IEEE Transactions on Antennas and Propagation [volume 59 number 1]

Citation preview

JANUARY 2011

VOLUME 59

NUMBER 1

IETPAK

(ISSN 0018-926X)

Editorial .. ......... ......... ........ ......... ......... ........ ... ....... ......... ........ ......... ......... ........ ..... M. A. Jensen

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PAPERS

Antennas Investigation Into the Application of Artificial Magnetic Conductors to Bandwidth Broadening, Gain Enhancement and Beam Shaping of Low Profile and Conventional Monopole Antennas ........ ......... ...... A. Foroozesh and L. Shafai The Effect of Insulating Layers on the Performance of Implanted Antennas .... ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ... F. Merli, B. Fuchs, J. R. Mosig, and A. K. Skrivervik Engineered Dielectric Pattern Nanoantenna: A Quantum Cascade Laser (QCL) Device Application ... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... J. Wu and H. Mosallaei Millimeter-Wave Substrate Integrated Waveguide Long Slot Leaky-Wave Antennas and Two-Dimensional Multibeam Applications ... ......... ........ ......... ........ .. ........ ......... ......... ....... Y. J. Cheng, W. Hong, K. Wu, and Y. Fan Antenna Miniaturization Using Slow Wave Enhancement Factor from Loaded Transmission Line Models ..... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ... P.-L. Chi, R. Waterhouse, and T. Itoh Topology Optimization of Sub-Wavelength Antennas ... ......... ......... . ....... ......... ..... A. Erentok and O. Sigmund Analysis and Characterization of a Multipole Reconfigurable Transmitarray Element .. ......... . J. Y. Lau and S. V. Hum Broadband Circularly Polarized Crossed Dipole With Parasitic Loop Resonators and Its Arrays ....... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ...... J.-W. Baik, T.-H. Lee, S. Pyo, S.-M. Han, J. Jeong, and Y.-S. Kim Arrays Frequency Selective Reflectarray Using Crossed-Dipole Elements With Square Loops for Wireless Communication Applications ... ......... . ....... ...... L. Li, Q. Chen, Q. Yuan, K. Sawaya, T. Maruyama, T. Furuno, and S. Uebayashi A Lightweight Organic X-Band Active Receiving Phased Array With Integrated SiGe Amplifiers and Phase Shifters . .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ . C. E. Patterson, T. K. Thrivikraman, A. M. Yepes, S. M. Begley, S. K. Bhattacharya, J. D. Cressler, and J. Papapolymerou Design of Non-Uniform Circular Antenna Arrays Using a Modified Invasive Weed Optimization Algorithm .. ......... .. .. ........ ......... ......... ........ ......... ......... ........ ........ G. G. Roy, S. Das, P. Chakraborty, and P. N. Suganthan Electromagnetics and Imaging On the Physical Limitations of the Interaction of a Spherical Aperture and a Random Field .... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... A. Alayón Glazunov, M. Gustafsson, and A. F. Molisch Electromagnetic Resonances of a Straight Wire .. ........ ......... ......... ........ J. M. Myers, S. S. Sandler, and T. T. Wu Nonmagnetic Ultrawideband Absorber With Optimal Thickness ......... ........ ....... ... ......... ........ .. A. Kazemzadeh Inverse Scattering for Soft Fault Diagnosis in Electric Transmission Lines ...... . .. Q. Zhang, M. Sorine, and M. Admane Underground Anomaly Detection by Electromagnetic Shock Waves ..... ........ ......... ......... ........ ....... A. S. Kesar

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(Contents Continued on p.1)

(Contents Continued from Front Cover) Numerical Techniques Computation of Scattering by DB Objects With Surface Integral Equation Method ..... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ... J. Markkanen, P. Ylä-Oijala, and A. Sihvola Optimized Numerical Evaluation of Singular and Near-Singular Potential Integrals Involving Junction Basis Functions .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ..... F. Vipiana and D. R. Wilton Singularity Evaluation of the Straight-Wire Mixed-Potential Integral Equation in the Method of Moments Procedure . .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... A. M. A. Jalloul and J. L. Young A Fast Numerical Method for Electromagnetic Scattering From Dielectric Rough Surfaces ..... . B. Liu, Z. Li, and Y. Du A Fast Hybrid Method for Scattering From a Large Object With Dihedral Effects Above a Large Rough Surface ...... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ..... G. Kubické and C. Bourlier Conformal FDTD Modeling of Imperfect Conductors at Millimeter Wave Bands ....... ......... ........ ........ G. Junkin Coefficients of Finite Difference Operator for Rectangular Cell NS-FDTD Method ..... ......... . T. Ohtani and Y. Kanai Modification of Real-Number and Binary PSO Algorithms for Accelerated Convergence .... A. Modiri and K. Kiasaleh Wireless Multipole and S-Parameter Antenna and Propagation Model .... ......... ........ ......... M. Haynes and M. Moghaddam Propagation Characteristics, Metrics, and Statistics for Virtual MIMO Performance in a Measured Outdoor Cell ...... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... . M. Webb, M. Yu, and M. Beach Angular and Shadowing Characteristics of Dense Multipath Components in Indoor Radio Channels .. ......... ......... .. .. ........ ......... ......... ........ ......... ........ J. Poutanen, J. Salmi, K. Haneda, V.-M. Kolmonen, and P. Vainikainen Channel Decomposition Method for Designing Body-Worn Antenna Diversity Systems ........ ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ..... G.-Y. Lee, D. Psychoudakis, C.-C. Chen, and J. L. Volakis Analysis and Optimization of Compact Suspended Plate MIMO Antennas ..... . Z. N. Chen, X. N. Low, and T. S. P. See Rigorous Prediction of the Ground Wave Above Flat and Rough Highly-Conducting One-Dimensional Sea Surfaces in HF-VHF Band . ......... ........ ......... ......... ........ ......... ......... ........ .. C. Bourlier, G. Kubické, and Y. Brelet

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COMMUNICATIONS

A Broadband -Strip Fed Printed Microstrip Antenna .. ......... ......... ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... ....... V. P. Sarin, M. S. Nishamol, D. Tony, C. K. Aanandan, P. Mohanan, and K. Vasudevan Compact Asymmetric-Slit Microstrip Antennas for Circular Polarization ...... .. .. Nasimuddin, X. Qing, and Z. N. Chen The Compact Circularly-Polarized Hollow Rectangular Dielectric Resonator Antenna With an Underlaid Quadrature Coupler ......... ......... ........ ......... ......... ........ ......... ......... ........ . E. H. Lim, K. W. Leung, and X. S. Fang Development of Shared Aperture Dual Polarized Microstrip Antenna at L-Band ........ ......... ........ .. S. Chakrabarti A Surface Wave Holographic Antenna for Broadside Radiation Excited by a Traveling Wave Patch Array ..... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... .. A. Sutinjo and M. Okoniewski Reduced Sideband Levels in Time-Modulated Arrays Using Half-Power Sub-Arraying Techniques ... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... . Y. Tong and A. Tennant Experimental Characterization of UWB Beamformers Based on Multidimensional Beam Filters ...... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... . L. Liang and S. V. Hum A New Approach for the FDTD Modeling of Antennas Over Periodic Structures ....... ......... .. D. Li and C. D. Sarris Efficient Incorporation of a PEC/PMC Plane in the Multiple-Grid Adaptive Integral Method ... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ .... M.-F. Wu, K. Yang, and A. E. Yılmaz An Unconditionally Stable 1-D FDTD Algorithm for Modeling Chiral Media Based on Similar LOD Method ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ....... Q.-X. Chu and D.-A. Cao Transmission of Pulsed Plane Wave Into Dispersive Half-Space: Prony’s Method Approximation ..... ...... A. M. Attiya Periodically Loaded Straight Wires for Radio Wave Transmission Control ...... ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ...... K. Iigusa, H. Harada, S. Kato, J. Hirokawa, and M. Ando An Empirical Model for Propagation Loss Through Tropical Woodland in Urban Areas at UHF ....... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ........ M. H. C. Dias and M. S. de Assis Miniature Ceramic Dual-PIFA Antenna to Support Band Group 1 UWB Functionality in Mobile Handset ..... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ....... D. Kearney, M. John, and M. J. Ammann Wideband Miniaturized Half Bowtie Printed Dipole Antenna With Integrated Balun for Wireless Applications ........ .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ..... W. S. Yeoh, K. L. Wong, and W. S. T. Rowe List of Reviewers for 2010 ....... ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... .

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IEEE ANTENNAS AND PROPAGATION SOCIETY All members of the IEEE are eligible for membership in the Antennas and Propagation Society and will receive on-line access to this TRANSACTIONS through IEEE Xplore upon payment of the annual Society membership fee of $24.00. Print subscriptions to this TRANSACTIONS are available to Society members for an additional fee of $36.00. For information on joining, write to the IEEE at the address below. Member copies of Transactions/Journals are for personal use only. ADMINISTRATIVE COMMITTEE M. ANDO, President R. D. NEVELS, President Elect M. W. SHIELDS, Secretary-Treasurer 2011 2012 2013 A. AKYURTLU *J. T. BERNHARD W. A. DAVIS H. LING M. OKONIEWSKI Honorary Life Members: R. C. HANSEN, W. R. STONE *Past President Committee Chairs and Representatives Antenna Measurements (AMTA): S. SCHNEIDER Finance: M. W. SHIELDS Publications: R. J. MARHEFKA Antennas & Wireless Propagation Letters Editor-in-Chief: Gold Representative: R. ADAMS RAB/TAB Transnational Committee Liaison: D. R. JACKSON G. LAZZI Historian: K. D. STEPHAN Region 10 Representative: H. NAKANO Applied Computational EM Society (ACES): A. F. PETERSON IEEE Press Liaison: R. J. MAILLOUX Sensor Council: A. I. ZAGHOUL, T. S. BIRD, M. W. SHIELDS Awards: A. F. PETERSON IEEE Magazine Committee: W. R. STONE Standards Committee—Antennas: M. H. FRANCIS Awards and Fellows: C. A. BALANIS IEEE Public Relations Representative: W. R. STONE Standards Committee—Propagation: D. V. THIEL Chapter Activities: L. C. KEMPEL IEEE Social Implications of Technology: R. L. HAUPT TABARC Correspondent: C. A. BALANIS CCIR: P. MCKENNA Institutional Listings: T. S. BIRD Committee on Man and Radiation: G. LAZZI Joint Committee on High-Power Electromagnetics: C. E. BAUM TAB Magazines Committee: W. R. STONE Constitution and Bylaws: O. KILIC Long-Range Planning: C. RHOADS TAB New Technology Directions Committee: A. I. ZAGHLOUL Digital Archive Editor-in-Chief: A. Q. MARTIN Magazine Editor-in-Chief: W. R. STONE TAB Public Relations Committee: W. R. STONE Distinguished Lecturers: J. C. VARDAXOGLOU Meetings Coordination: S. A. LONG TAB Transactions Committee: T. S. BIRD Education: D. F. KELLY Meetings Joint AP-S/URSI: M. A. JENSEN Transactions Editor-in-Chief: T. S. BIRD EAB Continuing Education: S. R. RENGARAJAN Membership: S. BALASUBRAMANIAM Transnational Committee: D. R. JACKSON Electronic Design Automation Council: M. VOUVAKIS Nano Technology Council: G. W. HANSON USAB Committee on Information Policy: S. WEIN Electronic Publications Editor-in-Chief: S. R. BEST New Technology Directions: S. C. HAGNESS USAB R&D Committee: A. C. SCHELL European Representatives: B. ARBESSER-RASTBURG Nominations: J. T. BERNHARD USNC/URSI : J. T. BERNHARDT Fellows Nominations Committee: J. L. VOLAKIS PACE: J. M. JOHNSON Women in Engineering Representative: P. F. WAHID AP Transactions website: http://ieeeaps.org/aps_trans/ Albuquerque: HARALD J. WAGNON Argentina: GUSTAVO FANO Atlanta: KRISHNA NAISHADHAM Australian Capital Territory: DAVID MURRAY Baltimore: MARK PACEK Bangalore, India: KALARICKAPARAMBIL VINOY Benelux: GUY VANDENBOSCH Boston: JOHN SANDORA Bulgaria: KATYA ASPARUHOVA Calcutta: DEBATOSH GUHA Central & South Italy: GUGLIELMO D’INZEO Central Texas: JEREMY PRUITT Chicago: HOWARD LIU Cleveland: MAX SCARDELLETTI Columbus: FERNANDO L. TEIXEIRA Connecticut: CHARLOTTE BLAIR Croatia: RADOVAN ZENTNER Czechoslovakia: MILAN POLIVKA Dallas: NARINDRA LAKHANPAL Dayton: ANDREW TERZUOLI Denver-Boulder: MICHAEL JANEZIC East Ukraine: OKSANA V. SHRAMKOVA Eastern North Carolina: TODD NICHOLS Egypt: HADIA EL-HENNAWY Finland: ARTTU LUUKANEN Florida West Coast: JING WANG

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION Is the leading international engineering journal on the general topics of electromagnetics, antennas and wave propagation. The journal is devoted to antennas, including analysis, design, development, measurement, and testing; radiation, propagation, and the interaction of electromagnetic waves with discrete and continuous media; and applications and systems pertinent to antennas, propagation, and sensing, such as applied optics, millimeter- and sub-millimeter-wave techniques, antenna signal processing and control, radio astronomy, and propagation and radiation aspects of terrestrial and space-based communication, including wireless, mobile, satellite, and telecommunications. Author contributions of relevant full length papers and shorter Communications are welcomed. See inside back cover for Editorial Board.

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Digital Object Identifier 10.1109/TAP.2010.2103214

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

2011 Editorial—A Tribute and a Challenge

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Y first editorial would be sorely misguided were it not to acknowledge the remarkable work of my predecessor, Dr. Trevor Bird. Dr. Bird served the society as Editor-in-Chief of this publication for six years. With the help of the Editorial Assistant Dallas Rolph (who has become part of the society “family” as a result of her dedication), Dr. Bird helped the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION grow to its current position not only as the premier journal highlighting research on antennas and propagation but also as a publication that stands out in the huge field of scientific venues. Currently, this TRANSACTIONS enjoys the second largest number of downloads from IEEE Xplore out of the over 30000 publications housed on this repository. Furthermore, the journal impact factor, which measures the relevancy of the publications printed in the journal, has risen to just under 2.5. This is all in addition to reductions in publication delays in the face of huge increases in the volume of submissions. We are indebted to Dr. Bird for his service. If you have not done so already, I hope that you will send him an email or approach him on a future occasion to express your appreciation for these efforts and congratulations for the achievements. Certainly, given these achievements, assuming responsibility for the TRANSACTIONS is a daunting proposition. With the help of our new Editorial Assistant Sara K. S. Hanks, the continued excellent service from our IEEE Staff Associate Editor Dawn L. Menendez, and the dedicated work of our 32 volunteer Associate Editors (approximately 65% of whom are new), I am committed to working hard to ensure that our TRANSACTIONS continues to increase in stature and impact. However, even with the impressive credentials and capabilities of the editorial staff, the continued vibrancy and success of the TRANSACTIONS depends critically on the excellent contributions from authors and on the dedicated work of reviewers. I know that I represent the entire editorial staff as I express my appreciation for the efforts of so many of you who contribute to the journal through these activities. As many of you are aware, the acceptance rate for papers submitted to the TRANSACTIONS is now below 50%, and given an ever increasing volume of submissions, we may well experience a further reduction in this acceptance rate in the future. Rejection is generally frustrating for authors. Furthermore, reviewers and Associate Editors often struggle to determine whether a marginal contribution should be rejected or should be allowed to undergo extensive revisions to see if it can be made suitable for publication. Given this observation, it is important for me to articulate expectations of work submitted to the Transactions and some guidelines for increasing the chances of eventual publication of a submitted paper. Specifically, authors should critically evaluate their work and consider the questions that reviewers and Associate Editors often ask when judging submitted manuscripts. Digital Object Identifier 10.1109/TAP.2010.2099050

1. Does the work offer new knowledge, new understanding, or new insights? Often, we receive papers that report on carefully-performed work but that fail to teach new insights or provide new understanding. It is essential that papers teach new principles, enhance understanding, or synthesize known material into a unified theory. If the paper uses only known principles to achieve a design, shows a single design outcome without teaching the underlying design principles, or reports on measured results without demonstrating observations of previously unknown characteristics or behaviors, then the scope of the manuscript is typically considered too narrow to warrant publication in an archival journal like the TRANSACTIONS. For example, a paper might show a single design of an antenna, but not teach the principles that allow readers to scale the design to other frequencies or apply the design techniques to other geometries. Similarly, a paper might report on measurements of an indoor propagation scenario that simply demonstrate that the observed results match those appearing in other publications. Such papers are of incremental value and generally are not found acceptable. A submission should therefore clearly articulate the scope of the contribution and how the publication advances understanding or insight. As part of this discussion, the manuscript should document the relevant prior work and discuss how the developments described in the submission overcome specific limitations associated with this previously-reported work. 2. Are the findings of the work discussed clearly in the context of the state-of-the-art? I have personally reviewed hundreds of papers for a variety of journals and conferences over the years. Frequently, I find that because the paper may formulate the problem in a way that differs from traditional solutions, the authors have a difficult time realizing that the end result is identical or at least closely-related to results that are known. While it is becoming infeasible as authors to ensure that we have identified all related material on a topic, it is certainly our responsibility to do our best to understand our results and how they fit into the existing body of knowledge. It is also our responsibility to use standard notation and generally accepted terms used in our profession. An excellent source of such terminology is the IEEE Standard Definition of Terms for Antennas (IEEE Standard 145–1993). Similar standards exist for testing of antennas and for propagation. It should be noted, however, that with the ever-increasing number of papers appearing in the literature, synthesis work that rigorously unifies many seemingly disparate contributions is becoming increasingly valuable and represents a welcome contribution. 3. Is the work adequately mature for archival publication? The pressures faced by those in academia and other research environments to publish can lead to a temptation

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

to submit work that is not yet ready to offer definitive conclusions or expositions of new understanding. It is important for submitted work to demonstrate maturity, a concept that is certainly related to item 2. One question I ask myself regarding my own publications is: “Can I offer a straightforward explanation of the principles that underpin our work?” Often, if the answer is “no,” I find that it is because I do not yet understand the topic adequately. The final documentation of a body of work should be able to offer a set of intuitive principles that can serve as a stepping stone to help other scientists or designers in their endeavors. If the work is not yet ready to achieve this, then authors should consider writing conference articles on the topic, as such publishing can help the authors to mature the work to a point where it is ready for submission to an archival venue (although authors must be careful to avoid duplicate submission of the same material, as outlined in item 4 below). 4. Does the reported work represent a significant extension beyond the work reported in prior publications by the authors? This of course represents the “duplicate publication” problem that has become a significant issue for the IEEE. For more on this topic, please see Dr. Bird’s Editorial in the January 2007 issue (IEEE Trans. Antennas Propag., vol. 55, no. 1, pp. 2–3, Jan. 2007). While the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION does not have a quantitative measure for specifying the allowable overlap between different publications, generally at least 30%–40% of the paper should represent material that has not yet been published or submitted elsewhere (this includes conference publications). 5. Is the manuscript concise? Sometimes, we as authors feel our work is important enough to warrant a large number of pages. But it is rare that reviewers agree with this. It is always a good idea to go through a paper looking for ways to reduce the page count without sacrificing the key

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information. The limit of eight printed pages for a regular submission without payment of mandatory overlength page charges has been chosen since it is accepted that most principles can be taught within this limit. Sometimes, additional pages are required, but regular papers should rarely exceed ten printed pages. For a review or tutorial article or for a paper truly reporting on a seminal advance, additional pages are likely appropriate, but authors should still focus on finding ways to concisely represent the important ideas. 6. Is the work presented in a logical way that steps the reader through from the problem formulation to the establishment of the principles that are being taught? Is the manuscript written clearly, with proper attention to grammar and style? Often, manuscripts that are rejected have done a poor job of logically stepping the reader through the development and teaching the desired principles. Sadly, some work is rejected simply because the writing is grammatically incorrect or stylistically poor. I challenge all authors to consider these questions as they prepare and submit their manuscripts. While satisfactorily answering all of these questions a) may not be a prerequisite for publication and b) will not guarantee acceptance, considering these questions before submitting a manuscript will certainly improve the chances that the manuscript will be accepted for publication. Likewise, reviewers can help to enhance the quality of the Transactions by asking such questions during their evaluations. I hope that we can work together to explore and present new and exciting areas of research that will help our community remain a vibrant and relevant part of the future research landscape.

MICHAEL A. JENSEN, Editor-in-Chief Department of Electrical and Computer Engineering Brigham Young University Provo, UT 84602 USA

Michael A. Jensen (S’93–M’95–SM’01–F’08) received the B.S. and M.S. degrees from Brigham Young University (BYU), Provo, UT, in 1990 and 1991, respectively, and the Ph.D. degree from the University of California, Los Angeles (UCLA), in 1994, all in electrical engineering. Since 1994, he has been at the Electrical and Computer Engineering Department, BYU, where he is currently a Professor and Department Chair. His research interests include antennas and propagation for communications, microwave circuit design, and multi-antenna signal processing Dr. Jensen is currently the Editor-in-Chief of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. Previously, he was an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS. He has been a member and Chair of the Joint Meetings Committee for the IEEE Antennas and Propagation Society, a member of the society AdCom, and Co-Chair and Technical Program Chair for five society-sponsored symposia. In 2002, he received the Harold A. Wheeler Applications Prize Paper Award in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION in recognition of his research on multi-antenna communication

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

Investigation Into the Application of Artificial Magnetic Conductors to Bandwidth Broadening, Gain Enhancement and Beam Shaping of Low Profile and Conventional Monopole Antennas Alireza Foroozesh, Member, IEEE, and Lotfollah Shafai, Life Fellow, IEEE

Abstract—The reflection coefficient phase is investigated for several different artificial magnetic conductors (AMCs) having canonical FSS-type shapes. Three of them are selected, each representing a different class, and fine tuned to exhibit identical resonant frequency. Polarization and angular dependence as well as the effects of losses on these structures are studied. Next, a low-profile inverted L-shape monopole antenna (ILSMA) is placed horizontally above the ground plane. Vertical monopole antenna (VMA) is also placed above them. It is shown that using some of the aforementioned AMCs, the input impedance of both ILSMA and VMA can not only be matched, but also the input impedance bandwidth enhancement as wide as 27% and 35% are obtained, respectively. The VMA study on AMC ground planes which reveals a counter-intuitive phenomenon has not been explored in the literature, previously. It is revealed that the broadband characteristics can also be achieved for smaller size of the AMC ground planes, which enables the antenna to be designed in compact size. It is also illustrated that reflection characteristics of the AMC is not sufficient to evaluate AMC performance when it is used as an antenna ground plane. This is illustrated through extensive simulation and measurement results. Index Terms—Antenna bandwidth, antenna gain, antenna input impedance, artificial magnetic conductor (AMC), monopole antenna, perfect electric conductor (PEC), perfect magnetic conductor (PMC).

I. INTRODUCTION INCE the advent of high impedance surfaces (HISs) or artificial magnetic conductors (AMCs) in [1], many researchers have used them to design novel electromagnetic devices or enhance the performance of the existing ones. One of the main applications of the artificial structures is to design low-profile or high-performance antennas, where they serve as the antenna ground plane [1]–[15]. As it is known, impenetrable ground planes are needed in many telecommunication systems to shield the electronics, lo-

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Manuscript received September 16, 2009; revised May 26, 2010; accepted July 04, 2010. Date of publication November 09, 2010; date of current version January 04, 2011. This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada. The authors are with the Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg MB R3T 5V6, Canada (e-mail: alireza@ee. umanitoba.ca; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090458

Fig. 1. Unit cells of several AMCs consisting of different metallizations. All structures are backed by a grounded dielectric slab made of Arlon Diclad having thickness of 1.6 mm. L is the periodicity of the unit cells, although it is only shown in part (a), and may differ from one shape to the other one. (a) Patch unit cell (AMC1) with L : and s : , (b) ring unit cell (AMC2) ,s : , and p : , (c) Jerusalem cross with L : ,s : ,p : ,t : , and (AMC3) with L q : , (d) : , remaining dimensions can be found from : , remaining dimensions can be found from parts (a) and (e), (e) part (a) and (e), (f) : , the remaining dimensions can be found from : and s : , the remaining dimensions can be part (c), (g) q found from part (b), (h) : , the remaining dimensions can be found : , : , the remaining dimensions can be from part (b), (i) found from part (b), (j) : , : , the remaining dimensions : ,q : , the remaining can be found from part (b), and (k) s dimensions can be found from part (b).

= 4 9 mm = 4 7 mm = 3 0 mm = 4 0 mm = 3 8 mm = 12 mm = 0 6 mm = 4 9 mm = 5 5 mm = 9 7 mm s = 1 45 mm w = 0 2 mm q = 9 7 mm = 2 5 mm = 2 0 mm s = 2 mm s = 2 5 mm t = 0 8 mm p = 2 5 mm t = 0 3 mm = 0 4 mm = 1 4 mm

cated beneath the antenna, from the radiation. The conventional ground plane made of a good electric conducting material is impenetrable and provides a fairly good shielding, and it is

0018-926X/$26.00 © 2010 IEEE

FOROOZESH AND SHAFAI: INVESTIGATION INTO THE APPLICATION OF AMCs TO BANDWIDTH BROADENING

Fig. 2. Reflection phase of the AMCs shown in Fig. 1.

normally approximated by a perfect electric conductor (PEC). However, it introduces an image with a negative current to that of a source, which is placed horizontally above the ground plane. On the other hand, in order for the planar antennas to be low profile, they have to be placed horizontally and very close to the ground plane beneath them. Therefore, current cancellation of the source antenna with its image, consequently results in a poor input impedance matching, which in turn prevents the antenna to radiate efficiently. On the other hand, AMCs and HISs, not only maintain appropriate shielding for the electronics beneath the antennas and redirecting the wave radiation to the upper half-space, but they also can provide good input impedance matching. As it is known, the image current introduced by a perfect magnetic conductor (PMC) is in parallel and in phase with its source, which is located horizontally above it. This fact is usually used to describe the improvement in the antenna input impedance characteristics [1], when AMCs or HISs are employed as the antenna ground plane. However, the electromagnetic interaction between the antenna and artificial ground plane is complicated [2], and thus the underlying phenomenology may not be limited only to the image concept. One of the purposes of this work is to address the shortcoming of using the image theory to describe the

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Fig. 3. (a) Reflection coefficient phase versus frequency for three different AMCs whose unit cells are shown in Fig. 1. (b) Reflection coefficient phase versus incident angle () for the same AMCs.

phenomenology involved in the antennas with AMC ground planes. Input impedance matching using high impedance surfaces have been previously reported in [1] and [2]. It has been reported that the spiral antenna can show more stable input impedance over the frequency band when these high impedance EBG-type surfaces are used [3] and [4]. However, one should note that the spiral antennas are inherently broadband. An improvement on the characteristics of an inverted F antenna (IFA) over high impedance ground plane has been reported in [5]. AMCs and HISs have also been used as the ground plane of the planar microstrip antennas to significantly enhance either impedance bandwidth or gain or both [6]–[10]. In this work, several different AMCs with different metallizations are investigated in terms of their reflection phases. Shorting pins are not used in their structures. Three of them are selected, one from each class, that exhibit the same resonant frequency. Their dependency on the angle, polarization and plane of the incident wave are studied. Effects of the resistive losses are also discussed thoroughly. Then, an inverted L-shape monopole antenna (ILSMA) is placed above these three AMCs, as well as, a conventional copper-made ground plane surface.

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

Fig. 4. (a) TE-TE and (b) TM-TM reflection coefficient magnitudes of AMC1. (c) TE-TE and (d) TM-TM reflection coefficient phases of AMC1.

It is illustrated that the ILSMA is not well matched on the conventional ground plane. This implies that although this antenna is low-profile it does not radiate efficiently. When the other three AMCs are utilized as the ground plane, not only the input impedance matching is achieved but also considerable input impedance bandwidth enhancements, as wide as 27%, are observed. By assuming that all the materials in the antenna structures are lossless, it is confirmed that this wideband behavior is not because of the AMC losses, but because of the unit cells’ shapes and configurations. Radiation patterns of these antennas are discussed as well, and their potential applications are proposed. Measurement results are also presented to support the simulations. Since in many applications, in addition to being low-profile, compactness is also a requirement for the antenna, the effects of the AMC size are investigated as well. Both simulations and measurements indicate that the ILSMA prevail wideband behavior on small AMCs, too. This demonstrates the capability of compact size design of the ILSMAs over AMCs. It is also shown that reflection phase characteristics of the AMC unit cell cannot, in general, predict the performance of the antennas above them. It is illustrated that employing two AMCs with different shapes but having similar reflection phase characteristics, results in two different antenna characteristics

when two identical monopole antennas are placed above them. This fact, which is not previously dealt with in the literature, is addressed in this paper. Characteristics of the vertical monopole antenna (VMA) over AMC ground planes are also explored in this paper. As it is known, a PMC ground plane does not provide a wideband impedance matching for the vertically located antennas such as VMAs, due to the introduction of the reverse image current beneath the ground plane. In spite of this property of PMC, it is shown that the designed AMCs maintain good impedance matching even for the VMAs. This fact has not been revealed in the literature before, since it is counter-intuitive that the AMCs be able to preserve wideband behavior for the vertically-flowing-current antennas. Interestingly, VMA over two different AMCs show bandwidths as high as 35.84% and 33.84%. Measurement results support the simulations. Far-field radiation patterns are also discussed. Because of the shape of the radiation patterns, wideband input impedance and being low-profile, these antennas find applications in vehicle-to-vehicle (V2V) communications [12]. The structure of the paper is as follows. In Section II, AMC design and characterization are presented. In Section III, simulation results of the antenna reflection coefficient over three

FOROOZESH AND SHAFAI: INVESTIGATION INTO THE APPLICATION OF AMCs TO BANDWIDTH BROADENING

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Fig. 5. (a) TE-TE and (b) TM-TM reflection coefficient magnitudes of AMC2. (c) TE-TE and (d) TM-TM reflection coefficient phases of AMC2.

different designed AMCs, as well as the conventional ground plane, are shown for both lossy and lossless materials. Effects of the ground plane size on the input impedance characteristics and radiation patterns of the antenna are investigated in Section IV. It is demonstrated that the ground plane size can be reduced to a quarter of the original one, while maintaining the broad bandwidths, to a very good extent. Measurement results of ILSMA verifying the simulations are presented in Section V. VMA characteristics are presented in Section VI. The applications of the proposed antennas, based on their performance, are discussed in Section VII. Finally, conclusions are drawn in Section VIII. II. AMC DESIGN AND CHARACTERIZATION By definition, an artificial magnetic conductor (AMC) is a structure, which shows close-to-zero reflection coefficient phase, when it is subjected to the normal TEM plane wave illumination [1]. In their first appearance, AMCs were introduced as the periodic patches shorted to the ground planes via metallic pins [1]. However, it was later shown, they can also be implemented by loading a grounded dielectric substrate with different FSS-type periodic metallizations [13]–[17]. In some cases, their EBG characteristics have also been studied [7], [17] and [18]. Although, optimizing the AMC unit cells, using

genetic algorithm, towards obtaining the desired reflection phase has been presented in [16], it is always instructive to investigate canonical geometries and classical shapes to gain physical insights. Several different AMC unit cells with various metallizations are depicted in Fig. 1. Their reflection phases for normal incident are plotted in Fig. 2 in the frequency range of 8.5-to-10.5 GHz. Patch-type AMC unit cell, shown in Fig. 1(a), and its modified version which is loaded by slots, shown in Fig. 1(c), have same reflection phase response as plotted in Fig. 2(a). However, extending the middle arms to touch the unit cell boundaries, i.e., connecting the adjacent unit cells as shown in Fig. 1(d), completely changes the reflection phase characteristics as can be seen in Fig. 2(a). This metallization has been introduced in [18] as one of the uni-planar EBGs (UC-EBGs). At this frequency range, the metallization, shown in Fig. 1(d) is no longer an AMC. This implies that the existing capacitance between the adjacent unit cells play a key role in reducing the resonance frequency and consequently compact unit cell design. The metallization, shown in Fig. 1(c), has the well known Jerusalem cross shape. In Fig. 1(f), only two middle arms, which connect the four sides, are removed. Interestingly, the reflection phases of both of these metallizations are very close as shown in Fig. 2(a).

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

Fig. 6. (a) TE-TE and (b) TM-TM reflection coefficient magnitudes of AMC3. (c) TE-TE and (d) TM-TM reflection coefficient phases of AMC3.

Fig. 8. Dimensions of the inverted L-shape monopole antenna used in this study.

Fig. 7. ILSMA over the (a) conventional ground plane (copper), (b) AMC1 (patch arrays), (c) AMC2 (ring arrays), and (d) AMC3 (Jerusalem cross arrays).

This indicates that the middle cross-shape conductors play an insignificant role compared to the side conductors. The other class of metallization studied in this work is the ring-type AMC unit cells. Some variations of this kind of metallization are shown in

Fig. 1(b), (g), (h), (i) and (j). Their reflection phases are plotted in Fig. 2(b). As can be understood from Fig. 2(b), loading the middle of the ring-type unit cells does not have any significant effects on the reflection phases. On the other hand, when the outer ring is loaded by small gaps, for example the one shown in Fig. 1(k), reflection phase response drastically changed as shown in Fig. 2(b). As can be seen, in this frequency, the metallization in Fig. 1(k) no longer represents an AMC unit cell, since the reflection phase is between 125 and 150 . Therefore, the outer ring determines the first resonant frequency in this type of metallizations. Moreover, one should note that the gaps between conducting parts of the two adjacent unit cells are kept 0.2 mm. This is the precision limitation imposed by the etching facility at the University of Manitoba. It is desirable to have more compact unit cells and the less the gap is the more compact the unit cell will become [14].

FOROOZESH AND SHAFAI: INVESTIGATION INTO THE APPLICATION OF AMCs TO BANDWIDTH BROADENING

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TABLE I SIMULATION AND MEASUREMENT RESULTS OF THE INPUT IMPEDANCE BANDWIDTH OF THE ILSMA OVER THREE DIFFERENT AMCS

Fig. 9. Magnitude of the reflection coefficients of the ILSMA over different ground planes. (a) Actual materials, copper and Arlon Diclad and (b) lossless materials are used.

Three different AMC unit cells, representing different AMC classes, are selected and investigated in more details. They are square patch (AMC1), square ring (AMC2) and Jerusalem cross (AMC3) metallizations and depicted in Fig. 1(a), (b) and (c), respectively. Their reflection coefficient phases versus frequency are plotted in Fig. 3(a), for the normal TEM incident plane wave. As can be observed, their reflection phases are very close to zero at 9.5 GHz for all cases. At 9.5 GHz, the AMCs reflection coeffiin Fig. 3(b). cient phases are drawn versus the incident angle These simulation results are obtained using the periodic moment method feature of the Ansoft Designer software package.

It is worthwhile mentioning some interesting observations. The reflection coefficient phases of all AMCs tend to approach zero at grazing angles, when the incident wave polarization is , whereas they approach for the polarization. This is consistent and similar with the results reported on different AMCs in [13] and [16]. The other interesting observation is the similarity of the reflection phases of the patch-type and ring-type AMCs, both over frequency and incident angle ranges. As can be seen, in Fig. 3(a), they are very close over the frequency range. As well, as shown in Fig. 3(b), their responses versus incident angles in different incident planes and for different polarizations are very similar. However, one should note that the unit cell size of the ring-type is almost 0.8 times of that of the patch-type. This indicates the smaller size of the AMC unit cells can be achieved using ring-type metallization. The reduction of the side dimensions in the case of the ring-type unit cell decreases the capacitance between the two adjacent unit cells. However, due to the shape of the ring, larger inductance compared to that of the patch-type FSS is introduced to the resonance system, which compensates for the size reduction and consequently same resonant frequency is achieved with the smaller size. Reflection coefficient magnitudes and phases versus freare plotted in quency for various incident angles in Figs. 4, 5 and 6 for AMC1, AMC2 and AMC3, respectively. Both TE-TE and TM-TM co-polar reflection coefficients are considered. TE-TM and TM-TE cross-polar reflection coefficients were negligible and thus are not shown. It is observed that the AMC1 and AMC2 are more broadband than AMC3, since their reflection phase curve have smoother slope around the resonant frequency (9.5 GHz). From the reflection coefficient magnitudes curves in Figs. 4 to 6, it is found out that the AMCs introduce some losses around the resonant frequency as well. These losses are more pronounced in TE-TE cases than TM-TM cases. However, the losses are insignificant and the reflection coefficient magnitudes are well above 0.9 and very close to unity. Detailed studies on the effects of different substrate thicknesses and dielectric properties on the reflection coefficient magnitude for TE-TE and TM-TM polarizations can be found in [14]. III. ILSMA CHARACTERISTICS ON LARGE AMCs In [6], it has been shown that the input impedance bandwidth and gain of a microstrip antenna on a mushroom-like high-impedance ground plane can be enhanced up to 21.08% and 10.32 dBi, respectively. Later in [7], it was shown that removing the vexing shorting pins, used in the mushroom-like HIS, can even be beneficial to the performance enhancement

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

Fig. 10. Radiation patterns of ILSMA over (a) PEC, (b) AMC1, (c) AMC2 and (3) AMC3 structures. AMCs’ grounded substrates are assumed to be infinite in the transverse direction.

in some of the antennas, although it appears counter-intuitive at the first glance. Not only was the input impedance bandwidth improved to 28% but the gain also enhanced to as high as 11.0 dBi. The importance of the work lies in the fact that a grounded dielectric slab loaded by conducting FSS-type periodic structures still can introduce AMCs and HISs [7]–[9]. In this work, characteristics of ILSMA on different AMCs are studied. Four ILSMAs over a conventional copper ground plane and three above-mentioned designed AMCs are shown in Fig. 7. Their profile dimensions are shown in Fig. 8. The corresponding and . Each and values in this study are: every AMC is truncated so that its corresponding unit cells are . accommodated in the area with the dimensions of Since the unit cell sizes are different for three different AMCs, their truncation number is different for each case. Accordingly, patch-type (AMC1), ring-type (AMC2), and Jerusalem crosstype (AMC3) consist of 29 29, 31 31 and 12 12 unit cells, respectively. Simulations are very cumbersome in terms of both computational time and required memory using a FEM-CAD (Ansoft HFSS). Therefore, a MoM-CAD planar structure analyzer (Ansoft Designer 4.0) was employed for simulations. A long via-hole shorting pin is connected to a wide strip which

together account for the bend wire of ILSMA. The relation between strip equivalent width and wire radius can be found in [17] as

(1) is the strip width of the equivalent simulated strip where and is the wire radius of the fabricated ILSMA, which is 0.635 mm. Making use of the aforementioned approximation in the MoM-CAD software package, efficiently circumvents the computational complexity involved in the FEM-CAD analysis of these antennas. Also, in the MoM-CAD simulations, the ground plane and dielectric substrate are considered infinite of the ILSMA over different in the transverse directions. ground planes are plotted in Fig. 9(a) and (b), respectively, when the actual materials (copper and Arlon Diclad) and lossless materials are used. Arlon Diclad has relative permittivity of 2.5 and tangent loss of 0.0022. Both results are in excellent agreement. This assures that the effects of lossy materials on bandwidth broadening in this type of designs are completely negligible.

FOROOZESH AND SHAFAI: INVESTIGATION INTO THE APPLICATION OF AMCs TO BANDWIDTH BROADENING

As shown in Fig. 9, simulation results confirm that the input impedance of the ILSMA over the conventional ground plane, either using copper or PEC, is not matched. The minimum in this case is about 4.02 dB around 11.0 GHz. As shown in Fig. 9, using AMC surfaces as the ILSMA ground planes, the input impedance matching is not only achieved around the operating frequency of 9.5 GHz, but its bandwidth is also enhanced considerably. One should note that the frequency of 9.5 GHz is the resonant frequency of the AMCs. Bandwidth ranges of the ILSMA, when it is placed on each and every aforementioned AMC, are tabulated in Table I. Simulation results demonstrate that when AMC1 and AMC2 are used as the ground plane, remarkable input impedance bandwidth of 27.73% and 22.22%, are achieved, respectively. Multiple resonances are observed at frequencies higher than 9.5 GHz when the AMC3 is used as the ground plane. In this work, the input impedance bandwidth is defined as the range of frequencies where the level of the is below 10 dB. Simulated radiation patterns of the aforementioned antennas are plotted in Fig. 10. As mentioned earlier, in the MoM analysis utilized in this work, dielectric substrate and ground plane are infinite in the transverse direction. Therefore, the radiation patterns only exist in the upper half-space. Simulated radiation patterns of the ILSMA are plotted in Fig. 10(a) in which infinite PEC ground plane is considered. A description of the radiation patterns shape can be as follows. The ILSMA has a vertical part at the center and an x-directed component in horizontal part. The vertical part introduces both x-z and y-z planes in the far-field. The x-directed horicomponent in the x-z plane and zontal part produces component in the y-z plane [19]. Therefore, in the y-z plane, component resembles to that of a vertical dipole over an infinite ground plane (dashed-line in Fig. 10(a)). On the other hand, in component is similar to that of an x-directed the y-z plane, dipole over an infinite ground plane (marked x-line in Fig. 10(a)) [19]. In the x-z plane, both horizontal and vertical segments of component. Therefore, is the sum the ILSMA produce component, howof these two contributions in the far-field. ever, is a cross-polar level introduced by the two segments in the x-z plane. This cross-polar level ideally has to be zero. As can be seen, its level is below 60 dBi, which is merely the precision error of the numerical method (MoM-CAD Ansoft Designer). Radiation patterns of an ILSMA over AMC1 and AMC2 are very similar to the case when an infinite PEC ground plane is tends to zero when approaches 90 used, except that the due to the effects of the infinite dielectric in the transverse direction. However, the radiation patterns of an ILSMA over AMC3 are different from the other ones, specifically in the x-z plane. This can be due to the relative large unit cells having more complicated shapes. IV. EFFECTS OF THE AMC SIZE ON ILSMA It is important in many applications for the antennas to be compact and small in size in addition to being low-profile. Therefore, it is worthwhile investigating the effects of the AMC ground plane size reduction on the performance of the low-proof file antennas already designed in the previous section. the ILSMAs versus frequency for various AMC sizes are plotted

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Fig. 11. jS j of the ILSMA over (a) AMC1, (b) AMC2 and (c) AMC3 for different number of the conducting periodic arrays of the AMCs.

in Fig. 11. As shown, of the ILSMA can maintain their broadband performance and stand significant size reductions. of the ILSMA when it is placed over Fig. 11(a) shows the the AMC1 for different numbers of unit cells. As can be seen, the performance of the antenna when the AMC1 consist of 29 29 unit cells down to the case consisting of 15 15 unit cells are consistent to an excellent extent. The same consistency is observed in Fig. 11(b) and (c) when AMC2 and AMC3 are

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

TABLE II LARGEST AND SMALLEST GROUND PLANE SIZES USED IN THIS PAPER

Fig. 12. Measured jS AMC ground planes.

j

versus frequency of the ILSMA over three different

used, respectively. Simulation results in Fig. 11, for various number of unit cells indicate that size reduction to the quarter , considered in size of the largest ground plane this work, does not degrade the broadband characteristics of the antennas. Such observations have been made in the previous of a half-wavelength dipole work as well [7], where the was examined over different PEC and PMC ground planes. It of an antenna is only affected can be concluded that the by the immediate ground plane beneath it and the extension of the ground plane does not have considerable impact on it. Dimensions and sizes of the unit cells and ground planes of the aforementioned calculated cases are summarized in Table II in terms of the wavelength of the antenna operating frequency. V. ILSMA MEASUREMENT RESULTS Four prototypes of the fabricated antenna over different ground planes are shown in Fig. 7. All ground planes, the conventional one and the AMC ones, have dimensions of . The measured of the ILSMAs are plotted in Fig. 12. It is evident that the ILSMA over the conventional is about 2.5 dB at ground plane is not matched, since its 9.5 GHz and well above 5 dB over the entire shown frequency range. This fact experimentally verifies that the low-profile wire antennas placed horizontally in close proximity of a conventional conducting ground plane exhibit poor input impedance matching. On the other hand, ILSMA over all other AMC ground planes are not only well matched but also demonstrate fairly broadband characteristics. A comparative study between MoM-CAD simulation and measurement results is performed in Table I. There is an excellent agreement between simulation and measurement results for the cases of AMC1 and AMC2. In

in both simulation the case of AMC3, the behavior of the and measurement results are identical. However, the multiple measurement results, as resonances occurring in the shown in Fig. 12, remain below 10 dB in a wider frequency range than those of the simulation results, as shown in Fig. 9. The measured radiation patterns of the above-mentioned conventional ILSMA over a finite size copper-made ground plane at three different frequencies are shown in Fig. 13(a), (c) and (e). The results can be compared against MoM-CAD simulations, shown in Fig. 13(b), (d), and (f). As can be observed, there is an excellent agreement between the simulation and measurement results for in x-z and y-z planes and in y-z plane. The level of in x-z plane should theoretically be 0 ( in dB) since neither vertical nor horizontal part of the ILSMA produces electric field component in x-z plane. As can be seen, that level is below 50 dB in simulation results which mainly shows the numerical precision of the MoM-CAD (Ansoft Designer). However, it is about 20 dB in measurement, which may be due to misalignment of ILSMA and cross polarization of the compact antenna test range (CATR) at the Antenna Lab of the University of Manitoba. It is interesting that the peak gain shifts from 90 in the infinite PEC ground plane case (Fig. 10(a)) to about 60 for the actual cases. This effect is due to the finite ground plane size which is well discussed in the literature [20]–[23]. Essentially, all the calculations on the monopole antennas over the finite-size ground planes in [20]–[23], illustrate that for the , finite ground planes whose dimensions are larger than main lobe may shift significantly from 90 and typically occurs in between 30 and 60 . The results shown in Figs. 10(a) and 13, are consistent with the calculations in [20]–[23]. Except for the cross-polar level, an excellent agreement between measurements and simulations is observed which verifies the accuracy of both measurement system and the MoM-CAD. This agreement in the PEC case serves as the reference for the other measured data obtained from the actual antennas to be discussed shortly in this paper. Radiation patterns of the above-mentioned ILSMA over difAMC ground planes are shown ferent finite-size in Fig. 14. Here, too, the peak gains of the radiation patterns occur at large angles, between 70 to 90 , in contrast to the cases with infinite size dielectric substrate and ground plane. As can be observed in Fig. 14, all peak gains are higher than 3 dBi which is considerably higher than those offered by the ILSMA over the PEC ground plane shown in Fig. 13. The main-lobe of the radiation patterns, shown in Fig. 14., are fairly wider than those shown in Fig. 13. This implies the usefulness of the AMC ground planes for enhancing the gain through matching improvement while maintaining the high directivity over a wider

FOROOZESH AND SHAFAI: INVESTIGATION INTO THE APPLICATION OF AMCs TO BANDWIDTH BROADENING

Fig. 13. (a), (c) and (e) are measured and (b), (d) and (f) are simulated radiation patterns of the ILSMA on 15 of 8.6, 9.0 and 9.4 GHz, respectively.

range of angles. These are two important radiation pattern qualities for terrestrial and vehicular applications, where the antenna . peak gains are desirable to be near the horizon, i.e., As mentioned earlier, reduced size antennas are needed in many practical applications. Therefore, it is worthwhile investigating the experimental performance of the aforementioned

2 15 cm

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Copper-made ground plane at frequencies

ILSMA over smaller AMC ground planes. Smaller AMC1 and AMC2 which are considered here, consist of 15 15 and 16 16 unit cells, respectively. This means that the size of the former is and that of the latter is . of the antennas are plotted in Fig. 15. As can Measured be observed, the ILSMAs on reduced-size AMC1 and AMC2

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Fig. 15. jS j of the corresponding ILSMAs over different reduced-size AMCs. Size of the AMC1 and AMC2 are 7:35 7:35 cm and 6:4 6:4 cm , respectively.

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Fig. 14. Typical measured radiation patterns of ILSMA on (a) AMC1, (b) AMC2 and (c) AMC3 as shown in Fig. 7(b), (c) and (d), respectively.

are well matched over a wide frequency band. Their input impedance bandwidths are about 32% and 33%, respectively. One might notice that these values are slightly higher than the simulation results reported in Table I. This is due to that fact that in the simulations the effects of the finite size dielectric and ground plane have not been considered since a 2.5D

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MoM-CAD simulator (Ansoft Designer) was used. Therefore, edge effects are ignored. This has more impact on the discrepancies between simulation and measurement results for small AMCs rather than larger AMCs as previously discussed and summarized in Table I. Measured far-field radiation patterns are plotted in Fig. 16. Radiation patterns of the ILSMA over the reduced-size AMC1, at frequencies 8.9, 9.2 and 9.5 GHz, are shown in Fig. 16(a), (c) and (e), respectively. Radiation patterns of the ILSMA over the reduced-size AMC2, at frequencies 8.9, 9.2 and 9.5 GHz, are shown in Fig. 16(b), (d) and (f), respectively. Interestingly, the ILSMA over AMC2 (ring metallization) suppress all the radiated far fields by more than 8 dB in the range to 30 of . Moreover, the level of the gain is almost of constant over 60 to 90 which makes it attractive for many practical applications. For the case of ILSMA over AMC1, directivity peak shifts from around 70 to 45 , when the AMC1 to . For the size is reduced from case of ILSMA over AMC2, directivity peak shifts from around 80 to 60 , when the AMC2 size is reduced from to . This shows that the main-lobe tends to move to lower angles as the ground plane reduces. This is consistent with the observation made for the cases of monopoles using conventional PEC ground planes. Despite the fact that all AMCs were shown to be useful in improving the antenna performances, behavior of the antennas cannot be accurately predicted based on merely the reflection properties of the AMCs. For example, AMC1 and AMC2 possess very similar reflection properties both in the frequency and incident angle ranges (Fig. 3). However, the far-field radiation patterns of the ILSMA above AMC1 are considerably different from those when ILSMA is placed above AMC2. A comparison between Fig. 14(a) and (b) and different plots shown in Fig. 16 elucidate this assertion. This indicates that the effects of the AMCs on the antennas above them is very complicated and beyond the image theory concept. In addition, one should note that the reflection properties of the AMCs are typically obtained based on the modal plane wave illuminations, in the absence of

FOROOZESH AND SHAFAI: INVESTIGATION INTO THE APPLICATION OF AMCs TO BANDWIDTH BROADENING

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Fig. 16. Measured radiation patterns of the ILSMA over the reduced-size AMC1 and AMC2 at 8.9 GHz, are shown in (a) and (b), respectively, at 9.2 GHz are shown in (c) and (d), respectively, and at 9.5 GHz, are shown in (e) and (f), respectively.

the excitation source above them. However, since the size of the existing AMC unit cells are comparable to the excitation source and wavelength of the operating frequency, the strong coupling between the source antenna and adjacent unit cells are inevitable. Therefore, determining the reflection properties of

the AMCs cannot successfully predict its performance prior to the full-wave analysis of the actual structures. Thus, viewing the AMC as an integrated surface, at least at their present forms when the unit cells are not negligibly small in wavelength, is not valid.

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Fig. 17. Fabricated VMAs over reduced-size AMC1 and AMC2 are shown on the right and left, respectively.

Fig. 18. Side view of a VMA over AMC ground plane.

Fig. 20. Ansoft HFSS simulation results of the input port reflection coefficients of the VMA over reduced size ground planes, (a) AMC1 and (b) AMC2. Dimensions are shown in Fig. 8.

Fig. 19. Measured and simulated results of the input port reflection coefficients of the VMA over different ground planes. Sizes of the AMC1 and AMC2 are 7:35 7:35 cm and 6:4 6:4 cm , respectively.

2

2

VI. VMA CHARACTERISTICS Vertical monopole antennas (VMAs) have long been known among the antenna practitioners. The theory of their functionality over conventional PEC ground planes are well explained in the classical text books such as [19]. However, their characteristics over PMC ground planes have not extensively been investigated in the literature. This is understandable, since there is no PMC available in nature, which may have made the investigation less tempting. However, since the invention of AMCs,

not adequate research has been reported on the behavior of vertically-flowing-current antennas over AMC ground planes. Vertical monopole antennas (VMA) over two different AMC ground planes are considered here and their characteristics are explored. The fabricated antennas are displayed in Fig. 17. The of a VMA, side view of the antennas is depicted in Fig. 18. whose length is 8 mm and its cross section radius is 0.635 mm, are shown in Fig. 19 when it is placed over AMC1, AMC2 and PEC ground planes. Both simulation and measurement results are displayed. In this part, simulations have been carried out using a FEM-CAD (Ansoft HFSS). The VMA over smaller size AMC1 (15 15 unit cells) and AMC2 (16 16 unit cells) exhibit 35.84% and 33.84% input impedance bandwidth, respectively. Their bandwidths are even wider than the same VMA over PEC surface as clearly noticeable from Fig. 19. The resonant frequency of the antenna can be adjusted by changing the VMA length. A parametric study on the VMA lengths is shown in Fig. 20. As expected, reducing the VMA length shifts the resonant frequency to higher values, as illustrated in Fig. 20. In some cases, for example when the VMA length is 6.25 mm and AMC1 is the ground plane, the bandwidth can also be increased

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Fig. 21. (a), (c) and (e) are simulated and (b), (d) and (f) are measured radiation patterns of a VMA over reduced-size patch-type AMC (AMC1). Corresponding frequencies for (a) and (b), (c) and (d), and (e) and (f) are 6.75 GHz, 8.6 GHz, and 9.5 GHz, respectively.

considerably. That the AMC surfaces can be useful in bandwidth enchantment and input impedance matching for both vertically and horizontally placed antennas has not been reported of an before in the literature. Both radiation patterns and ILSMA and a microstrip patch antenna over high impedance ground planes have been investigated in [1]. Radiation patterns

of a VMA over high impedance EBG surface have also been disof the VMA has not been cussed in [1]. Surprisingly, the reported in [1]. Impedance matching and broadening of a VMA over an AMC, presented in this paper, is counter-intuitive. However, this phenomenon indicates that the AMCs, at least at their present forms, cannot simulate PMC effectively. They should be

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Fig. 22. (a), (c) and (e) are simulated and (b), (d) and (f) are measured radiation patterns of a VMA over reduced-size ring-type AMC (AMC2). Corresponding frequencies for (a) and (b), (c) and (d), and (e) and (f) are 7.1 GHz, 9.5 GHz, and 10.2 GHz, respectively.

viewed only as a matching structure, since they apparently can match both vertically- and horizontally-placed antennas above them. Miniaturization, i.e., significant size reduction in wavelength, of the AMC unit cells may enable them to better mimic PMC properties.

