sidelobe level is used to express the sidelobe strength of the antenna, which is defined as the ratio of the maximum value of any sidelobe to the maximum value of the main lobe, and the unit is dB. The first side lobe closest to the main lobe has the highest

2.1 Antenna Electric Parameters

(3)

(4)

37

level. The radiation of antenna sidelobe is harmful to both communication and radar, which directly affects the performance of antenna. Front to back ratio (FBR): the front to back ratio of an antenna refers to the ratio of the maximum radiation direction (forward) level of the antenna to its opposite direction (reverse) level, usually in dB. The front to back ratio of the antenna reflects the forward and backward isolation degree or anti-interference ability of the antenna. The front to back ratio of the antenna should be as high as possible. Directivity coefficient: the average radiation power density (s) of the antenna at a point in the maximum radiation direction in the far region_max (Smax )av is the average radiation power density (s) at the same point of the isotropic antenna with the same average radiation power (S0 )av . The ratio of AV is recorded as D, i.e.   |E max |2  (Smax )av  D= Pr and R ar e same = Pr and R ar e same (S0 )av  |E 0 |2  (2.11) In the above equation, (Smax )av = |E max |2 /2η

(S0 )av = |E 0 |2 /2η

η

0

0

= 120Ω

0

(2.12)

(2.13)

(2.14)

For omnidirectional antenna, (S0 )av = Pr /4π R 2 |E max |2 60Pr √ 60Pr D |E max | = R D=

(2.15)

(2.16)

(2.17)

Therefore, when the average radiation power is the same, √ the field strength of the directional antenna in the maximum radiation direction is D times that of the non directional antenna, that is, the average radiation power in the maximum radiation direction increases to D times. This shows that part of the power radiated by the

38

2 The Basic Principle of Phased Array

antenna in other directions is enhanced to its maximum radiation direction, and the narrower the main lobe is, the more power is enhanced to the maximum radiation direction, and the greater the directivity coefficient is. If the normalized pattern function of the antenna is known, the mode and average radiation power density of the electric field intensity in the far region of the antenna in any direction in space are respectively. |E(θ, φ)| = |E max || f (θ, φ)|   |E max |2 | f (θ, φ)|2  |E(θ, φ)|2 = Sav (θ, φ) = 2η0 240π

(2.18)

(2.19)

So, the radiation power of the antenna can be written as:  Pr =

|E max |2 R 2 Sav (θ, φ)ds = 240π

S



2π 0

π

dϕ ∫| f (θ, φ)|2 sinθdθ

(2.20)

0

The directivity value can be written as: D=

∫2π 0

∫π0 |

4π f (θ, φ)|2 sinθdθdϕ

(2.21)

If | f (θ, φ)| = | f (θ )|, the pattern has nothing to do with φ, the directivity value can be rewritten as: D=

∫π0 |

2 f (θ )|2 sinθdθ

(2.22)

2.1.4 Efficiency Due to the ohmic loss of conductor and dielectric in the actual antenna, the average radiation power of the antenna is Pr . Generally, R is less than the average input power Pin of the antenna. Antenna efficiency is defined as the ratio of radiation power to input power of antenna, denoted as η A . Namely: ηA =

Pr Pr = Pr + Pd Pin

(2.23)

where Pd is the average loss power of the antenna, which is the same as the loss resistance Rd The relationship between Pd and Rd can be expressed as:

2.1 Antenna Electric Parameters

39

Pd =

1 2 I Rd 2 m

(2.24)

And Im is the maximum input current of the antenna. ηA =

Rr Rd + Rr

(2.25)

Therefore, in order to improve the efficiency of the antenna, the radiation resistance of the antenna should be increased as much as possible, and the loss resistance of the antenna should be reduced as much as possible. When the frequency is low, the radiation resistance is very small because the length of the antenna is very small compared with the wavelength, while the size of the general antenna makes the loss larger, η A is lower. In the microwave band, especially at the high end of the frequency, the antenna efficiency can be considered to be close to 1, that is, η A ≈1.

2.1.5 Gain In order to comprehensively measure the performance of antenna energy conversion and directivity, the directivity coefficient and antenna efficiency are usually combined, and a new characteristic parameter gain coefficient is introduced. The gain coefficient is defined as the ratio of the average power density of an antenna at a certain point in the maximum radiation direction in the far region to the average power density of a non-directional antenna with the same average input power at the same point, denoted as G, i.e. G=

(Smax )av Pin same, R same (S0 )av

(2.26)

(S0 )av = Pr /4π R 2

(2.27)

(Smax ) (Smax ) Pr G =  Pin av  = Dη A  =  Pr av Pin 4π R 2 4π R 2

(2.28)

It can be seen that the gain coefficient of the antenna is equal to the product of the directivity coefficient and the radiation efficiency of the antenna. In the microwave band, because of the high radiation efficiency of the antenna, the gain and directivity of the antenna are almost the same. In practical application, the gain of antenna is used more, and DB is used to express the gain coefficient, that is, the gain coefficient. G(dB) = 10lgG (dB)

(2.29)

40

2 The Basic Principle of Phased Array

The higher the gain of the antenna, the better. DB is the multiple relation, and the unit of gain is dBi. Compare the directivity coefficient and gain: By definition, gain and directivity coefficients are very similar, but they are different. (1)

(2)

The premise of comparison is different. Both gain and directivity are used to compare the power density of the two antennas, but gain is compared on the premise of equal input power, while directivity is compared on the premise of equal radiation power. As a comparison standard, the antenna is different. The standard antenna compared in gain is not directive and non-loss antenna, while the standard antenna compared in directivity coefficient only requires being not directive.

2.1.6 Polarization Linear polarization: vertical polarization, horizontal polarization. Circular polarization: left hand polarization (LHCP), right hand polarization (RHCP). They mean the axial ratio is smaller than 3 dB in the propagating direction. Polarization match. Polarization diversity. Depolarization.

2.2 Uniform Linear Array There are many requirements for antenna in wireless communication system. One of the most important requirements is high gain and low sidelobe. Array antenna is an important method to achieve this requirement. The antenna system composed of more than two antennas is called multiple antenna. Array antenna is the most commonly used multiple antenna, also known as antenna array. It is composed of the same antenna elements arranged in parallel. The single antenna is called antenna element, which is generally weak directional antenna, such as half wave dipole, slot antenna and so on. Because the phase difference of the electromagnetic field generated by each antenna element at the observation point varies with the direction, the combined field increases in some directions and weakens in others, so the array antenna has a different directivity from the unit antenna [1–3]. The superposition principle can be used to calculate the radiation field of a multielement antenna, because the radiation field of the antenna has a linear relationship with the source. If it is the field produced by the unit antenna, the total field of the multi antenna system is. When the antenna elements are continuously distributed, the summation is transformed into integration. When the field vector direction of each antenna element is the same, the vector sum becomes scalar sum. When the

2.2 Uniform Linear Array

41

Fig. 2.4 Uniform linear array

0

1

2

d

directivity functions of antenna elements are the same, the summation is further simplified as multiplication. At this time, the above superposition process evolves into the principle of pattern product, that is, the pattern of array antenna is the product of array factor and element factor. It can be seen that there are two conditions for the principle of pattern product: (1) the unit antennas have the same pattern function; (2) the unit antennas have the same spatial arrangement direction. At the same time, the unit antenna itself can be an array. The number of antenna elements in array antenna can be large, which can be composed of linear array, planar array, spatial array and other different forms. The following focuses on the linear array, which is the basis of the analysis of array antenna. The equidistant linear array is shown in Fig. 2.4. N array elements are arranged in a straight line at equal distance. The array elements are half wave dipoles with the same parameters, and the array element spacing is d. assuming that the received electromagnetic wave is plane wave, the angle between the signal direction and the normal direction of the linear array is θ, and the initial phase difference between two adjacent array elements is α, then the electric field received by the whole uniform linear array can be written as: E = E0

N −1 

exp[ jn(kd cos θ + α)]

(2.30)

n=0

k = 2π/λ. Let Δψ = kd cos θ + α, then E = E0

N −1 

exp( jnΔψ)

(2.31)

n=0

According to the reciprocity principle, the above formula can also express the emission electric field of uniform linear array. The above formula is the basis of synthetic pattern of antenna array.

42

2 The Basic Principle of Phased Array

If Δψ = 0, the above function reach the maximum |E|max = N |E 0 |, if a = 0, the maximum electrical field is in the plane being orthogonal to the axis of the array, and the magnitude of the maximum is N times to the element, which is just the array gain, and can be written as 20logN. Array can narrow the beam of the pattern. In order to enhance the directivity of the antenna, improve the gain coefficient of the antenna, or to obtain the required radiation characteristics, several identical antennas can be arranged according to certain rules and given appropriate excitation, which is called antenna array. The independent elements of an antenna array are called antenna elements or array elements. The array elements can be various types of antennas. According to the spatial arrangement of array elements, the antenna array can be divided into linear array, planar array and three-dimensional array. There is also a “conformal array” in which the elements are arranged on the surface of an object such as an aircraft or a missile (Fig. 2.5). The analysis and synthesis of discrete array antenna mainly depends on the following four factors: (1) the number of array elements; (2) the position of array

z

1-D array along x-axis

a3 x

a2

x3

a1 x1

x2

z

a0

1-D array along y-axis

y

a0

x0

a1 a2 a3 y y0 y1 y2 y3

x

(a)

(b)

z

z

z3 a3 1-D array along z-axis

2-D array in xoy-plane

z2 a2 z1 a1 z0

a0

x3

y

x2

x1

x0 y0 y1 y2 y3 y

x

x (c) Fig. 2.5 Common array antenna

(d)

2.2 Uniform Linear Array

43

Fig. 2.6 A1D linear array

elements in space; (3) the current amplitude distribution of array elements; (4) the current phase distribution of array elements. Array analysis is based on the above four factors, such as pattern, directivity, gain and impedance. The synthesis problem is to design the best array parameters (i.e. the above four factors) according to its radiation characteristics. The selection of array element type is mainly determined by polarization state, mutual coupling effect and feeding mode. In phased array antenna, it is also related to scanning range. In array antenna theory, if the mutual coupling between elements is a fixed factor with small changes, the field pattern function of the array antenna can be expressed by the multiplication of the array factor and the element pattern function. Let’s give a simple example to illustrate this problem, the antenna array shown in Fig. 2.6: In Fig. 2.6a: e j k·d 0 = 1

(2.32)

e j k·d 1 = e jkx d = e jkd sin θ cos ϕ

(2.33)

e j k·d 0 = e− jkx d/2 = e− jk(d/2) sin θ cos φ

(2.34)

e j k·d 1 = e jkx d/2 = e jk(d/2) sin θ cos φ

(2.35)

In Fig. 2.6b:

Let a = [a0 , a1 ] is the element coefficient, then the array factor can be written as: In Fig. 2.6a: A1 (θ, φ) = a0 + a1 e jkd sin θ cos φ

(2.36)

A2 (θ, φ) = a0 e− jk(d/2) sin θ cos φ + a1 e jk(d/2) sin θ cos θ

(2.37)

In Fig. 2.6b:

44

2 The Basic Principle of Phased Array

The above two expressions only differ by a phase constant, so the pattern will not be affected. when θ = 90◦ , in x-o-y plane, the array factor can be written as:   A(φ) = a0 + a1 e jkd cos φ 

(2.38)

The pattern can be written as:  2 g(φ) = |A(φ)|2 = a0 + a1 e jkd cos φ 

(2.39)

Figure 2.7 shows the pattern of the two-element array with interval distance equals to d = 0.25λ, d = 0.5λ, d = 1λ, The excitation amplitude are a = [a0 , a1 ] = [1, 1], a = [a0 , a1 ] = [1, −1], a = [a0 , a1 ] = [1, − j] respectively.

Fig. 2.7 Two element pattern with various interval distance and excitation amplitude

2.2 Uniform Linear Array

45

Fig. 2.8 The pattern when d ≥ λ

When the phase difference between the excitation amplitude a0 and a1 changes, the pattern will rotate, that is, the main beam points to different directions. When the main beam points to ϕ = 90◦ , the antenna array at this time is called a broadside array; when the main beam points to ϕ = 0◦ or ϕ = 180◦ , the antenna array is called an end-fire array. It can be seen from the figure above that as the main lobe of the pattern moves from ϕ = 90◦ to ϕ = 0◦ , the width of the main lobe gradually increases. In addition, when d ≥ λ, there will be multiple main lobes in the pattern. Such main lobes are called grating lobes. As shown in Fig. 2.8. Consider a two-dimensional array with three half-wave dipoles placed along the axis, one at the origin, one on the x-axis, and the other on the y-axis, with a spacing of d = λ/2. As shown in Fig. 2.9. Element excitation amplitude are a0 , a1 , a2 respectively, position vectors are d 1 = xd, d 2 = yd. Then: e j k·d 1 = e jkx d = e jkd sin θ cos φ

(2.40)

e j k·d 2 = e jk y d = e jkd sin θ sin φ

(2.41)

The array factor can be written as: A(θ, φ) = a0 + a1 e jkd sin θ cos φ + a2 e jkd sin θ sin φ

Fig. 2.9 Two-dimensional antenna array

(2.42)

46

2 The Basic Principle of Phased Array

Fig. 2.10 The pattern of the two-dimensional array

The normalized gain can be written as:    cos(0.5π cos θ ) 2  gtot (θ, φ) = |A(θ, φ)|2 g(θ, φ) = | A(θ, φ)|2   sin θ

(2.43)

g(θ, φ) is the directivity function of the half wave dipole. In the x-o-y plane (θ = 90◦ ), the directivity pattern can be written as: 2  gtot (θ, φ) = a0 + a1 e jkd cos φ + a2 e jkd sin φ 

(2.44)

Figure 2.10 presents the pattern with various excitation amplitude of the twodimensional array.

2.3 Principle of Pattern Multiplication 2.3.1 Principle of Pattern Multiplication Array antenna is a kind of special antenna form which is composed of several antenna units, which are arranged according to certain geometric rules. Compared with a single antenna, the array antenna can obtain the desired radiation characteristics

2.3 Principle of Pattern Multiplication

47

z

Fig. 2.11 N element antenna array with arbitrary arrangement

n

o y

x

through appropriate cell selection, arrangement and excitation settings, including the direction and maximum gain of the pattern beam. For the N separate same antenna unit arrays shown in Fig. 2.11, the direction function f (θ, ϕ) in the direction (θ, ϕ) can be expressed as: f (θ, ϕ) =

N 

In e jk rn r f n (θ, ϕ)

(2.45)

n=1

Here, In = |In |e jan (n = 1, 2, · · · N ) is the complex excitation coefficient of the nth element, an is the excitation phase of the nth element, k = 2π/λ is the wave number, r n = xn xˆ + yn yˆ + z n zˆ (n = 1, 2, · · · N ) is the unit vector at field point, and, f n (θ, ϕ) (n = 1, 2, · · · N ) is the direction function of the nth element. If all the elements are same, the direction function can be expressed by f 0 (θ, ϕ), so Eq. (2.45) can be rewritten as f (θ, ϕ) = f 0 (θ, ϕ)

N 

In e jk rn r = f 0 (θ, ϕ) f a (θ, ϕ)

(2.46)

n=1

Here, | f 0 (θ, ϕ)| is the element pattern function, which is only decided by geometry structure, size of the antenna, and is called the element factor. | f a (θ, ϕ)| is related to the current distribution on element, array space distribution and number of elements, which is called array factor. In Eq. (2.46), if all the elements are same, the array pattern is just the product of the element factor and array factor, this is just called the product theorem of pattern.

48

2 The Basic Principle of Phased Array

2.3.2 Ideal Array 2.3.2.1

Omnidirectional Element and Array

The ideal omnidirectional element means the far field is a sphere with radius 1, and the directivity is 0 dB, f e = 1 as shown in Fig. 2.12. So, the linear array pattern can be written as: f (θ, θ0 ) = f a (θ, θ0 ) f e = f a (θ, θ0 ) f a (θ, θ0 ) =

N 

e jk(n−1)dcos(θ−θ0 )

(2.47)

(2.48)

n=1

This equation means that the array beam is just determined by the array factor. For a linear array of eight ideal omnidirectional element with half-wavelength interspace, as shown in Fig. 2.13, the array beam can point to 0°, 30° and 60° during the scanning with the phase difference between the neighbor elements varying, which is given in Fig. 2.14. It is clear that the beam gain is same during the scanning. This case has been used in the wireless system to analyze the wireless system capacity and performances.

Fig. 2.12 Element factor of the ideal omnidirectional element Fig. 2.13 1 × 8 linear array with interval distance 0.5λ

0.5λ

2.3 Principle of Pattern Multiplication

49

Fig. 2.14 Array beam pointing to 0°, 30° and 60° for the linear array of eight ideal omnidirectional element with half-wavelength interspace

2.3.2.2

Dipole and Array

In the real system, ideal omnidirectional element doesn’t exist. In fact, dipole is the simplest element, the normalized far field can be written as f e = cosθ

(2.49)

It can be plotted as in Fig. 2.15. It is clear, the peak of the half wavelength element lobe is 1.76 dB at θ = 0o , but decreases with the angle increasing. The half wavelength dipole is extended to an eight elements linear array in Fig. 2.13. If ignore the coupling between antenna elements, the array factor can be similar as Eq. (2.47). So the array pattern can be get by Eq. (2.46). f = f a (θ, θ0 ) f e (θ ) =

N 

e jk(n−1)dcos(θ −θ0 ) cosθ

(2.50)

n=1

Directivity (/dB)

0

dipole

-10

-20

-30

-40 -80

-60

-40

-20

0

Fig. 2.15 Element factor of the half wavelength dipole

20

40

60

80

50

2 The Basic Principle of Phased Array

Fig. 2.16 Array beam pointing to 0°, 30°, 60° and 72° based on the half wave length dipole element

Here, we set main beam direction of the array factor θ0 = 0°, 15°, 30°, 45°, 60°, 75° and 90°, the array scanning beams are given in Fig. 2.16. It is clear, the main beam direction of the array is less than the main beam direction of the array factor. The beam gains decrease with the beam peak directions increase. Compare the omnidirectional elements array and half wavelength dipole array, their array factors are same, but the linear dipole array shows clear gain rolling off with the scanning angle increasing. The reason is mainly the far field of the dipole is cosθ , not omnidirectional. With the increase of scanning angle, the contribution of element factor to array gain decreases until there is no contribution, even negative. In fact, if considering the elements coupling, the gain rolling off will be more serious.

2.4 Wide Angle Scanning Array Many methods have been used to widen the scanning angle of array. Here we show two method to the wide-angle scanning array. The 1st one is the wide lobe element is used to large scanning angle array, which introduces the binary coding meta-surface layers into the antenna to widen the lobe width. Another one is to introduce the high impedance surface (HIS) to low profile antenna to realize the wide scanning angle array.

2.4.1 Millimeter Wave Array Based on Digital Coded Metamaterial Nowadays, due to spectral congestion in sub-6 GHz bands and the desire for high data rate, millimeter (mm) wave communication have been the key to the emerging 5G mobile communication. It can easily support gigabit-per-second (Gbps) data rates in wireless channel, and has attracted many researchers and leading researching

2.4 Wide Angle Scanning Array

51

organizations attention [4–6]. Broadband, multi-polarized, compact and conformal mm-wave antenna is a good candidate to support the extremely high data rate in 5G wireless communication. To date, in [7], a mm-wave microstrip mesh array with high gain and the capability of dual polarization is reported. In [8], a mm-wave dual-polarized L-shaped horn antenna with waveguide feed structure is proposed. However, their bandwidths are not wide enough. Many technologies have been employed to broaden the bandwidth of mm wave antenna in [9–11]. A third-order vertically coupled resonant structure is proposed in [9] and realized a wide bandwidth of 37% operating at Ka band. In [10], the U-slot structure is employed to broaden the bandwidth and the antenna have a relative wide bandwidth of 21.92% in mm-wave frequency. In [11], the Eshape patch is used to design broadband antenna, achieving a wide bandwidth of 23.5%, specifically from 31.6 to 40 GHz. The aforementioned antennas are linear polarized antennas. A dual-polarized magneto-electric dipole with bandwidth of 65.9% is excited by T-shaped strips at both input ports [12]. It is three-dimensional structure, and inconvenient to implement. In addition, antenna array plays an important role in mm-wave communication, which supports high-gain and the adaptive scanning beam to combat the increased path loss at mm-wave frequencies [5]. However, the available scanning angle is limited since the beamwidth of the antenna element is narrow and the mutual coupling among the elements of array increases with the scanning angle [13]. Therefore, a straight forward solution to this problem is to widen the beamwidth of the antenna element. There are many methods to broaden the beamwidth of the element, such as employing thick and high-permittivity substrate [14], introducing the metal wall [15], and using the distributed patch structure [16]. However, they have limitations such as narrow bandwidth and single polarization. In this part, a binary-code mm-wave antenna with broadband, dual-polarization and wide beamwidth is proposed. The driven patch and the parasitic patch are formed by series of small rectangular units optimized by binary codes with multi-objects. The designed mm wave antenna element can work from 21.8 to 33.2 GHz. And an 8-element linear array with more than 100° scanning angle is implemented too. The antenna element design and analysis are conducted in Sect. 2. Then the measured results and discussion are followed in Sect. 3 and the antenna array is shown in Sect. 4. Finally, the conclusion is drawn in the Sect. 5.

2.4.1.1

Binary Coding Grid Setting in Rough Design

In traditional grid setting, it is still difficult to guarantee a continuous structure, also, checking the continuity after the structure is build and then rebuilding the discontinuous structure will waste a lot of time. Here, a new method that set the grids one by one according to a certain order is presented to guarantee a continuous structure. Assuming that the area is divided into 10 × 10 grids and use 10-dimensional A-CLPSO for optimization [17]. A string of 90 binary digits is employed to guide the grids setting (why only use 90 digits to guide 100 grids’ setting is discussed later

52

2 The Basic Principle of Phased Array

after the whole process is instructed). To gain this string, the search range on each dimension is set as [0, 512] and the particle’s position on every dimension can be changed into a 9-digit binary number (the position firstly goes through an operator “int()” to be changed into integer from 0 to 511). After the values on the 1st dimension to the 10th dimension are changed one by one, a string of 90 binary digits is gained. Then the grids are set to “0” or “1” as following: Step 1 (Shown in Fig. 2.17a): The design area is initialized with the four grids in the center of the area set as “1” while other grids set as “NULL”. These four grids of “1” are named A, B, C and D (these named grids are called “letter” grids) and A is defined as B’s father grid (used as a coordinate reference in the next step), B is C’s father grid, C is D’s father grid, D is A’s father grid. Step 2 (Shown in Fig. 2.17b): Beginning from A and defining the direction that point from A to its father grid as “north”, the grid in the “east”, “south” and “west” of A is set as the value of the digit in the binary string one by one if the grid has not been set (is still “NULL”). If the grid is already set (is “0” or “1”), the corresponding digit in the binary string is reserved and the next grid’s setting will starts on that digit. Then, A is defined as the father grid of those grids generated by A in this step.

