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

2010

Dissertation Committee:

John L.Volakis, Co-Adviser Chi-Chih Chen, Co-Adviser Joel T. Johnson ABSTRACT

With space at a premium, there is strong interest to develop a single ultra wide- band (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. There- fore, it is not surprising that considerable attention has been devoted to electromag- netic 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 aper- tures, 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 op- eration. An important aspect of tightly coupled dipole arrays (TCDAs) is the capac- itive 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 ma- terials or EBGs on the ground plane. The latter, is of course, critical for retaining the aperture’s wideband behavior under conformal installations.

ii 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 ele- ment low-profile X-band array prototype is fabricated and measured. The conformal array is capable of scanning up to 70◦ and 60◦ 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 net- works. Good agreement between simulations and measurements confirm the proposed concepts.

iii Dedicated to my family.

iv 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 VITA

September 2, 1984 ...... Born - Gillette, Wyoming

May, 2006 ...... B.S. Electrical and Computer Eng., South Dakota School of Mines and Technology, Rapid City, SD August, 2009 ...... M.S. Electrical and Computer Eng., The Ohio State University, Columbus, OH September, 2006 - 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.592-595, 2008.

vi 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., 2010.

2. 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 Scan- ning,” in Proc. Antenna and Propagation International Symposium, IEEE, Toronto, Ontario, Canada, July 2010.

3. Volakis, J.L.; Kasemodel, J.A.; Chen, C.-C.; Sertel, K.; Tzanidis, I., “Wideband Conformal Metamaterial Apertures,” in Proc. Antenna Technology (iWAT), 2010 International Workshop on , vol., no., pp.1-4, 1-3 March 2010.

4. 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, 2010.

5. Kasemodel, J.A.; Chen, C.-C.; Volakis, J.L., “A Novel Non-symmetric Tightly Coupled Element for Wideband Phased Array Apertures,” in Proc. Antennas Appli- cations Symposium, Allerton, IL, Sept. 2009.

6. 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 2009.

7. Kasemodel, J.A.; Chen, C.-C., “A Measurement Setup for Characterizing An- tenna on an Infinite Ground Plane from 1 to 18 GHz,” in Proc. Antenna Measurement Technique Association Symposium, Boston, MA, November 2008.

8. Kasemodel, J.A.; Chen, C.-C.; Gupta, I.J.; Volakis, J.L., “Miniature Continu- ous Coverage Wideband GPS Antenna Array,” in Proc. Antennas and Propagation Society International Symposium, San Diego, CA, July 2008.

9. Kasemodel, J.A.; Chen, C.-C.; Gupta, I.J.; Volakis, J.L., “Compact Wideband Antenna Array for GNSS Receivers,” in Proc. Antenna Measurement Technique As- sociation Symposium, St. Louis, MO, November 2007.

FIELDS OF STUDY

vii Major Field: Electrical Engineering

Studies in: Applied Electromagnetics Antenna Design and Measurement Techniques

viii TABLE OF CONTENTS

Page

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita ...... vi

List of Tables ...... xi

List of Figures ...... xii

Chapters:

1. Introduction ...... 1

1.1 Motivation, Challenges and Objective ...... 1

2. Broadband Phased Array Aperture using Tightly Coupled Dipoles . . . . 5

2.1 Introduction ...... 5 2.2 Planar Phased Array Antenna Comparison ...... 6 2.2.1 Input Impedance ...... 7 2.2.2 Scan Element Pattern ...... 13 2.3 Equivalent Circuit ...... 17 2.4 Linear and Dual Linear Polarization Properties ...... 23 2.5 Feeding Network Consideration ...... 27 2.5.1 External 180◦ Hybrid ...... 29 2.5.2 Low Cost Partially Balanced Coaxial Cable Feed ...... 31 2.5.3 Impedance Matching ...... 33 2.6 Summary ...... 35

ix 3. Broadband Phased Array Antenna Miniaturization ...... 37

3.1 Introduction ...... 37 3.2 Antenna Miniaturization Concept ...... 38 3.3 Inductive Loading via Volumetric Meandering ...... 39 3.4 Ferrite Substrate Loading ...... 41 3.5 Capacitive Loading using a Non-Symmetric Element ...... 45 3.6 Dielectric Superstrate Loading ...... 53 3.7 Summary ...... 60

4. Realization of Non-Symmetric Tightly Coupled Dipole Arrays ...... 61

4.1 Introduction ...... 61 4.2 Wideband Balun ...... 62 4.3 Integration of Aperture and Feed ...... 63 4.4 Single Feed Demonstration ...... 65 4.5 64 Element Array Demonstration ...... 71 4.5.1 Scan Element Pattern ...... 71 4.5.2 Mutual Coupling and Scan Impedance ...... 75 4.5.3 Fully Excited Radiation Performance ...... 83 4.6 Summary ...... 91

5. Conclusion and Future Work ...... 93

Bibliography ...... 97

x LIST OF TABLES

Table Page

3.1 Miniaturized element performance comparison summary ...... 41

3.2 Ferrite resonant frequency comparison ...... 44

3.3 Dielectric constant for superstrate matching using Rogers TMM series array PCB ...... 56

xi LIST OF FIGURES

Figure Page

2.1 (a) Infinite current sheet over a ground plane, (b) tightly coupled dipole array implementation...... 6

2.2 Planar phased array antenna elements under investigation inside unit cell; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot. . . 8

2.3 Active resistance (solid) and reactance (dash) for various antenna ele- ◦ ments in free space scanned to θo = 0 ...... 9

2.4 Active reflection coefficient for different system impedances (Zo) of ◦ each antenna element in free space scanned to θo = 0 ; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot...... 11

2.5 Active reflection coefficient for various antenna elements in free space ◦ scanned to θo = 0 ...... 12

2.6 Active resistance (solid) and reactance (dash) for various antenna ele- ◦ ments when placed 8 mm over ground plane scanned to θo = 0 . . . . 12

2.7 Active reflection coefficient for various antenna elements when placed ◦ 8 mm over ground plane scanned to θo = 0 ...... 13

2.8 Active reflection coefficient for different system impedances (Zo) of each antenna element when placed 8 mm over a ground plane scanned ◦ to θo = 0 ; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot. 14