Radiation patterns of the VMAs on AMC1 and AMC2 are plotted in Figs. 21 and 22, respectively. In both Figs. 21 and 22, simulated radiation patterns are drawn in parts (a), (c) and (e) while the measured radiation patterns are plotted in parts (b), (d) and (f). According to Fig. 19, for the VMA over AMC1

FOROOZESH AND SHAFAI: INVESTIGATION INTO THE APPLICATION OF AMCs TO BANDWIDTH BROADENING

(patch-type), lower, middle and upper frequencies of the input impedance bandwidth are 6.75 GHz, 8.6 GHz, 9.5 GHz, respectively. In Fig. 21, radiation patterns plotted in parts (a) and (b), (c) and (d), and (e) and (f) correspond to frequencies 6.75, 8.6 and 9.5 GHz, respectively. In the same manner, for the VMA over AMC2 (ring-type), lower, middle and upper frequencies of the input impedance bandwidth are 7.1 GHz, 9.5 GHz and 10.2 GHz, respectively. In Fig. 22, radiation patterns plotted in parts (a) and (b), (c) and (d), and (e) and (f) correspond to frequencies 7.1, 9.5 and 10.2 GHz, respectively.

VII. APPLICATIONS As discussed in [12], in vehicle-to-vehicle (V2V) communications, low-profile antennas are required that look at the horizon, by having peak gains near the horizon. It was shown in the previous section that ILSMA over AMC, is low profile and provides wide bandwidths as well as appropriate radiation patterns for this purpose. Furthermore, these antennas can be designed in very compact sizes without any compromise in their performance. Therefore, ILSMA over small AMCs investigated earlier in this paper are good candidate for V2V communications system. Identical applications to the mobile station antennas have been proposed in [24], as well. It is specifically indicated in [24, Appendix 2] that the L-shape antennas are low-profile and offer both vertical and horizontal polarizations and their only shortcoming is their narrowband behavior. In this paper, a remedy of this shortcoming was proposed and elucidated in details both theoretically and experimentally. In addition to wireless communications, there are important and interesting satellite-to-vehicular communication programs, such as the digital audio broadcast, that require very broad coverage zones. In North America, the entire populated zones fall to 90 ). The within the elevation angles of zero to 65 ( radiation patterns of the monopole and ILSMA antennas over an AMC ground exhibit nearly constant gain over this range. Thus, they can find useful applications in satellite-to-ground communications.

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reveals that reflection phase property of an AMC is not a sufficient gauge to evaluate its performance. This fact had previously not been illustrated thoroughly in the literature. Next, the effects of the size reduction on two of the aforementioned AMCs were investigated theoretically and experimentally. It was revealed that ILSMA over AMCs can stand significant size reduction without any compromise in their input impedance bandwidth. However, their radiation patterns shape may be affected but not detrimentally. This feature is very appealing in many practical applications. Another important fact that was revealed in this paper was the usefulness of the AMC surfaces in bandwidth enhancement of the vertically-flowing-current antennas such as VMAs. In spite of PMCs that are useless and even destructive in input impedance matching of the VMAs, AMCs are beneficial through providing large input impedance bandwidth. Bandwidth as large as 35.84% was obtained both in simulations and experiments. This implies that the underlying phenomenon of using AMC ground plane is beyond the image theory and cannot sufficiently addressed without full-wave analysis of the actual antenna structure in the presence of the AMC ground plane. To the best of our knowledge, this problem has previously been neither tackled nor addressed in any literature. Moreover, it was demonstrated that both ILSMA and VMA over AMCs exhibit unique radiation patterns properties over a broadband range of frequencies that make them appealing for many applications. Some of these applications were mentioned throughout the paper. As a future work, it would be interesting to investigate the near-field characterization of the AMCs. As well, in general, miniaturization of AMC unit cells may be helpful in approximating AMC as integrated surface. ACKNOWLEDGMENT The authors would like to thank Dr. T. Tanaka for providing them with [12]. They also wish to thank C. Smit for fabrication of the AMCs and B. Tabachnick, the technologist of the Antenna Laboratory at the University of Manitoba for the antenna radiation pattern measurements.

VIII. CONCLUSION Several different AMCs were investigated in terms of their reflection phase characteristics versus frequency. Three of them selected, representing their corresponding classes. They were fine tuned so that exhibited the same resonant frequency. Then, an inverted L-shape monopole antenna (ILSMA) was placed above them as well as a conventional copper ground plane. It was illustrated that the ILSMA cannot be matched when it is closely placed above a conventional copper ground plane. Using the introduced artificial magnetic ground planes, it was demonstrated that, not only the input impedance matching was possible, but also the frequency bandwidths turned out to be significantly broadened. Bandwidth enhancement up to 27% in the simulations and experiments were observed. However, it was shown although two of the AMCs had similar reflection behavior versus both frequency and angle, they showed different input impedance and particularly radiation characteristics. This

REFERENCES [1] D. Sievenpiper, L. Zhang, R. F. J. Broas, N. G. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech., vol. 47, pp. 2059–2074, Nov. 1999. [2] F. Yang and Y. Rahmat-Samii, “Reflection phase characteristics of the EBG ground plane for low profile wire antennas,” IEEE Trans. Antennas Propag., vol. 51, pt. 1, pp. 2691–2703, Oct. 2003. [3] H. Nakano, K. Hitosugi, N. Tatsuzawa, D. Togashi, H. Mimaki, and J. Yamauchi, “Effects on the radiation characteristics of using a corrugated reflector with a helical antenna and an electromagnetic band-gap reflector with a spiral antenna,” IEEE Trans. Antennas Propag., vol. 53, pt. 1, pp. 191–199, Jan. 2005. [4] H. Nakano, K. Kikkawa, N. Kondo, Y. Iitsuka, and J. Yamauchi, “LowProfile equiangular spiral antenna backed by an EBG reflector,” IEEE Trans. Antennas Propag., vol. 57, pp. 1309–1318, Jan. 2009. [5] H. Nakano, Y. Asano, G. Tsutsumi, and J. Yamauchi, “A low-profile inverted F element array backed by an EBG reflector,” in Proc. IEEE Int. Symp. on Antennas and Propag., NM, Jul. 9–14, 2006, pp. 2985–2988.B.

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[6] D. Qu, L. Shafai, and A. Foroozesh, “Improving microstrip patch antenna performance using EBG substrates,” Inst. Elect. Eng. Proc.-Microw. Antennas. Propag., vol. 153, no. 6, pp. 558–563, Dec. 2006. [7] A. Foroozesh and L. Shafai, “Application of combined electric- and magnetic-conductor ground planes for antenna performance enhancement,” Can J. Elect. Comput. Eng., vol. 33, no. 2, pp. 87–98, Spring, 2008. [8] A. Foroozesh and L. Shafai, “Performance enhancement of a microstrip patch antenna using high impedance surfaces and different ground plane sizes,” in Proc. Int. Symp. of Antennas and Propagation, ISAP2007, Niigata, Japan, pp. 1158–1161. [9] L. Akhoondzadeh-Asl, D. J. Kern, P. S. Hall, and D. H. Werner, “Wideband dipoles on electromagnetic bandgap ground planes,” IEEE Trans. Antennas Propag., vol. 55, pp. 2426–2434, Sep. 2007. [10] S. R. Best and D. L. Hanna, “Design of a broadband dipole in close proximity to an EBG ground plane,” IEEE Antennas Propag. Mag., vol. 50, no. 6, pp. 52–64, Dec. 2008. [11] H. Xin, K. Matsugatani, M. Kim, J. Hacker, J. A. Higgins, M. Rosker, and M. Tanaka, “Mutual coupling reduction of low-profile monopole antennas on high-impedance ground plane,” Electron. Lett., vol. 38, no. 16, pp. 849–850, Aug. 2002. [12] K. Matsugatani, K. Sakakibara, N. Kikuma, and H. Hirayama, “Broadband planar antenna combining monopole element and electromagnetic bandgap,” IEICE Trans. Electron., vol. E91-C, no. 11, pp. 1778–1785, Nov. 2008. [13] M. A. Hiranandani, A. B. Yakovlev, and A. A. Kishk, “Artificial magnetic conductors realized by frequency-selective surfaces on a grounded dielectric slab for antenna applications,” IEE Proc.-Microw. Antennas. Propag., vol. 153, no. 5, pp. 487–493, Oct. 2006. [14] A. Foroozesh, “Analysis and design of the periodic structure based lowprofile planar high-gain antennas,” Ph.D. dissertation, Univ. Manitoba, Canada, 2007. [15] S.-S. Oh and L. Shafai, “Artificial magnetic conductor using split ring resonators and its applications to antennas,” Microw. Opt. Technol. Lett., vol. 48, pp. 329–334, Feb. 2006. [16] D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, “The deign synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces,” IEEE Trans. Antennas Propag., vol. 53, pp. 8–16, Jan. 2005. [17] G. Goussetis, A. P. Feresidis, and J. C. Vardaxoglou, “Tailoring AMC and EBG characteristics of periodic metallic arrays printed on grounded dielectric substrate,” IEEE Trans. Antennas Propag., vol. 54, pp. 82–89, Jan. 2006. [18] R. Coccioli, F.-R. Yang, K.-P. Ma, and T. Itoh, “Aperture-coupled patch antenna on UC-PBG substrate,” IEEE Trans. Microw. Theory Tech., vol. 47, pp. 2123–2130, Nov. 1999. [19] C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. New York: Wiley, 1997. [20] J. D. Kraus, Antennas. New York: McGraw-Hill, 1950. [21] C. A. Balanis, Advanced Engineering Electromagnetics. New York: Wiley, 1989. [22] W. L. Stutzman and G. E. Thiele, Antenna Theory and Design, 2nd ed. New York: Wiley, 1998. [23] S. N. Makarov, Antenna and EM modeling With MATLAB. New York: Wiley, 2002. [24] Mobile Antenna Systems Handbook, K. Fujimoto and J. R. James, Eds., 2nd ed. Norwood, MA: Artech House, 2001. Alireza Foroozesh (M’08) received the B.Sc. degree from Tehran Polytechnic, Tehran, Iran, in 1996, the M.Sc. from the Iran University of Science and Tech-

nology, Tehran, in 1999, and the Ph.D. degree from the University of Manitoba, Winnipeg, Manitoba, Canada, in 2007, all in electrical engineering. From May 2000 to July 2002, he was a Researcher with the Antenna Laboratory, Iran Telecommunication Research Center (ITRC), where he was involved in projects related to antenna design and measurement. He is currently a Postdoctoral Fellow with the Department of Electrical and Computer Engineering, University of Manitoba. His main research interest is the analysis and modeling of periodic structures and their applications to antennas and microwave systems. Dr. Foroozesh was the recipient of the Best Student Paper Award at the International Symposium on Antennas and Propagation (ISAP 2007) in Niigata, Japan. He received a Young Scientist Travel Grant at ISAP 2007, Niigata, Japan, and a Young Scientist Award at the Electromagnetic Theory Symposium (EMTS 2007), Ottawa, Canada.

Lotfollah Shafai (LF’07) received the B.Sc. degree from the University of Tehran, Tehran, Iran, in 1963 and the M.Sc. and Ph.D. degrees from the University of Toronto, Toronto, ON, Canada, in 1966 and 1969, all in electrical engineering. In November 1969, he joined the Department of Electrical and Computer Engineering, University of Manitoba as a Sessional Lecturer, becoming an Assistant Professor in 1970, Associate Professor in 1973, and Professor in 1979. Since 1975, he has made special efforts to link the University research to the industrial development, by assisting industries in the development of new products or establishing new technologies. To enhance the University of Manitoba contact with industry, in 1985 he assisted in establishing The Institute for Technology Development and was its Director until 1987, when he became the Head of the Electrical Engineering Department. His assistance to industry was instrumental in establishing an Industrial Research Chair in Applied Electromagnetics at the University of Manitoba in 1989, which he held until July 1994. Dr. Shafai has been a participant in nearly all Antennas and Propagation Symposia and participates on the Review Committees. He is a member of URSI Commission B and was its Chairman during 1985-88. In 1986, he established the Symposium on Antenna Technology and Applied Electromagnetics, ANTEM, at the University of Manitoba that is currently held every two years. He has been the recipient of numerous awards. In 1978, his contribution to the design of a small ground station for the Hermus satellite was selected as the 3rd Meritorious Industrial Design. In 1984, he received the Professional Engineers Merit Award and in 1985, “The Thinker” Award from Canadian Patents and Development Corporation. From the University of Manitoba, he received the “Research Awards” in 1983, 1987, and 1989, the Outreach Award in 1987 and the Sigma Xi, Senior Scientist Award in 1989. In 1990, he received the Maxwell Premium Award from the Institution of Engineering and Technology (London) and in 1993 and 1994, the Distinguished Achievement Awards from Corporate Higher Education Forum. In 1998, he received the Winnipeg RH Institute Foundation Medal for Excellence in Research. In 1999 and 2000, he received the University of Manitoba, Faculty Association Research Award. He is an elected Fellow of the IEEE since 1987 and was elected Life Fellow in 2007. He is a Fellow of The Royal Society of Canada in 1998. He was a recipient of the IEEE Third Millennium Medal in 2000 and in 2002 was elected a Fellow of The Canadian Academy of Engineering and Distinguished Professor at The University of Manitoba. He holds a Canada Research Chair in Applied Electromagnetics and is International Chair of URSI Commission B.

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The Effect of Insulating Layers on the Performance of Implanted Antennas Francesco Merli, Student Member, IEEE, Benjamin Fuchs, Member, IEEE, Juan R. Mosig, Fellow, IEEE, and Anja K. Skrivervik

Abstract—This work presents the analysis of the influence of insulation on implanted antennas for biotelemetry applications in the Medical Device Radiocommunications Service band. Our goal is finding the insulation properties that facilitate power transmission, thus enhancing the communication between the implanted antenna and an external receiver. For this purpose, it has been found that a simplified model of human tissues based on spherical geometries excited by ideal sources (electric dipole, magnetic dipole and Huygens source) provides reasonable accuracy while remaining very tractable due to its analytical formulation. Our results show that a proper choice of the biocompatible internal insulation material can improve the radiation efficiency of the implanted antenna (up to six times for the investigated cases). External insulation facilitates the electromagnetic transition from the biological tissue to the outer free space, reducing the power absorbed by the human body. Summarizing, this work gives insights on the enhancement of power transmission, obtained with the use of both internal, biocompatible and external, flexible insulations. Therefore, it provides useful information for the design of implanted antennas. Index Terms—Biocompatible antenna, implanted antennas, insulation, Medical Device Radiocommunications Service (MedRadio), spherical wave expansion.

I. INTRODUCTION OWADAYS there is a growing interest in devices for implantable biotelemetry applications in the Medical Device Radiocommunications Service (MedRadio, 401–406 MHz) [1]. In order to improve the comfort of the patient, the whole system, including the antenna, must be as small as possible. This, along with the choice of the MedRadio band, (formerly Medical Implantable Communication Services band) implies the use of an electrically small antenna [2]–[8]. Such antennas are very sensitive to their surrounding environment. The properties of implanted antennas (resonance frequency, bandwidth, efficiency, etc.) are indeed strongly affected by the presence of the human body. So as to predict these modifications, many ’body phantoms’ have been developed and are

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Manuscript received November 05, 2009; revised July 21, 2010; accepted October 13, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported in part by COST IC0603 Antenna Systems & Sensors for Information Technologies Society (ASSIST). F. Merli, J. R. Mosig, and A. K. Skrivervik are with the Laboratoire d’Electromagnétisme et d’Acoustique (LEMA), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland (e-mail: francesco.merli@epfl. ch). B. Fuchs is with the Institute of Electronics and Telecommunications of Rennes, UMR CNRS 6164, University of Rennes I, Rennes Cedex 35042, France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090465

available in [9] (and references therein) and [10]–[13]. These models describe the human body with different accuracy (in terms of geometry, number of tissues and voxel precision). Particular attention is paid to the fact that the human body is constituted of highly lossy materials for RF propagation, for instance at 403.5 MHz for muscle tissue [14]. Communication between the implanted antenna and the external base station is significantly affected. Hence, it is necessary to evaluate the power absorbed by the human tissues, both to predict the power link budget and to fulfill safety compliance [15]. Antennas immersed in lossy media have been deeply investigated for submarine and subsurface systems (for instance in [16]). Then, spherical multilayered models have been considered for various applications, including biomedical ones. It turns out that, although being a rough approximation of the human body, such multishell models are very useful [2], [17]–[21]. In this paper, the spherical model is first enriched with the presence of a realistic biocompatible insulation in proximity of the excitation as shown in Fig. 1. This material plays an important role for the mechanical, biological and electromagnetic properties of any implanted device. For instance, the biocompatible insulation is necessary to prevent metallic oxidation and to avoid any short-circuit effect due to the high conductivity of some human body tissues. In particular, the biocompatible insulation affects the electromagnetic radiation in different physical ways: it smooths the transition of the radiating wave between the source and the body model (this facilitates the radiation and increases the efficiency); it also reduces the coupling (i.e., dissipation) of the high near field terms of the electromagnetic radiation in the surrounding living tissue. The latter plays a principal role in the radiation efficiency of the implanted antenna. This work focuses on the power transmission enhancement that can be obtained with an internal insulation from an implanted source, as introduced in [3]–[6], [16], [22]. In particular, results regarding the effect of insulation layers on real sources are reported in [3]–[5]. Three distinct superstrates, that do no completely surround the source and have different thicknesses and (varying within 3 and 9), are considered in [3], while [4] presents only thickness variation and [5] emphasizes the impact of coating thickness over time. As clearly pointed out in these works, varying the insulation properties strongly modifies the radiation characteristics and hence the input impedances, matching and efficiencies. Radiation efficiencies at different resonant frequencies and/or matching levels are compared in [3]–[5]. Theoretical results on the broad band matching properties achievable by insulated implanted antennas are presented in [6], supported by a practical realization. Finally, a prominent study has been reported in [16], where the theoretical and numerical analysis

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TABLE I GEOMETRICAL AND ELECTRICAL DESCRIPTION OF THE ANALYZED BODY MODELS

Fig. 1. Three-dimensional view of the analyzed structure with the notations and the spherical coordinate system. The excitation is placed at the center of several concentric spherical dielectric shells in the air. The spherical shells enable one to model the air, the biocompatible insulation, the body layers as well the external insulation.

discusses the effect of insulation on electromagnetic field and current distributions. Although this work is performed with a different modeling frame, our findings mostly match the conclusions of the aforementioned, as evidenced in Sections II–VI. In this paper, the results shown in [22] are extended in order to give quantitative and qualitative insights on the effect of biocompatible materials in implanted antennas for telemetry applications. Both internal and external insulations are considered providing useful guidelines for the design of implanted antenna. Note that although the results are presented in MedRadio band, the numerical analysis can be straightforwardly extended to any other working frequency. This paper is organized as follows: Section II describes the properties (geometrical and electrical) of the investigated models as well as the analytical method, based on the spherical wave expansion, used to solve the electromagnetic problem. The numerical implementation of the code is discussed in Section III and validated by comparisons with a commercial software [23]. Section IV presents the obtained numerical results. In Section V, the model takes into account the presence of an external insulation layer, as depicted in Fig. 1. As the body model is a bounded lossy medium, the electromagnetic propagation between the body layer and the outside free space is investigated considering the presence of flexible insulations. Finally, conclusions are drawn in Section VI. II. MODELING AND ANALYSIS A. Human Body Model and Biocompatible Insulation Layer A multilayered spherical model provides worthwhile results despite the rough approximation of the human body, as previously discussed in [2], [17]–[20]. It represents indeed a good average of more complex models. For instance, radiation efficiencies, specific absorption rate (SAR) and power profiles have been presented in [2], [18], [20] and [17], [21]. Obviously, depending on the source modeling, unrealistically high values of the absolute electric field (therefore SAR) can be obtained

[24]. Nevertheless, even for SAR investigation, relative differences and tendencies are still correctly predicted, and this is very useful for the comprehension of the effects of biocompatible insulations. Hence this work, that mainly focuses on the effect of biocompatible insulation on radiation efficiency, considers and analyzes spherical body phantoms. The model, represented in Fig. 1, is composed of several concentric spherical shells whose dielectric properties are similar to those of real human tissues (values taken from [14]). Three body models, two homogeneous and one multilayered, are investigated. Table I reports the geometrical (shell radii) and physical description (dielectric properties) of the different body phantoms. The radii of the equivalent human tissues are set being inspired by [2]. The selected models are representative of the overall obtained results. The insulation layer is modeled as a homogeneous spherical shell whose dielectric properties are the same as real biocompatible materials. Since a discussion on biomaterials is out of the scope of this work, standard biocompatible insulations have been taken from [25] and [26]. For our application, that requires electromagnetic power transmission, high conductivity materials (such as gold or silver) are not appropriate. Thus, three polymers (polypropylene, peek and polyamide) and two ceramics (alumina and zirconia) have been selected as representative of the acceptable possibilities. Note that for physical reasons, detailed in Section II-D, excitation is first insulated by an air shell, in turn surrounded by biocompatible material, as shown in Fig. 1. B. Electromagnetic Analysis Method This Section sets the mathematical notations and describes how to compute the electromagnetic field. The following standard development, although well known from classical works [27] is summarized here for the sake of completeness and for a better understanding of Sections III–VI. In order to match the geometry of the analyzed structure shown in Fig. 1, the spherical coordinate system is used. Time is omitted for clarity. The electroharmonic dependence magnetic field is expanded on the spherical modal basis as follows:

where

(1)

MERLI et al.: THE EFFECT OF INSULATING LAYERS ON THE PERFORMANCE OF IMPLANTED ANTENNAS

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where and are the spherical modal coefficients and is the intrinsic medium impedance. and are the mode indexes, and is its complement in the set. The spherical wave vectors are

sent in general complex conjugate, save for which means the complement in the set . , are The net body loss, , and the net insulation loss, defined as follows:

(2)

(5)

where is the intrinsic wave number. and are the spherical Bessel function of the first kind and Hankel function of the second kind, respectively. As for the azimuthal dependency, stands for the associated Legendre polynomial of degree and order and . A mode matching technique (MMT) based on spherical wave functions is used to compute the interaction between concentric spherical homogeneous layers and the selected source [28]. This method is well suited to analyze our problem since, a priori, there are no limitations regarding the dimensions and electromagnetic properties (permittivity, permeability and losses) of the layers. The MMT gives direct access to the field everywhere in a source free region, with controlled accuracy, as shown in Section III-A.

where , and are the radii of the external body, the biocompatible insulation and the air shell, respectively. Conse, due to the presence of quently the total power attenuation, the equivalent body model and the realistic internal insulation, . is equal to The definition of the net body loss, , is different from the is divided by the radiated one used in [10], [13] where power in free space. Our definition is not influenced by the dielectric loading of the surrounding tissue. Moreover, the power , is always normalized to 0 dBm. radiated by the source,

C. Power Computation In presence of a lossy dielectric material of relative complex , such as the human body, the availpermittivity is equal to able source power

(3) where is the radiated power. represents the absorbed power related to both the near field ( , components) and far field ( component). In fact, in a free space environment, the near-field is mainly reactive while, in our case, it strongly dissipates in the surrounding materials (insulation and body) increasing the loss of power [4], [16]. By substituting (1) and (2) into (3) and using the orthogonality properties of spherical modal vectors, given in Appendix A, one gets, after some manipulations, the analytical expression of the radiated power at any distance

D. Excitation Ideal excitations are considered in this work. It is possible to model more realistic sources, as done in [2]. However, this leads to a significant increase of computation load which is not the goal of our work since we aim at providing some insights on the insulation layer influence. The ideal source is placed at the origin of the concentric multishell body model in order to be surrounded by an insulation layer. Infinitesimal electric and magnetic dipoles are used. A Huygens source is also modeled. It consists of crossed electric and magnetic dipoles and it has the properties of radiating only in the forward direction [29]. It can therefore be considered as representative of some relatively directive antennas, with a preferred off-body direction of radiation. As pointed out in [24], a Hertzian dipole radiating in an unbounded lossy medium must be supplied with infinite power, which is not physically meaningful. To overcome this problem, Tai suggested to insulate the dipole with a lossless sphere. This problem remains if the dipole is placed at the center of a bounded lossy layer (in this case spherical), as shown in Appendix B. Therefore it can be said that our acting source is a mathematical dipole source, surrounded and insulated by an air shell (Fig. 1). III. NUMERICAL VALIDATION OF THE METHOD A. Truncation Order

(4)

in the above formulas and are the impedance and the wave number in the medium, respectively. Overlined symbols repre-

requires a truncation order when numeriThe series cally implemented. Many studies have discussed the choice of in relation to the antenna size and with the focus on the far field accuracy (for instance [29], [30] and references therein). A convergence criterion, inspired by [30], is implemented to , at a evaluate the relative amount of the truncated power given distance including the near field ranges

(6)

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Fig. 2. Description of the investigated electromagnetic problem for the numerical comparison with FEKO: (a) geometry and (b) environment properties ( is the free space wavelength at 403.5 MHz). The Hertzian dipole, ^ = =3 and ^ = =4 oriented, is placed at x = 1, y = 1, z = 1 [mm].

In the above formula equals to in (4) replacing by . The truncation order is first set to be equal , where is the free space wave number and the to is then autoradius of the biggest shell, as depicted in Fig. 1. matically increased until the neglected power is below

(7) where is the subset of the radial distances under observation. B. Comparison With a Commercial Software Let us consider the electromagnetic problem described in Fig. 2, where a Hertzian electric dipole is surrounded by two spherical shells. For the sake of comparison, small spherical shells radii are used. The electric field is computed at 403.5 MHz and compared with the commercial code FEKO [23]. The MMT code and FEKO results are very close, as shown in Fig. 3. Logically, [Fig. 3(a)] than when the agreement is better when [Fig. 3(b)]. Slight discrepancies exist at the dielectric interfaces due to the mandatory FEKO’s meshing of the spherical surfaces. In fact, for the computation of near field results, the commercial software applies the method of moments (MoM) in combination with the Surface Equivalence Principle (SEP). The latter calls for the meshing (with triangular basis function) of the surface of the spherical shells. is plotted on The relative amount of truncated power Fig. 4 for different values of . As expected, the number of modes is critical when getting closer to the source. To reach , is thus required in shell number 1, whereas only 5 modes are sufficient from (free space). For the far field description, is enough. This

Fig. 3. Comparison of the x ^ component of the electric field over R (Fig. 2), between the MMT (solid line) code and FEKO (dotted line). Amplitude and phase are computed considering (a) N = 21 and (b) N = 11 which satisfy (7) for  equal to 140 and 70 dB, respectively. Vertical black lines indicate the shell boundaries.

0

0

is consistent with the classical recommendation as depicted in Fig. 5.

,

IV. BIOCOMPATIBLE INSULATION: NUMERICAL RESULTS AND DISCUSSION In this Section, we evaluate the effect of the internal biocompatible insulation. Three body models, described in Section II-A, are first analyzed in the presence of the electrical source. For the magnetic and the Huygens source, only the most relevant case is considered for the sake of clarity. The following characteristics are kept constant in the numerical analysis: — working frequency of 403.5 MHz; — the presence of 1 mm thick air insulation surrounding the excitation; — the results are computed with a neglected power lower than . This gives exact results over as the source is placed at the origin. the desired Five different biocompatible materials, described in Table II, are investigated. Their thicknesses range from 1 to 4 mm. The com, and , puted net body, insulation and total losses (i.e., respectively) are reported in Tables III–V when the implanted antenna is insulated by the five biocompatible insulators. For a better understanding of the influence of the biocompatible materials, Tables III–V report even the no-insulation (“none”) case.

MERLI et al.: THE EFFECT OF INSULATING LAYERS ON THE PERFORMANCE OF IMPLANTED ANTENNAS

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TABLE II BIOCOMPATIBLE INTERNAL INSULATIONS

Fig. 4. Computation of the relative amount of truncated power,  (r ), over R considering different values of N at 403.5 MHz for the problem described in Fig. 2.

Fig. 5. Comparison between the MMT code and FEKO of the electric far field at 403.5 MHz considering N = 1 in the yz -plane for the problem described in Fig. 2.

This happens when the model has no biocompatible insulation layer, and it includes only the lossless air shell and the body equivalent spherical layers. Finally, it must be pointed out that (with the same working frequency, dielectric properties and loss definitions) our results are in the same order of magnitude than those presented in [10]–[13] (where more complex body models are considered). A. Electrical Excitation 1) Model 1: IEEE Head Model: The use of the insulation layer strongly reduces the power dissipated in the body. Let us compare, in Table III, the value of the none case (56.4 dB) with the results obtained by varying all the other insulators’ thicknesses (i.e., 47.4, 42.2, 38.6 and 35.8 dB). A minimum improvement of 9 dB, and up to more than 20 dB, is found. Thus, the insulator is very useful to reduce the power absorbed by the body [3]. Consequently, the presence of the insulator reduces the total . With no insulation attenuated power

Fig. 6. Computation of P as a function of the radial distance at 403.5 MHz for the IEEE homogeneous head model considering different (a) polypropylene and (b) zirconia insulation thicknesses.

whereas for all insulation materials and thicknesses, is lower than 50.3 dB. In particular the use of zirconia (4 mm thick) gives the best result with a 19 dB improvement (i.e., ) while peek (1 mm thick) provides only a 6 dB increase (i.e., ). This implies a remarkably larger efficiency (up to six times) for the implanted source. Logically, and in agreement with [3], [4], [16], [33], inand . creasing the thickness of the insulation reduces

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TABLE III POWER LOSS [DB] FOR DIFFERENT INTERNAL INSULATIONS WITH AN ELECTRIC DIPOLE IN MODEL 1 (IEEE HEAD MODEL)

TABLE IV POWER LOSS [DB] FOR DIFFERENT INTERNAL INSULATIONS WITH AN ELECTRIC DIPOLE IN MODEL 2 (MUSCLE)

This behavior appears in Fig. 6, where the computed radiated power is higher when the insulation thickness increases. For with a 4 mm thick instance, in the case of zirconia, and insulation layer are around 12 dB and 10 dB lower than when a thinner layer is used. However, this reduction highly depends on the insulation dielectric properties. There is indeed only a when the peek thickness increases 2.3 dB reduction of from 1 to 4 mm (i.e., ) whereas 10.4 dB are gained in the case of zirconia. This result is very useful for the design of implanted antennas. In fact, as the volume of an implantable device is strictly limited, the radiator and the insulation dimensions have to be carefully chosen to optimize the radiation performances. Our values show that it is worth considering a thin peek insulation to allow the maximum volume for the antenna. On the contrary, in the case of zirconia, a relatively thicker insulation should be used. Moreover this dielectric material, due to its high , facilitates the reduction of the real antenna dimensions. and The use of zirconia gives always the best results for . Clearly this material not only has the lowest , but also closest to the IEEE head model, thereby reducing the the mismatch between the insulation and the body layer in agreement with [6]. On the other hand, peek presents the worst perand a low . formances, as it shows the highest Finally, the use of alumina or polyamide is almost equivalent of this (less than 0.1 dB variation) despite the fact that the ceramic is double of the polyamide. This is again explained by the improved matching due to the higher of the alumina. 2) Model 2: Muscle Model: All previous considerations, obtained with the IEEE head model, are still qualitatively confirmed in the muscle model, as reported in Table IV.

The dissipated powers in the muscle tissue, , are smaller than the (of around 2.5 dB) as muscle presents a lower IEEE head model (i.e., 0.6219 and 0.7989, respectively). On , the contrary, the power attenuated in the insulation layer, is always higher (of around 1 dB). This is due to the mismatch between insulation and body model, which is more important in the case of the muscle since its permittivity is higher than the one of IEEE head model (57.1 instead of 43.5). This also implies that the choice of the biocompatible mateand, thus, on the total lost rial has a deeper impact on the . For example, in the 1 mm case, we register a difpower ference of 3.6 dB between peek and zirconia against the 2.8 dB value found in the IEEE head model. The same trend applies for all other thickness values. 3) Model 3: Multilayered Model: The results in Table V (multilayered model) are close to those in Table IV (muscle model). The first body shell surrounding the excitation is indeed the muscle in both models. The presence of the fat and dry skin , and ) of less than 1 layers changes the power losses ( dB. This result is in agreement with [2], where the return losses of implanted antennas are very close when surrounded by these two body models. B. Magnetic Excitation The multilayered model with a 2 mm thick polyamide insulation is excited by a magnetic source. The choice of this insulation is justified as polymers are mechanically easier to manufacture and the polyamide has shown the best performances among them. Moreover, let us remind that polyamide presents performances very close to those of alumina, as shown in Section IV-A-I.

MERLI et al.: THE EFFECT OF INSULATING LAYERS ON THE PERFORMANCE OF IMPLANTED ANTENNAS

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TABLE V POWER LOSS [DB] FOR DIFFERENT INTERNAL INSULATIONS WITH AN ELECTRIC DIPOLE IN MODEL 3 (MULTILAYERED)

TABLE VI MAX SAR [DBW/KG] WITH DIFFERENT INTERNAL INSULATION THICKNESSES FOR THE MODELS OF SECTION IV

TABLE VII FLEXIBLE EXTERNAL INSULATIONS

Fig. 7. Comparison of P as a function of the radial distance at 403.5 MHz with the three different sources. The multilayered model is analyzed while considering the presence of polyamide 2 mm thick.

The power radiated through the body is compared in Fig. 7 for an electric and magnetic excitation. The magnetic source substantially reduces the absorbed power compared to the elecand instead of tric one ( , and ), for the same investigated model. The radiation of the magnetic source through a body is more efficient, as reported in [4], [22], [33]. The high magnetic near field does indeed not dissipate in the body since . Finally, for a human tissues have no magnetic losses magnetic source, the dielectric characteristics of the real insulation layers have a negligible influence, as shown in [22]. C. Huygens Source The power radiated through the body is computed for a Huygens source in the same conditions of the magnetic excitation. , and The level of the absorbed powers ( ) is between those of the electric and the magnetic excitation. Despite its 3 dB directivity, the radiation efficiency of the Huygens source is also between those of the electric and the magnetic dipoles. Indeed, it combines both sources. Therefore, the high electric near field coming from the electric dipole dissipates in the insulation and body layers, whereas the magnetic field is less affected.

The values reported in Tables III–V show, for a constant external diameter of the body shell, that the increase of the thickness of the insulation layer results in lower power dissipation in the living tissue. This conclusion holds true when different conditions for the body shell dimension are applied, such as constant volume [22] or thickness. In particular, the latter implies a slight increase of of less than 0.2 dB. D. Specific Absorption Rate The maximum Specific Absorption Rate (SAR) values have been computed for the presented body models. It is well known that accurate and precise SAR values are strongly dependent on the human body representation, the implant locations and several biological phenomena [34]. Nevertheless, despite the simplicity of the investigated body models, it is worth evaluating the peak SAR values in order to confirm the observations previously reported. Table VI reports the maximum values of SAR. These values are always found at the interface between the internal biocompatible layer and the human body. These peak values (with no spatial averaging) are obtained when the acting source (i.e., a mathematical dipole source surrounded by an air shell) radiates

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TABLE VIII POWER LOSS [DB] FOR DIFFERENT EXTERNAL INSULATIONS WITH THE HUYGENS SOURCE IN MODEL 3 (MULTILAYERED) AND A 2 MM THICK POLYAMIDE AS INTERNAL BIOCOMPATIBLE INSULATION

0 dBm at the 1 mm air shell interface. The mass density values can be found in [2]. Of course, the use of such ideal sources provides unrealistically high values of the absolute electric field (therefore SAR) [24]. Thus, results are presented in [dB/W] so as better appreciate relative variations. The presence of different insulation dielectric properties turns out to have a negligible effect on the obtained SAR values; therefore, only results versus the insulation thickness variation are reported. On the contrary, the relative peak SAR value variations with respect to the type of source and insulation thickness enables to derive valuable information, as reported below. In agreement with the results already reported, the presence of any insulation produces a large impact reducing SAR values by at least 14 dB compared to the case without insulation (none). In the case of an electric source excitation a difference of approximately 12 dB is found versus the insulation thickness, which is in perfect agreement with the values reported in Tables III–V. As previously discussed, the magnetic source presence reduces the electric near field coupling in the biological tissue, consequently decreasing the SAR values with respect to the electrical excitation. The Huygens source case is relatively closer to the electric one. This is in agreement with the results reported graphically in Fig. 7. As for the effect of the insulation thickness, an improvement of approximately 15 dB over the electric and magnetic cases (12 dB) is obtained in the presence of the Huygens source. Indeed, the increase of insulation thickness strongly reduces the coupling of the near field terms. Therefore, the far field component increases its relevance and the higher directivity inherent to the Huygens source plays a positive role since it reduces the SAR values. V. EXTERNAL INSULATION: NUMERICAL RESULTS AND DISCUSSION Our previous analysis clearly pointed out the importance of the biocompatible insulation layer. It is now logical to focus on the transition between the external body layer (skin) and the outer world (free space). The power transfer can be improved with the use of an insulation layer placed on the external surface of the human skin. For a practical wearable realization, one could imagine the use of an armband, belt or strap (for instance, as in tennis-elbow support). The presence of an external layer has already been deeply investigated for many applications but, to the authors’ best knowledge, not for implanted antennas for telemetry purposes

in the MedRadio band. Among these applications, let us mention: SAR distribution and the microwave power coupling in hyperthermia [35], the electromagnetic absorption due to the presence of clothing (for instance [36]), the microwave coupling in medical imaging system [37] and SAR reduction from an undesired external source [38]. According to the application, the external insulator is called clothing, bolus, matching layer or shield. The major difference between these applications and our problem is that the source is always external to the body. In this Section we focus on the power transmission enhancement that is achieved with the presence an the external insulator. A few types of materials are investigated. Those are: a polymer fiber, neoprene and silicon. Their dielectric properties are reported in Table VII, as well as the “ideal” case. The latter consists in the dielectric lossless shell that provides a perfect matching between the skin and the free space. The characteristics (permittivity and thickness) of this ideal matching layer are computed by analogy with the simple transmission line model [37]. This approximation is reasonable since only the far field term of the electromagnetic radiation is concerned, due to the electrically large distance between the source and the external layer. External layers are modeled as spherical shells, whose thicknesses range from 5 to 20 mm, placed just after the body tissues, as shown in Fig. 1. For the numerical analysis, we consider the same characteristics listed in Section IV, with the Huygens source as the excitation, a 2 mm thick polyamide internal insulation and the multilayered body model. The power attenuation in the internal 2 mm thick polyamide (as in Section IV-C). Table VIII reports shell is the power attenuation in the multilayered model and the external , respectively). Note that in this case insulation ( and is equal to with

(8) where coincides with the radius of the external insulation shell (Fig. 1). The cases of no external insulation (“none”) and the lossless matching layer (“ideal”) are also reported in Table VIII. The of 7.9 dB compared presence of the ideal insulation reduces . This means esto no insulation case tablishing a communication almost three-times more efficient. Although not practically realistic (its thickness is approximately

MERLI et al.: THE EFFECT OF INSULATING LAYERS ON THE PERFORMANCE OF IMPLANTED ANTENNAS

71 mm) the ideal external insulation case is interesting to set the optimal value of the power transmission out of the skin tissue. In agreement with [40], the presence of a thin external layer does not modify the values as much as the internal biocompatible insulator. For instance, the power transmission is enhanced of almost 2 dB by the presence of a 20 mm thick silicon layer. Although the investigated external insulations may not be the optimal ones, we have shown that their influence is not negligible.

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APPENDIX A SPHERICAL WAVE PROPERTIES and have several orThe spherical modal vectors thogonality properties. The one used to get the radiated power formula (4) are

(A-1) and

VI. CONCLUSION This work has analyzed the influence of insulation in implanted antennas for biotelemetry applications in the MedRadio band. Body models composed of concentric spherical homogeneous shells excited by ideal sources have been considered. The geometry of the structure allows to compute analytically the electromagnetic field with a Mode Matching Technique (MMT) based on spherical wave expansion. The MMT has been numerically validated by comparison with a full-wave commercial software. Moreover, a convergence criterion has been defined to compute, with controlled accuracy, the power radiated at any radial distance, including near field range. Two homogeneous and one multilayered models have been investigated, considering both internal and external insulations. The results obtained for the internal insulation provide guidelines, not only for the selection of the biocompatible material, but also for the implanted antenna design. In the strictly limited volume available for the implanted device, the dimensions of the antenna and insulation thickness must be carefully chosen so as optimize the radiation performances. For instance, a judicious choice of the internal biocompatible insulation leads up to a six-fold more efficient power transfer from the implanted source to the external receiver. The influence of the type of excitation (electric and magnetic dipole and Huygens source) has also been examined. As expected, since the body does not present any magnetic loss, the magnetic source is the most efficient. SAR values have been computed. Despite the limitations of the investigated body models, our results confirm the effective role of biocompatible internal insulation. Moreover, the important effect related to the near field coupling is once more emphasized by the Huygens source analysis. The influence of external insulation has also been considered. An ideal matching layer, between the skin tissue and the air, increases the power transmission of almost 8 dB. The capability of a few low-loss, flexible materials has been analyzed to reduce the mismatch between the body layer and the outer free space. Although far from the ideal case, around 2 dB can be gained with realistic external insulators. Despite the rough approximation of the human body and the use of ideal sources, the results presented above provide quantitative and qualitative insights on the power transmission enhancement that can be obtained with internal and external insulations. Moreover, presence of the insulation turns out to be an effective way to comply with SAR regulations.

(A-2) is a sphere centered at the origin and symbol.

is the Krönecker

APPENDIX B POWER COMPUTATION CONSIDERATIONS A Hertzian dipole radiating in an unbounded lossy medium must be supplied with infinite power, which is not physically meaningful, as shown in [24]. This still applies for a dipole placed in a bounded lossy spherical shell. Equation (4) can be rewritten (B-1) where and are complex values in a lossy shell. is a product of spherical modal coefficients and Bessel functions. If one lets approach zero in (B-1), one can easily show that becomes infinite. One term of (B-1) is indeed proportional to and this term has a dependency when tends toward zero, as shown in (B-2). The spherical and have the following asymptotic beHankel functions and for havior, given in [41, p. 437], as

(B-2) This result confirms and extends, using the spherical modal expansion, the demonstration given in [24]. REFERENCES [1] Medical Device Radiocommunications Service (MedRadio) Medical Implanted Communication System (MICS), 2009 [Online]. Available: http://www.fcc.gov/ [2] J. Kim and Y. Rahmat-Samii, “Implanted antennas inside a human body: Simulations, designs, and characterizations,” IEEE Trans. Microwave Theory Tech., vol. 52, pp. 1934–1943, Aug. 2004. [3] P. Soontornpipit, C. Furse, and Y. C. Chung, “Design of implantable microstrip antenna for communication with medical implants,” IEEE Trans. Microwave Theory Tech., vol. 52, pp. 1944–1951, Aug. 2004. [4] P. S. Hall and Y. Hao, Antennas and Propagation for Body-Centric Wireless Communications. Norwood, MA: Artech House, 2006, ch. 9.

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[5] R. Warty, M. R. Tofighi, U. Kawoos, and A. Rosen, “Characterization of implantable antennas for intracranial pressure monitoring: Reflection by and transmission through a scalp phantom,” IEEE Trans. Microwave Theory Tech., vol. 56, pp. 2366–2376, Oct. 2008. [6] T. Dissanayake, K. P. Esselle, and M. R. Yuce, “Dielectric loaded impedance matching for wideband implanted antennas,” IEEE Trans. Microwave Theory Tech., vol. 57, pp. 2480–2487, Oct. 2009. [7] S. Soora, K. Gosalia, M. S. Humayun, and G. Lazzi, “A comparison of two and three dimensional dipole antennas for an implantable retinal prosthesis,” IEEE Trans. Antennas Propag., vol. 56, pp. 622–629, Mar. 2008. [8] T. Karacolak, R. Cooper, and E. Topsakal, “Electrical properties of rat skin and design of implantable antennas for medical wireless telemetry,” IEEE Trans. Antennas Propag., vol. 57, pp. 2806–2812, Sep. 2009. [9] K. Ito, “Human body phantoms for evaluation of wearable and implantable antennas,” presented at the 2nd Eur. Conf. on Antennas and Propagation (EuCAP 2007), Edinburgh, Scotland, UK, Nov. 2007. [10] W. G. Scanlon, B. Burns, and N. E. Evans, “Radiowave propagation from a tissue-implanted source at 418 MHz and 916.5 MHz,” IEEE Trans. Biomed. Eng., vol. 47, pp. 527–534, Apr. 2000. [11] L. C. Chirwa, P. A. Hammond, S. Roy, and D. R. S. Cumming, “Electromagnetic radiation from ingested sources in the human intestine between 150 MHz and 1.2 GHz,” IEEE Trans. Biomed. Eng., vol. 50, pp. 484–492, Apr. 2003. [12] C. Miry, R. Gillard, and R. Loison, “An application of the multi-level dg-fdtd to the analysis of the transmission between a dipole in freespace and an implanted antenna in a simplified body model with various positions,” in Proc. 3rd Eur. Conf. on Antennas and Propagation EuCAP 2009, Mar. 23–27, 2009, pp. 67–70. [13] A. Sani, A. Alomainy, and Y. Hao, “Numerical characterization and link budget evaluation of wireless implants considering different digital human phantoms,” IEEE Trans. Microwave Theory Tech., vol. 57, pp. 2605–2613, Oct. 2009. [14] C. Gabriel, Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies Brooks Air Force Base, TX, 1996 [Online]. Available: http://niremf.ifac.cnr.it/tissprop/htmlclie/htmlclie.htm [15] Evaluating Compliance With FCC Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields, 97–01 ed. Washington, DC: Federal Communication Commission (FCC) Std. Supplement C, OET Bulletin 65, 2001. [16] R. W. P. King and G. S. Smith, Antennas in Matter: Fundamentals, Theory, and Applications, 1st ed. Cambridge, MA: The MIT Press, 1981. [17] C. M. Rappaport and F. R. Morgenthaler, “Optimal source distribution for hyperthermia at the center of a sphere of muscle tissue,” IEEE Trans. Microwave Theory Tech., vol. 35, pp. 1322–1327, Dec. 1987. [18] K. S. Nikita, G. S. Stamatakos, N. K. Uzunoglu, and A. Karafotias, “Analysis of the interaction between a layered spherical human head model and a finite-length dipole,” IEEE Trans. Microwave Theory Tech., vol. 48, pp. 2003–2013, Nov. 2000. [19] X.-K. K. L.-W. Li and M.-S. Leong, Spheroidal Wave Functions in Electromagnetic Theory, ser. Wiley Series in Microwave and Optical Engineering. New York: Wiley, 2002. [20] S. M. S. Reyhani and S. A. Ludwig, “An implanted spherical head model exposed to electromagnetic fields at a mobile communication frequency,” IEEE Trans. Biomed. Eng., vol. 53, pp. 2092–2101, Oct. 2006. [21] G. Cerri, R. De Leo, and G. Rosellini, “Evaluation of electromagnetic power deposition in a spherical multilayer head in the near field of a linear antenna,” Wireless Netw., vol. 3, pp. 499–510, 1997. [22] F. Merli, B. Fuchs, and A. K. Skrivervik, “Influence of insulation for implanted antennas,” in Proc. 3rd Eur. Conf. on Antennas and Propagation EuCAP 2009, Mar. 23–27, 2009, pp. 196–199. [23] Feko Suite 5.3 (Evaluation Version, Silver License) [Online]. Available: http://www.feko.info/ [24] C. T. Tai and R. E. Collin, “Radiation of a Hertzian dipole immersed in a dissipative medium,” IEEE Trans. Antennas Propag., vol. 48, no. 10, pp. 1501–1506, Oct. 2000. [25] Handbook of Materials for Medical Device ASM international, 2003, ch. 1. [26] Zeus [Online]. Available: http://www.zeusinc.com/technicalservices/ technicalbulletins/technicalinformation/biocompatibility.aspx [27] J. A. Stratton, Electromagnetic Theory. New York: MGraw-Hill, 1941.

[28] B. Fuchs, S. Palud, L. L. Coq, O. Lafond, M. Himdi, and S. Rondineau, “Scattering of spherically and hemispherically stratified lenses fed by any real source,” IEEE Trans. Antennas Propag., vol. 56, no. 2, pp. 450–460, Feb. 2008. [29] H. Mieras, “Radiation pattern computation of a spherical lens using mie series,” IEEE Trans. Antennas Propag., vol. 30, pp. 1221–1224, Nov. 1982. [30] F. Jensen and A. Frandsen, “On the number of modes in spherical wave expansion,” in Proc. AMTA-2004, Oct. 2004, pp. 489–494. [31] Ansoft High Frequency Structure Simulator (HFSS) v11.1 (2009), Material Library [Online]. Available: http://www.ansoft.com/products/hf/ hfss/ [32] T. Konaka, M. Sato, H. Asano, and S. Kubo, “Relative permittivity and dielectric loss tangent of substrate materials for high-tc superconducting film,” J. Supercond., vol. 4, no. 4, pp. 283–288, Aug. 1991. [33] A. Karlsson, “Physical limitations of antennas in a lossy medium,” IEEE Trans. Antennas Propag., vol. 52, no. 8, pp. 2027–2033, Aug. 2004. [34] P. R. Wainwright, “The relationship of temperature rise to specific absorption rate and current in the human leg for exposure to electromagnetic radiation in the high frequency band,” Phys. Med. Biol., vol. 48, no. 19, pp. 3143–3155, Oct. 2003. [35] P. R. Stauffer, F. Rossetto, M. Leencini, and G. B. Gentilli, “Radiation patterns of dual concentric conductor microstrip antennas for superficial hyperthermia,” IEEE Trans. Biomed. Eng., vol. 45, pp. 605–613, May 1998. [36] O. P. Gandhi and A. Riazi, “Absorption of millimeter waves by human beings and its biological implications,” IEEE Trans. Microwave Theory Tech., vol. 34, pp. 228–235, Feb. 1986. [37] C. Rappaport, “Determination of bolus dielectric constant for optimum coupling of microwaves through skin for breast cancer imaging,” Int. J. Antennas Propag., p. 5, 2008, Article ID 359582. [38] H.-Y. Chen and K.-Y. Shen, “Reduction of SAR in a human-head model wrapped in clothing materials,” Microwave Opt. Technol. Lett., vol. 37, no. 4, pp. 305–308, 2003. [39] Tables of Physical and Chemical Constants Section 2.6.5 Kaye & Laby [Online]. Available: http://www.kayelaby.npl.co.uk/toc/ [40] H. Massoudi, C. H. Durney, P. W. Barber, and M. F. Iskander, “Electromagnetic absorption in multilayered cylindrical models of man,” IEEE Trans. Microwave Theory Tech., vol. 27, pp. 825–830, Oct. 1979. [41] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover, 1965.

Francesco Merli (S’09) received the Laurea degree (cum laude) in telecommunication engineering from the University of Florence, Florence, Italy, in 2006. He is currently working towards the Ph.D. degree at Ecole Polytechnique Fédérale de Lausanne (EPFL). His research interests include analysis, design and realization of implantable, small and UWB antennas.

Benjamin Fuchs (S’06–M’08) received both the electronics engineering degree and the M.S. degree in electronics from the National Institute of Applied Science (INSA), Rennes, France, in 2004 and the Ph.D. degree from the University of Rennes 1, France, in 2007. In 2008, he was a Postdoctoral Research Fellow at the Swiss Federal Institute of Technology, Lausanne, Switzerland. In 2009, he joined the Institute of Electronics and Telecommunications of Rennes (IETR), as a Researcher at the Centre National de la Recherche Scientifique (CNRS). His research interests include mode matching techniques, millimeter-wave antennas, focusing devices (lens antennas) and beamforming.

MERLI et al.: THE EFFECT OF INSULATING LAYERS ON THE PERFORMANCE OF IMPLANTED ANTENNAS

Juan R. Mosig (S’76–M’87–SM’94–F’99) was born in Cádiz, Spain. He received the Electrical Engineer degree from the Universidad Politécnica de Madrid, Madrid, Spain, in 1973 and the Ph.D. degree from the Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, in 1983. Since 1991, he has been a Professor at EPFL where, since 2000, he has been the Head of the Laboratory of Electromagnetics and Acoustics (LEMA). He is also currently a co-Director of the College of Humanities and the Chairman of the EPFL Space Center, conducting many Swiss research projects for the European Space Agency (ESA). In 1984, he was a Visiting Research Associate with the Rochester Institute of Technology, Rochester, NY, and Syracuse University, Syracuse, NY. He has also held scientific appointments with the University of Rennes, France, the University of Nice, France, the Technical University of Denmark at Lyngby and the University of Colorado at Boulder. He has authored five chapters in books on planar antennas and circuits and over 100 peer-reviewed journal papers. His current research interests include electromagnetic theory, numerical methods, and planar antennas. Dr. Mosig is a also a Fellow of the IEEE, the chairperson of the European COST Action on Antennas “ASSIST” (2007–2011) and a founding member and acting Chair of the European Association & Conferences on Antennas and Propagation (EurAAP and EuCAP).