011101101000101001

(a)

(b)

011101101000101001

(c)

011101101000101001

(d)

(e)

(f)

Fig. 2.17 The structure construction process (the digits being used for the grid setting in current Fig are shown in bold): a Step1; b Step 2. When setting the third grid around A which is already a grid of “1” (it is named B but it has been set to “1” in the initialization), the third digit is reversed and the next setting starts on it; c Step 3; d Step 4; e Step 2, 3 in the second circulation. f Step 4 in the second circulation and then it is ready for the third circulation. Figure reproduced with permission from Ref. [17], © 2009 IEEE

2.4 Wide Angle Scanning Array

53

Step 3 (Shown in Fig. 2.17c): All the grids around B, then ones around C, then ones around D are set by the same method in Step 2. Step 4 (Shown in Fig. 2.17d): The new generated grids of “1” are named A, B, C… according to the order that they have been generated in Step 2 and Step 3, Then, all the previous “letter” grids’ name are canceled (they become back to grids of “1”). Now, the characteristic of the divided design area is back to Step 1 that there are some “letter” grids and every new “letter” grid has its own father grid to guide other grids’ setting around them. So, the next step circulates back to Step 2. The whole operation repeats Step 2, 3, 4 until either of the following conditions happen: 1. 2.

All the binary string is read over No new grid “1” is created.

An example is shown in Fig. 2.17 which illustrates how the grids are set when a particle’s position in the 10-dimensional A-CLPSO is at (237, 41, X, X, …, X) and thus the transformed binary string is 011101101000101001X…X (this example only shows the setting with the first 18 digits in the binary string, so only the 1st and the 2nd dimension are concerned) [17]. In this process, the created structure is continuous. However, grids generated by a certain father may block the later nearby generation of another father. For example, in Fig. 2.17e, because the nearby generation of B grid is earlier than C grid, when the upper grid of B grid is set, it blocks setting it again although it is also the left grid of C grid. Because of the blockade, in almost all the processes, only less than 80 digits have been read when the stop condition ➁ happen–although there are some grids are still “NULL”. So using a string of 100 binary will waste almost the last 20 or more binary digits. It means that a string of 90 binary is enough to create a completed structure. As an example, our aim is a multi-band monopole antenna, so the feed line should be connected with the antenna. To guarantee this characteristic, after creating the structure above, all the grids “0” are changed into grids “NULL” and then the two grids in the middle of the bottom line of design area are initialized as “1”. Then the other grids are set as “1” or “0” according to the method discussed above. Consider that the connection between antenna and feed line do not need too many grids, only the last 27 digits of the binary string is used to guide this connection generation.

2.4.1.2

Model and Geometry Structure of Antenna

The geometry of the proposed digit-code antenna element is shown in Fig. 2.18, which is composed of two substrates denoted by Substrate 1 and Substrate 2 and three copper layers connected by vias with radius of r 1 , as shown in Fig. 2.18b. Both two substrates are Arlon 250 with the thickness of 1.524 mm and relative permittivity of 2.5. For the three copper layers, the bottom layer is the ground plane, while the middle copper layer is the parasitic and the top layer is the driven patch. And the driven patch is fed by two symmetrical coaxial probes with SMA connector

54

2 The Basic Principle of Phased Array

Fig. 2.18 Configuration of proposed antenna. a 3-D view of proposed antenna. b exploded view showing individual layers c Driven patch. d Parasitic patch. Figure reproduced with permission from Ref. [18], © 2019 IEEE

underneath the ground plane. To facilitate weld between the coaxial probe and driven patch, two circular rings with a radius of r 2 are introduced. The proposed digit-code structures of driven and parasitic patches are shown in Fig. 2.18c, d, which consists of 10 × 10 grids with the size of w1 × w1 , and the initial value is based on the wave length of aim frequencies. The state of each grid is determined by a binary code, in which the code “1” represents a grid with metal and “0” represents air. The codes “0” and “1” are determined by int () function, which are given by:  int(x) =

0 0 < xi < 1 1 ≤ i ≤ 100 1 1 ≤ xi < 2

(2.51)

2.4 Wide Angle Scanning Array

55

Table 2.1 Optimized geometric parameters of the proposed antenna Parameters

w1

w2

a

r1

r2

h

Values (mm)

0.46

0.1

6.6

0.325

0.51

3.11

where, x i is a random variable [14]. Binary strings of driven and parasitic patches are divided into two mirror-symmetric structures to reduce binary digits from 100 to 55, and the optimization is then accelerated. Meanwhile, considering the point-to-point connection and its instable fabrication, some metal square patches with the size of w2 × w2 are introduced. The impedance bandwidth, upward radiation and beamwidth are set as optimization aim function, and optimize the xi samples on each grid and other size parameters by CST Microwave Studio software with the finite integration technique (FIT) method and PSO method. The parameters of the proposed antenna and representing states of grids are shown in Table 2.1 and Fig. 2.18, respectively. In Fig. 2.19a, the optimized final results of “0” and “1” distribution of the driven patch are shown, and the corresponding geometry structure of the patch is given in

Fig. 2.19 Binary codification of grid and its represent state (“0” represents substrate and “1” represents copper, “black” represents substrate and “yellow” represents copper). a Driven patch printed on substrate 1. b Parasitic patch printed on substrate 2. Figure reproduced with permission from Ref. [18], © 2019 IEEE

56

2 The Basic Principle of Phased Array

Fig. 2.19b. Similarly, the binary strings of the parasitic patch are in Fig. 2.19c, and the printed parasitic patch is in Fig. 2.19d. It is symmetrical around the diagonal line for the constructing method. If all grids are the state of “1”, the proposed binarycode antenna is returned to the dual-port microstrip antenna. Therefore, compared to the traditional antenna, more optimization parameters in the proposed antenna are introduced and optimized, which contributes to wider bandwidth and beamwidth. By optimizing the x i samples on each grid, some square slots are properly introduced and the shape of patch is modified. Moreover, several branches shaped in the top patch and parasitic patch are realized. These branches may resonate at different frequencies. All these frequency bands contribute to the final available broad band. Figure 2.20 shows the surface current on the driven patch and parasitic patch. It can be observed that several current paths are realized and different length of current paths correspond to different resonant frequencies [15]. Meanwhile, the current phase of the patch is modified, the phase of y-oriented current component along the curve B– B′ on the optimized patch is shown in Fig. 2.21. It can be observed that the variation of current phase along the curve B–B′ is significant. The extracted phase difference between C and D is almost 165° tending to out-of-phase. And the current elements with inverse phases increase the beam gain inclining horizontal direction, and widen the beamwidth [10]. The simulated polarization of the proposed antenna is depicted in Fig. 2.22. It can be observed that the +45° polarization is the co-polarization for port 1 in a wide beamwidth and the −45° polarization is the cross-polarization for port 1. while the amplitude of −45° polarization almost equal the +45° polarization in a small region near by the z axis, but the phase difference is almost 90° in this region, so the circular polarization is realized. Because of the proposed antenna is symmetric structure, the polarization of port 2 can be deduced correspondingly.

D

C B

B

(a)

(b)

Fig. 2.20 The surface current distribution on the driven patch and parasitic patch for port 1 at 25 GHz a driven patch b parasitic patch. Figure reproduced with permission from Ref. [18], © 2019 IEEE

2.4 Wide Angle Scanning Array

57

Fig. 2.21 Simulated surface current phase distribution of the proposed antenna for port 1 at 25 GHz [18]

Fig. 2.22 Simulated polarization of proposed antenna a Abs b Axial ratio c +45° polarization d −45° polarization. Figure reproduced with permission from Ref. [18], © 2019 IEEE

For comparison, the proposed antenna optimized by binary string is denoted by Ant 1 and the traditional dual-port microstrip antenna with parasitic patch is denoted by Ant 2. Figure 2.23 shows their comparison of reflection coefficient and isolation between the two ports. It can be observed that the simulated 10 dB bandwidth of Ant 1 is 11.4 GHz over 21.8–33.2 GHz (relative impedance bandwidth is 41.5%) and the

Fig. 2.23 Simulated return loss and isolation of Ant 1 and Ant 2. Figure reproduced with permission from Ref. [18], © 2019 IEEE

58

2 The Basic Principle of Phased Array

Fig. 2.24 Simulated radiation pattern of Ant 1 and Ant 2 for port 1 in x-o-z plane at 25 GHz. Figure reproduced with permission from Ref. [18], © 2019 IEEE

impedance bandwidth of Ant 2 is 6.9 GHz over 22.4–29.3 GHz (relative impedance bandwidth is 27.7%). It is noted that the bandwidth of Ant 1 is wider than Ant 2 by 13.8%. Furthermore, the port isolation of Ant 1 and Ant 2 is large than 10 dB over the impedance bandwidth, which means that, Ant 1 keeps good isolation between two ports after optimizing the random variable to modify the patch. Figure 2.24 illustrates the comparison of normalized radiation pattern in the x-o-z plane for port 1 at 25 GHz. It can be observed that the beamwidth of traditional patch Ant 2 is merely 73.4° , while Ant 1 has beamwidth up to 141° . Therefore, it is potential for Ant 1 to be adopted as an element in antenna array to realize wide-angle scanning.

2.4.1.3

Measured Result Analysis to the Prototype of the Antenna

In order to verify the simulation results, this section processes a binary coded antenna according to the above simulation results, and carries out the measurement in the dark room. The antenna entity and test environment are shown in Fig. 2.25. Fig. 2.26 shows the comparison of S parameters between simulation and test. The

Fig. 2.25 Simulated radiation pattern of Ant 1 and Ant 2. a The view of different layers b measurement environment. Figure reproduced with permission from Ref. [18], © 2019 IEEE

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Fig. 2.26 Measured and simulated S-parameters of proposed antenna. Figure reproduced with permission from Ref. [18], © 2019 IEEE

reflection coefficients of simulation and test basically coincide. The frequency range of return loss greater than 10 dB based on binary coded antenna is about 21.8 GHz to 33.2 GHz, and the relative impedance bandwidth is about 41.5%, showing good broadband performance. For the isolation of port 1 and port 2, the trend of simulation and test is almost the same, but due to the coaxial feeder and processing error in millimeter wave band, the isolation of test in frequency band is better than that of simulation. In a word, compared with S parameter, the machining and simulation have a good agreement. According to the comparison diagram of gain curve between test and simulation given in Fig. 2.27, it can be seen that the gain of the antenna in the whole frequency band is basically greater than 4 dB, and the maximum can reach 5.8db. Although the gain curve of the antenna in the actual measurement has a certain fluctuation compared with that in the simulation, the specific reason may be caused by the processing accuracy of the millimeter wave band antenna and the alignment of the reference line in the test, but the overall test curve is stable Line around the simulation curve, with good consistency. Figure 2.28 shows the radiation patterns in x-o-z plane and y-o-z plane of the simulation and test of antenna port 1 excitation. It can be seen that in x-O-z plane,

Fig. 2.27 Measured and simulated realized gain of proposed antenna. Figure reproduced with permission from Ref. [18], © 2019 IEEE

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2 The Basic Principle of Phased Array

Fig. 2.28 Measured and simulated realized gain of proposed antenna for port 1. a 24 GHz b 27.5 GHz c 30 GHz. Figure reproduced with permission from Ref. [18], © 2019 IEEE

the simulation and test of each frequency point of binary coded antenna have good agreement. At 24 GHz, the half power beamwidth of the antenna radiation pattern in the x-o-z plane is about 154 degrees, at 27.5 GHz, the half power beamwidth of the antenna radiation pattern in the x-o-z plane is about 128 degrees, and at 30 GHz, the half power beamwidth of the antenna radiation pattern in the x-o-z plane is about 149 degrees. It can be seen that the radiation pattern of the antenna is stable and the beam width is wide in the whole frequency band of x-o-z plane. In the y–o-z plane, the simulation and test of binary coded antenna at each frequency point are basically consistent. But because the antenna is a hybrid polarization antenna, the cross polarization of the antenna can’t be measured completely, so the amplitude pattern of the antenna is given in this section.

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2.4.1.4

61

Millimeter-Wave Array

It can be seen from the above section that the dual port antenna based on binary coding has good broadband and wide beam performance, and can be used as the element of large angle scanning array. On the one hand, when the array element has a wide bandwidth, its active standing wave is often better. On the other hand, according to the pattern product principle, the pattern function of the array is the pattern function of the element multiplied by the scan function of the array. Therefore, when the bandwidth of the array element is wide and the beam width of the pattern is wide, large angle scanning can be achieved after the array is assembled [19]. The binary coded antenna is used as the array element to realize a 1 × 8 lineararray along the x-axis. In order to control the influence of the grating lobe, the distance between the elements should be controlled about, λ/2 in which λ is the wavelength in free space. The center frequency of 27.5 GHz is taken as the reference, and the distance between the elements is set to be 4.6 mm. In order to verify the scanning performance of the antenna array, the simulation model of the antenna array is processed and tested in the dark room. When the antenna is tested, the phase feeder with equal gradient phase difference is used to feed and provide phase difference. The antenna array is shown in Fig. 2.29. The test results are shown in Fig. 2.30. It can be seen that the simulation results of the antenna are basically consistent with the measured results. At 24 GHz, the scanning range of the antenna can reach 130° and the gain roll off is less than 3 dB. When the antenna works at 27.5 GHz, the measured scanning angle range of the antenna is −50° to +50°, but because the radiation pattern of the antenna itself has an offset at 27.5 GHz, the gain roll off of the antenna reaches 4.1 dB at +50° and only 1.4 dB at −50°, so the simulated −60°scanning curve is given in Fig. 2.30b. It can be seen that the gain roll off of the antenna is less than 3 dB at −60°. However, due to the lack of feed line in the experiment, the scanning effect of −60° is not measured,

Fig. 2.29 The model of antenna array. a The simulated model b The measured model. Figure reproduced with permission from Ref. [18], © 2019 IEEE

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Fig. 2.30 Simulated and measured beam scanning of wide-angle scanning array. a 24 GHz b 27.5 GHz c 30 GHz. Figure reproduced with permission from Ref. [18], © 2019 IEEE

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but from the measured effect of −50° to +50° it can be seen that the measured effect of the antenna is basically stable. It can be inferred that the scanning angle range of the antenna can reach about 100° at 27.5 Ghz. The scanning effect of the antenna at 30 GHz is shown in Fig. 2.30c. Due to the influence of broadband, if 27.5 GHz is used as the center frequency point to set the spacing of array elements, for 30 GHz, the spacing of array elements is large, and grating lobe is easy to appear. However, because the half power beam width of the antenna element at 30 GHz is wide, the gain roll-off of the array within 100° scanning range is less than 3 dB. The gain range of the antenna is about 9.3 to 12.1 dBi at 24 GHz, 9.2 to 12.1 dBi at 27.5 GHz and 9 to 11.4 dBi at 30 GHz. In a word, the simulation and experimental results of the antenna array match well, and the array has good large angle scanning ability because of the unit’s broadband and wide beam performance.

2.4.1.5

Summary to the Binary Coding Millimeter-Wave Array

A comparison between the proposed antenna and other reported antennas is shown in Table 2.2. It is seen that the proposed antenna features wide bandwidth, dual polarization, and wide beamwidth. In addition, the phased array composed of the proposed antenna with wide-angle scanning can be readily achieved. In this section, a broadband dual-polarized binary coding antenna with wide beamwidth is presented for mm-wave applications, which is based on a two-layer structure as well as binary coded driven and parasitic patches. The measured prototype of antenna element demonstrated an impedance bandwidth of 41.5% at mmwave band, and a beamwidth large than 128° in x-o-z plane. Moreover, a 1♦8 phase array based on it, with a wide angle scanning of more than 100° over the available band is readily developed. Consequently, the proposed antenna and its array could be a good candidate for future 5G applications. Table 2.2 Comparisons between the proposed antenna and other models Ref

BW (%)

Polarization

Beamwidth

Beam-scanning angle (array) / ≥40°

[8]

16

Dual polarization

100°

[9]

37

Single polarization

/

[11]

23.5

Single polarization

/

/

[14]

12.6

Single polarization

102°

/

[16]

9.9

Single polarization

116°

/

Dual polarization

128°

≥100°

This work

41.5

Table reproduced with permission from Ref. [18], © 2019 IEEE

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2.4.2 Wide Angle Scanning Array Based on the HIS As an important type of antenna, dual polarization antenna is widely used in various communication scenarios because it can not only suppress the multipath effect and improve the channel stability, but also greatly improve the polarization diversity and reduce the communication cost. For example, mobile satellite communication (SATCOM), base station communication and synthetic aperture radar (SAR) and so on, use dual polarization antenna. In order to meet the increasingly rapid development of modern communication, dual polarization antenna needs wider impedance bandwidth, higher polarization isolation and stable radiation pattern. In addition, the miniaturization of low profile has become an important index of dual polarization antenna, which is particularly critical for high-speed carrier and satellite communication. For the high-speed mobile communication platform, the miniaturized lowprofile antenna can not only greatly reduce its own wind resistance, but also be easy to be conformal with the carrier. Therefore, on the basis of maintaining the aerodynamic characteristics of the carrier, it can greatly reduce the cost of the system and improve the communication stability [20]. On the other hand, the communication platform in high-speed mobile often needs to be in a complex moving environment. In order to maintain real-time, stable and efficient communication with satellites, the antenna (array) needs a certain large angle beam scanning ability [21, 22]. Therefore, it is of great value to design a miniaturized dual polarization antenna with low profile and form an array with large angle scanning. In this part, a low-profile dual polarization antenna is designed to meet the needs of S-band high-speed mobile carrier and satellite communication. The antenna consists of two pairs of cross dipoles, a high impedance surface (HIS) structure and parasitic structure. The dual polarization radiation is realized by exciting the cross dipole, and the high impedance surface is excited by the cross dipole to work with zero reflection phase and TE surface wave resonance mode, so as to achieve the effect of low profile and broadening the working bandwidth respectively. The parasitic structure and short circuit pin can improve the impedance matching and polarization isolation. Compared with the traditional high impedance surface, the proposed his can adjust the impedance matching of the antenna well while maintaining the zero-reflection phase and TE surface wave modes, so that the antenna has a wide bandwidth. Through simulation, processing and testing, it is found that the antenna has a very low profile (0.06 λ) of 7.5 mm, which can achieve a bandwidth of 2.0– 3.0 GHz, and the polarization isolation is more than 30 dB in the working band. Furthermore, the low-profile dual polarization antenna unit is expanded into a 1 × 8 phased array to realize beam scanning. In order to verify the scanning ability of the array, it is simulated, processed and tested. The results show that the array can achieve ±50° wide beam scanning in two polarization directions.

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2.4.2.1 A.

65

Dual Polarization Element Design Based on HIS

Antenna structure

The structure of low-profile dual polarization antenna unit based on high impedance surface is shown in Fig. 2.31 Configuration of the low-profile dual-polarized antenna element: (a) Three-dimensional view of the antenna. (b) Detailed drawing of the antenna. Figure reproduced with permission from Ref. [23], © 2019 IEEE. The antenna consists of three parts: two pairs of orthogonal cross dipoles, high impedance surface structure, parasitic and short circuit structure. Each pair of crossed dipoles consists of two "bow tie" shaped radiating arms printed on two layers of rogerro4350 dielectric plates. The thickness of the dielectric plate is 0.762 mm, the relative dielectric constant is 3.5, and the loss tangent is 0.0037. Taking x-polarization as an example, the radiation arm of the cross dipole in this direction is directly connected with the outer conductor of the coaxial line by welding, while the radiation arm on the upper dielectric plate is connected with the inner conductor of the coaxial line by a small section of microstrip line. The same is true for y-polarized cross dipoles. In order to avoid the short circuit of two pairs of crossed dipoles, a microstrip line connection structure similar to “bridge” is used in the middle part of the two pairs. In order to optimize the impedance matching, we design a small “bow tie” parasitic structure directly opposite each radiation arm of the cross dipole, and introduce two short-circuit pins directly opposite the coaxial line to improve the polarization isolation. The high impedance surface is printed on a 6 mm thick FR-4 dielectric plate with a relative permittivity of 4.4 and a loss tangent of 0.025. It is worth noting that the high impedance surface is composed of periodically arranged elements, which are separated by regular octagons and squares. Finally, the overall size of the antenna is about 73 mm × 73 mm × 7.5 mm. The specific parameters of the antenna are shown in Table 2.3. B.

