REALIZATION OF A PLANAR LOW-PROFILE BROADBAND PHASED ARRAY ANTENNA

Transcription

1 REALIZATION OF A PLANAR LOW-PROFILE BROADBAND PHASED ARRAY ANTENNA DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Justin A. Kasemodel, M.S., B.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 21 Dissertation Committee: John L.Volakis, Co-Adviser Chi-Chih Chen, Co-Adviser Joel T. Johnson

2 ABSTRACT With space at a premium, there is strong interest to develop a single ultra wideband (UWB) conformal phased array aperture capable of supporting communications, electronic warfare and radar functions. However, typical wideband designs transform into narrowband or multiband apertures when placed over a ground plane. Therefore, it is not surprising that considerable attention has been devoted to electromagnetic bandgap (EBG) surfaces to mitigate the ground plane s destructive interference. However, EBGs and other periodic ground planes are narrowband and not suited for wideband applications. As a result, developing low-cost planar phased array apertures, which are concurrently broadband and low-profile over a ground plane, remains a challenge. The array design presented herein is based on the infinite current sheet array (CSA) concept and uses tightly coupled dipole elements for wideband conformal operation. An important aspect of tightly coupled dipole arrays (TCDAs) is the capacitive coupling that enables the following: (1) allows field propagation to neighboring elements, (2) reduces dipole resonant frequency, (3) cancels ground plane inductance, yielding a low-profile, ultra wideband phased array aperture without using lossy materials or EBGs on the ground plane. The latter, is of course, critical for retaining the aperture s wideband behavior under conformal installations. ii

3 This dissertation focuses on the realization of wideband phased array apertures using tightly coupled dipole arrays. A methodology for designing planar apertures is presented including: element selection, material loading, and unbalanced to balanced conversion for wideband feeding. Multiple solutions and practical design examples are presented to increase bandwidth, reduce height, avoid common mode excitation and retain low-cost planar PCB manufacturability. Using one of these designs, a 64 element low-profile X-band array prototype is fabricated and measured. The conformal array is capable of scanning up to 7 and 6 in the E- and H-planes, respectively. The active VSWR is less than 2 from 8 to 12.5 GHz (1.6:1) and the array height is only λ/7 at the lowest frequency of operation. A unique feature of the proposed array is its planar layered PCB construction. Specifically, a single microwave laminate is used for the aperture while another supports all associated baluns and matching networks. Good agreement between simulations and measurements confirm the proposed concepts. iii

4 Dedicated to my family. iv

5 ACKNOWLEDGMENTS I would like to express my sincere appreciation to my advisor, Professor John L. Volakis, for his guidance and advice. Not only has he taught me the academic side of electromagnetics and engineering, but also the importance of communication about what it takes be a successful professional and leader. His guidance and support led me to present at conferences, publish papers and write proposals. I would also like to sincerely thank my Co-Advisor Dr. Chi-Chih Chen for interesting discussions and insight on antenna design, research methodology and measurement techniques. He has been a great friend, mentor and truly is an antenna and electromagnetics expert. Dr. Chen showed me different ways to approach a research problem and the steps necessary to accomplish any goal. His honesty, intelligence and open door policy has made the ElectroScience Lab a wonderful workplace and home for the last four years. I want to thank the other students in the Volakis antenna group for their challenging questions, interesting discussions and sharing their research during our weekly meetings. In addition, I want to specifically thank my colleges and close friends; Kenneth E. Browne, Mustafa Kuloglu, Brandan T. Strojny and Orbay Tuncay for their collaboration, proof reading, support and suggestions. v

6 VITA September 2, Born - Gillette, Wyoming May, B.S. Electrical and Computer Eng., South Dakota School of Mines and Technology, Rapid City, SD August, M.S. Electrical and Computer Eng., The Ohio State University, Columbus, OH September, 26 - present Graduate Research Fellow, The Ohio State University, Columbus, OH PUBLICATIONS Journal Publications 1. Kasemodel, J.A.; Chen, C.-C.; Volakis, J.L., Wideband Planar Array with Integrated Feed and Matching Network for Wide-Angle Scanning, Under review: Trans. Antennas and Propagation, IEEE. 2. Kasemodel, J.A.; O Brien, A.; Gupta, I.J.; Chen, C.-C.; Volakis, J.L., Small, Conformal Adaptive Antenna of Spiral Elements for GNSS Receivers, Under review: Trans. Antennas and Propagation, IEEE. 3. Kasemodel, J.A.; Volakis, J.L., A Planar Dual Linear Polarized Antenna with Integrated Balun, To appear in Antennas and Wireless Propagation Letters, IEEE. 4. Kasemodel, J.A.; Chen, C.-C.; Gupta, I.J.; Volakis, J.L., Miniature Continuous Coverage Antenna Array for GNSS Receivers, Antennas and Wireless Propagation Letters, IEEE, vol.7, no., pp , 28. vi

7 Conference Publications 1. Kasemodel, J.A.; Chen, C.-C.; Volakis, J.L., Low-profile Wideband Phased Array Antenna with Integrated Balun, Submitted to: Phased Array Symposium, IEEE, Baltimore, MD, Nov., Kasemodel, J.A.; Chen, C.-C.; Volakis, J.L., Low-Cost, Planar and Wideband Phased Array with Integrated Balun and Matching Network for Wide-Angle Scanning, in Proc. Antenna and Propagation International Symposium, IEEE, Toronto, Ontario, Canada, July Volakis, J.L.; Kasemodel, J.A.; Chen, C.-C.; Sertel, K.; Tzanidis, I., Wideband Conformal Metamaterial Apertures, in Proc. Antenna Technology (iwat), 21 International Workshop on, vol., no., pp.1-4, 1-3 March Kasemodel, J.A.; Chen, C.-C.; Volakis, J.L., Wideband Conformal Array with Integrated Feed and Matching Network for Wide-angle Scanning, in Proc. URSI National Radio Science Meeting, Boulder, CO, January, Kasemodel, J.A.; Chen, C.-C.; Volakis, J.L., A Novel Non-symmetric Tightly Coupled Element for Wideband Phased Array Apertures, in Proc. Antennas Applications Symposium, Allerton, IL, Sept Kasemodel, J.A.; Chen, C.-C.; Volakis, J.L., A Miniaturization Technique for Wideband Tightly Coupled Phased Arrays, in Proc. Antennas and Propagation Society International Symposium, Charleston, SC, June Kasemodel, J.A.; Chen, C.-C., A Measurement Setup for Characterizing Antenna on an Infinite Ground Plane from 1 to 18 GHz, in Proc. Antenna Measurement Technique Association Symposium, Boston, MA, November Kasemodel, J.A.; Chen, C.-C.; Gupta, I.J.; Volakis, J.L., Miniature Continuous Coverage Wideband GPS Antenna Array, in Proc. Antennas and Propagation Society International Symposium, San Diego, CA, July Kasemodel, J.A.; Chen, C.-C.; Gupta, I.J.; Volakis, J.L., Compact Wideband Antenna Array for GNSS Receivers, in Proc. Antenna Measurement Technique Association Symposium, St. Louis, MO, November 27. FIELDS OF STUDY vii

8 Major Field: Electrical Engineering Studies in: Applied Electromagnetics Antenna Design and Measurement Techniques viii

9 TABLE OF CONTENTS Page Abstract Dedication Acknowledgments Vita List of Tables ii iv v vi xi List of Figures xii Chapters: 1. Introduction Motivation, Challenges and Objective Broadband Phased Array Aperture using Tightly Coupled Dipoles Introduction Planar Phased Array Antenna Comparison Input Impedance Scan Element Pattern Equivalent Circuit Linear and Dual Linear Polarization Properties Feeding Network Consideration External 18 Hybrid Low Cost Partially Balanced Coaxial Cable Feed Impedance Matching Summary ix

10 3. Broadband Phased Array Antenna Miniaturization Introduction Antenna Miniaturization Concept Inductive Loading via Volumetric Meandering Ferrite Substrate Loading Capacitive Loading using a Non-Symmetric Element Dielectric Superstrate Loading Summary Realization of Non-Symmetric Tightly Coupled Dipole Arrays Introduction Wideband Balun Integration of Aperture and Feed Single Feed Demonstration Element Array Demonstration Scan Element Pattern Mutual Coupling and Scan Impedance Fully Excited Radiation Performance Summary Conclusion and Future Work Bibliography x

11 LIST OF TABLES Table Page 3.1 Miniaturized element performance comparison summary Ferrite resonant frequency comparison Dielectric constant for superstrate matching using Rogers TMM series array PCB xi

12 LIST OF FIGURES Figure Page 2.1 (a) Infinite current sheet over a ground plane, (b) tightly coupled dipole array implementation Planar phased array antenna elements under investigation inside unit cell; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot Active resistance (solid) and reactance (dash) for various antenna elements in free space scanned to θ o = Active reflection coefficient for different system impedances (Z o ) of each antenna element in free space scanned to θ o = ; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot Active reflection coefficient for various antenna elements in free space scanned to θ o = Active resistance (solid) and reactance (dash) for various antenna elements when placed 8 mm over ground plane scanned to θ o = Active reflection coefficient for various antenna elements when placed 8 mm over ground plane scanned to θ o = Active reflection coefficient for different system impedances (Z o ) of each antenna element when placed 8 mm over a ground plane scanned to θ o = ; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot E-Plane scan element pattern for the wire, bowtie, dipole and slot array when placed 8 mm over ground plane H-Plane scan element pattern for the wire, bowtie, dipole and slot array when placed 8 mm over ground plane xii

13 2.11 Simulated TCDA and calculated unit cell directivity Surface current at 1 GHz; (a) wire, (b) bowtie, (c) dipole, (d) slot Tightly coupled dipole array equivalent circuit in free space scanned to broadside Equivalent circuit for infinite array in free space Equivalent circuit for ground plane backed infinite array (a) Array impedance transformation for equivalent circuit. (b) Return loss comparison for the ideal array in free space and with ground plane (a) Periodic unit cell dipole geometry. (b) Full wave array simulation vs. equivalent circuit for different ground plane heights TCDA active reflection coefficient in free space and when placed 8 mm over ground plane scanned to θ o = Dipole scan element pattern at 1 GHz in the E-Plane (φ = ), D- Plane (φ = 45 ) and H-Plane (φ = 9 ) Dipole cross-polarization ratio over the upper hemisphere at 1 GHz Dipole cross-polarization ratio as a function of frequency when scanning towards θ o = 3, 45, 6 in the diagonal plane (φ = 45 ) Tightly coupled dipole elements; (a) single polarization, (b) dual polarization Boresight directivity of the single and dual polarized TCDA S-parameters of the dual polarized TCDA Typical planar phased array antenna unit cell depicting the aperture, interconnects and ground plane UWB balun using a 18 hybrid xiii

14 2.27 (a) Tapered coaxial cable feed with external 18 hybrid (not shown). (b) Broadside gain and realized gain using external hybrid Single coaxial cable balun with integrated matching circuit. The ground plane and unit cell outline are not shown Single coaxial cable tapered balun active reflection coefficient with and without ferrite bead choke. Note the common mode at 7.3 GHz Single cable tapered balun depicting common mode electric field distribution (left) and common mode suppression using a ferrite bead choke (right) Wideband impedance matching using a single transmission line with characteristic impedance Z m of length l m TCDA matching network example without matching (2 Ω) and with matching network connected to a 1 Ω system impedance Dipole unit cell with inductive miniaturization implemented using vertical meandering and a 2 Ω system impedance Dipole unit cell with inductive miniaturization implemented using vertical meandering TCDA ferrite substrate loading; (a) unit cell geometry, (b) active VSWR, (c) resistance, (d) reactance TCDA ferrite substrate loading while maintaining ground plane electrical separation; (a) unit cell geometry depicting reduced thickness with µ r = 5, (b) active VSWR, (c) resistance, (d) reactance Ferrite substrate electric field distribution; (a) rectangular cavity model, (b) side view in x-z plane Dual polarized array with non-symmetric elements; (a) unit cell geometry, (b) infinite array reflection coefficient, Z o = 2Ω,scanned to θ o = xiv