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Anja K. Skrivervik received the Electrical Engineering degree and the Ph.D. degree from Ecole Polytechnique Fédérale de Lausanne, in 1986 and 1992, respectively. Previously, she worked at the University of Rennes and in the industry before returning to EPFL in 1996 as an Assistant Professor, and where she is currently a “Professeur titulair.” Her teaching activities include courses on microwaves and on antennas. Her research activities include electrically small antennas, multi-frequency and ultrawideband antennas, numerical techniques for electromagnetic and microwave and millimeter wave MEMS. She is author or coauthor of more than 100 scientific publications. Prof. Skrivervik is very active in European collaboration and European projects. She is currently the Chairperson of the Swiss URSI, the Swiss representative for COST action 297 and a member of the board of the Center for High Speed Wireless Communications of the Swedish Foundation for Strategic Research.

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Engineered Dielectric Pattern Nanoantenna: A Quantum Cascade Laser (QCL) Device Application Jing Wu, Student Member, IEEE, and Hossein Mosallaei, Senior Member, IEEE

Abstract—The concept and modeling of a dielectric pattern nanoantenna integrated with a quantum cascade laser (QCL) source are presented, where a directive emission performance is achieved. A periodic dielectric configuration with optimized and different periodicities in transverse and propagating directions is created to engineer a band-edge dispersion diagram at a specific -vector. In addition, QCL source with directive emission of gain and vertical and horizontal narrow beamwidths of 14 and 12 , respectively, is achieved. This indicates about 2.5 and 4.5 times improvement in the vertical and horizontal beamwidths of the original QCL radiation. Highly-efficient power output is determined. A full wave analysis based on finite difference time domain (FDTD) technique is applied to comprehensively characterize the device and determine its physical parameters. The obtained nanoantenna can be integrated in THz, IR, and visible spectrums (scaling the geometry properly), and it has the potential for efficient long-range THz and optical energy communications. Index Terms—Dispersion diagram, metamaterial, nanoantenna, photonic crystal, quantum cascade laser.

I. INTRODUCTION PTICAL energy transmission over a long-range and in a short-period of time has attracted significant interests for nanoscale on-chip and between-systems communications. A possible solution for this importance can be realized by utilizing the concept of near-field guiding along the chains of plasmonic nanoparticles [1]. However, the loss of plasmonic structure reduces the opportunity for long-range energy propagation. Though optical guiding by generation of defect channel through a dielectric photonic band-gap crystal is an alternative option [2], this method cannot be used for inter-chip data communication. An antenna is a key component for long-range space communication. It will be of extreme importance if one can demonstrate this concept in THz and visible spectrums, creating optical nanoantennas for nanoscale wireless communications. When compared with traditional optical plasmonic guiding, where the , a nanaoantenna link radipower loss is associated with ates with power loss and is more efficient for long-range

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Manuscript received February 11, 2010; revised June 01, 2010; accepted July 19, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported in part by the U.S. National Science Foundation (NSF). The authors are with Applied EM & Optics Laboratory, ECE Department, Northeastern University, Boston, MA 02115 USA (e-mail: [email protected]. edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090480

energy propagation [3]. In addition, one can make an array of radiators to increase the antenna gain to any desired value. This is useful in optics where one can make a physically-small optical array of nanoantennas patterned on an available large aperture. The size may not be a restrictive issue in optics as one may experience in microwave. For instance, a quantum cascade laser (QCL) source has a very large facet area (several tens of wavelengths) [4], which can be structured suitably with a large array of nanoantennas. There have been some studies on realizing THz radiation using metallic elements, however, only a single element is considered as the antenna radiator [5]–[9]. Plasmonic nanoantennas have also been studied as possible optical radiators [10]–[12], but it is difficult to realize plasmonic resonance in lower frequencies and the THz band. Furthermore, dielectric gratings have the potential to manipulate the beam successfully in the THz and visible bands [13], [14]. The focus of this paper is to provide a systematic study of THz nanoantennas realized by a novel array of dielectric patterns. It is demonstrated that one can use an array of periodic dielectric pattern to manipulate a spherical wave and transform its phase front into a plane-wave type distribution. This is observed to result in a far-field directive emission. The concept is examined by integrating the nanoantenna with a QCL device to scan a narrow-beam radiation characteristic. A semiconductor QCL is a functional laser source which can distribute the energy in a wide angular spectrum. Recently, Capasso group has demonstrated an interesting solution to collimate the beam by patterning the QCL facet with 1D and 2D plasmonic gratings [4], [15]. Conceptually, the source propagation is transformed into a surface wave which is guided along the facet, and is shaped by the plasmonic grating for enhancing far-field radiation and energy concentration along the direction of interest [16]–[19]. However, as the QCL surface wave propagates mostly along one direction, controlling the beam radiation is mainly achieved in one plane (vertical plane). To spread the surface waves over the entire facet and control the beam in both the planes, one can make the size of the facet’s aperture smaller, but this will reduce the throughout power efficiency of the QCL. Subsequently, there will be a trade-off between the required divergence angles, and the QCL power output efficiency. The proposed plasmonic methodology is realized for mid-IR operation where the plasmonic material acts mostly like a metal. If one is interested in achieving an optical nanoantenna in the visible band, the concept cannot be generalized by scaling the size, as the plasmonic material will have a different property in this spectrum. A structured dielectric nanoantenna will be a great alternative for plasmonic configuration. Anisotropic dielectric media and

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WU AND MOSALLAEI: ENGINEERED DIELECTRIC PATTERN NANOANTENNA: A QCL DEVICE APPLICATION

photonic crystals operating in their band-edge have proven to show unique properties for achieving directive emission [20]–[26]. In this paper, a systematic study for a novel arrangement of dielectric rods nanoantenna controlling the amplitude and phase of a source distribution is presented. The basic idea constitutes transforming all -vectors (in Fourier space) into a specific direction. This can be enabled by optimizing a 3D periodic configuration of dielectric elements having different periodicities to engineer an anisotropic dispersion diagram and required band-edge performance [27]. The structure is integrated with a semiconductor QCL source to provide a directive emission laser device. The advantages are that the radiation beam can be controlled in both the planes, and one can implement the concept at any optical frequency of interest (by scaling the geometry accordingly). A finite difference time domain (FDTD) technique [28]–[30] is applied to fully characterize the performance of the QCL, the dielectric-patterned nanoantenna, and the complex configuration of the QCL integrated with the nanoantenna. The physics and fundamental concepts are comprehensively investigated. Near- and far-fields behaviors are investigated to successfully optimize the QCL nanoantenna structure and the desired radiation parameters.

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Fig. 1. The geometry of the QCL source. Active region is surrounded by cladding medium and generates an almost TEM wave.

II. QCL PERFORMANCE QCLs are optical sources operating based on inter-bands transitions in multiple quantum wells structures. Their emissions’ wavelengths extend from mid-to far-infrared, which makes them very capable devices for applications such as gas sensing, free-space optical communication, and imaging. Most of these areas of applications require light to be concentrated in a small solid-angle in the far-field region. However, as an edge-emitting semiconductor, a QCL usually has large beam divergence owing to the diffraction at their small light-emitting apertures. Their full-width divergence angles at half-maximum power are in the ranges of several tens of degrees, i.e., 30 to 60 [31]. Fig. 1 illustrates a typical model for a QCL geometry constructed to operate around the center wavelength [4]. The light is trapped inside an active region and is guided toward the aperture, where it can radiate from. The active region is considered to have an effective material of refractive index , with effective length and width of around 7 and , respectively [32]. It is surrounded by cladding medium 4 . This construcmade of indium phosphide (InP) with tion enables total internal reflection inside the active region and guides the wave successfully through the medium [33]. Further, as the refractive index of the active region is very close to that of TEM mode profile is developed. cladding, an almost . The structure has a substrate of material index To provide a 3D full wave numerical analysis for this configuration, the system is excited with an infinitesimal dipole located at the center of the active region, far from the QCL facet, and the FDTD technique is applied. The side-walls of the cladding region are tapered with lossy materials to ensure the generation of a dominant mode (as this is the case in practical realization). The results for the E and H modes profiles inside the active region are depicted in Fig. 2, illustrating a nearly single TEM mode

Fig. 2. Normalized E and H fields profiles inside the active region of the QCL source. (a) E along vertical direction, (b) E along horizontal direction, (c) H along vertical direction, (d) H along horizontal direction.

generation. The near-fields on the facet and in the vertical and horizontal planes are presented in Fig. 3. As observed, the fields diverge away from the facet. To better understand the radiation performance of the QCL source, the field patterns in the vertical and horizontal planes are obtained in Fig. 4. Large beamwidths of about and in those planes are evaluated. The directivity is approximately 12 dB. As mentioned earlier, for many optical systems, one requires concentrating the QCL’s beam in a small spot. Conventionally, the divergent beam is collimated with lenses or curved mirrors, which usually requires meticulous optical alignment. Furthermore, there are a limited number of other methods, such as incorporating a micro-machined lens or horn antenna onto the laser facet [34], [35], and using tapered laser waveguides with

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Fig. 3. Near-field distributions of the QCL source on (a) the facet (x to the beam divergence.

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0 z plane), (b) vertical plane (y 0 z plane), and (c) horizontal plane (x 0 y plane). Notice

Fig. 4. Radiation performance of the QCL source illustrating wide beamwidth and poor directivity.

laterally-expanded ends [36], [37]. However, it is not practical to reduce the vertical divergence by simply growing thick active cores, because these devices will require unrealistically high voltages for operation, and will have heat-dissipation problems. In this work, we offer a unique approach to collimate the beam based on the concept of periodic photonic crystals and anisotropic band-edge realization. The designed nanoantenna is deposited on the facet of the QCL to tailor the near-field and provide directive far-field emission. III. PHYSICS AND MODELING OF DIELECTRIC NANOANTENNA Photonic crystals (PCs) are periodic arrangements of dielectric elements which can prohibit the propagation of electromagnetic waves in a specific frequency spectrum, known as the bandgap phenomenon [38], [39]. Dielectric crystals have the benefits of having low loss and are less-dependent on frequency, when compared with plasmonic materials. Hence, they have been widely used for realizing novel optical components. This paper presents a unique application of PCs for producing directive QCL emission. Conceptually, to obtain a directive emission, one needs to translate all the -vectors of the source’s spherical wave into a desired direction to achieve

a uniform near-field profile. Transformation optics is required to translate a high-intensity local field into an array of radiators distributed along an aperture. To achieve this, one can think of realizing a cavity mode between two coupled impedance surfaces (supporting surface waves), where a plane wave can be tunneled through the system through the defect mode. To illustrate this idea, let us consider a periodic dielectric pattern with different periodicities in transverse and propagating directions, as depicted in Fig. 5(a). The structure is made of with square dielectric rods having material index cross-section of size . The periodicities along the and directions exhibit the same values of , while along the propagating direction (y) a different is employed. Utilizing different periperiodicity of odicities allows one to realize an anisotropic performance with an engineered dispersion diagram supporting a band-edge for -vectors along the surface of the PC, and stop-band for other directions (decaying modes). The FDTD full wave analysis with periodic boundary conditions is applied to characterize the structure and determine the dispersion diagram, as presented in Fig. 5(b). A to bandgap behavior from is obtained. At the band-edge only mode is supported. (or )- plane can proThe 2D dispersion diagram in vide better information in this regard, as is plotted in Fig. 6. or can exist, while As obtained, only the modes with propagation along the direction is forbidden. Furthermore, to better highlight the physics behind the analysis, we investigate transmission coefficient for a plane wave propagating along the and directions through the crystal. The performance is shown in Fig. 7. A pass-band through the gap region for the wave propagating along the z (transverse to is obtained. This is the defect mode crystal) at determined through the dispersion diagram analysis. An error of about 4% is observed that can be attributed to the finite-sized structure, assumed when analyzing the transmission coefficient along the wave propagation. Fig. 8(a) demonstrates a cavity structure made by an 8 low-dielectric material slab (i.e. , ) [40], [41], sandwiched between two periodic patterns surfaces (slices of our designed configuration) operating in their band-edges. The

WU AND MOSALLAEI: ENGINEERED DIELECTRIC PATTERN NANOANTENNA: A QCL DEVICE APPLICATION

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Fig. 5. (a) 3D PC metamaterial pattern with different periodicities in transverse and vertical directions, and (b) its dispersion diagram. The band-edge is clearly demonstrated.

Fig. 6. 2D kx (or kz )-ky vector plane dispersion diagram. Upper band edge is around f :  :  .

= 30 4 THz( = 9 87 m)

Fig. 8. (a) A cavity structure constructed from a low-dielectric material sandwiched between two PC layers and (b) its transmission performance. The defect mode is around the resonance of the cavity and the band-edge of the PC patterns.

Fig. 7. Transmission coefficients for plane-waves propagating along the y and z directions inside the PC.

transmission coefficient for a plane wave illuminating the structure from the left is determined in Fig. 8(b). The cavity allows tunneling the plane wave to the other side by generating the proper defect mode and through the coupling between its periodic layers walls (having band-edge dispersion diagram). This

can happen only for a normal incident wave, while for a slightly tilted incident wave the -vector will be positioned inside the bandgap, and thus no transmission will occur. The obtained where the transmission is around the frequency (dielectric wavelength). slab thickness is at Now, let us return to our original question of whether one can translate a point source radiation into a uniform near-field distribution. To address this, let us consider a small waveguide opened inside a finite-size source with dimensions less than which is coated by low-dielectric material of PEC and thickness of 4 . The structure is covered by

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Fig. 9. (a) Dielectric pattern nanoantenna, (b) its aperture near-field, and (c) the radiation characteristic. The beamwidths of about  achieved. Uniform aperture field provides directive radiation.

one layer of a designed periodic configuration (about 8 periods in transverse directions), and is depicted in Fig. 9(a). This geometry is equivalent to cavity model presented in Fig. 8(a); hence, one can expect that the point source radiation can be transaperture formed into a relatively uniform field along the size. The near-field and radiation characteristics are determined in Figs. 9(b) and 9(c), validating our expectations. The field is trapped inside the cavity and can radiate only along the -direction. The radiation pattern has a directivity of 19 dB with vertical and horizontal planes beamwidths of about and , respectively. It must be noted that when compared with the cavity design where the PC is considered to be plane, the operating frequency is slightly periodic in the shifted and optimized at (to compensate for the diffractions from the edges of the finite-size structure and consequently reduce the sidelobes). IV. NANOANTENNA ENGINEERING QCL RADIATION The proposed dielectric pattern nanoantenna will be an excellent candidate to be integrated with a QCL, for collimation of the radiated beam. To accomplish this, the facet of the QCL is coated with a plasmonic layer (which mostly acts like a conductor in this spectrum), and then an aperture with the same dimensions as the effective region of the active layer is opened through it. This will ensure an efficient throughout power for the system. The plasmonic layer is coated thick slab of low-dielectric index of medium by 4 (a spacer), and then the whole structure is covered by designed dielectric pattern nanoantenna. This configuration is depicted in Fig. 10. The dielectric pattern photonic crystal supports the band-edge mode with -vectors propagating along the surface. The small-aperture source excitation (with an almost dipole radiation) operates at the defect-mode of the cavity and hence all the -vectors are trapped inside the medium with its -component radiation towards the outside. One can envision the engineered dielectric pattern and its backed plasmonic layer, as a cavity constructed from a double-thickness slab medium sandwiched between two PC layers, where an input plane-wave can be transformed to the output port through the cavity defect mode and the coupled surface-waves supported

= 13

and 

= 11

are

Fig. 10. QCL device integrated with dielectric pattern nanoantenna.

by the PC layers. Hence, a localized wave around the middle of the cavity can provide an almost plane-wave phase-front on the structure’s aperture, enabling far-field directive emission. Figs. 11 and 12 illustrate the FDTD analysis of the QCL and its near-fields and radiation patterns characteristics. As observed, the near-field is distributed along the large size antenna aperture with tapered behavior around the edges, providing an array-type configuration with directive emission of 20 dB gain, and vertical and horizontal narrow beamwidths of about and , respectively. This is about 2.5-times improvement in the vertical plane, and 4.5-times improvement in the horizontal plane, of the QCL radiation beamwidths. The opto provide erating frequency is optimized at the best radiation performance. The near-fields performances in vertical and horizontal planes illustrate an almost successful beam collimation for the QCL emission (see Fig. 11). It must also be noted that one needs to slightly control the locations of the dielectric rods around the source aperture to ensure the best array elements arrangement in this region. The radiation efficiency of the QCL nanoantenna is around 80% when compared with the un-patterned case. Further enhancement in the directivity and performance in vertical and horizontal planes can be accomplished by tailoring the structured dielectric nanoantenna (especially around the source), extending the antenna aperture size, and cascading more numbers of PC layers in front of the device. Plasmonic

WU AND MOSALLAEI: ENGINEERED DIELECTRIC PATTERN NANOANTENNA: A QCL DEVICE APPLICATION

0

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0

Fig. 11. Near-field distributions of the QCL integrated with dielectric nanoantenna on (a) the facet (x z plane), (b) vertical plane (y z plane), and (c) horizontal plane (x y plane). As observed, when compared with Figs. 3, the fields are more concentrated (less-divergent) away from the device.

0

Fig. 12. Radiation performance of QCL nanoantenna demonstrating directive emission (20 dB) with narrow beamwidths of  and  . The beam is tilted down by 5 in vertical plane due to the geometry asymmetry in this direction. Radiation patterns are plotted in pattern coordinate system.

= 14

= 12

coating can also be used around the antenna boundary to reduce the edge diffractions. The QCL can provide tunable frequency operation and our PC nanoantenna can be integrated with the source to radiate successfully at the frequency of interest. Changing the frequency will degrade the antenna characteristic, because the key for achieving a directive performance is to operate at the band-edge of the dispersion diagram. Fig. 13 illustrates the radiation performance of the QCL nanoantenna with varying frequency. From the dispersion diagram shown in Fig. 5(b), it can be observed that above the band-edge, other modes can be generated and consequently the waves can be transmitted along other -vectors. Thus, the radiation pattern should have the peaks in other angles rather than the normal direction. Below the band-edge, the frequency is found to be within the stop-band region where no mode is allowed to be excited, and hence, the emission should be reduced considerably. The radiation patterns shown in Figs. 13 clearly confirm our dispersion diagram study. The concept of the proposed dielectric nanoantenna is very general and can be applied at any optical frequency of interest,

Fig. 13. Frequency-dependence investigation of the QCL nanoantenna. (a) Vertical plane, and (b) horizontal plane. Away from the band-edge the radiation patterns are degraded considerably.

by scaling the geometry accordingly (and using the proper materials parameters). V. SUMMARY In this paper, a novel approach for making QCL sources with directive emissions, using structured THz dielectric nanoan-

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tennas is presented. A periodic dielectric configuration with optimized and different periodicities in transverse and propagating directions is created to engineer the dispersion diagram and manipulate the performance of the source radiation. The dielectric pattern nanoantenna operates at the band-edge and can transform a point-source radiation into distributed array of radiators along a large-size aperture, enabling directive emission characteristic. FDTD technique with periodic boundary conditions is applied to fully characterize the performance of the complex periodic configuration and successfully obtain the concept and physical parameters of the designed nanoantenna. The structured nanoantenna is then integrated with the QCL source device. It is demonstrated that the source radiation is transformed into a tapered near-field distribution along the antenna aperture realizing an efficient far-field radiation with a directivity of 20 dB, and vertical and horizontal narrow beamwidths of about 14 and 12 , respectively. This is about 2.5 and 4.5 times improvements in the vertical and horizontal beamwidths of the radiation characteristics of the source itself, collimating the beam very successfully. The obtained QCL nanoantenna with narrow-beam radiation can enable efficient long-range photonic communication. Its ability to concentrate the beam in small and nanoscale spots can be employed in novel potential applications in nanophotonics, such as nanoimaging and engineered molecular-quantum interactions, among others. REFERENCES [1] E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science, vol. 311, no. 5758, pp. 189–193, Jan. 2006. [2] H. Mosallaei and Y. Rahmat-Samii, “Periodic band-gap and effective dielectric materials in electromagnetics: Characterization and applications in nanocavities and waveguides,” IEEE Trans. Antennas Propag., vol. 51, no. 3, pp. 549–563, Mar. 2003. [3] N. Engheta and A. Alu, “Can optical nanoantenna links compete with plasmonic waveguide connections?,” presented at the Frontiers is Optics (FiO)/Laser Science Conf. on Metamaterials in Emerging Technologies, Fairmont, San Jose, CA, Oct. 11–15, 2009. [4] N. Yu, J. Fan, Q. Wang, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nature Photon., vol. 2, pp. 564–570, Sep. 2008. [5] E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. Crozier, and F. Capasso, “Plasmonic laser antennas and related devices,” IEEE J. Sel. Topics Quant. Electron., vol. 14, no. 6, pp. 1448–1461, Nov. 2008. [6] E. R. Brown, A. W. M. Lee, J. E. Bjarnason, and B. S. Navi, “Characterization of a planar self-complementary square-spiral antenna in THz region,” Microw. Opt. Technol. Lett., vol. 48, no. 3, pp. 524–529, Mar. 2006. [7] R. M. Bilotta and E. R. Brown, “Spiral antennas and antenna array,” presented at the IEEE Antennas and Propagation Symp., Washington, DC, 2005. [8] C. Fattinger and D. Grischkowsky, “Terahertz beams,” Applied Phys. Lett., vol. 54, pp. 490–492, 1989. [9] M. V. Exter and D. Grischkowsky, “Characterization of an optoelectronic terahertz beam systems,” IEEE Trans. Microw. Theory Tech., vol. 38, pp. 1684–1690, 1990. [10] J. Li, “Theory of optical nanoantennas and arrays based on surface plasmon resonance of plasmonic nanoparticles,” Ph.D. dissertation, Univ. Pennsylvania, Philadelphia, 2007. [11] A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: The concept and design,” Opt. Exp., vol. 18, no. 1, pp. 123–133, 2010.

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[34] A. W. M. Lee et al., “High-power and high-temperature THz quantumcascade lasers based on lens-coupled metal-metal waveguides,” Opt. Lett., vol. 32, pp. 2840–2842, 2007. [35] M. I. Amanti, M. Fischer, C. Walther, G. Scalari, and J. Faist, “Horn antennas for terahertz quantum cascade lasers,” Electron. Lett., vol. 43, pp. 573–574, 2007. [36] M. Troccoli, C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, “Midinfrared quantum cascade laser amplifier for high power single-mode emission and improved beam quality,” Appl. Phys. Lett., vol. 80, pp. 4103–4105, 2002. [37] L. Nahle, J. Semmel, W. Kaiser, S. Hofling, and A. Forchel, “Tapered quantum cascade lasers,” Appl. Phys. Lett., vol. 91, p. 181122, 2007. [38] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals. Princeton, NJ: Princeton Univ. Press, 1995. [39] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett., vol. 58, no. 20, pp. 2059–2062, May 1987. [40] J.-Q. Xi, J. K. Kim, E. F. Schubert, D. Ye, T.-M. Lu, and S. Lin, “Very low-refractive-index optical thin films consisting of an array of SiO2 nanorods,” Opt. Lett., vol. 31, no. 5, pp. 601–603, Mar. 2006. [41] E. F. Schubert, J. K. Kim, and J.-Q. Xi, “Low-refractive-index materials: A new class of optical thin-film materials,” Phys. Stat. Sol. B, vol. 244, no. 8, pp. 3002–3008, 2007. Jing Wu (S’08) received the B.Sc. degree from the University of Science and Technology of China, Hefei, in 2006. He is currently working toward the Ph.D. degree at Northeastern University, Boston, MA. Since 2006, he has been a Graduate Research/Teaching Assistant in the Advanced EM and Optics Devices Laboratory, Northeastern University. His research interests include theory and applications of metamaterials, nanoelectromagnetics, optical nanoantennas, waves interactions in complex media and photonic bandgap structures.

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Hossein Mosallaei (S’98–SM’02) received the B.Sc. and M.Sc. degrees in electrical engineering from Shiraz University, Shiraz, Iran and the Ph.D. degree in electrical engineering from the University of California, Los Angeles, (UCLA), in 1991, 1994, and 2001, respectively. From 2002 to 2005, he was a Research Scientist in the EECS Department, University of Michigan. He is currently an Assistant Professor of Electrical and Computer Engineering, College of Engineering at Northeastern University, Boston, MA. His research focus is on electromagnetic and optical micro/nanoscale meta-devices. He has been actively involved in many multidisciplinary governmental sponsored projects such as AFOSR, AFRL, NSF, ONR, and DARPA, as well as industry sponsored projects. His group conducts research in the areas of multi-physics multi-scale computational models and functional RF & photonic components and systems. He is the holder of one U.S. patent. He has authored and coauthored over 100 technical journal articles and conference papers. Dr. Mosallaei is a full member of URSI and a member of the American Association for the Advancement of Science. He is listed in Who’s Who in Science and Engineering, in America and Who’s Who in the World. He was the recipient of student prize paper awards in AP-S 2000, 2001, 2003, and 2005 along with his students, the URSI Young Scientist Award in 2001, and RMTG award in 2002. His student won the Northeastern Dissertation-Writing Fellowship Award in 2010.

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Millimeter-Wave Substrate Integrated Waveguide Long Slot Leaky-Wave Antennas and Two-Dimensional Multibeam Applications Yu Jian Cheng, Member, IEEE, Wei Hong, Senior Member, IEEE, Ke Wu, Fellow, IEEE, and Yong Fan, Member, IEEE

Abstract—Two types of substrate integrated waveguide (SIW) long slot leaky-wave antennas with controllable sidelobe level are proposed and demonstrated in this paper. The first prototype is able to achieve an excellent sidelobe level of 27 7 dB by properly meandering a long slot etched on the broadside of a straight SIW section from the centerline toward the sidewall then back. But it is known that an asymmetrically curved slot would worsen the crosspolar level. To overcome this drawback, a modified leaky-wave antenna is proposed, which has a straight long slot etched on the broadside of a meandering SIW section. It yields an outstanding sidelobe level of 29 3 dB and also improves the cross-polar level by more than 11 dB at 35 GHz. Experimental results agree well with simulations, thus validating our design. Then, a two-dimensional (2-D) multibeam antenna is developed by combining such 14 leaky-wave antennas with an SIW beamforming network (BFN). It has features of scanning both in elevation orientation by varying frequency and in cross-plane direction by using the BFN. Excited at ports 1–10 of such a 2-D multibeam antenna at 35 GHz, angular region of 86.6 in azimuth can effectively be covered by 3 dB beam-width of ten pencil beams. Varying frequency from 33 GHz to 37 GHz, the angular region of 37.5 and 38.9 in elevation can be covered by 3 dB beam-width of those continuous scanning beams excited at ports 6 and 8 respectively. Index Terms—Frequency scanning antenna, leaky-wave antenna, long slot, low sidelobe level, substrate integrated waveguide (SIW), two-dimensional (2-D) multibeam.

I. INTRODUCTION ONG slot leaky-wave antennas exhibit many interesting features and have been widely studied in millimeter-wave applications [1]–[10]. Among various long slot antennas, the

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Manuscript received December 16, 2009; revised May 21, 2010; accepted September 09, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 61001028 and in part by Research Fund for the Doctoral Program of Higher Education of China (RFDP) under Grant 20100185110014. Y. J. Cheng and Y. Fan are with the EHF Key Lab of Fundamental Science, School of Electronic Engineering, University of Electronic Science and Technology of China (UESTC), Chengdu 611731, China (e-mail: [email protected]). W. Hong is with the State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China. K. Wu is with the Poly-Grames Research Center and Center for Radiofrequency Electronics Research of Quebec (CREER), Department of Electrical Engineering, Ecole Polytechnique (University of Montreal), Montreal QC H3V 1A2, Canada. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090471

Fig. 1. Configurations of SIW long slot leaky-wave antennas.

longitudinal straight version is the easiest configuration judging from its design and fabrication points of view. However, the most serious drawback of such a uniform straight slot antenna is its high sidelobe level. Fortunately, an optimum far-field pattern can be achieved by meandering a continuous long slot from the waveguide centerline toward the sidewall then back to the centerline [2], [3]. Such an optimum far-field pattern can be synthesized by properly tapering the aperture illumination. Nevertheless, for design based on conventional waveguide technology, the standard waveguide usually cannot be used directly and must be modified to meet the demand of design. The long slot on the broadside of waveguide has to be precisely machined with a specific meandering profile in order to synthesize the desired radiation properties. Both of them result in expensive and difficult manufacturing processes [7]. As one member of the new generation integrated circuits, the substrate integrated waveguide (SIW) technology combines the advantages of planar and nonplanar structures and has been proposed to tackle the abovementioned bottleneck problems. First of all, we designed a low sidelobe SIW meandering long slot leaky-wave antenna as shown in Fig. 1. The value of offset, , from the sidewall determines the leakage rate of the slot. Such a structure has several good attributes, namely low loss, low profile, low cost, and high performance in the millimeterwave band. As discussed in earlier publications, the cross-polar level of a curved slot is obviously higher than that of an equivalent length straight slot. If the slot is designed to be symmetrical, it will provide a better cross-polar cancellation than its asymmetry counterpart [3]. In this case, good radiation patterns always require an

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To simplify the analysis, we assumed that is the phase constant when no leakage occurs. At the dielectric-air interface, the waves should follow the Snell’s law of refraction as: (2) Fig. 2. Side elevation of leaky-wave antenna.

asymmetrical taper. Therefore, we can use a straight long slot instead of the meandering topology, but meandering the shapes of lateral walls properly to optimize the sidelobe level as shown in the bottom configuration of Fig. 1. The two adjoining walls are incurved with the same shape, and the distance between the two walls remains constant. Considering the sidewalls of an SIW are constructed by two rows of metalized vias, it is easy to locate these vias precisely through normal PCB process to realize the required meandering shape. Moreover, the fabrication of a straight long slot is more accurate compared with that of a meandering long slot. On the other hand, it has been recognized that the realization of multiple beams in two orthogonal planes seems difficult because of its complexity [11]–[14]. An approach of the two-dimensional (2-D) beam-scanning array was proposed in [15]. A pencil beam can be scanned in both elevation and azimuth directions by creating a one-dimensional (1-D) phased array of leaky-wave antennas. However, several phase shifters are required in that design. In the present work, a modified millimeter-wave 2-D multibeam antenna is proposed. Scanning in elevation is obtained in usual leaky-wave fashion by varying frequency. Scanning in the orthogonal plane is obtained by the use of a passive beamforming network (BFN) arranged in the feed structure of the 1-D leaky-wave array to avoid the use of expensive millimeter-wave phase shifters. A broadband BFN is needed to satisfy the demand for frequency scanning, thus an SIW BFN based on the parabolic reflector principle will be employed, which has a wide operation bandwidth [16], [17]. Section II introduces a four-step design process of SIW long slot leaky-wave antenna. Design methods of such two types of antennas are similar with respect to the same basic principle of operation. The fabrication tolerance is discussed as well. Then, measured results are presented, illustrating the agreement between theory and experiment. In Section III, 14 elements type 2 leaky-wave antennas are integrated with an SIW BFN based on the parabolic reflector principle to realize a compact and simple 2-D multibeam array. II. SIW LONG SLOT LEAKY-WAVE ANTENNA A. Design Procedure 1) Determination of SIW Dimensions: Fig. 2 shows a side elevation of the leaky-wave structure and gives the notations used in the following paper. is the propagation constant in SIW, and is the phase constant in SIW. They are related with each other [18] (1)

In (2), is the permittivity of the used substrate. With small attenuation , there is a pattern with a main beam pointing at the angle (3) In (3), is the propagation constant in free space, is the wavelength in free space and is the guide wavelength in SIW. will become small when leakage occurs, so in SIW without slot can be only regarded as the upper limiting case. If the required beam direction is , and the required operation frequency is , there is (4) In (4), is the SIW equivalent width, and is the speed of light in free space. Then, the corresponding SIW dimensions, such as SIW width , diameter of metallic via , and space between adjacent vias , can be determined by [19]: (5) In this design, the center frequency is set to be 35 GHz, the relative permittivity and height of the substrate is respectively 2.2 and 1.575 mm, and the SIW equivalent width is selected to be 3.5 mm. Then, the corresponding SIW dimensions are , , and , respectively. 2) Relationship Between (the Radiation Per Unit Length) (the Offset), and Relationship Between and : and Most of previous works determined the radiation properties of a long slot leaky-wave antenna by a numerical analysis of the fields in the slot. In this paper, Ansoft HFSS is used to determine radiation per unit length, , and normalized phase propagation , according to different offset, . per unit length, As shown in Fig. 3, a family of SIWs is modeled and the is cut on the top broadside straight long slot with different is set to be 0.45 mm, and of each SIW. The slot width is varied at every 0.01 mm from 1.75 mm to 2.95 mm. To accurately determine , the conductor material, including metalized vias and conductor layers, is set to be the perfect electric conductor (PEC), while the dielectric material is considered lossless. The SIW is extended with the equivalent solid sidewalls on both sides for excitations with wave ports. Now, the attenuation figure represents the radiated power since there are no transition mismatching and losses involved. As shown in Fig. 4, varies and has a considerable dynamic range. smoothly with Using (3), accurate with different leakage is calculated by the study of simulated radiation patterns. As shown in Fig. 5, is 0.35 when increases from the absolute variation

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

Fig. 3. Model for investigating the relationship between  (or =k ) and x .

Fig. 6. Aperture distribution of Taylor distribution with and corresponding calculated pattern.

035 dB sidelobe level,

Fig. 4. Relationship between  and x .

Fig. 7. Design curve for leaky-wave antenna with Taylor distribution with 35 dB sidelobe level.

0

Fig. 5. Relationship between =k and x .

1.75 mm to 2.95 mm. The average value of different corresponding to the used can be used to estimate the beam direction. Here, the 35 GHz beam direction is predicted to be 41 . In the simulation, we find that varies more quickly with for a wider slot. For example, when is 0.2 mm, varies is 1.4 mm, only 0.23 dB/mm as varies by 1 mm. When varies 0.83 dB/mm as varies by 1 mm. As the increases, more power is radiated toward the beginning of slot. It is difficult to get radiated over the entire length of slot with the desired amplitude taper. Moreover, considering the increment in on such a large scale, it is more difficult to etch the required shape of long slot precisely by existing PCB process in millimeter-wave frequency range. Therefore, it is better to choose a narrow long slot to optimally design an antenna with superior radiation pattern. equals to 1.4 mm is the optimum On the other side, value which keeps near to a constant in this study. It only with a variation provides a maximum . As such, the normalized leaky mode phase constant can be kept almost unchanged along all the antenna length so that all section of the antenna radiate at the same pointing

angle. If the pointing direction of the antenna needs to be accu. rate designed, we should choose the optimum But in this paper, we attempt to make a leaky-wave antenna with superior radiation pattern. Based on the overall consideration of design requirements and machining accuracy, we finally choose to be 0.45 mm. 3) Offset at Different Position : In this step, we calcu( at different position ) according to the collapsed late , then obtain the offset at different aperture distribution position , . The experimental array is set to follow the Taylor distribution sidelobe level. The required aperture distribution with and calculated radiation pattern are shown in Fig. 6. There is a and the desired amplimathematical relationship between [6], tude distribution (6) It is assumed that the leaky-wave antenna is terminated with a load, which absorbs a fraction, , of the input power ( ). In this design, the terminating load is designed to take ) of the power as a compromise between an5% ( tenna efficiency and moderate peak value for . For the same reason, the slot length, , is set to be 115 mm. Then, the can be calculated by (6). Next, based on Fig. 4, is plotted as shown in Fig. 7. The shape of the meandering slot or the meandering sidewall can be read off. 4) Modeling, Simulation and Optimization: Up to now, we can model the long slot SIW leaky-wave antennas and optimize their performances. To simplify the modeling and optimization, several straight lines are used to approximate the continuous

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TABLE I DIMENSIONS OF TWO LEAKY-WAVE ANTENNAS (UNIT: mm).

Fig. 10. Photograph of the fabricated leaky-wave antennas.

Fig. 11. Simulated and measured S11 of the type 1 leaky-wave antenna. Fig. 8. Simulated patterns of type 2 leaky-wave antenna with a fabrication tolerance of 20 m at 35 GHz. (The black line denotes the simulated pattern free from any tolerance problem, and the grey lines denote the simulated patterns with errors).

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Fig. 12. Simulated and measured S11 of the type 2 leaky-wave antenna.

Fig. 9. Simulated patterns of type 2 leaky-wave antenna with a fabrication tolerance of 100 m at 35 GHz. (The black line denotes the simulated pattern free from any tolerance problem, and the grey lines denote the simulated patterns with errors).

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curve as shown in Fig. 7. As long as the number of segment is enough, the approximate outline would be acceptable. In this design, we separate the meandering slot or the meandering lateral wall into seven segments. After full-wave simulation and optimization, the final dimensions of the meandering slot or the meandering sidewall are tabulated in Table I. B. Tolerance As usual, substrate properties such as thickness and dielectric constant have some specific manufacturing tolerances. There are

also other factors in fabrication process that could affect the performances of a structure such as the accuracy of position and the size of metalized via. All these parameters are known to influence the slot offset, the slot length and the SIW dimensions, which make the electrical performances of the fabricated prototype different from that ideally designed one. Thus, a tolerance analysis becomes necessary especially in such a low sidelobe antenna design. In this paper, the fabrication tolerance of our PCB process is (uniform distribution). With first of all assumed to be such a tolerance, Fig. 8 gives thirty simulated radiation patterns for type 2 antenna. It can be found that there is no visible difference between them regarding beam direction, gain, and 3 dB beam-width except the sidelobe level. However, the sidelobe . The simulated sidelobe level levels are all below of the proposed antenna in the ideal case of fabrication (free

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TABLE II

H-PLANE MEASUREMENTS OF LEAKY-WAVE ANTENNAS AT 35 GHz

TABLE III MEASUREMENTS OF TYPE 1 LEAK-WAVE ANTENNA AT DIFFERENT FREQUENCY

Fig. 13. 35 GHz H-plane co-polar and cross-polar patterns of type 1.

TABLE IV MEASUREMENTS OF TYPE 2 LEAK-WAVE ANTENNA AT DIFFERENT FREQUENCY

Fig. 14. 35 GHz H-plane co-polar and cross-polar patterns of type 2.

important for a mass-fabrication. Similar analysis can be implemented to determine the tolerance requirement of the used dielectric substrate. C. Experiments

Fig. 15. Measured H-plane radiation patterns of type 1 versus frequency.

from any tolerance problem) is , which demonstrates that the sidelobe level is deteriorated just a little bit under this fabrication condition. In other words, it can achieve a reasonably good sidelobe level with a PCB fabrication tolerance of . Then, a similar analysis is carried out for such an an. As shown in tenna with a fabrication tolerance of Fig. 9, the worst sidelobe level is up to and the beam to . In this case, it is very directions are detuned from difficult to respect the design specifications. This study helps us to determine a permissible fabrication tolerance in order to achieve a desired performance. It is very

Two types of SIW long slot leaky-wave antennas were fabricated on single-layer Rogers5880 substrate through a standard PCB process as shown in Fig. 10. Both of them are fed by the standard WR-28 waveguide. This is necessary to avoid the direct radiation from feed discontinuity which can affect the antenna performances. The reflections of type 1 and type 2 antennas were measured using a network analyzer E8363B. Simulated results, for prototypes with and without transition between SIW and waveguide, are both shown in Figs. 11–12. It is demonstrated that the measured and simulated results are in good agreement. The leaky-wave antennas have excellent VSWR over a wide band, but it is deteriorated in practice due to the transition. The measured reflections of different antennas are almost below within 33~37 GHz. These leaky-wave antennas were characterized in anechoic chamber. The output ports were terminated with 50 loads. Figs. 13–14 show the measured -plane co-polar and crosspolar radiation patterns of different leaky-wave antennas at 35 GHz. Table II summarizes some measured data, such as beam

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TABLE V SIMULATIONS OF THE 2-D MULTIBEAM ANTENNA EXCITED AT DIFFERENT INPUT PORTS AND AT DIFFERENT FREQUENCY

Fig. 16. Measured H-plane radiation patterns of type 2 versus frequency.

Fig. 17. Simulated 3 dB beam-width contour radiation patterns excited at ports 1–10 and operated at different frequency.

direction, gain, sidelobe level, cross-polar level, 3 dB beamwidth, and radiation efficiency. It is demonstrated that type 2 antenna has a much better cross-polar characteristic. Both of the antennas were tested at every 0.5 GHz from 33 GHz to 37 GHz. As shown in Figs. 15–16, type 1 can cover an angular region , ) and type 2 can cover an angular region of of ( , ) with 3 dB beam-width. Detailed measured ( data are listed in Tables III–IV, which contain beam direction, gain, sidelobe level, and 3 dB beam-width. When frequency increases, the beam is moved toward the propagation direction of the leaky-wave. III. 2-D MULTIBEAM ANTENNA The leaky-wave antenna discussed above can produce a plane but a fan pencil beam with narrow beam-width in beam with wide beam-width in plane. As described before,

an array of leaky-wave antennas fed by a BFN or several phase shifters can scan in both elevation and azimuth directions. In brief, such an array is fed from one end and is scanned in elevation by varying frequency. Scanning in the cross-plane is produced by the BFN or phase shifters arranged in its feeding structure. The BFN must be a wide-band component and it has good performances within the frequency band of interest, which is needed by the frequency scanning antenna. In this work, we combine fourteen type 2 leaky-wave antennas with a broadband SIW BFN based on the parabolic reflector principle to realize a 2-D beam-scanning. In addition, this scheme costs less than the use of a millimeter-wave phased array because no expensive phase shifters are required. The design of such an SIW BFN can be referenced in [16]. It has ten input ports and fourteen output ports, and the focal length is 30 mm. Each output port is connected to a leaky-wave antenna. Simulated 3 dB beam-width contour radiation patterns of such a 2-D frequency-phase scanning structure are shown in Fig. 17, when it is excited at different ports and operated at different frequency. Because the array spacing normalized to wavelength varies with frequency, increasing the frequency enables moving those beams (excited at different ports) closer and plane. Simulated results of narrows the beam coverage in 33.5, 35 and 36.5 GHz excited at ports 1–10 are listed in Table V. When operation frequency varies from 33 GHz to 37 GHz, such a 2-D multibeam antenna can almost cover the angular region , ) to (41.2 , )( ) with 3 dB from ( beam-width. The whole circuit is integrated in a single-layer Rogers 5880 substrate with standard PCB process as shown in Fig. 18. Figs. 19–20 show the measured -plane far-field radiation patterns excited at ports 6 and 8 at every 1 GHz from 33 GHz to 37 GHz. For port 6, the gains are measured to be 17.1 dBi, 17.5 dBi, 18.3 dBi, 19.1 dBi, 18.9 dBi, the beam directions are , , , , , and measured to be the sidelobe level are measured to be , , , , at 33, 34, 35, 36 and 37 GHz. Varying frequency from 33 GHz to 37 GHz, the angular region of 37.5 in elevation can be covered by 3 dB beam-width of those continuous scanning beams excited at port 6. For port 8, the gains are measured to be 17.9 dBi, 18.1 dBi, 18.9 dBi, 19.2 , dBi, 19.1 dBi, the beam directions are measured to be , , , , and the sidelobe level are measured to be , , , ,

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Fig. 20. Measured H-plane patterns excited at input port 8 versus frequency. Fig. 18. Fabricated SIW 2-D multibeam antenna.

Fig. 21. Measured E-plane patterns excited at different ports at 35 GHz. Fig. 19. Measured H-plane patterns excited at input port 6 versus frequency.

at 33, 34, 35, 36 and 37 GHz. Varying frequency from 33 GHz to 37 GHz, the angular region of 38.9 in elevation can be covered by 3 dB beam-width of those continuous scanning beams excited at port 8. The similar range in elevation can be covered excited at other ports as well. Fig. 21 presents the measured -plane far-field radiation patterns excited at different input ports at 35 GHz. The gains are measured to be 17.5 dBi, 18.5 dBi, 18.9 dBi, 18.3 dBi, 17.3 dBi, the beam , , 2.0 , 22.6 , directions are measured to be 41.8 excited at ports 2, 4, 6, 8 and 10. Excited at ports 1–10 of such a 2-D multibeam antenna at 35 GHz, the angular region of 86.6 in azimuth can be covered by 3 dB beam-width of ten pencil beams. The similar results in azimuth can be achieved at other frequency. IV. CONCLUSION Two types of millimeter-wave SIW long slot leaky-wave antennas are studied in detailed and realized with controllable radiation properties. The first type has a meandering slot etched on the broadside of a straight SIW, while the other type has a straight slot etched on the broadside of a meandering SIW. Both of them can achieve the optimum sidelobe level below . In addition, the second type can improve the than

cross-polar level more than 11 dB compared with the first counterpart. Varying frequency from 33 GHz to 37 GHz, type 1 covers the angular region of 33.9 and type 2 covers the angular region of 35.3 in elevation direction with 3 dB beam-width. Then, a 2-D multibeam antenna is structured by such fourteen leaky-wave antennas and an SIW BFN. It can operate from 33 GHz to 37 GHz, and ten beams can be generated at each frequency point. The solid angular region can be covered by several beams in azimuth and elevation directions. REFERENCES [1] P. Bonnaval, “Directional slot antenna for very high frequency,” U.S. patent 3978485, Aug. 31, 1976. [2] G. S. Scharp, “Continuous slot antennas,” U.S. patent 4328502, May 4, 1982. [3] F. Whetten and C. A. Balanis, “Meandering long slot leaky-wave antennas,” IEEE Trans. Antennas Propag., vol. 39, no. 11, pp. 1553–1559, Nov. 1991. [4] J. W. Sheen and Y. D. Lin, “Propagation characteristics of the slotline first higher order mode,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 11, pp. 1774–1781, Nov. 1998. [5] J. Joubert and J. A. G. Malherbe, “Moment method calculation of the propagation constant for leaky-wave modes in slotted rectangular waveguide,” IEE Proc. Microw. Antennas Propag., vol. 146, no. 6, pp. 411–415, Dec. 1999. [6] R. S. Elliott, Antenna Theory and Design, revised ed. Piscataway, NJ: IEEE Press, 2003. [7] J. L. Gómez-Tornero, A. T. Martínez, D. C. Rebenaque, M. Gugliemi, and A. Álvarez-Melcón, “Design of tapered leaky-wave antennas in hybrid waveguide-planar technology for millimeter wave band applications,” IEEE Trans. Antennas Propag., vol. 53, no. 8, pp. 2563–2578, Aug. 2005.

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[8] J. L. Gómez-Tornero, G. Goussetis, A. P. Feresid, and A. Álvarez-Melcón, “Control of leaky-mode propagation and radiation properties in hybrid dielectric-waveguide printed-circuit technology: Experimental results,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3383–3390, Nov. 2006. [9] J. Zehentner, J. Machac, and P. Zabloudil, “Novel entire top surface planar leaky wave antenna,” in Proc. 37th European Microw. Conf., Munich, Oct. 2007, pp. 372–375. [10] J. L. Volakis, Antenna Engineering Handbook, 4th ed. New York: McGraw-Hill, 2007. [11] R. C. Hansen, Phased Array Antennas. New York: Wiley, 1998. [12] Y. J. Cheng, W. Hong, K. Wu, Z. Q. Kuai, C. Yu, J. X. Chen, J. Y. Zhou, and H. J. Tang, “Substrate integrated waveguide (SIW) Rotman lens and its Ka-band multibeam array antenna applications,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp. 2504–2513, Aug. 2008. [13] Y. J. Cheng, W. Hong, and K. Wu, “Millimeter-wave multibeam antenna based on eight-port hybrid,” IEEE Microw. Wireless Compon. Lett., vol. 19, no. 4, pp. 212–214, Apr. 2009. [14] Y. J. Cheng, W. Hong, and K. Wu, “Design of a substrate integrated waveguide modified R-KR lens for millimetre-wave application,” IET Microw. Antennas Propag., vol. 4, no. 4, pp. 484–491, Apr. 2010. [15] A. A. Oliner, “A new class of scannable millimeter wave antennas,” in Proc. 20th European Microw. Conf., Budapest, Sep. 1990, pp. 95–104. [16] Y. J. Cheng, W. Hong, and K. Wu, “Millimeter-wave substrate integrated waveguide multibeam antenna based on the parabolic reflector principle,” IEEE Trans. Antennas Propag., vol. 56, no. 9, pp. 3055–3058, Sep. 2008. [17] M. Ettorre, M. A. Neto, G. Gerini, and S. Maci, “Leaky-wave slot array antenna fed by a dual reflector system,” IEEE Trans. Antennas Propag., vol. 56, no. 10, pp. 3143–3149, Oct. 2008. [18] D. Deslandes and K. Wu, “Substrate integrated waveguide leaky-wave antenna: concept and design considerations,” presented at the Asia-Pacific Microwave Conf., 2005. [19] Y. Cassivi, L. Perregrini, P. Arcioni, M. Bressan, K. Wu, and G. Conciauro, “Dispersion characteristics of substrate integrated rectangular waveguide,” IEEE Microw. Wireless Compon. Lett., vol. 12, no. 9, pp. 333–335, Sep. 2002.

Yu Jian Cheng (S’08–M’11) received the B.S. degree from the University of Electronic Science and Technology of China, in 2005 and the Ph.D. degree (without going through the conventional Master’s degree) from Southeast University, Nanjing, China, in 2010. His current research interests include microwave and millimeter-wave circuits, integrated antennas. Mr. Cheng serves as a reviewer for the IEEE Microwave and Wireless Components Letters, IEEE Antennas and Propagation Magazine and IEEE/ASME Journal of Microelectromechanical Systems.

Wei Hong (M’92–SM’07) received the B.S. degree from the University of Information Engineering, Zhengzhou, China, in 1982, and the M.S. and Ph.D. degrees from Southeast University, Nanjing, China, in 1985 and 1988, respectively. Since 1988, he has been with the State Key Laboratory of Millimeter Waves and serves for the director of the lab since 2003, and is currently a professor and the associate dean of the School of Information Science and Engineering, Southeast University. In 1993, 1995, 1996, 1997 and 1998, he was a short-term Visiting Scholar with the University of California at Berkeley and at Santa Cruz, respectively. He has been engaged in numerical methods for electromagnetic problems, millimeter wave theory and technology, antennas, electromagnetic scattering, RF technology for wireless communications etc. He has authored and coauthored over 200 technical publications, and authored two books of Principle and Application of the Method of Lines and Domain Decomposition Methods for Electromagnetic Problems.

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Dr. Hong is a senior member of CIE. He was thrice awarded the first-class Science and Technology Progress Prizes issued by the Ministry of Education of China and Jiangsu Province Government. He also received the Foundations for China Distinguished Young Investigators and for “Innovation Group” issued by NSF of China. He is Vice-President of the Microwave Society and Antenna Society of CIE, Chairperson of the IEEE MTT-S/AP-S/EMC-S Joint Nanjing Chapter, served as an Associate Editor of IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUE, and is an editor board member for IJAP, RFMiCAE, etc.

Ke Wu (M’87–SM’92–F’01) is currently a Professor of electrical engineering, and Tier-I Canada Research Chair in RF and millimeter-wave engineering with the École Polytechnique of Montréal, Montréal, QC, Canada. He holds the first Cheung Kong Endowed Chair Professorship (visiting) with Southeast University, the first Sir Yue-Kong Pao Chair Professorship (visiting) with Ningbo University, and an Honorary Professorship with the Nanjing University of Science and Technology and the City University of Hong Kong. He has been the Director of the Poly-Grames Research Center and the founding Director of the Center for Radiofrequency Electronics Research of Quebec (Regroupement stratégique, FRQNT). He has also held guest and visiting professorship in many universities around the world. He has authored or coauthored over 730 referred papers and a number of books/book chapters. He has served on the Editorial/Review Boards of many technical journals, transactions, and letters, as well as scientific encyclopedias as both an editor and guest editor. He holds numerous patents. His current research interests involve substrate integrated circuits (SICs), antenna arrays, advanced computer-aided design (CAD) and modeling techniques, and development of low-cost RF and millimeter-wave transceivers and sensors for wireless systems and biomedical applications. He is also interested in the modeling and design of microwave photonic circuits and systems. Dr. Wu is a Fellow of the Canadian Academy of Engineering (CAE) and the Royal Society of Canada (The Canadian Academy of the Sciences and Humanities). He is a member of the Electromagnetics Academy, Sigma Xi, and the URSI. He has held key positions in and has served on various panels and international committees including the chair of Technical Program Committees, International Steering Committees, and international conferences/symposia. He will be the General Chair of the 2012 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS). He is currently the chair of the joint IEEE Chapters of MTTS/APS/LEOS, Montréal, QC, Canada. He is an elected IEEE MTT-S Administrative Committee (AdCom) member (2006–2012) and is the chair of the IEEE MTT-S Member and Geographic Activities (MGA) Committee. He is an IEEE MTT-S Distinguished Microwave Lecturer (2009–2011). He was the recipient of many awards and prizes including the first IEEE MTT-S Outstanding Young Engineer Award, the 2004 Fessenden Medal of the IEEE Canada, and the 2009 Thomas W. Eadie Medal of the Royal Society of Canada.

Yong Fan (M’05) received the B.E. degree from Nanjing University of Science and Technology, Nanjing, Jiangsu, China, in 1985 and the M.S. degree from University of Electronic Science and Technology of China, Chengdu, Sichuan, China, in 1992. He is now with the School of Electronic Engineering, University of Electronic Science and Technology of China. His current research interests include electromagnetic theory, millimeter-wave technology, communication and system. He has authored and coauthored over 130 papers. Mr. Fan is a senior member of the Chinese Institute of Electronics. He received the first award of science and technology of national industry, the second award of science and technology progress of ministry of electronic industry, the third award of science and technology progress of ministry of information industry, and the third award of science and technology progress of Sichuan province (twice).