The Principle of the antenna

In order to realize the dual polarization radiation characteristics, the antenna can realize the dual polarization mode by exciting two pairs of orthogonal cross dipoles. In order to realize the directional radiation, a reflection cavity is needed, that is, a metal surface is placed under the cross dipole to realize the reflection of electromagnetic wave. The traditional method is to place a floor at a quarter wavelength below the cross dipole to achieve the maximum efficiency of electromagnetic reflection. However, it is inevitable that the antenna profile is too large to meet the requirements of miniaturization and low profile. In order to achieve the low profile and broadband characteristics of the antenna, a new high impedance (his) surface structure is introduced in this chapter, as shown in Fig. 2.32. When the cross dipole is placed above HIS, the antenna can work in two modes: zero reflection phase mode and TE surface wave resonance mode. When the reflection phase of the high impedance surface to the plane electromagnetic wave is zero, the first resonance point appears in the antenna system composed

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Fig. 2.31 Configuration of the low-profile dual-polarized antenna element: a Three-dimensional view of the antenna. b Detailed drawing of the antenna. Figure reproduced with permission from Ref. [23], © 2019 IEEE

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Table 2.3 Dimensions of the HIS-based low-profile dual-polarized antenna element (unit: mm) [23] Parameters

L1

L2

R1

R2

G

g

W1

Wr

3

2.4

72.97

0.6

4.5

6.02

Values

13.05

3.5

Parameters

Wg

Wm

values

1

6.67

Table reproduced with permission from Ref. [23], © 2019 IEEE

Fig. 2.32 Configuration of the unit cell of the HIS: a Simulated model. b Exploded view of the structure [24]

of the cross dipole and the high impedance surface, and the antenna can radiate efficiently in the range of the reflection phase of ±90°, which is called in-phase reflection region. Therefore, in order to select the appropriate resonance point, the reflection characteristics of high impedance surface need to be simulated and analyzed by CST. In CST, by setting periodic boundary conditions, only one element of the high impedance surface needs to be simulated to obtain the reflection characteristics of the whole structure, as shown in Fig. 2.32. It consists of two layers of Rogers 4350 dielectric plate, one layer of metal patch layer, one layer of FR-4 dielectric plate and floor. The size of the unit is l × l, the thickness of the FR-4 dielectric plate is h1 , and the thickness of the Rogers 4350 dielectric plate is h2 . Figure 2.33 discusses the effects of high impedance surface element size L, FR-4 dielectric thickness H1 and octagonal and square gap on the reflection characteristics, respectively. It can be seen from Fig. 2.33a that with the increase of cell size L, the zero-reflection phase point moves to the low frequency; Fig. 2.33b shows that when the thickness of FR-4 plate becomes smaller, the zero reflection phase point moves to the high frequency, and the change amplitude is larger; Fig. 2.33c shows that when the gap between regular octagon patch and square patch becomes larger, the zero reflection phase point moves to the high frequency. By comparing the above simulation results, we select the parameters of high impedance surface: l = 24.32 mm, gap = 1.1 mm, H = 6 mm, and the zero-reflection phase point of the structure is

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Fig. 2.33 Effects of different parameters on the reflection phase of the HIS: a Dimension of the unit. b Height of the substrate. c Gap between the metal patch [24]

2.15 GHz. The in-phase reflection range of ±90° is from 1.9 GHz to 2.5 GHz, meeting 31% of the relative bandwidth. When the cross dipole excites the high impedance surface, the TE surface wave on the high impedance surface will be excited, and the resonance frequency of the surface wave is the second resonance frequency of the whole antenna unit. The resonance point of TE surface wave is approximately determined by Eq. (2.52), where βTe is the propagation constant of TE surface wave, n is the number of elements

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Fig. 2.34 Dispersion diagram of the HIS [24]

in high impedance surface structure, and l is the size of elements. The dispersion characteristics of the high impedance surface can be obtained by the eigenmode solver in CST. Figure 2.34 shows the dispersion characteristic curve of a cell on a high impedance surface. It can be seen from the figure that when the phase change of the cell is 120°, the corresponding frequency is 2.7 GHz; in other words, when the high impedance surface is composed of three such cells, the phase change is exactly 360° and the corresponding frequency is 2.7 GHz, that is, the high impedance surface resonates at this frequency point. Through the introduction of the resonant point, the working bandwidth of the antenna can be broadened to a certain extent, and the broadband characteristics can be achieved: BTE × n × l = 2π

(2.52)

After determining the two working modes and corresponding sizes of the high impedance surface, it is necessary to combine the high impedance surface with the cross dipole for simulation analysis, so as to obtain the overall performance of the antenna. Here, the dual polarization antenna based on the new high impedance surface is compared with the antenna based on the traditional high impedance surface, as shown in Fig. 2.35. Figure 2.35a is a schematic diagram of a traditional antenna. It can be seen that the antenna uses the same cross dipole, and the high impedance surface

Fig. 2.35 Configuration of the a conventional and b proposed HIS-based antenna

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Fig. 2.36 Comparisons of the simulation results on the conventional and proposed HIS: a Reflection phase. b Dispersion diagram. Figure reproduced with permission from Ref. [23], © 2019 IEEE

at the bottom is composed of square metal patches. The material and thickness of the dielectric plate used in the two antennas are consistent. By optimizing the parameters of the traditional high impedance surface, the in-phase (±90°) reflection range and te surface wave resonance frequency can be obtained. The results are compared with those of the new high impedance surface, as shown in Fig. 2.36. It can be seen from Fig. 2.36a that the reflection characteristics of the two are almost the same, and the zero-reflection phase point is at 2.15 GHz. However, the dispersion characteristics of the two are slightly different. The resonance frequency of TE surface wave on traditional high impedance surface is about 3.1 GHz, while that of TE surface wave on new high impedance surface is about 2.7 GHz. Compared with the traditional high impedance surface, the resonant frequency points of the two modes are far away, while the new high impedance surface is close, so it is easier for the new high impedance surface to use the two resonant points to achieve a wider bandwidth. Further, the impedance matching of the two antennas can be obtained through the simulation of the two antennas as a whole. Figure 2.37 shows the input impedance curves and S parameters of the two antennas. It can be seen from Fig. 2.37a that at the first resonant frequency point (zero reflection phase point), the real part of the input impedance of the traditional antenna is about 100 Ω, and the imaginary part fluctuates violently around zero. For the new antenna, because of the use of regular octagon patch and the insertion of small square patch in the middle of octagon, the impedance matching can be optimized under the premise of meeting the two working

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Fig. 2.37 Comparisons of the simulation results on the dual-polarized antenna based on conventional and proposed HIS: a Input impedance. b S-parameters [24]

modes mentioned above. Therefore, the real part of the input impedance of the new antenna drops to 50 Ω at the first resonance point, and the imaginary part fluctuates slightly near zero. The final improved simulation results are shown in Fig. 2.37b. The impedance matching at the first resonant frequency point is greatly improved, which makes the −10 dB impedance bandwidth of the final antenna greatly expanded compared with the traditional antenna. However, it can be seen from Fig. 2.37b that although the impedance bandwidth of the improved antenna is wide, the port isolation of the antenna becomes worse at low frequencies. After analysis, it is considered that this phenomenon is caused by the unbalanced structure of the coaxial line, and this structure will also lead to the distortion of the antenna pattern [1]. Therefore, a short-circuit pin is introduced at the position symmetrical to the coaxial line, so as to improve the isolation of the antenna port and improve the pattern. The S parameters of the antenna with short circuit pin are shown in Fig. 2.38. It can be seen from the figure that when the short-circuit pin is introduced, the port isolation of the antenna at low frequency is greatly improved, and it can reach 25 dB in the frequency band from 1.8 GHz to 2.8 GHz. However, the impedance matching of the antenna deteriorates at this time. It can be seen from the figure that the return loss of the antenna becomes worse at low frequency. Through analysis, it is considered that this phenomenon is due to the introduction of short-circuit pin and the corresponding inductance, which affects the impedance matching of the antenna as a whole. As an

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Fig. 2.38 S-parameters of different stages of the proposed antenna. Figure reproduced with permission from Ref. [23], © 2019 IEEE

example, parasitic patches are added to the symmetrical position of each radiation arm of the cross dipole. The capacitance effect between the parasitic patch and its upper/lower radiation arm will counteract the inductance effect caused by the shortcircuit pin. The S parameters of the optimized parasitic structure are shown in the red line in Fig. 2.38. It can be seen that the return loss of the antenna is more than 10 dB in the frequency range of 2.0 GHz to 3.0 GHz. At the same time, the port isolation of the antenna can be greater than 25 dB in the range of 2.1 GHz to 3.0 GHz. C.

Experiment results analysis to the antenna

In order to verify the performance of the low-profile dual-polarized antenna based on the new high-impedance surface designed in the previous section, the antenna was processed and tested in this section. The processed antenna is shown in Fig. 2.39a. Each layer of the antenna is fixed by plastic screws. Finally, the antenna and the cable are welded and fed through the cable. Firstly, the S parameters of the antenna are measured by using the vector network analyzer, and the measured results are compared with the final simulation results obtained in the previous section, as shown in Fig. 2.40. It can be seen from the test

Fig. 2.39 a Prototype of the proposed antenna. b Measurement environment of the antenna [24]

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Fig. 2.40 Simulated and measured S-parameters of the antenna [24]

results that the return loss of the two ports of the antenna is greater than 10 dB in the range of 2.0–3.1 GHz, and the relative bandwidth of 43.1% can be achieved. The measured port isolation is more than 25 dB in the whole working frequency band, even more than 30 dB in the range of 2.2–2.8 GHz. Generally speaking, the measured results are consistent with the simulation results. The measured return loss is slightly larger than the simulated return loss, and it is obvious at two resonance points. After research, it is considered that because the two resonance points of the antenna are more sensitive to the thickness of the medium, and there is a certain error in the thickness of the medium plate in the processing, there will be an air layer when fixed with plastic screws, and there will be errors in the final welding process, so it will have a certain impact on the test results. Then the antenna pattern and gain are measured in the microwave anechoic chamber. The antenna test environment is shown in Fig. 2.39b. Because the two ports of the designed antenna are symmetrical, only one port in the X polarization direction is tested in the pattern measurement. Figure 2.41 shows the E-plane and H-plane radiation patterns measured at 2.2 GHz, 2.5 GHz and 2.8 GHz. It can be seen from the figure that the cross-polarization level of the antenna at three frequency points is lower than −20 dB. At 2.2 GHz and 2.5 GHz, the front to back ratio of Eplane and H-plane patterns is greater than 18 dB. At 2.8 GHz, the front to back ratio is reduced to 10 dB because the TE surface wave introduced by the second mode radiates at the edge of the antenna. In general, the test results of the antenna are consistent with the simulation results, which indicates that the antenna can achieve stable directional radiation in the working frequency band. Since the pattern of Y polarization is similar to that of X polarization, it is not given here. Finally, the gain of the antenna is tested, and the specific gain versus frequency curve is shown in Fig. 2.42. It can be seen from the figure that the gain measured by the antenna in the reworking band is basically maintained between 5 and 6 dBi, which is slightly lower than the simulation value, and is consistent with the variation trend of the simulation results. The small error result is mainly caused by the error in the process of machining and assembly. In general, the dual polarization antenna based on the new high impedance surface designed in this section can achieve 2.0–3.0 GHz bandwidth under the premise of

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2 The Basic Principle of Phased Array

Fig. 2.41 Simulated and measured radiation patterns of the antenna. a E-plane at 2.2 GHz. b Hplane at 2.2 GHz. c E-plane at 2.5 GHz. d H-plane at 2.5 GHz. e E-plane at 2.8 GHz. f H-plane at 2.8 GHz [24]

7.5 mm low profile, and the isolation is basically maintained at more than 25 dB. At the same time, the antenna can achieve stable directional radiation, low cross polarization level, high front to back ratio and stable gain.

2.4.2.2

The Dual-Polarization Array with Large Scanning Angle Based on HIS

In order to meet the requirements of high gain and beam scanning in practical application, it is necessary to group the antenna elements designed in the previous section.

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Fig. 2.42 Simulated and measured gains of the antenna. Figure reproduced with permission from Ref. [23], © 2019 IEEE

Because the antenna unit in the upper section has the characteristics of miniaturization, low profile, broadband and wide beam, it is easy to realize the function of wide angle scanning after array formation. In this section, the antenna unit is directly composed of a 1 × 8 linear-array. The simulation results show that the antenna unit has wide angle scanning characteristics, and can maintain two working modes of the antenna unit to a certain extent. Finally, the performance of the array is verified by processing and testing. A.

The Principle of the array

The antenna units designed in the previous section are directly composed to form a 1 × 8 array for simulation. The simulation model of antenna array is shown in Fig. 2.43. Figure 2.43a is a top view of the high impedance surface in the array; Fig. 2.43b is a top view of the whole antenna array, and the number of each unit in the array has been marked in the figure. According to the analysis in the previous section, there are two resonant modes in the antenna element of the antenna array: zero reflection phase mode and TE surface wave mode. Therefore, it is necessary to study the influence of array formation on these two modes. In order to compare with the array, we first simulate the electric

Fig. 2.43 Top view of a HIS of the array. b Array [24]

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2 The Basic Principle of Phased Array

field distribution on the x-o-z plane when the antenna element is excited in the Y polarization direction, as shown in Fig. 2.44. It can be seen from the figure that the electric field distribution of the antenna unit from 2.1 GHz to 2.3 GHz is concentrated on the top of the antenna, indicating that the antenna works in the same phase reflection range of ±90° as described in the previous section. This result is also consistent with the reflection phase curve in Fig. 2.36a. According to our analysis, when the working frequency of the antenna increases, the resonant mode of the antenna will mainly become TE surface wave resonant mode, and the TE surface wave propagates along the X direction. It can be seen from Fig. 2.44d–f that with the increase of frequency, the electric field distribution starts to concentrate from the top of the antenna to the edge of the antenna in the X direction. This phenomenon indicates that TE surface waves begin to resonate and propagate along the X direction. When the antenna element is excited in the Y polarization direction, the situation is the same, so the analysis is not done here. When the antenna elements form an array, the specific situation needs to be analyzed from the following two aspects: Mode 1: zero reflection phase resonance mode. In the previous section, the simulation of reflection phase of high impedance surface is completed in FSS/metallic template of CST, and the boundary condition of simulation model is set as unit cell boundary condition in the simulation template. That is to say, for a unit, the reflection characteristic obtained by simulation is the reflection characteristic of the structure composed of periodic arrangement of the unit. Therefore, when the structure and size of the high impedance surface do not change, the reflection characteristics of the corresponding array should remain unchanged in theory. Here we also give the electric field distribution of antenna unit 4 in the array. Figure 2.45 shows the electric field distribution on the YOZ plane when the antenna element 4 is excited in the X polarization direction. It can be seen from the figure that in the frequency range of 2.0 GHz to 2.3 GHz, the electric field is mainly concentrated above the antenna. Figure 2.46 shows the electric field distribution on the x-o-z plane when the

Fig. 2.44 Simulated electric field distribution of the antenna element at a 2.1 GHz. b 2.2 GHz. c 2.3 GHz. d 2.5 GHz. e 2.6 GHz. f 2.7 GHz [24]

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77

Fig. 2.45 Simulated electric field distribution in y–o-z plane when the x-polarization of the element 4 is excited at a 2.0 GHz. b 2.1 GHz. c 2.2 GHz. d 2.3 GHz [24]

Fig. 2.46 Simulated electric field distribution in x-o-z plane when the y-polarization of the element 4 is excited at a 2.0 GHz. b 2.1 GHz. c 2.2 GHz. d 2.3 GHz [24]

antenna operates in Y polarization. At the same time, the electric field component is mainly concentrated on the top. This means that the antenna in the array can also maintain the resonance mode of zero reflection phase in both polarization directions, which is the same as that of the element. Furthermore, because the array needs to realize beam scanning, it is necessary to discuss the reflection characteristics of high impedance surface when the incident electromagnetic wave angle is different.

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2 The Basic Principle of Phased Array

Figure 2.47 shows the reflection phase of the high impedance surface when the incident angle of the plane electromagnetic wave changes from 0 to 50 degrees. It can be seen that when the incident angle θ increases gradually, the frequency point corresponding to the zero-reflection phase moves from 2.15 GHz to 2.2 GHz. Generally speaking, the change amplitude is small and can be ignored. In a word, even when the array is scanning, the array can maintain the zero-reflection phase resonance mode as a unit. Mode 2: TE surface wave resonance mode. In order to determine the resonant point of TE surface wave resonance mode of antenna in the array, the electric field distribution of element 4 in the array is also given when it is excited in X polarization and Y polarization direction respectively. Figure 2.48 shows the distribution of the electric field on the array Y-O-Z plane at different frequencies when the antenna 4 is excited by X polarization. It can be seen

Fig. 2.47 Simulated reflection phase of the proposed HIS with different incident angle [24]

Fig. 2.48 Simulated electric field distribution in y-o-z plane when the x-polarization of the element 4 is excited at a 2.5 GHz. b 2.6 GHz. c 2.7 GHz. d 2.8 GHz [24]

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79

Fig. 2.49 Simulated electric field distribution in x-o-z plane when the y-polarization of the element 4 is excited at a 2.5 GHz. b 2.6 GHz. c 2.7 GHz. d 2.8 GHz [24]

that with the increase of frequency, the electric field distribution begins to shift from the positive direction of the antenna to both sides of the antenna, which means that the working mode of the antenna changes from the original zero reflection phase resonance mode to te surface wave resonance mode. Near 2.8 GHz, the electric field is mainly concentrated on both sides of the antenna, indicating that TE surface wave resonance is slightly higher than 2.7 GHz of the antenna unit. Figure 2.49 shows the distribution of the electric field on the x-o-z plane of the array at different frequencies when the antenna 4 is excited by Y polarization. It can also be seen that as the frequency changes from 2.5 GHz to 2.8 GHz, the electric field distribution shifts to both sides of the array along the X direction, which means that TE surface wave begins to propagate along the X direction. According to the above analysis, when the antenna elements form an array, the first working mode of the antenna elements, the zero-reflection phase working mode, can be maintained, even when the antenna array is in beam scanning, and the second working mode, the TE surface wave resonance mode, will also exist after the array is formed, except that the resonance frequency will shift slightly to the high frequency As a whole, it does not affect the performance of the array. B.

Experiment results analysis to array

In order to verify the performance of the designed antenna array, the antenna array shown in Fig. 2.43 is simulated, processed and tested. The physical figure of the processed antenna array and the experimental device are shown in Fig. 2.50a. Because the array needs to realize beam scanning, it needs to control the phase difference of

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2 The Basic Principle of Phased Array

Fig. 2.50 a View of the array and measurement system. b View of the measurement environment. Figure reproduced with permission from Ref. [23], © 2019 IEEE

the signals fed into each antenna unit, so it also needs to use the device to control the phase. Eight 4-bit S-band phase shifters are used to control the signals fed into each antenna unit. The control of the phase shifter is realized by an FPGA, and the FPGA can control the phase shifter by importing the corresponding control program into PC. The device used for measurement also has a 1:8 power divider and corresponding cables. The final antenna array is tested in a microwave anechoic chamber, as shown in Fig. 2.50b. In the process of array gain test, the reference plane is the interface of the array, and the insertion loss of phase shifter and other devices has been excluded. The specific test process is as follows: the input signal enters the phase shifter through the 1– 8 power divider, and the equal amplitude and phase difference signal is generated through the control of FPGA to enter each unit of the array. First, the total gain G1 of the whole phased array system (including phase shifters and other devices) can be measured. ‘Then, a standard gain horn antenna is placed at the position of the antenna array, and the horn antenna and the array antenna have the same reference plane. At this time, the gain G2 of the horn antenna can be measured. Then the total insertion loss L0 of phase shifter, power divider and cable can be measured by vector network analyzer. And the true gain G0 of horn antenna can be found out. Gain of final phased array system G3 = G 0 − (G 2 − G 1 ). The gain G of the antenna array itself G4 = G 3 + L 0 . Figure 2.51a, b show the simulation and test results of the scanning performance of the array in the X and Y polarization directions at 2.5 GHz, respectively. For the Y polarization direction, it can be seen that the gain of the array is 14.3 dBi and the sidelobe level (SLL) is −13.2 dBi when the array beam is pointing to 0°, and the gain of the array is 9.6 dBi and the sidelobe level (SLL) is −9.5 dBi when the array is scanning to 50°. The comparison between the test results and the simulation results is satisfactory. For the X polarization direction, it can be seen that the gain of the array is 13 when the array beam is pointing to 0° to find that they are almost

References

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Fig. 2.51 Simulated and measured beam scanning performance of the array at 2.5 GHz in a ypolarization and b x-polarization. Figure reproduced with permission from Ref. [23], © 2019 IEEE

consistent. Only when the array is scanned to 45° and 50° the gain is slightly less than the simulation result. 8 dBi, and the sidelobe level (SLL) is −12.8 dBi; when the array is scanned to 50° the gain of the array is 10.3 dBi, and the sidelobe level (SLL) becomes −8.8 dBi. The test results are consistent with the simulation results. In a word, the low-profile dual polarization antenna array designed in this section based on the previous antenna unit can achieve ±50° wide angle scanning in two polarization directions on the premise of meeting the low profile (0.06 λ), and the sidelobe level is lower than −10 dBi.

2.5 Summary This chapter first introduces the important parameters that need to be used in the antenna design, then introduces the related theory of phased array, and finally designs two wide-angle scanning arrays.