15 3.7 Baseline non-symmetric TCDA; (a) unit cell geometry for parameter study, (b) input impedance with t1 = 2 mm, t2 = 1 mm, t3 =.5 mm, g = 1 mil, α = 18 with the array placed 8 mm above the ground plane scanned to θ o = Baseline TCDA scan element pattern; (a) E-plane, (b) H-plane Non-symmetric TCDA; (a) geometry with t1 = 2 and 5 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 varied, t2 = 1 mm, t3 =.5 mm, g = 1 mil, α = 18, scanned to θ o = Non-symmetric TCDA; (a) geometry with t2 =.25 and 3 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = t2 + g +.25 mm, t2 varied, t3 =.5 mm, g = 1 mil, α = 18, scanned to θ o = Non-symmetric TCDA; (a) geometry with t3 =.5 and 3 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, t2 = 1 mm, t3 varied, g = 1 mil, α = 18, scanned to θ o = (a) TCDA input impedance, (b) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, t2 = 1 mm, t3 =.5 mm, g varied, α = 18, scanned to θ o = Non-symmetric TCDA; (a) geometry with α = 45 and α = 275, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, t2 = 1 mm, t3 =.5 mm, g = 1 mil, scanned to θ o = Ground plane backed TCDA printed on a PCB with a single layer dielectric superstrate of thickness t 1, and dielectric constant ε (a) TCDA unit cell geometry printed on 2 mil thick TMM3. (b) Input impedance for different ground plane heights TCDA reactance for different ground plane heights xv

16 3.17 TCDA with single dielectric superstrate with ɛ 1 = 1.8 of varying thickness, t 1, scanned to θ o = ; (a) input impedance and (b) corresponding resistance (solid) and reactance (dash) TCDA with two-layer dielectric superstrate with ɛ 1 = 2.2 of λ c,g /4 thickness and ɛ 2 = 1.4 of varying thickness, t 2, scanned to θ o = ; (a) input impedance and (b) corresponding resistance (solid) and reactance (dash) Proposed wideband microstrip coupled line ring hybrid with balanced twin-wire output, a = mm, D =.88 mm, w1 = 38 mil, w2 = 2 mil, w3 = 17 mil, g2 = 3 mil, d = 5 mm; (a) geometry and (b) S parameters Non-symmetric tightly coupled dipole array unit cell with radome, integrated feed and matching network, the dimensions are: t1 = 1.75 mm, t2 =.75 mm, t3 = 1 mm, g = 7 mil, α = 85, a =.8128 mm, D = 1.4 mm, w1 = 3 mil, w2 = 2 mil, w3 = 17 mil, w4 = 24 mil, g2 = 3 mil, ɛ s = 1.7; (a) geometry and (b) active reflection coefficient at broadside Performance of the array unit cell in Fig. 4.2(a); (a) broadside radiation, (b) active VSWR over multiple principal plane scan angles Non-symmetric tightly coupled dipole array prototype (radome removed); (a) fabricated 8 8 array, (b) center element reflection coefficient with single and multiple elements excitations Measured principal plane co-polarized ( ) and cross-polarized (- - -) scan element pattern when the center element is excited and all others are terminated using 1 Ω resistors; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 1 GHz, (d) H-plane at 1 GHz, (e) E-plane at 12 GHz, (f) H-plane at 12 GHz Array (8x8) broadside gain vs. frequency when the center element is excited and all others are terminated using 1 Ω resistors; (a) E-plane, (b) H-plane Electric field magnitude; (a) probe location with strong coupling and (b) improved probe location with minimal coupling xvi

17 4.8 Non-symmetric TCDA unit cell geometry with WAIM superstrate, integrated microstrip balun and twin wire matching network interconnects, t1 = 1.75 mm, t2 =.75 mm, t3 = 1 mm, g = 7 mil, α = 85, a =.8128 mm, D = 1.4 mm, w1 = 48 mil, w2 = 2 mil, w3 = 17 mil, w4 = 14 mil, g2 = 3mil, ɛ s = Performance of the array unit cell in Fig. 4.8; (a) broadside radiation, (b) active VSWR over multiple E-plane and H-plane scan angles X-band 64 element linearly polarized array prototype; (a) with radome, (b) radome removed, (c) aperture removed displaying balun and twinwire interconnects, (d) SMP input connects underneath ground plane Radiation pattern measurement setup with fiberglass support Finite array broadside realized gain with element 29 excited and remaining elements terminated in 5 Ω loads E-plane scan element pattern at 1 GHz with element 29 excited and remaining elements terminated in 5 Ω loads H-plane scan element pattern at 1 GHz with element 29 excited and remaining elements terminated in 5 Ω loads Measured principal plane co-polarized ( ) and cross-polarized (- - -) average scan element pattern and standard deviation error bars for all elements; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 1 GHz, (d) H-plane at 1 GHz, (e) E-plane at 12.5 GHz, (f) H-plane at 12.5 GHz SMA cable assembly with adapters and SMP cable. The original calibration plane is denoted (I), where the desired calibration plane is depicted as III Measured reflection coefficient with the SMP cabled shorted; (a) frequency domain, (b) time-domain, (c) time-gated time-domain Measured reflection coefficient with the SMP cabled shorted; (a) Smith chart format to manually determine port extension delay, (b) copper tape short circuited manual amplitude port extension xvii

18 4.19 Measured reflection coefficient with the SMP cabled shorted; (a) SMA calibration, (b) proposed calibration procedure using time-gating and port extension, (c) 64 element phased array mutual coupling measurement setup Mutual coupling across aperture with element 29 excited; (a) simulated 8 GHz, (b) measured 8 GHz, (c) simulated 1 GHz, (d) measured 1 GHz, (e) simulated 12.5 GHz, (f) measured at 12.5 GHz Measured and simulated mutual coupling vs. frequency with element 29 excited; (a) element 1-4, (b) element 5-8, (c) element 9-12, (d) element 13-16, (e) element 17-2, (f) element Measured and simulated mutual coupling vs. frequency with element 29 excited; (a) element 25-28, (b) element 29-32, (c) element 33-36, (d) element 37-4, (e) element 41-44, (f) element Measured and simulated mutual coupling vs. frequency with element 29 excited; (a) element 49-52, (b) element 53-56, (c) element 57-6, (d) element Measured and simulated finite array element 29 active reflection coefficient scanned to θ o =, φ o = Measured principal plane co-polarized ( ) and cross-polarized (- - -) realized gain beam scanning performance from θ o = -6 to 6 in 1 increments; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 1 GHz, (d) H-plane at 1 GHz, (e) E-plane at 12.5 GHz, (f) H-plane at 12.5 GHz Finite array E-plane radiation pattern at 1 GHz scanned to θ o =, 3, 6, φ o = Finite array H-plane radiation pattern at 1 GHz scanned to θ o =, 3, 6, φ o = Finite array broadside realized gain as a function of frequency with all elements excited xviii

19 CHAPTER 1 INTRODUCTION 1.1 Motivation, Challenges and Objective Traditional phased array designs are based on a single element s isolated performance. It is of course well documented that mutual coupling in an array can cause detrimental changes such as; element impedance variations, polarization degradation and undesirable radiation patterns. In fact, mutual coupling is responsible for one of the more difficult aspects of phased array design, that of uniform scan impedance. However, in contrast to traditional array design, a fundamentally different approach was recently proposed by Munk [2, 3]. Specifically, interelement capacitive mutual coupling is used to cancel the ground plane inductance enabling wideband performance. This is similar to frequency selective surfaces (FSS), another tightly coupled periodic structure [4]. An important aspect of designing wideband phased arrays is element choice. Using the traditional approach, an UWB array would require wideband elements such as; transverse electromagnetic (TEM) horn [5], bunny-ear [6], tapered slot or Vivaldi [7] and body-of-revolution (BOR) elements [8]. However, all these elements are threedimensional and require a large dimension normal to the aperture surface, typically a 1

20 depth on the order of.5-2 λ L, where λ L is the wavelength at the lowest operational frequency. Further, due to the three-dimensional nature of these elements, they are costly and often difficult to fabricate. In addition, depending on the element width, arraying these elements close together to avoid grating lobes (commonly.5 λ H where λ H is the wavelength at the highest frequency) is non-trivial. In this dissertation, we expand on the concepts proposed by Munk and present a new conformal array design that has several advantages; (1) inherently low-profile, (2) conformal mounting on platforms (where a metallic ground plane is used), (3) simple element geometry for simulation ease and (4) enables significant opportunity for cost reduction using planar printed circuit board (PCB) technology to fabricate the array aperture and feed circuitry. We also present practical realization and experimental verification of a low-profile planar TCDA with an integrated balun capable of wideangle scanning. The key contributions of this dissertation are: Developed a deeper understanding of tightly coupled dipole arrays and how capacitive mutual coupling cancels the ground plane inductance and improves bandwidth using equivalent circuits and full wave simulation. Investigated, for the first time, multiple forms of phased array antenna miniaturization using capacitive/inductive treatments and material loading. A new non-symmetric element was developed to control mutual coupling and therefore provide miniaturization and manipulate input impedance independently. Developed multiple low-cost feed designs that incorporate balanced to unbalanced conversion and impedance matching while concurrently avoiding common mode excitations and maintaining a low-profile. 2

21 Designed, fabricated and validated a wideband planar 64 element X-band array capable of scanning up to 7 and 6 in E- and H-planes respectively, with an active voltage standing wave ratio (VSWR) < 2 from GHz. The conformal array is placed λ L /7 over a ground plane at the lowest frequency of operation and fed using a microstrip hybrid. The latter, printed directly on the ground plane, maintains the array s low-profile and simple layered planar PCB construction. This dissertation is organized as follows: Chapter 2 starts with an introduction to planar phased array antennas and demonstrates the unique capability of tightly coupled dipole arrays to become increasingly wideband in the presence of a ground plane. Specifically, we discuss how TCDAs operate and why capacitive mutual coupling is beneficial. This is done using convenient and easy to understand equivalent circuits validated with full wave simulations. Next, specific TCDA designs and polarization properties are explored for single and dual linear polarized apertures. Subsequently, feeding networks are discussed incorporating impedance matching, unbalanced to balanced conversion and avoiding common modes. In Chapter 3, antenna miniaturization using inductive and capacitive loading is employed to design a wideband phased array antenna aperture. The specific aperture is based on an infinite periodic array of dipoles geometrically modified to provide additional design degrees of freedom to control mutual coupling. Specifically, each arm on the dipole is different than the other, or non-symmetric, enabling efficient tuning of inductance and capacitance, independently. The arms are identical near their center feed portion, but change towards the ends, forming a ball-and-cup configuration. 3

22 Additionally, dielectric superstrates and magnetic substrates are presented to further improve bandwidth, miniaturize and reduce height. Chapter 4 presents an experimental demonstration of a 64 element (8 8) linear polarized array prototype operating at X-band ( GHz) [9]. Specifically, a planar wideband feed providing impedance matching and unbalanced to balanced conversion (while maintaining the array s low-profile) is designed and integrated with the antenna aperture. Practical realization challenges are identified and methods to overcome such issues are proposed and verified experimentally. Agreement between infinite and finite array simulations are confirmed over multiple scan angles. Indeed, the wide-angle scanning (up to 7 with a VSWR < 2) over a 1.6:1 bandwidth is a key feature given the low-profile of the array. The dissertation is concluded with a summary of the important contributions and discusses avenues for future wideband planar phased array antenna research. 4

23 CHAPTER 2 BROADBAND PHASED ARRAY APERTURE USING TIGHTLY COUPLED DIPOLES 2.1 Introduction A motivational concept for planar phased array apertures was first proposed by Wheeler [1]. Wheeler showed an infinite planar current sheet as a simple phased array aperture and detailed important phased array quantities such as scan impedance for both E-plane (plane containing the electric field vector in the direction of maximum radiation) and H-plane (plane containing the magnetic field vector in the direction of maximum radiation). However, no specific antenna types were discussed. Fig. 2.1 illustrates the infinite current sheet concept and its implementation using a tightly coupled dipole array. In Section 2.2 we compare several planar phased array antennas performance in an infinite array environment by examining their scan element pattern and input impedance for free space and ground plane backed or conformal installations. The tightly coupled dipole array s unique capability to become increasingly wideband in conformal installations is investigated in Section 2.3 using equivalent circuits validated with full wave simulation. In Section 2.4, the polarization purity of the TCDA 5

24 (a) (b) Figure 2.1: (a) Infinite current sheet over a ground plane, (b) tightly coupled dipole array implementation. over the complete upper hemisphere is presented. Additionally, linear and dual linear polarized TCDA apertures are shown to maintain low cross-polarization and high isolation. Finally, balanced feeding techniques are investigated in Section 2.5 to suppress undesired common modes. An impedance matching circuit amendable to TCDA realization is also presented. 2.2 Planar Phased Array Antenna Comparison In this section, 4 commonly used planar phased array antennas are investigated. These are: (a) Periodically fed wire or connected dipole [1 13] (b) Connected self-complementary bowtie [14 17] (c) Tightly coupled dipole [2, 3, 18] (d) Slot array [19 25]. 6