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

Antenna Miniaturization Using Slow Wave Enhancement Factor from Loaded Transmission Line Models Pei-Ling Chi, Student Member, IEEE, Rod Waterhouse, Senior Member, IEEE, and Tatsuo Itoh, Life Fellow, IEEE

Abstract—Miniaturization of slow wave antennas exploiting the slow wave enhancement factor is presented. The printed antennas are periodically loaded with shunt capacitors to slow down the guided wave in the structures. In this paper, the loaded unit cell of the equivalent transmission line model is utilized to extract the slow wave enhancement factor, the ratio of the loaded to the unloaded propagation constants of the wave in the antennas. From this model, the slow wave enhancement factor of a loaded antenna agrees very well with the miniaturization factor, and therefore load parameters in the circuit model can be readily obtained when a specific size reduction is attempted. This claim was substantiated by demonstrating two small radiators, a high-frequency (HF) slotloop antenna and a planar inverted F antenna (PIFA), to achieve the desired size reductions. Experimental results show that both of the antennas demonstrate greater than ten-times size reduction from their unloaded counterparts at the expense of the degraded gains and impedance bandwidths. Specifically, the loaded slot loop presents the predicted gain and measured bandwidth on the order 2, respectively. Thereof 34 9 dBi and 0.38% for VSWR fore, a matching network derived from filter design techniques is proposed to increase the antenna bandwidth so that a measured fractional bandwidth of 1.78% is achieved. The slot loop combined with the impedance matching circuit occupies a footprint size of 0 031 0 0 017 0 at the operating frequency. On the other hand, the measured radiation gain and bandwidth of the loaded PIFA are reduced to 22 6 dBi and 0.15% for VSWR 2, respectively, with a footprint of 0 013 0 0 018 0 at the operating frequency. Index Terms—Periodic structure, slow wave, small antenna, transmission line model.

I. INTRODUCTION

A

S communication systems equipment is downsized substantially, their integral elements need to be reduced accordingly. Antennas usually occupy substantial real estate in the front-end modules, indicating that their sizes are critical to the overall volume. This is particularly crucial if the operating frequency is low such as in the high frequency (HF) band. There

Manuscript received April 01, 2009; revised October 13, 2009; accepted July 27, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported by the ONR STTR Phase II Program, Topic#: N06-T032. P.-L. Chi and T. Itoh are with the Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA 90095 USA (e-mail: peiling@ ee.ucla.edu). R. Waterhouse is with Pharad LLC, Glen Burnie, MD 21061 USA (e-mail: rwaterhouse@ pharad.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090452

have been many techniques employed to attempt size reduction. The application of high dielectric constant substrates to enhance the effective permittivity is the easiest way to reduce the guided wavelength and thus the physical size of antennas [1]–[3]. Similarly, magnetic materials of high permeability can be utilized for size reduction [4]. In [5], [6], footprints are reduced with particular antenna layouts, such as folded and meandered configurations. These complicated antenna structures are not straightforwardly determined, however, and they involve time-consuming parametric optimization. One class of miniaturization is to seek for particular materials of higher-order or controllable dispersion relations. For example, degenerate band edge crystals exhibit 4th order - curves at the band edges and thus resonances can be reduced to lower frequencies [7]. In addition, artificial left-handed metamaterials have been found capable of tailoring the dispersion characteristics to desired frequency responses by optimizing the constituent unit cells, which lend themselves to the application of miniaturization [8], [9]. Alternatively, antennas can be modeled as transmission lines, allowing the transmission line theory to be applied. In this scenario, a physically short transmission line can exhibit a considerable electrical length by increasing the equivalent inductance or/and capacitance per unit length. This results in a slow wave structure with an enhanced propagation constant. Examples of increasing the effective propagation constants are the inductive or capacitive elements loaded to the radiating elements [10]–[13] and the uniplanar compact photonic bandgap transmission line [14]. Slot-loop antennas have dipole-like radiation characteristics but provide wider impedance bandwidths [15]–[18]. Furthermore, capacitive loading is mechanically easier by mounting chip capacitors across the slot. By taking this advantage, a preliminary work for a slow wave slot loop has already been reported [19], where shunt capacitors were distributed periodically along the slot loop and the loaded transmission line model characterizing the slow wave antenna was briefly addressed. By the same token, the transmission line model was used to investigate the input impedance of a wideband spiral antenna [20]. In this paper, complete characterization of the developed antennas is carried out by the periodically loaded transmission line models. The load effect on the propagation constant, characteristic impedance, and appearance of the stop-band region versus the load parameters are studied thoroughly. By exploiting the transmission line model, the calculated slow wave enhancement factor, the ratio of the loaded to the unloaded propagation constants, agrees very well with the miniaturization factor. Subsequently, antennas can

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CHI et al.: ANTENNA MINIATURIZATION USING SWE FACTOR FROM LOADED TRANSMISSION LINE MODELS

be specifically miniaturized using those load parameters with the desired slow wave enhancement factor. In this paper, the developed capacitor-loaded HF slot-loop antenna and PIFA are significantly miniaturized based on this methodology and are capable of operating at one-eleventh the frequencies of the unloaded antennas. Antenna gains and impedance bandwidths are, however, deteriorated as a result of miniaturization. The predicted antenna gain and measured bandwidth of the loaded and 0.38% at 24 MHz, respectively. slot loop are In addition, the measured radiation gain and bandwidth of and 0.15% for the loaded PIFA are reduced to , respectively. Thereby, the trade-off of the radiation efficiency versus size reduction factor is investigated as well. The fundamental lower bound of the radiation quality factor ( ) derived by Chu indicates that the maximum impedance bandwidth is limited and can be increased at the expense of the efficiency or the system complexity. In the present paper, two impedance matching networks are developed for the miniaturized slot-loop antenna to overcome the issue of impedance mismatch. The first network is constructed based on an section matching circuit and is narrowband. On the other hand, an impedance matching network derived from filter design techniques is proposed to increase the antenna impedance bandwidth. The underlying principle of realizing this matching circuit is to regard the antenna as a resonant load around resonance, and the elements in the matching circuit can be determined by specifications as in filter designs [21]. Utilizing the virtues of the compactness and better performance of surface-mount chip components at UHF frequencies and lower, the proposed HF antenna with the filter-type matching circuit avoids a complicated layout [22] and its fractional bandwidth in the is substantially improved to 1.78% for , experiment while occupying a small area is the free space wavelength at resonance. where The configuration of this paper is as follows. In Section II, development of the equivalent transmission line is described along with the circuit characterization by giving an example. In the end, a design procedure that enables miniaturized antennas to be achieved is outlined. In Section III we present our antenna examples of how we applied the proposed slow wave procedure to printed antennas: a slot-loop antenna and PIFA. Simulated and measured results are given. In this section we also explain bandwidth of these electhe procedure used to enhance the trically small antennas. Section IV provides a summary of the results presented. II. DESIGN PROCEDURE OF A SLOW-WAVE BASED MINIATURIZED ANTENNA WITH FLEXIBLE SIZE REDUCTION In the present paper, slow wave structures periodically loaded with shunt capacitors are employed as the mechanism for antenna miniaturization with regards to the implementation convenience for the proposed antennas. When depicted in a dispersion ( - ) diagram, a capacitor-loaded slow wave structure and has a proprepresents a line underneath the air line agation mode with propagation constant larger than the propof the unloaded (host) structure, as shown agation constant in Fig. 1 along with an inset of the unit cell. Please note that the

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Fig. 1. The illustration of a capacitor-loaded slow wave structure in the k - diagram.

dispersion curve for the unloaded structure can be non-linear, which is the case when dispersive transmission lines are considered as the host lines, such as the microstrip lines and slot lines [23]. The propagation constant is a function of the load capacitance and period for a given host transmission line and as the entire structure is increasingly loaded by larger capacitance or/and smaller period, the corresponding is increased toward the abscissa and the loaded structure is electrically longer despite the same physical length. The loaded transmission line model with periodic boundary conditions is applied to characterize the behavior of a periodic loaded antenna and developed in the Advanced Design System (ADS). Please note that the loaded propagation constant is obtained from the ABCD matrix of a loaded unit cell, where the ABCD matrix characterizes the unique feature of a particular unit cell and therefore it is independent of the termination loads. Furthermore, when the periodicity is well maintained, the unit-cell model (as the inset shown in Fig. 1) can fully represent the property of the loaded structure, such as its propagaof the tion constant. Therefore, the characteristic impedance host transmission line, the load interval , and the load capacitance need to be determined. The characteristic impedance is determined by two steps. First, a particular transmission line best suited to describe the radiating element is assigned as the host transmission line. Second, the impedance is determined by antenna structural and material parameters. For example, a slot-loop antenna is represented by a slot line with depending on the slot width and substrate. In addition, the load interval and load capacitance are used as parameters to engineer the loaded propagation constant . An example is given here. The slow wave enhancement (SWE) factor, defined as the ratio of the loaded to the unloaded propagation constants as follows

(1) is of particular interest due to its proportionality to the miniaturization factor. Two approaches, viz. increasing the load capacitance and decreasing the load interval, are found effective to increase the propagation constant , or the SWE as indicated in [24]. Fig. 2 investigates the SWE with respect to the load capacitance of a capacitor-loaded unit cell. The characteristic

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Fig. 3. Variation of the Bloch impedance for the capacitor-loaded unit cell. The : and a capacitance sweep is from 10 pF to 100 pF with a fixed Z : at 300 MHz. load interval d =

= 7 6 degrees

Fig. 2. (a) The SWE ( = ) versus loaded shunt capacitance for the capacitorloaded unit cell. The capacitance sweep is from 10 pF to 100 pF with a fixed Z : and a load interval d = : at 300 MHz, (b) the corresponding frequency responses of the capacitor-loaded unit cell versus .

= 75 44

= 7 6 degrees

d

impedance of this unit cell is determined from a 2 mm wide , and slot line on a substrate of thickness 0.508 mm and thus is approximated to be 75.44 from the numerical equations provided in [25]. In addition, the electrical length of the ). As the unit cell is fixed at 7.6 degrees at 300 MHz ( capacitance is increased from 10 pF to 100 pF, the SWE is in) corresponds to the creased as expected and the unity ( unloaded case ( ). It is observed from Fig. 2(a) the rate of this enhancement is, however, diminished as the capacitance is continually increased. In addition, the stop bands are encountered as the structure is increasingly loaded when the SWE is inversely proportional to the frequency. These stop bands can be easily verified and occur at frequencies where the product is equal to as shown in Fig. 2(b). For implementation, one should avoid stop-band occurrences in the operational range of of the same example is also interest. The Bloch impedance investigated in Fig. 3 and is continuously decreased at a retarded rate as the capacitive load is increased. From the transmission line theory, the reduced impedance is expected as a result of the increase in the effective capacitance per unit cell (length). Moreover, the Bloch impedances approach zero at frequencies where the respective stop bands occur. In order to compensate the mismatch factor, a series inductance should be commensurately added as mentioned in [20]. In order to optimize antenna performance, the influence of the Bloch impedance (of a unit cell) on the input impedance is studied. Corresponding to the capacitor-loaded unit cell of the

= 75 44

Fig. 4. Calculated input VSWRs of the CPW-fed capacitor-loaded slot-loop antennas (with an inset) with 5 cases of different Z s. The corresponding quality factors (Qs) are included in the figure. The slot width, load period, substrate thickness and dielectric constant of the antennas are 2 mm, 20 mm, 0.508 mm, and 4.5, respectively.

slot line discussed previously, a slot-loop antenna fed by the 50 coplanar waveguide (CPW) is used. Input VSWRs of different Bloch impedances loops were calculated by full-wave simulations in the High Frequency Structure Simulator (HFSS). By periodically loading the slot loop with 1.2 pF, 5 pF, 25 pF, 60 pF, and 100 pF capacitors at an interval of 20 mm, Bloch ims of 49.89 , 29.91 , 14.3 , 9.32 , and 7.24 pedances are generated. As shown in Fig. 4, the impedance matching is not significantly improved as the Bloch impedance approaches 50 , which manifests the effect of the excitation mechanism. In addition, antenna miniaturization is observed from the increased radiation quality factor ( ), defined as the inverse of the 3-dB impedance fractional bandwidth (half-power bandwidth), as the is gradually reduced. Most importantly, Bloch impedance the miniaturization factor, as the resonance frequency of the unloaded antenna compared to the respective resonance frequencies of the loaded antenna in Fig. 4, coincides very well with the SWE obtained from the developed circuit model. Table I compares the miniaturization factors with SWEs based on the circuit model. Excellent agreement is achieved which implies the feasibility of the developed transmission line model. Practically, when a particular size reduction using the loaded slow wave antennas is attempted, the required structure can be implemented by employing the corresponding load parameters. In order to facilitate fabrication of the antenna prototype of interest (the slot-loop and PIFA), only shunt capacitors are considered in

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TABLE I FULL-WAVE MINIATURIZATION FACTOR VERSUS SWE FOR THE LOADED SLOT-LOOP ANTENNA

the present paper. The design procedure of a loaded slow wave antenna with specific miniaturization is as follows. Step 1) Establish the equivalent loaded unit cell for the loaded antenna. Three parameters involved in the of the model are the characteristic impedance host transmission line, the unit-cell electrical length , and the shunt capacitance . Step 2) Investigate the SWE as functions of the load parameters. The SWE is obtained by taking the ratio of the loaded to the unloaded propagation constants of the unit-cell circuits. Step 3) Employ those load parameters resulting in the desired SWE. Disregard those solutions with stop bands near or at frequencies of interest. Step 4) Consider other fabrication factors. For example, a small load period would increase the fabrication difficulty, leading to fabrication errors. In the following section, two miniaturized antennas based on the loaded slow wave structure are demonstrated as examples using the SWE approach. III. ANTENNA MINIATURIZATION USING THE SWE APPROACH A. The Capacitor-Loaded and Miniaturized HF Slot-Loop Antenna With -Section Matching Circuit Using predicted load parameters from the unit-cell circuit model, a miniaturization of the capacitor-loaded HF slot-loop antenna is demonstrated as follows. Furthermore, two matching networks are presented to improve the impedance performance of the small slot-loop antenna, including an -section matching circuit here and an advanced four-pole matching network based on the filter design techniques in Section III-B. The antenna prototype used for miniaturization is a slot loop. Applying the slot line model to this slot loop, the characteristic impedance for the slot line can be determined from the slot-loop width , substrate information, and the operating frequency. In this example, shunt capacitors are periodically distributed along the aperture. Fig. 5 illustrates the configuration of the proposed loaded HF slot-loop antenna. The associated unit-cell model can be referred to the inset in Fig. 2(a). Employing those particular and an substrate of thickvalues ( ness 0.508 mm) exemplified in Section II, the SWEs with re, and slot spect to the load capacitance , load period are investigated in Fig. 6. Each investigation is perline formed by one variable sweep at a time while the rest are kept as labeled. As expected, the SWE increases when the structure

Fig. 5. (a) The configuration of the proposed capacitor-loaded HF slot-loop antenna with the L-section matching circuit. (b) Photograph of the fabricated antenna.

is increasingly loaded (with increased load capacitance or decreased load interval). Furthermore, the SWE becomes larger with the host characteristic impedance. The shunt capacitance , at 300 MHz (20 mm), corresponds to a SWE of 10.4 as can be and observed in the figure. These values will be used for fabrication later. In viewpoint of miniaturization design, the slot width is able to engineer the SWE through the corresponding characof the loop. At around several hundred teristic impedance MHz the wider slot width corresponds to higher characteristic impedance, and therefore the higher miniaturization effectiveness. The input match of the antenna is not, however, benefited by choosing a particular slot width. This is shown already in Section II where the input VSWR of a 50 Bloch impedance loop is not satisfactory. In addition, from the antenna figure of merit, the radiation efficiency is almost unchanged with respect to the slot width. Therefore, in the present paper, the slot width of the loop is chosen at the convenience of capacitor placement. Fig. 5(b) shows the photograph of the proposed capacitor-loaded HF slot-loop antenna combined with the -section matching circuit. The slot-loop antenna was fed by CPW and and thickness built on an Arlon AR 450 substrate with 0.508 mm. The unloaded slot-loop antenna was designed to have one wavelength resonance at 255.2 MHz and is able to operate at high frequency (HF: 3–30 MHz) after proper size reduction. Here, the Vishay/Dale 1206 SMD 100 pF lumped capacitors are mounted across the slot and the dimensions for the fabricated slow wave slot-loop antenna are as follows (see Fig. 5(a)): , , , , , , , and

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Fig. 6. SWE investigation for the capacitor-loaded HF slot-loop antenna (a) SWE vs. load capacitance (b) SWE vs. load period (c) SWE vs. characteristic impedance of the slot line.

Fig. 7. Measured and calculated jS j of the loaded HF slot-loop antenna with and without the L-section matching circuit.

. The measurement was taken with the Anritsu MS2034A vector network analyzer. Fig. 7 shows the measured for the loaded slot-loop with and without and simulated the matching circuit. As observed from the figure, the measured responses agree well with the simulated results. Impedance matching matching is significantly improved due to the circuit where a series inductance and a shunt are used. The matched slot loop has capacitance of at 24 MHz with a fractional a measured , which is considerably bandwidth 0.38% for reduced as expected from its unloaded counterpart with a bandwidth 7.07%. Lumped elements are exploited for the compactness and easy implementation of the matching network, which avoids configuring space-consuming and complicated matching patterns especially in HF bands. From experimental results, the one wavelength resonant frequency was effectively reduced from the 255.2 MHz to 24 MHz, showing a size reduction of 10.6. Compared to the predicted SWE of 10.4, this result confirms the applicability using SWEs in designs of antenna miniaturization. Due to the limited facilities, our chamber can only accommodate radiation measurements down to 300 – 400 MHz. Therefore only the calculated radiation gains of the proposed loaded HF slot-loop antenna with matching circuits are presented. It should be noted that the predicted and measured results for the loaded PIFA (see Section III-C) are in good agreement. Fig. 8

Fig. 8. Calculated radiation gains of the loaded HF slot-loop antennas with the L-section and four-pole filter-type impedance matching networks, respectively.

shows the predicted radiation gains of the loaded antenna where dipole-like radiation patterns are observed as shown in [19]. The and principal planes of this antenna are parallel to the and planes in Fig. 5(a) respectively. From simulated results, the maximum radiation gain for the loaded slot-loop antenna (with radiation effiwith the matching circuit is ). This is resulted from the considerable size ciency reduction compared to the unloaded antenna. As a fundamental trade-off exists between size reduction and antenna radiation efficiency, a compromise needs to be made when considering size reduction. Fig. 9 establishes the HFSS calculated radiation efficiency with relation to the size reduction for both small antennas in this paper. The effect of the matching networks on the radiation efficiency of the HF slot-loop antenna is investigated as well. Both the conductor and dielectric losses are considered in our full-wave simulation. The lumped-element loss is not included here for two reasons. First, based on the comparison at the frequencies of interest (at around 400 MHz for the capacitors used in the loaded PIFA and at around 25 MHz for all the lumped elements used in the loaded slot-loop) the measured responses of the lumped elements are in good agreement with those of the respective ideal models. Second, to the best of the authors’ knowledge, the measured -parameters cannot be embedded

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Fig. 9. Predicted radiation efficiency  with respect to the size reduction.

into the HFSS simulation environment. The equivalent loss resistance needs to be extracted from the measured -parameters in order to simulate the behavior of a non-ideal lumped element in HFSS. Essentially, the radiation efficiency of the loaded HF antenna decreases with size reduction as electrically smaller antennas are well known for the poor radiation capability. Despite the good agreement between lossless models and measured results of lumped elements, the measured efficiency of the HF slot-loop antenna may suffer more losses (as compared to the predicted efficiency) from the fabrication error and the possible lumped-element loss provided that the nearby cable radiation is perfectly prevented (see Section III-C). Furthermore, when the -section impedance matching circuit is used, the radiation efficiency is reduced further. Higher density of current distribution on the metal surface around lumped elements (of matching networks) was observed in the model, which invokes increased conductor loss. Several approaches can be applied to improve the radiation efficiency. For example, antennas built on thicker substrates are prone to radiate [26]. Similar to the monopole concept, antennas backed with large ground planes are able to increase the forward directivity [27]. Moreover, stacked structures composed of antenna substrates mounted with a high dielectric superstrate can be employed [28]–[30]. All of the above methods, however, inevitably lead to bulky antenna structures and increasing fabrication expenses. Due to the large wavelength at HF frequencies, conventional man-portable antennas that can operate in this band typically have low gains. For example, a 10 foot monopole has a gain of at 2 MHz [31]. For applications such as approximately short range communications (less than 0.5 miles) and medium range communications (less than 12 miles) these levels of gain are acceptable. A new application currently under consideration for HF communications is for disaster recovery units. Here HF communications are being considered because of the advantageous propagation characteristics of this frequency range through concrete and other building materials as well as tunnels, or obstructed passages. Although exactly fair comparison is not possible, it is noted that the proposed slot-loop antenna has a lower radiation gain as compared to that of a size-comparable monopole antenna backed with the same ground plane dimensions as our antenna at 24 MHz. Our further investigation on the gain shows that the capacitive loading in our structure creates the current discontinuity and introduces the additional

Fig. 10. (a) Illustration and (b) corresponding implementation of the impedance matching network using filter design techniques [21] for the loaded HF slot-loop antenna. Four-pole prototype matching circuit (including the antenna) is used in this case.

ohmic loss, deteriorating the radiation efficiency. Nevertheless, due to the planar nature, the loaded slot-loop antenna provides higher portability and integrability with other components. B. The Proposed Filter-Type Matching Network for the Bandwidth-Improved HF Slot-Loop Antenna In last subsection, an -section matching circuit improved the impedance matching significantly. However, the instantaneous bandwidth is greatly limited due to the inherent property of the electrically small antennas. In order to effectively increase the bandwidth, in this subsection, the filter design technique [21] is applied to the realization of an increased bandwidth matching network for the miniature slot-loop antenna. The underlying principle of implementing antenna matching circuits based on the filter design approach is to consider the antenna to be a resonant load around resonance. In many situations, antennas can be approximated as series or parallel resonators over the frequency range of interest. Therefore, elements in the matching circuit are conceived as the remaining components in a band-pass filter and can be determined by the , circuit order , the maximum in-band attenuation and the equal-ripple fractional bandwidth . Using filter-like impedance matching circuits enables a considerable bandwidth improvement as desired. It is found, however, that the highfeature of the small antenna mainly restrict the capability. In addition, the degraded radiation efficiency of the HF slot-loop due to the lumped elements in filter-type matching circuit will be discussed later. The illustration of the impedance matching network under consideration is exhibited in Fig. 10(a). For the slot-loop antenna, it is observed that around resonance the input admittance locus of the antenna varies along a constant conductance circle and therefore is best suited to be modeled as a parallel resonator. In order to compensate for the high- of the antenna, a filter order equal to 4 is chosen and further increase in is found with diminishing bandwidth improvement. The admittance inverters s are introduced between stages to allow for input

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TABLE II LUMPED-ELEMENT PARAMETERS IN THE MATCHING CIRCUIT FOR THE LOADED SLOT-LOOP ANTENNA

impedance match to , usually 50 . Of many admittance inverter realizations, the particular circuit shown as the inset in Fig. 10(a) is used. Note that the negative shunt capacitance at both sides can be absorbed into the nearby capacitance in resonators or equivalently equated to an inductance. In other words, in place of the negative shunt ( ) is the equivalent

Fig. 11. Measured and calculated jS j of the loaded HF slot-loop antenna with the filter-type impedance matching network. The measured jS j of the HF slot-loop antenna with L-section matching circuit is included for comparison.

(2) where the resonant frequency of the antenna is used for narrowband approximation. Eventually, the corresponding implementation of the impedance matching network is of the config, , , uration shown in Fig. 10(b). The capacitances result from the corresponding capacitances in the center and and come of each inverter realization. The inductances from the negative capacitance equivalences as aforementioned. need to be adjusted Furthermore, the values of , , and for nearby negative shunt capacitances. The design specifica, tions of this filter-like matching circuit are as follows: , in-band ripple level , and . Based on these specific terms, lumped-element parameters in the matching network are determined and can be found using the look-up diagrams in [21]. Table II lists the element values. We sourced the lumped components for the matching circuit from Mouser Electronics Inc. The big capacitance or inductance was made up from several smaller values. Otherwise, exact (or close enough to) lumped element as shown in Table II was mounted. Thereby, 17 lumped-element values are employed in the matching network and as follows: Murata 0805 SMD Monolith 2.4 pF, Xicon 1206 Ceramic Chip 470 pF, Vishay/Vitramon 1206 Ceramic 430 pF, Kemet 1206 SMD Ceramic 51 pF, Vishay/Vitramon 1206 Ceramic 33 pF, Kemet 1206 SMD Ceramic 27 pF, Murata 0805 SMD Monolith 16 pF, Vishay/Vitramon 1206 Ceramic 15 pF, AVX 1206 SMD Ceramic 0.5 pF, Murata 0805 SMD Monolith 11 pF, Murata 0805 SMD Monolith 9 pF, Xicon 0805 Ceramic Chip 1 pF, AVX 0603 SMD Microwave Thin-F 0.4 pF, Dielectric Laboratories 0.7 pF, Vishay/Dale 1008 SMD Ind 68 nH, KOA Speer . SurSMD Ind 72 nH, and Vishay/Dale High Current 1.2 face mount chip components are used in the proposed matching circuit due to the compactness and implementation simplicity. As compared to the distributed and complicated layout in [22], the present HF matching network is beneficial especially when the space-saving and time-saving (optimization iterations are reduced) designs are concerned. of the slot-loop antenna Fig. 11 shows the measured with the filter-type impedance matching circuit, where the photograph of the matching circuit is inserted. Please note that

Fig. 12. The configuration of the proposed capacitor-loaded PIFA with an inset of its unit-cell model.

matching circuit was connected to the antenna in the measurement and the introduced electrical length between these two is negligible at such a low frequency (HF). The simulated result is included for comparison. Note that the calculated double resonances are decreased to a single resonance in the experiment. This is ascribed to the lowered inter-coupling between resonators and might be resulted from the tolerance of lumped-element values in the matching circuit. In addition, as mentioned previously, bandwidth is broadened due to the degraded quality factor from fabrication error. Most importantly, the instantaneous bandwidth is enlarged significantly as shown with the -section in Fig. 11, where the set of antenna and filter-type impedance matching circuits are compared. Note that the higher resonant frequency is obtained for the antenna with the filter-type impedance matching network. This is a consequence of the addition of a shunt inductance to the resonant antenna in order for wider fractional bandwidth implementation. The impedance bandwidth is improved from 0.38% ( -section circuit) to 1.78% (filter-type circuit) due to the employment of the filter-type matching circuit. The assembly of the miniaturized slot-loop antenna with the proposed impedance matching network demonstrates a wider impedance , match of 1.78% while requiring a small area where is the free space wavelength at operational frequency.

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Fig. 13. SWE investigation for the capacitor-loaded PIFA (a) SWE vs. load capacitance, (b) SWE vs. load period, (c) SWE vs. characteristic impedance of the microstrip line.

Radiation patterns of this antenna are calculated and shown in Fig. 8 as well. Compared to the antenna with the -section matching network, reduced radiation efficiency in Fig. 9 is observed for the antenna employing the filter-type matching is further denetwork. This calculated efficiency . Although graded from the previous antenna with ideal lumped elements are modeled in simulation, it should be noted that current discontinuity due to the increased number of lumped elements in the matching network (the filter-type circuit) will lead to a higher conductor loss as compared to the antenna with a simpler matching network (the -section circuit). The inference of dense current distribution around the filter-type matching network is observed in the full-wave simulation.

Fig. 14. Photograph of the fabricated capacitor-loaded PIFA.

C. The Capacitor-Loaded and Miniaturized PIFA In this subsection, a loaded and miniaturized PIFA is given as an example based on the SWE design methodology. The patch with antenna prototype used for miniaturization is a shorting pins connected to the bottom ground plane of the substrate at one end. Applying the microstrip line model to this of the equivalent patch, the characteristic impedance transmission line can be determined by the geometrical and material parameters of the patch. In addition, shunt capacitors are mounted in parallel along the longitudinal direction. Fig. 12 depicts the configuration of the proposed capacitor-loaded PIFA with its unit-cell model. The SWE as functions of the , and host-line charload capacitance , load period was investigated using the unit-cell acteristic impedance model and shown in Fig. 13. Each SWE curve is obtained by a respective parameter sweep when the other two are fixed as indicated in legend. The cross, triangle, and square symbols are associated with the load capacitance sweep, load period sweep, and host line characteristic impedance sweep, respectively. As before, the SWE increases when the structure is increasingly loaded (with increased load capacitance or decreased load period). Furthermore, the SWE increases with the host characteristic impedance. The combination of shunt capacitance , at 4 GHz (1.5 mm), and provides a SWE of 9.485 and is chosen for implementation. Fig. 14 shows the photograph of the fabricated loaded PIFA fed by a coaxial cable. The loaded antenna was built on a Rogers

RT/Duroid 5880 substrate with and thickness 3.175 mm. The Murata 0805 SMD Monolith 8 pF shunt capacitors resonance. The diare mounted laterally in the direction of mensions for this slow wave PIFA are as follows (see Fig. 12): , , , and . Please note that the loaded PIFA has identical dimensions as the unloaded PIFA, except loaded by capacitors. The measurement was taken with the Anritsu MS2034A vector network analyzer. Fig. 15 depicts the measured and simfor both the loaded and unloaded antennas. The ulated experimental results show good agreement with the simulated of at data. The unloaded PIFA has a measured 3.98 GHz with a fractional bandwidth 4.07% for while the of the loaded PIFA is at 0.374 GHz with a fractional bandwidth 0.15%. The significantly reduced bandwidth is the typical feature of electrically small antennas. Moreover, the measured impedance bandwidths for both cases are wider than the simulated results. In other words, a lowered quality factor is resulted from the experiment and may be ascribed to the extra loss from the fabrication error. The skewed response at around 0.4 GHz may be ascribed to two reasons. First, the experimental period of the capacitors placement may be less than that (1.5 mm) in simulation, which increases the miniaturization factor due to a heavier loading. Second, the tolerance from the shunt capacitors will also lead to a resonance resfrequency shift. As observed from the responses, the onant frequency was effectively reduced from the 3.98 GHz to

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of the loaded PIFA is also shown in Fig. 9 and it drops significantly compared to the loaded slot-loop antenna. This can be attributed to the significant conductor loss associated with the PIFA, which has much higher current density on the small patch. IV. CONCLUSION

Fig. 15. Measured and calculated jS

j

for the loaded and unloaded PIFAs.

In the present paper, two antennas are significantly miniaturized using slow wave structures obtained by periodically loading shunt capacitors. Implementation is accelerated by employing those load parameters leading to a SWE for the desired size reduction. The experimental data show that the electrical sizes of the loaded and matched antennas are reduced to one-eleventh of their respectively unloaded counterparts. The radiation capability and impedance bandwidth, however, degrade rapidly for both antennas. The predicted antenna gain and measured bandwidth for the loaded slot loop are and 0.38% at 24 MHz, respectively. The further implementation of the proposed filter-type matching circuit on the loaded slot loop improves the bandwidth to 1.78% and meanwhile, the entire structure occupies a small footprint of , where is the free space wavelength at operational frequency. In addition, the measured radiation gain and 0.15%, respecand bandwidth are reduced to tively, for the electrically very small PIFA with a footprint of at the operational frequency. Measured results validate the efficiency of the proposed design approach. ACKNOWLEDGMENT

Fig. 16. Measured and calculated radiation patterns for the (a) loaded and (b) unloaded PIFAs.

0.374 GHz, which shows a size reduction of 10.6. The loaded at 0.374 PIFA occupies a small footprint of GHz. The excellent approximation to experimental miniaturization verifies the effectiveness of using the circuit-based SWE for loaded and miniaturized antenna designs. Furthermore, normalized radiation patterns of the proposed loaded and unloaded PIFAs were measured and compared to the calculated results in Fig. 16. Good agreement is observed. The and principal and planes in planes of this antenna are parallel to the Fig. 12 respectively. Note that the shielding effect on the backward radiation is reduced notably in the loaded situation since the electrical size of the ground plane is shrunk accordingly with operating frequency reduction. In order to prevent radiation from the coaxial cable, the ferrite beads were connected to prevent current flowing on the cable. The measured maximum , which is radiation gain for this loaded antenna is accurately predicted in the full-wave simulation with a peak ra( ). The measurement diation gain of accuracy for the small antennas might have contributed to the gain deviation. As mentioned previously, though ferrite beads were used during the measurement, there still can be some that leaks through the cable. Moreover, the broadening of the response might contribute to additional radiation gain. In addition, this loaded antenna is operating near the performance edge of our chamber (400 MHz). The calculated radiation efficiency

The authors gratefully acknowledge the support of, and technical discussions with, D. Arceo, J. Rockway and J. Allen from SPAWAR, San Diego. REFERENCES [1] T. K. Lo, C. –O. Ho, Y. Hwang, E. K. W. Lam, and B. Lee, “Miniature aperture-coupled microstrip antenna of very high permittivity,” Electron. Lett., vol. 33, no. 1, pp. 9–10, Jan. 1997. [2] K. Hettak and G. Y. Delisle, “A novel reduced size CPW-coupled patch antenna topology for millimeter waves applications,” in Proc. IEEE AP-S Int. Symp., Jun. 20–25, 2004, pp. 3840–3843. [3] K. W. Leung and K. M. Luk, “Circular dielectric resonator antenna of high dielectric constant for low-profile applications,” in Proc. IEE Antennas and Propag. Conf., Apr. 4–7, 1995, pp. 517–519. [4] Y. Shirakata, N. Hidaka, M. Ishitsuka, A. Teramoto, and T. Ohmi, “High permeability and low loss Ni-Fe composite material for high-frequency applications,” IEEE Trans. Magn., vol. 44, pp. 2100–2106, Sep. 2008. [5] Z. Chen, T. See, and X. Qing, “Ultra-wideband antennas with miniaturized size, reduced ground plane reliance, and enhanced diversity,” in Proc. IEEE iWAT Int. Workshop, Mar. 4–6, 2008, pp. 24–27. [6] A. Djaiz, T. Denidni, and M. Nedil, “A new CPW-feed miniaturized antenna with bandwidth enhancement for biomedical localization applications,” in Proc. IEEE AP-S Int. Symp., Jun. 9–15, 2007, pp. 5439–5442. [7] G. Mumcu, K. Sertel, and J. L. Volakis, “Miniature antenna using printed coupled lines emulating degenerate band edge crystals,” IEEE Trans. Antennas Propag., vol. 57, no. 6, pp. 1618–1624, Jun. 2009. [8] C. –J. Lee, K. M. K. H. Leong, and T. Itoh, “Compact dual-band antenna using an anisotropic metamaterial,” in Proc. 36th Eur. Microw. Conf., Sep. 10–15, 2006, pp. 1044–1047. [9] C. –J. Lee, K. M. K. H. Leong, and T. Itoh, “Composite right/lefthanded transmission line based compact resonant antennas for RF module integration,” IEEE Trans. Antennas Propag., vol. 54, no. 8, pp. 2283–2291, Aug. 2006.

CHI et al.: ANTENNA MINIATURIZATION USING SWE FACTOR FROM LOADED TRANSMISSION LINE MODELS

[10] N. Behdad and K. Sarabandi, “Bandwidth enhancement and further size reduction of a class of miniaturized slot antennas,” IEEE Trans. Antennas Propag., vol. 52, no. 8, pp. 1928–1935, Aug. 2004. [11] C. Chiu, K. Shum, and C. Chan, “A tunable via-patch loaded PIFA with size reduction,” IEEE Trans. Antennas Propag., vol. 55, no. 1, pp. 65–71, Jan. 2007. [12] C. Rowell and R. Murch, “A capacitively loaded PIFA for compact mobile telephone handsets,” IEEE Trans. Antennas Propag., vol. 45, no. 5, pp. 837–842, May 1997. [13] R. Azadegan and K. Sarabandi, “A novel approach for miniaturization of slot antennas,” IEEE Trans. Antennas Propag., vol. 51, no. 3, pp. 421–429, Mar. 2003. [14] F. -R. Yang, K. -P. Ma, Y. Qian, and T. Itoh, “A uniplanar compact photonic-bandgap (UC-PBG) structure and its applications for microwave circuits,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 8, pp. 1509–1514, Aug. 1999. [15] J. –S. Chen, “Triple-frequency annular-ring slot antennas fed by CPW and microstrip line,” in Proc. IEEE AP-S Int. Symp., Jun. 22–27, 2003, pp. 557–560. [16] W. –S. Chen and K. –L. Wong, “A compact waveguide-fed printed slot antenna for dual-frequency operation,” in IEEE AP-S Int. Symp., Jul. 8–13, 2001, pp. 140–143. [17] G. Forma and J. M. Laheurte, “Compact oscillating slot loop antenna with conductor backing,” Electron. Lett., vol. 32, no. 18, pp. 1633–1635, Aug. 1996. [18] N. Lenin and P. H. Rao, “Broadband printed square slot loop antenna,” in Proc. IEEE AP-S Int. Symp., Jul. 3–8, 2005, pp. 557–560. [19] P. -L. Chi, K. Leong, R. Waterhouse, and T. Itoh, “A miniaturized CPW-fed capacitor-loaded slot-loop antenna,” in Proc. IEEE ISSSE Int. Symp., Jul.-Aug. 30–2, 2007, pp. 595–598. [20] M. Lee, B. A. Kramer, C.–C. Chen, and J. L. Volakis, “Distributed lumped loads and lossy transmission line model for wideband spiral antenna miniaturization and characterization,” IEEE Trans. Antennas Propag., vol. 55, no. 10, pp. 2671–2678, Oct. 2007. [21] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance- Matching Networks, and Coupling Structures. New York: McGraw-Hill, 1964, sec. 8.03, 11.08. [22] Y. Tsutsumi, H. Kanaya, and K. Yoshida, “Design and performance of an electrically small slot loop antenna with a miniaturized superconducting matching circuit,” IEEE Trans. Appl. Supercond., vol. 15, no. 2, pp. 1020–1023, Jun. 2005. [23] K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed. Boston, MA: Artech House, 1996. [24] D. M. Pozar, Microwave Engineering, 2nd ed. New York: Wiley, 1998. [25] R. Janaswamy and D. H. Schaubert, “Characteristic impedance of a wide slotline on low-permittivity substrates,” IEEE Trans. Microw. Theory Tech., vol. 34, no. 8, pp. 900–902, Aug. 1986. [26] W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd ed. New York: Wiley, 1998, ch. 5, p. 215. [27] M.–C. Huynh and W. Stutzman, “Ground plane effects on planar inverted-F antenna (PIFA) performance,” IEE Proc. Microw. Antennas Propag., vol. 150, no. 4, Aug. 2003. [28] W. Tan, Z. Shen, and Z. Shao, “Radiation of high-gain cavity-backed slot antennas through a two-layer superstrate,” IEEE Antennas Propag. Mag., vol. 50, no. 3, pp. 78–87, Jun. 2008. [29] H. Vettikalladi, O. Lafond, and M. Himdi, “High-efficient and highgain superstrate antenna for 60-GHz indoor communication,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 1422–1425, 2009. [30] C. –Y. Huang, J. –Y. Wu, and K. –L. Wong, “High-gain compact circularly polarized microstrip antenna,” Electron. Lett., vol. 34, no. 8, pp. 712–713, Apr. 1998. [31] Model No. RR6309 Raven Research [Online]. Available: www.ravenresearch.com Pei-Ling Chi (S’08) received the B.S. and M.S. degrees in communication engineering from National Chiao Tung University (NCTU), Hsinchu, Taiwan, R.O.C., in 2004 and 2006, respectively. She is currently working toward the Ph.D. degree at the University of California at Los Angeles (UCLA). Her research interests include the analysis and design of antennas and microwave circuits.

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Rod Waterhouse (S’90–M’92–SM’01) received the B.Eng., M.S., and Ph.D. degrees in electrical engineering from the University of Queensland, Australia, in 1987, 1989, and 1994, respectively. In 1994, he joined RMIT University as a Lecturer and become a Senior Lecturer in 1997, and an Associate Professor in 2002. From 2001 to 2003, he was with the venture-backed Dorsal Networks which was later acquired by Corvis Corporation. In 2004, he co-founded Pharad, an antenna and wireless communications company, where he is now Vice President. He is also a Senior Fellow within the Department of Electrical and Electronic Engineering, University of Melbourne. His research interests include antennas, electromagnetics and microwave photonics engineering. He has over 260 publications in these fields, including two books and four book chapters. Dr. Waterhouse is an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATIONS. He chaired the IEEE Victorian MTTS/APS Chapter from 1998 to 2001 and in 2000 received an IEEE Third Millennium Medal for Outstanding Achievements and Contributions.

Tatsuo Itoh (S’69–M’69–SM’74–F’82–LF’06) received the Ph.D. degree in electrical engineering from the University of Illinois, Urbana, in 1969. From September 1966 to April 1976, he was with the Electrical Engineering Department, University of Illinois. From April 1976 to August 1977, he was a Senior Research Engineer in the Radio Physics Laboratory, SRI International, Menlo Park, CA. From August 1977 to June 1978, he was an Associate Professor at the University of Kentucky, Lexington. In July 1978, he joined the faculty at The University of Texas at Austin, where he became a Professor of Electrical Engineering in 1981 and Director of the Electrical Engineering Research Laboratory in 1984. During the summer of 1979, he was a guest researcher at AEG-Telefunken, Ulm, West Germany. In September 1983, he was selected to hold the Hayden Head Centennial Professorship of Engineering at The University of Texas. In September 1984, he was appointed Associate Chairman for Research and Planning of the Electrical and Computer Engineering Department at The University of Texas. In January 1991, he joined the University of California, Los Angeles as Professor of Electrical Engineering and holder of the TRW Endowed Chair in Microwave and Millimeter Wave Electronics (currently Northrop Grumman Endowed Chair). He was an Honorary Visiting Professor at Nanjing Institute of Technology, China and at Japan Defense Academy. In April 1994, he was appointed as Adjunct Research Officer for Communications Research Laboratory, Ministry of Post and Telecommunication, Tokyo, Japan. He currently was Visiting Professor at University of Leeds, United Kingdom. He has published 375 journal publications, 775 refereed conference presentations and has written 43 books/book chapters in the area of microwaves, millimeter-waves, antennas and numerical electromagnetics. He generated 68 Ph.D. students. Dr. Itoh is a Fellow of the IEEE, a member of the Institute of Electronics and Communication Engineers of Japan, and Commissions B and D of USNC/URSI. He received a number of awards including the Shida Award from Japanese Ministry of Post and Telecommunications in 1998, Japan Microwave Prize in 1998, IEEE Third Millennium Medal in 2000, and IEEE MTT Distinguished Educator Award in 2000. He was an elected member of National Academy of Engineering in 2003. He served as an Associate Editor of the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES from 1983 to 1985. He serves on the Administrative Committee of the IEEE Microwave Theory and Techniques Society. He was Vice President of the Microwave Theory and Techniques Society in 1989 and President in 1990. He was the Editor-in-Chief of the IEEE Microwave and Guided Wave Letters from 1991 through 1994. He was elected as an Honorary Life Member of MTT Society in 1994. He was the Chairman of USNC/URSI Commission D from 1988 to 1990, and Chairman of Commission D of the International URSI from 1993 to 1996. He was Chair of Long Range Planning Committee of URSI. He serves on advisory boards and committees of a number of organizations. He served as Distinguished Microwave Lecturer on Microwave Applications of Metamaterial Structures of IEEE MTT-S for 2004 – 2006.

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Topology Optimization of Sub-Wavelength Antennas Aycan Erentok and Ole Sigmund

Abstract—We propose a topology optimization strategy for the systematic design of a three-dimensional (3D), conductor-based sub-wavelength antenna. The post-processed finite-element (FE) models of the optimized structure are shown to be self-resonant, efficient and exhibit distorted omnidirectional, elliptically polarized value far-field radiation patterns. The computed approximate for this antenna is ( 0) 7 74 for 0 = 2 350 8 MHz and it is 1.64 times larger than the theoretical lower bound value. Index Terms—Antenna design, electrically small antennas, factor, topology optimization.

I. INTRODUCTION

E

MERGING wireless communication applications demand antenna technologies that offer compact antennas with large operating frequency bandwidth, 50 Ohms impedance matching at the RF front-end component interface, certain pattern characteristics (elliptical and/or circular polarization), good isolation to neighboring radiating systems and high radiation efficiency. The market also asks for cost effective configurations that can be easily integrated with other RF front-end components. These requirements, however, are contradictory in nature [1]–[3]; and thus, achieving these specifications is a challenging problem in antenna design technology. For example, an electric dipole with decreasing frequency exhibits decreasing radiation resistance and increasing capacitance producing a large impedance mismatch to any common RF front-end component [4]. In addition, achievable operational bandwidth is fundamentally bounded by the inverse of the so-called Chu-limit [5]–[10]. The earlier work in small antenna design technology is extensively covered in [11]. The more recent approaches to achieve this goal include fractal curve antennas [12]–[15], electrically small microstrip patches incorporating shorting ports [16], space-filling curve antennas [17]–[20], packing of conductor wires into an electrically small volume using folded spherical helix geometry [21], [22], a small disk-loaded folded monopole [23], spherically shaped conductor radiators consisting of identical conductor arms arranged in axially symmetric fashion Manuscript received November 23, 2008; revised August 17, 2009; accepted July 27, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported in part by the Danish Agency for Science, Technology and Innovation through the grant “Topology Optimization of Electromagnetic Metamaterials for Miniaturization of Wireless Communication Antennas (TopAnt)” and in part by an Eurohorcs/ESF European Young Investigator Award (EURYI, www.esf.org/euryi). A. Erentok was with the Technical University of Denmark, Lyngby DK-2800, Denmark. He is now with NOKIA, Ulm D-89081, Germany (e-mail: aycan. [email protected]). O. Sigmund is with the Department of Mechanical Engineering, Section for Solid Mechanics, Technical University of Denmark, Lyngby DK-2800, Denmark (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090451

[24], electrically small/compact metamaterial-based antennas [26]–[30] and metamaterial-inspired antennas [31]. Because they rely on various combinations of circuit and radiating components, they all have benefits and drawbacks. This paper proposes a systematic design paradigm for three-dimensional (3D), conductor-based sub-wavelength antenna design based on the topology optimization method. From early on, particular antenna topologies have been optimized based on parameter studies and more systematic gradient based algorithms. However, here the obtainable efficiency is dependent on the right choice of the initial antenna topology. More recently, a number of studies have optimized the antenna topologies themselves using evolutionary methods like Genetic Algorithms [32]–[35] and Particle Swarm methods [36], [37]. Such non-deterministic methods require huge amounts of function evaluations which limits their use to rather simple optimization problems with relatively few design variables and rather cheap performance evaluations. In contrast to these, the gradient-based topology optimization method [38], [39] usually converges within a few hundred function evaluations even for number of design variables in the order of tens or hundreds of thousands. The topology optimization method was originally developed for mechanical problems but has been applied to a number of other physical application areas [39], including electromagnetic applications like photonic crystal-based waveguides [40], [41], band gap materials [42] and dielectric patch antennas [43]–[45]. To our knowledge the previous applications of topology optimization to electromagnetic problems all considered distribution of dielectric materials, hence we believe that this paper is the first to solve electromagnetic problems with optimal distribution of solely conducting (metallic) material. The proposed topology optimization strategy for the systematic design of conductor based antennas can be applied to any kind of simple or complex design domain geometries. The outcome of the optimization process may not always be a novel antenna design but may provide structures similar to existing antenna concepts confirming the efficiencies of these existing designs. This paper focuses on one simple design domain scenario, and discusses the RF performance of the resulting topology optimized antenna. In this presentation, we use two methods to compute the apof a tuned antenna: a) approximate proximate quality factor value evaluated using antenna’s impedance at its input terminals [46, Eq. 96] and b) approximate value obtained using an exact matched voltage-wave-standing-ratio (VSWR) bandwidth of a tuned antenna [46, Eq. 95]. The approximate value of a single resonant antenna is given by

(1) where is the antenna’s feed point impedance at the resonant frequency. Throughout the paper,

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the fractional matched VSWR bandwidth of a tuned antenna is computed for a specific value about its tuned frequency under the condition that the characteristic feedof is equal to the antenna’s tuned impedance line impedance at , where parameter correspond to a constant VSWR value. The approximate value obtained from the exact matched VSWR bandwidth for is (2) is the fractional matched VSWR bandwidth where at . The approximate values computed using (1) and (2) are based on the assumption that the resonant frequency ranges are far away from antiresonant ranges, e.g., the absolute derivative of the real part of the impedance is much smaller that the derivative of the imaginary part of the impedance at the resonant frequency [46, Eq. 27]. The lower bound on the quality factor for a circular polarized antenna is approximately half that of a linearly polarized antenna and expressed as [10, Eq. 30] (3) where and are the radiation efficiency and the electrical radius of the antenna at , respectively. The ratio of the computed approximate quality factor obtained from (1) or (2) to the lower bound on the quality factor obtained for a circular polaris . ized antenna at As a matter of definitions to be used throughout this paper, an time dependence is assumed throughout. An electrically small antenna in free space is defined by the constraint , where the free space wavelength , that being the frequency of operation and is the speed of light, is the corresponding wave number, and is the radius of an imaginary sphere circumscribing the maximum dimension of the antenna. Free space is defined with , where and are the free space permittivity and permeability values, respectively. The conductivity of the copper . material used in all of the numerical cases is II. TOPOLOGY OPTIMIZATION In conventional optimization approaches the topology is fixed a priori and simple sizing and shape parameters constitute the design variables. In the topology optimization approach material can be distributed freely in the design domain without any geometrical restrictions, allowing for complex geometrical and topological changes. Simply explained the topology optimization method consists of the following steps. First, a modeling coaxial cable, indomain including also a finite perfect electric conductor (PEC) ground plane and radiation boundary condition is discretized using a finite element (FE) method. A subset of the modeling domain is defined as the design domain. The antenna structure is defined by the distribution of conductor material in the design domain. This distribution is determined by an element-wise conductor density , for , where distribution is the total number of designs variables corresponding to the number of elements that are used to mesh the design domain.

Fig. 1. The flow of computations for the density-based topology optimization method.

Next follows an iterative procedure consisting of alternating finite element analyses, sensitivity analyses and math-programming based density design updates. Despite of large numbers in the order of – ), converof design variables (i.e., gence is typically obtained within a few hundred iterations (FE evaluations). Fig. 1 shows the flow of computations for the density-based topology optimization method. The challenges in applying the topology optimization method to new physical application consist in: a) setting up an efficient and accurate FE model, b) defining appropriate objective and constraint functions, c) defining a proper function for the relation between the density (design variable) and material property (here conductivity) and d) deriving the sensitivities for the gradient-based optimization approach. In the following we discuss these four issues in more detail. A. FEM-Model When dealing with a known antenna geometry it is customary to model conductor-air interfaces with either PEC boundary conditions or as impedance boundary conditions. In this way there is no need for discretizations finer than the skin-depth in order to model this effect accurately. When, as in topology optimization, the geometry is unknown, it is not immediately possible to use PEC or impedance boundary conditions and hence we must in principle work with a very fine discretization to resolve the skin-depth. 1 With our present computational resources and the considered problem dimensions it has not been possible to obtain a discretization that provides convergence of the stored energy. However, our numerical studies indicate that the transmitted energy does converge even for rather coarse discretizations. Although the measure of the stored energy may be inaccurate for the FE-model used in the topology optimization process, we perform a post-processing of the optimized designs 1We are currently developing a new finite element formulation that allows for impedance boundary conditions on each element edge and hence will alleviate the need for fine discretizations to resolve the skin depth. So far the idea has been implemented for planar problems [47] but in future work it will be extended to 3D and antenna design.