References

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2 The Basic Principle of Phased Array

1. Balanis CA (2003) Antenna theory: analysis and design[J]. IEEE Antennas Propag Soc Newsl 24(6):28–29 2. Zhong S (2011) Antenna theory and technology [M]. Electronic Industry Press 3. Lu W (2004) Antenna theory and technology [M]. Xi’an University of Electronic Science and Technology Press 4. Andrews JG et al (2014) What will 5G be? IEEE J Sel Areas Commun 32(6):1065–1082 5. Rappaport TS et al (2013) Millimeter wave mobile communications for 5G cellular: it will work! IEEE Access 1:335–349 6. Qiao J, Shen XS, Mark JW, Shen Q, He Y, Lei L (2015) Enabling device-to-device communications in millimeter-wave 5G cellular networks. IEEE Commun Mag 53(1):209–215 7. Chen Z, Zhang YP, Bisognin A, Titz D, Ferrero F, Luxey C (2016) A 94-GHz dual-polarized microstrip mesh array antenna in LTCC technology. IEEE Antennas Wirel Propag Lett 15:634– 637 8. Schulwitz L, Mortazawi A (2006) Millimeter-wave dual polarized L-shaped horn antenna for wide-angle phased arrays. IEEE Trans Antennas Propag 54(9):2663–2668 9. Mao C, Gao S, Wang Y (2017) Broadband high-gain beam-scanning antenna array for millimeter-wave applications. IEEE Trans Antennas Propag 65(9):4864–4868 10. Xu J, Ke H, He Y, Luo Y (2018) A wideband u-slot microstrip patch antenna for large-angle mmw beam scanning. 2018 IEEE international conference on computer and communication engineering technology (CCET). Beijing, pp 142–145 11. He W, Jin R, Geng J (2008) E-shape patch with wideband and circular polarization for millimeter-wave communication. IEEE Trans Antennas Propag 56(3):893–895 12. Wu BQ, Luk K (2009) A broadband dual-polarized magneto-electric dipole antenna with simple feeds. IEEE Antennas Wirel Propag Lett 8:60–63 13. Hansen RC (2009) Phased array antennas, 2nd edn. Wiley, New York, NY, USA 14. Ng K, Chan CH, Luk K (2015) Low-cost vertical patch antenna with wide axial-ratio beamwidth for handheld satellite communications terminals. IEEE Trans Antennas Propag 63(4):1417– 1424 15. Yang GW, Li JY, Zhou SG, Qi YX (2017) A wide-angle E-plane scanning linear array antenna with wide beam elements. IEEE Antennas Wireless Propag Lett 16(1):2923–2991 16. Chen X, Qin P, Guo YJ, Fu G (2017) Low-profile and wide-beamwidth dual-polarized distributed microstrip antenna. IEEE Access 5:2272–2280 17. Wu H et al (2009) An improved comprehensive learning particle swarm optimization and its application to the semiautomatic design of antennas. IEEE Trans Antennas Propag 57(10):3018–3028 18. Wang L, Geng J-P et al (2020) Wideband dual-polarized binary coding antenna with wide beamwidth and its array for millimeter-wave applications. IEEE Antennas Wirel Propag Lett 19(4):636–640. https://doi.org/10.1109/LAWP.2020.2974160 19. Gabriel R, Gottl M, Klinger G. Antenna array 20. Chen Q, Hu Z, Shen Z et al (2018) 2–18 GHz conformal low-profile log-periodic array on a cylindrical conductor [J]. IEEE Trans Antennas Propag 66(2):729–736 21. Lou T, Yang XX, Qiu H, et al (2019) Compact dual-polarized continuous transverse stub array with two-dimension beam scanning [J]. IEEE Trans Antennas Propag 1–1 22. Wen YQ, Gao S, Wang BZ, et al (2018) Dual-polarized and wide-angle scanning microstrip phased array [J]. IEEE Trans Antennas Propag 1–1 23. Wu H, Geng J et al (2020) A low-profile wideband dual-polarized antenna based on an improved HIS and its broad-angle beam-scanning array. IEEE Antennas Wirel Propag Lett 19(3):383– 387. https://doi.org/10.1109/LAWP.2020.2967223 24. Wu H (2020) Research on miniaturized antenna and broad-angle scanning array, Master thesis. Shanghai Jiao Tong University 25. Yang F, Rahmat-Samii Y (2001) Wide-band E-shaped patch antennas for wireless communications. IEEE Trans Antennas Propag 49(7):1094–1100

Chapter 3

The Generalized Principle of Pattern Multiplication

Abstract This chapter mainly propose the generalized principle of pattern multiplication and give the details of the connotation of the key concepts and boundary. By comparing the performances of the omnidirectional antenna, dipole and the ideal phase mode antenna, the array based on the phase mode antenna performs high gain and large angle beam scanning.

3.1 Introduction In the traditional principle of pattern multiplication, the element used usually have the fixed pattern with narrow beam width. Therefore, at the large scanning angle which is bigger than the HPBW coverage of the element, the element makes little contribution to the gain of the array. Besides, when the array scans to a large angle, the equivalent separation distance between the antenna elements decreases, the mutual coupling increased deteriorates the active pattern of the elements. Limited HPBW and mutual coupling are two main factors which limits the scanning range of the phased array. Although the beam width of element can be broadened in some way, the antenna gain will decrease correspondingly. The existing phased array construction constrains the performance of the array. In this chapter, in order to improve the performance of the phased array, we propose the phased array based on the phase-mode antenna (PMA) element and the generalized principle of pattern multiplication (GPPM) to achieve high gain wide-angle scanning characteristic together [1–4].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 J. Geng et al., Generalized Principle of Pattern Multiplication and Its Applications, Modern Antenna, https://doi.org/10.1007/978-981-19-3559-6_3

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3 The Generalized Principle of Pattern Multiplication

3.2 Phase Mode Element and the Generalized Element Factor 3.2.1 Ideal Phase Mode Antenna The electric current on the surface of the antenna is the source which is responsible for the radiation, and different surface current distributions are called different modes. We can construct multiple modes on the antenna surface based on the multi-port antenna. These modes can work independently as the basic mode or simultaneously as the mixed mode. If the mode of the multi-port antenna changes with the phase difference between the ports, the proposed antenna can be called phased mode antenna. Here we give the expression of an ideal phase mode antenna: f (θ, θm ) = cos(θ − θ me ), and θme varies with phase difference. θme is the main beam direction of the element. In Fig. 3.1, the ideal phase mode antenna have the maximum directivity value equals to 1.76 dBi and omnidirectional HPBW coverage owing to its continuously changed main lobe direction. The ideal phase mode antenna owns high gain and wide HPBW at the same time.

3.2.1.1

Example of the Phase Mode Antenna

Figure 3.2 presents one actual example of the phase mode antenna, the pattern of proposed antenna can vary with the phase difference between the two ports. The geometry of the proposed antenna is shown in Fig. 3.2 by controlling phase of two input ports, the surfaces current distribution on spoof surface plasmon polaritons (SSPPs) transmission line can be changed. The SSPPs transmission line can achieve two states, one is the odd mode and the other is the even mode. Hence, the proposed

Directivity (dBi)

5

θ m =0° θ m =15° θ m =30° θ m =45° θ m =60t θ m =75° θ m =90°

0 -5 -10 -15 -20 -40

-20

0

20

θ (°) Fig. 3.1 GEF element pattern

40

60

80

3.2 Phase Mode Element and the Generalized Element Factor

85

Fig. 3.2 Example of the phase mode antenna

SSPPs antenna can obtain broadside radiation pattern in the case of equal phase between the two ports, and end-fire radiation pattern in the case of phase reversal between the two ports. In Fig. 3.3, the proposed SSPPs antenna have the end-fire pattern in the odd mode at 7.4, 7.7, 8.0 and 8.3 GHz.

Fig. 3.3 Radiation patterns of the SSPPs antenna in the odd mode at 7.4, 7.7, 8.0 and 8.3 GHz

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3 The Generalized Principle of Pattern Multiplication

Fig. 3.4 Radiation patterns of the SSPPs antenna in the even mode at 7.4, 7.7, 8.0 and 8.3 GHz

In Fig. 3.4, the proposed SSPPs antenna have the broadside pattern in the even mode at 7.4, 7.7, 8.0 and 8.3 GHz. Besides the above dual ports phase mode antenna, several phase mode antenna with dual ports have been studied [3–6], and they more or less show the beam scanning characteristics.

3.2.2 Generalized Element Factor Traditional array antenna element generally has only single radiation state, so it’s difficult to solve the problem that the gain fluctuation is big at the large scanning angle. Meanwhile, antenna element generally has only single polarization form, resulting in a waste of resources. The generalized element factor based on the phase mode antenna is proposed to solve these problem. The phase mode antennas generally have the form of dual-port or multi-port, the phase difference between the ports is used to excite different phase mode modes, and finally wide-angle scanning, arbitrary polarization and 3D scanning can be achieved.

3.2 Phase Mode Element and the Generalized Element Factor

87

Generalized element factor, also known as Generalized Element factor, or GEF for short. For a multi-port phase mode antenna element, when the element is expanded into an array, the normalized pattern of the phase mode antenna element is called the generalized element factor. As mentioned above, the generalized element factor is determined by the mixed current distribution pattern excited by the excitation signal of multiple ports and it’s initial phase. When the phase difference of the excitation signal of each port changes, the far field radiation characteristics of the unit aperture (The beam direction, or polarization, etc.) will change accordingly. When the phase difference of each mode changes slowly and uniformly, it is a steady-state generalized element factor. When the phase difference of each mode changes with time, it is a time-varyinggeneralized  element factor.    f e = f θ φ, θ, φem ϕ1 (t), ϕ2 (t), . . . ϕ p (t) , θθ m ϕ1 (t), ϕ2 (t), . . . , ϕ p (t) , ∅ is Azimuth angle, θ is angle  (φem , θθ m ) is the element (1, 2,  away from the z axis, …, p) excitation phase ϕ1 (t), ϕ2 (t), . . . , ϕ p (t) and the corresponding main beam direction. 1.

Ideal reconfigurable element factor in the form of impulse function Ideal reconfigurable element factor in the form of impulse function can be written as: f 0 (θ, ϕ) = δ(θ − θ0 , ϕ − ϕ0 )

2.

element factor in the form of impulse function is δ(θ0 , ϕ0 ), when the array scan to(θ0 , ϕ0 ), the directivity value of the element factor in infinite in(θ0 , ϕ0 ), zero in other angles, At the same time, it only needs that the array factor is not zero at this angle, and the overall directivity value is infinite at this angle. For the array, it indicates that the array only radiates energy at this angle。 Ideal reconfigurable element factor in the form of rectangular impulse function Ideal reconfigurable element factor in the form of rectangular impulse function can be written as: θ − θ0 ϕ − ϕ0 ) · r ect ( ) θ ϕ   x−x0  1 x − x0 1,  a  ≤ 2 , a > 0 )= r ect ( 0, else a f 0 (θ, ϕ) = r ect (

3.

(3.1)

(3.2)

(3.3)

Ideal reconfigurable element factor in the form of cosine function Ideal reconfigurable element factor in the form of cosine function can be written as: θ − θ0 ϕ − ϕ0 ) · h cos( ) θ ϕ  1   0 0 x − x0 cos(π x−x ≤ 2, a > 0 ),  x−x a a )= cos( 0, else a f 0 (θ, ϕ) = h cos(

(3.4)

(3.5)

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3 The Generalized Principle of Pattern Multiplication

3.

Continuous reconfigurable element factor and discrete reconfigurable element factor For the above three types of element factor, if (θ0 , ϕ0 ) is continuously obtained, the element factor is called continuous reconfigurable element factor, if (θ0 , ϕ0 ) is discretely obtained, the element factor is called Continuous reconfigurable element factor.

Continuously reconfigurable element factors can be directed at any angle, but it is difficult to achieve. After discretizing it into n fixed angle element factors, the angle θ0 that each fixed angle element factor needs to cover, then the array scan angle is θ = θ0 × n

(3.6)

θ is the angle that the array needs to cover. If θ0 is too large, the beam will be too wide and the energy radiation will not be concentrated, resulting in low gain. If θ0 is too small, n will be very large, which will increase the difficulty of unit reconstruction control and even make it impossible to design.

3.3 Phase Mode Element Array and the Generalized Principle of Pattern Multiplication 3.3.1 Generalized Array Factor The generalized array factor is a spatially reconfigurable filter, and the filter function of the filter in each angle of space forms a function set. As the size of the array increases, the degree of freedom of the array factor increases. Theoretically, the array factor that satisfies the ultra-wide-angle scan can always be found, that is, the extreme value of the functional. It can be assumed that a general form of N-element antenna array does not consider the variable of spatial position, and each antenna element has two free quantities of feed phase α and feed amplitude I at the same time. The set of functionals {F1 (α, I ), F2 (α, I ), F3 (α, I ), . . . Fn (α, I)}, where α and I are both N-dimensional vectors, representing feed phase and feed amplitude of N antenna elements. Adjusting the phase and amplitude of the feed can always achieve precise orientation of the array factor or even frequency compensation in the desired direction, which is the problem of solving the extreme value of the functional; if the mutual coupling of the antenna elements is considered, it can also be eliminated. In engineering, the assignment of the amplitude and phase of the antenna is also called weighting. How to choose the optimal algorithm weighting to achieve the best effect is one of the difficulties that the academic circle is eager to explore. The design of the generalized array factor is to take the feed amplitude, phase, and array element distribution into consideration, so as to design the optimal array factor:

3.3 Phase Mode Element Array and the Generalized Principle …

89

Fig. 3.5 Arbitrary N element array

The antenna element distribution of any N-element array is shown in Fig. 3.5. The antenna elements are generally of the same form. Assuming that the polarization direction of the antenna is controlled by the variable β, the polarization of the antenna can be written as L(β). Suppose the position vector of the nth antenna element is rn , the feed amplitude is |cn |, the phase is α, and the reference antenna is at the origin of the coordinates: Cn = 1, αn =0, the radiated electric field of the reference antenna can be written as: E(θ, ϕ) = L(β) f (θ, ϕ)

e− jkr 4πr

(3.7)

f(θ, ϕ) is the element pattern function. The distance from the nth antenna element to the far field point can be approximated as: Rn = r − r ∗ r n

(3.8)

kRn is the phase difference, the phase difference between the antenna elements superimposes each other in the far field to change the pattern shape of the antenna array. When considering the lag phase kRn , the feed amplitude and phase of the array element, the total field generated by all antennas in the array can be expressed as: N

e− jkr +kr ·r n n=1 4πr − jkr +kr ·r n N e L(β)Cn e jαn = f (θ, ϕ) n=1 4πr

E(θ, ϕ) =

Cn L(β)e jαn f (θ, ϕ)

(3.9)

Pattern function of antenna array can be written as the multiplication of the element factor and the array factor:

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3 The Generalized Principle of Pattern Multiplication

D(θ, ϕ) = f(θ, ϕ)F(θ, ϕ)

(3.10)

Array factor can be written as: F(θ, ϕ) =

N 

Cn L(β)e jαn

n=1

e− jkr +kr ·r n 4πr

(3.11)

By adjusting the feed amplitude, phase, and array element distribution, the main lobe angle and zero pole position of the array factor pattern can be adjusted to eliminate interference and compensate for gain. It is impossible to completely eliminate the mutual coupling of the array, but through the correction of the array factor, this mutual coupling can be appropriately compensated. The specific method is as follows: To simplify the analysis, for an ideal linear array of N elements, the weighted directional mode of the amplitude and phase can be characterized as: F(θ, ϕ) =

N 

− →− → rn

In e − j k

− →− → rn

= [In ]1∗N [e− j k

] N ∗1

(3.12)

n=1

⎡

⎤ sinθ cosϕ → → → 2π − ⎣ sinθ sinϕ ⎦, − r is the signal incident direction vector, − rn is r = 2π λ λ cosθ the position vector of the corresponding ⎡ array element. ⎤ S11 S12 ... S1N ⎢ S S ... S ⎥ 2N ⎥ ⎢ 21 22 ⎥ ⎢ . . ⎥ ⎢ . Consider the scattering matrix [s]⎢ ⎥: ⎢ . . ... . ⎥ ⎢ ⎥ ⎢ . . . ⎥ ⎢ ⎥ ⎢ S N 1 S N 2 ... S N N ⎥ Then consider the pattern after mutual coupling: − → k =

− →− → rn

F  (θ, ϕ) = [In ]1∗N [S] N ∗N [e− j k

] N ∗1

(3.13)

If In  = [In ][S]−1 ,F  (θ, ϕ) = F(θ, ϕ). Therefore, after the mutual coupling matrix is measured, the matrix factor can be changed by weighting the amplitude and phase to eliminate the effect of mutual coupling. The mutual coupling matrix can be obtained by full-wave simulation.

3.3.2 Generalized Principle of Pattern Multiplication f (θ, θm ) = f a (θ, θma ) × f e (θ, θme )

(3.14)

3.3 Phase Mode Element Array and the Generalized Principle …

91

Formula (3.13) shows that the main beam direction of the the array can be controlled by the array factor and the element factor together. In the array factor, the beam direction is controlled by changing the phase difference between the elements, and in the generalized element factor, main the beam direction of the element can be controlled by controlling the phase difference between the ports. Formula (3.13) is called the generalized principle of pattern multiplication [3, 7].

3.3.3 Extended Array As shown in Fig. 3.6, we establish a linear array with interval distance 0.5λ. The performance of the array constitute of GEF is presented. Generalized element factor: f (θ, θm ) = cos(θ − θ me ), and θme varies with phase difference [4]. As shown in Fig. 3.7, the generalized element factor has the maximum directivity value equals to 1.76 dBi, and omnidirectional pattern due to its continuously changed main lobe direction. The generalized element factor owns high gain and wide HPBW at the same time. In Fig. 3.8, the array scanning performance composed of the GEF element is presented. The main beam direction of the array factor is always kept the same as the

Fig. 3.6 1 × 8 linear array with interval distance 0.5λ

Directivity (dBi)

5 0 -5 -10 -15 -20 -40

-20

0

20

θ (°) Fig. 3.7 GEF element pattern

40

θme=0° θme=15° θme=30° θme=45° θme=60° θme=75° θ60 me=90°

80

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3 The Generalized Principle of Pattern Multiplication

12 Directivity (dBi)

10

θme=0° θme=15° θme=30° θme=45° θme=60° θme=75° θme=90°

8 6 4 2 0 0

10

20

30

40 θ (o)

50

60

70

80

90

Fig. 3.8 Array constitute of GEF element

main beam direction of the element factor. So the array scan with no gain fluctuation with the directivity value equals to 10.76dBi.

3.3.4 Comparison Among the Array Consist of Different Element In Fig. 3.9, the gain variation of the array composed of three types of element while scanning is shown. The directivity value of the array composed of the omnidirectional element is always smaller than array composed of the GEF element while scanning and the array composed of the dipole element scan with bigger gain fluctuation [4]. 12

Directivity /dB

11 10 9 8 array scanning---omnidirectional element array scanning---dipole element array scanning---generalized element factor

7 6 0

10

20

30

40

50

60

70

80

θ (o) Fig. 3.9 Gain variation of the array constitute of three types of element while scanning

90

References

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3.4 Connotation and Boundary of the Generalized Principle of Pattern Multiplication 3.4.1 Connotation f (θ, θm ) = f a (θ, θma ) × f e (θ, θme )

(3.15)

Formula (3.14) shows that not only the array beam direction can be controlled by the array factor and the element factor together. In the array factor, the beam direction is controlled by changing the phase difference between the antenna elements, and in the generalized element factor, the beam direction is controlled by controlling the phase difference between the two ports [3, 7].

3.4.2 Boundary In Formula (3.14), in order to maintain the high gain of the array, θma =θme shall be set. At this time, the array beam points to θm = θ ma =θme . In real situations, the scanning range of θme may be restricted. At this time, the beam directions of the array, the array factor, and the element factor generally satisfy the Formula (3.15): |θ me | ≤ |θm | ≤ |θma |

(3.16)

3.5 Summary This chapter first proposed the generalized element factor, and the generalized principle of the pattern multiplication is proposed based on the generalized element factor. Then the array designed based on generalized principle of the pattern multiplication can simultaneously achieve high gain and wide-angle scanning is proved theoretically, which greatly improves array performance. Finally, the connotation and boundary conditions of the generalized principle of the pattern multiplication are given.

References 1. Wang K et al (2019) Pattern reconfigurable antenna applying spoof surface plasmon polaritons. In: 2019 13th European conference on antennas and propagation (EuCAP), pp 1–2. Krakow, Poland

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2. Liu E, Geng J, Wang K, Zhou H, Ren C, Zhang J, Zhao X, Liang X, Jin R Generalized principle of pattern multiplication based on the phase antenna element. In: Proceedings IEEE AP-S society international symposium, July, 2020, pp 353–354. 2020 IEEE international symposium on antennas and propagation and north American radio science meeting (AP-S/URSI 2020) 3. Liu E, Geng J, Wang K, Zhou H, Ren C, Zhang J, Zhao X, Liang X, Jin R Multi-mode phase slots antenna with dual ports. In: Proceedings IEEE AP-S society international symposium, July, 2020, pp 691–692. 2020 IEEE international symposium on antennas and propagation and north American radio science meeting (AP-S/URSI 2020) 4. Liu E (2021) The research on the multi-band low profile antenna and the wide-angle scanning array, Master thesis, Shanghai Jiao Tong University 5. Jing Z, Geng J, Wang K, Zhou H, Ren C, Yang S, Liang X, Jin R (2020) Space scanning SSPPs antenna with phase mode by Ddual-port feeding. In: 2020 Asia-Pacific microwave conference (APMC2020), Hongkong 6. Ren C, Geng J, Zhou H, Wang K, Lu J, Zhang DSY, Yang S, He C, Liang X, Jin R (2021) A dual-port antenna with reconfigurable metasurface. In: Proceedings IEEE AP-S society international symposium, 2021 IEEE international symposium on antennas and propagation and north American radio science meeting (AP-S/URSI 2021) 7. Liu E, Geng J, Wang K, Zhou H, Ren C, Lu J, Yang S, He C, Zhao X, Liang X, Jin R (2022) The generalized principle of pattern multiplication and its application to wide-angle scanning array based on phase mode antenna. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.201 54851.v1

Chapter 4

The Phased-Mode Slots Aperture Unit and Its Array

Abstract This chapter mainly discusses the electromagnetics essential characteristics of the phase mode antenna and the mathematic principle of the generalized principle of pattern multiplication. The phase mode slots aperture unit is designed, and its main lobe can scan in space with the phase difference between dual ports of the aperture. The extended 1D array with 0.7 wavelength based on the phase mode slots aperture can scan widest from −78° to 78°. In further, an improved compacted phase mode slots aperture element with size of 0.4 wavelength is designed. And its extended 1D array can scan from −76° to 76° with the 1st side lobe level −13.7 dB.