25 We remark that the tightly coupled dipole array is identical to the wire array, except for a very small gap (in this case.2 mil) separates the elements. An interesting wideband antenna omitted from this study is the fragmented aperture antenna [26 3]. Fragmented arrays are designed using genetic algorithms and commonly use material loading to achieve large bandwidths. Instead, our goal here is to develop wideband arrays without materials. Planar ground-plane-backed spiral arrays are also wideband but suffer from element resonances [31, 32]. Therefore, they are not considered. To evaluate the performance of the proposed elements a commercial finite element software, Ansoft HFSS v11, is used with periodic boundary conditions [33 35] and Floquet ports to simulate an infinite array. A unit cell size of 11.5 mm was used to suppress grating lobes below 13 GHz (λ H /2). Each element was modeled as infinitely thin perfect electric conducting (PEC) sheets (grey) and excited using a lumped port (red) as depicted in Fig Actual feeding structures will be considered separately. In addition, the element study was not exhaustive. Specifically, the antenna s geometry was not optimized for maximum bandwidth Input Impedance The free space infinite array scan impedance at broadside is shown in Fig Scan impedance is the impedance observed at an antenna s terminals when proper voltages are applied to all array elements. Throughout this dissertation, a -1 db active reflection coefficient or VSWR < 2 will be used to determine operational bandwidth, unless otherwise specified. Here, bandwidth is defined as f H /f L : 1, where f H and f L are the highest and lowest frequencies where the active reflection coefficient is less than -1 db. 7

26 3 mm z y.5 mm.5 mm x 1 mm 1 mm 11.5 mm 11.5 mm (a) (b).1 mil 3 mm.5 mm.5 mm 1 mm 1 mm 11.5 mm 11.5 mm (c) (d) Figure 2.2: Planar phased array antenna elements under investigation inside unit cell; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot. 8

27 Refereing to Fig. 2.3, we observe that the wire array reactance is inductive at low frequencies (< 11 GHz) and becomes capacitive for higher frequencies. Also, as expected, the connected complementary bowtie resistance is constant over the entire bandwidth and equal to η /2 with zero reactance (note that η /2 = 6π Ω, i.e. half the free space wave impedance, η ). The dipole array is heavily capacitive, then passes through resonance at 8 GHz while maintaining fairly constant resistance. This is desirable to cancel the inductive ground plane inductance in conformal applications. After resonance, the dipole array is inductive and the resistance increases. In contrast, the slot array resistance at 1 GHz is η /2 with little reactance. For higher frequencies, the impedance quickly becomes capacitive then passes though resonance and becomes inductive while the resistance decreases significantly. Impedance (Ω) Wire Bowtie Dipole Slot Free Space Frequency (GHz) Figure 2.3: Active resistance (solid) and reactance (dash) for various antenna elements in free space scanned to θ o =. 9

28 To determine the system impedance (Z o ) that maximizes each element s bandwidth, a 2-D representation of the active reflection coefficient (at broadside) is plotted for various system impedances in Fig The system impedances selected to maximize bandwidth for the wire, bowtie, dipole and slot element was 275 Ω, η /2 Ω, 155 Ω and 1 Ω, respectively. The corresponding free space active reflection coefficient for each element is shown in Fig The connected bowtie maintains an impressive reflection coefficient < -2 db from 1-16 GHz. That is, it delivers the very best performance. The wire antenna maintains a reflection coefficient of -15 db from 1-13 GHz and the slot array operates from 1-9 GHz. The slot array has limited high frequency bandwidth due to excessive inductance. Also, the dipole array has the smallest usable bandwidth from 5-16 GHz. Concluding, the connected bowtie array has the largest instantaneous bandwidth and maintains the smallest reflection coefficient of the studied element types and is clearly the element of choice for free space UWB phased arrays. This is due to the complementary geometry and therefore it s impedance is η /2 and frequency independent. To evaluate the array s performance over a ground plane, each element was positioned 8 mm (.35λ H ) over a PEC sheet. As Fig. 2.6 depicts, the wire and bowtie resistance peak is above 4 Ω and the reactance changes very rapidly versus frequency. The slot antenna has little reactance variation over the band, but the resistance approaches 375 Ω at 4 GHz and drops below 5 Ω above 8 GHz. This is contrary to the tightly coupled dipole array s resistance which has less fluctuation. Further, the TCDA reactance variation is less than the wire or bowtie and oscillates around Ω. 1

29 (a) (b) (c) (d) Figure 2.4: Active reflection coefficient for different system impedances (Z o ) of each antenna element in free space scanned to θ o = ; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot. 11

30 5 1 Γ (db) Wire: Free Space, Z o = 275 Ω Bowtie: Free Space, Z o = η o /2 Ω Dipole: Free Space, Z o = 155 Ω Slot: Free Space, Z o = 1 Ω Frequency (GHz) Figure 2.5: Active reflection coefficient for various antenna elements in free space scanned to θ o =. Impedance (Ω) Ground Plane Wire Bowtie Dipole Slot Frequency (GHz) Figure 2.6: Active resistance (solid) and reactance (dash) for various antenna elements when placed 8 mm over ground plane scanned to θ o =. 12

31 The ground-plane-backed reflection coefficient is shown in Fig Again, for this comparison, the system impedance for the wire, bowtie, dipole and slot array was selected using Fig. 2.8 to be 275 Ω, 35 Ω, 165 Ω, 31 Ω, respectively. Therefore, maximizing each element s bandwidth. The wire, bowtie, and slot array bandwidth are significantly reduced in presence of the ground plane. However, the TCDA performance improves when placed over a ground plane and maintains a 4.3:1 bandwidth. It is therefore attractive for conformal applications. By comparison, the wire antenna has an instantaneous bandwidth of 6-16 GHz (2.7:1), bowtie array GHz (2:1) and the slot array operates from GHz (1.6:1). 5 1 Γ (db) Wire: Ground Plane, Z o = 275 Ω Bowtie: Ground Plane, Z o = 35 Ω Dipole: Ground Plane, Z o = 165 Ω Slot: Ground Plane, Z o = 31 Ω Frequency (GHz) Figure 2.7: Active reflection coefficient for various antenna elements when placed 8 mm over ground plane scanned to θ o = Scan Element Pattern Having demonstrated that ground plane backed TCDAs provide more than double the bandwidth of other planar apertures, we proceed to investigate each antennas 13

32 (a) (b) (c) (d) Figure 2.8: Active reflection coefficient for different system impedances (Z o ) of each antenna element when placed 8 mm over a ground plane scanned to θ o = ; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot. 14

33 scan element pattern (SEP). Scan element pattern, formally called the active element pattern [36], is the array pattern when only one element is fed while all others are terminated in matched loads. The SEP includes the element pattern and all mutual coupling effects as it was extracted from an infinite array analysis and depicts the arrays scanning capability. In addition, the SEP is used to determine if the array has blind spots, i.e. a null in the radiation pattern where the array gain would drastically drop if scanned to that particular direction in space. The overall array pattern (ignoring edge effects) can be computed using the scan element pattern and array factor for a given finite array size and lattice [37]. Arrays operating in free space radiate bidirectionally and therefore have limited applications. As such, wideband ground plane backed arrays are of considerable interest and the SEP study was limited to ground plane backed arrays. The conformal SEP for all elements is depicted in Fig. 2.9 and Fig. 2.1 for the E- and H-plane, respectively. As each element is small (< λ H /2), they adequately sample the infinite current sheet and have identical scan elements patterns. Therefore, no element has a scanning advantage and only the element s input impedance is critical. For simulation verification, we next consider the TCDA broadside directivity and compare it to the theoretical maximum. Specifically, using (2.1), the maximum directivity of an aperture can be calculated assuming uniform illumination. Comparing the boresight (θ = ) SEP to the maximum directivity (D) possible for the given unit cell area (A), good agreement is observed, implying 1% aperture efficiency, see Fig Hence, the periodic boundary conditions, radiation boundary and ground plane are modeled correctly. D = 4πA λ 2 (2.1) 15

34 1 E Plane SEP 5 Directivity (dbi) 5 2 GHz 1 4 GHz 6 GHz 8 GHz 15 1 GHz 12 GHz 14 GHz Theta (degrees) Figure 2.9: E-Plane scan element pattern for the wire, bowtie, dipole and slot array when placed 8 mm over ground plane. 1 H Plane SEP 5 Directivity (dbi) 5 2 GHz 1 4 GHz 6 GHz 8 GHz 15 1 GHz 12 GHz 14 GHz Theta (degrees) Figure 2.1: H-Plane scan element pattern for the wire, bowtie, dipole and slot array when placed 8 mm over ground plane. 16

35 6 4 Theoretical Max TCDA 2 Gain (dbi) Frequency (GHz) Figure 2.11: Simulated TCDA and calculated unit cell directivity. Given the SEP uniformity among elements, the surface electric current distribution at 1 GHz is plotted in Fig The x-directed current contributes to radiation and is similar among elements. The small gap between neighboring dipole elements has a very strong current concentration and capacitively loads the antenna. As such, the TCDA impedance is capacitive and cancels the ground planes inductive loading. This is the key reason for its wideband performance when placed on a ground plane. This is demonstrated using equivalent circuits discussed next. 2.3 Equivalent Circuit As shown in the previous section, TCDA s bandwidth increases when placed above a ground plane. This is profoundly different than electrically connected arrays whose bandwidth reduces in the presence of the ground plane. In this section, we explain the ground plane effect using simple and easy-to-understand equivalent circuits. The motivating factor for capacitive versus inductive coupling is shown below in Fig

36 (a) (b) (c) (d) Figure 2.12: Surface current at 1 GHz; (a) wire, (b) bowtie, (c) dipole, (d) slot. 18

37 One can think of a wire array as a dipole array connected with infinite capacitance (C mutual = ). As infinite capacitance is a short, a inductively coupled dipole array is a wire array, which are extremely narrowband over a ground plane. Therefore, planar wideband phased array antennas over a ground plane should be capacitively coupled and not electrically shorted together. L wire L wire L wire L wire C Mutual C Tip CMutual C Tip C Mutual L wire L wire 2L wire C Tip C Tip + C Mutual C Mutual R Figure 2.13: Tightly coupled dipole array equivalent circuit in free space scanned to broadside. The mutual capacitance (C mutual ) is parallel to the dipole self tip-to-tip (C tip ) capacitance. As the equivalent capacitance forms a serial RLC network, it can be used to maintain resonance for low frequencies where the dipole wire self inductance (L wire ) is small, (2.2). We remark that the radiation resistance (R) was omitted from the top and bottom-left sections in Fig for clarity. 19

38 f r = 1 LC (2.2) To illustrate the ground planes impedance canceling capabilities, a simple ideal numerical example is presented using a ground plane backed array equivalent circuit. To explain the equivalent circuit formulation an array in free space was first examined, see Fig An ideal array is assumed to operate in free space, meeting all the criteria in which the equivalent circuit is valid; namely, elements are electrically small with no grating lobes [2]. The infinite planar 2D periodic array is positioned between two free space half planes. Each half plane can be represented as a infinite transmission line with characteristic impedance 2R Ao. The input impedance of the array in free space (denoted by the subscript o ), is defined as Z a = R Ao + jx Ao. It is calculated by the parallel combination of each half space transmission line in series with the array reactance X Ao as shown in Fig jx Ao o o 2R Ao jx Ao 2R Ao 2R Ao 2RAo Z A= R Ao +jx Ao Array Z A Z A Figure 2.14: Equivalent circuit for infinite array in free space. The equivalent circuit in Fig was extended to include a ground plane. The array is positioned a distance (d) above the ground plane as shown in Fig The free space array resistance (R Ao ) is assumed to be a constant 2 Ω from

39 GHz. Furthermore, the free space array reactance (X Ao ) is assumed to vary linearly from -2j to +2j over the respective frequency range. The array impedance is an idealized case used for illustrative purposes; however, for tightly coupled dipole arrays the assumption of constant resistance and a capacitive to inductive reactance variation is reasonable. The array is positioned λ/4 above the ground plane at the center frequency (d = 8.8 mm at 8.5 GHz). The ground plane impedance is calculated using the traditional short circuit transmission line equation, then moved a distance (d) through a transmission line with characteristic impedance (2R Ao ), to the array plane (Z gp ) becoming parallel to twice the array resistance (2R Ao ). The array reactance (X Ao ) is then added in series to obtain the final ground plane compensated impedance. The ground plane inductive reactance partially cancel the dipole capacitive reactance for frequencies below the center frequency, while for higher frequencies the capacitive ground plane partially cancel with array inductive reactance. The resultant impedance is effectively compressed and forms three resonances compared to the single free space resonance. The return loss bandwidth improvement is also illustrated in Fig. 2.16b, the array with ground plane has a 4:1 bandwidth compared to the free space array bandwidth of 1.8:1. d d d o o jx Ao jx Ao 2R Ao 2R Ao 2R Ao 2R Ao Array Z A Z A Figure 2.15: Equivalent circuit for ground plane backed infinite array. 21