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and model them with the appropriate impedance boundary conditions in order to provide accurate performance estimates of the final designs. B. Objective and Constraint Functions For the antenna design problem, several goals (objective functions) of the optimization can be thought of. If we want an antenna with high radiation efficiency and large bandwidth, the most obvious objective function will be to minimize the quality factor , i.e., the ratio between the stored energy and the radiated power. However, as discussed above, we do not have an accurate estimate of the stored energy. The research studies on large bandwidth electrically small antennas show that a passive, self-resonant antenna can demonstrate a low behavior if the radiator utilizes its available design volume efficiently [1], [2], [4], [5], [22]–[24]. In this study, we force optimization to use only a spherical shell volume to design a radiator, i.e., this configuration provides the largest electrically small antenna volume for given domain radius at design frequency. A large operational bandwidth should be observed if the optimization can maximize the radiated power at the far-field region by defining a 3D spherical shell based geometry from thousands of design variables at the design frequency. We thus focus our objective function to optimize the radiated power at the far-field region obtained from a 3D spherical shell domain coaxial cable. Although the that is fed by a geometry of the design domain considered here is quite simple, one of the advantages of the topology optimization method is that it can be applied to any kind of simple or complex design domain geometries and hence also to design domains conforming to prespecified surfaces like e.g., mobile phone covers. The radiated power is approximated by the integrated power density in the far-field region using (4) and are the electric-field vector, the free-space where , impedance and the infinitesimal area on the surface of a hemisphere of radius at the far-field region, respectively. Note that this measure of the radiated power is an approximate quantity at the target since the far-field region was defined for frequency. Although not strictly necessary, we also define a material , where and are the volume constraint: volume of element and the total volume constraint, respectively. Usually, the constraint is not active in the optimization process but it may be used in order to prevent the algorithm in ending up with inactive and unattached regions of conducting material. C. Material Interpolation Function Providing a good material interpolation function, i.e., a relation between the design variable and the conductivity has turned out to be the most difficult part of the present topology optimization application. Basically, we have to define ) a function that returns the conductivity of air (i.e., for and the conductivity of the conductor (i.e.,

) for . Had the materials been simple dielectric and air, the contrast would be small (e.g., and ) and one could use a simple linear in. Deterpolation scheme like spite of the continuous design variables, the results for photonic crystal-based waveguiding problems using this simple linear interpolation tend to end up in discrete 0/1-solutions because maximum contrast enhances the waveguiding properties [41], [48]. In the present case a simple linear interpolation does not work. Partly because of the huge contrast between the conductivity of air and conductor and partly because there is no “self-penalization” in the problem, i.e., the design variables will not naturally take 0–1 values at the end of the optimization process and hence it will be difficult to extract the optimal antenna shape from the optimized density distribution. In other topology optimization applications [39] it is common to use a power-law interpolation that penalizes intermediate density values, however, this scheme has only been partly successful for the present application. Instead, we found that the following interpolation scheme suggested in [43] provides good convergence (5) where and are the minimum (air) and maximum (copper) conductivity values. is made non-zero for numerical reasons. The Note that small value, however, hardly influences the propagation properties in the void (free space) regions of the design domain. This interpolation scheme provides a seemingly good scaling of the density to conductivity ratio and it coerces 0/1-designs by assigning very low conductivity values to intermediate density values, thereby making it uneconomical to use intermediate density areas when the total volume of material is restricted. D. Sensitivity Analysis Describing the full sensitivity analysis is out of the scope of this paper—the interested reader is referred to the monograph [39] or the paper [48]. In short, however, the sensitivities can be obtained for almost free when the original finite element problem has been solved. The trick is to use the adjoint method that involves solving the original FE-problem but this time with a new right-hand side (load) that is obtained as the objective function differentiated with respect to the electric field. The sensitivities are then obtained by simple element integrations over the original and adjoint fields [48]. The computational cost of the sensitivity analysis is ignorable compared to that of the FE analysis if the factorized system matrix can be reused for the computation of the adjoint problem. If this is not the case (which applies to our COMSOL implementation), the computational cost of the sensitivity analysis is still comparable to the cost of the original finite element solution. In any case, the cheap sensitivity analysis is the key-factor behind the efficiency of the topology optimization method. E. Practical Implementation In practice we have implemented the topology optimization procedure in a MATLAB environment with calls to the commercial FE software COMSOL (version 3.4) for evaluations of ob-

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Fig. 2. Finite-element configuration used in COMSOL 3.4 to model the antenna optimization domain.

jective functions, constraints and the associated sensitivity analysis. An example of such a code applied to fluid mechanics problems is found in [49]. The material redistribution is determined by the math-programming based optimization routine Method of Moving Asymptotes (MMA) [50]. In order to prevent numerical oscillations and ensure convergence of the design with mesh-refinement we regularize the density distribution problem by the density filtering method [51], [52]. The iteration process is terminated when design changes go below a certain tolerance. Typically, the algorithm converges in 50 to 100 iterations. However, compared to the second authors long-time acquired experience with various topology optimization applications it is found that the present problem is very sensitive to the right choice of interpolations schemes, initial material distributions and other optimization parameters. This sensitivity may be attributed partly to the problem of finding a well-suited interpolation function and partly to the fact that the considered problems are extremely sensitive to design variations when the design is close to resonance but on the other hand very insensitive to design changes when the design is far from resonance. Despite of above mentioned difficulties the following example demonstrates that an efficient sub-wavelength antenna can be obtained by the suggested approach although it is clear that more research has to be performed in order to turn the approach into a generally applicable and efficient antenna design scheme. III. NUMERICAL INVESTIGATIONS A. Density-Based Topology Optimization Configuration: COMSOL Simulations Fig. 2 demonstrates the FE configuration used in COMSOL to model the antenna design domain and free-space far-field region. First, a free-space radiation region above the PEC ground plane is modeled using a hemisphere with . Next, a hemispherical shell geometry design domain is constructed by subtracting two hemispheres above the ground plane, e.g., inner and outer radius values are and , respectively. A small fraction of the hemispherical shell volume is assigned to have the electrical properties of copper in order to connect the design domain to the coaxial cable, i.e., this small

Fig. 3. Iteration history for frequency of interest f intermediate designs.

= 300 MHz Inserts show

copper region is labeled as a sub-wavelength monopole antenna , element in Fig. 2 and specified using the , planes. The modified hemispherical shell design domain including the small copper volume is centered over the ground plane. The radius of the inner coaxial pin and the power available and , respecfrom the generator is tively. The characteristic impedance of the coax TEM mode is . The optimization problem is initialized using for all design a solid copper hemispherical shell, i.e., variables. The total analysis model is discretized using almost 150,000 tetrahedral first order edge elements, the total number of design variables is 16,769, the filter radius is 6 mm and the target frequency is . The optimization is subject to a 60% volume constraint. The density-based topology optimization process successfully distributes the conductor material using only 45% of its initial design volume, i.e., the volume constraint is not active. The iteration history shown in Fig. 3 clearly demonstrates the efficiency of the optimization method, where the optimal radiated power at the far-field region is obtained after only 30 iterations for a total number 16,769 design variables. The radiated power at the far-field region by the antenna and its and 76%, predicted radiation efficiency are respectively. We emphasize that the optimization result is not necessarily a global optimum since we are dealing with non-convex optimization problems. The final 3D conductivity distribution in Cartesian coordinates is shown in Fig. 4. The optimized conductivity distribution of the antenna shows transition regions between copper and free-space areas whose width depends on the minimum-length scale introduced by the regularization filter. The disconnected domain from the main structure along the positive -axis, shown in Fig. 4, is a numerical artifact and can be removed by introducing a stricter volume constraint. Snapshots from the design process are

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Fig. 4. The final 3D density distribution results obtained from the density-based topology optimization method.

included in Fig. 3 where it is seen how the structure develops from a solid shell (initial guess) to the optimized design. Fig. 3 also shows the convergence of the reflection coefficient. One can observe a 3 dB impedance matching at the 5th optimization step, however, the radiation efficiency of the antenna is response poor at this stage. After the 20th iteration step, the becomes flat and the optimization results in a built-in matching network that delivers more than 90% input power to the antenna. The antenna radiates 76% of the available power into the far-field region. The material distribution at this iteration step, as shown in Fig. 3, also provides some hints on the nature of the matching network. The distributed conductive material in 3D consists of a spherical plate, a short grounding leg connecting the spherical pattern to the infinitely large PEC ground plane and a feeding pin. The final optimized antenna pattern shown in Fig. 4 converges to a structure similar to the well-known planar inverted-F antenna (PIFA) design. The differences in shorting strip structure, current distribution and far-field radiation patterns between our topology optimized antenna, for the given spherical shell design scenario, and the PIFA design is discussed later in the text. Note that the predicted radiation efficiency is rather low; this is due to the transition regions having low conductivity values and limited resolution of the FE mesh. The transition regions can be removed using post-processing algorithms and/or commercial software tools, i.e., iso-density curve provided by MATLAB is frequently used in compliance minimization problems [53]. Accurate FE analysis requires element sizes smaller than the skin-depth to resolve the EM field in the conductive material. As noted before, our current computational resources limit our ability to satisfy this computational resolution during the design process. On the other hand, due to this computational artifact, optimal material distributions seek solutions that use minimal conductive material in the design domain to improve the radiated power at the far-field region. Better radiation efficiency predictions will be shown using post-processed versions of the optimized antenna configuration to overcome these limitations. We also note that the structured mesh option provided in COMSOL

Fig. 5. The approximate 3D HFSS model of the optimized antenna design. The electrical properties of this configuration, Design 1, is assigned to have the default copper material. The numbers indicate x and y coordinates and hence the last coordinate can be determined by these coordinates and the radius.

3.4 might produce a more accurate radiation efficiency value; however, this aspect has not yet been pursued further. B. HFSS Simulations The exact physical realization of the optimal design requires a 5-axis milling machine or a laser direct structuring (LDS) technology. In order to produce an antenna that can be fabricated in our workshop facilities, we propose simpler antenna structures based on the optimized conductive material distribution shown in Fig. 4. The post-processed representation was based on the shape of the optimized conductive material distribution. The first derived geometry simplification, Design 1, is shown in Fig. 5 including coordinate specifications. The radius, shell thickness and minimum feature size of the hemispherical shell are 80 mm, 4 mm and 1 mm, respectively. The ANSOFT’s HFSS model was used for the post-processed antenna to provide an independent numerical confirmation for the optimized antenna configuration. In addition, in contrast to the initial modeling limitations due to the nature of the density-based topology

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Fig. 6. The S reflection coefficient values of Design 1 as a function of the frequency. The reflection coefficient values were obtained using a Z transmission line feed.

= 50 Ohms

optimization method; default boundary condition accurately estimates the conductive loss in the copper material, and thus radiation efficiency, for the post-processed design. reflection coefficient values of the post-processed anThe tenna configuration, Design 1, matched to the coaxial feed is plotted in Fig. 6 as a function of the frefrequency points of in Fig. 6 are quency. The 321.2 MHz and 342.4 MHz, respectively. Consequently, the bandwidth value is at . Fig. 7 shows predicted values of the tuned complex input impedance for Design 1 as a function of the frequency. The proposed antenna exhibits a resonance at having a resistance value of and a predicted radiation efficiency in excess of 99.99%. Note that a lossless inductor was used to tune the antenna’s reactance to zero at its resonant frequency. The fractional matched VSWR bandwidth for is 3.66% at , and consequently . The approximate value computed using the antenna’s impedance at the feed point is . All of these approximate quality factor values are in quite good agreement and are times larger than the absolute lower bound value for this antenna design: , . We note that even though the computed fractional VSWR bandwidth does not include the anti-resonance point, the resonance and anti-resonance points may still be too close to provide reliable approximate values [46]. Fig. 8 demonstrates the surface current plot of the proposed design at . There are two major current flows present on the surface of the antenna: a) a current flow on the antenna from the feed to the edge along the -axis, and b) a current circulation between the antenna’s feed and PEC ground plane. The inductive behavior of the current circulation dominates the antenna’s reactance behavior at lower frequencies, where the electrical size of the current loop becomes smaller and radiator exhibits an electrically small loop behavior. The current flows on the two sides of the design, along the -axis in the

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Fig. 7. The tuned complex input impedance response of Design 1 as a function of frequency. The anti-resonance and resonant frequencies are found at !  : and !  : , respectively.

2 2 303 14 MHz

= 2 2 331 1 MHz

=

Fig. 8. The surface current distribution of Design 1 over a ground plane at !  : .

= 2 2 331 1 MHz

-plane, are out of phase and their current magnitudes are different due to asymmetry in the antenna design. The electric-field distribution between the spherical asymmetric top part and the ground plane provides the capacitance to the system. The inductive behavior of the antenna at higher frequencies suggests that the distance between the spherical asymmetric top part and the ground plane increases, and consequently capacitance decreases. Fig. 9 shows the far-field radiation patterns of Design 1 . The antenna exhibits a distorted omat nidirectional, elliptically polarized radiation pattern over a PEC ground plane. The field components were normalized with the maximum component. The large component is mainly due the current flow on the surface of the spherical shell from the antenna’s feed to the edge of the antenna along the -axis. The component at in elevation plane is different from zero due the current circulation between the feed and ground plane in the -plane. The asymmetric field pattern is expected due to the non-uniform current distribution on the

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= 2 2 331 1 MHz = 90

Fig. 9. Far-field radiation plots of Design 1 at !  : : E j and E =j E j radiation components in elevation (a) E =j plane  , and (b) E =j E j radiation component in  plane.

max( ) ( = 90 )

max( ) max( )

spherical shell surface. Consequently, according to the surface current and far-field radiation pattern plots, the antenna has both TE and TM fundamental modes. As noted earlier, the fundamental working principle of the distributed conductor material in 3D is similar to a PIFA design. The radiation performance of both designs depend on feeding location and distance to the shorting strip, distance above ground plane and neighboring metal components. The topology optimized structure demonstrates good matching properties over a wide frequency range compare to the conventional PIFA designs due to enforced current distribution on the spherical shell and its tapered shorting strip. Note that the optimization has chosen to use a certain width and not a simple shorting strip to provide the well-known built-in matching network topology. In fact, using a wider shorting post is one of the many techniques reported in literature to enhance the radiation performance of the original PIFA design. The topology optimized

antenna has an elliptically polarized radiation pattern due to its horizontal polarized radiation component: a conventional PIFA exhibits an omnidirectional, linearly polarized radiation pattern. The real benefit of the topology optimization technique will be more visible for more complex design problems since the modeling domain also is allowed to contain other conductive structures representing the true near-field environment of the antenna. An example is an antenna module of a mobile phone with embedded audio speaker and/or camera components. We will consider such more complex design problems in future work. We consider a number of variations of Design 1 to further simplify the geometry and to improve the predicted value. Fig. 10 demonstrates the new antenna design and its design parameters. This antenna configuration exploits the symmetry and consists of three major parts: a) a feeding arm that is symmetric along the -axis, b) a fully symmetric spherical cap and c) a conductor arm that connects the rest of the antenna to the PEC ground plane. The antenna is fed by a coaxial pin, where the inner pin of the coaxial cable extends from the ground plane to the lower edge of the antenna. The shell thickness value, the height and radius of the inner pin are 2 mm, 4 mm and 0.65 mm, respectively. Two antenna designs having different conductor arm configurations will be analyzed to explore computed approximate values and their relation to the location of the resonance and anti-resonance points. The main difference between Design 2 and Design 3, as will be shown shortly, is the separation of the resonant and anti-resonant frequencies. The far-end edge of the spherical geometry in Design 1 is slightly reduced and thus, as expected, the resonant frequency is shifted to higher frequencies. Design 2 and Design 3 antenna configurations are identical except for the height of the conductor arm, i.e., design parameter is 20 mm and 40 mm, respectively, for Design 2 and Design 3. The other parameter values are set to , , , and . The modification in the height of the conductor arm connecting to the ground plane changes the path of the current circulation. The current path to the PEC ground plane corresponds to an electrically small loop antenna: the radiator shows an inductive reactance behavior at frequencies smaller than the resonant frequency . The shorter current path at longer wavelengths dominates the reactance behavior of the radiator. On the other hand, a relatively larger current path to the PEC ground plane at corresponds to a nominal increase in the electrically small loop size. The increase in the electrically small loop size reduces the large inductance contribution from the current path to the PEC ground plane causing a relative increase in the capacitance of the antenna’s reactance behavior. A larger capacitance value deepens the resonance dip and separates the resonance and anti-resonance frequency points. In addition, the magnitude of the resistance curve also increases. Fig. 11 compares the tuned resistance and reactance behaviors of Design 2 and Design 3 as functions of frequency. The anti-resonance and resonant frequencies of Design 2 (Design 3) are located at 329.19 MHz (293.7 MHz) and 350.8 MHz (355.6 MHz), respectively. Consequently, the difference

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Fig. 10. The proposed antenna configuration based on Design 1 and its design parameters. This antenna configuration was designed to exploit the symmetry to get a more uniform current distribution on the antenna.

Fig. 12. The S reflection coefficient values of Design 2 and Design 3 as a function of the frequency. The reflection coefficient values were obtained using aZ transmission line feed.

= 50 Ohms

Fig. 11. The tuned complex input impedance responses of Design 2 and Design 3 as a function of frequency: (a) radiation resistance, and (b) radiation reactance. The anti-resonance and resonant frequencies of Design 2 (Design 3) are located at 329.19 MHz (293.7 MHz) and 350.8 MHz (355.6 MHz), respectively.

between the resonant and anti-resonant frequencies for Design 2 and Design 3 are 21.61 MHz and 61.9 MHz, respectively. The reflection coefficient values of Design 2 and Design 3 matched to the matched transmission line feed are plotted in Fig. 12 as a function of frequency. The frequency points of for Design 2 (Design 3) in Fig. 12 are 336.31 MHz (341.62 MHz) and 368.7 MHz (372.29 MHz), respectively. Consequently, the bandwidth for Design 2 (Design 3) are at . The resistance values of Design 2 and Design 3 are, respectively, and , and their predicted radiation efficiencies are in excess of 99.99%. The fractional matched VSWR bandwidth for at for Design 2 (Design 3) is 5.32% (5.42%), and consequently . The approximate value computed for Design 2 (Design 3) using the antenna’s impedance at

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Fig. 14. Far-field radiation plots of Design 2 and Design 3 at ! = 2 2 350:8 MHz and ! = 2 2 355:6 MHz, respectively: (a) E = max(E ) and E = max(E ) radiation components in elevation plane ( = 90 ), and (b) E = max(E ) components in  = 90 plane. j

j

j

Fig. 13. The surface current distribution of (a) Design 2, and (b) Design 3 at !  : and !  : , respectively.

= 2 2 350 8 MHz

j

j

j

= 2 2 355 6 MHz

feed point is . Again, all the computed approximate quality factor values obtained for Design2 (Design 3) show very good agreement and are times larger than the lower bound value for this proposed antenna configuration: , . The comparisons of the computed approximate values using two methods for two different antenna designs reveal that the predicted quality factor for Design 2 provides an accurate estimate of the antenna’s performance. Note that the conductor losses may be underestimated in simulation results. The exact value calculation using measured EM fields for the proposed antennas are in progress, and their results will be reported elsewhere. The measured radiation efficiency of the proposed

antenna designs can be slightly smaller and, thus, the computed values should be modified accordingly. Fig. 13 demonstrates the surface current plot of Design 2 and and , Design 3 at respectively. The symmetric nature of the proposed design provided a more uniform and in-phase current distribution on the antenna surface. The surface currents are mainly concentrated on the feeding arm and the conductor arm that connects the antenna to the PEC ground plane. The predicted far-field radiation pattern shows a slightly distorted omnidirectional elliptically polarized field pattern as shown in Fig. 14. A more uniform far-field radiation pattern lowers the quality factor of the antenna. The component of Design 2 and Design 3 at is slightly larger than the initial design due to the larger and uniformly circulating currents between feed and ground plane. The

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Fig. 15. The axial ratio pattern of Design 2 and Design 3 in elevation plane ( = 90 ) at ! = 2 350:8 MHz and ! = 2 355:6 MHz, respectively.

2

2

plot of the axial ratio pattern in the elevation plane is demonstrated in Fig. 15. The near-field electric and magnetic field dis-and -planes, respectribution of the resonant mode in tively, are depicted in Fig. 16. The electric field shows a sign reversal across the surface of the antenna demonstrating similar characteristics as a number of existing antennas, i.e., 4-arm folded spherical helix dipole and an axially symmetric array of 4 conductor arms forming a spherically shaped antenna [4], [24]. The proposed sub-wavelength antenna designs are on the electrically small antenna limit and this approach may provide attractive alternatives to existing electrically-small antennas. IV. CONCLUSIONS The topology optimization method has been used to design a three-dimensional (3D), solely conductor-based, large bandwidth, efficient and sub-wavelength antenna. The density-based topology optimization method converged to an optimized radiated power at the far-field region after only 30 iterations for a total of 16,769 design variables. We note, however, that in our experience, optimal distribution of conductor using topology optimization is more sensitive to initial conditions and optimization parameters compared to purely dielectric-based topology optimization problems. The proposed topology optimization strategy for the systematic design of an antenna design can be applied to any kind of simple or complex design domain geometries. In addition, modeling domain can also contain other conductive structures representing the true near-field environment of the antenna. Based on post-processing of the topology optimized antenna configuration three simplified designs are proposed: Design 1, Design 2 and Design 3. Design 1 is based on a direct interpretation of the optimized conductive material distribution. We

Fig. 16. (a) E-field and (b) H-field distribution plots over ground plane for the Design 2 obtained using a Z = 50 Ohms transmission line feed at ! = 2 350:8 MHz.

2

also considered two variations of Design 1 to further simply the geometry and to obtain a more uniform current distribution on the proposed geometry. The presented antenna models are shown to be self-resonant, efficient and readily matched to a source. The main difference between Design 2 and Design 3 is the separation of the resonant and anti-resonant frequencies. bandwidth for Design 1, Design 2 and Design The 3 matched to a matched transmission line feed are, respectively, , 9.23% and 8.62%. The approximate value computed for Design 2 (Design 3) using antenna’s impedance at feed point is . All the computed approximate quality factor values obtained for Design2 (Design 3) showed very good agreement and are times larger than the lower bound value for this proposed antenna configuration: , . The predicted efficiency values for all of the proposed antenna designs are in excess of 99% and the far-field radiation pattern shows a slightly distorted omnidirectional elliptically polarized field pattern.

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ACKNOWLEDGMENT The authors wish to thank professors O. Breinbjerg and R. W. Ziolkowski for inspiring discussions on the presented work. They also wish to thank A. D. Yaghjian as well as two anonymous reviewers for providing useful discussions that led to important modifications of this manuscript. REFERENCES [1] H. A. Wheeler, “Fundamental limitations of small antennas,” IRE Proc., vol. 35, pp. 1479–1484, Dec. 1947. [2] H. A. Wheeler, “Small antennas,” IEEE Trans. Antennas Propag., vol. AP-23, Jul. 1975. [3] R. Mittra, “Challenges in antenna designs and some novel techniques for meeting them,” presented at the Loughborough Antennas and Propag. Conf., Loughborough, U.K., Apr. 2–3, 2007. electrically small linear and elliptical polarized [4] S. R. Best, “Low spherical dipole antennas,” IEEE Trans. Antennas Propag., vol. 53, no. 3, pp. 1047–1053, Mar. 2005. [5] L. J. Chu, “Physical limitations of omnidirectional antennas,” J. Appl. Phys., vol. 19, pp. 1163–1175, Dec. 1948. [6] R. E. Collin and S. Rothschild, “Evaluation of antenna ,” IEEE Trans. Antennas Propag., vol. AP-12, no. 1, pp. 23–27, Jan. 1964. [7] R. L. Fante, “Quality factor of general ideal antennas,” IEEE Trans. Antennas Propag., vol. AP-17, no. 3, pp. 151–155, Mar. 1969. [8] R. C. Hansen, “Fundamental limitations in antennas,” Proc. IEEE, vol. 69, pp. 170–181, Feb. 1981. [9] L. Fante, “Maximum possible gain for an arbitrary ideal antenna with specified quality factor,” IEEE Trans. Antennas Propag., vol. AP-40, no. 12, pp. 1586–1588, Dec. 1992. [10] J. S. McLean, “A re-examination of the fundamental limits on the radiation of electrically small antennas,” IEEE Trans. Antennas Propag., vol. AP-44, pp. 672–676, May 1996. [11] K. Fujimoto et al., Small Antennas. London, U.K.: Research Studies Press, 1987. [12] Y. Kim and D. L. Jaggard, “The fractal random array,” Proc. IEEE, vol. 74, pp. 1278–1280, Sep. 1986. [13] C. Puente, J. Romeu, and A. Cardama, “Fractal antennas,” in Frontiers in Electromagnetics, D. H. Werner and R. Mittra, Eds. Piscataway, NJ: IEEE Press, 2000, pp. 48–93. [14] D. H. Werner, R. L. Haupt, and P. L. Werner, “Fractal antenna engineering: The theory and design of fractal antenna arrays,” IEEE Antennas Propag. Mag., vol. 41, no. 5, pp. 37–59, Oct. 1999. [15] D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antennas Propag. Mag., vol. 45, no. 1, pp. 38–56, Feb. 2003. [16] R. B. Waterhouse, S. D. Targonski, and D. M. Kokotoff, “Design and performance of small printed antennas,” IEEE Trans. Antennas Propag., vol. 46, pp. 1629–1629, Nov. 2003. [17] K. J. Vinoy, K. A. Jose, V. K. Varadan, and V. V. Varadan, “Hilbert curve fractal antenna: A small resonant antenna for VHF/UHF applications,” Microw. Opt. Techn. Lett., vol. 29, no. 4, pp. 215–219, May 2001. [18] J. Zhu, A. Hoorfar, and N. Engheta, “Peano antennas,” IEEE Antennas Wireless Propag. Lett., vol. 3, pp. 71–74, 2004. [19] J. Zhu, A. Hoorfar, and N. Engheta, “Bandwidth, cross polarization, and feed-point characteristics of matched Hilbert antennas,” IEEE Antennas Wireless Propag. Lett., vol. 2, pp. 2–5, 2003. [20] J. Zhu, A. Hoorfar, and N. Engheta, “A comparison of the performance properties of the Hilbert curve fractal and meander line monopole antennas,” Microw. Opt. Tech. Lett., vol. 35, no. 4, pp. 258–262, Nov. 2002. [21] J. Zhu, A. Hoorfar, and N. Engheta, “A discussion on the properties of electrically small self-resonant wire antennas,” IEEE Antennas Propag. Mag., vol. 46, no. 6, pp. 9–22, Dec. 2004. [22] J. Zhu, A. Hoorfar, and N. Engheta, “The radiation properties of electrically small folded spherical helix antennas,” IEEE Trans. Antennas Propag., vol. 52, no. 4, pp. 953–960, Apr. 2004. [23] J. Zhu, A. Hoorfar, and N. Engheta, “Small broadband disk loaded folded monopole antennas,” presented at the Applications Symp., Sep. 2004. [24] H. R. Stuart and C. Tran, “Small spherical antennas using arrays of electromagnetically coupled planar elements,” IEEE Antennas Wireless Propag. Lett., vol. 6, pp. 7–10, 2007. [25] R. W. Ziolkowski and A. D. Kipple, “Application of double negative materials to increase the power radiated by electrically small antennas,” IEEE Trans. Antennas Propag., vol. 51, pp. 2626–2626, Oct. 2003.

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Aycan Erentok received the B.S. (cum laude and honors), M.S., and Ph.D. degrees in electrical engineering from the University of Arizona, Tucson, in 2001, 2003 and 2007, respectively. He spent summer 2006 at the ATD/DPD (INTEL Chandler Campus) and worked on system level power delivery network measurements using IFDIM methodology. He was employed as a Postdoctoral Research Fellow at the Technical University of Denmark, Lyngby, from May 2007 to August 2008. He joined NOKIA, Ulm, Germany, in September 2008, where he is currently working as a Senior Antenna Specialist. His research interest includes electrically small antennas, EM optimization algorithms and effects of metamaterials on antenna performance.

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Ole Sigmund received the M.Sc., Ph.D., and Dr. Techn. degrees from the Technical University of Denmark, Lyngby, in 1991, 1994 and 2001, respectively. Currently, he is a full Professor at the Department of Mechanical Engineering, Section for Solid Mechanics, Technical University of Denmark. Previously, he has been a Research Assistant at the University of Essen, Germany (1991–1992) and a Postgraduate Fellow at Princeton Materials Institute, Princeton University, Princeton, NJ (1995–1996). He has been the PI of a number of larger nationally and internationally funded research projects and he has published more than 76 research papers in peer-reviewed international journals and coauthored the monograph Topology Optimization—Theory, Methods and Applications (Springer, 2004). His principal research interests are theoretical extensions and applications of topology optimization theoretical extensions and applications of topology optimization methods to the design of extremal materials, smart materials, compliant mechanisms, microelectromechanical systems, crashworthiness, fluid systems and wave-propagation problems in acoustics, elasticity, nano-optics, metamaterials and antennas. Prof. Sigmund is a member of the Royal (Danish) Academy of Sciences and Letters and the (Danish) Academy of Technical Sciences.

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Analysis and Characterization of a Multipole Reconfigurable Transmitarray Element Jonathan Yun Lau, Student Member, IEEE, and Sean Victor Hum, Member, IEEE

Abstract—A reconfigurable transmitarray element is presented that operates at 5.5 GHz and is low-profile, low-cost and easy to fabricate. The design consists of a three-layer structure implementing two slot-coupled patch antennas. Varactor diodes are used to load the patches and slot to create a third-order resonant structure. A simple circuit-based analysis approach is used to predict the response of the unit cell based on the location of its poles and zeros. Simulation and experimental results are presented, with experimental results achieving 245 of phase agility with less than 3 dB of variation in transmission magnitude throughout the tuning range. The effects of diode loss, angle of incidence, and mutual coupling are investigated. The element is also capable of functioning as a low-loss reconfigurable reflectarray element, making it particularly versatile for different scanning configurations. Index Terms—Antenna arrays, lens antennas, microstrip arrays, reconfigurable antennas, reflectarrays, varactors.

I. INTRODUCTION S wireless technologies increase in popularity, the need for low-cost and high-gain reconfigurable antennas has emerged. High gain antennas are needed for increasing system range, as well as alleviating the effect of multipath and co-channel interference. Low fabrication cost, low complexity, and small physical size are factors that are crucial for viability. While conceptually simple and elegant, phased arrays require large feed networks and circuits that are costly, lossy, and bulky. Optically-inspired antenna architectures such as reflectarrays have recently been shown to be practical for implementing low-cost reconfigurable apertures. Transmitarrays, also known as array lenses or quasi-optical antenna arrays, have also recently been proposed as low-cost alternatives to phased arrays, and have the additional advantage of eliminating feed blockage. This work presents a reconfigurable transmitarray element design that is low-cost and easy to fabricate. In addition, the proposed transmitarray element can also function in a reflectarray mode, resulting in a microwave array that can function as both a lens and a reflector. A transmitarray, as shown in Fig. 1, is essentially a discretized lens, where a surface is partitioned into an array of transmis-

A

Manuscript received August 10, 2009; revised June 01, 2010; accepted September 14, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors are with the Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, ON, Canada (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090456

Fig. 1. Typical transmitarray configuration.

sive elements with varying phase shifts. Fixed transmitarray element designs typically consist of two antennas that are coupled using a slot [1] or a stripline transmission line [2], where the structure’s physical features are tuned to yield a particular phase shift. Most transmitarray designs use coupled patch antennas because they are easy to fabricate. Furthermore, the patch antenna’s ground plane isolates the input from the output, and makes the coupling network between the two antennas easier to design. Other fixed transmitarray element approaches, such as layers of coupled rings [3], result in greater transmission bandwidth, but at the cost of physical size, where multiple widelyspaced substrate layers are required. The primary challenge in the design of a reconfigurable transmitarray is achieving electronic phase shift control for each individual element. Many electronic tuning techniques have been presented for reflectarrays. One such technique involves manipulating the DC voltage across a varactor diode [4]–[6] or micro-electromechanical system (MEMS) capacitor [7], [8] to tune the component’s capacitance. By changing the capacitance, resonant structures such as patches can be loaded and their phase responses tuned. Similarly, MEMS switches [9] or PIN diodes [10] have been used to connect or disconnect components for reactive loading. Other techniques also include mechanically raising and lowering the patch [11] or changing the dielectric properties of the substrate [12], [13] to change the phase response. An electronically tunable transmitarray element, consisting of two stripline-coupled patches, was demonstrated in [14]. By loading a patch with varactor diodes, the resonant frequency of the patch could be manipulated, yielding about 90 of phase agility in the transmission. This is insufficient to produce beamforming over large spatial ranges except in very small apertures. In [15], a reconfigurable lens array was presented using MEMS

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LAU AND HUM: ANALYSIS AND CHARACTERIZATION OF A MULTIPOLE RECONFIGURABLE TRANSMITARRAY ELEMENT

switches that enabled array elements to have four possible discrete phase tunings. Despite the heavy phase quantization, the array successfully demonstrated reconfigurable beamforming. The principle of controlling microwaves passing through a structure is also found in frequency selective surfaces (FSSs) [16] and spatial power-combining amplifiers [17]. However, the design objectives in these two related fields differ from those in transmitarray design. FSS structures are typically designed for a particular magnitude response, while transmitarray elements are designed for a specific phase response. On the other hand, for spatial power combiners, the goal is to maximize power with the collimating element located very close to the array, but the goal for transmitarrays is beam synthesis for a transmitter or receiver that is located far away from the aperture. Thus, concepts from the design of reconfigurable reflectarrays, FSSs, spatial power combiners, and existing transmitarrays can be leveraged to further the design of reconfigurable transmitarray unit cells. However, to date, tunable unit cells with the necessary 360 of phase shift have not yet been demonstrated. Furthermore, existing designs commonly use many substrate layers making them bulky and difficult to fabricate. This motivates the proposed transmitarray element design. II. ELEMENT DESIGN In this section, we present a reconfigurable transmitarray element design, expanding on earlier work on a transmitarray cell concept presented in [18]. The element is intended for implementation in a full array with 30 mm 30 mm spacing, which at 5.5 GHz. is

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Fig. 2. Pole angle and distance.

minimize cost and physical size, the first step is to characterize the required order of complexity in the structure. That is, we must determine the number of layers and components required to achieve 360 of tunable phase shift, with as constant a transmission magnitude as possible. For reasons that will become clear, we focus on the use of coupled resonators to realize the transmitarray element, due to their ease of fabrication and intuitive design. While this transmitarray element does not operate on guided fields, we will examine the element as a guided-wave filter, as is common in FSS design [19], with spatial coupling into unit cells modeled using TEM ports for the broadside illumination case. Consider a passive linear time-invariant filter with a particular magnitude and phase response. From filter theory, let the and zeros response be characterized by a set of poles on the complex plane, such that the transfer function is

A. Design Motivation While it is conceptually simple to build a tunable transmitarray using two antennas coupled to a guided-wave variable phase-shifter, it is difficult to implement in practice. Losses, fabrication complexity, and physical size constraints are among several of the challenges. Drawbacks of using phase-shifters to implement phase agility include their large physical size and insertion loss. Furthermore, we note that while transmitarray design is similar to reflectarray design, which has been well-studied, there is a crucial difference that makes transmitarray design more challenging. In both cases, to form a pencil beam, the phase shift from the source to the transmitarray element to the aperture plane must be equal for every possible radiation path. For a reflectarray, all of the incident power is reflected regardless of the frequency and unit cell design, assuming lossless tuning elements. At frequencies well below and well above the resonant frequency of the element, a reflectarray will reflect the incident wave perfectly with 180 of phase shift (again, ignoring loss). However, with a transmitarray, those cases will result in most of the incident power being reflected, and little transmission through the structure, since the input and output of each element is not properly matched to free-space. Thus, the magnitude of transmission is an additional design consideration for transmitarray elements. For this design, we consider utilizing only passive microwave structures and lumped elements to achieve the phase shifting. To

The steady-state response at a particular operating frequency is defined by on imaginary axis of the complex plane, and of the system. It is well known that the is equivalent to the is magnitude response at a particular operating frequency given by the product of the distances to each zero on the complex plane, divided by the product of the distances to each pole. Likewise, the phase response is given by the sum of the angles to each zero, minus the sum of the angles to each pole. Now, for a single pole or zero in the left-half plane (for stability), the corresponding angle with any point on the imaginary axis and . Therefore, each pole or zero, if aris between bitrarily moved, can contribute a maximum of 180 of phase , as shown in Fig. 2. To maintain a response tunability in constant magnitude response, the pole locus should maintain a . constant distance to the operating frequency point For example, consider the two-pole circuit shown in Fig. 3, which can model two inductively-coupled patch antennas. The of the circuit can be shown to be

(1)

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Fig. 3. Example two-pole circuit.

Fig. 4. Example two-resonator complex poles and response, with s and s loci as C is varied, with L L nH and Z . (a) Pole loci on the complex plane, (b) transmission response S .

=

=1

= 50

and the two positive-frequency poles from the denominator given by

(2) (3) where and are the inductance and capacitance of the shunt is the port impedance, and is the coupling inresonators, ductance. Suppose the phase response of this structure is tuned by changing the capacitance (by using a varactor diode, for example), which in turn changes the resonant frequency. Then, the loci of the poles is elliptical with foci on the real axis, as pF and shown in Fig. 4(a). Consider two capacitances pF that result in the pairs of poles shown. The corresponding frequency response for those two capacitances are shown in Fig. 4(b).

Ultimately the desired effect of the tuning is to change the phase response of the circuit without significantly changing its magnitude response. The maximum phase response from tuning is achieved when the poles can be moved as far as possible along the locus. In the example shown, it is not possible to achieve 360 of phase tunability given the elliptical curvature of the loci. Due to the trajectory of the poles (and zeros) of the structure, the magnitude response varies considerably over the range where most of the phase shift is developed. Furthermore, very large changes in would be required to produce the large phase shifts needed in beamforming applications. and , the size of the ellipses For different values of changes, but large variations in inductance are needed to significantly alter the loci. In the degenerate case where the locus is an infinite ellipse encircling the left-half plane, even though 360 of phase shift may be theoretically achieved, the variation would be large, making the of locus point distances to magnitude response vary too greatly. Therefore, a minimum of three resonances are needed to achieve 360 of phase tunability with an acceptable amount of variation in insertion loss. It is well known that flatter transmission magnitude curves can be achieved by increasing a filter’s order, or the number of resonant structures. However, with microwave structures, each additional resonator requires more physical space, and incurs more loss and fabrication complexity. For this reason, our design aims to achieve maximum phase tunability and transmission constancy with a minimum order filter using only three resonators. Consider a system with three poles which are moved as shown in Fig. 5. As the poles are shifted, the corresponding magnitude and phase responses are also shifted in Fig. 5(b). With more poles, each pole needs to move less to effect a given amount of total phase change, so the transmission magnitude can be kept more constant. If we consider a single frequency in Fig. 5(b), we see it is possible to achieve 360 of phase tunability with nearly constant magnitude using three poles. The proposed unit cell will thus use three conjugate pole-pairs to attempt to provide the necessary phase agility in the design. In this work, the transmitarray element consists of two microstrip patches on either side of a ground plane coupled by a small slot aperture, as shown in Fig. 6. Each patch is split in half with a small gap in between, and varactor diodes inserted to connect the two halves. Another varactor diode is also inserted at the center of the slot, connecting the two sides of the slot (control hardware for biasing has been omitted). Fig. 6 also shows the two TEM ports used for defining -parameters. By image theory, a TEM wave in a waveguide with periodic boundary conditions simulates a broadside plane wave incident on an infinite array of identical elements [20]. Three tunable poles or zeros implies that there are three resis onance points (where a resonance is a point at which real). Microstrip patch antennas are essentially leaky resonators, which are easy to fabricate. So in this design, the two microstrip patch antennas with embedded series varactors are used as two tunable resonators. A varactor is added across the slot to form a third resonator. Together, these structures act as three coupled tunable resonators. The structure has an advantage in that it can achieve a pole trajectory similar to that shown in Fig. 5 using

LAU AND HUM: ANALYSIS AND CHARACTERIZATION OF A MULTIPOLE RECONFIGURABLE TRANSMITARRAY ELEMENT

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TABLE I ELEMENT DIMENSIONS AND PARAMETERS

B. Circuit Modeling

Fig. 5. Example three-resonator complex poles and response. (a) Poles on the complex plane, (b) transmission response S .

We can approximately model the transmitarray element resonators, as shown using three inductively-coupled shunt in Fig. 7. Due to the complex three-dimensional nature of the transmitarray structure, an equivalent lumped element circuit with quantities explicitly relating physical geometries to parameters cannot be developed. Nevertheless, we can discuss how the circuit components manifest themselves in the actual design, and how their values affect the overall behavior. 1) Patch: It is well known that a single resonating patch can resonator with parameters and be modeled as a shunt [21]. A transformer is shown to represent the impedance transformation by the patch to the 377 free-space ports. The capacitance combines the patch and varactor diode capacitance to form a single tunable capacitance. 2) Slot: A small aperture coupling can be viewed as a waveguide discontinuity modeled using a T-network of inductors and [22]. 3) Slot Varactor: The varactor diode placed across the slot can be modeled as a variable capacitor . Together with the element in the slot model, and form a third shunt resonator between the two patch resonators. C. Element Implementation

Fig. 6. Reconfigurable transmitarray element structure.

Fig. 7. Circuit model.

only tunable capacitances, due to the shunt nature of the resonators in Fig. 7. This is an advantage since tunable inductors are not easily realized.

The parameters used in the simulation and fabrication of the element are summarized in Table I. The size of the patch was selected such that it resonates at 5.5 GHz. A square shape was selected so that the distance between adjacent array patches is maximized, to minimize mutual coupling. We note that while the patch is square, it is designed to resonate along the axis parallel to the electric field vector shown in Fig. 6. The length of the slot (5.0 mm) affects the series coupling inductance . The inductance is increased as the length of the slot is reduced, but consequently, the amount of coupling is also reduced. The inis needed for the two patches to create two disductance tinct resonances, since in the case that , the two coupled patches degenerate into a single resonator. The width of the slot (2.0 mm) controls the amount of power that is coupled through the slot. The thickness of the substrate affects the resonance quality factor of the patch. A thicker substrate results in the patches being less resonant because power is more easily radiated. On the complex plane, the thicker the substrate, the further the poles are located from the -axis, resulting in the movement of the

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TABLE II SPECIAL CONFIGURATIONS

poles having less impact on the phase response. On the other hand, the thinner the substrate, the closer the poles are located to the -axis, and so the ripples in the magnitude response are mm was more pronounced. The substrate thickness of selected because it provided a balance between phase tuning . range and magnitude variation of There are three tunable components in the design: two varactor diodes on the patches, and one varactor diode across the slot. The capacitance across each varactor can be reduced by increasing the reverse-bias voltage across the varactor. In this design, the bias voltages of the two patch varactor diodes are kept the same because the structure does not couple power between the spatial ports when the patch resonant frequencies are different. Therefore, there are two degrees of freedom in the structure: the patch varactor bias and the slot varactor bias. Each pair of patch and slot varactor bias voltages results in a different set of -parameters. Therefore, we define a configuration (e.g., Configuration 30) to be the pair of patch and slot varactor diode bias voltages that result in the corresponding (e.g., 30 ), and with the greatest achievable . We define special configurations in Table II for convenience in later discussions. An obvious challenge with loading a slot with a varactor diode is that the varactor cannot be readily biased. Any discontinuities along the edge of the slot significantly alter the behavior of the slot. While surface mount capacitors can be used as RF shorts, their physical size with respect to the slot also significantly alter the slot’s behavior. To solve this problem, two conducting layers separated by a very thin dielectric layer were used to compose the ground plane, as shown in Fig. 8. The thin dielectric layer, realized using a microwave bonding film, not only provided DC isolation between the two layers but also behaved as an RF short. In this way, the ground plane could be partitioned to provide DC biasing to the slot varactor diode, while appearing to be a contiguous RF ground plane. As the varactor diode has a physical height of 1.3 mm, a cavity was milled into the underside of the upper substrate, and a small hole cut in the bonding film to accommodate the diode. This biasing solution has the benefit that there are no extra conducting layers needed, since two microstrip layers have four conducting planes, and bonding film would otherwise have been required to bind the two layers as well. We note that a practical concern with using varactor diodes is their susceptibility to nonlinear effects. For MGV100-20 varactor diodes embedded in a reflectarray element, it has been demonstrated in [7] that for an input power density less than dBm 0.6 W/m , which corresponds to an input power of into a WR-187 waveguide, the resulting third-order intermodulation levels are too low to be measured. The third-order in-

Fig. 8. Element design.

Fig. 9. Rectangular waveguide characterization setup.

tercept point, which varies with tuning, is at approximately 190 W/m , or 20 dBm in a WR-187 waveguide. Thus, using these particular diodes, the transmitarray element is perfectly capable of distortionless operation for receive applications. For larger power-handling capabilities, a bandpass FSS [23] could be overlaid on top of the array. Alternatively, tunable MEMS capacitors, which are highly linear and have less loss, can be used instead of varactor diodes [7]. D. Element Testing To characterize the transmitarray element, a single element was placed in a WR-187 rectangular waveguide (47.55 mm 22.15 mm). As mentioned earlier, the conducting walls of the waveguide simulate a plane wave incidence on an infinite array of identical elements [20]. At 5.5 GHz, the waveguide mode simulates illumination at 35 off-broadside in the H-plane. The simulation configuration is shown in Fig. 9. This method of characterization was also used in [4]. The effects of the 35 angle of incidence will be discussed further in Section III.B. III. SIMULATION RESULTS FDTD simulations of the structure were carried out using the SEMCAD X simulation platform by SPEAG [24]. Fig. 10 shows and for Configuration C. At 5.5 GHz, was the

LAU AND HUM: ANALYSIS AND CHARACTERIZATION OF A MULTIPOLE RECONFIGURABLE TRANSMITARRAY ELEMENT

Fig. 10. Simulated S

for Configuration C.

Fig. 11. Simulated S

for different element configurations.

dB and the phase response was 196 . There is some insertion loss due to the parasitic resistance in the varactor diodes, which corresponds to 2 of series resistance. A 0.4 nH parasitic series inductance was also included in the diode model. This magnitude and phase response confirms that the structure indeed has three poles, as the total phase change between 4.5 GHz and 6.5 GHz is almost 500 . We note that though the center , its contribution to the phase pole only has a shallow dip in response is evident. Figs. 11 and 12 show the transmission and reflection plots for different element configurations. By properly selecting the voltages in the configurations, we can achieve 260 of phase varies by less than 3 dB. Contunability at 5.5 GHz where figurations 95 through 355 achieve insertion losses and phase responses from 95 to 255 . We can also see that the phase response is almost linear, with a 45 phase bandwidth of about 120 MHz, or about 2%. A. Effect of Diode Loss We note that the total phase agility achieved is significantly less than 360 . This is caused by the series parasitic resistance of about 2 in the varactor diodes that results in resonator loss.

Fig. 12. Simulated S

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for different element configurations.

Fig. 13. The effect of varactor diode loss. (a) Configuration B, (b) configuration C.

The more loss a resonator has, the further the poles are located -axis, resulting in reduced phase range when the from the poles are moved. To better understand this, the effect of loss for Configurations B and C are shown in Fig. 13, where the series resistance in the varactor diodes is varied in simulation. While loss only has a small effect on the transmission phase, the tuning phase range is reduced because the width of the bandpass region is reduced. As a result, the range of configurations over is usable is reduced. The parasitic loss has varying which effects across different configurations, where the reduction in ranges from about 1.5 dB for some configurations to about 3 dB for others. The dielectric loss of the substrate and conductor losses are negligible in comparison to varactor resistive losses. In the curves shown with zero varactor parasitic resistance, the peak transmission is less than 0 dB because a small amount of power

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Fig. 15. Mutual coupling simulation waveguides. (a) E-plane coupling, (b) H-plane coupling.

Fig. 14. Comparison of transmission responses for 0 (TEM mode) and 35 (TE mode) angles of incidence for Configurations B, D, and F.

is reflected from the element ( dB), and not due to dielectric and conductor losses. As semiconductor/MEMS technology advances, the parasitic resistances in tuning elements will be reduced, resulting in increased phase range. Another option would be to increase the number of pole-pairs to four, though this would potentially necessitate increased fabrication complexity. B. Effect of Angle of Incidence Ordinary rectangular waveguide supporting the mode is used because it is very difficult to realize an actual rectangular TEM (parallel-plate) waveguide for experimentation. As menmode in a WR-187 waveguide simulates tioned earlier, the an angle of incidence of 35 at 5.5 GHz. In [25], it was concluded that for microstrip patch reflectarrays, the angle of incidence has little effect on behavior for angles less than 40 . Since the fundamental structure of this transmitarray element is very similar to that of a microstrip reflectarray, we expect that the 35 angle of incidence would also have an insignificant impact. To verify this claim, two sets of simulations were performed for Configurations B, D, and F (specified in Table II). The first set simulated the element in a 47.55 mm 30 mm rectangular mode as the WR-187 waveguide, which supports the same waveguide, but has an increased E-plane dimension (labeled in Fig. 9) so that the simulated array of elements are spaced by 30 mm. The second set of simulations used a 30 mm 30 mm waveguide with periodic boundary conditions, which simulates results, shown in broadside incidence. A comparison of the Fig. 14, reveals that there is little difference between the two responses, in both magnitude and phase. Thus, we conclude that the results produced in the WR-187 waveguide generalize well to broadside incidence, and expected angles of incidence in f/D ratios greater than at least 0.714.

Fig. 16. Simulated mutual coupling for pairs of configurations.

Two sets of dual-waveguide simulations, shown in Fig. 15, were used to quantify the E-plane (yz-plane) and H-plane (xz-plane) mutual coupling between adjacent elements. In each case, the waveguides to the left of the elements in the figures are isolated parallel plate waveguides, with perfect electric conductor (PEC) and perfect magnetic conductor (PMC) boundaries, into which a plane wave at broadside incidence is excited. On the right side, however, the wall separating the waveguides is removed so that power is allowed to couple from element 1 into element 2. On both sides, elements experience the simulated effect of being of the in an infinite array. As the input port is excited, the system reveals the amount of coupling between adjacent elements. The E-plane and H-plane coupling between two adjacent elements of different configurations is shown in Fig. 16. Both identically-configured (e.g., Configuration A for both elements 1 and 2, labeled A-A) and differently-configured (e.g., element 1 with Configuration D and element 2 with Configuration A, labeled D-A) combinations were studied. From the plots, we see dB and the H-plane that E-plane coupling did not exceed coupling did not exceed dB for the configurations tested. Thus, we conclude that while mutual coupling exists between the elements, its effects are minimal.

C. Effect of Mutual Coupling An important consideration in array design is the effect of mutual coupling between elements and its corresponding effect on the transmitarray scattering characteristics. In this section, we use 30 mm 30 mm waveguides to study the effect of mutual coupling for a proposed array element spacing of 30 mm.

IV. EXPERIMENTAL RESULTS An experimental transmitarray element was fabricated on Rogers Duroid 6002 and tested in a custom harness, as shown in Fig. 17, which was connected to WR-187 rectangular waveguide in the configuration shown in Fig. 9. The element

LAU AND HUM: ANALYSIS AND CHARACTERIZATION OF A MULTIPOLE RECONFIGURABLE TRANSMITARRAY ELEMENT

Fig. 17. Experimental waveguide test harness.

Fig. 19. Measured S

(angle).

Fig. 18. Measured S

Fig. 20. Measured S

for optimal configurations.

Fig. 21. Measured S

for optimal configurations.

(magnitude).

voltages were controlled using a custom programmable voltage controller. The patch and slot voltages were swept to create two-dimenplots shown in Figs. 18 and 19. Because there are sional two degrees of freedom in the control, many different configurations yield the same phase shift, but different magnitude responses. The black line in the figures denotes the locus of config. urations that yielded particular phase shifts with maximal The -parameters of the structure for the optimal configurations are shown in Figs. 20 and 21. Comparison with Figs. 11 and 12 reveals that they are very similar. Because the RF chokes used in the biasing were self-resonant at 5.35 GHz, we expect the experimental and simulated results to diverge slightly as we move away from that frequency. The magnitude and phase responses at 5.5 GHz of both experimental and simulated results are shown in Fig. 22, and we can see that the achieved transmission and reflection agree well and , with a maximum of dB. If we for both vary by less than 3 dB require that , or that be less than 10 dB, then the fabricated element achieves about 245 of phase tunability. However, depending on the beamforming algorithm used, larger variations can be accommodated. If the magnitude variation rein

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quirement is relaxed to 10 dB, then the element provides 330 of phase agility. A. Functionality as a Reflectarray Element A useful result from the transmitarray element design is its capacity to also function as a reflectarray element, if desired.

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Fig. 22. Transmitarray performance.

insertion loss variation. Diode loss incurred up to 3 dB of reduction in transmission magnitude, while the angle of incidence and mutual coupling were shown to have minimal effects on the cell’s performance. Requiring only two bonded microstrip substrates, the simplicity of the structure makes it practical in terms of cost, space, and ease of fabrication. Finally, the design is also able to function in reflectarray mode which can be advantageous in certain scanning configurations. Our future work in this area is focused on several investigations. One of our goals is to address the current design’s need for two independent control voltages, which adds complexity to the beamforming system. We believe it is possible to simplify the control of the resonators such that only one control voltage is necessary. Another issue apparent from the design is that loss in the varactor diodes diminishes the phase range of the unit cell. Future work will explore ways of mitigating this loss and/or expanding the order of the cell while maintaining a simple design. Finally, future investigations will also explore a full planar transmitarray composed of the proposed elements and its scanning characteristics.

REFERENCES

Fig. 23. Measured S

for 1 V slot varactor bias.