2.9 E-Plane scan element pattern for the wire, bowtie, dipole and slot array when placed 8 mm over ground plane...... 16

2.10 H-Plane scan element pattern for the wire, bowtie, dipole and slot array when placed 8 mm over ground plane...... 16

xii 2.11 Simulated TCDA and calculated unit cell directivity...... 17

2.12 Surface current at 10 GHz; (a) wire, (b) bowtie, (c) dipole, (d) slot. . 18

2.13 Tightly coupled dipole array equivalent circuit in free space scanned to broadside...... 19

2.14 Equivalent circuit for infinite array in free space...... 20

2.15 Equivalent circuit for ground plane backed infinite array...... 21

2.16 (a) Array impedance transformation for equivalent circuit. (b) Return loss comparison for the ideal array in free space and with ground plane. 22

2.17 (a) Periodic unit cell dipole geometry. (b) Full wave array simulation vs. equivalent circuit for different ground plane heights...... 23

2.18 TCDA active reflection coefficient in free space and when placed 8 mm ◦ over ground plane scanned to θo = 0 ...... 24

2.19 Dipole scan element pattern at 10 GHz in the E-Plane (φ = 0◦), D- Plane (φ = 45◦) and H-Plane (φ = 90◦)...... 25

2.20 Dipole cross-polarization ratio over the upper hemisphere at 10 GHz. 26

2.21 Dipole cross-polarization ratio as a function of frequency when scan- ◦ ◦ ◦ ◦ ning towards θo = 30 , 45 , 60 in the diagonal plane (φ = 45 ). . . . . 26

2.22 Tightly coupled dipole elements; (a) single polarization, (b) dual po- larization...... 27

2.23 Boresight directivity of the single and dual polarized TCDA...... 28

2.24 S-parameters of the dual polarized TCDA...... 28

2.25 Typical planar phased array antenna unit cell depicting the aperture, interconnects and ground plane...... 29

2.26 UWB balun using a 180◦ hybrid...... 30

xiii 2.27 (a) Tapered coaxial cable feed with external 180◦ hybrid (not shown). (b) Broadside gain and realized gain using external hybrid...... 31

2.28 Single coaxial cable balun with integrated matching circuit. The ground plane and unit cell outline are not shown...... 32

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

2.30 Single cable tapered balun depicting common mode electric field distri- bution (left) and common mode suppression using a ferrite bead choke (right)...... 34

2.31 Wideband impedance matching using a single transmission line with characteristic impedance Zm of length lm...... 35

2.32 TCDA matching network example without matching (200 Ω) and with matching network connected to a 100 Ω system impedance...... 36

3.1 Dipole unit cell with inductive miniaturization implemented using ver- tical meandering and a 200 Ω system impedance...... 40

3.2 Dipole unit cell with inductive miniaturization implemented using ver- tical meandering...... 40

3.3 TCDA ferrite substrate loading; (a) unit cell geometry, (b) active VSWR, (c) resistance, (d) reactance...... 42

3.4 TCDA ferrite substrate loading while maintaining ground plane elec- trical separation; (a) unit cell geometry depicting reduced thickness with µr = 5, (b) active VSWR, (c) resistance, (d) reactance...... 44

3.5 Ferrite substrate electric field distribution; (a) rectangular cavity model, (b) side view in x-z plane...... 45

3.6 Dual polarized array with non-symmetric elements; (a) unit cell ge- ometry, (b) infinite array reflection coefficient, Zo = 200Ω,scanned to ◦ θo = 0 ...... 46

xiv 3.7 Baseline non-symmetric TCDA; (a) unit cell geometry for parameter study, (b) input impedance with t1 = 2 mm, t2 = 1 mm, t3 = 0.5 mm, g = 10 mil, α = 180◦ with the array placed 8 mm above the ground ◦ plane scanned to θo = 0 ...... 48

3.8 Baseline TCDA scan element pattern; (a) E-plane, (b) H-plane. . . . 48

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 = 0.5 mm, g = 10 mil, α = 180◦, scanned ◦ to θo = 0 ...... 49

3.10 Non-symmetric TCDA; (a) geometry with t2 = 0.25 and 3 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = t2 + g + 0.25 mm, t2 varied, t3 = 0.5 mm, g = 10 ◦ ◦ mil, α = 180 , scanned to θo = 0 ...... 51

3.11 Non-symmetric TCDA; (a) geometry with t3 = 0.5 and 3 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, t2 = 1 mm, t3 varied, g = 10 mil, α = 180◦, ◦ scanned to θo = 0 ...... 52

3.12 (a) TCDA input impedance, (b) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, t2 = 1 mm, t3 = 0.5 mm, g varied, ◦ ◦ α = 180 , scanned to θo = 0 ...... 53

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 = 0.5 mm, g = 10 mil, scanned ◦ to θo = 0 ...... 54

3.14 Ground plane backed TCDA printed on a PCB with a single layer dielectric superstrate of thickness t1, and dielectric constant ε1. . . . . 55

3.15 (a) TCDA unit cell geometry printed on 20 mil thick TMM3 . (b) Input impedance for different ground plane heights...... 57

3.16 TCDA reactance for different ground plane heights...... 57

xv 3.17 TCDA with single dielectric superstrate with ²1 = 1.8 of varying thick- ◦ ness, t1, scanned to θo = 0 ; (a) input impedance and (b) corresponding resistance (solid) and reactance (dash)...... 58

3.18 TCDA with two-layer dielectric superstrate with ²1 = 2.2 of λc,g/4 ◦ thickness and ²2 = 1.4 of varying thickness, t2, scanned to θo = 0 ; (a) input impedance and (b) corresponding resistance (solid) and reactance (dash)...... 59

4.1 Proposed wideband microstrip coupled line ring hybrid with balanced twin-wire output, a = 0.64516 mm, D = 0.88 mm, w1 = 38 mil, w2 = 20 mil, w3 = 17 mil, g2 = 3 mil, d = 5 mm; (a) geometry and (b) S parameters...... 63

4.2 Non-symmetric tightly coupled dipole array unit cell with radome, in- tegrated feed and matching network, the dimensions are: t1 = 1.75 mm, t2 = 0.75 mm, t3 = 1 mm, g = 7 mil, α = 85◦, a = 0.8128 mm, D = 1.4 mm, w1 = 30 mil, w2 = 20 mil, w3 = 17 mil, w4 = 24 mil, g2 = 3 mil, ²s = 1.7; (a) geometry and (b) active reflection coefficient at broadside...... 64