40 j1 Z o = 2Ω, Freq: 1 16 GHz j.5 j2 Z gp R Ao + jx Ao 2R Ao Z gp Free Space: R Ao + jx Ao, Zo=2Ω (2R Ao Z gp ) + jx Ao With Ground Plane: (2R Ao Z gp ) + jx Ao, Zo=21Ω j Γ (db) 1 j.2 15 j.5 j1 j Frequency (GHz) (a) (b) Figure 2.16: (a) Array impedance transformation for equivalent circuit. (b) Return loss comparison for the ideal array in free space and with ground plane. To verify the equivalent circuit and ground plane impedance compensation effectiveness, a physically realizable tightly coupled dipole array was examined. To construct the equivalent circuit, the free space array input impedance was first found using HFSS, for the unit cell dipole geometry in Fig. 2.17(a). The element to element spacing was 11.5 mm (λ H /2 at 13 GHz), ensuring no grating lobes and the dipole length was mm, yielding a.125 mm gap between adjacent dipoles. The array was then positioned over a ground plane and simulated while the separation distance was varied from 4-1 mm (in 2 mm steps). The simulated conformal array impedance was then compared to the equivalent circuit calculated impedance. As seen in Fig. 2.17, the equivalent circuit impedance curves are in good agreement with full wave simulations (for all ground plane heights). The calculated resistance is typically lower than that of full wave simulation, but follows the simulated impedance curves and provides the reader with an intuitive feel for ground plane spacing effects 22

41 and verifies the equivalent circuit which was introduced to demonstrate impedance cancelation ability of capacitive coupled dipole arrays above a ground plane. j1 Z o = 1Ω, Freq: 1 16 GHz j.2 j.5 j2 Sim: R Ao + jx Ao Calc: d=4mm Sim: d=4mm Calc: d=6mm Sim: d=6mm Calc: d=8mm Sim: d=8mm Calc: d=1cm Sim: d=1cm j.2 j.5 j2 j1 (a) (b) Figure 2.17: (a) Periodic unit cell dipole geometry. (b) Full wave array simulation vs. equivalent circuit for different ground plane heights. After verifying the equivalent circuit model, the simulated TCDA (with 8 mm ground plane separation) reflection coefficient was calculated using a system impedance of 15 Ω. Fig shows similar conformal performance improvement as the ideal equivalent circuit demonstration in Fig Linear and Dual Linear Polarization Properties After analyzing the principal plane SEP and impedance properties of each antenna element, next we considered polarization purity. This study is limited to tightly coupled dipole arrays as they have the largest conformal bandwidth. Using the antenna in Fig. 2.12(d), we examined the E-, H- and D-plane co-polarization and 23

42 Free Space: Zo=1Ω With Ground Plane: Zo=15Ω 5 Γ (db) Frequency (GHz) Figure 2.18: TCDA active reflection coefficient in free space and when placed 8 mm over ground plane scanned to θ o =. cross-polarization level. The D-plane is defined as the diagonal plane (φ = 45 ). The Ludwig third definition of polarization was used [38], as they are the field components typically measured in a far-field antenna range. As such, the co-polarized component (E x ) and cross-polarized component (E y ) is calculate using (2.3) and (2.4). E x = E θ cos φ E φ sin φ (2.3) E y = E θ sin φ + E φ cos φ (2.4). From Fig. 2.19, the principal plane cross-polarization level is > 6 db below the co-polarized component at 1 GHz. The cross-polarization level is db at θ = 3 and the co-polarized directivity is 1 db, yielding a cross-polarization ratio of db. 24

43 The cross-polarization level over the complete upper hemisphere at 1 GHz is shown in Fig Similar to Vivaldi [39, 4] and slot arrays [41], the diagonal plane has the highest cross-polarization level. A -25 db cross-polarization ratio is maintained for conical scanning up to 25 and increases quickly outside of the principal planes. 1 1 GHz SEP 1 Directivity (dbi) E Plane: Co Pol D Plane: Co Pol H Plane: Co Pol E Plane: Cross Pol D Plane: Cross Pol H Plane: Cross Pol Theta (degrees) Figure 2.19: Dipole scan element pattern at 1 GHz in the E-Plane (φ = ), D-Plane (φ = 45 ) and H-Plane (φ = 9 ). It can be seen from Fig. 2.21, the cross-polarization ratio at θ o = 3, 45, 6 is constant vs. frequency. We remark that this is an optimistic cross-polarization ratio as any vertical (or z-directed) currents will typically increase the cross-polarization level. Furthermore, as no vertical feed lines are used in the simulation, the crosspolarization ratio is approximately 1 db to 15 db lower than 3D Vivaldi elements which support vertical currents. We also examined the cross-polarization and mutual coupling for a dual linear polarized TCDA with co-incident phase center as depicted in Fig Fig shows 25

44 Figure 2.2: Dipole cross-polarization ratio over the upper hemisphere at 1 GHz. Cross polarization ratio (db) φ = 45 θ = 3 θ = 45 θ = Frequency (GHz) Figure 2.21: Dipole cross-polarization ratio as a function of frequency when scanning towards θ o = 3, 45, 6 in the diagonal plane (φ = 45 ). 26

45 the co- and cross-polarization level at boresight for linear and dual linear polarized TCDAs. As expected, both have identical co-polarized directivity and the crosspolarization level is minimally effected and greater than 6 db below the co-polarized component. Referring to Fig. 2.24, the input refection coefficient S 11 remains unchanged and the mutual coupling S 21 between orthogonal polarizations is less than -7 db. Again, we remark that this is an optimistic result, as no balun and feeding circuit was modeled. This will be addressed in the next section. 2 mm.1 mil 3 mm.5 mm 2 mm.1 mil 3 mm.5 mm 1 mm 1 mm 11.5 mm (a) 11.5 mm (b) Figure 2.22: Tightly coupled dipole elements; (a) single polarization, (b) dual polarization. 2.5 Feeding Network Consideration Until now, the phased array antennas under investigation were excited in HFSS using an ideal lumped port on the aperture surface. This allowed important concepts and impedance properties to be demonstrated without including feeding effects. The purpose of this section is to discuss feeding network considerations necessary for 27

46 Directivity (dbi) Single: Co Pol Single: Cross Pol Dual: Co Pol Dual: Cross Pol Frequency (GHz) Figure 2.23: Boresight directivity of the single and dual polarized TCDA Magnitude (db) S 11 S Frequency (GHz) Figure 2.24: S-parameters of the dual polarized TCDA. 28

47 TCDA realization. This is depicted in Fig. 2.25, where a planar phased array antenna over a ground plane requires interconnects between the aperture and ground plane. In addition, typical unit cell dimensions are shown with a ground plane separation <.4λ H. This is necessary to avoid boresight radiation cancelation from the ground plane image current when a.5λ ground plane separation is used. A wideband TCDA requires a wideband balanced feed as each element is a balanced dipole. Therefor, this section will present several ways to achieve unbalanced to balanced (balun) feed conversion for planar phased array antennas. Furthermore, typical TCDAs have an input impedance 15-3 Ω depending on element geometry. As a result, a matching circuit must be used to connect the array to 5 Ω system impedances. Figure 2.25: Typical planar phased array antenna unit cell depicting the aperture, interconnects and ground plane. 29

48 2.5.1 External 18 Hybrid A commonly used balun employs a external 18 hybrid where the two outer coaxial shields are soldered together and the remaining center conductors form a 1 Ω balanced transmission line as shown in Fig The hybrid serves to make the center conductors of the output cables opposite in polarity whereas the outer conductor provides a means for shielding. This type of feed arrangement has been used to feed wideband spiral antennas [42] and for the TCDA prototype development by Harris et al. [3]. Shielding is critical because an unshielded feed line, such as twin-wire or co-planar strip can excite a common mode [13, 43] when the feed line and antenna are 1λ long. Common mode excitation and suppression is addressed in the next section. Figure 2.26: UWB balun using a 18 hybrid. Using a external hybrid, the TCDA antenna can be fed through the ground plane using coaxial cables as depicted in Fig. 2.27(a). In addition, the coaxial cables were tapered for improved balun performance. The linear taper controls the current on the outer conductor by forcing it to flow on one side, thus, canceling the adjacent cable shield current. Fig. 2.27(b) displays the unit cell realized gain, which is within.25 3

49 db of the directivity from 5-15 GHz, demonstrating a 1 Ω balanced impedance match. Although the hybrid and coaxial lines are bulky and expensive it serves as a baseline using commercial off the shelf (COTS) parts. Furthermore, depending on the frequency range a wideband 18 hybrid with 4:1 or 1:1 bandwidth can be multiple wavelengths long and therefore troublesome to fit inside the array lattice which is typically on the order of λ H / cm= 13GHz Gain Realized Gain, Z o =1.7cm above ground (a) (b) Figure 2.27: (a) Tapered coaxial cable feed with external 18 hybrid (not shown). (b) Broadside gain and realized gain using external hybrid Low Cost Partially Balanced Coaxial Cable Feed A first attempt to remove the costly 18 hybrid is shown in Fig It consists of a single coaxial cable (standard semi-rigid.46 diameter) with the outer conductor linearly tapered forming a narrow strip. The narrow outer strip and center conductor have a characteristic impedance of approximately 13 Ω. The tapering is necessary for impedance matching the antenna to 5 Ω and will be discussed in the next section. 31

50 a b c d (a) Coaxial cable Teflon (b) Outer shield removed for 13 parallel plate line (c) Taper section for partial balun and impedance taper (d) Ferrite bead Figure 2.28: Single coaxial cable balun with integrated matching circuit. The ground plane and unit cell outline are not shown. Due to tight size constraints, the tapered section is small (λ/17 at 4 GHz) effectively limiting balun performance. For proper operation the taper should be at least λ/2 at the lowest operating frequency [44]. An impedance anomaly is observed in Fig where the unbalanced current forms a common mode at 7.3 GHz. To circumvent the problem, a lossless ferrite bead with µ r = 2 was added around the base of the coaxial cable, effectively choking the unbalanced current. Ferrite beads at X-band are not currently available, but can be used for TCDA arrays operating at L- band and below. The reflection coefficient is shown in Fig. 2.29, clearly demonstrating the ferrite beads effectiveness. In addition, the vector electric field at 7.3 GHz with and without ferrite bead is shown in Fig We observe that the common mode (or monopole mode) has a strong electric field between the dipole arms and ground plane. The common mode frequency occurs when the dipole length (l d ) and round trip feed length (2l f ) is 1λ long (denoted as χ in Fig. 2.3). Therefore, the common mode frequency (in GHz) can be predicted using f cm 3 mm. (2.5) χ 32

51 Where χ is defined as χ = l d + 2l f. (2.6) Substituting (2.6) into (2.5) gives (2.7). Substituting the element geometry and material parameters, the common mode is predicted at 7.3 GHz. We remark that ɛ pcb is the PCB board permittivity the array is printed on (in this case TMM3, ɛ pcb = 3) and ɛ cable is the coaxial cable dielectric constant of 2.4. The taper length and dipole geometry was not optimized to minimize the reflection coefficient. However, the feed concept is demonstrated. f cm 3 mm ɛ 11.5 mm pcb (8 mm) 7.3 GHz (2.7) ɛ 2 cable 5 Γ (db) 1 15 No Ferrite Bead With Ferrite Bead Frequency (GHz) Figure 2.29: Single coaxial cable tapered balun active reflection coefficient with and without ferrite bead choke. Note the common mode at 7.3 GHz. 33

52 11.5 mm 8 mm Figure 2.3: Single cable tapered balun depicting common mode electric field distribution (left) and common mode suppression using a ferrite bead choke (right) Impedance Matching Typical TCDAs have a large input impedance (Z a 15-3 Ω). As a result, a matching circuit must be used to connect the array to common 5 Ω system impedances. A matching circuit for TCDAs is shown in Fig. 2.31, where the antenna is connected to a small transmission line of length, l m, with characteristic impedance Z m. The matching impedance is bound by the following relationship, Z in < Z m < Z a, for 5 Ω and 1 Ω system impedances. Concurrently, to maintain the arrays inherent low-profile, the matching circuit length should approximately equal the array ground plane separation distance, d. This is critical, as a balun circuit can be printed behind or on the ground plane. Interconnects between the TCDA aperture and balun circuitry are necessary and can be concurrently used for impedance matching. 34