When the slot varactor bias voltage is fixed at 1 V to maximagnitude mize its capacitance, the resulting achievable and phase response curves are shown in Fig. 23. As a reflectarray element, this design can achieve more than 300 of phase tunability, with less than 4 dB of magnitude variation. The insertion loss is consistent with typical varactor diode-tuned reflectarray elements [6]. The ability of the transmitarray element to function as a reflectarray is useful in many scenarios. A planar array of such elements can beam scan not only in the forward direction as a transmitarray, but also in the reverse direction as a reflectarray, effectively doubling the scanning range. If used in a conformal array, some parts of the array can be made to transmit, while other parts of the array can be made to reflect, all using the same basic array element. V. CONCLUSION Reconfigurable transmitarrays are promising candidates for low-cost, high-gain beamforming systems. However, the lack of reconfigurable transmitarray unit cells possessing the necessary phase agility has been an obstacle in their development. In this paper, we have presented a simple, circuit-based analysis technique that employs concepts of coupled resonators to aid in the design of a three-pole transmitarray unit cell. We have designed, simulated, and experimentally demonstrated a transmitarray element design that achieves 245 of phase agility with 3 dB of

[1] D. M. Pozar, “Flat lens antenna concept using aperture coupled microstrip patches,” Electron. Lett., vol. 32, no. 23, pp. 2109–2111, Nov. 1996. [2] P. P. de la Torre and M. Sierra-Castaner, “Design of a 12 GHz transmitarray,” presented at the IEEE Proc. AP-S Int. Symp., Jun. 2007. [3] C. G. M. Ryan, J. R. Bray, Y. M. M. Antar, M. R. Chaharmir, J. Shaker, and A. Ittipiboon, “A broadband transmitarray using double square ring elements,” presented at the Int. Symp. on Antenna Technol. and Appl. Electromagn. and the Canadian Radio Sci. Meeting, Feb. 2009. [4] S. V. Hum, M. Okoniewski, and R. J. Davies, “Realizing an electronically tunable reflectarray using varactor diode-tuned elements,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 6, pp. 422–424, Jun. 2005. [5] M. Riel and J.-J. Laurin, “Design of an electronically beam scanning reflectarray using aperture-coupled elements,” IEEE Trans. Antennas Propag., vol. 55, no. 5, pp. 1260–1266, May 2007. [6] S. V. Hum, M. Okoniewski, and R. J. Davies, “Modeling and design of electronically tunable reflectarrays,” IEEE Trans. Antennas Propag., vol. 55, no. 8, pp. 2200–2210, Aug. 2007. [7] S. V. Hum, G. McFeetors, and M. Okoniewski, “Integrated MEMS reflectarray elements,” presented at the European Conf. Antennas and Propag., Nov. 2006. [8] J. Perruisseau-Carrier and A. K. Skrivervik, “Monolithic MEMS-based reflectarray cell digitally reconfigurable over a 360 phase range,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 138–141, 2008. [9] H. Rajagopalan, Y. Rahmat-Samii, and W. A. Imbriale, “RF MEMS actuated reconfigurable reflectarray patch-slot element,” IEEE Trans. Antennas Propag., vol. 56, no. 12, pp. 3689–3699, Dec. 2008. [10] C. Apert, T. Koleck, P. Dumon, T. Dousset, and C. Renard, “ERASP: A new reflectarray antenna for space applications,” presented at the Eur. Conf. Antennas and Propag., Nov. 2006. [11] J. P. Gianvittorio and Y. Rahmat-Samii, “Reconfigurable patch antennas for steerable reflectarray applications,” IEEE Trans. Antennas Propag., vol. 54, no. 5, pp. 1388–1392, May 2006. [12] W. Hu, M. Y. Ismail, R. Cahill, H. S. Gamble, R. Dickie, V. F. Fusco, D. Linton, S. P. Rea, and N. Grant, “Tunable liquid crystal reflectarray patch element,” Electron. Lett., vol. 42, no. 9, pp. 509–511, Apr. 2006. [13] A. Moessinger, S. Dieter, R. Jakoby, W. Menzel, and S. Mueller, “Reconfigurable LC-reflectarray setup and characterisation,” presented at the Eur. Conf. Antennas and Propag., Mar. 2009. [14] P. P. de la Torre and M. Sierra-Castaner, “Electronically reconfigurable patches for transmit-array structures at 12 GHz,” presented at the IEEE AP-S Int. Symp., Jul. 2008. [15] C.-C. Cheng, B. Lakshminarayanan, and A. Abbaspour-Tamijani, “A programmable lens-array antenna with monolithically integrated MEMS switches,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 8, pp. 1874–1884, Aug. 2009.

LAU AND HUM: ANALYSIS AND CHARACTERIZATION OF A MULTIPOLE RECONFIGURABLE TRANSMITARRAY ELEMENT

[16] B. A. Munk, Frequency Selective Surfaces: Theory and Design. New York: Wiley-Interscience, 2000. [17] M. P. DeLisio and R. A. York, “Quasi-optical and spatial power combining,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp. 929–936, Mar. 2002. [18] J. Y. Lau and S. V. Hum, “A low-cost reconfigurable transmitarray element,” presented at the IEEE AP-S Int. Symp., Jun. 2009. [19] A. Abbaspour-Tamijani, K. Sarabandi, and G. M. Rebeiz, “Antenna-filter-antenna arrays as a class of bandpass frequency-selective surfaces,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 1781–1789, Aug. 2004. [20] P. Hannan and M. Balfour, “Simulation of a phased-array antenna in waveguide,” IEEE Trans. Antennas Propag., vol. 13, no. 3, pp. 342–353, May 1965. [21] C. A. Balanis, Antenna Theory: Analysis and Design, 3rd ed. Hoboken, NJ: Wiley, 2005. [22] N. Marcuvitz, Waveguide Handbook. New York: McGraw-Hill, 1951. [23] A. Abbaspour-Tamijani, K. Sarabandi, and G. M. Rebeiz, “A millimetre-wave bandpass filter-lens array,” IET Microw., Antennas, Propag., vol. 1, no. 2, pp. 388–395, Apr. 2007. [24] SPEAG, SEMCAD X 2010 [Online]. Available: http://www.speag. com [25] S. D. Targonski and D. M. Pozar, “Analysis and design of a microstrip reflectarray using patches of variable size,” presented at the IEEE AP-S Int. Symp., Jun. 1994.

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Jonathan Yun Lau (S’07) was born in Calgary, AB, Canada. He received three B.Sc. degrees in computer engineering, psychology, and applied mathematics from the University of Calgary, in 2005 and the M.A.Sc. degree in electrical and computer engineering from the University of Toronto, Toronto, ON, Canada, in 2007, where he is currently working toward the Ph.D. degree. His research interests are in the areas of transmitarrays and reconfigurable antenna systems. Mr. Lau received the APEGGA Gold Medal Award in 2005 for his undergraduate achievements. He has received a number of scholarships for his graduate work including the NSERC Canada Graduate Scholarship, Bell University Labs Scholarship, and Ontario Graduate Scholarship in Science and Technology.

Sean Victor Hum (S’95–M’03) was born in Calgary, AB, Canada. He received the B.Sc., M.Sc., and Ph.D. degrees from the University of Calgary, in 1999, 2001, and 2006 respectively. In 2006, he joined the Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, ON, Canada, where he currently serves as an Assistant Professor. His present research interests lie in the area of reconfigurable RF antennas and systems, antenna arrays, and ultrawideband communications. Prof. Hum received the Governor General’s Gold Medal for his master’s degree work on radio-on-fiber systems in 2001. In 2004, he received a IEEE Antennas and Propagation Society Student Paper award for his work on electronically tunable reflectarrays. In 2006, he received an ASTech Leaders of Tomorrow award for his work in this area. He is also the recipient of three teaching awards. He served on the steering committee and technical program committee for the 2010 IEEE AP-S International Symposium on Antennas and Propagation. In August 2010, he was appointed as an Associate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION.

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Broadband Circularly Polarized Crossed Dipole With Parasitic Loop Resonators and Its Arrays Jung-Woo Baik, Member, IEEE, Tae-Hak Lee, Student Member, IEEE, Seongmin Pyo, Student Member, IEEE, Sang-Min Han, Senior Member, IEEE, Jichai Jeong, Senior Member, IEEE, and Young-Sik Kim, Member, IEEE

Abstract—A novel printed crossed dipole with broad axial ratio (AR) bandwidth is proposed. The proposed dipole consists of two dipoles crossed through a 90 phase delay line, which produces one minimum AR point due to the sequentially rotated configuration and four parasitic loops, which generate one additional minimum AR point. By combining these two minimum AR points, the proposed dipole achieves a broadband circularly polarized (CP) performance. The proposed antenna has not only a broad 3 dB AR bandwidth of 28.6% (0.75 GHz, 2.25–3.0 GHz) with respect to the CP center frequency 2.625 GHz, but also a broad impedance bandwidth for a voltage standing wave ratio (VSWR) 2 of 38.2% (0.93 GHz, 1.97–2.9 GHz) centered at 2.435 GHz and a peak CP gain of 8.34 dBic. Its arrays of 1 2 and 2 2 arrangement yield 3 dB AR bandwidths of 50.7% (1.36 GHz, 2–3.36 GHz) with respect to the CP center frequency, 2.68 GHz, and 56.4% (1.53 GHz, 1.95–3.48 GHz) at the CP center frequency, 2.715 GHz, respectively. This paper deals with the designs and experimental results of the proposed crossed dipole with parasitic loop resonators and its arrays. Index Terms—Broad axial ratio bandwidth, circularly polarized dipole, crossed dipole, dipole array.

I. INTRODUCTION

C

IRCULARLY polarized (CP) antennas have received much attention in various modern wireless communications, such as wireless local network (WLAN) [1], satellite communication [2], radio frequency identification (RFID) [3], direct broadcasting system (DBS) [4], and the global positioning system (GPS) [5] due to the reduction in multi-path effects and the flexibility in the orientation angle between the transmitter and receiver. In general, the design concepts researched for a CP antenna are compactness [6], operating frequency selectivity [7], multiband [8], and broadband CP operation. Especially, CP antennas

Manuscript received October 29, 2009; revised April 26, 2010; accepted July 31, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government [NRF-2009-352-D00224]. J.-W. Baik was with the Research Institute for Information and Communication Technology, Korea University, Seoul, Korea. He is now with the Broadcasting and Telecommunications Convergence Research Laboratory, ETRI, Daejeon 305-700, Korea (e-mail: ([email protected]). T.-H. Lee, S. Pyo, J. Jeong, and Y.-S. Kim are with the Department of Computer and Radio Communications Engineering, Korea University, Seoul 136713, Korea (e-mail: [email protected]). S.-M. Han is with the Department of Information and Communication Engineering, Soonchunhyang University, Asan 336-745, Chungnam, Korea. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090463

with broad axial ratio (AR) bandwidth have been widely investigated, because they can be utilized for several wireless communication systems simultaneously, which can provide a compact configuration. Techniques for broad AR bandwidth in CP antennas are classified into the radiating element and feed network types. In terms of the radiating element, broadband CP antennas have employed several approaches such as a parasitic element [9], [10], a travelling-wave radiating element [11]–[15], a stacked structure [16]–[18], a dielectric resonator [19]–[21], and a coplanar waveguide (CPW)-fed square slot [22], [23]. In regard to a feed network, series coupled feed [24]–[26], broadband hybrid coupler [27]–[29], aperture coupled feed [30], [31], driven patch coupled feed [32], and sequentially rotated configuration [33]–[37] have been investigated. By comparison, several dipole CP antennas for broad AR bandwidth have been constantly proposed, because a dipole has many attractive features such as lower cost, lighter weight, and simpler design [15], [38]–[41]. The CP dipole presented in [38] is realized by employing two orthogonal dipoles with different proper lengths, which ensures that the real part of their input admittances are equal and the phases of the input admittances differ by 90 . In [15] and [39], CP antennas with a 2 dB AR bandwidth of 20–27% are achieved by using a dual rhombic loop configuration. The antenna in [40] has the 3 dB AR bandwidth of 20% using the crossed bow-tie dipole instead of a crossed dipole for a broad AR bandwidth. In [41], a broadband CP performance is accomplished by combining strip dipoles with slots. Recently, a simple crossed dipole with a broad AR bandwidth of 15.6% has been proposed. It uses a sequentially rotated configuration in itself [42]. This dipole CP antenna has a broadband CP performance due to the sequential phase of the four legs of the dipole. In this paper, a crossed dipole antenna with four parasitic loops is proposed for a broader CP bandwidth than that of the conventional crossed dipole CP antenna [42]. And, its array antennas of 1 2 and 2 2 arrangements are implemented to further improve the AR and impedance bandwidth. The two crossed dipole elements of the 1 2 array are placed with a 90 phase difference. Similarly, the four elements of the 2 2 array have a sequentially rotated configuration and the respective crossed dipole is oriented to a phase of 0 , 90 , 180 , and 270 . In Section II, a single crossed dipole with four parasitic open loops is introduced with the detailed design principle and analyzed numerically. Section III demonstrates the design of the 1 2 and 2 2 dipole arrays along with the experimental results.

0018-926X/$26.00 © 2010 IEEE

BAIK et al.: BROADBAND CP CROSSED DIPOLE WITH PARASITIC LOOP RESONATORS AND ITS ARRAYS

Fig. 1. Geometry of the printed crossed dipole with four parasitic loop resonators. (a) Top view and (b) bottom view of the substrate. (c) Side view.

II. DESIGN OF SINGLE CROSSED DIPOLE WITH FOUR LOOP RESONATORS A. Dipole Design and Numerical Analysis The geometry of the proposed crossed dipole antenna with four parasitic loop resonators is shown in Fig. 1. The printed dipole is fabricated on an RT/Duroid 5880 substrate with a relative permittivity of 2.2 and thickness of 1.6 mm. As illustrated in Fig. 1, the proposed antenna consists of two crossed dipoles, the which acts as a phase delay rounded microstrip line with line ( is the guided wavelength at the center frequency), four , and a reparasitic loops, a semi-rigid coaxial cable with flector. Each half of the printed dipole shown in Fig. 1(a) and (b) is placed on the opposite side of the substrate and is symmetrical with respect to a semi-rigid coax feed, and four parasitic loops with a gap are printed on the top side of the substrate. Each half of the crossed dipole is connected to the inner core and outer shield conductor of a semi-rigid coaxial cable. The inner core can be connected to the half of the crossed dipole printed on the top side of the substrate through the etched hole shown in Fig. 1(b). As shown in Fig. 1(c), a crossed dipole with parasitic loops printed on the substrate is distanced from a reflector utilized for high gain and excitation of the balanced mode without a balun structure. The semi-rigid coaxial cable is inserted across the small hole on the reflector in order to link itself with the proposed crossed dipole antenna. The substrate with the antenna pattern is fixed to the reflector using a mount post which is made of a teflon with a relative permittivity of 2.1. Basically, a crossed dipole can produce broadband CP performance because of a sequential phase of four legs of the dipole [42]. The single minimum AR point can be achieved from the crossed dipole. The designed CP center frequency of the dipole is 2.4 GHz. For achieving broader CP bandwidth than that of the crossed dipole, the parasitic open loop resonators are employed. The gap is placed asymmetrically with respect to the reference

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plane for achieving the additional minimum AR point. The 3 dB AR bandwidth can be controlled by the gap position and gap width . The open loop resonator is essentially a half-wavelength res( onator because the fundamental mode number is , is the circumference of a loop and ), while the open loop resonator used in the proposed antenna operates , since two orthogonal legs with properly when the phase difference of 90 are simultaneously coupled with the open loop resonator. Therefore, the additional minimum AR point can be produced at the frequency of mode number (3 GHz). The fundamental resonant frequency of the is 1.5 GHz. open loop with In the proposed dipole, the balanced mode can be excited befrom a reflector prevents the produccause a distance of tion of an induced current on the outside of the coaxial shield conductor ( is the free-space wavelength at the CP center frequency). In other words, the open circuit is produced at the point connected between the crossed dipole and a semi-rigid coax, distance from the short circuit conwhich is caused by the nected between a reflector and the outer shield conductor of a semi-rigid coax. This open circuit prevents the current from being induced on the outer shield conductor of a semi-rigid coax. Therefore, the proposed dipole is fed by the coaxial cable without a balun structure. The parameters of the crossed dipole shown in Fig. 1 are , , , , , , , , , , and . In the antenna, the of the crossed dipole is designed to be wide enough for width the impedance matching and bandwidth of the proposed dipole. The proposed antenna has a broader CP performance than that of the previous crossed dipole without parasitic elements, because of the four parasitic loop resonators. The parasitic resonators additionally produce the minimum AR point at the upper band of a fundamental minimum AR point, which indicates the minimum AR point that is only produced by the crossed dipole without parasitic loops. Fig. 2 shows the simulated input impedance loci of the crossed dipole with four parasitic loop resonators, with at 2.1 GHz. A semi-rigid coaxial with 75 is used as a quarter-wavelength impedance transformer for impedance matching. The simulation has been carried out using Ansoft HFSS based on the finite-element method [43]. For achieving a broad impedance bandwidth capable of a broad AR bandwidth, the width of the printed dipole is designed to be wider than that of the conventional crossed dipole [42]. To examine the effect of the dipole width , the simulated reare plotted in Fig. 3. Fig. 4 shows turn losses as a function of the simulated ARs versus gap , which is placed in the parasitic loop resonator. Although the minimum AR is generated when , is selected in order to achieve a broad AR bandwidth. Fig. 5 plots the simulated return losses and ARs versus the gap position . It can be seen from Figs. 4 and 5 that the AR near 3 GHz is worse than that near 2.4 GHz. This means the following two facts. First, the AR near 3 GHz is dominantly affected by the parasitic loop resonators. Second, the parasitic

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Fig. 2. Simulated input impedance loci.

Fig. 3. Simulated return losses versus a dipole width w .

Fig. 4. Simulated axial ratios versus gap g .

loop is not excited from the two orthogonal dipole legs with the exact phase difference of 90 around 3 GHz. B. Experimental Results Figs. 6 and 7 show the simulated and measured frequency responses of the proposed crossed dipole antenna with four parasitic loops. The Figures show that the measured return loss, gain, and AR are in good agreement with the simulated values. Two

Fig. 5. Simulated return losses and axial ratios versus l .

Fig. 6. Measured and simulated return losses of the single crossed dipole antenna with four parasitic loops.

Fig. 7. Measured and simulated axial ratios and gains of the single crossed dipole with parasitic loops.

resonant frequencies, 2.03 and 2.57 GHz, which are the measured result shown in Fig. 6, are generated by the dipoles with and , as shown in dipole lengths, Fig. 1. As shown in Fig. 6, the simulated 10 dB impedance bandwidth is 1 GHz (41.7% at 2.4 GHz) which is 1.9–2.9 GHz. The measured 10 dB impedance bandwidth is 0.93 GHz (38.2% at the center frequency of 2.435 GHz), which is 1.97–2.9 GHz. From the AR results shown in Fig. 7, the simulated

BAIK et al.: BROADBAND CP CROSSED DIPOLE WITH PARASITIC LOOP RESONATORS AND ITS ARRAYS

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Fig. 8. Measured linearly spinning radiation patterns of the single crossed dipole at 2.52 GHz. Fig. 9. Photograph of the single crossed dipole antenna with four parasitic loops.

and measured 3 dB AR bandwidths are 0.79 GHz (2.19–2.98 GHz, 30.6% at the CP center frequency of 2.585 GHz) and 0.75 GHz (2.25–3.0 GHz, 28.6% at 2.625 GHz), respectively, because of the sequentially rotated configuration in itself and four parasitic loop resonators, which produce the two minimum AR points. In other words, the two deep points of simulated AR curve in region I and II shown in Fig. 7 are generated by the crossed dipole and parasitic loops with gap , respectively. In the proposed CP antenna, a broadband CP performance is achievable via the proper combination of the two minimum AR points, which are produced at 2.40 and 3.0 GHz. The simulated and measured minimum ARs are 1.08 and 0.08 dB at the frequency of 2.37 and 2.52 GHz, respectively. In Fig. 7, both the simulated and measured gains in the respective 3 dB AR bandwidth ranges from 8.3 to 8.7 dBic and from 7.9 to 8.7 dBic, respectively. And, the measured peak gain at 2.52 GHz, which is the minimum AR frequency, is 8.34 dBic, as shown in Fig. 7. The difference between the simulated and measured results shown in Figs. 6 and 7 may be caused by imperfect symmetry between the two printed dipoles and inexact distance between the substrate with the fabricated antenna pattern and reflector in the mechanical mounting. The measured linearly spinning radiation patterns at 2.52 GHz shown in Fig. 8(a) and (b) are for the two orthogonal - and -planes, respectively. It can be seen planes of the from Fig. 8 that a good AR can be achieved in the boresight direction. The half-power beamwidths of the measured radi- and -planes are and ation patterns in the 65 , respectively. The proposed dipole radiates a right hand (RH) CP wave within a 3 dB AR, due to the sequentially right-handed phase of four dipole legs, which is caused via a microstrip phase delay line with one-quarter wavelength at the CP center frequency of 2.52 GHz, and a parasitic loop with a right-handed surface current. Fig. 9 shows the photograph of the fabricated antenna.

III. ARRAY DESIGN AND EXPERIMENTAL RESULTS The arrangements of the crossed dipole with parasitic loop resonators for the 1 2 and 2 2 arrays, which have a sequentially rotated configuration, are shown in Fig. 10(a) and (b). Two broadband feed networks for the 1 2 and 2 2 arrays are designed via an annealing optimization technique that is a well

Fig. 10. Geometries of 1 (b) 2 2 array.

2

2 2 and 2 2 2 crossed dipole arrays. (a) 1 2 2 array.

known method for designing a sequentially rotated feed network [33]. In Fig. 10(a), the two crossed dipole elements of the 1 2 crossed dipole array with parasitic loops are placed with a 90 rotation. Similarly, the four elements of the 2 2 array are sequentially rotated with a phase of 0 , 90 , 180 , and 270 . These sequentially rotated configurations produce a broad AR bandwidth. The space between two adjacent elements is selected to be 88 mm, which is 0.71 , in order to minimize mutual coupling without substantial degradation of the radiation pattern by the sidelobes [33]. Fig. 11 shows the photographs of the 1 2 and 2 2 arrays illustrated in Fig. 10. Fig. 12 shows the simulated and measured frequency responses of the proposed 1 2 dipole array. The measured -parameter is in good agreement with the simulated value. The simulated and measured 10 dB impedance

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Fig. 11. Photographs of the manufactured two arrays. (a) 1 arrays.

Fig. 12. Measured and simulated return losses of 1

2 2 and (b) 2 2 2

2 2 crossed dipole array.

Fig. 13. Measured and simulated ARs and gains of 1

2 2 crossed dipole array.

bandwidths are 1.45 GHz (1.8–3.25 GHz), which is 57.4% at the center frequency of 2.525 GHz and 1.31 GHz (1.94–3.25 GHz), which is 50.5% with respect to the center frequency of 2.595 GHz, respectively. Fig. 13 plots the simulated and measured ARs and RHCP gains against the frequency range at 1.8–3.6 GHz for the 1 2 crossed dipole array with parasitic loop resonators. The simulated and measured 3 dB AR bandwidths are 1.34 GHz

2

Fig. 14. Measured radiation patterns of 1 2 crossed dipole array in the and -planes. (a) 2.2 GHz. (b) 2.52 GHz. (c) 3.0 GHz.

YZ

XZ -

(1.97–3.31 GHz, 50.8% at the CP center frequency of 2.64 GHz) and 1.36 GHz (2–3.36 GHz, 50.7% with respect to the CP center frequency of 2.68 GHz), respectively. From Fig. 13, the simulated and measured CP peak gains within a voltage standing wave ratio (VSWR) 2 and AR 3 are 11.8 dBic at 2.99 GHz and 11.7 dBic at 2.6 GHz, respectively. With increasing operating frequency near 3.1 GHz, the gain is decreased, because of the increment of a sidelobe level and a shift of the direction of maximum radiation in the -axis. Fig. 14 shows the measured radiation patterns of the 1 2 array shown in Fig. 10(a). The results are obtained via a linearly spinning antenna measurement system. Since the two radiating elements are arranged in the -axis, the radiation pat-plane have narrower beamwidths than those in terns in the -plane. Based on Fig. 14, it can be seen that the sidelobe the of the radiation pattern becomes enlarged as the operating frequency is increased, while those of the radiation patterns in the -plane remain almost unchanged with increasing frequency. The results plotted in Fig. 14 imply that a good and broadband CP performance can be achieved from a 1 2 dipole array. Fig. 15 shows the simulated and measured return losses of 2 dipole array illustrated in Fig. 10(b). As shown in the 2 Fig. 15, two bandwidths at 2.03–2.83 GHz (33.0% centered at 2.43 GHz) and 3.07–3.22 GHz (4.7% centered at 3.145 GHz)

BAIK et al.: BROADBAND CP CROSSED DIPOLE WITH PARASITIC LOOP RESONATORS AND ITS ARRAYS

Fig. 15. Measured and simulated return losses of 2

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2 2 crossed dipole array.

Fig. 16. Measured and simulated ARs and gains of 2

2 2 crossed dipole array.

are exhibited in the simulated result, due to an insufficient impedance match with respect to VSWR 2 near 3 GHz. Similarly, both bandwidths, exhibited at 1.93–2.93 GHz (41.2% centered at 2.43 GHz) and 3.12–3.31 GHz (5.9% centered at 3.215 GHz) are exhibited in the measured result. This mismatch may be caused by the fact that the fabricated 2 2 feed network is based on an inaccuracy of each characteristic impedance. Fig. 16 plots the simulated and measured frequency responses, which are the CP gain and AR in the boresight 2 dipole array with broadband CP opdirection of the 2 eration. It can be seen from Fig. 16 that the trends shown in the simulated and measured results are similar. The simulated and measured CP peak gains in the boresight within the 3 dB AR bandwidth are 14.4 dBic at 2.69 GHz and 14.2 dBic at 2.6 GHz, respectively. The decrement of gain exhibited around 3.3 GHz (See Fig. 16) is caused by the shifting of the maximum radiation direction. In the AR results, the simulated and measured 3 dB AR bandwidths are 1.46 GHz (1.95–3.41 GHz, 54.5% with respect to the center frequency of 2.68 GHz) and 1.53 GHz (1.95–3.48 GHz, 56.4% with regard to the center frequency of 2.715 GHz), respectively. The curves of AR near 2.1 and 3.1 GHz are protrusive, because of the characteristics 2 sequentially rotated configuration employed for of the 2 a broad AR bandwidth. This phenomenon is also exhibited in cases utilizing a sequentially rotated feed network [33], [34].

2

Fig. 17. Measured radiation patterns of 2 2 crossed dipole array in the and -planes. (a) 1.98 GHz. (b) 2.46 GHz. (c) 2.8 GHz. (d) 3.0 GHz.

YZ

XZ -

Fig. 17 shows the measured radiation patterns at several operating frequencies in the two orthogonal planes. In Fig. 17(a), the beamwidth is broader than those of the others plotted in Fig. 17(b)–(d), because of the relative long wavelength at 1.98 GHz. As shown in Fig. 17, the spinning radiation patterns at 2.46 and 2.8 GHz are well symmetrical in the - and -planes, while the radiation patterns at 1.98 and 3 GHz are slightly asymmetrical in the two orthogonal planes, due to the geometry of the crossed dipole with parasitic loop resonators and the distance between the dipole and reflector, which is optimized at the CP center frequency of 2.52 GHz. For easy comparison, the CP radiation performances of the proposed antennas and the others are summarized in Table I.

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TABLE I COMPARISON BETWEEN THE PROPOSED ANTENNAS AND THE OTHER BROADBAND CP ANTENNAS

IV. CONCLUSION In this paper, a printed crossed dipole with four parasitic loop resonators is proposed for a broad AR bandwidth. Since a single crossed dipole with a sequentially rotated configuration in itself and parasitic loops near the dipole produce two AR minimum points, a broadband CP performance can be easily achieved. The proposed dipole antenna has not only a broad 3 dB AR bandwidth of 0.75 GHz at 2.25–3.0 GHz (28.6% with respect to the CP center frequency of 2.625 GHz), but also a broad impedance bandwidth of 0.93 GHz at 1.97–2.9 GHz (38.2% centered at 2.435 GHz). Moreover, the two arrays of 1 2 and 2 2 arrangement are implemented and used in experiments to increase the AR bandwidth via a sequentially rotated constitution of feed networks. The measured 10 dB impedance bandwidth and AR bandwidth in the 1 2 array are 1.31 GHz (1.94–3.25 GHz), which is 50.5% with respect to the center frequency of 2.595 GHz, and 1.36 GHz, which is 50.7% with respect to the CP center frequency of 2.68 GHz. In the 2 2 array, the measured 10 dB impedance bandwidths in the two bands are 1 GHz (41.2% at 2.43 GHz) and 0.19 GHz (5.9% at 3.215 GHz). The measured 3 dB AR bandwidth is 1.53 GHz (56.4% at 2.715 GHz). The proposed antenna as a prototype and its arrays may be used in the applications such as the wireless communication system that can cover all cases of GPS L1 (1.565–1.585 GHz), Wibro (2.3–2.39 GHz), WLAN (2.400–2.484 GHz), and RFID (2.446–2.454 GHz) using the frequency scaling technique due to its broadband CP performance. REFERENCES [1] K.-L. Wong, F.-R. Hsiao, and C.-L. Tang, “A low-profile omnidirectional circularly polarized antenna for WLAN access point,” in IEEE Antennas Propag. Soc. Int. Symp. Dig., Monterey, CA, Jun. 2004, pp. 2580–2583.

[2] E. Arnieri, L. Boccia, G. Amendola, and G. D. Massa, “A compact high gain antenna for small satellite applications,” IEEE Trans. Antennas Propag., vol. 55, no. 2, pp. 277–282, Feb. 2007. [3] H. L. Chung, X. Qing, and Z. Ning, “Broadband circularly polarized stacked patch antenna for UHF RFID applications,” in IEEE Antennas Propag. Soc. Int. Symp. Dig., Honolulu, HI, Jun. 2007, pp. 1189–1192. [4] K. Sakakibara, Y. Kimura, J. Hirokawa, M. Ando, and N. Goto, “A two-beam slotted leaky waveguide array for mobile reception of dualpolarization DBS,” IEEE Trans. Vehic. Tech., vol. 48, no. 1, pp. 1–7, Jan. 1999. [5] X. L. Bao, G. Ruvio, M. J. Ammann, and M. John, “A novel GPS patch antenna on a fractal hi-impedance surface substrate,” IEEE Antennas Wireless Propag. Lett., vol. 5, no. 1, pp. 323–326, Dec. 2006. [6] W.-S. Chen, C.-K. Wu, and K.-L. Wong, “Novel compact circularly polarized square microstrip antenna,” IEEE Trans. Antennas Propag., vol. 49, no. 3, pp. 340–342, Mar. 2001. [7] H. K. Ng and K. W. Leung, “Frequency tuning of the linearly and circularly polarized dielectric resonator antennas using multiple parasitic strips,” IEEE Trans. Antennas Propag., vol. 54, no. 1, pp. 225–230, Jan. 2006. [8] X. L. Bao and M. J. Ammann, “Dual-frequency circularly-polarized patch antenna with compact size and small frequency ratio,” IEEE Trans. Antennas Propag., vol. 55, no. 7, pp. 2104–2107, July 2007. [9] R. L. Li, A. Traille, J. Laskar, and M. M. Tentzeris, “Bandwidth and gain improvement of a circularly polarized dual-rhombic loop antenna,” IEEE Antennas Wireless Propag. Lett., vol. 5, pp. 84–87, 2006. [10] R. L. Li, J. Laskar, and M. M. Tentzeris, “Wideband probe-fed circularly polarised circular loop antenna,” Electron. Lett., vol. 41, no. 18, pp. 997–999, Sep. 2005. [11] M. Sumi, K. Hirasawa, and S. Shi, “Two rectangular loops fed in series for broadband circular polarization and impedance matching,” IEEE Trans. Antennas Propag., vol. 52, no. 2, pp. 551–554, Feb. 2004. [12] Y. Zhang and L. Zhu, “Printed dual spiral-loop wire antenna for broadband circular polarization,” IEEE Trans. Antennas Propag., vol. 54, no. 1, pp. 284–288, Jan. 2006. [13] R. L. Li and V. F. Fusco, “Circularly polarized twisted loop antenna,” IEEE Trans. Antennas Propag., vol. 50, no. 10, pp. 1377–1381, Oct. 2002. [14] Y. Li, Q. Xue, E. K. N. Yung, and Y. Long, “Circularly-polarised microstrip leaky-wave antenna,” Electron. Lett., vol. 43, no. 14, July 2007. [15] H. Morishita, H. Hamada, K. Nishida, and T. Nagao, “A wideband circularly polarized dipole antenna,” in IEEE Antennas Propag. Soc. Int. Symp. Dig., Atlanta, GA, Jun. 1998, pp. 2348–2350. [16] Y.-T. Chen, S.-W. Wu, and J.-S. Low, “Broadband circularly-polarised slot antenna array,” Electron. Lett., vol. 43, no. 24, pp. 1323–1324, Nov. 2007. [17] T. Sudha, T. S. Vedavathy, and N. Bhat, “Wideband single-fed circularly polarised patch antenna,” Electron. Lett., vol. 40, no. 11, pp. 648–649, May 2004. [18] K. L. Chung and H. K. Kan, “Stacked quasi-elliptical patch array with circular polarisation,” Electron. Lett., vol. 43, no. 10, pp. 555–556, May 2007. [19] K. L. Leung, “Circularly polarized dielectric resonator antenna excited by a shorted annular slot with a backing cavity,” IEEE Trans. Antennas Propag., vol. 52, no. 10, pp. 2765–2769, Oct. 2004. [20] L. C. Y. Chu, D. Guha, and Y. M. M. Antar, “Comb-shaped circularly polarised dielectric resonator antenna,” Electron. Lett., vol. 42, no. 14, pp. 785–787, July 2006. [21] J.-S. Row, “Experimental study of circularly polarised microstrip antennas loaded with superstrate,” Electron. Lett., vol. 41, no. 21, pp. 1155–1157, Oct. 2005. [22] Y. B. Chen, X. F. Liu, Y. C. Jiao, and F. S. Zhang, “CPW-fed broadband circularly polarised square slot antenna,” Electron. Lett., vol. 42, no. 19, pp. 1074–1075, Sep. 2006. [23] C. C. Chou, K. H. Lin, and H. L. Su, “Broadband circularly polarised crosspatch-loaded square slot antenna,” Electron. Lett., vol. 43, no. 9, pp. 485–486, Apr. 2007.

BAIK et al.: BROADBAND CP CROSSED DIPOLE WITH PARASITIC LOOP RESONATORS AND ITS ARRAYS

[24] J.-S. Row, C. Y. D. Sim, and K.-W. Lin, “Broadband printed ring-slot array with circular polarisation,” Electron. Lett., vol. 41, no. 3, pp. 110–112, Feb. 2005. [25] J.-S. Row, “The design of a squarer-ring slot antenna for circular polarization,” IEEE Trans. Antennas Propag., vol. 53, no. 6, pp. 1967–1972, June 2005. [26] J.-F. Wu and J.-S. Row, “Broadband circularly-polarised microstrip antenna with switchable polarisation sense,” Electron. Lett., vol. 42, no. 24, pp. 1374–1375, Nov. 2006. [27] X. M. Qing and Y. W. M. Chia, “Circularly polarised circular ring slot antenna fed by stripline hybrid coupler,” Electron. Lett., vol. 35, no. 25, pp. 2154–2155, Dec. 1999. [28] L. Bian, Y.-X. Guo, L. C. Ong, and X.-Q. Shi, “Wideband circularlypolarized patch antenna,” IEEE Trans. Antennas Propag., vol. 54, no. 9, pp. 2682–2686, Sep. 2006. [29] K.-W. Khoo, Y.-X. Guo, and L. C. Ong, “Wideband circularly polarized dielectric resonator antenna,” IEEE Trans. Antennas Propag., vol. 55, no. 7, pp. 1929–1932, July 2007. [30] S. Gao, Y. Qin, and A. Sambell, “Broadband circularly polarised high efficiency active antenna,” Electron. Lett., vol. 42, no. 5, pp. 258–260, Mar. 2006. [31] J.-Y. Sze, C.-I. G. Hsu, M.-H. Ho, Y.-H. Ou, and M.-T. Wu, “Design of circularly polarized annular-ring slot antennas fed by a double-bent microstripline,” IEEE Trans. Antennas Propag., vol. 55, no. 11, pp. 3134–3139, Nov. 2007. [32] Nasimuddin and K. P. Esselle, “New feed system for wideband circularly polarised stacked microstrip antenna,” Proc. IET Microw. Antennas Propag., vol. 1, no. 5, pp. 1086–1091, Oct. 2007. [33] H. Evans, P. Gale, B. Aljibouri, E. G. Lim, E. Korolkeiwicz, and A. Sambell, “Application of simulated annealing to design of serial feed sequentially rotated 2 2 antenna array,” Electron. Lett., vol. 36, no. 24, pp. 1987–1988, Nov. 2000. [34] H. Evans, P. Gale, and A. Sambell, “Performance of 4 4 sequentially rotated patch antenna array using series feed,” Electron. Lett., vol. 39, no. 6, pp. 493–494, Mar. 2003. [35] K. M. Lum, C. Laohapensaeng, and C. Free, “A novel traveling-wave feed technique for circularly polarized planar antennas,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 3, pp. 180–182, Mar. 2005. [36] S. Gao, Y. Qin, and A. Sambell, “Low-cost broadband circularly polarized printed antennas and array,” IEEE Antennas Propag. Mag., vol. 49, no. 4, pp. 57–64, Aug. 2007. [37] D. Roscoe, L. Shafai, and A. Ittipiboon, “Circularly polarised travelling-wave printed line antennas,” Electron. Lett., vol. 25, no. 20, pp. 1407–1408, Sep. 1989. [38] M. F. Bolster, “A new type of circular polarizer using crossed dipoles,” IRE Trans. Microw. Theory Tech., vol. 9, no. 5, pp. 385–388, Sep. 1961. [39] H. Morishita, K. Hirasawa, and T. Nagao, “Circularly polarized wire antenna with a dual rhombic loop,” Proc. IEE Microw. Antennas Propag., vol. 145, no. 3, pp. 219–224, Jun. 1998. [40] S. D. Kulkarni and S. N. Makarov, “A circularly polarized UHF antenna at 550–700 MHz,” in IEEE Antennas Propag. Soc. Int. Symp. Dig., Honolulu, Hawaii, Jun. 2007, pp. 2981–2984. [41] K. Ito, “Circularly polarised printed antenna with wide axial-ratio bandwidth using strip dipoles and slots,” Proc. IEE Microw. Antennas Propag., vol. 130, no. 6, pp. 397–402, Oct. 1983. [42] J.-W. Baik, K.-J. Lee, W.-S. Yoon, T.-H. Lee, and Y.-S. Kim, “Circularly polarised printed crossed dipole antennas with broadband axial ratio,” Electron. Lett., vol. 44, no. 13, pp. 785–786, Jun. 2008. [43] “HFSS User Manual,” Ansoft Corp., Pittsburgh, PA, 2005.

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Jung-Woo Baik (A’08–M’10) received the B.S. degree in electronic engineering from Kumoh National Institute of Technology, Gumi, Korea, in Aug. 2002, and the M.S. and Ph.D. degrees in radio science and engineering from Korea University, Seoul, in 2005 and 2008, respectively. From September 2008 to August 2009, he worked as a Research Professor in the Research Institute for Information and Communication Technology at Korea University. From September 2009 to February 2010, he worked as a Postdoctoral Research Fellow in the Poly-Grames Research Center at École Polytechnique de Montréal,

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Canada. He is now with the Broadcasting and Telecommunications Convergence Research Laboratory, ETRI, Daejeon, Korea. He has authored and coauthored over 53 technical conference, letter, and journal papers. His research interests include RF and microwave components, passive/active antennas, wave propagation, and EM theories. Mr. Baik was a recipient of the Graduate Fellowship presented by the Foundation of LG Group. He is now a recipient of a Postdoctoral Fellowship presented by National Research Foundation (NRF) of Korea.

Tae-Hak Lee (S’10) received the B.S. degree in electronic engineering from Konkuk university, Seoul, Korea, in 2007, and is currently working toward the Ph.D. degree in the M.S. and Ph.D. unified course at Korea University, Seoul. From 2007 to 2009, he was a Teaching Assistant for electromagnetics and microwave engineering classes. His recent research interests include the passive/active antennas, and especially wave propagation modeling for LF bands.

Seongmin Pyo (S’09) received the B.S. and M.S. degrees in electrical engineering from Korea University, Seoul, Korea, in 2002 and 2004, respectively, and is currently working toward the Ph.D. degree at Korea University, Seoul. In 2004, he became a Senior Member of Technical Staff with the Pantech Company Ltd., where his research activities included design and analysis of antennas and RF components and circuits for code-division multiple-access (CDMA) cellular systems. In 2007, he became a Senior Researcher with the Research Institute of Information and Communication Technology, Korea University. Since 2008, he has been with Korea University, where he is currently a Research and Teaching Assistant with the Radio Communication Technology Laboratory. His main research interests include antennas and RF and microwave passive components and circuits for communication systems based on metamaterial-based EM theories and their applications.

Sang-Min Han (S’02–M’03–SM’10) was born in Seoul, Korea. He received the B.S., M.S., and Ph.D. degrees in radio sciences and engineering from Korea University, Seoul, in 1996, 1998, and 2003, respectively. From 1999 to 2001, he was a Lecturer with the School of Electrical Engineering, Korea University. From 2003 to 2004, he was a Postdoctoral Researcher with the Microwave Electronics Laboratory, University of California at Los Angeles (UCLA). From January 2005 to August 2007, he was a Senior Research Engineer with the Samsung Advanced Institute of Technology (SAIT), Yongin, Korea, where he was a Project Leader of the RF System Architecture Team. In September 2007, he joined Soonchunhyang University, Korea as an Assistant Professor. He is currently an Associate Editor of the journal of the Korean Institute of Information Technology (JKIIT) and the Korean Academia-Industrial cooperation Society (JKAIS). He has authored or coauthored over 100 technical conference, letters, and journal papers. He has registered or filed over 40 patents in RF/microwave technology. His research interests include advanced RF/microwave system architectures, active integrated antenna systems, and metamaterial components. Prof. Han appears in Marquis’ Who’s Who in Science and Engineering (2006–2007) and Marquis’ Who’s Who in Asia (2007).

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Jichai Jeong (SM’96) received the B.S. degree from Korea University, Seoul, in 1980, the M.S. degree from KAIST, in 1982, and the Ph.D. degree in electrical engineering from Carnegie Mellon University, Pittsburgh, PA, in 1988. From 1982 to 1985, he worked as a Researcher at Korea Institute of Science and Technology. From 1988 to 1993, he was a Member of Technical Staff with AT&T Bell Laboratories, Murray Hill, NJ, where he worked in optoelectronic integrated circuits and semiconductor lasers for optical communications. From 1993 to 1995, he was on the faculty of the Electrical Engineering Department, Pohang University of Science and Technology. In 1995, he joined the faculty of the Radio Engineering Department at Korea University. His current research interests include modeling and simulation of RFICs, RF components, and optical components and transmission systems for fiber optic communications.

Young-Sik Kim (S’82–M’86) received the B.S. degree in electronics engineering from Korea University, Seoul, in 1973, and the M.S. and Ph.D. degrees in electrical engineering from the University of Massachusetts at Amherst, in 1986 and 1988, respectively. From 1988 to 1989, he was a Postdoctoral Research Fellow at the University of Massachusetts at Amherst. From 1989 to 1993, he was with the Mobile Communications Division, Korea Electronics and Telecommunications Research Institute, Daejeon. Since 1993, he has been with the Department of Radio Communication Engineering, Korea University, where he is currently a Professor. His main field of interest is millimeter-wave antennas and front-end systems and mobile telecommunication systems.

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 1, JANUARY 2011

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Frequency Selective Reflectarray Using Crossed-Dipole Elements With Square Loops for Wireless Communication Applications Long Li, Member, IEEE, Qiang Chen, Member, IEEE, Qiaowei Yuan, Kunio Sawaya, Senior Member, IEEE, Tamami Maruyama, Member, IEEE, Tatsuo Furuno, Member, IEEE, and Shinji Uebayashi, Member, IEEE

Abstract—A new frequency selective reflectarray (FSR) comprising a crossed-dipole array and a frequency selective surface (FSS) of square loops printed on both sides of a dielectric substrate is presented for wireless communication applications. The reflectarray functions as a reflector, and generates the desired reflected beam shape while steering the primary wave source in the desired direction. Moreover, the FSR should be partially transparent for propagation channels of other communication systems working in other frequency bands. Some new FSR designs comprising 11 by 7 elements for dual-source and dual-polarized operation are given and verified by simulation and experiment. Furthermore, the FSR is applied to a WCDMA system to eliminate blind spots in communications between the base station and mobile users. A practical link budget analysis demonstrates the effectiveness of the FSR to improve the quality of communications. Finally, the proximity effect of concrete wall on the FSR is discussed to illustrate the applicability and flexibility of the proposed frequency selective reflectarray. Index Terms—Blindness, crossed-dipole, frequency selective reflectarray (FSR), link budget analysis, square-loop FSS, WCDMA.

I. INTRODUCTION microstrip reflectarray is a flat low-profile reflector consisting of an array of microstrip patch elements that reflects a beam in a specified direction when illuminated by a primary source. The planar reflectarray is rapidly becoming an attractive alternative to the conventional parabolic reflector antenna because of its advantages such as the ability to surface mount the reflectarray due to its low mass and volume, its ease of deployment, low manufacturing cost, scannable beam, etc.

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Manuscript received July 28, 2009; revised April 30, 2010; accepted June 23, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported in part by the Program for New Century Excellent Talents in University, China and in part by the National Natural Science Foundation of China under Contract 61072017. L. Li is with School of Electronic Engineering, Xidian University, Xi’an 710071, China (e-mail: [email protected]). Q. Chen and K. Sawaya are with the Department of Electrical and Communication Engineering, Tohoku University, Sendai 980-8579, Japan (e-mail: [email protected]; [email protected]). Q. W. Yuan is with Sendai National College of Technology, Sendai 989-3128, Japan (e-mail: [email protected]). T. Maruyama, T. Furuno, and S. Uebayashi are with NTT DoCoMo, Kanagawa 239-8536, Japan (e-mail: [email protected]; furuno@ nttdocomo.co.jp; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090455

Fig. 1. Frequency selective reflectarray surface mounted onto walls for reflection and penetration of different communication systems.

[1]–[3]. In wireless communications such as in a large-scale indoor/outdoor base station in a wireless local area network (WLAN) or distributed control system (DCS), planar reflectarray antennas can be mounted on the ceiling or a house wall to reflect beams covering different areas, especially blind spots for the primary source. It is also desirable that the reflectarray minimizes blockage of propagation channels from other communication systems, as illustrated in Fig. 1. The conventional microstrip reflectarray consists of an array of microstrip patches or dipoles printed on a thin metal-grounded dielectric substrate the role of which is to convert a spherical wave produced by a feed antenna into a plane wave. The concept of the reflectarray is based on phase compensation for each element dimension to achieve cophase reradiation and to concentrate the scattered wave toward a specific direction. Many phasing schemes have been recently developed [1]–[11]. The most common approach is to use identical patches with different-length transmission delay lines attached to the patches for phase compensation [1], [3]. Other approaches include the use of different sized patches without delay lines to introduce a nearly in-phase aperture [4]–[6] or using variable rotation angles of a patch [7]. In this paper, a new idea for a reflectarray design is presented in that the reflectarray can function as a reflector, and generate the desired reflection beam shape and direction for a primary wave source, while achieving partial transparency for propagation channels of other communication systems working in other frequency bands. A microstrip reflectarray using crossed-dipole

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Fig. 2. Reflection and transmission coefficients of square-loop FSS using an infinite periodic model.

elements with a frequency selective surface (FSS) comprising square loops is designed to demonstrate the effectiveness of the proposed idea. In Section II, an infinite periodic model is used to analyze the reflection and transmission coefficients of the new crossed-dipole elements with a square-loop FSS. Section III presents an analysis and design of the frequency selective reflectarray (FSR) using crossed-dipole elements with a square-loop FSS. The properties of the new reflectarray are discussed and compared to those of the conventional microstrip reflectarray. We experimentally verified the radiation pattern and transmission coefficient of the FSR with 11 by 7 elements. New designs for dual-source and dual-polarized FSR are given in Section IV. Furthermore, an FSR is designed and applied to a WCDMA system for eliminating blindness of communications between the base station and mobile users. A practical link budget analysis described in Section V shows the effectiveness of the FSR to improve the quality of communications. Finally, Section VI discusses the influence of the presence of a concrete wall on the FSR, when the FSR is surface mounted in the proximity of a house wall. II. CROSSED-DIPOLE ELEMENTS WITH SQUARE-LOOP FSS An FSS is a surface that exhibits different reflection and/or transmission properties as a function of frequency [12]. An array of loops acts as a band-stop filter, which is characterized by the fundamental resonance of loops when the circumference of the elements is approximately one wavelength in the dielectric surrounding them. An infinite periodic model using the HFSS simulation [13] was performed to analyze the reflection and transmission coefficients of the square-loop FSS, as shown in Fig. 2, in which periodic boundary conditions (PBCs) are assumed around the unit cell. The period in both the and directions is and the circumference of the square loop is 23.8 mm. The square-loop array is attached to the bottom surthick and has face of a dielectric substrate that is (CGP-500 with a loss tana relative permittivity of gent of 0.0018). The reflection and transmission coefficients of the square-loop FSS versus the frequency are shown in Fig. 2.

Fig. 3. Reflection coefficients versus length of crossed-dipole elements at 12 GHz using CGP-500 substrate.

It can be seen that a total reflection occurs at the resonant frequency of 12 GHz, and the reflection phase is 180 . Considering this feature, a metal ground plane of the microstrip reflectarray can be replaced with the loop-FSS for a certain frequency band. In this work, a new reflectarray comprising a printed crosseddipole array and square-loop FSS on opposite surfaces of the dielectric substrate is proposed and designed. First, the effect of the crossed-dipole array on the square-loop FSS should be considered. Fig. 3 shows the reflection coefficients of the composite unit cell versus the length of the crossed-dipole elements for different incidence angles and polarizations at 12 GHz. This figure shows that the variation in the reflection loss is within 2 dB for both TE and TM polarizations, when the length of the crossed-dipole elements varies from the minimum length of 0.5 mm to the maximum length of 13.6 mm. We analyzed the effect of mutual coupling between the crossed-dipole elements and the square-loop FSS based on the reflection coefficient, as shown in Fig. 4. It can be found that the mutual coupling is very strong when the substrate thickness is thin, especially when the length of the crossed-dipole elements is approximately half a dielectric wavelength. This results in significant leakage of energy. When the thickness is increased, the performance is favorable for designing a reflectarray of varying dipole lengths. III. ANALYSIS AND DESIGN OF FSR USING CROSSED-DIPOLE ELEMENTS WITH SQUARE-LOOP FSS The key technique in the design of a reflectarray is how the individual elements are designed to scatter the incident wave with the proper phase compensation to produce a beam toward a specific direction. The configuration of the frequency selective reflectarray is shown in Fig. 5. The reradiated field from the crossed-dipole in an arbitrary direction, , will be of the form [1]

(1)

LI et al.: FSR USING CROSSED-DIPOLE ELEMENTS WITH SQUARE LOOPS FOR WIRELESS COMMUNICATION APPLICATIONS

Fig. 4. Reflection coefficient characteristics versus the length of crossed-dipole elements and substrate thickness.

Fig. 5. Configuration of frequency selective reflectarray.

where is the feed pattern function, is the pattern function and are the position of the crossed-dipole elements. element and the feed horn antenna, respecvectors of the tively. is the desired main-beam pointing direction of the reis the required phase of the scattered field from flectarray. the element. The conditions that enable an array aperture are given distribution to be cophase in the desired direction by [11] (2) where is the distance from the feed source to the array element, i.e., . The wave number is . It is noted that is the working frequency given as of the FSS ground. In the design of microstrip reflectarray, the dimensions or the shape of the reflecting elements must be changed in order to obtain the required reflection phase. The compensated phase curve can be calculated by analyzing the infinite periodic array of identical microstrip elements [13]. After obtaining the phase curve, the resonant length of the element is determined to , in the field scattered from the elproduce a phase shift, ement. Fig. 6 shows the reflection phase curve of the crosseddipole element with square-loop FSS. Compared to the reflection phase curve of the crossed-dipole elements with a conven-

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Fig. 6. Comparison of reflection phase of crossed-dipole with square-loop FSS and metal ground plane.

tional ground plane, it can be found that the proposed element structure has a slowly varying phase curve, which yields a reduction in the phase error caused by fabrication error in element size in practice. Generally, the phase of the reflection coefficient is dependent not only on the element size but also on the angle of incidence of plane wave. However, it was shown that the reflection phases are not greatly affected by the incidence angles, even when the incidence angle is more than 45 [4], [14]. In this study, taking into account the grating lobe cri, the scan angle for the reflectarray teria designed here is restricted to less than or equal to 45 . Therefore, the FSR was simply designed based on the reflection phase characteristics of a plane wave that is normal incident. In order to validate the element structure of the crossed-dipole elements with the square-loop FSS, a 30 -beam-steering reflectarray along the -axis operating at 12 GHz was designed. When we use higher frequency to keep enough bandwidth for achieving high-speed broadband mobile communication systems, it is a significant problem that radio waves can not reach out-of-sight areas. To address the problem, we proposed to use a passive reflector that enables to control the reflected wave direction and coverage. Here we adopt 12 GHz for this study. Fig. 7(a) and (b) show the top and bottom surfaces of the reflectarray geometry using 11 7 crossed dipoles of variable size and a square-loop FSS, respectively. The element spacing is in both the and directions. The substrate thickness and relative permittivity are assumed to be and , respectively. The feed may be positioned at an arbitrary angle and distance from the reflectarray, while it should be sufficiently far away from the reflectarray so that the incident wave can be treated as a plane wave. In the present design, the incident plane wave arrives from -axis direction of in the corresponding spherical coordinate, and the main beam is scanned in -axis direction of . The incidence plane wave can be either TM or TE polarized due to the symmetric crossed-dipole design. The dimensions of all elements are determined based on (2) and Fig. 6. A full-wave simulation using HFSS for the radiation pattern in the xoz plane with an incident TE-polarized plane wave was performed. The results are shown in Fig. 8. In order to verify the

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Fig. 9. Measurement system for reflectarray at NTT DoCoMo, Kanagawa.

Fig. 7. (a) Crossed-dipole array on the top of designed reflectarray. (b) Squareloop FSS on the bottom of designed reflectarray.