4.3 Performance of the array unit cell in Fig. 4.2(a); (a) broadside radia- tion, (b) active VSWR over multiple principal plane scan angles. . . . 65

4.4 Non-symmetric tightly coupled dipole array prototype (radome re- moved); (a) fabricated 8 × 8 array, (b) center element reflection coef- ficient with single and multiple elements excitations...... 66

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 100 Ω resistors; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 10 GHz, (d) H-plane at 10 GHz, (e) E-plane at 12 GHz, (f) H-plane at 12 GHz...... 68

4.6 Array (8x8) broadside gain vs. frequency when the center element is excited and all others are terminated using 100 Ω resistors; (a) E-plane, (b) H-plane...... 69

4.7 Electric field magnitude; (a) probe location with strong coupling and (b) improved probe location with minimal coupling...... 69

xvi 4.8 Non-symmetric TCDA unit cell geometry with WAIM superstrate, in- tegrated microstrip balun and twin wire matching network intercon- nects, t1 = 1.75 mm, t2 = 0.75 mm, t3 = 1 mm, g = 7 mil, α = 85◦, a = 0.8128 mm, D = 1.4 mm, w1 = 48 mil, w2 = 20 mil, w3 = 17 mil, w4 = 14 mil, g2 = 3mil, ²s = 1.7...... 70

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. . . 70

4.10 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

4.11 Radiation pattern measurement setup with fiberglass support. . . . . 73

4.12 Finite array broadside realized gain with element 29 excited and re- maining elements terminated in 50 Ω loads...... 73

4.13 E-plane scan element pattern at 10 GHz with element 29 excited and remaining elements terminated in 50 Ω loads...... 74

4.14 H-plane scan element pattern at 10 GHz with element 29 excited and remaining elements terminated in 50 Ω loads...... 74

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 10 GHz, (d) H-plane at 10 GHz, (e) E-plane at 12.5 GHz, (f) H-plane at 12.5 GHz...... 76

4.16 SMA cable assembly with adapters and SMP cable. The original cal- ibration plane is denoted (I), where the desired calibration plane is depicted as III...... 77

4.17 Measured reflection coefficient with the SMP cabled shorted; (a) fre- quency domain, (b) time-domain, (c) time-gated time-domain. . . . . 78

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...... 80

xvii 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 measure- ment setup...... 81

4.20 Mutual coupling across aperture with element 29 excited; (a) simulated 8 GHz, (b) measured 8 GHz, (c) simulated 10 GHz, (d) measured 10 GHz, (e) simulated 12.5 GHz, (f) measured at 12.5 GHz...... 84

4.21 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 - 20, (f) element 21 - 24...... 85

4.22 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 - 40, (e) element 41 - 44, (f) element 45 - 48. . . . 86

4.23 Measured and simulated mutual coupling vs. frequency with element 29 excited; (a) element 49 - 52, (b) element 53 - 56, (c) element 57 - 60, (d) element 61 - 64...... 87

4.24 Measured and simulated finite array element 29 active reflection coef- ◦ ◦ ficient scanned to θo = 0 , φo = 0 ...... 88

4.25 Measured principal plane co-polarized (—) and cross-polarized (- - -) ◦ ◦ ◦ realized gain beam scanning performance from θo = -60 to 60 in 10 increments; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 10 GHz, (d) H-plane at 10 GHz, (e) E-plane at 12.5 GHz, (f) H-plane at 12.5 GHz...... 89

4.26 Finite array E-plane radiation pattern at 10 GHz scanned to θo = ◦ ◦ ◦ ◦ 0 , 30 , 60 , φo = 0 ...... 90

4.27 Finite array H-plane radiation pattern at 10 GHz scanned to θo = ◦ ◦ ◦ ◦ 0 , 30 , 60 , φo = 90 ...... 90

4.28 Finite array broadside realized gain as a function of frequency with all elements excited...... 91

xviii CHAPTER 1

INTRODUCTION

1.1 Motivation, Challenges and Objective

Traditional phased array designs are based on a single element’s isolated perfor- mance. 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 perfor- mance. 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 three- dimensional and require a large dimension normal to the aperture surface, typically a

1 depth on the order of 0.5 - 2 λL, where λL 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 λH where

λH 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 wide- angle 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 minia-

turization 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 unbal-

anced conversion and impedance matching while concurrently avoiding common

mode excitations and maintaining a low-profile.

2 • Designed, fabricated and validated a wideband planar 64 element X-band array

capable of scanning up to 70◦ and 60◦ in E- and H-planes respectively, with

an active voltage standing wave ratio (VSWR) < 2 from 8 - 12.5 GHz. The

conformal array is placed λL/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 demon- strates the unique capability of tightly coupled dipole arrays to become increasingly wideband in the presence of a ground plane. Specifically, we discuss how TCDAs op- erate 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 incorporat- ing 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 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 (8 - 12.5 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 70◦ 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 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 vali- dated with full wave simulation. In Section 2.4, the polarization purity of the TCDA

5 (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 sup-

press 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 [10–13]

(b) Connected self-complementary bowtie [14–17]

(c) Tightly coupled dipole [2,3,18]

(d) Slot array [19–25].

6 We remark that the tightly coupled dipole array is identical to the wire array, except for a very small gap (in this case 0.2 mil) separates the elements. An interesting wideband antenna omitted from this study is the fragmented aperture antenna [26–

30]. 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 (λH /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. 2.2. 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.

2.2.1 Input Impedance

The free space infinite array scan impedance at broadside is shown in Fig. 2.3. Scan impedance is the impedance observed at an antenna’s terminals when proper voltages are applied to all array elements. Throughout this dissertation, a -10 dB active reflection coefficient or VSWR < 2 will be used to determine operational bandwidth, unless otherwise specified. Here, bandwidth is defined as fH /fL : 1, where fH and fL are the highest and lowest frequencies where the active reflection coefficient is less than -10 dB.

7 3 mm

z y 0.5 mm 0.5 mm x 1 mm 1 mm

11.5 mm 11.5 mm Wire Bowtie Dipole(a) (b)

0.10.1 mil mil 3 mm

0.5 mm 0.5 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 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 = 60π 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.