4.1 Introduction Phased array antenna has attracted more and more attention in many applications, such as radar, satellite communication and so on. Phased array antennas with wideangle scanning capability are attractive in many cases. However, due to the mutual coupling between the beam width of the array elements and the antenna elements, the scanning range of the phased array is limited. For conventional phased array antennas, the main beam is usually scanned from −45° to +45°, and the gain fluctuation is 4–5 dB [1]. Many researches have published in reducing the mutual coupling [2–6]. Ground defected structure (DGS) [2], electromagnetic bandgap (EBG) structure [3] and the metamaterial polarization-rotator [4] has been proved useful in reducing the mutual. Connecting a coupling compensation network to the array [5, 6] is also an efficient way to alleviate the mutual coupling. The wider beam of the element is beneficial to extend the scanning range, and many works have been done to widen the HPBW of the element [7–12]. The HPBW can be easily enlarged by extending the size of the substrate [7], applying highpermittivity substrates [8], or combining electric dipole and the magnetic dipole into the element [9]. Reconfigurable antenna [10–12] is also proved useful in extending the scanning coverage of the phased array, however additional active loss will be introduced.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 J. Geng et al., Generalized Principle of Pattern Multiplication and Its Applications, Modern Antenna, https://doi.org/10.1007/978-981-19-3559-6_4

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96

4 The Phased-Mode Slots Aperture Unit and Its Array

In the traditional array, each antenna element is usually fed by a single port or independently fed by two orthogonally polarized ports. Each unit generally works in a fixed mode. In fact, each unit has an aperture, and the current amplitude distribution on the aperture determines the electromagnetic radiation characteristics. The current amplitude distribution on the aperture is the aperture mode. If the current amplitude distribution of the unit can change, that is, the mode can be changed, the corresponding radiation characteristics will also change. If the mode of the aperture changes with the phase of the external excitation signal, the mode changes with the phase, that is, a phase mode aperture or phase mode antenna element is formed. Based on the phase mode antenna to construct an array, the main beam direction of the array is controlled by the array factor and the PMA together. At this time, the corresponding array is called the phase mode array, also called the generalized array. Obviously, the introduction of the generalized element factor increases the degree of freedom of the array, making it possible to realize high-gain and large-angle scanning simultaneously. It provides new ideas and directions for the development of the array. In this chapter, to broaden the scanning range of the phased array, we firstly proposed the phase-mode antenna (PMA) element, which is excited by dual port. Different from the fixed element pattern of single port antenna, the proposed phase mode antenna offers multimode patterns which change continuously with the phase difference between its two ports. And the pattern can be expressed as the generalized element factor (GEF). Secondly, we proposed the generalized principle of pattern multiplication (GPPM) based on the PMA element, the main beam direction of the proposed array can be tuned by the array factor and the GEF of the PMA element together to achieve wide scanning angle with high gain.

4.2 Phase Mode Element Based on the Two Slots Aperture 4.2.1 Element Model [13, 14, 22] Figure 4.1 presents the configuration of the phase mode antenna (PMA). As shown in Fig. 4.1a, the antenna is mainly composed of three parts: the feed structure, the radiation slots and the metal ground. The feed layer is placed on top of the Arlon AD 250C substrate with a thickness of 0.762 mm, and the radiation slots are placed on the bottom layer. The metal ground is placed below the antenna layer h = 45 mm. In Fig. 4.1b, the microstrip line is bent 90° at the end of the microstrip lines to increase the isolation between the two ports, and the two input ports connect the microstrip line with varied phase. In the transition region above the slot, the width of the microstrip line is narrowed to achieve better impedance matching. In Fig. 4.1c, Two open slots in the x direction are fed by microstrip lines respectively, and the short slot in the y direction is inserted into the slot in the x direction.

4.2 Phase Mode Element Based on the Two Slots Aperture

97 Feed line layer 1

Monopole slot layer 2

h

GND layer 3

Z Y X

(a) L1

Port 1 W5

L5

W2

L8

L6

Port 2

W7

W1

L4

L7 Y (b)

Z

X (c)

L2

Fig. 4.1 Antenna structure a 3-D dimensional schematic diagram, b front view, c back view

Figure 4.1b, c give the top view and back view of the antenna respectively. Port 1 and port 2 are fed with different phases to generate various modes. Table 4.1 lists the initial values of the important parameters of the antenna. Table 4.1 Parameters of the proposed phase-mode antenna

Parameters

L1

L2

L3

Values/mm

5

64.5

87.5

Parameters

W1

W2

W3

Values/mm

24

70

150

98

4 The Phased-Mode Slots Aperture Unit and Its Array

Fig. 4.2 Phase mode antenna

J m2

J m1

As shown in Fig. 4.2, when these two microstrip lines are fed, they will excite − → − → two slots respectively. E 1 and E 2 in the slots are excited by the equivalent magnetic −→ −→ current Jm1 and Jm2 respectively. As shown Figs. 4.1 and 4.2, the antenna structure is rotational symmetrical. Assume the external excitation signals in two ports are same in magnitude with phase ∅1 and ∅2 respectively. − → − → − → − → So, E 1 and E 2 can be written as E 1 (∅1 ) and E 2 (∅2 ), the magnetic current density − → Jm can be written as: − → − − → Jm = → n × E

(4.1)

−→ − − → Jm1 = → n × E 1 (∅1 )

(4.2)

−→ − − → Jm2 = → n × E 2 (∅2 )

(4.3)

Then, we can write:

− → The electric vector potential F is found from a retard volume integral over the − → magnetic current density Jm . Apply the radiation approximation, it can be written as: [15] − → F =ε



′

e− jkr − → · Jm · dv′ 4πr

(4.4)

The electric potential of the two slots are individually written as Eqs. (4.5) and (4.6): − → F1 = ε



′

e− jkr −→ · Jm1 · dv′ 4πr

(4.5)

4.2 Phase Mode Element Based on the Two Slots Aperture

− → F2 = ε



99

′

e− jkr −→ · Jm2 · dv′ 4πr

(4.6)

In the far-field region, the magnetic field is proportional to the electric vector − → potential, and the electric field is perpendicular to H . The equations are written as (4.7) and (4.8): − → − → H = −jw F

(4.7)

− → − → → E = η− r ×H

(4.8)

The combined electric-field of the two slots can be calculated using the Eq. (4.9): −−−−−→ − → − → → E combined = −jωη− r × ( F1 + F2 )

(4.9)

In further, assume the phase difference between the two ports is Δ∅: Δ∅ = ∅2 − ∅1

(4.10)

Apparently, the combined electric field is the function of phase difference Δ∅. It can be written as: −−−−−→ E combined = f (Δ∅)

(4.11)

In conclusion, by changing the phase difference Δ∅ between the two ports which −→ −→ feed the slots, Jm1 and Jm2 will also change, pattern changes at the same time. That is to say, mode conversion is achieved by tuning the phase difference Δ∅ between the two ports.   −→ −→ −→ Here, if Jm1 and Jm2 are isolated enough, the far field E f 1 and E f 2 from Jm1 (∅1 ) −→ and Jm2 (∅2 ) can be written as follows respectively. − → → E f 1 (∅1 ) = −jω− r × F1 (∅1 )

(4.12)

− → → E f 2 (∅2 ) = −jω− r × F2 (∅2 )

(4.13)









E f1 (∅1 ) and E f2 (∅2 ) are just the basic modes, and Eq. (4.9) can be rewritten as: −−−−−→ −→ −→ −→ −→ E combined = E f 1 (∅1 ) + E f 2 (∅2 ) = E f 1 (∅1 ) + E f 2 (∅1 + Δ∅)

(4.14)

100

4 The Phased-Mode Slots Aperture Unit and Its Array

−−−−−→ As shown in Eqs. (4.11) and (4.14), the combined electric field E combined is just the −→ −→ −−−−−→ combination of two basic modes E f 1 (∅1 ) and E f 2 (∅2 ). In another side, E combined varies with the phase difference Δ∅. So, there are many modes working in this antenna based on phase difference Δ∅, and the antenna is called phase-mode antenna (PMA).

4.2.2 Element Electromagnetic Model In Fig. 4.3, the electric field distributions generated by adjusting the phase difference Δ∅ is given to verify the phase-mode characteristic of the proposed PMA. As shown in the Fig. 4.3, different electric field distributions are generated because of different phase difference Δ∅. In Fig. 4.3a, only the port 1 is excited, the electric fields are mainly distributed in the right slot, and only little electric field is coupled into the left slot. In Fig. 4.3b, only the port 2 is excited, the electric fields distribution is symmetrical to results in Fig. 4.3a. In Fig. 4.3c, port1 and port2 are excited in-phase, and the excited electric fields are distributed in the two slots with reverse direction. In Fig. 4.3d–f, port1 and port2 are excited with Δ∅ = 45◦ , 90◦ , 120◦ , respectively, the excited electric fields are distributed in the two slots, and the phase of the electric field in the left slot lags about 135◦ , 90◦ , 60◦ comparing to phase of the electric field in the right slot, respectively.

Fig. 4.3 Simulated electric field distributions in x-o-y plane varies with the phase difference Δ∅ between the two ports. a port1 excited separately, b port2 excited separately, c Δ∅ = 0°, d Δ∅= 45°, e Δ∅ = 90◦ , f Δ∅ = 120°, g Δ∅ = 180°

4.2 Phase Mode Element Based on the Two Slots Aperture

101

Fig. 4.4 Simulated power flow distribution in x-o-z plane varies with the phase difference Δ∅ between the two ports, a port1 excited separately, b port2 excited separately, c Δ∅ = 0◦ , d Δ∅ = 45◦ , e Δ∅ = 90◦ , f Δ∅ = 120◦ , g Δ∅ = 180◦

In Fig. 4.3g, port1 and port2 are excited out-of-phase, the excited electric fields are distributed in the two slots with the same directions. It is clearly that various distribution of electric field corresponds to various mode are generated by changing the phase difference Δ∅. As shown in the Fig. 4.4 different power flow distribution of the PMA in the x-o-z plane are generated because of different phase difference Δ∅. In Fig. 4.4a, only port 1 is excited, the power mainly flows to direction θ = 40°. In Fig. 4.4 (c), Δ∅ = 0°, the power mainly flows to θ = ±40°. In Fig. 4.4d–f, Δ∅ are 45°, 90° and 120° respectively, the power mainly flows to θ = −41°, −34°, −28°. In Fig. 4.4g, Δ∅ = 180°, the power mainly flows to θ = 0°, because the equivalent magnetic currents in the two slots are same in direction. It’s true that as phase difference Δ∅ between the two ports changes, the distribution of power flow also changes. As shown in the Fig. 4.5, different radiation patterns in x-o-z plane are generated because of different phase difference Δ∅. In Fig. 4.5g, Δ∅ = 0°, the main lobe of PMA(θem ) is −48°, In Fig. 4.5d–f, Δ∅ are 45°, 90° and 120° respectively, θem = −41°, −34°, −28° respectively, In Fig. 4.5a, only port 1 is excited. θem = 40°, In Fig. 4.5a, only port 2 is excited. θem = −40°. It’s true that the mode can be switched by adjusting the phase difference between the ports.

4.2.3 Element Performance PMA is designed through the simulation and analysis. As shown in Fig. 4.6, the antenna was fabricated according to the optimized parameters in Table 4.2.

102

4 The Phased-Mode Slots Aperture Unit and Its Array

Fig. 4.5 Simulated pattern in x-o-z plane varies with the phase difference Δ∅ between the two ports of the proposed antenna, a port1 excited separately, b port2 excited separately, c Δ∅ = 0◦ , d Δ∅ = 45◦ , e Δ∅ = 90◦ , f Δ∅ = 120◦ , g Δ∅ = 180◦

Fig. 4.6 Fabricated prototype of the proposed antenna Table 4.2 Optimized parameters of the proposed antenna Parameters

L1

L2

L3

L4

L5

Values/mm

5

64.5

87.5

27.5

11.4

Parameters

L6

L7

L8

W1

W2

Values/mm

5.5

26.25

5.5

24

70

Parameters

W3

W4

W5

W6

W7

Values/mm

150

1

2.5

5

1.5

4.2 Phase Mode Element Based on the Two Slots Aperture

103

S-Parameters (dB)

0 -10 -20 -30

Simulated |S11| Simulated |S21|

-40 2.0

2.1

2.2

2.3

Measured |S11| Measured |S21| 2.4

2.5

2.6

2.7

2.8

2.9

3.0

Frequency (GHz) Fig. 4.7 Comparison of the simulated and measured S-Parameters of the proposed multi-mode phase antenna

4.2.3.1

S-parameters

Figure 4.7 presents the comparison between the measured and simulated sparameters. The proposed antenna has a 34% relative impedance bandwidth, ranging from 2.08 to 2.93 GHz (|S11 | |θme |, when the scanning angle θm varies from −40° to −70°. The side effect in this case widens the array beam at large θm and decrease the gain too. Generally, the proposed phased array with the PMA based on GPPM is useful in obtaining the wide angle scanning characteristic. Table 4.6 shows the comparison between the proposed array based on the PMA element and other phased array. At f = 2.3 GHz, the phased array we designed can scan from −78° to 78° and the first side lobe level is −7.7 dB. At f = 2.4 GHz, the array that we proposed can scan from −70° to 70°, and the first side lobe level is -6.7 dB. It’s also worthy noted that the maximum gain of the proposed array reaches 13.7 dBi @ 2.3 GHz and 14.4 dBi @ 2.4 GHz. And they are almost equal to the max gains of others array with 8 elements, which verifies the higher efficiency of the proposed array based on GPPM consist of only 4 PMAs. Table 4.6 Comparison with other phased array References Scanning range 1st SLL@ largest Element numbers Max. gain of the array scanning angle (dB) [17]

−64°–64°

−12

64

20.7

[18]

−60°–60°

−14

49

–

[19]

−60°–60°

−3.5

8

13.2

[20]

−65°–65°

−17.1

8

12.1

[21]

−50°–50°

−10.3

8

14.3

Proposed *f

L

−78°–78°@f L

−7.8

4

13.7

−70°–70°@f c

−6.7

4

14.4

= 2.3 GHz, f C = 2.4 GHz

112

4 The Phased-Mode Slots Aperture Unit and Its Array

The phased array we proposed is efficient in improving the performance of the phased array, obtaining the higher gain and wider scanning range at the same time.

4.4 Improved Compacted PMA [14, 22] The above PMA in Fig. 4.1 has been demonstrated lobe steering performances with the varying phase differences between dual ports. And its extension array in Figs. 4.13 and 4.14 has performed good wide angle range scanning characteristics. But the size of the PMA is about 0.7 wavelength, so that the center distance between the adjacent units is 0.7 wavelength too, which is harm to large angle scanning. Here we improved the phase mode antenna with dual port to compacted.

4.4.1 Geometry Structure of the Improved Phase Mode Antenna The improved compacted PMA (ICPMA) is shown in Fig. 4.17. The structure of the ICPMA is similar as in Fig. 4.1, and includes the feeding structure, the radiation monopole slots side by side and the metallic ground. The feeding microstrip lines are printed on the top layer of Arlon AD 250C substrate with a thickness of 0.762 mm. The relative permittivity (εr ) is 2.5, and the loss tangent is 0.0018. The radiation monopole slots are placed on the bottom layer of the substrate. In Fig. 4.17a, two x-oriented slots are fed by microstrip lines, respectively. And the width of the antenna is mainly depended on the x-oriented slots. To decrease the width, the end of the x-oriented slot is bended, and the semicircle slots are introduced into the end part. Secondly, the corners of the monopole-slot layer are fillet to be round to decrease the coupling in array. The other parts are similar as in Fig. 4.1. And the details are shown in Fig. 4.17b, c. The ground plane is placed h = 45 mm below the monopole slot layer with air substrate, and the important parameters of the antenna element are listed in Table 4.7.

4.4.2 The EM Characteristics of the Improved Compacted Phase Mode Antenna To further validate the phase mode radiation characteristic of the proposed improved compacted phase mode antenna (ICPMA), the configuration of the ICPMA with phase difference Δ∅ between dual ports is given in Fig. 4.18, and the 3D radiation patterns of the PMA with various phase difference Δ∅ between the two ports or

4.4 Improved Compacted PMA …

113 Feed line layer 1 Monopole slot layer 2

GND layer 3

Z

Y X

(a)

L1

Port 1

L8

W5

W2

L6 L5

R0

W7 Port 2

W1

L4

L7 X Z

Y

L2

(b)

(c)

Fig. 4.17 Antenna geometry. a Three-dimensional (3-D) view of the proposed improved compacted phase mode antenna. b Top view of the proposed improved compacted phase mode antenna. c Back view of the proposed improved compacted phase mode antenna Table 4.7 Parameters of the proposed phase mode antenna

Fig. 4.18 The configuration of the phase mode antenna with phase difference Δ∅ between dual ports

Parameters

L1

L2

L3

Values/mm

5

64.5

87.5

Parameters

W1

W2

W3

Values/mm

24

70

150

Parameters

L4

L5

h

Values/mm

Xx

11

45

114

4 The Phased-Mode Slots Aperture Unit and Its Array

Fig. 4.19 Simulated pattern in x-o-z plane varies with the phase difference Δ∅ between the two ports of the proposed antenna, a port1 excited separately, b port2 excited separately, c Δ∅ = 0°, d Δ∅ = 45°, e Δ∅ = 90°, f Δ∅ = 120°, g Δ∅ = 180°

single port independent feed are shown in Fig. 4.19. The main lobes of these patterns are in x-o-z plane, and the directions of the lobes change continuously with the conversion of the mode. It’s clear that by changing the phase difference Δ∅ between the two ports, the pattern changes at the same time. The main lobe of the proposed ICPMA points to θem = 0◦ when the phase difference Δ∅ = 180◦ , and θem = −26◦ by Δ∅ = 120◦ , θem = −38◦ by Δ∅ = 90◦ , θem = −48◦ by Δ∅ = 45◦ , θem = −53◦ by Δ∅ = 0◦ . The main lobe of the proposed ICPMA points to 36◦ with only port 1 excited, but − 36◦ with only port 2 excited. That is to say, mode conversion is achieved by adjusting the phase difference between the magnetic currents. It’s clear that by changing the phase difference Δ∅ between the two ports, the pattern changes at the same time. The main lobe of the proposed PMA points to θem = 0◦ when the phase difference Δ∅ = 180◦ , and θem = −28◦ by Δ∅ = 120◦ , θem = −34◦ by Δ∅ = 90◦ , θem = −41◦ by Δ∅ = 45◦ , θem = −48◦ by Δ∅ =0◦ . The main lobe of the proposed antenna points to 40◦ with only port 1 excited, but − 40◦ with only port 2 excited. That is to say, mode conversion is achieved by adjusting the phase difference between the magnetic currents. Due to the symmetry of the PMA, the patterns will appear in the symmetrical directions for negative Δ∅.

4.4 Improved Compacted PMA …

115

0

|S11| (dB)

-10 -20

L 5=10 mm L 5=11 mm L 5=12 mm

-30 -40 1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Frequency (GHz) Fig. 4.20 Effect of L 5 on |S11 | performance

4.4.3 Key Parameter Analysis Similar as above, the key parameters of the ICPMA are the length of the thinner microstrip line part L 5 and the distance between the antenna monopole slot layer and the ground plane h, too.

4.4.3.1

L5

The parameter L 5 (the length of the thinner microstrip line part) is critical to the |S11 | performance. Figure 4.20 shows the simulated |S11 | values versus frequency for L 5 = 10 mm, 11 and 12 mm. It is observed that the increase of L 5 from 10 to 12 mm greatly affects the impedance matching of the proposed ICPMA. When L 5 = 10 mm, the impedance matching frequency band (|S11 | < −10dB) ranges from 2.07 to 2.31 GHz with the minimum |S11 | value equals to −12.98 dB. When L 5 = 11 mm, the impedance matching frequency band ranges from 1.92 to 2.08 GHz with the minimum |S11 | value equals to −40 dB. When L 5 = 12 mm, the impedance matching frequency band ranges from 1.87 to 1.95 GHz with the minimum |S11 | value equals to −13 dB. It is worth noting that with the increase of L 5 , impedance matching band moves to lower band. L 5 = 11 mm is chosen for its relatively low |S 11 | value.

4.4.3.2

h

h is the distance between the monopole slot layer and the ground plane. By adjusting the parameter h, the gain and the main beam direction of the proposed ICPMA changes a lot for various phase difference Δ∅. Figure 4.21 shows the gain and main beam direction versus phase difference for various h. It’ s observed that as h increases from 40 to 50 mm, the main beam direction increases for various mode while the

4 The Phased-Mode Slots Aperture Unit and Its Array Direction of main lobe, h=40mm Direction of main lobe, h=45mm Direction of main lobe, h=50mm

70 60

Gain, h=40mm Gain, h=45mm Gain, h=50mm

9 8

50 40

7

30 20

Gain (dB)

Direction of the main lobe (degree)

116

6

10 0

5

0

30

60

90

120

150

180

Phase difference between two ports (degree) Fig. 4.21 Effect of h on gainand lobe directions of the multi-mode antenna with phase difference Δ∅

Table 4.8 Optimized parameters of the proposed antenna Parameters

L1

L2

L3

L4

L5

Values/mm

5

64.5

87.5

27.5

11

Parameters

L6

L7

L8

W1

W2

Values/mm

5.5

26.25

5.5

24

70

Parameters

W3

W4

W5

W6

W7

Values/mm

150

1

2.5

5

1.5

gain decreases for various mode. The choice, h = 45 mm, is a compromise between these two issues. In this case, the main beam of the proposed phase antenna scans from 0◦ to −53◦ . The optimized parameters of the proposed PMA are shown in Table 4.8. The ICPMA has been designed through the processing of simulations and analysis. The ICPMA prototype is manufactured according to the optimized values of parameters in Table 4.8. The fabricated ICPMA prototype antenna is shown in Fig. 4.22.

4.4.4 S Parameters The simulated and measured S-parameters curves are shown in Fig. 4.23. The simulated available work band of |S11 | < −10 and |S21 | < −10 dB is from 1.93 to 2.07 GHz, about 7% to the center frequency. But the measured work band with |S11 | < −10 and |S21 | < −10 dB is from 1.94 to 2.2 GHz, about 13% to the center frequency, which is wider than the simulation. For the rotational symmetrical structure and feeding

4.4 Improved Compacted PMA …

117

φ2 =φ1 +Δφ

φ1 Port 1 (a)

Port 2 (b)

Fig. 4.22 The improved compacted phase mode antenna (ICPMA), a fabricated prototype of the ICPMA; b the configuration of the ICPMA with phase difference Δ∅ between dual ports

S-Parameters (dB)

0 -10

Simulated | S11 |

-20

Measured | S11 | -30

Simulated | S21 | Measured | S21 |

-40 1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

Frequency (GHz) Fig. 4.23 Comparison of the simulated and measured S-parameters of the proposed improved phase mode antenna

ports, measured and simulated |S 22 | are generally same as those of |S11 |, respectively. Here, we only show |S 11 | curves in Fig. 4.23. Compared to the simulation results, the measured |S 11 | curve drifts to higher frequency, and the measured isolation curve |S 21 | moves little to lower frequency, but it is larger than 15 dB during the available work band. Generally, the measured S-parameters curves are similar with the simulations, and the small bias are from the fabrication errors. In another side, at 2.0 GHz, the width L 2 of the monopole slot layer is only 60 mm, about 0.4λ f =2GHz .