53 l m Z m Z a Z in Figure 2.31: Wideband impedance matching using a single transmission line with characteristic impedance Z m of length l m. As an example, consider a TCDA with impedance (Z a ) depicted in Fig The antenna impedance locus is centered around 2 Ω and has an active VSWR < 2 from GHz. However, as mentioned earlier, dipole elements are commonly feed using external commercial of the self (COTS) 18 hybrids having a 1 Ω impedance. Therefore, we used the matching circuit from Fig with l m = 9.25 mm and characteristic impedance of 145 Ω. The resultant input impedance and corresponding VSWR is shown as the red dash trace, demonstrating the TCDA is well matched to a system impedance of 1 Ω over a 4.5:1 bandwidth. 2.6 Summary In this chapter, we presented, for the first time a direct comparison of the scan element pattern and input impedance of 4 common planar wideband phased array antennas found in literature. We demonstrated that a tightly coupled dipole array offers superior conformal performance compared to a periodically fed wire, connected bowtie and slot array. A unique feature of TCDAs is the capacitive mutual coupling 35

54 j.5 j1 Z o = 1, Freq: 1-16 GHz j Z a, no matching, Z o =2 Z in, with matching, Z o =1 4 j VSWR j j.5 -j1 -j2 Z a, no matching Z in, Zo line =145, l=.925cm Frequency (GHz) Figure 2.32: TCDA matching network example without matching (2 Ω) and with matching network connected to a 1 Ω system impedance. which was demonstrated in Section 2.3 to cancel the ground plane inductive loading using equivalent circuits and full wave simulation. This is contrary to arrays operating in free space where the dipole antenna has the smallest bandwidth. Connected bowtie apertures in free space were shown to maintain greater than 16:1 bandwidth with a reflection coefficient below -2 db. However, the array became extremely narrowband when placed over a ground plane. As conformal installations is the focus of this dissertation, the polarization properties of conformal linear and dual linear polarized TCDA apertures were shown to maintain low cross-polarization levels. We also discussed important feed considerations such as unbalanced to balanced conversion, shielding for common mode suppression and impedance matching. The next chapter discusses how antenna miniaturization can be used to extend the lower operating frequency and increase instantaneous bandwidth of TCDAs. 36

55 CHAPTER 3 BROADBAND PHASED ARRAY ANTENNA MINIATURIZATION 3.1 Introduction In this chapter, we use established broadband miniaturization techniques to lower the frequency of operation, increase instantaneous bandwidth and reduce height of phased array antennas. We focus specifically on TCDAs, but the concepts can be extended to other planar phased array antennas as well. The chapter starts by briefly discussing broadband miniaturization concepts in Section 3.2. In Section 3.3, we present multiple inductive loading techniques and apply them to TCDAs. Initially, the dipole inductance is increased via volumetric meandering. Subsequently, ferrite materials between the antenna and ground plane are presented in Section 3.4 to reduce height and improved bandwidth. In Section 3.5, capacitive reactive loading is implemented using a novel element with additional degrees of freedom to cancel the ground plane inductance and achieve wider bandwidths in conformal settings. Each dipole arm is different than the other (or non-symmetric), enabling better independent control of the elements self inductance and mutual capacitance. As such, input 37

56 impedance and wave velocity can be controlled independently. To further miniaturize and provide environmental protection, we study single and two-layer dielectric superstrates in Section Antenna Miniaturization Concept The goal of this section is to develop an intuitive understanding of antenna miniaturization. The basic concept of miniaturization is reducing the phase velocity of the wave guided by the antenna. The phase velocity v p and characteristic impedance Z o of a TEM wave is determined by v p = 1 LC = 1 µɛ, L µ Z o = G C = G ɛ. (3.1) Where L is the series inductance per unit length, C is the shunt capacitance per unit length and G is a geometrical scaling factor. Therefore, an antenna can be miniaturized by increasing the serial inductance and/or shunt capacitance in the form of material or reactive loading [45,46]. Reactive loading is defined by modifying the antenna geometry in such a way that the local stored electric or magnetic energy density is increased or decreased. Similarly, lumped inductors and capacitors can be used although they are typically narrowband, lossy and restrict the arrays power handling capability. The main issue with reactive loading is its implementation and integration into the antenna structure. For some antennas, it can be very difficult, if not impossible, to implement capacitive and/or inductive loading. In this chapter, we will demonstrate broadband inductive and capacitive loading by modifying the antenna geometry and using materials. 38

57 3.3 Inductive Loading via Volumetric Meandering Several inductive meandering techniques were investigated to explore miniaturization. Namely, we considered planar [47 49] and volumetric meandering [5, 51] to increase the dipole inductance (L wire ). However, planar meandering adds minimal inductance, while vertical meandering increases the inductance significantly. Due to the close proximity to the ground plane and relatively fat dipoles, the majority of electric field is normal to the printed dipole. This approach is similar to using corrugations to realize a inductive surfaces [52, 53]. Volumetric meandering was implemented using a constant vertical depth of.58 mm as depicted in Fig In this case, the depth was chosen to be equal to the PCB thickness (standard Rogers 33 microwave laminate) for easy and low cost implementation using standard plated via technology. The associated dipole is 1.8 mm wide with nine meander segments (each.45 mm long) per arm leaving a.2 mm gap between each dipole. Using more segments provides diminishing returns due to increased serial capacitance between meandering sections. The miniaturized dipole array s simulated active VSWR is shown in Fig. 3.2, when the element is positioned 9 mm above a ground plane. As seen, the input impedance is well matched to 2 Ω. It is of interest to compare the performance of our inductively loaded array [54] to the CSA demonstrated by Munk [3]. As depicted in Table 3.1, our design shows significant improvement in terms of usable bandwidth, element s size at the lowest operating frequency and ground plane separation. It should be noted that dielectric sheets (as used in [3]) above the dipole array can further improve scan impedance and increase impedance bandwidth [2 4]. This will be considered later in this chapter. 39

58 Figure 3.1: Dipole unit cell with inductive miniaturization implemented using vertical meandering and a 2 Ω system impedance VSWR Frequency (GHz) Figure 3.2: Dipole unit cell with inductive miniaturization implemented using vertical meandering. 4

59 Table 3.1: Miniaturized element performance comparison summary Vertical Meander Munk CSA [3] VSWR < GHz (5:1) 4-18 GHz (4.5:1) Element Size f high.5λ o.65λ o Element Size f low.1λ o.15λ o Ground Plane Separation λ o /12.8 λ o /1 3.4 Ferrite Substrate Loading Having presented inductive reactive loading, now inductive material loading is considered using ferrites. In this study, we use ideal ferrite materials to demonstrate miniaturization. Specifically, loss-less ferrite materials with constant permeability vs. frequency and ɛ r = 1 are implemented and simulations are used to study the effect of magnetic materials between the ground plane and antenna. Fig. 3.3 depicts the element geometry and input impedance for broadside scan while varying the substrate µ r. We remark that the frequency range and element geometry is same TCDA element presented in Chapter 2 to maintain continuity. As such, the frequency range is above current ferrite materials availability. However, the concepts presented can be easily scaled to VHF/UHF apertures where commercial ferrite materials are available. As expected, increasing the substrate permeability lowers the frequency of operation and increases the resistance below 4 GHz, however, several impedance anomalies are observed. Examining the µ r = 3 case, the instantaneous bandwidth is GHz (5.2:1). The resistance approaches zero at 1.5 GHz due to the λ g /2 guided wavelength ground plane separation where the image current cancels radiation. As expected, when the permeability is further increased 41

60 the cancelation occurs at lower frequencies. In addition, an undesired ferrite material mode is excited. Ferrite No ferrite µ r =3 µ r =5 µ r =7 8 mm VSWR Ground Plane 11.5 mm Frequency (GHz) (a) (b) No ferrite µ r =3 µ r =5 µ r = No ferrite µ r =3 µ r =5 µ r =7 Resistance (Ω) Reactance (Ω) Frequency (GHz) (c) Frequency (GHz) (d) Figure 3.3: TCDA ferrite substrate loading; (a) unit cell geometry, (b) active VSWR, (c) resistance, (d) reactance. To isolate and remove the ground plane cancelation problem, we repeated the study while maintaining the ferrite electrical thickness. Fig. 3.4 depicts the performance when scaling the thickness and subsequent ground plane separation by 1/ µ r. 42

61 Significant miniaturization is achieved using µ r = 3 and the impedance anomaly at 1.5 GHz is removed. The array height is 4.6 mm or λ L /3 and provides an instantaneous bandwidth from GHz (7:1). Ferrite loading with µ r = 5 and 7 provides more miniaturization by reducing the low frequency cutoff to 1.93 and 1.7 GHz, respectively. However, similar to the previous study an undesired ferrite material mode is excited. The mode limits the high frequency operation of the array to 12 GHz and 1.3 GHz and thus reduces the bandwidth to 6.2:1 and 5.8:1, respectively. The electric field inside the ferrite material is shown in Fig. 3.5 and resembles a TM 21 rectangular resonant cavity. As such, the impedance anomaly can be predicted using rectangular resonant cavity model. The rectangular resonant cavity frequency is determined using (3.2) [55]. Substituting the number of variations in the x, y, z directions, the TM 21 ferrite mode resonant frequency is determined using the ferrite µ r and unit cell width (a, b) in (3.3). f mnl = c (mπ ) 2 ( nπ 2π + µ r ɛ r a b ) 2 + ( lπ d ) 2 (3.2) f 21 = (2π ) 2 c ( π ) 2. 2π + (3.3) µ r a b Table 3.2 compares the HFSS simulated impedance anomaly and the predicted TM 21 resonant frequency using (3.3). The calculated resonant frequency is within 6.3% and improves to 1.8% with µ r = 7. The improved accuracy for higher µ r is due to an increased y-directed field variation as opposed to slightly less variation with lower µ r values. If the TM 21 mode is suppressed, the µ r = 7 loaded TCDA operates from GHz (8.2:1) and is extremely low-profile, λ L /56. 43

62 No ferrite µ r =3 µ r =5 µ r =7 r = 5 8mm r VSWR Ground Plane 11.5 mm Frequency (GHz) (a) (b) No ferrite µ r =3 µ r =5 µ r = No ferrite µ r =3 µ r =5 µ r =7 Resistance (Ω) Reactance (Ω) Frequency (GHz) (c) Frequency (GHz) (d) Figure 3.4: TCDA ferrite substrate loading while maintaining ground plane electrical separation; (a) unit cell geometry depicting reduced thickness with µ r = 5, (b) active VSWR, (c) resistance, (d) reactance. Table 3.2: Ferrite resonant frequency comparison HFSS TM 21 µ r GHz GHz % difference

63 z d z x a b y x y (a) (b) Figure 3.5: Ferrite substrate electric field distribution; (a) rectangular cavity model, (b) side view in x-z plane. 3.5 Capacitive Loading using a Non-Symmetric Element To capacitively miniaturize the dipole antenna for use in tightly coupled arrays, the dipole tip-to-tip capacitance can be increased to lower the array s operating frequency. A larger tip capacitance can be realized by enlarging the dipole width near the end of the element. As the mutual capacitance is in parallel with the dipole tip capacitance and dominates, one can more effectively miniaturize by increasing C mutual as in [2], where interdigitated capacitors were used. Similarly, lumped or discrete SMD capacitors can be used, but insertion loss limits the frequency range and the arrays power handing capability is significantly reduced. An alternate approach to increase mutual coupling and control radiation resistance is developed using a novel non-symmetric element. Specific design parameters are presented via parametric studies to achieve miniaturization and control input impedance. In this section, we introduce a novel non-symmetric dipole element depicted in Fig. 3.6(a) [56]. Each arm on the dipole is different than the other or non-symmetric. 45

64 This allows one to better control the elements self inductance and mutual capacitance independently. In this case, the arms are similar near the center feed portion but change shape towards the end of the dipole, forming a ball-and-cup. The results shown in Fig. 3.6(b) are a proof of concept. It demonstrates that nonsymmetric elements are broadband and justifies a more rigorous study. In particular, each element s non-symmetric qualities can be exaggerated for improved UWB performance (typically 4:1) or perhaps optimizing the bandwidth for a specific application. Due to the periodic structure of the array, one can think of the aperture as a transmission line with series inductance and shunt capacitance. The non-symmetric arms can be used to create radically different designs than the symmetric ones currently found in literature. Unit Cell 1.15 cm= 13 GHz.8 cm above ground plane (a) (b) Figure 3.6: Dual polarized array with non-symmetric elements; (a) unit cell geometry, (b) infinite array reflection coefficient, Z o = 2Ω,scanned to θ o =. 46