Free Space 400 350 Wire Bowtie 300 Dipole 250 Slot

) 200 Ω 150 100 50

Impedance ( 0 −50 −100 −150

−200 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 2.3: Active resistance (solid) and reactance (dash) for various antenna elements ◦ in free space scanned to θo = 0 .

9 To determine the system impedance (Zo) that maximizes each element’s band- width, a 2-D representation of the active reflection coefficient (at broadside) is plot- ted for various system impedances in Fig. 2.4. The system impedances selected to maximize bandwidth for the wire, bowtie, dipole and slot element was 275 Ω, η◦/2

Ω, 155 Ω and 100 Ω, respectively.

The corresponding free space active reflection coefficient for each element is shown in Fig. 2.5. The connected bowtie maintains an impressive reflection coefficient < -20 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 posi- tioned 8 mm (0.35λH ) over a PEC sheet. As Fig. 2.6 depicts, the wire and bowtie re- sistance peak is above 400 Ω and the reactance changes very rapidly versus frequency.

The slot antenna has little reactance variation over the band, but the resistance ap- proaches 375 Ω at 4 GHz and drops below 50 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 0 Ω.

10 (a) (b)

(c) (d)

Figure 2.4: Active reflection coefficient for different system impedances (Zo) of each ◦ antenna element in free space scanned to θo = 0 ; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot.

11 0

−5

−10

−15 | (dB) Γ |

Wire: Free Space, Z = 275 Ω −20 o Bowtie: Free Space, Z = η /2 Ω o o Dipole: Free Space, Z = 155 Ω −25 o Slot: Free Space, Z = 100 Ω o −30 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 2.5: Active reflection coefficient for various antenna elements in free space ◦ scanned to θo = 0 .

Ground Plane 400 350 Wire Bowtie 300 Dipole 250 Slot

) 200 Ω 150 100 50

Impedance ( 0 −50 −100 −150

−200 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 2.6: Active resistance (solid) and reactance (dash) for various antenna elements ◦ when placed 8 mm over ground plane scanned to θo = 0 .

12 The ground-plane-backed reflection coefficient is shown in Fig. 2.7. 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, 350 Ω, 165 Ω, 310 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 perfor- mance 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 4.2 - 8.9 GHz

(2:1) and the slot array operates from 3.2 - 5.23 GHz (1.6:1).

0

−5

−10

−15 | (dB) Γ |

−20 Wire: Ground Plane, Z = 275 Ω o Bowtie: Ground Plane, Z = 350 Ω o −25 Dipole: Ground Plane, Z = 165 Ω o Slot: Ground Plane, Z = 310 Ω o −30 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 2.7: Active reflection coefficient for various antenna elements when placed 8 ◦ mm over ground plane scanned to θo = 0 .

2.2.2 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 (a) (b)

(c) (d)

Figure 2.8: Active reflection coefficient for different system impedances (Zo) of each ◦ antenna element when placed 8 mm over a ground plane scanned to θo = 0 ; (a) wire or connected dipoles, (b) bowtie, (c) dipole, (d) slot.

14 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. 2.10 for the E- and H-plane, respectively. As each element is small (< λH /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 di- rectivity of an aperture can be calculated assuming uniform illumination. Comparing the boresight (θ = 0◦) SEP to the maximum directivity (D) possible for the given unit cell area (A), good agreement is observed, implying 100% aperture efficiency, see

Fig. 2.11. Hence, the periodic boundary conditions, radiation boundary and ground plane are modeled correctly. 4πA D = (2.1) λ2

15 E−Plane SEP 10

5

0

−5

2 GHz Directivity (dBi) −10 4 GHz 6 GHz 8 GHz −15 10 GHz 12 GHz 14 GHz −20 −90 −60 −30 0 30 60 90 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.

H−Plane SEP 10

5

0

−5 2 GHz

Directivity (dBi) 4 GHz −10 6 GHz 8 GHz −15 10 GHz 12 GHz 14 GHz −20 −90 −60 −30 0 30 60 90 Theta (degrees)

Figure 2.10: H-Plane scan element pattern for the wire, bowtie, dipole and slot array when placed 8 mm over ground plane.

16 6 Theoretical Max TCDA 4

2

0

−2

−4 Gain (dBi)

−6

−8

−10

−12 2 4 6 8 10 12 14 Frequency (GHz)

Figure 2.11: Simulated TCDA and calculated unit cell directivity.

Given the SEP uniformity among elements, the surface electric current distribu- tion at 10 GHz is plotted in Fig. 2.12. 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. 2.13.

17 (a) (b)

(c) (d)

Figure 2.12: Surface current at 10 GHz; (a) wire, (b) bowtie, (c) dipole, (d) slot.

18 One can think of a wire array as a dipole array connected with infinite capacitance

(Cmutual = ∞). 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.

Lwire Lwire Lwire Lwire

C CMutual Mutual CMutual CTip CTip

Lwire Lwire 2Lwire

CTip CTip + CMutual

R CMutual

Figure 2.13: Tightly coupled dipole array equivalent circuit in free space scanned to broadside.

The mutual capacitance (Cmutual) is parallel to the dipole self tip-to-tip (Ctip) 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

(Lwire) is small, (2.2). We remark that the radiation resistance (R) was omitted from the top and bottom-left sections in Fig. 2.13 for clarity.

19 1 fr = √ (2.2) LC 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 exam- ined, see Fig. 2.14. 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 2RAo. The input impedance of the array in free space (denoted by the subscript o), is defined as Za = RAo + jXAo. It is calculated by the parallel combination of each half space transmission line in series with the array reactance XAo as shown in Fig. 2.14.

jXAo jX Ao 2R 2R Z R +jX Ho Ho 2RAo 2RAo Ao Ao A= Ao Ao

Array Z ZA A

Figure 2.14: Equivalent circuit for infinite array in free space.