Fig. 8. Comparison of simulation and measurement results of radiation pattern in xoz plane of the designed FSR.

design, we fabricated the FSR and conducted experiments. The measurement of the radiation pattern was performed in an anechoic chamber at NTT DoCoMo, Kanagawa, Japan. The configuration for the measurement is shown in Fig. 9. For comparison, the measurement results are also shown in Fig. 8. It should be noted that a small azimuth region of approximately 20 degrees can not be measured due to the mechanical limitation of turntable in this measurement system, nonetheless, the measurement results are in good agreement with the simulation results. Both the measurement and simulation results show that the main beam is directed at 30 . Thus, the reflectarray using

Fig. 10. (a) Experimental models of FSR and conventional metal ground reflectarray. (b) Comparison of measured electrical field magnitude of the two reflectarrays in the direction of the main beam.

the crossed-dipole array with the square-loop FSS satisfies the requirements regarding the main beam position very well. The performance and design for the TM-polarized incidence waves can be similarly obtained due to symmetry [9]. To compare the loop FSS reflectarray and the conventional metal ground plane reflectarray based on the directivity bandwidth, an 11 7 crossed-dipole reflectarray with a metal ground plane was also designed and simulated. as shown in Fig. 10(a). Fig. 10(b) shows the measured electrical field magnitude in the direction of the main beam for two kinds of reflectarrays for

LI et al.: FSR USING CROSSED-DIPOLE ELEMENTS WITH SQUARE LOOPS FOR WIRELESS COMMUNICATION APPLICATIONS

Fig. 11. Measured transmission coefficient S21 of the FSR versus frequency of in near-zone using a pair of standard-gain horn antennas.

an incident TE-polarized plane wave, which represents the performance of the directivity against frequency. Directivity of the reflectarray can be defined as the ratio of the scattered intensity in the direction of the main beam from the reflectarray to the scattered intensity averaged over all directions [15]. As shown in Fig. 10(b), below the working frequency of the loop FSS, the directivity of the designed reflectarray drops suddenly, which indicates that the incidence wave partly penetrates through the reflectarray. In other words, the reflectarray is partially transparent to lower frequency band waves compared to the operating frequency, resulting in a reduction in the blockage effect to other communication systems. The 2 dB directivity-drop bandwidth of the reflectarray is approximately 9.1%. However, the maximum directivity of the FSR is about 1.5 dB less than that for the metal ground reflectarray. This is due to the incomplete reflection of the frequency selective surface in an actual environment. Some leakage is inevitable. Furthermore, a near-zone transmission measurement was performed to verify the frequency selective characteristics of the FSR. The results are shown in Fig. 11. The FSR and conventional reflectarray were placed between a pair of standard gain horn antennas (8.2 GHz–12.5 GHz) for transmission measurement, respectively. Since the dimensions of the experimental models are relatively small, the measurement distance was set in the near-zone. Although it is not very accurate, this experiment can provide insight into the frequency selective characteristics of the FSR. Fig. 11 shows that when the working frequency is outside the FSS band, the FSR is partially transparent to other wave sources. IV. DUAL-SOURCE AND DUAL-POLARIZED FSR By using non-symmetric crossed dipoles, we can design a new FSR with dual-source and dual-polarized operation, as shown in Fig. 12. The bottom surface is still a square-loop FSS, which is the same as that in Fig. 7(b). The material used to fabricate this FSR is also CGP-500. The design target is aimed to dual-source and dual polarized incidence. One inciwith horizontal dence source is from polarization, and the main beam is steered in the direction . Meanwhile, the other incidence of

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Fig. 12. Top surface of dual-source and dual-polarization operation FSR, and bottom surface is still a square-loop FSS, which is the same in Fig. 7(b).

with vertical posource is from larization, and the main beam is scanned in the direction of , i.e., normal reflection. In the first case, only horizontal dipole elements along the x-axis will be excited, but in the second case, only vertical dipole elements along the y-axis will be excited. According to the orthogonality of the crossed-dipole elements, the two polarizations are independent, even if the two sources are excited simultaneously. Tables I and II give the dimensions of all dipoles along the x- and y-axes, respectively. Both simulations and experiments demonstrate the performance of the dual-source and dual-polarized FSR, as shown in Fig. 13. It is noted that an additional beam at around 30 deg is observed in the Fig. 13(b), which is due to the measuring system error. Because the transmitted and received horn antennas are located at the same incidence plane in this case, the conventional reflected wave based on the Snell reflection law from testing targets except the FSR is also detected. V. LINK BUDGET ANALYSIS IN WCDMA SYSTEM In wideband wireless communications for mobile users, eliminating the blind spots of a base station antenna in a densely populated downtown district is a significant problem. Generally, RF boosters are used to extend the cellular coverage area, but standard RF boosters require transceivers, power supplies, cables, etc., which incur a high cost and have large requirements in terms of installation space. Considering the wireless communication system model shown in Fig. 14 [14], a planar reflectarray is used as a reflector that is set on the top of a building or surface mounted onto a wall. Through proper design, it can steer the main beam to cover the blind spots of base station antennas. The merits of parallel installation are that we can take into account quake-resistance standards and integrate the equipment with surrounding environment such as into billboards [10]. However, if a metallic reflector is used, it is very difficult to direct the reflected beam in a specified direction even if using a tilt adjuster. A frequency selective reflectarray was designed and applied to a wideband CDMA (WCDMA) system. The WCDMA (Rel.99) system requires a paired spectrum: one band (1920–1980 MHz) for uplinks and one (2110–2170 MHz) for downlinks [16]. Here the central operating frequency of

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TABLE I DIMENSIONS OF HORIZONTAL DIPOLES (UNIT: mm)

Fig. 14. Elimination of blindness using reflectarrays in wireless communication system.

Fig. 13. Measured and simulated radiation patterns of dual-source and dual-polarized FSR, (a) Excited Source 1 with H-pol. (b) Excited Source 2 with V-pol.

Fig. 15. Frequency selective reflectarray of 11 by 7 elements at working frequency of 2 GHz.

the FSR is set to 2000 MHz and the required bandwidth must be greater than 10% to cover both the uplink and downlink spectra. According to previous design methods and frequency transformation schemes, we designed a 45 -beam-steering FSR that functions at 2 GHz. For the downlink, a plane wave is transmitted from a base station antenna at the incidence to the FSR and the reflected angle of main-beam is steered 45 in the xoz plane, and vice versa for the uplink. The FSR with 11 by 7 elements is shown in Fig. 15.

For convenient verification through experiments, a scale-down model working at 12 GHz is fabricated and measured, which means that all dimensions of the crossed-dipole reflectarray and square-loop FSS are one sixth of those in Fig. 15. So the whole size of the reflectarray is and . The substrate thickness is , and permittivity is still 2.6 (CGP-500). Fig. 16(a) shows the measured and simulated radiation patterns of the reflectarray in the xoz plane. The figure shows that the designed FSR clearly

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TABLE II DIMENSIONS OF VERTICAL DIPOLES (UNIT: mm)

Fig. 17. Bistatic RCS of FSR and metal plate with the same dimensions for downlink at 2120 MHz.

shown in Fig. 14, we give a simple link budget analysis for the WCDMA (Rel.99) system. We consider in radar range equation

(3)

Fig. 16. (a) Measured and simulated radiation patterns of the scaled-down model of reflectarray at 12 GHz. (b) Directivity of designed WCDMA reflectarray versus frequency.

satisfies the requirement regarding the main beam position. Fig. 16(b) shows the computed directivity against the frequency. As shown in the figure, the 2 dB directivity-drop bandwidth of 12.5% is achieved to cover the uplink and downlink spectra. To demonstrate the elimination of the blind spots using the reflectarray in the model of the wireless communication system

where the first item represents the power density incident on the reflectarray, the second item indicates the scattering power density at the receiver from the reflectarray, and the third item denotes the effective area of the receiver antenna. Term is the bistatic radar cross section (RCS) of the reflectarray. The bistatic RCS of the FSR functioning at 2120 MHz in the downlink is shown in Fig. 17. For comparison, the bistatic RCS of a metal plate with the same dimensions as the reflectarray is also given in Fig. 17. Considering conventional cellular mobile communications, and are 500 meters and 40 we assume the maximum meters, respectively. Generally, the transmitter and receiver antenna gains are 10 dBi and 0 dBi, respectively. Therefore, we [16] can predict the maximum propagation loss by using various reflectors, as shown in Fig. 18. The dashed line shown in Fig. 18 represents the threshold of the propagation loss. Blind spots occur if the propagation loss is greater than the value of 128 dB. The results show that if we use an FSR with 7 elements, the signal propagation loss can be reduced 11

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Fig. 18. Link budget analysis of propagation gain in WCDMA (Rel. 99) system using various reflectors.

Fig. 19. Infinite periodic model of square-loop FSS with concrete wall for reflection and transmission analysis.

effectively, which successfully eliminates the blindness in the original communication environment. However, when using a metal plate as the reflector, it does not work even if the size of the plate is increased. Similar conclusions for the uplink can be obtained, which demonstrate the effectiveness of the proposed reflectarray. VI. DISCUSSION OF PROXIMITY EFFECT OF CONCRETE WALL One of advantages of microstrip reflectarray is surface mountable with lower mass and volume. The possible applications are shown in Figs. 1 and 14, where the FSR is surface mounted onto a house wall for indoor and outdoor wireless communications. Meanwhile, we should take into account the proximity effect of concrete wall on the FSR in a practical application, because the presence of the wall will change the frequency response of the square-loop FSS. Considering the infinite periodic model shown in Fig. 19, we analyze the transmission and reflection characteristics of the square-loop FSS in the proximity of a concrete wall. The central working frequency is set to 2 GHz for the WCDMA system. Generally, the effective relative permittivity of a concrete wall at around 2 GHz [17], and the wall thickness is varies from 20 mm to 300 mm. In this paper, we choose the

Fig. 20. Frequency response of square-loop FSS with concrete wall under various parameter values of d. (a) Transmission coefficient, (b) Reflection coefficient.

wall thickness is 200 mm. For the sake of convenient reference, we assume a parameter of to represent the distance between , it means the square-loop FSS and the concrete wall. If , there is an air that the FSS contacts the wall, and if layer between the FSS and the wall, which is usually consistent with the facts. The period in both the and directions is and the circumference of the square loop is 146.4 mm. The square-loop array is attached to the bottom surface of thick and has a rela dielectric substrate that is (CGP-500 with a loss tangent ative permittivity of of 0.0018). Fig. 20(a) and (b) show the simulated frequency response of transmission and reflection coefficients under various parameter values of . As a reference, the transmission and reflection characteristics of the same square-loop FSS but without wall are also shown in Fig. 20. It can be seen that the presence of a concrete wall really affects the frequency response of the square-loop FSS, especially , the resonant frein close proximity to the wall. When quency of the square-loop FSS is moved to 1.2 GHz. However, (i.e., by adjusting the thickness of air layer, when ), the resonant frequency will return to 2 GHz. In this case, the reflection coefficient is still very good, only 0.284 dB at 2 GHz. It should be pointed out that the reflection coefficient of the original square-loop FSS without wall is 0.185 dB

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Fig. 22. Reflection and transmission coefficients of the square-loop FSS in close proximity to a wall, in which the substrate is made of a low permittivity foam material, i.e., polymethacrylamid hard foam.

Fig. 21. (a) Simulation model of the FSR surface mounted on concrete wall; (b) Comparison of radiation patterns of the FSR with and without wall.

at 2 GHz. Furthermore, it is shown that the wave penetration through the FSS and wall is still excellent to low-frequency band, but some attenuation to high-frequency band due to the loss of a concrete wall. The FSR with 11 by 7 elements shown in Fig. 15 was designed for WCDMA system without considering the influence of a wall. When the FSR is applied to a practical environment, it can be surface mounted on a wall but with an air interval of 15 mm. A plane wave is transmitted from a base station antenna at to the FSR and the incidence angle of the reflected main-beam is steered 45 in the xoz plane. The simulation model is shown in Fig. 21(a), and the radiation pattern of the FSR with wall is shown in Fig. 21(b). For a comparison, the simulated radiation pattern of the FSR without wall is also shown in this figure. It can be seen that the influence of the wall on the FSR turns out to be negligible in such case. The designed FSR with/without wall clearly satisfies the requirement regarding the main beam position. Based on the analysis above, we have known that when is greater than or equal to 0.1 central operating wavelength, the influence of a wall on the FSR is less. Therefore, the design principal and method of a FSR can be independent on the wall

in such conditions. It is applicable to the practical engineering when the FSR is surface mounted on a wall with an air interval of 15 mm. Furthermore, it can be seen from Fig. 20 that the FSS will resonant at lower frequency when it is placed in close proximity to a concrete wall. Therefore, we may utilize more practical and low-cost substrates to design a FSR, such as polymethacrylamid , ) [18]. The various hard foam ( thicknesses of this foam are available. Fig. 22 shows the reflection and transmission properties of the square-loop FSS which is attached to the bottom surface of a polymethacrylamid hard foam with thickness of 19.2 mm. It is found that the resonant frequency of the FSS could return to 2 GHz by adjusting the . It is worth air-layer thickness to the correct fit, as pointing out that we make use of the interaction between the FSS and the wall (i.e. proximity effects) to design a FSR in this case. But for the previous design shown in Fig. 21, we would like to eliminate or degrade the proximity effects of a wall by inserting a thick layer of air. It is helpful for decreasing the insertion loss to properly increase the thickness of air-layer, while the dimension of the square-loop should be adjusted to resonate at operating frequency in that case, as illustrated in Fig. 22. Therefore, it is more flexible to design a FSR in practical applications when we take the proximity effect of the wall and parameter into account. VII. CONCLUSION This paper presented a new concept for designing a frequency selective reflectarray (FSR) for wireless communication applications. The FSR has the ability to function as a reflector and steer reflected beam for a special frequency-band wave, while achieving partial transparency for the other frequency-band waves. A simple example of a reflectarray, which consists of a printed crossed-dipole array with a square-loop FSS on the opposite surface of the dielectric substrate, was presented to indicate the feasibility. The designed symmetric crossed-dipole FSR is independent of polarization. Measurement results

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agree well with the simulation results, which show that the performance of the FSR satisfies the requirements for the main beam position very well. A new design for the FSR using non-symmetric crossed dipoles, which can be used for dual-source and dual-polarized operation with two main beams simultaneously, was proposed and tested. Furthermore, the FSR was implemented in a WCDMA system to eliminate the blind spots in wireless mobile communications. A link budget analysis of propagation loss has demonstrated the effectiveness of the proposed frequency selective reflectarray. When the FSR is surface mounted onto a house wall in practical applications, the proximity effect of the concrete wall on the FSR should be considered. The analyzed results indicate that it is more flexible to design the FSR by introducing an air interval between the wall and FSR. ACKNOWLEDGMENT The authors gratefully acknowledge the helpful comments and suggestions provided by reviewers. REFERENCES [1] J. Huang, Analysis of a microstrip reflectarray antenna for microspacecraft applications TDA Progress Rep. 42-120, Feb. 1995, pp. 153–173. [2] D. M. Pozar, T. S. Targonsky, and H. D. Syrigos, “Design of millimeter wave microstrip reflectarrays,” IEEE Trans. Antennas Propag., vol. 45, no. 2, pp. 287–295, 1997. [3] D. C. Chang and M. C. Huang, “Multiple-polarization microstrip reflectarray antenna with high efficiency and low cross-polarization,” IEEE Trans. Antennas Propag., vol. 43, pp. 829–834, Aug. 1995. [4] S. D. Targonski and D. M. Pozar, “Analysis and design of a microstrip reflectarray using patches of variable size,” in IEEE AP-S/URSI Int. Symp. Dig., Seattle, WA, Jun. 20–24, 1994, pp. 1820–1823. [5] J. A. Encinar, “Design of two-layer printed reflectarrays using patches of variable size,” IEEE Trans. Antennas Propag., vol. 49, pp. 1403–1410, Oct. 2001. [6] D. Pilz and W. Menzel, “Full wave analysis of a planar reflector antenna,” in Proc. Asia-Pacific Microwave Conf., Dec. 2–5, 1997, pp. 225–227. [7] J. Huang and R. J. Pogorzelski, “A ka-band microstrip reflectarray with elements having variable rotation angles,” IEEE Trans. Antennas Propag., vol. 46, pp. 650–656, May 1998. [8] D. M. Pozar and S. D. Targonski, “A microstrip reflectarray using crossed dipoles,” in Proc. IEEE Antennas and Propagation Society Int. Symp., Jun. 21–26, 1998, vol. 2, pp. 1008–1011. [9] L. Li, Q. Chen, Q. W. Yuan, K. Sawaya, T. Maruyama, T. Furuno, and S. Uebayashi, “Microstrip reflectarray using crossed-dipole with frequency selective surface of loops,” presented at the Int. Symp. on Antenna and Propagation (ISAP2008), Taipei, Taiwan, Oct. 27–30, 2008. [10] T. Maruyama, T. Furuno, and S. Uebayashi, “Experiment and analysis of reflect beam direction control using a reflector having periodic tapered mushroom-like structure,” presented at the Int. Symp. on Antenna and Propagation (ISAP2008), Taipei, Taiwan, Oct. 27–30, 2008. [11] K. W. Lam, “On the Analysis and Design of Microstrip Reflectarrays,” Ph.D. dissertation, City University of Hong Kong, Kowloon, 2002. [12] B. A. Munk, “Frequency-selective surfaces and periodic structures,” in Antennas for All Applications, J. D. Kraus, Ed., R. J. Marhefka, Ed., 3rd ed. New York: McGraw-Hill, 2002. [13] R. Remski, “Analysis of PBG surfaces using Ansoft HFSS,” Microwave J., vol. 43, no. 9, pp. 190–198, Sep. 2000. [14] L. Li, Q. Chen, Q. W. Yuan, K. Sawaya, T. Maruyama, T. Furuno, and S. Uebayashi, “Novel broadband planar reflectarray with parasitic dipoles for wireless communication applications,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 881–885, 2009. [15] C. A. Balanis, Antenna Theory Analysis and Design, 3rd ed. Hoboken, NJ: Wiley, 2005. [16] H. Holma and A. Toskala, WCDMA for UMTS: HSPA Evolution and LTE, 4th ed. Hoboken, NJ: Wiley, 2007.

[17] E. Richalot, M. Bonilla, M. F. Wang, V. Fouad-Hanna, H. Baudrand, and J. Wiart, “Electromagnetic propagation into reinforced-concrete walls,” IEEE Trans. Microwave Theory Tech., vol. 48, no. 3, pp. 357–366, Mar. 2000. [18] J.-F. Zurcher, “The SSFIP: A global concept for high performance broadband planar antennas,” Electron. Lett., vol. 24, no. 23, pp. 1433–1435, Nov. 1988. Long Li (M’06) was born in Guizhou, China. He received the B.E. and Ph.D. degrees in electromagnetic fields and microwave technology from Xidian University, Xi’an, China, in 1998 and 2005, respectively. He joined the School of Electronic Engineering, Xidian University, in 2005 and was promoted to Associate Professor in 2006. He was a Senior Research Associate in the Wireless Communications Research Center, City University of Hong Kong, in 2006. He received the Japan Society for Promotion of Science (JSPS) Postdoctoral Fellowship and visited Tohoku University, Sendai, Japan, as a JSPS Fellow from Nov. 2006 to Nov. 2008. He is currently a Professor in the School of Electronic Engineering, Xidian University. His research interests include computational electromagnetics, electromagnetic compatibility, and novel artificial metamaterials. Dr. Li received the Nomination Award of National Excellent Doctoral Dissertation of China in 2007 and won the Best Paper Award in the International Symposium on Antennas and Propagation in 2008. He received the Program for New Century Excellent Talents in University of the Ministry of Education of China in 2010. He is a senior member of the Chinese Institute of Electronics (CIE) and the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan.

Qiang Chen (M’94) received the B.E. degree from Xidian University, Xi’an, China, in 1986, and the M.E. and D.E. degrees from Tohoku University, Sendai, Japan, in 1991 and 1994, respectively. He is currently an Associate Professor with the Department of Electrical Communications, Tohoku University. His primary research interests include computational electromagnetics, array antennas, and antenna measurement. Dr. Chen received the Young Scientists Award in 1993, the Best Paper Award and Zen-ichi Kiyasu Award in 2009 from the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan. He is a member of the IEICE. He served as the Secretary and Treasurer of IEEE Antennas and Propagation Society Japan Chapter in 1998, the Secretary of Technical Committee on Electromagnetic Compatibility of IEICE from 2004 to 2006, the Secretary of Technical Committee on Antennas and Propagation of IEICE from 2008 to 2010. He has been an Associate Editor of IEICE Transactions on Communications since 2007.

Qiaowei Yuan received the B.E., M.E., and Ph.D. degrees from Xidian University, Xi’an, China, in 1986, 1989 and 1997, respectively. From 1990 to 1991, she was a special research student at Tohoku University, Sendai, Japan. From 1992 to 1995, she worked in Sendai Research and Development Laboratories, Matsushita Communication Company, Ltd., engaging in research and design of the compact antennas for 2rd generation mobile phone. From 1997 to 2002, she was a Researcher in the Sendai Research and Development Center, Oi Electric Company, Ltd., engaged in the research and design of small antennas for pager communication and the parabolic antenna for 26.5 GHz fixed wireless access (FWA) communication. From 2002 to 2007, she was a Researcher with the Intelligent Cosmos Research Institute, Sendai, Japan, involved in the research and development of adaptive array antenna and RF circuits for mobile communications. From 2007 to 2008, she was an Associate Professor at Tokyo University of Agriculture and Technology. She is currently an Associate Professor at Sendai National College of Technology. Dr. Yuan received the Best Paper Award and Zen-ichi Kiyasu Award in 2009 from the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan.

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Kunio Sawaya (SM’02) received the B.E., M.E. and Ph.D. degrees from Tohoku University, Sendai, Japan, in 1971, 1973 and 1976, respectively. He is presently a Professor in the Department of Electrical and Communication Engineering at Tohoku University. His areas of interests are antennas in plasma, antennas for mobile communications, theory of scattering and diffraction, antennas for plasma heating, and array antennas. Prof. Sawaya received the Young Scientists Award in 1981, the Paper Award in 1988, Communications Society Excellent Paper Award in 2006, and the Zen-ichi Kiyasu Award in 2009, all from the Institute of Electronics, Information and Communication Engineers (IEICE). He served as the Chairperson of the Technical Group of Antennas and Propagation of IEICE from 2001 to 2003, the Chairperson of the Organizing and Steering Committees of the 2004 International Symposium on Antennas and Propagation (ISAP’04), and the President of the Communications Society of IEICE from 2009 to 2010. He is a fellow of IEICE and a member of the Institute of Image Information and Television Engineers of Japan.

Tamami Maruyama (M’91) received the B.S. and M.S. degrees from Tsuda College, Tokyo, Japan, in 1985 and 1988, respectively, and the Ph.D. degree from Tohoku University, Sendai, Japan, in 2001. She is a Senior Research Engineer at NTT DoCoMo Research Laboratories. In 1988, she joined Nippon Telegraph and Telephone (NTT) Corporation. In 2003, she joined NTT DoCoMo Inc. Her main research interests include optimum antenna design method, genetic algorithm, application of metamaterials and reflectarray for wireless communication, design of multi-frequency antennas for digital mobile communication base stations, small sector antennas for indoor high-speed wireless LANs and small multi-band antenna for handset applied genetic algorithm. Dr. Maruyama received the Young Engineer Award from the IEEE AP-S Tokyo Chapter in 1995, an Excellent Paper Award from IEICE in 1998, and the Best Paper Award from ISAP 2007. She is a member of the Electronics, Information and Communication Engineers (IEICE) of Japan.

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Tatsuo Furuno (M’95) received the B.S. degree from Niigata University, Japan, in 1986. He joined Nippon Telegraph and Telephone (NTT) Corporation and engaged in the research and development of cordless telephone system, radio propagation characteristics for PHS (Personal Handy-phone System) and Wireless LAN. He joined NTT DoCoMo in 1999 and engaged in the research and development of public wireless LAN service, indoor radio propagation, and cognitive radio. He is currently a Senior Research Engineer at NTT DoCoMo Research Laboratories.

Shinji Uebayashi (M’82) received the B.E., M.E., and D.E. degrees in electronic engineering from Nagoya University, Nagoya, Japan, in 1981, 1983, and 1986, respectively. From 1986 to 1992, he was with the NTT Laboratories, Yokosuka, Japan, where he worked on the development of digital cellular system (PDC). From 1992 to 2009, he was with NTT DoCoMo, Inc., where he worked on the development of the W-CDMA cellular system and EMC for cellular systems. He is presently a Professor in the School of Information Science and Technology, Chukyo University. His research interests include radio propagation, wireless communication and positioning.

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A Lightweight Organic X-Band Active Receiving Phased Array With Integrated SiGe Amplifiers and Phase Shifters Chad E. Patterson, Student Member, IEEE, Tushar K. Thrivikraman, Student Member, IEEE, Ana M. Yepes, Member, IEEE, Sean M. Begley, Member, IEEE, Swapan K. Bhattacharya, John D. Cressler, Fellow, IEEE, and John Papapolymerou, Fellow, IEEE

Abstract—This paper presents for the first time an X-band antenna array with integrated silicon germanium low noise amplifiers (LNA) and 3-bit phase shifters (PS). LNAs and PSs were successfully integrated onto an 8 2 lightweight antenna utilizing a multilayer liquid crystal polymer (LCP) feed substrate laminated with a duroid antenna layer. A baseline passive 8 2 antenna is measured along with a SiGe integrated 8 2 receive antenna for comparison of results. The active antenna array weighs only 3.5 ounces and consumes 53 mW of dc power. Successful comparisons of the measured and simulated results verify a working phased array with a return loss better than 10 dB across the frequency band of 9.25 GHz–9.75 GHz. A comparison of radiation patterns for the 8 2 baseline antenna and the 8 2 SiGe integrated antenna show a 25 dB increase in gain (1 ). The SiGe integrated antenna demonstrated a predictable beam steering capability of 41 . Combined antenna and receiver performance yielded a merit of 9 1 dB K and noise figure of 5.6 dB. Index Terms—Active arrays, integrated circuit packaging, phased arrays, receivers, scanning antennas.

I. INTRODUCTION

A

T microwave frequencies, there has been much work on the conceptualization and development of active phased array radars [1]. A struggle to lower costs and reduce weight while maintaining high performance is a primary motivation for this research. With rapid growth in the field of wireless communications and consistent need for high-performance circuitry at

Manuscript received December 18, 2009; revised May 29, 2010; accepted August 07, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. This work was supported in part by NASA under Grant NNX08AN22G, LCP and duroid materials supplied by Rogers Corporation. C. E. Patterson, T. K. Thrivikraman, S. K. Bhattacharya, J. D. Cressler and J. Papapolymerou are with the Electrical and Computer Engineering Department, Georgia Institute of Technology, Atlanta, GA 30332, USA (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; john. [email protected]). A. M. Yepes was with the Electrical and Computer Engineering Department, Georgia Institute of Technology, Atlanta, GA 30332, USA. She is now with Intel’s PC Client Group, Santa Clara, CA 95054 USA (e-mail: [email protected]). S. M. Begley is with the Sensors and Electromagnetic Applications Laboratory, Georgia Tech Research Institute, Smyrna, GA 30080 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090473

lower costs, the integration of RF circuits in a large processing format has become increasingly attractive. New materials are being explored for advanced antenna design that are thinner, lighter and have better high frequency characteristics, making a wider range of applications possible [2]. In recent years, Liquid Crystal Polymer (LCP) has been established as an exceptional microwave organic dielectric due to its key performance and packaging advantages. There is an abundance of literature investigating the benefits of LCP including [3]–[8]; some key advantages are listed below: • Superior cost/performance index; • Flexibility for application in conformal flex circuits; • Low permittivity and low dielectric loss with minimum dispersion up to 110 GHz; • Low coefficient of thermal expansion; • Near-hermetic; • Naturally flame retardant; • 3D multi-layer integration; • Compatible with sequential build up process in a printed circuit board foundry. The selected organic substrate in this study is a combination of low loss LCP and low loss RT/duroid 5880LZ. A lightweight composition is an essential attribute for all applications where portability is of importance. This includes both airborne and ground devices. The RT/duroid 5880LZ was selected primarily for its lower density and process compatibility with LCP. Adin substrate ditionally, it is accessible in thicker form ( thickness), not commercially available for LCP, which allows higher achievable bandwidths. Moreover, a compact lightweight power supply board was integrated with the antenna and the SiGe components to maintain maneuverability. It has been successfully shown that the integration of SiGe with radar systems is a low cost solution. The potential for several integrated functions on a single chip that offers high performance at lower cost keeps this technology in high demand SiGe [9], [10]. Recent publications have incorporated 0.35 technology with microstrip antennas yielding high performance at reduced costs compared to other MMIC technologies [11], [12]. These works show the integration of SiGe with radar applications but never before has it been fully integrated onto the antenna substrate and with a demonstrated beam steering until now. Furthermore, the active components in this paper utilize the BiCMOS SiGe technology. In [13], state of the art 0.13

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this technology is applied to a system-on-chip (SOC) approach where the active antenna is fully integrated on to silicon. This approach, however, limits antenna performance due to the restriction of real estate as well as added losses from the substrate. The work in this paper utilizes a system-on-package (SOP) approach integrating SiGe technologies with the benefits of high gain antennas on low-loss organic substrates. Previously, a 4 1 antenna array was presented with a fully integrated SiGe LNA for low power applications in an all LCP platform [14]. Although substrate level integration was demonstrated with good correlation of simulated and measured radiation patterns at X-band, no beam steering could be achieved. This paper makes further progress by incorporating a phase shifter (PS) component and enabling a beam steering and 100 capability. A 1.27 mm thick duroid with 75 thick LCP layers were combined to design an organic 8 2 antenna array. SiGe low noise amplifiers (LNA) and SiGe PS chips were packaged and biased with a substrate level distribution network. This paper is the first successful demonstration of a fully integrated, lightweight, high gain X-band receive phased array with BiCMOS SiGe LNAs and phase shifters. This work uti0.13 lizes advanced MMIC technologies and packaging techniques. The work presented in this paper could easily be extended to include additional SiGe components and a larger antenna array.

Fig. 1. Stack up of multilayer 8 with four elements.

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2 2 antenna array showing only one column

II. ANTENNA ARRAY OVERVIEW An 8 2 antenna array was designed for operation at 9.5 GHz with a bandwidth of 500 MHz. It is a multilayered aperture coupled microstrip patch antenna fabricated on Rogers 3850/HT Liquid Crystal Polymer (LCP) and Rogers RT/duroid 5880LZ. in the -dimenIt was optimized for beam scanning of sion. The expression for the required and element spacing of the array is given as

(1) and was determined using the scan angle ( for and for ) and maximum frequency (9.75 GHz). The element spacing for the (beam scan direction) and dimension were calculated to be a maximum of 22.9 mm and 30.7 mm, respectively. These numbers reflect only the maximum spacing required to meet the necessary scan angle. The actual element spacing chosen was less than the calculated in order to increase the maximum scan angle and thus effectively reducing the appearance of the grating lobe at the optimized scan angle of 20 . The final antenna design utilizes two columns, spaced apart, that are uniformly fed in parallel and are comapart. The prised of eight microstrip patches spaced stack up of the antenna is shown in Fig. 1. This design utilizes (50 core plus 25 two LCP layers consisting of 75 bondply) and 100 thicknesses laminated to a 1.27 mm thick LCP bondply. Two bond ply layers duroid layer using a 25 each) were needed for the multi-layer lamination, (25 leading to a total thickness of 1.47 mm. Thin LCP layers were used to limit radiation losses through the large feed network

Fig. 2. Dimensions for each aperture coupled patch.

and a thicker duroid layer was used to achieve the necessary bandwidth. On top of the stack, there are two columns of eight microstrip antenna elements measuring 13 mm 9.45 mm. The elements in each column are spaced 27 mm apart and the columns are spaced 20 mm apart. The aperture layer contains sixteen slots measuring 5.436 mm 0.444 mm and centered directly below each patch element. The dimensions of a single aperture coupled patch are illustrated in Fig. 2. Part of the antenna feed network is embedded in the LCP and fed through a signal via from the bottom layer. This is to allow additional room for packaging components on the bottom metallization feed layer. The embedded feed layer uses 50 line stubs to excite the aperture coupled patches. These have a and a stub length of 2.488 mm from the line width of 236 center of the aperture. For both the embedded and bottom feed layers, reactive 3 dB power dividers are used to parallel feed microstrip-to-cpw the antenna array. There are several 50 transitions on the bottom layer to accommodate the integrated wide circuit packaging. These cpw lines consist of a 375 gap and 2680 wide ground lines. These signal line, 100 ground lines have vias connecting to the ground layer to prevent unwanted propagating modes. The microstrip lines on this layer wide. are 446 This antenna design, shown in Fig. 3, was modeled using Ansoft High Frequency Structure Simulator (HFSS). The return loss and far-field patterns were simulated and optimized for the design frequency and required bandwidth. The design clearly

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Fig. 4. Phase shifter block-level topology [17].

Fig. 3. HFSS model of 8

2 2 antenna array.

makes a return loss better than 10 dB across the 500 MHz bandwidth. The gain was also simulated at 9.5 GHz and predicted to be 15.2 dB. These results are discussed further in Section IV.

Fig. 5. Layout for packaged LNA.

III. SIGE CHIP PACKAGING AND INTEGRATION In order to steer the beam of the antenna array and maintain a large antenna gain, individual Silicon Germanium (SiGe) low noise amplifiers (LNA) and phase shifters (PS) were incorporated into each column of the design. Each component was first packaged individually on LCP and characterized. Once a packaging scheme was successfully implemented for each component, both components were packaged in series on LCP and measured. This allowed for a better understanding of the effects attributed to the integration of these components on the antenna array. A. Low-Noise Amplifier Circuit Description The LNA was fabricated in a 0.13 BiCMOS SiGe technology and designed using the inductively degenerated cascode architecture. The circuit was designed for ultra-low noise performance while simultaneously achieving a power match. It consumes only 22 mW of dc power and has a reported 17 dB of and 1.37 dB noise figure across X-band gain (9.5–10.5 GHz). The LNA has a self-bias circuitry to simplify total design and requires only a 2.5 V dc supply. It is matched to 50 at all RF ports on chip, thus no matching network is needed on package. Further details of the LNA design are discussed in [15]. B. Phase Shifter Circuit Description The phase shifter consists of two LNAs and a 3-bit CMOS phase shifter illustrated in Fig. 4. It consumes only 4 mW of of over 10 dB, a noise dc power while achieving a gain figure less than 5 dB, and an OTOI of over 10 dBm. In addition, the RMS gain and phase errors were reported less than 0.5 dB and 2 , respectively. The internal LNAs were designed using the power-constrained inductive degeneration design technique outlined in [16]. The Hi/Lo pass phase shifter was designed using CMOS single-pole, double throw (SPDT) switches to toggle between hi-and low-pass filter sections. This device requires several dc supplies. This includes a 0.85 V and 1.5 V bias for each LNA and a 1.2 V and 2.4 V bias for

Fig. 6. Layout for packaged phase shifter.

each bit on the phase shifter. It is matched to 50 at all RF ports on chip, thus no matching network is needed on package. A more comprehensive description of the full phase shifter can be found in [17]. C. Packaging The LNA chip was diced from its original wafer using a soft wide cutting blade. The die size was kept to a minimum 50 to reduce wire bond length. After dicing, the chip dimensions . The PS did not were measured to be 820 require dicing and has measured dimensions of 2 mm 3 mm . Prior to packaging, both LNA and PS were measured on chip to ensure performance integrity. Each device was packaged separately on LCP to make certain both would perform properly when integrated on the antenna array. For continuity, the same cpw feed line structure used in the antenna design was incorporated for these tests. The packaging layout for both is shown in Figs. 5 and 6. The 4.7 resistor seen in Fig. 6 is used as an RF block for a wire bond that will connect the RF input of the PS to a dc bias line. Both chips were mounted using silver epoxy and allowed to cure for 20 minutes at 120 . The chip pads were then wire bonded onto the copper traces on LCP. The wire bonds were done using a wedge-wedge wire bonder utilizing a 38 diameter gold bond wire. This type of wire bonder uses ultra sonic energy to make a weld between contact points, therefore, avoids

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Fig. 7. Comparative S-parameter plot of unpackaged and packaged LNA.

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Fig. 8. Comparative S-parameter plot of unpackaged and packaged phase shifter.

the use of heat and excessive pressure which could damage the components. D. LNA Measurements Measurements of both the wafer level and package level LNA were done using ground-signal-ground (GSG) cpw probes. The drawing a current of about LNA was biased at 8.5 mA. The S-parameters were recorded using an Agilent E8361C PNA. Measurement comparisons of the bare LNA versus the packaged LNA are shown in Fig. 7. This plot shows a slight degradation of performance in the packaged LNA which is expected due to the added parasitics from the wire bonds. Over the frequency of interest, there is 0.5 dB of loss in the output gain for the packaged LNA. At 9.5 GHz, the plot shows a packaged gain of 16.2 dB. Although this number will vary slightly for each LNA, it is expected that it will increase the antenna gain by approximately 16 dB.

Fig. 9. Comparison phase plot of unpackaged and packaged phase shifter for each state.

E. PS Measurements S-parameters of the packaged PS were taken using the same measurement setup and biased according to the specifications in [17]. Measurement comparisons of the bare PS versus the packaged PS are shown in Fig. 8. This plot shows only slight degradation of performance in the of the packaged PS. At 9.5 GHz, the plot shows about 11 dB of added gain to the antenna from this packaged component. Obviously, this number will vary slightly for each PS and for each phase state. Also, as shown in Fig. 9, there is a slight error in phase shift for each state. This will be accounted for while predicting the steering angle of the radiation patterns. The largest disparity in phase shift between 9.25 GHz and 9.75 GHz for the unpackaged and packaged die was measured to be 5.8 . The measured packaged phase shift recorded at 9.5 GHz for each state is shown in Table I. F. LNA & PS Measurements After verifying the LNA and PS could be successfully packaged on LCP, the next step was to package both in series on LCP. The packaged LNA and PS are shown in Fig. 10. The effective

TABLE I COMPARISON OF PATTERN BEAM STEERING @ 9.5 GHz

S-parameters were estimated by using those acquired from the individually packaged LNA and PS and using Agilent ADS to simulate them in series. The measured and simulated S-parameters are shown in Fig. 11. It is seen that the measurements match very closely with the simulations. From these results, it is shown that the packaged LNA and PS will add about 26.6 dB of gain to the antenna array. Since the simulated gain of the 8 2 baseline antenna is 15.2 dBi, it was predicted that the 8 2 with

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Fig. 12. Picture of packaged LNA and phase shifter on antenna array.

Fig. 10. Picture of packaged LNA and phase shifter on antenna array.

Fig. 13. Picture of packaged antenna array with low power supply board and phase shifter bit controller.

IV. ANTENNA MEASUREMENTS

Fig. 11. Comparison of measured and simulated S-parameters for LNA and phase shifter packaged in series onto LCP.

packaged LNA and PS would have a front-end system gain of around 41.8 dBi. This gain could be improved by increasing the bias voltage to compensate for the added loss from packaging; however, this is not recommended as it would stress the bias circuitry and potentially damage the chips. G. LNA & PS Integration on 8

2 Antenna Array

The baseline 8 2 antenna array was modified to integrate the LNA and PS using the same packaging layout seen in Fig. 10. This layout was integrated into the already existing cpw feed lines. Also, the dc bias lines were extended out to 2 mm 2 mm pads where a wire could be attached for easier control. A picture of the antenna with the integrated LNA and PS is shown in Fig. 12.

After fabrication of both the baseline antenna and the LNA/PS integrated antenna, SMA connectors were attached to the inputs. Because the active antenna required various dc supplies to properly power it, a low power supply board was built to accommodate all the necessary voltages. This board requires only a 5 V dc supply drawing 0.455 A and is capable of providing all the necessary dc biases for the LNA and PS. Also, since the phase shifter bits are controlled by a supply of 1.2 V or 2.4 V, a switch board was assembled for toggling through all the phase states. The entire setup is seen in Fig. 13 and weighs only 12.6 ounces. The antenna array alone with only a short wiring harness weighs 3.5 ounces and consumes a total of 53 mW of dc power. Using this setup, the return loss was measured on the network analyzer. An anechoic chamber was used to obtain the radiation patterns. Using measurements and simulated results of the antennas and active components, the front-end gain, and noise figure (NF) of the antenna system are determined. A picture of the antenna under test in the anechoic chamber is shown in Fig. 14. A. Return Loss Both antennas were measured using an Agilent PNA. As shown in Fig. 15, the antennas maintained a return loss better than 10 dB across the desired frequency band. The simulation

PATTERSON et al.: A LIGHTWEIGHT ORGANIC X-BAND ACTIVE RECEIVING PHASED ARRAY WITH INTEGRATED SIGE AMPLIFIERS

Fig. 17. H-plane at 9.5 GHz of the 8

Fig. 14. Picture of 8 chamber.

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2 2 baseline antenna array.

antenna array being measured in the anechoic

Fig. 18. Gain versus frequency of the 8

2 2 baseline antenna array.

results compared to the measured baseline antenna are very close and show only a 100 MHz shift in frequency. B. Radiation Patterns

Fig. 15. S11 plot of the simulated and measured 8

Fig. 16. E-plane at 9.5 GHz of the 8

2 2 antenna arrays.

2 2 baseline antenna array.

An anechoic chamber was used to measure the radiation patterns from 8.5 to 10.5 GHz. Each antenna was mounted vertically on a stand, as shown in Fig. 14, and placed in the near-field of an X-band rectangular waveguide antenna. A cylindrical scan was used to accommodate the broad beam width in the azimuth direction. The active phased array was biased according to the specifications outlined previously. After completion of the radiation patterns, the broadside gain of both antennas was measured over the frequency band. This data was compiled with the near-field data and transformed to the far-field. Plots of the measured E & H planes taken at 9.5 GHz are compared with results simulated in HFSS. As shown in Figs. 16 and 17, the 8 2 baseline antenna results are very closely matched to those in simulation. The broadside gain of the baseline antenna was measured to be 15.1 dBi. The location of peaks and nulls correspond very well and the max gain is within 0.1 dB of the simulated results. A plot of the measured gain over frequency compared with simulations is shown in Fig. 18. Over the frequency band of interest (9.25 GHz –9.75 GHz), there is a 1.2 dB variation in gain. Measurements for the 8 2 antenna with packaged LNA and PS are shown in Figs. 19–27. It is seen that these measurements are very close to the predicted radiation patterns. The estimated radiation patterns in Figs. 19 and 20 use the simulated results for

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Fig. 19. E-plane of co-pol and cross-pol at 9.5 GHz for the 8 with packaged SiGe LNA and SiGe phase shifter.

Fig. 20. H-plane of co-pol and cross-pol at 9.5 GHz for the 8 with packaged SiGe LNA and SiGe phase shifter.

Fig. 21. Normalized E-plane at 9.5 GHz of the 8 degrees phase change.

2 2 antenna array

2 2 antenna array

2 2 antenna array with 44

the baseline antenna adjusted by the predicted additional gain of 26.6 dB provided by the packaged LNA and PS. The measured front-end system gain at broadside seen in these figures is 40.1 dBi. Using the gain of the baseline antenna as a control, the additional gain supplied from the LNA and PS is calculated to be 25 dB. The low cross-polarization gain shown in these figures confirm the linear polarization of the antenna. The beam steering capability is shown in Figs. 21–27. The radiation patterns are normalized to compare the measured beam steering

Fig. 22. Normalized E-plane at 9.5 GHz of the 8 degrees phase change.

Fig. 23. Normalized E-plane at 9.5 GHz of the 8 degrees phase change.

Fig. 24. Normalized E-plane at 9.5 GHz of the 8 degrees phase change.

2 2 antenna array with 87

2 2 antenna array with 129

2 2 antenna array with 170

with the simulated beam steering predicted in HFSS. The beam steering angles are more clearly seen in Table I. The measured beam steering angle compared to simulation has a maximum error of 5.5 and an rms error of 3.2 . A comparison of antenna gain over the frequency band is plotted in Fig. 28. It is seen that the 3 dB bandwidth for the gain is over 10% for all beam steering states, which is well beyond the 500 MHz design requirement. The 3 dB beam widths at 9.5 GHz are seen in Table II. The simulated results of the passive antenna match very closely with

PATTERSON et al.: A LIGHTWEIGHT ORGANIC X-BAND ACTIVE RECEIVING PHASED ARRAY WITH INTEGRATED SIGE AMPLIFIERS

Fig. 25. Normalized E-plane at 9.5 GHz of the 8 degrees phase change.

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2 2 antenna array with 215 Fig. 28. Gain versus frequency of the 8

2 2 antenna array for all phase changes.

TABLE II 3 dB BEAM WIDTHS @ 9.5 GHz

Fig. 26. Normalized E-plane at 9.5 GHz of the 8 degrees phase change.

2 2 antenna array with 257

ratio, , referenced at the output of the antenna. In this work, these parameters were calculated using

(2) and

(3)

Fig. 27. Normalized E-plane at 9.5 GHz of the 8 degrees phase change.

2 2 antenna array with 299

the measured results of the baseline antenna and, as expected, are very similar to the results of the active antenna. Because the 8 2 with packaged LNA and PS is a receive antenna, it is important to calculate the added noise performance of the system. As discussed in [18] and [19], this is conventionally , and figure-of-merit done by calculating the noise figure,

is the standard reference temperature 290 K, is the where directivity of the antenna, and and are the Ohmic loss and mismatch loss, respectively, in the feed line between the antenna element and LNA. From these equations, it is clear that , is sufficiently large, the feed line when the LNA gain, loss and LNA noise figure will have the most effect on performance and the components following it will have a negligible effect. Since this is true of this case, only the PS term is included in this calculation and the loss of the antenna feed line after the PS is ignored. The directivity was calculated to be 19.7 dBi using the measured radiation patterns at 9.5 GHz. The loss in the feed line, and the noise figure of the packaged LNA and PS were simulated in HFSS and ADS, respectively. These simulations showed a of 3.9 dB, a of 0.1 dB, a of 1.4 dB, and a of 5.7 dB. The already measured gain of the packaged

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LNA at 9.5 GHz is 16.2 dB. Using these results, the NF of the is . For this antenna, system is 5.6 dB and the , has the largest impact on these the Ohmic feed line loss, parameters and can be directly improved by moving the LNA and PS closer to the antenna elements. This would significantly lower the noise figure, thus increasing the G/T ratio.

V. CONCLUSION SiGe LNAs and PSs were successfully integrated onto an 8 2 antenna array fabricated using LCP and duroid material. The measured return loss and radiation patterns were very comparable to those simulated. Using a passive version of the active array, a comparison showed excellent results from the packaged LNA and PS. The packaged components supplied an additional 25 dB of increased gain to the antenna for a total of 40.1 dBi in front-end system gain. The combined antenna and receiver perof and a NF of 5.6 dB. formance yielded a of beam steering caAdditionally, the antenna exhibited pability. This is the first demonstration of such a lightweight, active receive antenna array in X-band built with low cost PCB fabrication technologies and Si-based RF electronics.

ACKNOWLEDGMENT The authors would like to thank the assistance of G. Hampton, G. Hopkins, V. Tripp, C. Bailey, B. Wilson, B. Hudson and T. Heath of the Georgia Tech Research Institute for help in antenna pattern measurements and Laureen Rose of Georgia Tech for help with wire bonding. The authors would also like to thank Metro Circuits, in Rochester, NY, for fabrication of the antennas.

REFERENCES [1] E. Brookner, “Phased-array and radar breakthroughs,” in Proc. IEEE Radar Conf., 2006, pp. 37–42. [2] A. Moussessian et al., “An active membrane phased array radar,” in IEEE MTT-S Int. Microwave Symp. Dig., 2005, pp. 1711–1714. [3] E. C. Culbertson, “A new laminate material for high performance PCBs: Liquid crystal polymer copper clad films,” in Proc. 45th Electronic Components and Technology Conf., 1995, pp. 520–523. [4] C. E. Patterson, T. K. Thrivikraman, S. K. Bhattacharya, C. Poh, J. D. Cressler, and J. Papapolymerou, “Organic wafer-scale packaging for X-band SiGe low noise amplifier,” in Proc. 39th Eur. Microwave Conf., Rome, 2009, pp. 141–144. [5] A. Geise, U. Strohmaier, and A. F. Jacob, “Investigations of transmission lines and resonant structures on flexed liquid crystal polymer (LCP) substrates up to 67 GHz,” in Proc. 39th Eur. Microwave Conf., Rome, 2009, pp. 735–738. [6] D. C. Thompson, O. Tantot, H. Jallageas, G. E. Ponchak, M. M. Tentzeris, and J. Papapolymerou, “Characterization of liquid crystal polymer material and transmission lines on LCP substrates from 30–110 GHz,” IEEE Trans. Microwave Theory Tech., vol. 52, pp. 1343–1352, Apr. 2004. [7] N. Kingsley, D. E. Anagnostou, M. M. Tentzeris, and J. Papapolymerou, “RF MEMS sequentially reconfigurable Sierpinski antenna on a flexible organic substrate with novel dc-biasing technique,” J. Microelectromechan. Syst., vol. 16, pp. 1185–1192, Oct. 2007. [8] M. M. Tentzeris et al., “3-D-integrated RF and millimeter-wave functions and modules using liquid crystal polymer (LCP) system-on-package technology,” IEEE Trans. Adv. Pack., vol. 27, pp. 332–340, Jun. 2008.

[9] X. Guan, H. Hashemi, and A. Hajimiri, “A fully integrated 24-GHz eight-element phased-array receiver in silicon,” IEEE J. Solid-State Circuits, vol. 39, pp. 2311–2320, Dec. 2004. [10] K.-J. Koh and G. Rebeiz, “An X-and Ku-band 8-element phased-array receiver in 0.18- SiGe BiCMOS technology,” IEEE J. Solid-State Circuits, vol. 43, pp. 1360–1371, Jun. 2008. [11] N. Billström, K. Axelsson, and B. Lumetzverger, “X-band sub-antenna for low cost AESA radars,” in Proc. 39th Eur. Microwave Conf., Rome, 2009, pp. 910–913. [12] M. Borgarino, A. Polemi, and A. Mazzanti, “Low-cost micro waveradiometer front-end for industrial applications,” IEEE Trans. Microwave Theory Tech., vol. 57, pp. 3011–3018, Dec. 2009. [13] A. Babakhani, X. Guan, A. Komijani, A. Natarajan, and A. Hajimiri, “A 77-GHz phased-array transceiver with on-chip antennas in silicon: Receiver and antennas,” IEEE J. Solid-State Circuits, vol. 41, pp. 2795–2806, Dec. 2006. [14] C. E. Patterson, A. M. Yepes, T. K. Thrivikraman, S. K. Bhattacharya, J. D. Cressler, and J. Papapolymerou, “A lightweight X-band organic antenna array with integrated SiGe amplifier,” in Proc. IEEE Radio and Wireless Symp., Jan. 2010, pp. 84–87. [15] W.-M. L. Kuo, Q. Liang, J. D. Cressler, and M. A. Mitchell, “An X-Band SiGe LNA with 1.36 dB mean noise figure for monolithic phased array transmit/receive radar modules,” in IEEE RFIC Symp. Dig., 2006, pp. 498–501. [16] T. K. Thrivikraman, W.-M. L. Kuo, J. P. Comeau, J. D. Cressler, P. W. Marshall, and M. A. Mitchell, “A 2 mW, sub-2 dB noise figure, SiGe low-noise amplifier for X-band high-altitude or space-based radar applications,” in IEEE RFIC Symp. Dig., 2007, pp. 629–632. [17] T. K. Thrivikraman, W.-M. L. Kuo, and J. D. Cressler, “A two-channel, ultra-low-power, SiGe BiCMOS receiver front-end for X-band phased array radars,” IEEE BCTM, pp. 43–46, 2009. [18] J. J. Lee, “G/T and noise figure of active array antennas,” IEEE Trans. Antennas Propag., vol. 41, no. 2, pp. 241–244, Feb. 1993. [19] U. R. Kraft, “Gain and G/T of multielement receive antennas with active beamforming networks,” IEEE Trans. Antennas Propag., vol. 48, no. 12, pp. 1818–1828, Dec. 2000.

m

Chad E. Patterson (M’09) received the B.S. and M.S. degrees in electrical engineering from the Georgia Institute of Technology (Georgia Tech), Atlanta, in 2006 and 2008, respectively, where he is working toward the Ph.D. degree. He is currently a member of the Microwave Circuit Technology (MircTech) group at Georgia Tech. His research focuses on the design, fabrication and characterization of microwave/ millimeter wave passive components and packaging solutions for next-generation communication and radar antennas. Prior to joining the MircTech team, he was employed as an intern at the Army Research Laboratory in Adelphi, MD, where he worked on high frequency antenna design and automated antenna measurement systems.

Tushar K. Thrivikraman (S’09) received the M.S. degree in electrical engineering from the Georgia Institute of Technology (Georgia Tech), Atlanta, in 2007 and the joint B.S. and B.B.A. degree from Georgia Tech and Emory University, Atlanta, in 2002. He is currently working toward the Ph.D. degree at Georgia Tech. He is a member of the Silicon Germanium Devices and Circuit Research Team at Georgia Tech, concentrating on the design of next-generation radar and communication modules focusing on extreme environment and space applications. Prior to joining the Georgia Tech, he was a Defense Career Intern at the Robins Air Force Base, testing and supporting operations for radar systems.

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Ana M. Yepes (M’10) received the B.S. and M.S. degrees in electrical engineering from the Georgia Institute of Technology, Atlanta, in 2008 and 2010, respectively. Her Master’s research focused on multilayer organics (MLO) microstrip antenna arrays for environmental sensing applications. She currently works as a Rotation Engineer with Intel’s PC Client Group, Santa Clara, CA. She has coauthored several technical papers. Ms. Yepes received the 2010 IEEE Antennas and Propagation Predoctoral Research Award.

Sean M. Begley (M’08) received the B.E. degree in computer engineering and the M.S. degree in electrical engineering from Vanderbilt University, Nashville, TN, in 2006 and 2008, respectively. Since 2008, he has been employed at the Sensors and Electromagnetic Applications Laboratory, Georgia Tech Research Institute. His professional interests include FPGA design, circuit design and printed circuit board layout, hardware/software interfacing, software development, hardware prototyping, electronic attack and electronic protection. He has been involved in development of custom prototype radar systems, testing existing radar systems, and designing electronic attack hardware. He is also involved in the development and testing of electronic attack and electronic protections techniques.

Swapan K. Bhattacharya received the M.S. and Ph.D. degrees from the Indian Institute of Technology, Kharagpur, India. He is a Senior Research Scientist with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta. His research interests include micro-system integration with emphasis on thin film materials and processes, antennas, MEMS, RFID, embedded actives, and printed paper electronics. He has coauthored over 200 technical publications and edited a book on composite material. He has taught professional development courses on embedded passives at numerous international conferences. Dr. Bhattacharya served as Poster Committee Chair in IEEE ECTC and Chair of Embedded Passives Track of the ASME InterPACK Conference. As a member of the leadership committee, he has organized several international conferences.