65 To characterize the non-symmetric TCDA, it was parameterized with the following five variables; t1 (cup width), t2 (ball width), t3 (arm width), g (element separation gap) and α (cup opening angle). For conformal realization, the associated array was placed 8 mm above a ground plane and remains fixed during parametric analysis. The broadside scan input impedance is shown in Fig. 3.7(b). The corresponding principal plane scan element pattern is shown in Fig We observe the E-plane SEP is similar to the H-plane pattern for 45 θ 45 and fairly constant over a broad range of frequencies. However, at low elevation angles (towards grazing) the E and H-plane patterns deviate substantially. The E-plane pattern has sharper nulls, while the H-plane pattern vanishes at θ = ± 9. The latter is associated by radiation cancelation at horizon from the ground plane image current. Although the element is non-symmetric in the E-plane, the SEP is symmetric around θ = due to strong mutual coupling. For all parameter sweeps, the SEP remains constant (within 1 db of Fig. 3.8) and thus are omitted. It is therefore only necessary to study the input or scan impedance of each non-symmetric TCDA design. The first parameter studied was t1. As t1 is increased, the resistance is significantly reduced, while the low frequency reactance is reduced. Furthermore, the high frequency reactance increases, effectively shifting the input impedance on the smith chart and increasing the loop diameter as shown in Fig This is due to an increased tip-to-tip capacitance formed by the large cup size. Frequencies below 5 GHz are minimally effected. To facilitate sweeping t2, while not shorting the element to it s neighbor, t1 had to also increase accordingly. In an effort to separate the effects, t1 was increased to maintain the same cup trace width, namely,.25 mm for all values of t2. As t2 47

66 j1 Z o = 2Ω, Freq: 2 16 GHz t1 g j.5 j2.5 mm j.2.5 mm t3 j.2 t mm j.5 j1 j2 (a) (b) Figure 3.7: Baseline non-symmetric TCDA; (a) unit cell geometry for parameter study, (b) input impedance with t1 = 2 mm, t2 = 1 mm, t3 =.5 mm, g = 1 mil, α = 18 with the array placed 8 mm above the ground plane scanned to θ o = Gain (db) 5 2GHz 4GHz 6GHz 1 8GHz 1GHz 12GHz 14GHz Theta (degree) (a) Gain (db) 5 2GHz 4GHz 6GHz 1 8GHz 1GHz 12GHz 14GHz Theta (degree) (b) Figure 3.8: Baseline TCDA scan element pattern; (a) E-plane, (b) H-plane. 48

67 j1 Z o = 2Ω, Freq: 2 16 GHz 2mm 5mm j.5 j2 t1=2mm t1=3mm t1=4mm t1=5mm j j.2 j.5 j2 j1 (a) (b) 4 3 Impdance (Ω) t1=2mm t1=3mm t1=4mm t1=5mm Frequency (GHz) (c) Figure 3.9: Non-symmetric TCDA; (a) geometry with t1 = 2 and 5 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 varied, t2 = 1 mm, t3 =.5 mm, g = 1 mil, α = 18, scanned to θ o =. 49

68 increases, the resistance increases over the entire frequency range. In a similar fashion, the reactance is substantially reduced for low frequencies, becoming less capacitive. For a small ball width (t2 =.25 mm) the first resonance occurs at 12 GHz, but for larger sizes the first resonance occurs much lower, for example 2.2 GHz when t2 = 3 mm. When t2 is increased, the element is effectively miniaturized, a result of increased mutual coupling. For larger t2 values, the ball and cup capacitive junction area increases, resulting in a larger mutual and tip-to-tip capacitance, see Fig The next parameter studied was the arm width or t3. To accommodate large t3 values, t1 and t2 had to be increased to 3 mm and 2 mm respectively, otherwise the element would be electrically connected to is neighbor. As t3 increases, the loop size on the smith chart also increases and shifts to the left, implying a reduction of resistance and a larger reactance variation over the band, see Fig Below 5 GHz the resistance is constant while for higher frequencies the resistance is halved when increasing t3 to 3 mm from.5 mm. The decrease in resistance is attributed to a reduction of the wire inductance shown by a increased capacitive reactance over the entire frequency range. The next parameter of interest is the gap separating the ball and cup, g. When the separation gap is small, a significant increase in mutual coupling effectively miniaturizes the antenna. This is observed by a resistance increase for all frequencies, while simultaneously decreasing the low frequency capacitive reactance and high frequency inductance as shown in Fig The gap separation should be as small as possible (within manufacturing tolerances) to ensure strong mutual coupling, enabling the array to operate to lower frequencies. 5

69 .25mm 3mm j1 Z o = 2Ω, Freq: 2 16 GHz j.5 j2 t2=.25mm t2=.5mm t2=1mm t2=2mm t2=3mm j j.2 j.5 j2 j1 (a) (b) 4 3 Impdance (Ω) 2 1 t2=.25mm t2=.5mm t2=1mm t2=2mm t2=3mm Frequency (GHz) (c) Figure 3.1: Non-symmetric TCDA; (a) geometry with t2 =.25 and 3 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = t2 + g +.25 mm, t2 varied, t3 =.5 mm, g = 1 mil, α = 18, scanned to θ o =. 51

70 .5mm 3mm j.5 j1 Z o = 2Ω, Freq: 2 16 GHz j2 t3=.5mm t3=1mm t3=2mm t3=3mm j j.2 j.5 j2 j1 (a) (b) Impdance (Ω) 1 1 t3=.5mm t3=1mm t3=2mm t3=3mm Frequency (GHz) (c) Figure 3.11: Non-symmetric TCDA; (a) geometry with t3 =.5 and 3 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, t2 = 1 mm, t3 varied, g = 1 mil, α = 18, scanned to θ o =. 52

71 4 j1 Z o = 2Ω, Freq: 2 16 GHz j.5 j2 g=5mil g=15mil g=25mil g=35mil 3 2 j Impdance (Ω) 1 g=5mil g=15mil g=25mil g=35mil j.2 1 j.5 j1 j Frequency (GHz) (a) (b) Figure 3.12: (a) TCDA input impedance, (b) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, t2 = 1 mm, t3 =.5 mm, g varied, α = 18, scanned to θ o =. The final parameter investigated is the cup opening angle α. The values investigated were in 6 steps. When α decreases a similar performance trend is observed when g is reduced. Specifically, as α is reduced, the amount of mutual coupling increases due to a larger capacitive area. For all cases the anti-resonance point (6.5 GHz) stays the same, while the first resonance point is miniaturized up to 1% when α decreases from 275 to 45. Based on the performance of this novel element we integrate the antenna with a balun and fabricate a 64 element prototype in Chapter 4 to demonstrate its wideband performance. 3.6 Dielectric Superstrate Loading Another way to capacitively load the aperture is using dielectric materials. To determine the superstrate dielectric constant a linearly polarized plane wave at normal incidence is considered. The plane wave is assumed to propagate in an infinite medium 53

72 j1 Z o = 2Ω, Freq: 2 16 GHz j.5 j2 α=45 α=15 α=165 α=225 α=275 = 45 = 275 j j.2 j.5 j2 j1 (a) (b) 4 3 Impdance (Ω) 2 1 α=45 α=15 α=165 α=225 α= Frequency (GHz) (c) Figure 3.13: Non-symmetric TCDA; (a) geometry with α = 45 and α = 275, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, t2 = 1 mm, t3 =.5 mm, g = 1 mil, scanned to θ o =. 54

73 with a dielectric constant equal to the array PCB permittivity with thickness h. A dielectric superstrate of thickness, t 1, and dielectric constant ε 1 is then positioned between it and free space, as shown in Fig t 1 h d 1 Superstrate Array PCB Figure 3.14: Ground plane backed TCDA printed on a PCB with a single layer dielectric superstrate of thickness t 1, and dielectric constant ε 1. The reflection coefficient at each material interface is given by Γ i,i+1 = η i η i+1 η i + η i+1 (3.4) where the wave impedance in the dielectric medium can be written as η i = η ɛi. (3.5) Simplifying (3.4) using (3.5) gives Γ i,i+1 = ɛi+1 ɛ i ɛi + ɛ i+1. (3.6) To solve for the required superstrate dielectric constant, (3.6) is used to form a system of equations to match the PCB dielectric constant to free space using single or double dielectric superstrate(s). Finding the minimum reflection coefficient and requisite dielectric constants was performed using MATLAB. Table 3.3 summarizes the 55

74 minimum reflection coefficient (given single and dual layer loading) using commercial Rogers TMM series high frequency laminates as the array PCB. Table 3.3: Dielectric constant for superstrate matching using Rogers TMM series array PCB Single Double PCB ɛ P CB ɛ i Γ (db) ɛ i ɛ i+1 Γ (db) TMM TMM TMM TMM Based on [2], the superstrate thickness should be λ c,g /4 at the center frequency of the operational bandwidth. Assuming the array has constant resistance and the reactance is assumed to vary linearly from capacitive to inductive and resonate at f c. However, typical TCDAs are generally more capacitive and less inductive as indicated in Fig. 3.15(b). Furthermore, resonance is significantly altered by ground plane separation as depicted in Fig and not related to the traditional λ/2 dipole length. Due to the ambiguity of resonance, initially λ c /4 was assumed to equal the ground plane separation (d = 8 mm) yielding f c = GHz. Using (3.7), a superstrate thickness was calculated to be 6.58 mm (λ c,g /4 at GHz). Several thicknesses were then simulated, varying from λ c,g /1 to λ c,g /3. t = λ c,g 4 = λ c 4 ɛ r (3.7) 56

75 j1 Z o = 2Ω, Freq: 1 16 GHz j.5 j2 j j.2 j.5 j1 j2 d=4mm d=6mm d=8mm d=1cm (a) (b) Figure 3.15: (a) TCDA unit cell geometry printed on 2 mil thick TMM3. (b) Input impedance for different ground plane heights. 3 2 d=4mm d=6mm d=8cm d=1cm 1 Reactance (Ω) Frequency (GHz) Figure 3.16: TCDA reactance for different ground plane heights. 57

76 j1 Z o = 2Ω, Freq: 1 16 GHz j.5 j2 t 1 = t =λ \1 1 c,g 2 t 1 =λ c,g \6 t 1 =λ c,g \4 15 t 1 =λ c,g \3 j Impdance (Ω) 5 5 t 1 = j.2 1 t 1 =λ c,g \1 t 1 =λ c,g \6 15 t 1 =λ c,g \4 j.5 j1 j2 t 1 =λ c,g \ Frequency (GHz) (a) (b) Figure 3.17: TCDA with single dielectric superstrate with ɛ 1 = 1.8 of varying thickness, t 1, scanned to θ o = ; (a) input impedance and (b) corresponding resistance (solid) and reactance (dash). When the superstrate thickness increases, the peak resistance is reduced and shifted from 7 GHz to 4.75 GHz. As the thickness approaches λ g /4, a second loop on the smith chart is formed, see Fig which increases the resistance at 12 GHz to 17 Ω from 1 Ω. Furthermore, the reactance increases and remains fairly constant from 9-14 GHz. As the superstrate thickness becomes larger than λ g /4, the second high frequency resistance peak increases at the expense of reducing the first resistance peak at 5 GHz. There is little reactance change below 4 GHz, however, the resistance increases substantially from 2-4 GHz as the superstrate thickness is increased. Generally, as the superstrate thickness increases the high frequency impedance rotates clockwise on the smith chart as shown in Fig. 3.17(a). When the thickness is approximately λ g /4 a second loop of similar size is formed. For thicker substrates the low frequency loop is pulled or compressed while the second loop expands. 58

77 A similar thickness analysis was performed using a two-layer dielectric superstrate. The same TCDA, PCB, and ground plane separation was used was used as before. The first superstrate was λ c,g /4 thick at GHz and had ɛ 1 = 2.2. The second superstrate had a dielectric constant (ɛ 2 ) of 1.4 and thickness (t 2 ) was varied from λ c,g /1 to λ c,g /3 (see Fig. 3.18). The second superstrate provides little miniaturization, but rather improves the mid band impedance fluctuation. The first resonance peak frequency is constant for all t 2 values while the second peak is reduced and shifted lower in frequency. For t 2 λ c,g /4, the reactance variation is reduced from 4-14 GHz. Given the minor improvements the second superstrate offers, care should be primarily focused on the first superstrate as it dominates. j1 Z o = 2Ω, Freq: 1 16 GHz j.5 j2 t 2 = t 2 =λ c,g \1 2 t 2 =λ c,g \6 t 2 =λ c,g \4 15 t 2 =λ c,g \3 j Impdance (Ω) 5 5 t 2 = j.2 1 t 2 =λ c,g \1 t 2 =λ c,g \6 15 t 2 =λ c,g \4 j.5 j1 j2 t 2 =λ c,g \ Frequency (GHz) (a) (b) Figure 3.18: TCDA with two-layer dielectric superstrate with ɛ 1 = 2.2 of λ c,g /4 thickness and ɛ 2 = 1.4 of varying thickness, t 2, scanned to θ o = ; (a) input impedance and (b) corresponding resistance (solid) and reactance (dash). 59