The equivalent circuit in Fig. 2.14 was extended to include a ground plane. The array is positioned a distance (d) above the ground plane as shown in Fig. 2.15. The free space array resistance (RAo) is assumed to be a constant 200 Ω from 1 - 16

20 GHz. Furthermore, the free space array reactance (XAo) is assumed to vary linearly from -200j to +200j 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 cal- culated using the traditional short circuit transmission line equation, then moved a distance (d) through a transmission line with characteristic impedance (2RAo), to the array plane (Zgp) becoming parallel to twice the array resistance (2RAo). The array reactance (XAo) is then added in series to obtain the final ground plane compensated impedance. The ground plane inductive reactance partially cancel the dipole capaci- tive 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

jXAo jXAo Ho Ho 2R 2R 2RAo 2RAo Ao Ao

Z Array ZA A

Figure 2.15: Equivalent circuit for ground plane backed infinite array.

21 Z = 200Ω, Freq: 1−16 GHz j1 o

Z gp j0.5 R + jX j2 Ao Ao 0 2R || Z Ao gp Free Space: R + jX , Zo=200Ω (2R || Z ) + jX Ao Ao Ao gp Ao With Ground Plane: (2R || Z ) + jX , Zo=210Ω Ao gp Ao j0.2 −5

0 −10

0.2 0.5 1 2 | (dB) Γ |

−j0.2 −15

−j0.5 −j2 −20 1 2 4 6 8 10 12 14 16

−j1 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 ef- fectiveness, 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 el- ement spacing was 11.5 mm (λH /2 at 13 GHz), ensuring no grating lobes and the dipole length was 11.25 mm, yielding a 0.125 mm gap between adjacent dipoles. The array was then positioned over a ground plane and simulated while the separation distance was varied from 4 - 10 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 typ- ically 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 and verifies the equivalent circuit which was introduced to demonstrate impedance cancelation ability of capacitive coupled dipole arrays above a ground plane.

Z = 100Ω, Freq: 1−16 GHz j1 o

Sim: R + jX Ao Ao j0.5 j2 Calc: d=4mm Sim: d=4mm Calc: d=6mm Sim: d=6mm Calc: d=8mm Sim: d=8mm Calc: d=1cm Sim: d=1cm j0.2

0 0.2 0.5 1 2

−j0.2

−j0.5 −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 150 Ω. Fig. 2.18 shows similar conformal performance improvement as the ideal equivalent circuit demonstration in Fig. 2.16.

2.4 Linear and Dual Linear Polarization Properties

After analyzing the principal plane SEP and impedance properties of each an- tenna 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 0 Free Space: Zo=100Ω With Ground Plane: Zo=150Ω

−5

−10 | (dB) Γ |

−15

−20 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 2.18: TCDA active reflection coefficient in free space and when placed 8 mm ◦ over ground plane scanned to θo = 0 .

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

(Ex) and cross-polarized component (Ey) is calculate using (2.3) and (2.4).

Ex = Eθ cos φ − Eφ sin φ (2.3)

Ey = Eθ sin φ + Eφ cos φ (2.4)

.

From Fig. 2.19, the principal plane cross-polarization level is > 60 dB below the co-polarized component at 10 GHz. The cross-polarization level is -21.5 dB at θ = 30◦ and the co-polarized directivity is 1 dB, yielding a cross-polarization ratio of -22.5 dB.

24 The cross-polarization level over the complete upper hemisphere at 10 GHz is shown in Fig. 2.20. Similar to Vivaldi [39, 40] 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.

10 GHz SEP 10

0

−10

−20

−30 E−Plane: Co−Pol D−Plane: Co−Pol −40 H−Plane: Co−Pol E−Plane: Cross−Pol Directivity (dBi) −50 D−Plane: Cross−Pol H−Plane: Cross−Pol −60

−70

−80 −90 −60 −30 0 30 60 90 Theta (degrees)

Figure 2.19: Dipole scan element pattern at 10 GHz in the E-Plane (φ = 0◦), D-Plane (φ = 45◦) and H-Plane (φ = 90◦).

◦ ◦ ◦ It can be seen from Fig. 2.21, the cross-polarization ratio at θo = 30 , 45 , 60 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 cross- polarization ratio is approximately 10 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 po- larized TCDA with co-incident phase center as depicted in Fig. 2.22. Fig. 2.23 shows

25 Figure 2.20: Dipole cross-polarization ratio over the upper hemisphere at 10 GHz.

° φ = 45 0 ° −2.5 θ = 30 ° θ = 45 −5 ° θ = 60 −7.5

−10

−12.5

−15

−17.5

Cross−polarization ratio (dB) −20

−22.5

−25 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 2.21: Dipole cross-polarization ratio as a function of frequency when scanning ◦ ◦ ◦ ◦ towards θo = 30 , 45 , 60 in the diagonal plane (φ = 45 ).

26 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 cross- polarization level is minimally effected and greater than 60 dB below the co-polarized component. Referring to Fig. 2.24, the input refection coefficient |S11| remains un- changed and the mutual coupling |S21| between orthogonal polarizations is less than

-70 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.

0.1 mil 0.1 mil 3 mm 3 mm 2 mm 2 mm 0.5 mm 0.5 mm 1 mm 1 mm

11.5 mm 11.5 mm (a) (b)

Figure 2.22: Tightly coupled dipole elements; (a) single polarization, (b) dual polar- ization.

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 10 0 −10 −20 −30 Single: Co−Pol −40 Single: Cross−Pol −50 Dual: Co−Pol Dual: Cross−Pol

Directivity (dBi) −60 −70 −80 −90

−100 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 2.23: Boresight directivity of the single and dual polarized TCDA.

0

−10

−20

−30 S 11 −40 S 21 −50

−60 Magnitude (dB) −70

−80

−90

−100 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 2.24: S-parameters of the dual polarized TCDA.

28 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

< 0.4λH . This is necessary to avoid boresight radiation cancelation from the ground plane image current when a 0.5λ 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 ≈ 150 - 300 Ω depending on element geometry. As a result, a matching circuit must be used to connect the array to 50 Ω system impedances.

Figure 2.25: Typical planar phased array antenna unit cell depicting the aperture, interconnects and ground plane.

29 2.5.1 External 180◦ Hybrid

A commonly used balun employs a external 180◦ hybrid where the two outer coaxial shields are soldered together and the remaining center conductors form a

100 Ω balanced transmission line as shown in Fig. 2.26. 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 180◦ 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 0.25

30 dB of the directivity from 5 - 15 GHz, demonstrating a 100 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 180◦ hybrid with 4:1 or 10:1 bandwidth can be multiple wavelengths long and therefore troublesome to fit inside the array lattice which is typically on the order of λH /2.