4.4.5 Radiation Performances Varying with Phase Difference As shown in Fig. 4.22b, the ICPMA is fed from dual ports with two phase shifter respectively. The phase difference between these two ports is Δ∅ = ∅2 − ∅1 .

118

4 The Phased-Mode Slots Aperture Unit and Its Array 0

0 -10

330

Mea Sim

30

300

0 330

60

300

0

Mea Sim

30

330

60

300

60

Mea Sim

30

-20 -30 270

90

270

90

270

90

-20 -10 0

240

120 210

240

150

210

180

30

300

Mea Sim 60

270

240

120 150

(d)

(c)

0 330

30

270

120 150 180

(e)

330

30

300

90

240

0

Mea Sim 60

210

150 180

300

90

180

210

150

(b)

0

210

120

180

(a) 330

240

120

Mea Sim 60

270

90

240

120 210

150 180

(f)

Fig. 4.24 Measured and simulated pattern in x-o-z plane changes with the phase difference Δ∅ between the two ports at f = 2.0 GHz. a port1 excited separately, b Δ∅ = 0°, c Δ∅ = 60°, d Δ∅ = 90°, e Δ∅ = 130°, f Δ∅ = 180°

The measured patterns of ICPMA at f = 2.0 GHz for different phase difference Δ∅ in x-o-z plane are shown in Fig. 4.24. At f = 2.0 GHz, in Fig. 4.24a, the main lobe of the measured pattern points to θem = −34° with half power beam width (HPBW) 80° in the case of only port 1 being excited. In Fig. 4.24b–f, the two ports are excited simultaneously. The measured main lobe of the ICPMA points to θem = −56.5° with HPBW = 57.5° by Δ∅ = 0◦ , and θem = −37.5° with HPBW = 69.5° by Δ∅ = 60°, θem = −34.5° with HPBW = 77.5° by Δ∅ = 90°, θem = −19° with HPBW = 87° by Δ∅ = 130°, θem = −1° with HPBW = 90° by Δ∅ = 180°. It is clear that θem the direction of the measured main lobe of the ICPMA at f = 2.0 GHz moves from −37.5° to −1° with the phase difference Δ∅ from 0° to 180°, and the corresponding HPBW increases from 57.5° to 90°. And the measured patterns at different Δ∅ are almost consistent with the simulated results, especially the main lobe directions and HPBW, respectively. Figure 4.25 shows that the measured main lobe direction and gain of the proposed ICPMA vary with the phase difference Δ∅. And the above measured results are close to the simulation results too. The measured gain is 6.36–8 dBi with the phase difference Δ∅ from 0° to 180°. And the measured gain fluctuation is larger 0.26 dBi ~ 0.82 dBi in the whole scanning. The error is from the power divider, the digital

4.5 Improved Compacted PMA Array with Smaller Elements Spacing 0.4λ Sim. Gain Meas. Gain Sim. Direction of main lobe Meas. direction of main lobe

9 8

0 -10 -20

7

-30

6

-40

5

-50

4 3 0

20

40

60

80

100

120

140

160

Lobe direction (degree)

10

Gain (dBi)

119

-60 180

Phase difference (degree) Fig. 4.25 Compare the measured gains with varied phase difference Δ∅ and the simulated gains, the measured direction of the lobe and the simulated direction of the lobe of the improved compacted PMA at f = 2.0 GHz

phase shift system and the connectors, which introduce additional insert loss and measured errors.

4.5 Improved Compacted PMA Array with Smaller Elements Spacing 0.4λ [14, 22] According to the generalized principle of the pattern multiplication (GPPM) and GEF model of the PMA in above, the designed PMA s just the good choice to the generalized element factor with continuously steering main lobe direction by varying the phase difference Δ∅ between the modes. That is to say, the normalized far field pattern of the PMA can be expressed as GEF Eq. (4.4–4.15) with Δ∅. Here we discrete some samples of the element lobe scanning directions and gains from the proposed PMA Fig. 4.22, which are list in Table 4.9. Table 4.9 Main lobe direction and the gain of the proposed improved compacted multimode antenna in different mode Δ∅(°)

0

60

90

130

180

Direction of the main lobe θme (°)

−56.5

−37.5

−34.5

−19

−1

Gain (dB)

6.21

7.43

7.94

7.66

7.95

120

4 The Phased-Mode Slots Aperture Unit and Its Array

4.5.1 Configuration of the Array with ICPMA Based on GPPM In further, we construct a 1 × 8 ULA with the proposed ICPMA above. And the structure and configuration principle of the array is shown in Fig. 4.26. The ICPMA elements evenly distributed with distance da = 60 mm (about 0.4λ @2 GHz) in Fig. 4.26a. The phases of the modes in PMA element are ∅1 and ∅2 , and the phase difference between these two ports is Δ∅ = ∅2 − ∅1 . The phase difference between neighbor elements is ζ . As discussed in GEF of the PMA, the main lobe direction θme scans in θ field with phase difference Δ∅. And in Fig. 4.26, the main beam direction of the θma scans in θ field with ζ , so combining the varying of Δ∅ and ζ can achieve better array beam gains and wide scanning angle, as discussed in GPPM. To balance the array scanning beam gain and scanning angle, the combination of Δ∅ and ζ is optimized. The operating guideline of the array is as follows: (1) (2)

When the scanning angle ranges of θm varies from 0° to −30°,θma = θm = θme , to obtain low gain fluctuation. When the scanning angle ranges of θm varies from −40° to −90°,θma > θme , to obtain low side lobe level and wide angle scanning.

The optimized combination between the θma andθme is shown in the Table 4.10. As discussed above, the min beam direction of array factor is tuned by phase difference ζ between neighbor elements, which is obtained by the following equation:

Fig. 4.26 Configuration of array by ICMPA based on GPPM, a array structure with uniform space distance da, and b the configuration principle of the array with phase shifters

4.5 Improved Compacted PMA Array with Smaller Elements Spacing 0.4λ

121

Table 4.10 Optimized combination θm

0°

−20°

−39°

−58°

−73°

θma

−0°

−20°

−40°

−60°

−90°

θme

0°

−20°

−35°

−48°

−50°

Table 4.11 Optimized phase difference combination of Δ∅ AND ζ θm

0°

−20°

−39°

−58°

−73°

∅1

0°

0°

0°

0°

0°

∅2 = ∅1 + Δ∅

180◦

ζ

130°

90°

60°

30°

51.7°

97.19◦

130.9◦

151.2◦

ζ = k · da · sin(θma )

(4.21)

By adjusting the α, the main beam direction θma of the array factor can be tuned, based on the combination of θma and θme in the Table 4.10 to the array beam scanning from 0° to −73°, the corresponding phase combination is presented in the Table 4.11. Finally, the proposed array is manufactured as shown in Fig. 4.27, which is 1 × 4 array, and is constructed by Fr4 frame. The space between the centers of two adjacent elements is set as 0.4λ, where λ is the wavelength in free space corresponding to the center working frequency of 2 GHz. The EBG walls are inserted between adjacent elements to keep enough isolations between adjacent elements, and better the active return losses of the elements. The size of the phased array is 252 mm × 150 mm. And eight SMA ports feed from under the ground. The completed phased array by ICPMA elements with phase shifters and feed network are measured in the anechoic chamber.

4.5.2 Performances of the Array with ICPMA Based on GPPM According to the phase difference combination of Δ∅ and ζ in Table 4.11, the beam scanning of the proposed array is measured in the anechoic chamber. The measured array beam scanning and simulated results are shown in Fig. 4.28 at f = 2.0 GHz, 2.1 GHz respectively. In Fig. 4.28a, f = 2.0 GHz, the measured beams point to 0◦ , −20◦ , −40◦ , − ◦ 74 respectively, and the gains fluctuate during 0–3.3 dB. Certainly, the HPBW is increased from 29◦ to 60◦ during array beam scanning from 0◦ to −74◦ . The measured results in Fig. 4.28a are similar with those of the simulation results at f = 2.0 GHz in Fig. 4.28b except that there are some small errors for |θ m | ≥ 39◦ . The errors are from the digital phase shifter, which is calibrated with fixed step about 1.4° at center

122

4 The Phased-Mode Slots Aperture Unit and Its Array

Fig. 4.27 Structure of the 1 × 4 array with improved compacted phase mode antenna. a Front view and b side view of array

frequency 2.4 GHz. The cumulative digital phase shift errors from the frequency offset is too large to affect the main beam direction θm . In Fig. 4.28c, f = 2.1 GHz, the measured beams point to 0°, −20°, −40°, and −76° respectively. And the gains fluctuate 0–1.25 dB. The measured side lobes are lower than −5 dB. Certainly, the HPBW is increased from 27 to 45° during array beam scanning from 0° to −76°. The measured results in Fig. 4.28c are similar to those of the simulation results at f = 2.1 GHz in Fig. 4.28d. The measured gains during beam scanning at f = 2.0 GHz by the proposed phased array are shown in Fig. 4.29. Being similar with the simulation results, the measured gain curves are stable when the scanning angle is in −74o to 74.

4.5.3 Comparison Generally, the proposed phased array with the PMA based on GPPM shows strong potential to wide scanning angle with high gains. The proposed phased arrays based on PMA and ICPMA and others reported phased array are compared in Table 4.12.

-5

-120

-90

-60

-30

0

30

60

90

150

180

-150

-120

-90

-60

0

30

(c)

Theta (degree)

-30

(a)

60

90

120

Meas:0° Meas:-20° Meas:-40° Meas:-76°

150

180

-30 -180

-25

-20

-15

-10

-5

0

-150

-150

-120

-120

-90

-90

-60

-60

0

0

30

30

(d)

Theta (degree)

-30

(b)

degree (°)

-30

60

60

90

90

120

Sim:0° Sim:-20° Sim:-40° Sim:-72°

120

Sim:0° Sim:-20° Sim:-39° Sim:-73°

150

150

180

180

Fig. 4.28 The measured scanning patterns of the array based on the PMA element at a 2.0 GHz, c 2.1 GHz, and the simulated scanning patterns of the array based on the PMA element at b 2.0 GHz, d 2.1 GHz

-30 -180

-25

-20

-15

-10

-5

0

degree (°)

120

-30 -180

-150

-25

-20

-15

-30 -180

Meas:0° Meas:-20° Meas:-40° Meas:-74°

-10

-5

0

-25

-20

-15

-10

Magnitude (dB) Magnitude (dB)

Magnitude (dB)

Magnitude (dB)

0

4.5 Improved Compacted PMA Array with Smaller Elements Spacing 0.4λ 123

124

4 The Phased-Mode Slots Aperture Unit and Its Array 13

Gain (dB)

12

Simu_2GHz Meas_2GHz

11 10 9 8 0

10

20

30

40

50

60

70

80

theta (degree) Fig. 4.29 Compare the simulated and the measured gains varying with scanning angle at 2 GHz

Table 4.12 Comparison with other reported phased array References

Element spacing

Scanning range

1st SLL@ largest scanning angle (dB)

Element numbers

Max. gain of the array (dBi)

[17]

0.48λ @4.95 GHz

−64° to 64°

−12

64

20.7

[18]

0.33λ @10 GHz 0.55λ @16.8 GHz

−60° to 60°

−14

49

–

[19]

≥0.59λ @5.8 GHz

−60° to 60°

−3.5

8

13.2

[20]

0.42λ @27.5 GHz

−65° to 65°

−17.1

8

12.1

[21]

0.53λ @2.2 GHz

−50° to 50°

−10.3

8

14.3

PMA

0.7λ @ f C1

−78° to 78°@f L1

−7.8

4

13.7

−70° to 70°@f c1

−6.7

4

14.3

ICPMA

0.4λ @ f C2

−76° to 76°@f H2

−13.7

4

11.5

−74° to 74°@f c2

−12.5

4

11.9

Proposed

L1 = 2.3 GHz, f C1 = 2.4 GHz (PMA) f H2 = 2.1 GHz, f C2 = 2.0 GHz (ICPMA) *f

The proposed phased array based on PMA can scan the largest scanning angle from −78° to 78° with the 1st side lobe level −7.8 dB at lower frequency f = 2.3 GHz. At center frequency f = 2.4 GHz, the proposed phased array can scan from −70° to 70° with the 1st side lobe level −6.7 dB, and the gains fluctuate 0–5.6 dB. In another

4.6 Summary

125

side, the max gains of the proposed array arrive 13.7 dBi @2.3 GHz and 14.4 dBi @ 2.4 GHz. And they are almost equal to the max gains of others array with 8 elements, which verifies the higher efficiency of the proposed array based on GPPM consist of only 4 PMAs. Based on the improved compacted phase mode antenna, the proposed phased array can scan the largest scanning angle from −74° to 74° with the 1st side lobe level −12.5 dB at lower frequency f = 2.0 GHz. At frequency f = 2.1 GHz, the proposed phased array can scan from −76° to 76° with the 1st side lobe level − 13.7 dB, and the gains fluctuate 0–1.25 dB. In another side, the max gains of the proposed array arrive 11.9 dBi @2.0 GHz and 11.5 dBi @ 2.1 GHz. The proposed phased array based on PMA or ICPMA is more fit to radar or wireless communication with wide scanning angle and high gain. The proposed array configuration method based on the GEF of PMA and GPPM is useful to obtain wide angle scanning and high gain simultaneously.

4.6 Summary The generalized element factor (GEF) is proposed, which is the function of the phase difference of the basic modes. The phase mode antenna with dual ports is presented as an example of the GEF, and verifies the advantage of the GEF that can obtain high gain and wide angle steering simultaneously. The proposed PMA is equivalent to dual independent magnetic currents with varying phase difference, so that the main lobe of the PMA can scan from −40° to +40° in the available work band 2.08 to 2.93 GHz. Secondly, the generalized principle of pattern multiplication (GPPM) is introduced with GEF. So, the phased array with PMA elements and 0.7λ elements spacing based on the GPPM is constructed. With the varying phase difference Δ∅ between the basic modes in PMA element and the phase difference ζ between the neighbor PMA elements, the proposed phased array beam can scan wider from −78° to 78° at lower frequency f = 2.3 GHz, and the 1st side lobe level −7.8 dB at the largest scanning angle −78°. At center frequency f = 2.4 GHz, it can scan from −70° to 70° and the 1st side lobe level −6.7 dB at the largest scanning angle −70°. In further, to better the scanning performances and verify the generalized principle of pattern multiplication (GPPM) in smaller interval array, the improved compacted phase mode antenna (ICPMA) is introduced for GEF. And the phased array with ICPMA elements and 0.4λ elements spacing based on the GPPM is constructed. With the varying phase difference Δ∅ between the basic modes in ICPMA element and the phase difference ζ between the neighbor ICPMA elements, the proposed phased array beam can scan wider from −74° to 74° at lower frequency f = 2.0 GHz, and the 1st side lobe level −12.5 dB at the largest scanning angle −74°. At frequency f = 2.1 GHz, it can scan from −76° to 76° and the 1st side lobe level −13.7 dB at the largest scanning angle −76°.

126

4 The Phased-Mode Slots Aperture Unit and Its Array

Based on the GPPM using the PMA or ICPMA as an example of the GEF, the experimental results verify the advantage of GMMP owning high gain and wideangle scanning characteristics simultaneously. The presented phase array based on PMA and GPPM shows attractive promotion in wireless transmission and remote sensing.

References 1. Neto A, Cavallo D, Gerini G, Toso G (2009) Scanning performances of wideband connected arrays in the presence of a backing reflector. IEEE Trans Antennas Propag 57(10):3092–3102 2. Salehi M, Ghorbani A (2007) Elimination of scan blindness in microstrip scanning array antennas using defected ground structure. In: 2007 European microwave conference, Munich, pp 482–484 3. Donzelli G, Capolino F, Boscolo S, Midrio M (2007) Elimination of scan blindness in phased array antennas using a grounded-dielectric EBG material. IEEE Antennas Wirel Propag Lett 6:106–109 4. Cheng Y, Ding X, Shao W, Wang B (2017) Reduction of mutual coupling between patch antennas using a polarization-conversion isolator. IEEE Antennas Wirel Propag Lett 16:1257– 1260 5. Xia R, Qu S, Li P, Yang D, Yang S, Nie Z (2015) Wide-angle scanning phased array using an efficient decoupling network. IEEE Trans Antennas Propag 63(11):5161–5165 6. Hannan P, Lerner D, Knittel G (1965) Impedance matching a phased-array antenna over wide scan angles by connecting circuits. IEEE Trans Antennas Propag 13(1):28–34 7. He HD (2002) A novel widebeam circular polarisation antenna-microstrip dielectric antenna. In: Proceedings of international conference microwave millimeter wave technology, pp 48–50. Beijing 8. Toko America, Inc. (1997) A miniature patch antenna for GPS applications. Microw J 116–118 9. Siu HW, Luk KM (2009) A dual-polarized magneto-electric dipole with dielectric loading. IEEE Trans Antennas Propag 57(3):616–623 10. Ding X, Wang BZ, He GQ (2013) Research on a millimeter-wave phased array with wide-angle scanning performance. IEEE Trans Antennas Propag 61(10):5319–532411 11. Zhang S, Huff GH, Feng J, Bernhard JT (2004) A pattern reconfigurable microstrip parasitic array. IEEE Trans Antennas Propag 52(10):2773–2776 12. Pal A, Mehta A, Lewis R, Clow N (2015) A wide-band wide-angle scanning phased array with pattern reconfigurable square loop antennas. In: 2015 9th European conference on antennas and propagation (EuCAP), Lisbon, pp 1–4 13. Liu E, Geng J, Wang K, Zhou H, Ren C, Zhang J, Zhao X, Liang X, Jin R (2020) Multimode phase slots antenna with dual ports. In: Proceedings IEEE AP-S society international symposium, pp 691–692; 2020 IEEE international symposium on antennas and propagation and north American radio science meeting (AP-S/URSI 2020) 14. Erwei Liu, The research on the multi-band low profile antenna and the wide-angle scanning array, Master thesis, Shanghai Jiao Tong University, 2021. 15. Balanis CA (2005) Antenna theory: analysis and design, 3rd edn. Wiley, New York 16. Liu E, Geng J et al (2020) Generalized principle of pattern multiplication based on the phase antenna element. In: Proceedings IEEE AP-S society international symposium, pp 353–354 17. Gao G, Ding X, Cheng Y, Shao W (2019) Dual-polarized wide-angle scanning phased array based on mutimode patch elements. IEEE Antennas Wirel Propag Lett 18(3):546–550 18. Valavan SE, Tran D, Yarovoy AG, Roederer AG (2014) Dual-band wide-angle scanning planar phased array in X/Ku-bands. IEEE Trans Antennas Propag 62(5):2514–2521

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19. Bai Y, Xiao S, Tang M, Ding Z, Wang B (2011) Wide-angle scanning phased array with pattern reconfigurable elements. IEEE Trans Antennas Propag 59(11):4071–4076 20. Wang L et al (2020) Wideband dual-polarized binary coding antenna with wide beamwidth and its array for millimeter-wave applications. IEEE Antennas Wirel Propag Lett 19(4):636–640 21. Wu H et al (2020) A low-profile wideband dual-polarized antenna based on an improved his and its broad-angle beam-scanning array. IEEE Antennas Wirel Propag Lett 19(3):383–387 22. Liu E, Geng J, Wang K, Zhou H, Ren C, Lu J, Yang S, He C, Zhao X, Liang X, Jin R (2022) The generalized principle of pattern multiplication and its application to wide-angle scanning array based on phase mode antenna. TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.201 54851.v1

Chapter 5

The Phased-Mode SSPPs Antenna and Its 1D Array to Scan in 3D Space

Abstract In this chapter, a phase mode SSPPs antenna with dual port is proposed, its mian lobe can scan in the 3D space. Based on the generalized principle of pattern multiplication, the phase mode SSPPs antenna is extended to three kinds of 1D arrays with different arrangements. By changing the generalized array factor (GAF) and generalized element factor (GEF) simultaneously, all three arrays can scan along both θ - and Φ-dimensions at the same time.

5.1 Introduction Sub-6 GHz band is a backup of the next-generation system (5G) plans [1]. Phased array is in great demand in sub-6 GHz band to meet multi mobile terminal tracking and flexible beam switching applications. And it requires in-depth work with wide-angle beam scanning in broad bandwidth with stable high gain. Typically, there are numerous different approaches to wide-angle scanning, such as tightly coupled arrays, wide beam elements, and pattern reconfigurable technologies. Tightly coupled dipole arrays (TCDAs) have been reported in [2–5], showing remarkable broadband and wide-angle beam scanning capabilities. The linear TCDA in [6] has a main-beam scanning coverage from −45° to +45° in E-plane by applying a four-channel beam-steering control board. However, due to the linear distribution, the conventional array can only scan in one-dimensional (1D) space. Wide beam element technology is widely investigated to improve the gain of the array at low elevation angles [7, 8]. By employing binary code, a wide beamwidth antenna element and its extended eight-element phased array are proposed in [9], which can achieve scanning from −50° to +50°. The pattern-reconfigurable antennas (PRAs) are utilized for beam steering by switching their modes in different subspaces. Using PRA elements to jointly realize wide-angle scanning is an effective method with low sidelobe requirement concerned [10–13]. A linear array with eight PRA elements was designed in [14] for the ±81° scanning range in the elevation plane. Nevertheless, besides the additional modules of active circuits and control part, the states of the switch are limited.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 J. Geng et al., Generalized Principle of Pattern Multiplication and Its Applications, Modern Antenna, https://doi.org/10.1007/978-981-19-3559-6_5

129

130

5 The Phased-Mode SSPPs Antenna and Its 1D …

In fact, the single-port feeding form of traditional antenna element, with fixed element factor, makes the array scanning only depend on the array factor varying with phase. Furthermore, for conventional arrays, 3D space scanning requires 2D phased array at least. Therefore, it is a challenging task to reduce the dimension of array arrangement on the premise of 3D scanning. To address this issue, a kind of structure, spoof surface plasmon polaritons (SSPPs), is recommended. As an extension of surface plasmon polaritons (SPPs) in the optical frequencies, SSPPs structure has been widely applied to broadband absorbers [15, 16], microwave circuits [17], antennas [18–25], polarization modulators [26] and dynamically tunable integrated devices [27, 28]. Also, SSPPs structure has great application potential in future beam scanning technologies due to their inherent properties of strong field confinement and energy localization. Generally, there are two fundamental modes supported on SSPPs structure, even mode and odd mode. End-fire beams with high gain are provided by traveling waves of odd mode, while broadside beams are radiated by standing waves of even mode, which makes it an ideal candidate for wide-angle scanning. Usually, only one mode can be excited by the single-port SSPPs antenna. In [29], the SSPPs antenna is designed for radar cross section (RCS) reduction performances by placing a monopole at a certain distance beside the SSPPs structure for coupling and feeding, where merely odd mode is excited. Then the antenna is extended to a 5 × 5 array, which performs high gain and low RCS characteristics, but no scanning. A pattern reconfigurable antenna applying SSPPs is proposed in [30], which innovatively realizes the radiation switching between odd mode and even mode of SSPPs structure under single port condition. It supports the end-fire lobe at odd mode and the quasi-omnidirectional lobe at even mode, but lacks the intermediate states between those two modes, and is not competent for beam scanning. In this chapter, a phase-mode SSPPs antenna with dual-port is proposed, which can work in odd mode, even mode and mixed modes with the characteristic of spatial lobe scanning simply by varying the phase difference between the two ports of one antenna element. Hence, the presented antenna is qualified to cover 1/8 spherical space by lobe scanning in the band of 4.6–5.6 GHz. Based on the proposed SSPPs antenna element and combined with the generalized principle of pattern multiplication (GPPM), continuous 3D scanning is realized by the simple 1D linear array. To validate the concept, two arrays are simulated, fabricated and measured. Array 2 is readily to scan from 0° to 73° along θ-direction, and from 90 ◦ to 140 ◦ along Φ-direction. Also, its scanning coverage of 3 dB beam width is 0° < Φ < 90°, 0° < θ < 90°. Array 3 shows wide scanning range from 0° to 90° along θ-direction, and from 50° to 90° along Φ-direction, and its 3 dB coverage of the main beam scanning is 0° < Φ < 180°, 0° < θ < 90°. This is an alternative method of designing 3D scanning phased arrays with phase-mode SSPPs antenna [31]. The chapter is organized as follows. Section 5.2 presents the configuration and principle of the phase-mode SSPPs antenna. Sections 5.3 and 5.4 is dedicated to the verification of two kinds of linear arrays which can scan both along θ- and Φ-direction. Summary remarks are given in Sect. 5.5.