78 3.7 Summary In this chapter, general miniaturization methods were discussed and multiple TCDA implementations were presented. Specifically, in Section 3.2 we used equivalent transmission line concepts such as phase velocity slow down to describe antenna miniaturization. As such, this chapter presented multiple methods of increasing serial inductance and shunt capacitance using reactive and material treatments. Inductive reactive loading was implemented using volumetric meandering in Section 3.3. The meandering improves bandwidth approximately 15%, and can be implemented using plated vias and traditional PCB manufacturing maintaining the arrays low-cost and planar assembly. Inductive material loading using ferrites was presented in Section 3.4 and improves TCDA bandwidth up to 7:1 while reducing the array thickness to λ L /3 using an µ r = 3. For µ r > 3 an undesired TM 21 ferrite material mode is excited and can be predicted using rectangular resonant cavity analysis. Moreover, suppressing the mode results in extremely large bandwidth (8.2:1) and is very low-profile (λ L /56). Capacitive loading was achieved by controlling the mutual capacitance between neighboring elements using a novel non-symmetric element. Multiple parameter sweeps were presented in Section 3.5 to control input impedance and miniaturize the element. The non-symmetric element has similar bandwidths to properly designed symmetric TCDAs while providing the ability to control the elements resistance and reactance more independently. Finally, single and dual dielectric superstrate loading was presented in Section 3.6. A guideline for determining the substrate dielectric constant and thickness was developed and shown to increase low frequency resistance and reduce impedance variation vs. frequency. 6

79 CHAPTER 4 REALIZATION OF NON-SYMMETRIC TIGHTLY COUPLED DIPOLE ARRAYS 4.1 Introduction In this chapter, we design, fabricate and experimentally verify a new wide-scanning conformal array with integrated balun and matching network. The developed antenna is based on the non-symmetric element presented in Section 3.5. The non-symmetric qualities can be manipulated for UWB performance or improved operation over a specific bandwidth using the additional degrees of freedom to cancel the ground plane inductance. A design example for the latter is developed to operate at X-band ( GHz). A unique feature of the proposed array is the planar layered PCB construction. Specifically, a single microwave laminate is used for the array aperture while another supports all associated baluns and matching networks. This chapter is organized as follows: a wideband hybrid feed providing unbalanced to balanced conversion while maintaining the array s low-profile is presented in Section 4.2. The balun is printed on the array ground plane and connects to the array aperture using small twin-wire transmission lines. In Section 4.3, the aperture is integrated with the balun and radome. Furthermore, wide-angle scanning up to 75 is 61

80 shown. Experimental demonstration of a 64 element (8 8) X-band array prototype with a single driven element is presented in Section 4.4. The prototype is used to verify numerical simulation and addresses fabrication difficulties. An improved feed to enhance scanning performance and reduce cross-polarization is designed, fabricated and measured in Section 4.5. Measurements and simulation are in good agreement and 6 scanning is verified experimentally. 4.2 Wideband Balun A wideband tightly coupled dipole array requires a wideband feed. As such, in this section we propose a modified planar wideband ring hybrid printed on the array ground plane. The hybrid employs coupled microstrip lines for bandwidth improvement [57]. The required even (Z even ) and odd (Z odd ) mode coupled line impedances are Ω and 3.2 Ω, respectively. However, the required coupled line separation g required is < 1 mil for a 25 mil thick Rogers 326 microwave laminate. The small coupled line separation is beyond traditional fabrication capabilities and limits realization of the maximum 2:1 theoretical ring bandwidth. As a 1.7:1 bandwidth is necessary for the desired frequency range, the coupled line gap was increased to 3 mil. Using a microstrip trace width (w3) of 15 mil, the corresponding impedances are Z even = 14.6 Ω and Z odd = 39.7 Ω. The ring was then optimized to provide a return loss > 1 db from GHz or > 15 db from GHz and maintained a balanced output transmission S 21 > -.75 db from GHz. See Fig. 4.1 for the final design layout and performance. Concurrently, the insertion loss is <.5 db. The ring hybrid has a 5 Ω SMA coaxial cable input and two output ports that extend inside the ring, 18 out-of-phase from each other. As a result, the fields 62

81 add in series forming a 1 Ω balanced line. Unlike the design in [57], the unused terminated sum (or in-phase) port was removed, reducing complexity and cost. In addition, the insertion loss was improved by approximately.25 db. D 5 25mil RO326 w2 a Port 2 5mm w3 g2 Port 1 w1 S (db) 1 15 S 11 S 21 Ground Plane Frequency (GHz) (a) (b) Figure 4.1: Proposed wideband microstrip coupled line ring hybrid with balanced twin-wire output, a = mm, D =.88 mm, w1 = 38 mil, w2 = 2 mil, w3 = 17 mil, g2 = 3 mil, d = 5 mm; (a) geometry and (b) S parameters. 4.3 Integration of Aperture and Feed Due to the large array input resistance (Z a 2 Ω to 3 Ω), the element cannot be directly connected to the ring hybrid. Instead, a small transmission line (of characteristic impedance 136 Ω) is used to match the array to the hybrid. As depicted in Fig. 4.2(a), a twin-wire (diameter: a =.8128 mm, separation: D = 1.4 mm) was employed. The array and balun is printed on standard Rogers 323 and 326 microwave laminates respectively, maintaining the arrays low-cost. To facilitate a wider scanning range and provide protection, a 6.35 mm thick wide-angle impedance 63

82 matching (WAIM) superstrate [58] having a dielectric constant (ε s ) of 1.7 was added. The non-symmetric TCDA unit cell with integrated balun and impedance matching interconnects is shown in Fig. 4.2(a). The broadside active reflection coefficient is < -1 db from GHz, as illustrated in Fig. 4.2(b). s 5 Γ (db) 1 15 (a) Frequency (GHz) (b) Figure 4.2: Non-symmetric tightly coupled dipole array unit cell with radome, integrated feed and matching network, the dimensions are: t1 = 1.75 mm, t2 =.75 mm, t3 = 1 mm, g = 7 mil, α = 85, a =.8128 mm, D = 1.4 mm, w1 = 3 mil, w2 = 2 mil, w3 = 17 mil, w4 = 24 mil, g2 = 3 mil, ɛ s = 1.7; (a) geometry and (b) active reflection coefficient at broadside. The boresight directivity and realized gain is shown in Fig. 4.3(a). As indicated, the realized gain approaches the maximum aperture directivity from GHz (within.3 db). Furthermore, the radiation efficiency is greater than 93% including all dielectric and copper conductor losses. Of importance is the remarkable scanning 64

83 performance of this array, as depicted in Fig. 4.3(b). It maintains an active VSWR < 2.5 from 7.5 GHz to 13 GHz for scanning up to 75 in the E-plane and 6 in H-plane. 4 4 dbi 2 2 4πA/λ 2 Realized Gain VSWR Boresight E3 H3 E6 H6 E Frequency (GHz) (a) Frequency (GHz) (b) Figure 4.3: Performance of the array unit cell in Fig. 4.2(a); (a) broadside radiation, (b) active VSWR over multiple principal plane scan angles. 4.4 Single Feed Demonstration To verify the proposed design, a small finite (8 8) array was simulated, fabricated and measured. For simulation and measurement, the array was mounted on a 12 " square aluminum ground plane. As depicted in Fig. 4.4(a), the array and balun circuitry are completely planar. A solder mask was employed on the array and balun PCBs to enable soldering ease. In addition, each board was extended.5 around the array aperture to facilitate 4 nylon bolts. The finite array prototype was also simulated using HFSS. The simulation mesh is 1.83 million tetrahedral with a memory usage of 61.1 GB and takes approximately 4 hours for each frequency point using a Dual Xeon 2.5 GHz Quad Core workstation. We note that the only difference 65

84 between fabricated and simulated geometries is the solder mask and spray adhesive for assembly. Fig. 4.4(b) depicts the reflection coefficient for a single excited element near the center, while the remaining elements are terminated with 1 Ω resistors at the array surface. The agreement between simulation and measurement are reasonable and show similar resonances at 8.75 GHz and 11.5 GHz. Simulations also verified that the center element s active reflection coefficient (inside the 8 8 array) approaches that of the infinite array performance at broadside. As a result, we conclude that the prototype array is large enough to emulate the input impedance of an infinite array while scanning to broadside and verifies unit cell simulations. 5 Measured: 1 excited Simulation: 1 excited Infinite Simulation Simulation: 64 excited Excited Active Γ (db) (a) Frequency (GHz) (b) Figure 4.4: Non-symmetric tightly coupled dipole array prototype (radome removed); (a) fabricated 8 8 array, (b) center element reflection coefficient with single and multiple elements excitations. Fig. 4.5 shows the E- and H-plane scan element patterns, which are in excellent agreement with simulation. The main beam 5 db gain fluctuation is due to finite array 66

85 truncation and the resistive termination at the array surface. Specifically, the surface mount 1 Ω resistors are not matched loads to the antenna terminal impedance, therefore neighboring elements re-radiate destructively and constructively. We note that the E-plane null at θ = ±6 is due to the 12 finite ground plane used in measurements. The cross-polarization is approximately -1 to -15 db over the principal plane scanning range. Further efforts discovered the microstrip probe input was coupling directly to the ring hybrid and contributed to the cross-polarized field component. The probe location was then relocated to minimize probe-ring coupling as depicted in Fig We remark the array aperture without feed maintains a cross-polarized level 6 db below co-polarized gain in the principal planes. The reduced cross-polarization unit cell geometry is depicted in Fig The boresight directivity and realized gain using the reduced cross-polarization probe location is shown in Fig. 4.9(a). We observe that the realized gain approaches the directivity from GHz and cross polarization is < -2 db, a 1-15 db improvement over the previous probe location. Furthermore, the realized gain is within.3 db of the maximum aperture directivity. With reduced probe coupling the array maintains an active VSWR < 2 for scanning up to 7 in the E-plane and 6 for H-plane as depicted in Fig. 4.9(b). These results are believed to be the best reported in terms of array height and wide-angle scanning over a wide bandwidth (1.6:1 with a VSWR < 2) fed with 5 Ω unbalanced inputs. In contrast, other wideband arrays can provide more bandwidth (3:1 and higher) but are thick and typically are limited to 45 scanning [59 63]. 67

86 5 Freq=8 GHz 5 Freq=8 GHz 5 5 Realized Gain (dbi) 1 15 Realized Gain (dbi) Measured:Co Pol 25 Measured:Cross Pol Simulated:Co Pol Simulated:Cross Pol Theta (degrees) Measured:Co Pol 25 Measured:Cross Pol Simulated:Co Pol Simulated:Cross Pol Theta (degrees) (a) (b) 5 Freq=1 GHz 5 Freq=1 GHz 5 5 Realized Gain (dbi) 1 15 Realized Gain (dbi) Measured:Co Pol 25 Measured:Cross Pol Simulated:Co Pol Simulated:Cross Pol Theta (degrees) Measured:Co Pol 25 Measured:Cross Pol Simulated:Co Pol Simulated:Cross Pol Theta (degrees) (c) (d) 5 Freq=12 GHz 5 Freq=12 GHz 5 5 Realized Gain (dbi) 1 15 Realized Gain (dbi) Measured:Co Pol 25 Measured:Cross Pol Simulated:Co Pol Simulated:Cross Pol Theta (degrees) Measured:Co Pol 25 Measured:Cross Pol Simulated:Co Pol Simulated:Cross Pol Theta (degrees) (e) (f) Figure 4.5: Measured principal plane co-polarized ( ) and cross-polarized (- - -) scan element pattern when the center element is excited and all others are terminated using 1 Ω resistors; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 1 GHz, (d) H-plane at 1 GHz, (e) E-plane at 12 GHz, (f) H-plane at 12 GHz. 68