1.15cm=O/2 Gain @ 13GHz Realized Gain, Zo=100:

.7cm above ground

(a) (b)

Figure 2.27: (a) Tapered coaxial cable feed with external 180◦ hybrid (not shown). (b) Broadside gain and realized gain using external hybrid.

2.5.2 Low Cost Partially Balanced Coaxial Cable Feed

A first attempt to remove the costly 180◦ hybrid is shown in Fig. 2.28. It consists of a single coaxial cable (standard semi-rigid 0.046” diameter) with the outer conductor linearly tapered forming a narrow strip. The narrow outer strip and center conductor have a characteristic impedance of approximately 130 Ω. The tapering is necessary for impedance matching the antenna to 50 Ω and will be discussed in the next section.

31 (a) Coaxial cable a Teflon (b) Outer shield b removed for 130: parallel plate line

c (c) Taper section for partial balun and d 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) ef- fectively 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. 2.29 where the unbalanced current forms a common mode at 7.3 GHz. To circumvent the problem, a lossless ferrite bead with µr = 200 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. 2.30. 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 (ld) and round trip feed length (2lf ) is 1λ long (denoted as χ in Fig. 2.30). Therefore, the common mode frequency (in GHz) can be predicted using

300 mm f ≈ . (2.5) cm χ 32 Where χ is defined as

χ = ld + 2lf . (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 ²pcb is the PCB board permittivity the array is printed on (in this case TMM3, ²pcb = 3) and ²cable 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.

300 mm fcm ≈ q ≈ 7.3 GHz (2.7) ²pcb+1 √ 11.5 mm 2 + 2(8 mm) ²cable

0

−5

−10 | (dB) Γ |

−15

No Ferrite Bead With Ferrite Bead −20 1 2 4 6 8 10 12 14 16 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 11.5 mm

8 mm

F

Figure 2.30: Single cable tapered balun depicting common mode electric field distri- bution (left) and common mode suppression using a ferrite bead choke (right).

2.5.3 Impedance Matching

Typical TCDAs have a large input impedance (Za ≈ 150 - 300 Ω). As a re- sult, a matching circuit must be used to connect the array to common 50 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, lm, with characteristic impedance

Zm. The matching impedance is bound by the following relationship, Zin < Zm < Za, for 50 Ω and 100 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 be- hind or on the ground plane. Interconnects between the TCDA aperture and balun circuitry are necessary and can be concurrently used for impedance matching.

34 lm

Zm Za

Zin

Figure 2.31: Wideband impedance matching using a single transmission line with characteristic impedance Zm of length lm.

As an example, consider a TCDA with impedance (Za) depicted in Fig. 2.32.

The antenna impedance locus is centered around 200 Ω and has an active VSWR <

2 from 3.5 - 13.5 GHz. However, as mentioned earlier, dipole elements are commonly feed using external commercial of the self (COTS) 180◦ hybrids having a 100 Ω impedance. Therefore, we used the matching circuit from Fig. 2.31 with lm = 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 100 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 Z = 100 , Freq: 1-16 GHz 5 j1 o : Z , no matching, Z =200 a o : j0.5 j2 4.5 Z , with matching, Z =100 in o :

4

j0.2 3.5

3 0 0.2 0.5 1 2 VSWR 2.5

2 -j0.2

1.5

-j0.5 -j2 1 1 2 4 6 8 10 12 14 16 Z , no matching -j1 a Frequency (GHz) Z , Zo =145 , l=0.925cm in line :

Figure 2.32: TCDA matching network example without matching (200 Ω) and with matching network connected to a 100 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 -20 dB. However, the array became extremely narrowband when placed over a ground plane.

As conformal installations is the focus of this dissertation, the polarization prop- erties of conformal linear and dual linear polarized TCDA apertures were shown to maintain low cross-polarization levels. We also discussed important feed considera- tions such as unbalanced to balanced conversion, shielding for common mode suppres- sion and impedance matching. The next chapter discusses how antenna miniaturiza- tion can be used to extend the lower operating frequency and increase instantaneous bandwidth of TCDAs.

36 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 re- duce 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 indepen- dent control of the elements self inductance and mutual capacitance. As such, input

37 impedance and wave velocity can be controlled independently. To further miniatur- ize and provide environmental protection, we study single and two-layer dielectric superstrates in Section 3.6.

3.2 Antenna Miniaturization Concept

The goal of this section is to develop an intuitive understanding of antenna minia- turization. The basic concept of miniaturization is reducing the phase velocity of the wave guided by the antenna. The phase velocity vp and characteristic impedance Zo of a TEM wave is determined by r r 1 1 L µ vp = √ = √ ,Zo = G = G . (3.1) LC µ² C ²

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 3.3 Inductive Loading via Volumetric Meandering

Several inductive meandering techniques were investigated to explore miniatur- ization. Namely, we considered planar [47–49] and volumetric meandering [50,51] to increase the dipole inductance (Lwire). However, planar meandering adds minimal in- ductance, 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 0.508 mm as depicted in Fig. 3.1. In this case, the depth was chosen to be equal to the

PCB thickness (standard Rogers 3003 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 0.45 mm long) per arm leaving a 0.2 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 200 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 Figure 3.1: Dipole unit cell with inductive miniaturization implemented using vertical meandering and a 200 Ω system impedance.

5

4.5

4

3.5

3 VSWR 2.5

2

1.5

1 1 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 3.2: Dipole unit cell with inductive miniaturization implemented using vertical meandering.

40 Table 3.1: Miniaturized element performance comparison summary Vertical Meander Munk CSA [3] VSWR < 3 2.6 - 13.3 GHz (5:1) 4 - 18 GHz (4.5:1)

Element Size fhigh 0.5λo 0.65λo

Element Size flow 0.1λo 0.15λo

Ground Plane Separation λo/12.8 λo/10

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 ²r = 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 µr. 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 µr = 3 case, the instan- taneous bandwidth is 1.85 - 9.6 GHz (5.2:1). The resistance approaches zero at 10.5

GHz due to the λg/2 guided wavelength ground plane separation where the image current cancels radiation. As expected, when the permeability is further increased

41 the cancelation occurs at lower frequencies. In addition, an undesired ferrite material mode is excited.