5.2 Phase Mode SSPPs Antenna Element Fig. 5.1 Configuration of the SSPPs antenna with phased-mode. Figure reproduced with permission from Ref. [32], © 2021 IEEE

131

L1 W1

Dz

p

substrate d

monopole

Lm Z X

Y

ground

W0 port2

h

port1

5.2 Phase Mode SSPPs Antenna Element 5.2.1 Element Model The proposed space scanning SSPPs antenna with phase-mode by dual-port feeding is shown in Fig. 5.1. It is fabricated on an Arlon AD255 substrate with the thickness of 1.524 mm (εr =2.55 and tanδ =0.0018). The proposed antenna consists of three parts, two trapezoidal monopoles, a rhombic modulated SSPPs structure loaded with four circular patches and a 3-mm-thick ground made of aluminum. The circular patches are placed symmetrically on both sides of the SSPPs structure. The trapezoidal monopoles are designed to match the impedance of 50 Ω. The electromagnetic (EM) wave from the trapezoidal monopole is coupled into the SSPPs structure. The SSPPs waves propagate along the symmetric SSPPs structure and two diamond-shaped metal modulation units, and finally radiate outward at the end. The ground is placed perpendicular to the substrate, with the size of 43 mm × 30 mm × 3 mm. The overall size of the substrate is 35.6 mm × 40 mm × 1.524 mm. The dimensions of the rhombic patches are L 1 and W1 . The length of monopole is λ/4 approximately (λ is the equivalent wavelength of central operating frequency). The period and width of the SSPPs structure is designed as p and a. The total length of the antenna is about half wavelength at 5.2 GHz. It is worth noting that two pairs of parabolic grooves are etched on both sides of the SSPPs structure, the purpose of which is to increase the realized gain and improve the end-fire performance. The antenna is modeled and simulated by CST Microwave Studio software. Initial geometric parameters of the proposed antenna are Dz = 5 mm, d = 3 mm, L m = 13 mm, L 1 = 10.5 mm, a = 0.4 mm, p= 0.8 mm, h = 8 mm, W1 = 4 mm.

5.2.2 Element Electromagnetic Model Port1 and port2 are fed with EM signals with the same amplitude but different phases. As shown in Fig. 5.2, the phases of port1 and port2 are defined as ϕ1 and ϕ2

132

5 The Phased-Mode SSPPs Antenna and Its 1D …

Fig. 5.2 Schematic diagram of the SSPPs antenna with phased-mode. Figure reproduced with permission from Ref. [32], © 2021 IEEE

respectively, with the phase difference between the two ports Δϕ = ϕ2 − ϕ1 . In SSPPs waveguide, there are two fundamental surface wave transmission modes, odd mode and even mode, which differ in their ability to restrain EM waves. Therefore, when the EM waves from the monopole are coupled into SSPPs structure, the surface current distribution on the SSPPs structure changes as the phase difference Δϕ between the two ports changes. When only either port1 or port2 works, the SSPPs structure acts as a director, and traveling waves of the dominant odd mode is excited, generating end-fire lobe. If two ports work at the same time with different Δϕ, odd mode, even mode and mixed modes of the two are generated. The current distributions on the two arms of SSPPs structure in two modes are shown in Fig. 5.3. Note that in the odd mode, the current flow on the left arm is the same as that on the right arm. However, since the monopole is located on the one side Z

Z

J l ( x, z )

J r ( x, z )

J l ( x, z )

J r ( x, z )

X

X

(a)

(b)

Fig. 5.3 Current distributions in the SSPPs structure a odd mode, b even mode. Figure reproduced with permission from Ref. [32], © 2021 IEEE

5.2 Phase Mode SSPPs Antenna Element

133

of the SSPPs structure, the magnitudes of current distribution on the left and right arm are different. Therefore, J1l (x, z) and J1r (x, z) are the magnitudes of the current on the left and right arms when only port1 is excited, while J2l (x, z) and J2r (x, z) are the magnitudes of current on the two arms when only port2 is excited. Meanwhile, ξ1 (x, z) and ξ2 (x, z) are the spatial transmission phases from port1 and port2 to the SSPPs arms, respectively. The coupling between the two ports is ignored, then the current distribution of SSPPs structure when only port1 or port2 is excited can be expressed as J1 J2



= a x · [J1l (x, z) + J1r (x, z)] · e jξ1 (x,z)

= J x · [J2l (x, z) + J2r (x, z)] · e jξ2 (x,z) ·e jπ

(5.1) (5.2)

When port1 and port2 are fed separately, their current amplitude distribution is antisymmetric, and the phase is opposite. J1l (x, z) = J2r (x, z) = Ja (x, z)

(5.3)

J1r (x, z) = J2l (x, z) = Jb (x, z)

(5.4)

When two ports work simultaneously, phases ϕ1 and ϕ2 are added to port1 and port2 respectively, then total current distribution on the SSPPs structure is:





J = a 1 e jϕ1 + a 2 e jϕ2 t



= J x · [J1l (x, z) + J1r (x, z)] · e jξ1 (x,z) · e jϕ1

+ a x · [J2l (x, z) + J2r (x, z)] · e

= a x · [Ja (x, z) + Jb (x, z)] · e

jξ2 (x,z)

j ϕ1

jπ

(5.5)

·e ·e   j ξ1 (x,z) · e − e jξ2 (x,z) e j·ϕ jϕ2

When Δϕ = 0◦ , the total current distribution on SSPPs structure is: J t0

  = a x · [Ja (x, z) + Jb (x, z)] · e jϕ1 · e jξ1 (x,z) − e jξ2 (x,z)

(5.6)

As shown in formula (5.6), the current directions of the left and right arms are opposite when Δϕ = 0◦ , so the antenna works in even mode. When Δϕ = 180◦ , the total current of SSPPs structure is:   J t180 = a x · [Ja (x, z) + Jb (x, z)] · e jϕ1 · e jξ1 (x,z) + e jξ2 (x,z)



(5.7)

As shown in formula (5.7), the current directions of the left and right arms are the same when Δϕ = 180◦ , thus the antenna works in odd mode.

134

5 The Phased-Mode SSPPs Antenna and Its 1D … 697 V/m 400 0

-400 -697

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Fig. 5.4 Simulated E x component varies with the phase difference between the two ports of the proposed antenna. a Δϕ = 0◦ , b Δϕ = 60◦ , c Δϕ = 90◦ , d Δϕ = 135◦ , e Δϕ = 180◦ , f only port1 excited, g only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE

Simulated E x components varying with the phase difference Δϕ between the two ports is demonstrated in Fig. 5.4. When Δϕ = 0°, clear even mode SSPPs characteristic can be obtained in accordance with symmetric magnitudes of electric field and reversed directions in Fig. 5.4a. When Δϕ = 180◦ , the antenna generates odd SSPPs waves seeing that both magnitudes and phases are the same on the left and right arms in Fig. 5.4e. Obviously, when Δϕ = 60°, 90° and 135°, the electric field distributions are in transitional states with Δϕ between 0° and 180°, as shown in Fig. 5.4b–d. Also, when only one port is fed, the distribution of E x component is not completely symmetric as illustrated in Fig. 5.4f, g. However, the electric field distribution still shows dominant odd mode characteristics. Corresponding to Fig. 5.4, simulated power flow in Fig. 5.5 shows the main whereabouts of energy under different phase differences Δϕ. Firstly, Fig. 5.5a demonstrates the viewing angle of observing the power flow of the antenna, that is, viewed from the top. In that way, the two monopoles and SSPPs structure are located below the substrate. Secondly, in Fig. 5.5b, it can be clearly seen that when Δϕ = 0°, the power flow mainly points to the +y and −y directions, which corresponds to the broadside lobe in the even mode. Then, when Δϕ = 60°, 90° and 135°, the power flow distributions are in transitional states with Δϕ between 0◦ and 180◦ , as illustrated in Fig. 5.5c–e. Ultimately, when Δϕ = 180°, the power flow points to the +z direction in Fig. 5.5f, which represents the end-fire lobe in the odd mode. In summary, as the phase difference gradually increases from 0° to 180°, the power flow first presents a trend of 45° rotation to the +x direction in the horizontal direction, and then mainly deflects to the end of SSPPs structure in the vertical direction. The power flow of the proposed antenna when port 1 or port 2 is fed separately are demonstrated in SSPPs structure Z

Y

V . A / m2

+Y

618

-Y

-300

300

X

0

port2 port1

(a)

(b)

+Z

-618

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 5.5 Simulated power flow varies with the phase difference between the two ports of the proposed antenna. a Top view of the proposed antenna, b Δϕ = 0◦ , c Δϕ = 60◦ , d Δϕ = 90◦ , e Δϕ = 135◦ , f Δϕ = 180◦ , g only port1 excited, h only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE

5.2 Phase Mode SSPPs Antenna Element

135

Fig. 5.5g, h. Since the monopole is located on one side of the SSPPs structure, the efficiency of energy coupling to the other side is low, as a result, the energy is concentrated on the side near the monopole. To summarize, the power flows of the proposed antenna under different phase differences Δϕ point to different directions in the 3D space. 3D patterns varying with the phase difference Δϕ and single port excitation are shown in Fig. 5.6. Distinctly, as the phase difference Δϕ changes, the radiation patterns realize 3D scanning in 1/8 of the spherical space where X > 0, Y > 0, and Z > 0. Then, the 3 dB beam width of main lobe in Fig. 5.6 are projected on the (Φ, θ ) coordinate space, as shown in Fig. 5.7. The abscissa Φ represents the phi-angle of the far field pattern, while the ordinate θ manifests the theta-angle. Unlike traditional 4.42

dBi

1.7 -1.03

Z X

Y

(a)

(b)

(c)

(d)

(e)

(f)

(g)

-5.58

Fig. 5.6 Simulated 3D pattern varies with the phase difference between the two ports of the proposed antenna. a Δϕ = 0◦ , b Δϕ = 60◦ , c Δϕ = 90◦ , d Δϕ = 135◦ , e Δϕ = 180◦ , f only port1 excited, g only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE

Fig. 5.7 Fabricated prototype of the proposed antenna. Figure reproduced with permission from Ref. [32], © 2021 IEEE

136

5 The Phased-Mode SSPPs Antenna and Its 1D …

scanning antennas, the proposed SSPPs antenna is qualified to scan large angle in (Φ, θ) space, and the 3 dB beam widths are competent to cover a wide range. In the 3D space of 0°< Φ < 180°, 0°< θ < 90°, by changing the phase difference Δϕ between two ports, the main lobe can continuously cover the most (Φ, θ) range except that the ranges of 0°< Φ < 45°, 30°< θ < 90°. When the phase difference Δϕ between two ports is 0°, the coordinates of the main lobe pointing in the (Φ, θ ) coordinate system are (90°, 60°), and (105°, 60°) at Δϕ = 60°, (120°,60°) at Δϕ = 90°, (10°, 0°) at Δϕ = 135°, (0°, 0°) at Δϕ = 180°, (105°, 45°) with only port1 being excited, (75°, 45°) with only port2 being excited, respectively. In summary, it is clear that different modes of the SSPPs structure can be excited by varying the phase differences Δϕ, so it is named the phase mode SSPPs antenna elements.

5.2.3 Element Performance The prototype of the proposed phase-mode SSPPs antenna was fabricated, and it was measured in a microwave anechoic chamber. A photograph of the prototype antenna is shown in Fig. 5.7. It is composed of two parts: (1) a printed circuit board (PCB) printed with SSPPs structure and two monopoles and (2) a 3 mm thick aluminum ground placed perpendicularly to the substrate. As shown in Fig. 5.2, the power splitter divides the signal into two parts with equal amplitude and same phase. And phase shifters are used for phase difference control. Two monopoles are fed through the SMA connector. Simulated and measured |S11 | and |S21 | are depicted in Fig. 5.8 for comparison. It is observed that the simulated and measured |S11 | are consistent in trend, except that the measured result is a little higher than the simulated one, which is due to fabrication errors. The measured impedance bandwidth is from 4.5-6 GHz, with

S-Parameters (dB)

0

Simulated|S 11 | Measured|S 11 |

Simulated|S 21 | Measured|S 21 |

-10

-20

-30 4.0

4.5

5.0 5.5 Frequency (GHz)

6.0

6.5

Fig. 5.8 The simulated and measured S-parameters. Figure reproduced with permission from Ref. [32], © 2021 IEEE

5.2 Phase Mode SSPPs Antenna Element

137

a relative bandwidth of 28.6%. In the operational frequency band, simulated and measured |S21 | are both less than −12.5 dB with the same tendency. |S22 | is almost the same as |S11 | due to the structural symmetry of two ports. The realized gains at the center frequency of 5.2 GHz are shown in Fig. 5.9 under varied phase differences Δϕ. At 5.2 GHz, the measured gain fluctuates within the range of 3.4–4.4 dBi when the phase difference Δϕ is 0◦ , 60◦ , 100◦ , 135◦ , and 180◦ . The measured gain is basically in agreement with the simulated one. In order to facilitate the observation of the spatial scanning characteristics of the proposed antenna element, simulated and measured spatial scanning patterns in the (Φ, θ ) coordinate space are shown in Fig. 5.10 and Fig. 5.11, respectively. As seen, 4.6

Gain (dB)

4.4

Simulated-Gain Measured-Gain

4.2 4.0 3.8 3.6 3.4

0

30

60 90 120 Phase difference (degree)

150

180

Fig. 5.9 The simulated and measured gains varying with phase difference at 5.2 GHz. Figure reproduced with permission from Ref. [32], © 2021 IEEE

0

0

0

0

0

0

30

30

30

30

30

30

θ /degree

0 30

90 0

90 45 90 135 180 0 Φ /degree

(a)

45 90 135 180

90 0

(b)

60

60

60

60

60

90 45 90 135 180 0

(c)

90 45 90 135 180 0

(d)

(e)

5.00 2.00 -5.00

60

60 90 45 90 135 180 0

dB

90 45 90 135 180 0

45 90 135 180

(f)

(g)

Fig. 5.10 Simulated patterns in (Φ, θ ) coordinate space varies with the phase difference between the two ports of the proposed antenna. a Δϕ = 0◦ b Δϕ = 60◦ c Δϕ = 90◦ d Δϕ = 135◦ e Δϕ = 180◦ f only port1 excited g only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE 0

0

0

0

0

0

30

30

30

30

30

30

θ /degree

0 30 60 90 0

(a)

90 45 90 135 180 0

(b)

60

60

60

60 90 45 90 135 180 0 Φ /degree

90 45 90 135 180 0

(c)

90 45 90 135 180 0

(d)

60 45 90 135 180

(e)

90 0

dB

5.00 2.00 -5.00

60 90 45 90 135 180 0

(f)

45

90 135 180

(g)

Fig. 5.11 Measured patterns in (Φ, θ ) coordinate space varies with the phase difference between the two ports of the proposed antenna. a Δϕ = 0◦ b Δϕ = 60◦ c Δϕ = 90◦ d Δϕ = 135◦ e Δϕ = 180◦ f only port1 excited g only port2 excited. Figure reproduced with permission from Ref. [32], © 2021 IEEE

138

5 The Phased-Mode SSPPs Antenna and Its 1D …

the 3 dB beam width coverage is represented by the red area in the Figs. 5.10 and 5.11. When Δϕ = 0°, the main lobe corresponds to the even mode in the 3D pattern of Fig. 5.6. Obviously, as the phase difference Δϕ increases from 0° to 90°, main lobe is uniformly scanned from Φ = 90° to Φ = 120° along the Φ-direction. On the other hand, as Δϕ increases, the coverage of main lobe in the θ -direction also increases. Then, when Δϕ = 135° and 180°, the main lobe has a more obvious scanning trend along θ -direction. Corresponding to 3D pattern in Fig. 5.6d, e, the main lobe starts to deflect towards the +z direction. When Δϕ = 180 ◦ , an end-fire beam towards +z axis in odd mode is formed. In summary, by changing the phase difference Δϕ between two feeding ports, the transition from the broadside lobe in the even mode to the end-fire lobe in the odd mode can be realized, and the continuous intermediate states between these two modes are formed at the same time. 3D scanning is realized in the 1/8 spherical space of X > 0, Y > 0, and Z > 0. The patterns in (Φ, θ ) coordinate space measured in a SATIMO SG64 3D microwave anechoic chamber are shown in Fig. 5.11. During the experiment, the antenna remains stationary. In the near-field of the antenna, there are several probes that rotate 360° around the antenna to measure the near-field patterns. Then they are transformed into far-field patterns in the (Φ, θ ) coordinate system by calculation. Due to the disturbance when the probes rotate, the calculated far-field patterns have more burrs comparing with the simulated results. In addition, the accuracy is limited during the measurement, and only one set of pattern data can be obtained every 5° of rotation, which makes the measurement and simulation results slightly different. The measured 3D patterns are consistent with the simulation results in trend, which is sufficient to prove that the proposed antenna has the ability to scan in 3D space. The proposed SSPPs antenna is compared with other reported SSPPs antennas and phase-mode antenna in Table 5.1. Our proposed SSPPs antenna is competent to achieve continuous transition from broadside lobe to end-fire lobe by working in Table 5.1 Comparison with other reported SSPPs antenna and phase-mode antenna References

Working mode

[30]

Number of modes

Scanning principle

Main lobe scanning range

3 dB coverage scanning range

Even mode and 2 odd mode

Cannot scan

–

–

[33]

Even mode

1

Frequency scanning

1D, −14.3° to +18.6°

–

[34]

Phase mode

Continuous multiple modes

Phase mode scanning

1D, −60° to + 60°

–

[35]

Odd mode

1

Frequency scanning

1D, −60° to + 63°

–

Proposed

Even mode, odd mode and multi-mode

Continuous multiple modes

Phase mode scanning

3D, Φ: +90° to +120° θ: 0° to +60°

3D, 0° < Φ < + 180°, 0° < θ < +90°

Table reproduced with permission from Ref. [32], © 2021 IEEE

5.3 Extended 1D Array: 1

139

different modes, so that it presents the ability of spatial lobe 3D scanning and wide coverage with more diverse and continuous modes.