John D. Cressler (F’01) received the Ph.D. degree from Columbia University, New York, in 1990. He was an IBM Researcher from 1984 to 1992, and on the faculty of Auburn University, Auburn, AL, from 1992 to 2002. Since 2002, he has been on the faculty of the Georgia Institute of Technology, Atlanta, where he is currently the Ken Byers Professor of Electrical and Computer Engineering. His research interests include: Si-based (SiGe/strained-Si) heterostructure devices and technology, mixed-signal circuits built from these

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devices, radiation effects, cryogenic electronics, device-to-circuit interactions, noise and reliability physics, device-level simulation, and compact circuit modeling. He has published over 500 scientific papers related to his research, and is the coauthor of Silicon-Germanium Heterojunction Bipolar Transistors (2003), the editor of The Silicon Heterostructure Handbook: Materials, Fabrication, Devices, Circuits, and Applications of SiGe and Si Strained-Layer Epitaxy (2006), and the author of Silicon Earth: Introduction to the Microelectronics and Nanotechnology Revolution (2009). During his academic career he has graduated 27 Ph.D. students and 28 M.S. students. Dr. Cressler has served as an Associate Editor for the IEEE Journal of SolidState Circuits, the IEEE TRANSACTIONS ON NUCLEAR SCIENCE, and the IEEE TRANSACTIONS ON ELECTRON DEVICES. He has been active on numerous conference program committees, including as the Technical Program Chair of the 1998 ISSCC and 2007 NSREC. He has received a number of awards for both his teaching and research, and is an IEEE Fellow.

John Papapolymerou (F’10) received the B.S.E.E. degree from the National Technical University of Athens, Athens, Greece, in 1993, and the M.S.E.E. and Ph.D. degrees from the University of Michigan, Ann Arbor, in 1994 and 1999, respectively. From 1999 to 2001, he was an Assistant Professor at the Department of Electrical and Computer Engineering of the University of Arizona, Tucson and during the summers of 2000 and 2003 he was a Visiting Professor at the University of Limoges, France. From 2001 to 2005 and 2005 to 2009, he was an Assistant Professor and Associate Professor, respectively, at the School of Electrical and Computer Engineering of the Georgia Institute of Technology, where he is currently a Professor. He has authored or coauthored over 260 publications in peer-reviewed journals and conferences. His research interests include the implementation of micromachining techniques and MEMS devices in microwave, millimeter-wave and THz circuits and the development of both passive and active planar circuits on semiconductor (Si/SiGe, GaAs) and organic substrates (liquid crystal polymer-LCP, LTCC) for system-on-a-chip (SOC)/ system-on-a-package (SOP) RF front ends. Dr. Papapolymerou is the Chair for Commission D of the US National Committee of URSI. He was Associate Editor for the IEEE Microwave and Wireless Component Letters (2004–2007) and the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION (2004–2010). He currently serves as an Associate Editor for the IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. During 2004, he was the Chair of the IEEE MTT/AP Atlanta Chapter. He was the recipient of the 2010 IEEE Antennas and Propagation Society (AP-S) John Kraus Antenna Award, the 2009 IEEE Microwave Theory and Techniques-Society (MTT-S) Outstanding Young Engineer Award, the 2009 School of ECE Outstanding Junior Faculty Award, the 2004 Army Research Office (ARO) Young Investigator Award, the 2002 National Science Foundation (NSF) CAREER award, the best paper award at the 3rd IEEE International Conference on Microwave and Millimeter-Wave Technology (ICMMT2002), Beijing, China and the 1997 Outstanding Graduate Student Instructional Assistant Award presented by the American Society for Engineering Education (ASEE), The University of Michigan Chapter. His students have also been recipients of several awards including the Best Student Paper Award presented at the 2004 IEEE Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems, the 2007 IEEE MTT-S Graduate Fellowship, and the 2007/2008 and 2008/2009 IEEE MTT-S Undergraduate Scholarship/Fellowship.

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Design of Non-Uniform Circular Antenna Arrays Using a Modified Invasive Weed Optimization Algorithm Gourab Ghosh Roy, Swagatam Das, Member, IEEE, Prithwish Chakraborty, and Ponnuthurai N. Suganthan, Senior Member, IEEE

Abstract—An ecologically inspired optimization algorithm, called invasive weed optimization (IWO), is presented for the design of non-uniform, planar, and circular antenna arrays that can achieve minimum side lobe levels for a specific first null beamwidth while avoiding the mutual coupling effects simultaneously. IWO recently emerged as a derivative-free real parameter optimizer that mimics the ecological behavior of colonizing weeds. For the present application, classical IWO has been modified by introducing a more explorative routine of changing the standard deviation of the seed population (equivalent to mutation step-size in evolutionary algorithms) of the algorithm. Simulation results over three significant instances of the circular array design problem have been presented to illustrate the effectiveness of the modified IWO algorithm. The design results obtained with modified IWO have been shown to comfortably beat those obtained with other state-of-the-art metaheuristics like genetic algorithm (GA), particle swarm optimization (PSO), original IWO and differential evolution (DE) in a statistically meaningful way. Index Terms—Circular antenna arrays, differential evolution (DE), genetic algorithms (GAs), invasive weed optimization (IWO), particle swarm optimization (PSO), real parameter optimization, sidelobe suppression.

I. INTRODUCTION

I

N several occasions, a single element antenna is unable to meet the gain or highly directive radiation pattern requirements especially suited for long distance communication. Antenna arrays are formed to circumvent such problems by combining many individual antenna elements in certain electrical and geometrical configurations [1]–[3]. The primary design objective of antenna array geometry is to determine the positions of array elements that jointly produce a radiation pattern to match the desired pattern as closely as possible [4].

Manuscript received January 18, 2010; revised June 01, 2010; accepted August 07, 2010. Date of publication November 01, 2010; date of current version January 04, 2011. G. G. Roy, S. Das, and P. Chakraborty are with the Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata, India. P. N. Suganthan is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore (e-mail: myself_ [email protected]; [email protected]; prithwish1611@gmail. com; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090477

Since the classical derivative-based optimization techniques are prone to getting trapped in local optima and are strongly sensitive to initialization, metaheuristic approaches have been used to achieve optimized side lobe level (SLL) and null control from the designed linear arrays, e.g., see [5]–[10]. However, the design of arrays with geometrical shapes other than linear has not been studied to the same extent, although their importance has been steadily on the rise. Circular shaped antenna arrays find various applications in sonar, radar, mobile and commercial satellite communication systems [11]–[13]. The first metaheuristic approach towards the design of circular arrays can be traced in the work of Panduro et al. [14] who applied the real-coded genetic algorithm (GA) for designing circular arrays with maximal side lobe level reduction coupled with the constraint of a fixed beam width. Shihab et al. in [15] applied the particle swarm optimization (PSO) algorithm that draws inspiration from the intelligent collective behavior of a group of social creatures, to the same problem and achieved better results as compared to those reported in [14]. Recently Panduro et al. [16] compared three powerful population-based optimization algorithms—PSO, GA, and differential evolution (DE) on the design problem of scanned circular arrays. The algorithms were compared on a single instantiation of the design problem with number of antenna elements equal to 12 and for a uniform separation of by optimizing excitation current amplitudes and phase perturbations with a view to studying the behavior of array factor for the scanning range of 0 to 360 in angular steps of 30 . In this paper, we use an improved variant of one recently developed metaheuristic algorithm, called the invasive weed optimization (IWO) [17], for designing non-uniform circular arrays with optimized performance with respect to SLL, direc. Since tivity, and null control in a scanning range of its inception, IWO has found several successful applications in engineering [17]–[22]. As evident from publications like [23], IWO is recently making a distinct place of its own in computational electromagnetics. However, to the best of our knowledge, till date, powerful performance of IWO has not been exploited to optimize the amplitude excitation and spacing between the elements of a circular antenna array to produce a radiation pattern with optimal performance. We provide detailed simulation results over three instantiations of the design problem here. Comparisons with the results of other well-known real-parameter optimizers like GA, PSO, original IWO, and DE [24] reflect the superiority of the proposed modified IWO in a statistically significant fashion.

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II. THE IWO ALGORITHM AND ITS MODIFICATION Mehrabian and Lucas proposed the IWO algorithm [17] for solving continuous optimization problems in 2006. IWO emulates the process of weeds colonization and distribution in an ecosystem. The algorithm may be summarized as follows.

1. Initialization: A finite number of weeds are initialized randomly in the search space. 2. Reproduction: Each member of the population is allowed to produce seeds depending on its own, as well as the colony’s lowest and highest fitness, such that, the number of seeds produced by a weed increases linearly from lowest possible seed for a weed with the worst fitness to the maximum number of seeds for a plant with the best fitness. 3. Spatial distribution: The generated seeds are randomly scattered over the -dimensional search space by perturbing them with normally distributed random numbers with zero mean and a variable variance. This step ensures that the produced seeds will be generated around the parent weed, leading to a local search around each plant. However, the standard deviation (sd) of the random function is made to and are the decrease over the iterations. If maximum and minimum standard deviations and if pow is a real number, then the standard deviation for a particular iteration can be given as in (1): (1) where iter is the current iteration number and equals the maximum number of iterations allowed. This step ensures that the probability of dropping a seed in a distant area decreases nonlinearly with iterations, which results in grouping fitter plants and elimination of weaker plants. 2. Competitive Exclusion: Some kind of competition between plants is needed for limiting maximum number of plants in a colony. Initially, the plants in a colony will reproduce fast and all the produced plants will be included in the existing colony, until the number of plants in the colony reaches a maximum . However, it is expected that by this time value the fitter plants have reproduced more when compared to weaker plants. From then on, only the fittest plants up to pop_max, among the existing ones and the reproduced ones, are taken in the colony and steps 2 to 4 are repeated until the maximum number of iterations has been reached, . This i.e., the colony size is fixed from thereon to method is known as competitive exclusion and is also a selection procedure of IWO. The flow chart representing the algorithm is been shown in Fig. 1. Some modifications are incorporated in the classical IWO algorithm to enhance the performance. IWO with the suggested modifications performs much better than the classical IWO, a fact that is validated through experimental results on standard

Fig. 1. A flowchart representation of the IWO algorithm.

benchmark functions in Appendix I. The weed population has been initialized following a linear random distribution. We have, however, modified (1) as

(2) The term adds an enveloped as well as periodical variation in sd, which helps in exploring the better solutions quickly and prevents the new solutions from discarding an optimal solution when the sd is relatively large. Suppose we consider an optimization problem where a scalar function needs to be minimized. In classical IWO, the seeds are generated from a plant with a certain standard deviation, which is decreased as number of iterations increases. Thus, the plants slowly undergo a behavioral transformation from an explorative nature to an exploitative one. In many engineering problems as this one, often the primary goal is not only to locate the global optima but to find the best possible result utilizing fewer resources. Keeping this in mind, the routine of decreasing sd is

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The expression for the array factor in the represented as

plane can be

(2) Now

and

can be given as

(3)

Fig. 2. Comparison of the variations of standard deviation (sd) with iterations for the classical and modified IWO.

is the total number of elements in the circular array. where direction, the excitation When the peak of the array is in phase of the th element can be written as (4) Then, the array factor of a non-uniform circular array simplifies to the following form:

(5)

Fig. 3. Geometry of a non-uniform circular antenna array with radiators.

N isotropic

and (i.e., ) values of Parameters of this expression are the elements. Without loss of generality one may consider the peak of the radiation pattern to be directed along the -axis, i.e., . IV. DESIGNING THE FITNESS FUNCTION

modified, such that if the weeds are near a suspected optimal solution then it can exploit it quickly rather than wait for the standard deviation to decrease to a reasonable value, which might occur near the end of the run. In our proposed strategy the standard deviation actually varies within an envelope. Hence, lesser values of sd are obtained much before the end of the run. This facilitates quicker detection of optimal solutions and better results as compared to the classical IWO, as verified on six numerical benchmarks in Appendix I. Fig. 2 illustrates the decrement of sd with iterations for classical IWO and the modified IWO.

The objective is to design a circular antenna array with minimum SLLs for a specific first null beam width (FNBW). While the first criterion ensures maximum directivity of the antenna, the second criteria is of paramount importance in the modern world where the focus is increasingly on miniaturization. For directivity purposes, we have incorporated the maximum side lobe level in addition to the average side lobe level in the fitness function. The following objective functions represent these requirements in a mathematical form: (6)

III. ARRAY FACTOR OF THE CIRCULAR ARRAY The antenna array to be considered here is non-uniform and planar, i.e., the elements are non-uniformly spaced on a circle plane, as shown in Fig. 3. We consider of radius in the the elements in the circular antenna array to be isotropic sources so that the radiation pattern of this array can be described by its array factor. Now to formulate the array factor, we need the ex, phase , the angular position citation current amplitude of the th element, and the circular arc separation between any two adjacent elements ( —the distance between elements and ) as the parameters of the array.

(7) (8) and are the two angles at the null, is the angle where the maximum side lobe level is obtained in the lower band and, is the angle where the maximum side lobe level is obtained in the where

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TABLE I PARAMETRIC SETUP (r IS THE DIFFERENCE BETWEEN THE MAXIMUM AND MINIMUM POSSIBLE VALUES OF THE d-TH DECISION VARIABLE)

lower band . Combining all these objectives, one can formulate a final cost function as (9) where, “ ,” “ ,” and ” ” represent the weights assigned to the functions. Following [15] we keep the weights of the three components equal to 1 in (9). This puts equal emphasis on the three design-objectives being considered here and hence is unbiased towards any specific objective, which may be easy for a specific algorithm. Since we are considering non-uniformly spaced circular array, coupling will be different from one element to another. This is especially critical as we are considering the radiation in the plane of the antenna array. In order to circumvent the mutual coupling effect, we minimize the combined cost function in (9) subjected to the following constraints [25]: (10) Here we use a constraint handling technique based on Superiority of the Feasible solution (SF). In SF [26], when two solution and are compared, is regarded as superior to vectors under the following conditions. is feasible and is not. 1) and are both feasible and has a smaller objec2) . tive value (in a minimization problem) than and are both infeasible, but has a smaller 3) overall constraint violation as computed by:

(11)

where and is the maximum violation of constraint obtained so far. Therefore, in SF, feasible ones are always considered better than the infeasible ones. Two infeasible solutions are compared based on their overall constraint

violations only, while two feasible solutions are compared based on their objective function values only. Comparison of infeasible solutions based on the overall constraint violation aims to push the infeasible solutions to feasible region, while comparison of two feasible solutions on the objective value improves the overall solution. V. RESULTS To illustrate the superiority of the proposed method, three instantiations of the design problem are solved by using the modified IWO, classical IWO [17], PSO [15], real coded GA [16], and DE. The DE-variant used here is called DE/rand/1/bin and is the most popular one in DE literature [24]. The three instantiations are arrays with 8, 10, and 12 elements. The FNBW is assumed to be a constant, corresponding to a uniform circular spacing between the elements. To array with a uniform meet the requirements of practical considerations, normalization is done for the current amplitudes with maximum value of the amplitude being set equal to 1. The control parameters for modified IWO and classical IWO were set through a series of parameter tuning experiments. The parameters for DE, PSO, and GA were set following the guidelines provided in [15], [16]. Once set, the same parametric values were used for each algorithm to solve all three instantiations. For GA, we used two-point crossovers along with standard single point mutation and ranking selection. The parametric setup for all the algorithms are shown in Table I. Note that the modified IWO and classical IWO were let start from the same initial population over all runs on each problem. Table II compares the algorithms on the quality of the optimal solutions achieved finally by each of them in terms of the mean and the standard deviation (within parentheses) of the best-of-run values for 50 independent runs of each of the five algorithms. -values obtained through the Wilkoxon’s rank sum test [27] between the best algorithm and each of the other algorithms over the three design instances are presented in Table III. If the -values are less than 0.05 (5% significance level), it is a strong evidence against the null hypothesis, indicating that the

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TABLE II MEAN AND STANDARD DEVIATIONS OF THE FINAL COST FUNCTION VALUES ALONG WITH THE MEAN VALUE AT NULL OBTAINED

TABLE III

P -VALUES OBTAINED WITH WILCOXON’S RANK SUM TEST COMPARING THE BEST-PERFORMING

ALGORITHM

WITH ALL OTHER CONTESTANTS ON THREE DESIGN INSTANCES

better final cost function values achieved by the best algorithm in each case is statistically significant and has not occurred by chance. From Table III, it is easy to note that the modified IWO outperforms the classical IWO, GA, PSO, and DE in a statistically significant fashion. In Table IV, we provide the best values of the optimized variables ( in terms of wavelength and the normalized currents ) obtained over 50 runs of the modified IWO algorithm. Table V presents best values (out of 50 independent runs) of the two figures of merit—the SLL (in decibels) and the directivity (in decibels) of the circular array (in terms of wavelength) obtained with the five algorithms over three instances of the design problem. Fig. 4 depicts the radiation patterns of the circular antenna arrays (corresponding to best of the 50 runs in each case) obtained with five algorithms for 8, 10, and 12 element arrays. Convergence characteristics of the five algorithms over all problems are shown in Fig. 5 in terms of the cost function values (in logarithmic scale) of the median run of each algorithm versus the number of cost function evaluations (FEs). The best characteristics graphs in Fig. 5 have been marked in blue. Fig. 5 reveals that not only does modified IWO find the lowest cost function value in each case, but it does so, by consuming

least amount of computational cost. Although it is a common practice in the evolutionary computing domain to measure the timing efficiency of stochastic optimization algorithms in terms of the number of FEs, in order to further envisage this point, in Table VI, we also provide the mean and standard deviation of the CPU time (in seconds) taken by each algorithm to reach a threshold cost function value over the three design instances. Note that to obtain an unbiased comparative performance, for the three design instances, this value is chosen to be somewhat larger than the minimum cost value found by each algorithm in Table II. Table VI shows that the modified IWO reaches the threshold cost value with the lowest number of FEs and that in turn corresponds to the lowest CPU time in seconds. Experiments for obtaining the data in Table VI were performed on a Pentium IV, 2.2 GHz PC, with 512 KB cache and 2 GB of main memory in Windows Server 2003 environment. VI. CONCLUSION Designing non-uniform circular antenna arrays with minimum SLL and maximum directivity is a challenging optimization problem in computational electromagnetics. In this paper, we proposed an improved variant of the recently developed,

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Fig. 5. Convergence characteristics of five contestant algorithms over three instances of the circular array design problem. (a) For number of elements , (b) for number of elements , (c) for number of elements .

N = 10

Fig. 4. Normalized radiation patterns for circular arrays of different number of elements obtained using four or five different optimization techniques. (a) For , (b) for number of elements , (c) for number number of elements of elements .

N =8 N = 12

N = 10

ecologically inspired metaheuristic algorithm called Invasive Weed Optimization (IWO) and demonstrated through simulation experiments, the superiority of the proposed technique in comparison to the classical IWO and three other state-of-the-art stochastic optimizers over three standard instances of the circular array design problem. We formulated the design problem as an optimization task on the basis of a cost function that takes

N =8 N = 12

care of the average side lobe levels and the null control. The cost function is minimized satisfying a constraint so that the mutual coupling effect between the array elements may be avoided. Our simulation experiments indicated that the modified IWO could comfortably outperform PSO, DE, GA, and classical IWO over 8, 10, and 12 element array design problems, based on metrics such as average final accuracy, best obtained design figures of merit (like SLL and directivity), convergence speed, and robustness. All these factors together have been considered for optimal results in our design problem and these accounts for the significance of this work.

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TABLE IV DESIGN VARIABLES OBTAINED WITH MODIFIED IWO ALGORITHM

TABLE V DESIGN FIGURES OF MERIT OBTAINED IN THE BEST (OUT OF 50) RUN OF THE FIVE ALGORITHMS ON THREE DESIGN INSTANCES

TABLE VI A COMPARISON OF ABSOLUTE RUN-TIMES OF THE ALGORITHMS

Future research will focus on exploring the design of other array geometries and concentric circular arrays with IWO and its variants. Also treating the different components of the cost function given in (10) as a multi-objective optimization problem may prove to be a significant avenue of future investigation, but some problem-specific expert’s knowledge may have to be incorporated then for pointing out the best solution from the Pareto-optimal set produced by a multi-objective optimizer. APPENDIX I In this section, we provide the results of testing the performance of the modified IWO and classical IWO over six repre-

sentative benchmark functions from the test suite of the Congress on Evolutionary Computation (CEC) 2005 Special Session and Competition on Real Parameter Optimization [28]. Although we tested on a large number of benchmarks, we provide only a few representative results to save space. All the benchdimensions. 50 indepenmarks have been tested for dent runs of each of the algorithms were carried out and the average and the standard deviation of the best-of-run values were number of FEs. recorded. Each run was continued till The mean and the standard deviation (within parentheses) of the best-of-run values for 50 runs of the two algorithms are presented in Table A1 over six benchmarks. The -values obtained

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TABLE A1 AVERAGE AND STANDARD DEVIATION OF THE BEST-OF-RUN SOLUTION FOR 30-DIMENSIONAL FUNCTIONS

through Wilkoxon’s rank sum test have also been reported in the 4th column of Table A1. Note that to make the comparison fair, both the algorithms were let start from the same initial population for each run on each problem. Table A1 clearly indicates that the performance of the modified IWO is statistically superior to that of the classical IWO. Since both the algorithms started from same initial populations, any difference in their performances should be attributed to their internal search operators and selection of their control parameters. Thus, the superior performance of modified IWO clearly substantiates the effectiveness of the modifications proposed in Section II of this paper.

REFERENCES [1] Handbook of Antennas in Wireless Communications, L. C. Godara, Ed. . Boca Raton, FL: CRC, 2002. [2] Adaptive Antenna Arrays: Trends and Applications, S. Chandran, Ed. . New York: Springer, 2004. [3] Adaptive Antennas for Wireless Communications, G. V. Tsoulos, Ed. . Piscataway, NJ: IEEE Press, 2001. [4] Electromagnetic Optimization by Genetic Algorithms, Y. RahmatSamii and E. Michielssen, Eds.. New York: Wiley, 1999. [5] A. Udina, N. M. Martin, and L. C. Jain, “Linear antenna array optimization by genetic means,” presented at the 3rd Int. Conf. on Knowledge-Based Intelligent Information Engineering Systems Adelaide, Australia, Sep. 1999. [6] Y. Cengiz and H. Tokat, “Linear antenna array design with use of genetic, memetic and tabu search optimization algorithms,” Progr. Electromagn. Res. (PIER) C, vol. 1, pp. 63–72, 2008. [7] W.-C. Weng, F. Yang, and A. Z. Elsherbeni, “Linear antenna array synthesis using Taguchi’s method: A novel optimization technique in electromagnetics,” IEEE Trans. Antennas Propag., vol. 55, no. 3, pp. 723–730, Mar. 2007. [8] F. J. Ares-Pena, A. Rodriguez-Gonzalez, E. Villanueva-Lopez, and S. R. Rengarajan, “Genetic algorithms in the design and optimization of antenna array patterns,” IEEE Trans. Antennas Propag., vol. 47, pp. 506–510, Mar. 1999. [9] Y. B. Tian and J. Qian, “Improve the performance of a linear array by changing the spaces among array elements in terms of genetic algorithm,” IEEE Trans. Antennas Propag., vol. 53, pp. 2226–2230, Jul. 2005. [10] M. M. Khodier and C. G. Christodoulou, “Linear array geometry synthesis with minimum side lobe level and null control using particle swarm optimization,” IEEE Trans. Antennas Propag., vol. 53, no. 8, pp. 2674–2679, Aug. 2005.

[11] M. I. H. Dessouky, A. Sharshar, and Y. A. Albagory, “Efficient sidelobe reduction technique for small-sized concentric circular arrays,” Progr. Electromagn. Res., vol. PIER 65, pp. 187–200, 2006. [12] L. Gurel and O. Ergul, “Design and simulation of circular arrays of trapezoidal-tooth log-periodic antennas via genetic optimization,” Progr. Electromagn. Res., vol. PIER 85, pp. 243–260, 2008. [13] M. Dessouky, H. Sharshar, and Y. Albagory, “A novel tapered beamforming window for uniform concentric circular arrays,” J. Electromag. Waves Applicat., vol. 20, no. 14, pp. 2077–2089, 2006. [14] M. Panduro, A. L. Mendez, R. Dominguez, and G. Romero, “Design of non-uniform circular antenna arrays for side lobe reduction using the method of genetic algorithms,” Int. J. Electron. Commun., vol. (AEU) 60, pp. 713–717, 2006. [15] M. Shihab, Y. Najjar, N. Dib, and M. Khodier, “Design of non-uniform circular antenna arrays using particle swarm optimization,” J. Elect. Eng., vol. 59, no. 4, pp. 216–220, 2008. [16] M. A. Panduro, C. A. Brizuela, L. I. Balderas, and D. A. Acosta, “A comparison of genetic algorithms, particle swarm optimization and the differential evolution method for the design of scannable circular antenna arrays,” Progr. Electromagn. Res. B, vol. 13, pp. 171–186, 2009. [17] A. R. Mehrabian and C. Lucas, “A novel numerical optimization algorithm inspired from weed colonization,” Ecolog. Inform., vol. 1, pp. 355–366, 2006. [18] A. R. Mehrabian and A. Yousefi-Koma, “Optimal positioning of piezoelectric actuators on a smart fin using bio-inspired algorithms,” Aerosp. Science Technol., vol. 11, pp. 174–182, 2007. [19] H. Rad and C. Lucas, “A recommender system based on invasive weed optimization algorithm,” IEEE Congr. Evol. Comput., vol. CEC 2007, pp. 4297–4304, Sep. 2007. [20] A. R. Mallahzadeh, H. Oraizi, and Z. Davoodi-Rad, “Application of the invasive weed optimization technique for antenna configurations,” Progr. Electromagn. Res., vol. PIER 79, pp. 137–150, 2008. [21] A. R. Mallahzadeh, S. Es’haghi, and A. Alipour, “Design of an E-shaped MIMO antenna using IWO algorithm for wireless application at 5.8 GHz,” Progr. Electromagn. Res., vol. PIER 90, pp. 187–203, 2009. [22] A. R. Mallahzadeh, S. Es’haghi, and H. R. Hassani, “Compact U-array MIMO antenna designs using IWO algorithm,” Int. J. RF Microw. Comput.-Aided Eng., vol. 19, no. 5, pp. 568–576, Jul. 2009. [23] S. Karimkashi and A. A. Kishk, “Invasive weed optimization and its features in electromagnetics,” IEEE Trans. Antennas Propag., vol. 58, no. 4, pp. 1269–1278, Apr. 2010. [24] K. Price, R. Storn, and J. Lampinen, Differential Evolution—A Practical Approach to Global Optimization. Berlin: Springer, 2005. [25] M. A. Panduroa, D. H. Covarrubiasa, C. A. Brizuelaa, and F. R. Maranteb, “A multi-objective approach in the linear antenna array design,” Int. J. Electron. Commun., vol. (AEÜ) 59, pp. 205–212, 2005. [26] K. Deb, “An efficient constraint handling method for genetic algorithms,” Comput. Methods Appl. Mechan. Eng., vol. 186, pp. 311–338, 2000. [27] F. Wilcoxon, “Individual comparisons by ranking methods,” Biometrics, vol. 1, pp. 80–83, 1945.

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[28] P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y.-P. Chen, A. Auger, and S. Tiwari, “Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization,” Nanyang Technological University, Singapore and KanGAL Tech. Rep. 2005005, Kanpur Genetic Algorithms Laboratory, IIT Kanpur, May 2005. Gourab Ghosh Roy received the Bachelor of Electronics and Telecommunication Engineering degree from Jadavpur University, Kolkata, India, in June, 2010. He is currently working toward the Masters degree at Ohio State University, Columbus He has worked in the field of computational intelligence, with special focus on the analysis and application of soft computing techniques in different problems of engineering design. His other research interests include machine learning, image processing and control engineering.

Swagatam Das (M’10) received the B.E. Tel.E., M.E. Tel. E., and Ph.D. degrees, all from Jadavpur University, Kolkata, India. He is presently serving as an Assistant Professor in the Department of Electronics and Telecommunication Engineering, Jadavpur University. His current research interests include evolutionary computing, swarm intelligence, pattern recognition, bioinformatics, control systems engineering, and digital signal processing. He has published more than 100 research articles in peer-reviewed journals and international conferences. Dr. Das serves as an Associate Editor of the Information Sciences journal (Elsevier) and as an editorial board member of the International Journal of Artificial Intelligence and Soft Computing and International Journal of Adaptive and Autonomous Communication Systems. He is the founding Co-Editor-in-Chief of Swarm and Evolutionary Computation, an international journal from Elsevier.

Prithwish Chakraborty received the Bachelor of Electronics and Telecommunication Engineering degree from Jadavpur University, Kolkata, India, in June, 2010. He is currently working toward the Masters degree at the Virginia Polytechnic Institute and State University, Blacksburg. His chief research interests include evolutionary computing, electromagnetics, bioinformatics, and control engineering.

Ponnuthurai N. Suganthan (SM’00) received the B.A. degree, the Postgraduate Certificate, and the M.A. degree in electrical and information engineering from the University of Cambridge, Cambridge, U.K., in 1990, 1992, and 1994, respectively, and the Ph.D. degree in electrical and electronic engineering from the School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore, in 1996. He was a Predoctoral Research Assistant in the Department of Electrical Engineering, University of Sydney, Sydney, New South Wales, Australia, from 1995 to 1996, and a Lecturer in the Department of Computer Science and Electrical Engineering, University of Queensland, Brisbane St. Lucia, Queensland, Australia, from 1996 to 1999. From 1999 to 2003, he was an Assistant Professor in the School of Electrical and Electronics Engineering, Nanyang Technological University, where he is currently an Associate Professor. His research interests include evolutionary computation, applications of evolutionary computation, neural networks, pattern recognition, and bioinformatics. Prof. Suganthan is an Associate Editor of the IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION and the J. Pattern Recognition. He is the founding Co-Editor-in-Chief of Swarm and Evolutionary Computation, an international journal from Elsevier.

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On the Physical Limitations of the Interaction of a Spherical Aperture and a Random Field Andrés Alayón Glazunov, Member, IEEE, Mats Gustafsson, Member, IEEE, and Andreas F. Molisch, Fellow, IEEE

Abstract—This paper derives physical limitations on the interactions of antennas exciting TM or TE modes (but not both) and wireless propagation channels. The derivation is based on the spherical vector wave expansion of the electromagnetic field outside a sphere circumscribing the antennas. The result is an extension of the seminal work of Chu on the classical limitations on maximum antenna gain and radiation . Rather than maximizing antenna gain in a single direction we obtain physical limitations on the antenna gain pattern, which is directly translated to more condensed parameters, i.e., the instantaneous effective gain i and the mean effective gain e if instantaneous realizations or correlation statistics of the expansion coefficients of the electromagnetic field are known, respectively. The obtained limitations are on the maximum of i and e , which establish a trade-off between link gain and . Index Terms—Mean effective gain, physical bounds, quality factor, spherical vector waves.

I. INTRODUCTION

B

ANDWIDTH is a valuable resource. In wireless communication systems it can be employed to provide high data rates and/or to accommodate several communication standards operating over a wide range of frequencies on the same, commonly small, communication device such as a wireless handheld terminal. Antennas are therefore required to exhibit large bandwidths while occupying a small volume. This is a challenging requirement ruled by physical limitations. It is well-known that the radiation properties of an antenna are related to its size [1], [2]. For example, the radiation , which is defined as the ratio of the power stored by the reactive field of an antenna to the power

Manuscript received February 19, 2009; revised November 27, 2009; accepted March 18, 2010. Date of publication November 09, 2010; date of current version January 04, 2011. This work was supported in part by the SSF High Speed Wireless Center and in part by an INGVAR grant from the Swedish Foundation for Strategic Research. A. Alayón Glazunov was with the Department of Electrical and Information Technology, Lund University, SE-221 00 Lund, Sweden. He is now with the Department of Electrical Engineering, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden (e-mail: [email protected]). M. Gustafsson is with the Department of Electrical and Information Technology, Lund University, SE-221 00 Lund, Sweden (e-mail: [email protected]). A. F. Molisch was with Mitsubishi Electric Research Labs, Cambridge, MA 02139 USA and also with the Department of Electrical and Information Technology, Lund University, SE-221 00 Lund, Sweden. He is now with the Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2090639

loss, considerably increases as the electrical size1 of the antenna decreases [2]. For narrowband antennas, radiation is inversely proportional to the fractional bandwidth of the antenna.2 Thus, a high antenna is highly undesirable, since it leads to a narrow impedance bandwidth for electrically small antennas as well as poor radiation efficiency due to high ohmic and dielectric losses. Physical performance limits of antennas were initially established by Wheeler, [1], and Chu, [2]. In his work, Chu derived the lowest possible radiation , the maximum gain and the maximum possible gain-to- ratio for linearly polarized omnidirectional antennas using the spherical vector wave expansion of the electromagnetic field outside the sphere of minimum radius that completely encloses the antenna. Since then, this problem has drawn the attention of many researchers, [3]–[12] with a summary in [13]. Recently, Chu’s classical results have been refined by new, more precise and general performance limits that depend upon the shapes and materials of the antennas [14]. Traditionally, investigation of antenna performance limits have involved either (i) the maximization of the antenna gain, , in some specific direction or (ii) the minimization of the radiation , or (iii) the maximization of the ratio between them, , [2], [9]. The latter criterion provides the condition for the minimum to achieve a certain gain or as the condition for the maximum gain achievable at a given . Hence, the maximum ratio provides a compromise between gain and bandwidth is roughly proportional to the inverse of the antenna since bandwidth [15]. In most cellular and wireless LAN systems, the mean effective gain (MEG) is a more important quantity than the maximum antenna gain. This can be understood as follows: In communication links with a pronounced line-of-sight (LOS) propagation path between the receiver and the transmitter, the antenna gain is indeed a good measure of the communication efficiency of the antenna, which can be assessed from the Friis equation [16], [17], and it is clear that the gain should be maximized into the direction of the LOS component. On the other hand, in multipath propagation channels with no dominant component (nonline-of-sight, NLOS), the maximization of the antenna gain in a single or specific direction is of less relevance. Rather, we prefer antennas that are capable of receiving all relevant multipath components. Hence, for maximizing performance in NLOS scenarios, antenna gain is not equally efficient as a figure of merit of an antenna. We need instead a description that takes into account the strength of the multipath components (MPCs) 1The electrical size is defined as the product ka, where k is the wave-number and a is the radius of the smallest sphere circumscribing the antenna. 2For antennas with very large bandwidth, and thus Q < 1, a direct relationship is difficult to define. Therefore, following Chu’s approach in [2], we always use maxfQ; 1g rather than Q to evaluate the radiation quality of an antenna.

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in the different directions, as well as the antenna gain in all those directions. In this case the radiation gain pattern of the antenna and the radiation efficiency of the antenna3 together with the polarization-dependent, angular distribution of the MPC strength provide a more useful description. However, such a full characterization of antennas becomes too cumbersome for most practical purposes. For this reason, the Mean Effective Gain (MEG) (see, e.g., [18]–[20] for further discussion on MEG) is a more useful measure of the link quality in a given propagation environment. By definition the MEG incorporates parameters that describe both the antenna and the propagation channel. Essentially, its definition is based on the partial antenna gain patterns4 weighted by the power-angular spectrum (PAS) of the two orthogonal polarizations, respectively, and the cross-polarization ratio (XPR) of the propagation channel.5 We can actually distinguish between two link gain parameters, namely the MEG, , which weights the gain pattern by the average PAS and XPR, and the “instantaneous” effective gain, , which weights the pattern by a realization of the (stochastically varying) channel. Since most propagation channels in today’s wireless systems are NLOS, rather than maximizing the antenna gain in a specific direction, we aim at obtaining the maximum MEG and the maximum instantaneous gain. and are maximized when In [20] we showed that both the receive (or transmit) antenna coefficients equal the complex conjugates of the expansion coefficients of the incoming field and in spherical vector waves. In this case, the maximum are bounded by , where stands for the radiation efficiency of the antenna port . Conjugate mode-matching provides a maximization of the link gain performance of an antenna in a multipath channel, however, without taking into account the physical limitations imposed by the antennas. Hence, the maxand was made independently of bandwidth imization of constraints, which will result in rather narrowband antennas. In this paper we therefore generalize results obtained by Chu and Wheeler to antennas in multi-path propagation channels. We do this by using the spherical vector wave expansion of the electromagnetic field outside the minimum sphere enclosing the antenna, [20]. The obtained limitations are on the maximum of and , which establish a trade-off between link gain or maximum for and , i.e., they provide the maximum or the minimum for given or . The main a given findings are summarized as follows: 1) If realizations of the channel are known, the transmission coefficients (or reception coefficients for reciprocal are given by the complex antennas) that optimize conjugate of the spherical vector wave expansion coefficients of the field impinging at the antenna, , weighted by the inverse of the radiation quality of the mode of order , . Thus, the contribution of higher order modes increases will be attenuated (filtered out), because 3i.e., how much of the input power at some reference plane or point is actually radiated by the antenna. 4The partial antenna gain patterns are defined in two orthogonal polarizations, their sum being equal to the total antenna gain pattern. For 100% effective antennas the antenna gain pattern equals the antenna directivity. 5i.e., the ratio of the power in the  -polarization to the power in the -polarization.

with the mode order . The corresponding and both meaning that both the depend on the realizations of antenna gain pattern and the bandwidth of the antenna must change adaptively. On the other hand for electrically small antennas the optimal bandwidth coincides with Chu’s predictions and is independent of the channel, while the antenna gain pattern (dipole modes) must still be adaptively changed. Electrically small antennas are the most efficient ones in terms of the use of the available channel modes. 2) If only the correlation matrix of the channel is known, the transmission coefficients (or reception coefficients for reare given by the ciprocal antennas) that optimize eigenvector corresponding to the largest eigenvalue of the correlation matrix of the spherical vector wave expansion , coefficients of the field impinging at the antenna, of the mode weighted by the inverse of the radiation of order , . Here again, the contribution of higher-order increases with modes will be attenuated (filtered out) as the mode order . The corresponding and both depend on the correlation matrix of . For electrically small antennas the optimal bandwidth coincides with Chu’s predictions and is independent of the correlation properties of the channel. On the other hand, the optimal antenna gain pattern (dipole modes) depends on the correlation properties of the channel. Electrically small antennas are the most efficient with respect to the use of the available channel modes in this case too. 3) The optimal performance of multi-port antenna systems with no mutual coupling, i.e., non-interacting ports is dictated by the optimal performance of the single-port antenna case since each port must have identical performance. The remainder of the paper is organized as follows. Section II presents a brief introduction to the spherical vector wave expansion of the electromagnetic field, the antenna scattering matrix, the mean effective gain, the instantaneous effective gain and the radiation of the antenna. In Section III we state and solve and for antennas enthe maximization problem of closed in a spherical volume. Here, we also present numerical results that illustrate our results based on a generic propagation channel. The conclusions are provided in Section IV. II. SPHERICAL VECTOR WAVE EXPANSION OF AN ANTENNA, THE PROPAGATION CHANNEL FIELDS AND RELATED PARAMETERS In [20] we developed a formalism for analyzing the interaction between the antennas and the propagation channel, where the spherical vector wave expansion of the electromagnetic field and the scattering matrix were employed as the two main modeling tools. We present next the main points of these tools. Consider an antenna system enclosed by an (imaginary) , outside this sphere sphere of radius . The electric field, can be expanded in outgoing spherical vector waves and incoming spherical vector waves as, [21], [22] (1)

ALAYÓN GLAZUNOV et al.: ON THE PHYSICAL LIMITATIONS OF THE INTERACTION OF A SPHERICAL APERTURE

where

is the multi-index identified with the number , is the wave-number and is the free-space impedance; see Appendix A for a brief discussion of spherical vector waves. The scattering matrix of an -port antenna provides a full description of all its properties [22]. The scattering matrix reand waves, , lates the incoming signals, the outgoing signals, and waves , the matrix containing the complex antenna reflection coefficients, , the matrix containing the antenna receiving coef, the matrix containing the antenna transficients, mitting coefficients, and the matrix containing the antenna scattering coefficients, (2) For reciprocal antennas we also notice that the following relationship is valid [22] (3) where and are elements of matrices and respectively. The received (outgoing) signals are given by

, (4)

while the transmitted signals are related to the outgoing waves as (5)

and is the average received power; denotes expectation over the ensemble, and the different ensemble realizations can be interpreted as being taken over time, space or frequency. MEG is a measure of the communication efficiency of a given antenna over the multipath propagation channel [18]. . The instantaIt should be noticed that in general neous effective gain is a measure of link efficiency that monitors the fast fading variation over a small-scale area while MEG is a measure of link efficiency averaged over the small-scale variation. B. Radiation

of Antennas

The field modes contribute to the radiated power and to the reactive power. Hence, each mode is characterized by its own radiation quality factor8 , which for a lossless antenna is defined as the ratio of the energy stored to the radiated energy [5]. increases rapidly as the electrical size of the antenna The , becomes smaller than the mode number , i.e., when where is the ratio of the minimum sphere enclosing the anis the radius of the radiansphere [1]. tenna and The inverse of the radiation factor of an antenna is usually used as an estimate of the fractional bandwidth of an antenna, for , where is the center frequency i.e., is the bandwidth expressed as the difference and between the highest and the lowest frequency occupied by the antenna. For a nonresonant antenna, which is tuned to resonance by a reactive element, i.e., the input impedance of the antenna becomes purely real, the radiation is defined as, [15]

A. “Instantaneous” Effective Gain and Mean Effective Gain ports in Consider now a multi-port antenna system with receive mode. Assume further that the propagation channel6 is characterized by a random process as described in [20]. Then, we can compute the “instantaneous” effective gain as (6) is the “instantaneous” where is the “instanreceived (or link) power and taneous” power of the available electromagnetic signals, where is the Frobenius norm. The symbol denotes Hermitian transpose. Besides the instantaneous power it is also relevant to quantify the average received power. The mean effective gain (MEG) [18], [19] defined in terms of the spherical vector wave expansion coefficients can be computed as [20] (7) where is the mode correlation matrix and is the average power7 of the available electromagnetic signals 6It is worthwhile to notice that through the paper we assume that the spatial properties of the propagation channel are preserved over the considered bandwidth. This assumption is the more accurate the narrower the bandwidth considered and is sufficient for current communications systems [23], [24]. 7A useful normalization of the average link power is obtained from the energy conservation law and the addition law of spherical vector harmonics.

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(8) is the angular frequency, is the stored magwhere is the stored electric energy and is the disnetic energy, sipated power, which for lossless antennas equals the radiated . At the resonance frequency, the stored magnetic power and electric field energies are equal, . Analytic exof mode are given in [5], which pressions for the radiation and modes are the same for both independently of index

(9) denote the spherical Hankel function of the 2nd kind where denotes the real part of x. [25] and The definition of the radiation -factor in the case of a multiple-antenna system with multiple input ports or a number of separate antennas in close proximity is not as straightforward as for the single-port antenna case [2], [15]. As previously, we assume that the antenna system is circumscribed by a sphere. We further assume that there is no mutual coupling between 8The

Q of any mode given by the multi-index (ml) depends only on l.

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the antenna ports. This situation is often desirable when designing wireless communication systems since it usually implies low signal correlation and therefore increased diversity performance. Hence, the multi-port antenna system is basically a single radiating system.9 Thus, the -factor is computed as the ratio of the power stored by the reactive field of the whole antenna system to the sum of power losses from all antenna ports. Hence, the radiation factor of a vertically or horizontally polarized antenna can be expressed in terms of the expansion in spherical waves as (10) where the matrix

is a diagonal matrix given by (11)

where is given by (10) and is the matrix containing the antenna transmitting coefficients. This definition represents an , average behavior. For the single-port antenna case, i.e., or modes are excited by when the antenna, the radiation is then given by [5] (12) where we have introduced the notation for the transmission coefficient of the single-port antenna. The -factor of the six lowest order modes is , which is the minimum achievable , when only one polarization is excited. On the other hand the combination of and one mode gives a lower -factor, one [7]. We can now obtain the of a lossless antenna expanded in is a spherical vector waves from (10)–(12). The radiation property of the antenna and the fields related to it. The -factor does not always provide a perfect description of an antenna in terms of bandwidth, it however dictates antenna performance with a clear impact of antenna size on antenna gain. Moreover, the physical implications are straightforward, antennas with high -factors have a large amounts of reactive energy stored in the near zone. This in turn implies that coupling to electromagnetic objects in the near-field zone will produce high losses and in general large currents, narrow bandwidth, and large frequency sensitivity. III. OPTIMUM ANTENNA-CHANNEL INTERACTION We now proceed to derive the maximum of and of both multi-port antennas and single-port antennas when or modes are excited. It is solely 9An optional definition is more sensitive to the actual performance of specific antenna port. According to this definition the radiation is the average over each antenna port

Q

(T) Q(T) (T) (T) where (T) denotes the i column of the T matrix. Clearly, this definition perfectly coincides with (10) if the transmission vectors (T) are the same for all i. Q=N

straightforward to see that a general mathematical formulation of the problem reads as (13) , is given by (10) and when where or , when evaluating , where evaluating are the field expansion coefficients corresponding to either TM or TE modes. Observing that we have assumed multi-port antennas with no mutual-coupling between ports each antenna can now be “adapted” to the field independently from each other. Hence, or is identhe performance of each port in terms of tical to the single-port case, which is mathematically derived in Appendices B and C. Clearly, since the following relations are valid (14) (15) where is the number of ports it suffices to consider the singleport antenna case. In the following we have chosen to restrict both the link power . and the available power to the same range of modes Our goal is therefore to study the interaction of an antenna that can sense field modes (TE or TM but not both) with maximum index of at most . Hence, the performance of an antenna is compared to the field exciting the same modes. In this case the performance, e.g., the link power obtained with an electrically small antenna can in fact be larger compared to the performance of larger antenna as we are going to see in the next sections. However, if the performance of two antennas are compared relative the same available power, then, obviously the larger antenna will perform better than or equal to the electrically small antenna under same conditions. A. Maximum

of Ideal Antennas

that maximize The transmission coefficients, are obtained as (see Appendix B for a derivation) (16) is a vector containing the complex conjugated values where of the expansion coefficients of the field impinging on the anin order to tenna, the index has been interchanged with represent the link gain as a function of transmission coefficients instead of reception coefficients, the index takes on 1 or 2 depending on the type of antenna. with corresponding and are The optimum ratio given by (17) (18) (19)

ALAYÓN GLAZUNOV et al.: ON THE PHYSICAL LIMITATIONS OF THE INTERACTION OF A SPHERICAL APERTURE

We see from (16)–(19) that the radiation of the partial modes of the antenna have a filtering effect on the modes of the propagation channel, , i.e., the optimum transmission coefficients of an antenna, in the sense of the maximum ratio , in a propagation channel characterized by the expansion coefficients of the field impinging on the antenna, , are attenuated by the inverse of the radiation of the corresponding partial waves as the electric length increases for a multipole index and vice versa. and the corresponding and are, in general, Both stochastic variables due to the stochastic nature of the propagation channel. Hence, the optimal antenna must adapt its transmission coefficients to the realizations of the propagation channel.10 Obviously, optimal performance must be related to a specific propagation channel. In other words, when defining optimal performance of an antenna in a wireless propagation channel or optimal antenna-channel interaction, the statistics of the channel, , must be specified. It is also straightforward in to see that for all , , and it holds that agreement with [20]. 11 the radiation For electrically small antennas field of the antenna will be dominated by the dipole modes and therefore only the first term is of relevance, [2], [7], leading to the following result (20) (21) (22) Several conclusions can be drawn from (20)–(22). First we see that for lossless, electrically small antennas exciting TM or TE modes only the radiation is identical to the radiation quality factor of the antenna in “free-space,” i.e., it is independent of the propagation channel. Hence, in our analysis bandwidth considerations of electrically small antennas in fading channels remain the same as the ones predicted by Chu for “spherical antennas.” Moreover, only dipole modes are used and link gain optimization based on the conjugate mode-matching criterion established in [20] applies. Hence, the optimum instantaneous effective gain is completely determined by the expansion coefficients of the propagation channel in spherical vector waves. This is a remarkable result since it means that for electrically small antennas, mode-matching of the lowest three modes (TE or TM) results in maximum link gain with channel adaptation while variable bandwidth is not required. In the opposite limiting case when the size of the antenna be, the ancomes large compared to the wavelength, i.e., tennas will show a potentially broadband behavior as predicted , we set it to be unity since by Chu. In this case, when has no physical meaning in terms of bandwidth, i.e., the relative bandwidth cannot be larger than 200%. Therefore 10Even if deemed not practical a variable antenna must also change accordingly. 11The 0.5 threshold is used since for 10.

Q

kr

Q means that the bandwidth of the 0:5 the radiation quality factor

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instead of the matrix containing the quality factor , a modi,12 where is the identity fied matrix is used, as for all . The distribution of matrix. Hence, the optimum in this limit is independent of , for a constant . Indeed, since is set to 1 as then13 (23) Hence, in the large frequency limit all modes up to will contribute equally to the instantaneous effective gain. In order to illustrate the theory derived above we now proceed to a numerical evaluation using a simple channel model (for justifications of the different assumptions in this model, see [20]) based on the more advanced channel models presented in [23], [24]. The model for the AoA for each of the two orthogonal polarizations assumes a two-dimensional Laplacian distribution in spherical coordinates, i.e., , where eleva, azimuth angle and x stands tion angle for either of - or -polarization, and the shape is controlled by the distribution parameters . We further asemulating chansume that nels of small and large angle spread, respectively; and , . Since (16)–(19) are independent of the cross-polarization ratio (XPR14) of the channel, 0 dB is used. of the Fig. 1 illustrates the filtering effect of the radiation partial modes of the antenna on the transmission coefficients given in (16). The channel coefficients were obtained for a single realization of the channel according to the distribution described and the maximum multi pole order . above for of the antenna We clearly see that for a given electrical size only a subset of all available modes will contribute to the radiated field due to the high losses associated with the higher order modes. As we pointed out early, instantaneous parameters are based on quantities that can be modeled as continuous random variables, which are best described by probability distributions. , and will be characterized by their Therefore, both cumulative distribution functions (cdf), [26], or rather by some values corresponding to some fixed probability levels, i.e., at level of the cdf. some at three probability levels, Fig. 2 shows the maximum 1%, 50% and 99%, as a function of . Clearly, for small and constant , the median ratio15 as well as the spread16 around the median increase with the electrical length . Observe that the as increases since we have only median converges17 to TM or TE modes at our disposal, but not both, therefore in average only half of the available power is used. However, for 12The

max operator acts elementwise.

13Observe

a

that k k

ja

= j where  = 1 or 2.

ja

j and that ka k =

14The XPR of a channel is defined as the ratio of the power of the vertically polarized waves to the power of horizontally polarized waves, [18]. 15The median is obtained as the value corresponding to the 50% level of the cdf. 16Here the spread is evaluated as the difference between values corresponding to the 1% and 99% levels of the cdf. 17This is of course an intuitive result, which will be investigated in the future.

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Fig. 1. Absolute value of the 8 lowest TE modes, a), and TM modes b), of a realization of the channel; antenna transmission coefficients obtained according : and TE modes, c) and TM modes, d), and antenna transto (16) for ka . mission coefficients for TE modes, e) and TM modes, f) for ka

=05

=2

( = 0 1 rad) ( = 10 rad) =1

Fig. 3. G in a propagation channel with small angle spread  : and in a propagation channel with large angle spread  . Results are obtained at three cdf levels: 1%, 50% and 99% and for L , 2, 3, 4. When Q < , it is considered to be unity.

1

( = 0 1 rad) ( = 10 rad) =1

( =

Fig. 4. Q in a propagation channel with small angle spread  : and in a propagation channel with large angle spread  . Results are obtained at three cdf levels: 1%, 50% and 99% and for L , 2, 3, 4. When Q < , it is considered to be unity.

some realizations the mode matching can sometimes result in a better and sometimes worse depending on whether one of the TE or TM mode power is predominantly larger than the other for a given channel realization. For large the behavior of the median is similar to the small case. Namely, comparing the left and right plots we see that the small and large are basically identical. However, the spread around the median is much larger for the larger and it decreases with . In the limand for large the variance converges to iting case the same value independently of . This behavior can be better and understood by examining the corresponding results for shown in Fig. 3 and Fig. 4, respectively. In the low limiting case decreases as is increasing since the performance of the antenna that excites modes with “waste” their

power due to large losses connected with large . As the electrical size of the antenna increases, exciting higher modes leads to an increase in the link power. However, this happens at the expense of smaller bandwidth as shown in Fig. 4. For a fixed increasing results in an increase of until a certain after which the cdf remains constant in the sense of the distribution parameters, with a well marked cutoff. Hence, no further mode “diversity gain” can be achieved due to limited degrees is independent of for . of freedom. Observe that increases, higher Clearly, to achieve better performance as -index multipoles should be excited and therefore should be increased. The smaller variance of for small is explained by the fact that realizations of the channel modes, , are more correlated compared to that of large . However, as both and increase,

Fig. 2. Maximum G =Q in a propagation channel with small angle spread  : and in a propagation channel with large angle spread  . Results are obtained at three cdf levels: 1%, 50% and 99% and for L , 2, 3, 4. When Q < , it is considered to be unity.

( = 0 1 rad) 10 rad) =1

1

1

ALAYÓN GLAZUNOV et al.: ON THE PHYSICAL LIMITATIONS OF THE INTERACTION OF A SPHERICAL APERTURE

G =Q

Fig. 5. Maximum in a propagation channel with small angle spread ( = 0 1 rad) and in a propagation channel with large angle spread ( = 1, it is considered 10 rad). Results are obtained for = 1, 2, 3, 4. When to be unity.



:

L

Q