5 No ferrite µ =3 4.5 r µ =5 r Ferrite 4 µ =7 r 3.5

3 VSWR 8 mm 2.5

2

1.5

1 Ground Plane 11.5 mm 1 2 4 6 8 10 12 14 16 Frequency (GHz) (a) (b)

500 500 No ferrite No ferrite 450 µ =3 r 400 µ =3 r µ 400 =5 µ =5 r 300 r µ =7 µ =7 350 r 200 r ) ) Ω 300 Ω 100

250 0

200 −100 Resistance ( Reactance ( 150 −200

100 −300

50 −400

0 −500 1 2 4 6 8 10 12 14 16 1 2 4 6 8 10 12 14 16 Frequency (GHz) Frequency (GHz) (c) (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 perfor- √ mance when scaling the thickness and subsequent ground plane separation by 1/ µr.

42 Significant miniaturization is achieved using µr = 3 and the impedance anomaly at

10.5 GHz is removed. The array height is 4.6 mm or λL/30 and provides an instan- taneous bandwidth from 2.2 - 15.7 GHz (7:1). Ferrite loading with µr = 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 mate- rial mode is excited. The mode limits the high frequency operation of the array to 12

GHz and 10.3 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

TM210 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 TM210 ferrite mode resonant frequency is determined using the ferrite

µr and unit cell width (a, b) in (3.3).

s µ ¶ c ³mπ ´2 ³nπ ´2 lπ 2 fmnl = √ + + (3.2) 2π µr²r a b d

sµ ¶ c 2π 2 ³π ´2 f210 = √ + . (3.3) 2π µr a b Table 3.2 compares the HFSS simulated impedance anomaly and the predicted

TM210 resonant frequency using (3.3). The calculated resonant frequency is within

6.3% and improves to 1.8% with µr = 7. The improved accuracy for higher µr is due to an increased y-directed field variation as opposed to slightly less variation with lower µr values. If the TM210 mode is suppressed, the µr = 7 loaded TCDA operates from 1.76 - 14.4 GHz (8.2:1) and is extremely low-profile, λL/56.

43 5 No ferrite µ =3 4.5 r µ =5 r 4 µ =7 r 3.5 P = 5 r 3 VSWR 8 mm 2.5 2 Pr 1.5

11.5 mm 1 Ground Plane 1 2 4 6 8 10 12 14 16 Frequency (GHz) (a) (b)

500 500 No ferrite No ferrite 450 µ =3 r 400 µ =3 r µ 400 =5 µ =5 r 300 r µ =7 µ =7 350 r 200 r ) ) Ω 300 Ω 100

250 0

200 −100 Resistance ( Reactance ( 150 −200

100 −300

50 −400

0 −500 1 2 4 6 8 10 12 14 16 1 2 4 6 8 10 12 14 16 Frequency (GHz) Frequency (GHz) (c) (d)

Figure 3.4: TCDA ferrite substrate loading while maintaining ground plane electrical separation; (a) unit cell geometry depicting reduced thickness with µr = 5, (b) active VSWR, (c) resistance, (d) reactance.

Table 3.2: Ferrite resonant frequency comparison

HFSS TM210

µr GHz GHz % difference 3 15.8 16.8 6.3 5 12.6 13.0 3.2 7 10.8 11.0 1.8

44 z z d

0

a b y x 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 fre- quency. 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 ca- pacitance and dominates, one can more effectively miniaturize by increasing Cmutual 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 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 non- symmetric elements are broadband and justifies a more rigorous study. In particular, each element’s non-symmetric qualities can be exaggerated for improved UWB perfor- mance (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 trans- mission 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=O/2 @ 13 GHz

0.8 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, Zo = 200Ω,scanned to θo = 0 .

46 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. 3.8. 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 = ± 90◦. 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 = 0◦ 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 signifi- cantly 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. 3.9. This is due to an in- creased 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, 0.25 mm for all values of t2. As t2

47 Z = 200Ω, Freq: 2−16 GHz j1 o

t1 j0.5 j2 g

j0.2 0.5mm

0.5 mm 0 0.2 0.5 1 2

−j0.2 t3

t2 −j0.5 −j2 11.5 mm −j1 (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 = 0.5 mm, g = 10 mil, ◦ ◦ α = 180 with the array placed 8 mm above the ground plane scanned to θo = 0 .

10 10

5 5

0 0

Gain (dB) −5 Gain (dB) −5 2GHz 2GHz 4GHz 4GHz 6GHz 6GHz −10 8GHz −10 8GHz 10GHz 10GHz 12GHz 12GHz 14GHz 14GHz −15 −15 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degree) Theta (degree) (a) (b)

Figure 3.8: Baseline TCDA scan element pattern; (a) E-plane, (b) H-plane.

48 Z = 200Ω, Freq: 2−16 GHz j1 o

t1=2mm j0.5 j2 t1=3mm t1=4mm 2mm 5mm t1=5mm

j0.2 j0.2

0 0.2 0.5 1 2

-j0.2−j0.2

−j0.5 −j2

−j1 (a) (b)

400

300

200 ) Ω

100 Impdance ( 0 t1=2mm t1=3mm −100 t1=4mm t1=5mm

−200 2 4 6 8 10 12 14 16 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 = 0.5 mm, g = 10 mil, α = 180 , scanned to θo = 0 .

49 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 = 0.25 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. 3.10.

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. 3.11. Below 5 GHz the resistance is constant while for higher frequencies the resistance is halved when increasing t3 to 3 mm from 0.5 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 minia- turizes 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. 3.12. The gap separation should be as small as possi- ble (within manufacturing tolerances) to ensure strong mutual coupling, enabling the array to operate to lower frequencies.

50 0.25mm 3mm Z = 200Ω, Freq: 2−16 GHz j1 o

t2=0.25mm j0.5 j2 t2=0.5mm t2=1mm t2=2mm t2=3mm

j0.2

0 0.2 0.5 1 2

−j0.2

−j0.5 −j2

−j1 (a) (b)

400

300

200 ) Ω t2=0.25mm 100 t2=0.5mm t2=1mm t2=2mm Impdance ( t2=3mm 0

−100

−200 2 4 6 8 10 12 14 16 Frequency (GHz) (c)

Figure 3.10: Non-symmetric TCDA; (a) geometry with t2 = 0.25 and 3 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = t2 + ◦ ◦ g + 0.25 mm, t2 varied, t3 = 0.5 mm, g = 10 mil, α = 180 , scanned to θo = 0 .