5.3 Extended 1D Array: 1 The traditional principle of pattern multiplication is that the pattern of linear array is equal to the array factor multiplied by the element factor. f (θ, θm ) = f a (θ, θma ) × f e (θ )

(5.8)

where f (θ, θm ) is the pattern of array, f a (θ, θma ) is array factor, f e (θ ) is element factor. θm is the direction of the main beam of array, θma is the main beam direction of array factor. In Eq. (5.8), only the array scanning along the θ-direction is considered, while scanning maybe along the θ- and Φ-direction essentially. Only the beam direction of the array factor θma is used to control the scanning characteristics, but the effect of the element factor f e (θ ) is limited. Now, redefine the main beam direction of array as f (θ, Φ, θm , Φm ), generalized array factor (GAF) as f a (θ, Φ, θma , Φma ), generalized element factor (GEF) as f e (θ, Φ, θme , Φme ), with both scanning along θ - and Φ- directions considered. θm and Φm are the main beam directions of array in the dimensions of θ and Φ, respectively. Φ is the abscissa-axis and θ is the ordinate-axis, then Φ and θ will construct a coordinate (Φ, θ, r ), indicating the direction of the main beam of array in space. θma and Φma are the main beam directions of array factor in the (Φ, θ ) space, θme and Φme are the main lobe directions of element factor. For the GEF, θme and Φme of f e (θ, Φ, θme , Φme ) are determined by the phase difference Δϕ between the two ports of the antenna element, which can be shown as follow: f e (θ, Φ, θme , Φme ) = f e (θ, Φ, θme (ϕ2 − ϕ1 ), Φme (ϕ2 − ϕ1 )) = f e (θ, Φ, θme (Δϕ), Φme (Δϕ))

(5.9)

The GAF can be expressed as: f a (θ, Φ, θma , Φma ) = f a (θ, Φ, θma (τ ), Φma (τ ))

(5.10)

τ is the phase difference between the adjacent antenna elements in the 1D array, and Φma should be constant. Φma (τ ) = constant

(5.11)

140

5 The Phased-Mode SSPPs Antenna and Its 1D …

The array factor is adjusted by changing the phase difference τ between the antenna elements. Therefore, the GPPM can be written as follow: f (θ, Φ, θm , Φm ) = f a (θ, Φ, θma , Φma ) × f e (θ, Φ, θme , Φme ) = f a (θ, Φ, θma (τ )) × f e (θ, Φ, θme (Δϕ), Φme (Δϕ))

(5.12)

For a 1D linear array, the array factor can only adjust 1D beam scanning, that is, scan along the θ -direction. Here, through specific structures and phase modes, the antenna element, that is, the element factor, can simultaneously perform beam scanning both along the Φ- and θ -directions. This is just our proposed phase-SSPPs antenna element in Section II. It is noted that in theory, the 1D linear array can achieve 3D scanning in wide range. The working principle of a four-element linear array based on GPPM is demonstrated in Fig. 5.12. The phase difference between the neighbored antenna elements is τ , which is used to adjust the GAF. The GAF can only scan along θ -direction. The element phase difference Δϕ between two ports of each antenna element remains the same, which is used to control the GEF. The GEF can not only scan along θ -direction, but also along Φ-direction. If the main lobes of the GEF and the GAF point to the same direction, a high gain array scanning along θ -direction can be obtained. By making the GAF pointing within the 3 dB beam coverage of the GEF, the 1D linear array can also scan along the Φ-direction. The phases adjusted at the ports from left to right are {ϕ1 ,ϕ1 + Δϕ,ϕ1 + τ ,ϕ1 + Δϕ + τ ,ϕ1 + 2τ ,ϕ1 + Δϕ + 2τ ,ϕ1 + 3τ ,ϕ1 + Δϕ + 3τ }. Table 5.2 shows the main lobe direction and 3 dB coverage of the antenna element

Fig. 5.12 Configuration of array by generalized principle of pattern multiplication. Figure reproduced with permission from Ref. [32], © 2021 IEEE

Table 5.2 The scanning capability of the antenna element controlled by phase difference Δϕ

Δϕ

0°

60°

90°

(Φm , θm )

(90°, 60°)

(105°, 60°)

(120°, 60°)

3 dB beam coverage

Φ: 65°–120° θ: 45°–90°

Φ: 90°–120° θ: 35°–90°

Φ: 100°–135° θ:10°–90°

Δϕ

135°

180°

–

(Φm , θm )

(10°, 0°)

(0°, 0°)

–

3 dB beam coverage

Φ: 0°–180° θ: 0°–60°

Φ: 0°–180° θ: 0°–30°

–

Table reproduced with permission from Ref. [32], © 2019 IEEE

5.3 Extended 1D Array: 1

141

d 10 Z

d 11 X

Y

Port1

Port2 Port3

Port4 Port5

Port6 Port7

Port8

Fig. 5.13 Configuration of array 1 based on the proposed antenna. Figure reproduced with permission from Ref. [32], © 2021 IEEE d2

Z X

(a)

45º Y

Port2

Port1

Port4

Port3

Port6

Port5

Port8

Port7

(b)

Fig. 5.14 Configuration of array 2 based on the proposed antenna a fabricated prototype, b simulated prototype. Figure reproduced with permission from Ref. [32], © 2021 IEEE

in the range of Φ from 0° to 180° and θ from 0° to 90° under differentΔϕ. Three types of arrays are initially proposed according to the angle between the normal direction of the element plane and the array axis. Array 1 means the four antenna elements are arranged side by side in x-o-z plane. Since the width of the antenna element itself is about 0.6λ (λ is the wavelength corresponding to the center frequency of 5.2 GHz), the center distance between the antenna elements d10 is greater than 0.5λ. As shown in the Fig. 5.13, when d10 = 0.7λ, the distance between port2 and port3 is d11 = 0.16λ. This leads to the isolation between port2 and port3 about −7 dB. When d11 = 0.5λ, then d10 >> λ, which results in grating lobes being easily generated. Therefore, Array 1 is not suitable for large-angle scanning. Array 2 is that the elements are arranged in parallel along the x-axis, and each rotates 45° around the central axis of the SSPPs structure as shown in Fig. 5.14. And Array 3 means the four antenna elements are in parallel along the normal direction of the antenna element plane as shown in Fig. 5.20. The isolation of Array 2 and Array 3 are both better than 13 dB.

5.3.1 Array Construction The antenna element of 1D array is rotated 45◦ along the z-axis in order to decrease the coupling between port2 and port3, which is Array 2. The configuration of fabricated

142

5 The Phased-Mode SSPPs Antenna and Its 1D …

and simulated prototype of Array 2 is depicted in Fig. 5.14. The center distance of each antenna element is d2 = 0.7λ. Measurement mechanism of proposed four-element linear array is shown in Fig. 5.15. Here, feeding network is composed of a one-to-two equal-split power divider and two one-to-four equal-split dividers. The combination of τ and Δϕ when Array 2 scanning along θ -and Φ-directions are exhibited in Table 5.3 and Table 5.4, respectively. (Φm , θm ) represents the direction of the main beam in the (Φ, θ ) coordinate system under different combination of τ and Δϕ. Based on Table 5.3 and Table 5.4, Array 2 can scan from 0◦ to 73◦ along θ -direction, with realized gain in the range of 6.5–10.4 dBi, and scan from 90◦ to 140◦ along Φ-direction, with realized gain 6.1–11.7 dBi. Fig. 5.15 Four-element linear array with phase shifters and feeding network. Figure reproduced with permission from Ref. [32], © 2021 IEEE

Antenna

Feeding network

Phase shifter

Table 5.3 Optimized phase difference combination Of Δϕ and τ when array 2 scanning along θ-direction

τ

Δϕ

(Φm , θm )

Gain/dBi

0°

180°

(0°, 0°)

8.7

−100°

180°

(0°, 20°)

7.8

170°

150°

(0°, 40°)

9

100°

100°

(0°, 60°)

10.4

50°

120°

(0°, 73°)

6.5

Table reproduced with permission from Ref. [32], © 2021 IEEE

Table 5.4 Optimized phase difference combination Of Δϕ and τ when array 2 scanning along ϕ-direction

τ

Δϕ

(Φm , θm )

Gain/dBi

0°

100°

(90°, 50°)

11.7

50°

60°

(100°, 50°)

11.5

90°

90°

(110°, 50°)

8.3

120°

0°

(120°, 50°)

9.43

170°

0°

(140°, 50°)

6.1

Table reproduced with permission from Ref. [32], © 2021 IEEE

5.3 Extended 1D Array: 1

143

5.3.2 Array Performance Corresponding to Table 5.3, the measured and simulated 3D patterns scanning along θ -direction are shown in Fig. 5.16 and Fig. 5.17 respectively. The position of the main beam in the (Φ, θ ) coordinate system is marked with black dots, which is (Φm , θm ). The red area represents the 3 dB beam width coverage in the (Φ, θ ) coordinate system. When Array 2 scans along θ-direction, the maximum beam direction in the Φ-dimension Φm remains unchanged at 0°. The measured beams are mainly concentrated in the range of Φ = 70°–90° and θ = 0°–10° in (a), Φ = 50°–65° and θ = 20°–40° in (b), Φ = 30°–40° and θ = 30°–60° in (c), Φ = 0°–30° and θ = 60°–85° in (d), Φ = 0°–25° and θ = 60°–90° in (e). And the main beams point to (Φm , θm ) = (0°, 0°) with Δϕ = 180° and τ = 0° in (a), (Φm , θm ) = (0°, 20°) with Δϕ = 180° and τ = −100° in (b), (Φm , θm ) = (0°, 40°) with Δϕ = 150° and τ = 170° in (c),(Φm , θm ) = (0°, 60°) with Δϕ = 100° and τ = 100° in (d), (Φm , θm ) = (0°, 73°) with Δϕ = 120° and τ = 50° in (e). Comparing Figs. 5.16 and 5.17, it can be concluded that the simulation results are consistent with the measured ones, and the proposed 1D Array 2 realizes scanning along θ-direction. Corresponding to Table 5.4, the measured and simulated 3D patterns scanning along Φ-direction are shown in Figs. 5.18 and 5.19. The maximum beam direction θm in the θ-dimension remains unchanged at 50°. The measured beams are mainly concentrated in the range of Φ = 90°–105° and θ = 0°–120° in (a), Φ = 90°–120°

Fig. 5.16 Measured pattern of array 2 scanning along θ-direction. a (Φm , θm ) = (0°, 0°) at Δϕ = 180◦ and τ = 0◦ ; b (Φm , θm ) = (0°, 20°) at Δϕ = 180° and τ = −100°; c (Φm , θm ) = (0°, 40°) at Δϕ = 150° and τ = 170°; d (Φm , θm ) = (0°, 60°) at Δϕ = 100° and τ = 100°; e (Φm , θm ) = ( 0°, 73°) at Δϕ = 120° and τ = 50°. Figure reproduced with permission from Ref. [32], © 2021 IEEE

Fig. 5.17 Simulated pattern of array 2 scanning along θ-direction. a (Φm , θm ) = (0°, 0°) at Δϕ = 180◦ and τ = 0◦ ; b (Φm , θm ) = (0°, 20°) at Δϕ = 180° and τ = −100°; c (Φm , θm ) = (0°, 40°) at Δϕ = 150° and τ = 170°; d (Φm , θm ) = (0°, 60°) at Δϕ = 100° and τ = 100°; e (Φm , θm ) = (0°, 73°) at Δϕ = 120° and τ = 50°. Figure reproduced with permission from Ref. [32], © 2021 IEEE

144

5 The Phased-Mode SSPPs Antenna and Its 1D …

Fig. 5.18 Measured pattern of array 2 scanning along Φ-direction. a (Φm , θm ) = (90°, 50°) at Δϕ = 100◦ and τ = 0◦ ; b (Φm , θm ) = (100°, 50°) at Δϕ = 60° and τ = 50°; c (Φm , θm ) = (110°, 50°) at Δϕ = 90° and τ = 90°; d (Φm , θm ) = (120°, 50°) at Δϕ = 0° and τ = 120°; e (Φm , θm ) = (140°, 50°) at Δϕ = 0° and τ = 170°. Figure reproduced with permission from Ref. [32], © 2021 IEEE

Fig. 5.19 Simulated pattern of array 2 scanning along Φ-direction. a (Φm , θm ) = (90°, 50°) at Δϕ = 100◦ and τ = 0◦ ; b (Φm , θm ) = (100°, 50°) at Δϕ = 60° and τ = 50°; c (Φm , θm ) = (110°, 50°) at Δϕ = 90° and τ = 90°; d (Φm , θm ) = (120°, 50°) at Δϕ = 0° and τ = 120°; e (Φm , θm ) = (140°, 50°) at Δϕ = 0° and τ = 170°. Figure reproduced with permission from Ref. [32], © 2021 IEEE

and θ = 10°–110° in (b), Φ = 90°–135° and θ = 20°–115° in (c), Φ = 110°–180° and θ = 20°–120° in (d), Φ = 120°–180° and θ = 10°–120° in (e). And the main beams point to (Φm , θm ) = (90°, 50°) with Δϕ = 100° and τ = 0° in (a), (Φm , θm ) = (100°, 50°) with Δϕ = 60° and τ = 50° in (b), (Φm , θm ) = (110°, 50°) with Δϕ = 90° and τ = 90° in (c),(Φm , θm ) = (120°, 50°) with Δϕ = 0° and τ = 120° in (d), (Φm , θm ) = (140°, 50°) with Δϕ = 0° and τ = 170° in (e). Comparing Figs. 5.18 and 5.19, it can be observed that the simulation results are in good agreement with the measured ones, and the proposed 1D Array 2 realizes scanning along Φ-direction. In summary, Array 2 is competent to scan both along θ - and Φ-direction, and the total 3 dB coverage of the main beam can cover the space of 0° < Φ < 140°, 0° < θ < 90°.

Z X

(a)

Y

d3

(b)

Fig. 5.20 Configuration of array 3 based on the proposed antenna. a Fabricated prototype, b simulated prototype. Figure reproduced with permission from Ref. [32], © 2021 IEEE

5.4 Extended 1D Array: 2 Table 5.5 Optimized phase difference combination of Δϕ and τ when array 3 scanning along θ-direction

145 τ

Δϕ

(Φm , θm )

Gain/dBi 11.1

0°

180°

(90°, 0°)

250°

180°

(90°, 10°)

9.41

160°

180°

(90°, 30°)

8.2

100°

0°

(90°, 50°)

70°

0°

(90°, 70°)

50°

0°

(90°, 90°)

9.75 10.1 9.36

Table reproduced with permission from Ref. [32], © 2019 IEEE

Table 5.6 Optimized phase difference combination of Δϕ and τ when array 3 scanning along ϕ-direction

τ

Δϕ

(Φm , θm )

Gain/dBi

50°

0°

(90°, 90°)

9.36

100°

60°

(90°, 70°)

9.13

140°

120°

(90°, 50°)

6

Table reproduced with permission from Ref. [32], © 2019 IEEE

5.4 Extended 1D Array: 2 5.4.1 Array Construction Another linear array based on the above proposed phase mode SSPPS antenna is presented in Fig. 5.20 to further decrease the coupling between adjacent ports. The antenna elements are placed one after the other in a line along the central axis of the antenna element. The parallel array can also realize scanning in two dimensions by simultaneously adjusting the port phase difference Δϕ of the antenna elements and the array phase difference τ between the elements. The numerical tables of τ and Δϕ needed for Array 3 to scan in θ - and Φ-directions are demonstrated in Tables 5.5 and 5.6. The beam scanning angle and realized gain are also shown in these two tables. Based on Table 5.5 and Table 5.6, Array 3 can scan from 0° to 90° along θ -direction, with realized gain in the range of 8.2–11.1 dBi, and scan from 50° to 90° along Φ-direction, with realized gain in the range of 6–9.36 dBi.

5.4.2 Array Performance Corresponding to Table 5.5, the measured and simulated 3D patterns scanning along θ -direction are demonstrated in Fig. 5.21 and Fig. 5.22 respectively. When Array 3 scans along θ-direction, the maximum beam direction Φm in the Φ-dimension remains unchanged at 90°. The measured beams are mainly concentrated in the range of Φ = 60°–120° and θ = 60°–90° in (a), Φ = 55°–25° and θ = 50°–90° in

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Fig. 5.21 Measured pattern of array 3 scanning along θ-angle. a (Φm , θm ) = (90°, 90°) at Δϕ = 0◦ and τ = 50◦ ; b (Φm , θm ) = (90°, 70°) at Δϕ = 0° and τ = 70°; c (Φm , θm ) = (90°, 50°) at Δϕ = 0° and τ = 100°; d (Φm , θm ) = (90°, 30°) at Δϕ = 180° and τ = 160°; e (Φm , θm ) = (90°, 10°) at Δϕ = 180° and τ = 250°; f (Φm , θm ) = (90°, 0°) at Δϕ = 180° and τ = 0°

Fig. 5.22 Simulated pattern of array 3 scanning along θ-angle. a (Φm , θm ) = (90°, 90°) at Δϕ = 0 ◦ and τ = 50◦ ; b (Φ , θ ) = (90°, 70°) at Δϕ = 0° and τ = 70°; c (Φ , θ ) = (90°, 50°) at Δϕ = m m m m 0° and τ = 100°; d (Φm , θm ) = (90°, 30°) at Δϕ = 180° and τ = 160°; e (Φm , θm ) = (90°, 10°) at Δϕ = 180° and τ = 250°; f (Φm , θm ) = (90°, 0°) at Δϕ = 180° and τ = 0°. Figure reproduced with permission from Ref. [32], © 2021 IEEE

(b), Φ = 55°–65°, 115°–125°,and θ = 40°–90° in (c), Φ = 20°–40°, 140°–160° and θ = 20°–90° in (d), Φ = 0°–25°, 155°–180°and θ = 0°–40° in (e), Φ = 0°–20°, 160°–180°and θ = 0°–20° in (f). And the main beam points to (Φm , θm ) = (90°, 90°) with Δϕ = 0° and τ = 50° in (a), (Φm , θm ) = (90°, 70°) with Δϕ = 0° and τ = 70° in (b), (Φm , θm ) = (90°, 50°) with Δϕ = 0° and τ = 100° in (c),(Φm , θm ) = (90°, 30°) with Δϕ = 160° and τ = 180° in (d), (Φm , θm ) = (90°, 10°) with Δϕ = 180° and τ = 250° in (e), (Φm , θm ) = (90°, 0°) with Δϕ = 180° and τ = 0° in (f). Comparing Figs. 5.21 and 5.22, it can be concluded that the measured results are consistent with the measured ones, and the proposed 1D Array 3 realizes scanning along θ -direction. Corresponding to Table 5.6, the measured and simulated 3D patterns scanning along Φ-direction are shown in Fig. 5.23. The maximum beam direction in the θ-dimension θm remains unchanged at 90°. The measured beams are mainly concentrated in the range of Φ = 80°–90° and θ = 50°–120° in (a), Φ = 60°–90° and θ = 45°–135° in (b), Φ = 40°–85° and θ = 45°–135° in (c). And the main beams point to (Φm , θm ) = (90°, 90°) with Δϕ = 0° and τ = 50° in (a), (Φm , θm ) = (70°, 90°) with Δϕ = 60° and τ = 100° in (b), (Φm , θm ) = (50°, 90°) with Δϕ = 120° and τ = 140° in (c). Comparing Fig. 5.23a–c and d–f, it can be observed that the measured results are in good agreement with the simulated ones, and the proposed 1D Array 3 realizes scanning along Φ-direction.

5.5 Summary

147

Fig. 5.23 Measured and simulated pattern of Array 3 scanning along Φ-angle. Measured results: a (Φm , θm ) = (90°, 50°) at Δϕ = 120◦ and τ = 140◦ ; b (Φm , θm ) = (90°, 70°) at Δϕ = 60◦ and τ = 100◦ ; and c (Φm , θm ) = (90°, 90°) at Δϕ = 0◦ and τ = 50◦ ; simulated results: d (Φm , θm ) = (90°, 50°) at Δϕ = 120◦ and τ = 140◦ ; e (Φm , θm ) = (90°, 70°) at Δϕ = 60◦ and τ = 100◦ ; and f (Φm , θm ) = (90°, 90°) at Δϕ = 0◦ and τ = 50◦ . Figure reproduced with permission from Ref. [32], © 2021 IEEE

In conclusion, Array 3 is competent to scan both along θ - and Φ-direction, and the total 3 dB coverage of the main beam can cover the space of 0° < Φ < 180°, 0° < θ < 90°.

5.5 Summary The proposed Array 2 and Array 3 are compared with other reported phased arrays in Table 5.7. As a 1D linear array, the proposed Array 2 can achieve scanning from 0° to 73° along θ -direction and 90°-140° along Φ-direction, and its 3 dB coverage of the main beam can well scan over the space of 0° < Φ < 140°, 0° < θ < 90°. The proposed Array 3 can achieve scanning from 0° to 90° along θ -direction and 50°-90° along Φ-direction and its 3 dB coverage of the main beam can almost scan over the space of 0° < Φ < 180°, 0° < θ < 90°. Both of them can realize a wide 3D scanning coverage, and are very useful to wide angle scanning phased arrays of radar and wireless communication. A phase-mode SSPPs antenna with dual-port is investigated. The SSPPs structure is in the middle, and it is fed by two monopoles on two sides of the SSPPs structure. By changing the phase difference Δϕ between two monopoles, the SSPPs antenna can work in odd mode, even mode and hybrid modes. When the phase difference Δϕ = 0◦ , broadside lobe in even mode is excited; when Δϕ = 180◦ , end-fire lobe in odd mode is radiated; when 0◦ < Δϕ < 180◦ , mixed modes of the two are generated, and finally the continuous spatial scanning capability of changing from broadside lobe to end-fire lobe is realized. In different phase modes, the realized gain of the proposed antenna is 3.4–4.4 dBi. Furthermore, based on the proposed SSPPs antenna element, and combined with the generalized principle of pattern multiplication (GPPM), three kinds of linear arrays with different arrangements are constructed. By changing the generalized array factor (GAF) and generalized element factor (GEF) simultaneously, all three arrays can scan along both θ - and Φ-dimensions at the same time. The element isolation of Array 2 and Array 3 are both greater than 13 dB. Array 2 can scan from 0° to 73° along θ -direction, with realized gain in the range of 6.5–10.4 dBi, and scan

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Table 5.7 Comparison with other reported phased array References

BW (GHz)

Dimensionality of scanning

Main beam scanning range

3 dB beam width Gain scanning Range fluctuation (dBi)

[36]

4.92–5.07

2-D (8 × 8)

64 ◦ both in E-plane and H-plane

–

4.5

[37]

3.21–5.09

1-D (1 ×9)

60 ◦ in E-plane

–

3

[38]

0.5–2

1-D (1 × 26)

60 ◦ in E-plane

–

–

[39]

5.13–5.28

2-D (8 × 8)

75 ◦ both in E-plane and H-plane

–

2.8

Proposed array2

4.5–6

1-D (1 × 4)

73 ◦ along θ-direction and 50 ◦ along Φ-direction

0° < Φ < 140° 0° < θ < 90°

θ-direction: 3.9 Φ-direction: 5.6

Proposed array3

4.5–6

1-D (1 ×4)

90 ◦ along θ-direction and 40 ◦ along Φ-direction

0° < Φ < 180° 0° < θ < 90°

θ-direction: 2.9 Φ-direction: 3.36

Table reproduced with permission from Ref. [32], © 2021 IEEE

from 90° to 140° along Φ-direction, with realized gain in the range of 6.1–11.7 dBi, and its 3 dB coverage of the main beam can well scan over the space of 0° < Φ < 140°, 0° < θ < 90°. Array 3 can scan from 0 ◦ to 90 ◦ along θ -direction, with realized gain in the range of 8.2–11.1 dBi, and scan from 50 ◦ to 90 ◦ along Φ-direction, with realized gain in the range of 6–9.36 dBi, and its 3 dB coverage of the main beam can almost scan over the space of 0° < Φ < 180°, 0° < θ < 90°. The phase-mode SSPPs antenna and extended 1D linear arrays based on GPPM presents great promotion in future remote sensing and wireless communication.

References

149

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