87 5 5 Realized Gain (dbi) ] Measured:Co Pol 25 Measured:Cross Pol Simulated:Co Pol Simulated:Cross Pol Frequency (GHz) Figure 4.6: Array (8x8) broadside gain vs. frequency when the center element is excited and all others are terminated using 1 Ω resistors; (a) E-plane, (b) H-plane. (a) (b) Figure 4.7: Electric field magnitude; (a) probe location with strong coupling and (b) improved probe location with minimal coupling. 69

88 Figure 4.8: Non-symmetric TCDA unit cell geometry with WAIM superstrate, integrated microstrip balun and twin wire matching network interconnects, t1 = 1.75 mm, t2 =.75 mm, t3 = 1 mm, g = 7 mil, α = 85, a =.8128 mm, D = 1.4 mm, w1 = 48 mil, w2 = 2 mil, w3 = 17 mil, w4 = 14 mil, g2 = 3mil, ɛ s = dbi πA/λ 2 Realized Gain: Co Pol Realized Gain: Cross Pol Realized Gain: Cross Pol [8] Active VSWR Boresight E45 H45 E6 H6 E Frequency (GHz) (a) Frequency (GHz) (b) Figure 4.9: Performance of the array unit cell in Fig. 4.8; (a) broadside radiation, (b) active VSWR over multiple E-plane and H-plane scan angles. 7

89 Element Array Demonstration Similar to the previous section, an 8 8 array for fabrication and measurement verification was developed using the reduced probe coupling feed from Fig The ground plane size was reduced to 3.5 " (the same size as the feed board) removing the E-plane SEP null using the previous 12 ground plane setup (Fig. 4.5). In addition, 64 SMP (or GPO) connectors were used as the array interface as depicted in Fig Scan Element Pattern The array was mounted on a fiberglass pylon in the ElectroScience Laboratory compact range as depicted in Fig Fig displays the measured and simulated realized gain vs. frequency for a single element (number 29) excited with all others terminated using 5 Ω SMP loads. The measured and simulated results are in good agreement. Especially considering the finite array simulation size including multiple dielectric layers and detailed feed geometries. The E- and H-plane SEP for element 29 at 1 GHz is shown in Fig and Fig. 4.14, respectively. The cross-polarization is approximately -2 db or lower over most of the principal plane scanning range, a 1 db improvement. Due to the relative small size of the test array, edge effects dominate. Therefore, the SEP and active impedance of each element varies considerably [64]. As such, the increased level of cross-polarization near θ = 2 is not representative of the cross-polarization level while scanning. To illustrate the scan element pattern variation from truncation, the measured average SEP and standard deviation from each element is shown in Fig The error bars indicate the amount of pattern variation across the aperture and would 71

90 Element 8 Element 64 z x y.5 (a) Radome Array PCB Foam Balun PCB Element 1 (b) (c) (d) Figure 4.1: X-band 64 element linearly polarized array prototype; (a) with radome, (b) radome removed, (c) aperture removed displaying balun and twin-wire interconnects, (d) SMP input connects underneath ground plane. 72

91 y x Figure 4.11: Radiation pattern measurement setup with fiberglass support. 5 Element 29 Excited at Broadside Realized Gain (dbi) Measured:Co Pol Measured:Cross Pol Simulated:Co Pol Simulated:Cross Pol Frequency (GHz) Figure 4.12: Finite array broadside realized gain with element 29 excited and remaining elements terminated in 5 Ω loads. 73

92 5 Freq=1 GHz, E Plane Realized Gain (dbi) Measured: Co Pol Measured: Cross Pol Simulated: Co Pol Simulated: Cross Pol Theta (degrees) Figure 4.13: E-plane scan element pattern at 1 GHz with element 29 excited and remaining elements terminated in 5 Ω loads. 5 Freq=1 GHz, H Plane Realized Gain (dbi) Measured: Co Pol Measured: Cross Pol Simulated: Co Pol Simulated: Cross Pol Theta (degrees) Figure 4.14: H-plane scan element pattern at 1 GHz with element 29 excited and remaining elements terminated in 5 Ω loads. 74

93 be zero if the array was infinite implying no truncation. As expected, the H-plane average SEP and standard deviation is symmetric around θ =. However, the E-plane co-polarized gain has a large variation at θ = 15, a result of edge effects from strong E-plane mutual coupling. This is demonstrated in the next section by examination of the element to element mutual coupling Mutual Coupling and Scan Impedance Measuring the scan impedance of a UWB phased array is a challenging and tedious microwave measurement. Specifically, the full mutual coupling or scattering matrix [S], over a large range of frequencies is required with accurate amplitude and phase information. The problem is further exacerbated at higher frequencies (X-band and above) where standard SMA connectors are too large to fit within the array lattice. Therefore, non-sma connectors, such as SMP or GPO are often used to excite each antenna. As SMP connectors were used in the array prototype, an in-situ calibration procedure was developed to accurately measure the mutual coupling between elements over a large frequency range without an SMP calibration kit. The calibration plane is determined using a port extension and time gating procedure. To illustrate the measurement procedure, an Agilent Technologies N5242A PNA-X Network Analyzer with a frequency span from 1 MHz to 18 GHz, IF bandwidth of 1 khz and 321 points was used. Fig shows the network analyzer SMA cable with a SMP semi-rigid cable attached. Initially, calibration was performed at plane (I) using traditional SMA mechanical calibration standards (open, short, load). Transitioning from plane I to II is a SMA-F to SMA-F bullet connector allowing a 6 " semi-rigid SMP cable to be attached. The SMP connector interface which connects 75

94 5 Freq=8 GHz, E Plane 5 Freq=8 GHz, H Plane Realized Gain (dbi) Realized Gain (dbi) Theta (degrees) (a) Theta (degrees) (b) 5 Freq=1 GHz, E Plane 5 Freq=1 GHz, H Plane Realized Gain (dbi) Realized Gain (dbi) Theta (degrees) (c) Theta (degrees) (d) 5 Freq=12.5 GHz, E Plane 5 Freq=12.5 GHz, H Plane Realized Gain (dbi) Realized Gain (dbi) Theta (degrees) (e) Theta (degrees) (f) Figure 4.15: Measured principal plane co-polarized ( ) and cross-polarized (- - -) average scan element pattern and standard deviation error bars for all elements; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 1 GHz, (d) H-plane at 1 GHz, (e) E-plane at 12.5 GHz, (f) H-plane at 12.5 GHz. 76

95 to the array is denoted as III. As no SMP calibration kit was available, a time-gating and port extension technique was developed to compensate for the loss and electrical delay in the semi-rigid cable as well as remove reflections from each connector. III II I Figure 4.16: SMA cable assembly with adapters and SMP cable. The original calibration plane is denoted (I), where the desired calibration plane is depicted as III. Fig. 4.17(a) displays the reflection coefficient of the connector assembly in Fig when the end of the SMP cable is shorted using copper tape. The associated time domain response is shown in Fig. 4.17(b). It is important to note that the proposed calibration process uses a short circuit at the end of the SMP cable reducing the potential for spurious radiation. We note that the short circuit was implemented with copper tape (instead of a SMP short connector) ensuring the correct phase reference plane. A 1.25 db ripple is observed in Fig. 4.17(a). The ripple is due to multiple reflections seen at planes I, II and III. Each reflection is readily identified in Fig. 4.17(b). Label A shows the reflections from the SMA bullet connector (plane I and II). Label B is the desired short circuit reflection seen at the end of the SMP cable (plane III). Multiple reflections between the SMP cable and SMA connectors are identified as labels C - F. To remove the unwanted reflections, time-gating was implemented as 77

96 A B C D E F (a) (b) (c) Figure 4.17: Measured reflection coefficient with the SMP cabled shorted; (a) frequency domain, (b) time-domain, (c) time-gated time-domain. 78

97 shown in Fig. 4.17(c). At this point, the ripples from Fig. 4.17(a) are diminished. However, the phase delay and insertion loss of the SMP cable and SMA connectors have not been removed. This is remedied using the network analyzer s auto port extension capability using the copper tape short. The VNA auto port extension yields a low frequency (4.58 GHz) and high frequency (13.53 GHz) insertion loss of mdb and mdb, respectively. In addition, the delay through the cable and connectors was determined to be psec. The algorithm for auto port extension is not perfect. Subsequently, a more accurate phase delay is manually determined by manually adjusting the phase delay to center the trace on the short section of the Smith chart. An 86.5 psec delay was determined by compressing the impedance trace as depicted in Fig. 4.18(a). The loss values are also manually fine tuned by viewing the log-magnitude plot as shown in Fig. 4.18(b). The high and low band insertion loss values are adjusted such that the short circuited reflection is centered around the db line. The final insertion loss values was found to be 26 mdb and 485 mdb, respectively. After port extension, the measurement plane has been successfully moved to the desired SMP interface (plane III). For comparison, the original raw and calibrated copper tape short circuited S 22 responses are compared in Fig As shown, there is a considerable difference between the two sets of data. Using time-gating and port extension, more accurate measurements can be made at the correct reference plane. Fig. 4.19(c) shows the application of the calibration procedure to measure the prototype array mutual coupling. First, a full 2 port SMA calibration was performed. Then, each port was further calibrated using the procedure outlined above. Finally, a new time-gate is used to measure the full mutual coupling matrix of the 64 element 79

98 (a) (b) Figure 4.18: Measured reflection coefficient with the SMP cabled shorted; (a) Smith chart format to manually determine port extension delay, (b) copper tape short circuited manual amplitude port extension. 8

99 array when element 29 is excited. The proposed calibration procedure ultimately leads to very precise and accurate S parameter measurements (magnitude and phase) at the correct SMP connector interface. (a) (b) (c) Figure 4.19: Measured reflection coefficient with the SMP cabled shorted; (a) SMA calibration, (b) proposed calibration procedure using time-gating and port extension, (c) 64 element phased array mutual coupling measurement setup. 81

100 Fig. 4.2 shows the simulated and measured mutual coupling across the aperture with element 29 excited ( S n,29, where n= 1:64) at 1 GHz. The E-plane mutual coupling to the nearest element is approximately 12 db stronger than H-plane coupling at 1 GHz. Therefore, E-plane truncation is more severe than H-plane as discussed in the previous section. The simulated and measured mutual coupling vs. frequency for each element is shown in Figs The agreement at 1 GHz is very good but diverges near the operational band edges. This is explained by examining the driven elements self reflection coefficient ( S 29,29 ) in Fig. 4.23(b). The measured reflection is 3 db below simulation at 1 GHz and is larger than predicted over most of the frequency range. Since the input reflection is larger, less energy is delivered to the antenna and subsequently the measured mutual coupling is less than simulation. Further investigations found that excess solder from the manufacturing process coated the copper twin-wire transmission line near the feed board interface. As a result, a large capacitance is formed by the enlarged twin-wire diameter which reduces the characteristic impedance and de-tunes the antenna. We remark that if less solder and uniform twin-wire separation gap was maintained, the measured impedances would agree better with simulation. After the full S parameter matrix is known, the active reflection coefficient was calculated using (4.1). Where a j, k x and k y is defined as Γ ii (θ o, φ o ) = N S ij a j (4.1) j=1 a j = a j e j(x jk x+y j k y) 82

101 k x = k o sin(θ o ) cos(φ o ) k y = k o sin(θ o ) sin(φ o ). As expected, the measured active reflection does not agree with simulation, a direct result of the self impedance mismatch because of fabrication imperfections. However, as each element reflection coefficient is within 3 db of simulation and below -6 db over the desired frequency range, the realized gain SEP measurements presented in the previous section and fully excited beam steering performance in the next section is minimally affected Fully Excited Radiation Performance Of particular interest is the fully excited array gain and polarization level while scanning. To demonstrate the wide-angle scanning performance of the non-symmetric TCDA prototype, the radiation pattern from each element was combined with uniform weighting using MATLAB. We note that the simulated realized gain incorporates the active (or scan) reflection coefficient mismatch for each element where the measured patterns (and subsequently post-processed combined pattern) uses each element s self reflection coefficient (S 11, S 22, etc.). The measured principal plane beam scanning performance at low (8 GHz), middle (1 GHz) and high (12.5 GHz) frequencies is displayed in Fig The aforementioned E-plane truncation is evident in Fig. 4.25(a) where the beam splits scanning to θ o = 6. The cross-polarization level while scanning is at least 15 db below the co-polarized component except at 8 GHz in the H-plane, again a result from truncation. At 12.5 GHz (where the array is electrically larger) both planes show a 83

102 (a) (b) (c) (d) (e) (f) Figure 4.2: Mutual coupling across aperture with element 29 excited; (a) simulated 8 GHz, (b) measured 8 GHz, (c) simulated 1 GHz, (d) measured 1 GHz, (e) simulated 12.5 GHz, (f) measured at 12.5 GHz. 84