51 Z = 200Ω, Freq: 2−16 GHz j1 o

t3=0.5mm j0.5 j2 t3=1mm 0.5mm 3mm t3=2mm t3=3mm

j0.2

0 0.2 0.5 1 2

−j0.2

−j0.5 −j2

−j1 (a) (b)

400

300

200 ) Ω

100 Impdance ( 0

t3=0.5mm t3=1mm −100 t3=2mm t3=3mm

−200 2 4 6 8 10 12 14 16 Frequency (GHz) (c)

Figure 3.11: Non-symmetric TCDA; (a) geometry with t3 = 0.5 and 3 mm, (b) input impedance, (c) corresponding resistance (solid) and reactance (dash) with t1 = 2 mm, ◦ ◦ t2 = 1 mm, t3 varied, g = 10 mil, α = 180 , scanned to θo = 0 .

52 400

Z = 200Ω, Freq: 2−16 GHz j1 o

g=5mil 300 j0.5 j2 g=15mil g=25mil g=35mil

200

j0.2 ) Ω g=5mil g=15mil 100 g=25mil

0 g=35mil

0.2 0.5 1 2 Impdance ( 0

−j0.2 −100

−j2 −j0.5 −200 2 4 6 8 10 12 14 16 −j1 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 = 0.5 mm, g varied, α = 180◦, ◦ scanned to θo = 0 .

The final parameter investigated is the cup opening angle α. The values investi- gated were 45◦ - 275◦ in 60◦ 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

100% 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 Z = 200Ω, Freq: 2−16 GHz j1 o

α=45° j0.5 j2 α=105° α=165° α=225° α=275°

j0.2 = 45° Į Į= 275°

0 0.2 0.5 1 2

−j0.2

−j0.5 −j2

−j1 (a) (b)

400

300

200

) α=45° Ω α=105° 100 α=165° α=225° α °

Impdance ( =275 0

−100

−200 2 4 6 8 10 12 14 16 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 = 0.5 mm, g = 10 mil, scanned to θo = 0 .

54 with a dielectric constant equal to the array PCB permittivity with thickness h.A dielectric superstrate of thickness, t1, and dielectric constant ε1 is then positioned between it and free space, as shown in Fig. 3.14.

h t1 d

H1 Superstrate Array PCB

Figure 3.14: Ground plane backed TCDA printed on a PCB with a single layer dielectric superstrate of thickness t1, and dielectric constant ε1.

The reflection coefficient at each material interface is given by

ηi − ηi+1 Γi,i+1 = (3.4) ηi + ηi+1 where the wave impedance in the dielectric medium can be written as

η0 ηi = √ . (3.5) ²i

Simplifying (3.4) using (3.5) gives √ √ ²i+1 − ²i Γi,i+1 = √ √ . (3.6) ²i + ²i+1

To solve for the required superstrate dielectric constant, (3.6) is used to form a sys- tem of equations to match the PCB dielectric constant to free space using single or double dielectric superstrate(s). Finding the minimum reflection coefficient and req- uisite dielectric constants was performed using MATLAB. Table 3.3 summarizes the

55 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 ²PCB ²i Γ (dB) ²i ²i+1 Γ (dB) TMM3 3.27 1.80 -16.7 2.20 1.48 -20.1 TMM4 4.5 2.12 -14.6 2.73 1.65 -18.1 TMM6 6 2.45 -13.7 3.30 1.82 -16.5 TMM10 9.2 3.03 -11.4 4.39 2.10 -14.8

Based on [2], the superstrate thickness should be λc,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 fc. 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. 3.16 and not related to the traditional λ/2 dipole length.

Due to the ambiguity of resonance, initially λc/4 was assumed to equal the ground plane separation (d = 8 mm) yielding fc = 9.375 GHz. Using (3.7), a superstrate thickness was calculated to be 6.58 mm (λc,g/4 at 9.375 GHz). Several thicknesses were then simulated, varying from λc,g/10 to λc,g/3.

λ λ t = c,g = √c (3.7) 4 4 ²r

56 Z = 200Ω, Freq: 1−16 GHz j1 o

j0.5 j2

j0.2

0 0.2 0.5 1 2

−j0.2

d=4mm −j0.5 −j2 d=6mm d=8mm −j1 d=1cm (a) (b)

Figure 3.15: (a) TCDA unit cell geometry printed on 20 mil thick TMM3 . (b) Input impedance for different ground plane heights.

300

d=4mm d=6mm 200 d=8cm d=1cm

100 ) Ω

0 Reactance (

−100

−200

−300 2 4 6 8 10 12 14 16 Frequency (GHz)

Figure 3.16: TCDA reactance for different ground plane heights.

57 Z = 200Ω, Freq: 1−16 GHz j1 o

t =0 1

j0.5 j2 t =λ \10 200 1 c,g t =λ \6 1 c,g t =λ \4 150 1 c,g t =λ \3 1 c,g j0.2 100

) 50 Ω

0 0.2 0.5 1 2 0

Impdance ( −50 t =0 1 −j0.2 t =λ \10 −100 1 c,g t =λ \6 1 c,g t =λ \4 −150 1 c,g t =λ \3 −j0.5 −j2 1 c,g −200 2 4 6 8 10 12 14 16 −j1 Frequency (GHz) (a) (b)

Figure 3.17: TCDA with single dielectric superstrate with ²1 = 1.8 of varying thick- ◦ ness, t1, scanned to θo = 0 ; (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 λg/4, a second loop on the smith chart is formed, see Fig. 3.17 which increases the resistance at 12 GHz to

170 Ω from 100 Ω. Furthermore, the reactance increases and remains fairly constant from 9 - 14 GHz. As the superstrate thickness becomes larger than λg/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. Gen- erally, 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 approx- imately λg/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 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 λc,g/4 thick at 9.375 GHz and had ²1 = 2.2. The second superstrate had a dielectric constant (²2) of 1.4 and thickness (t2) was varied from

λc,g/10 to λc,g/3 (see Fig. 3.18). The second superstrate provides little miniaturiza- tion, but rather improves the mid band impedance fluctuation. The first resonance peak frequency is constant for all t2 values while the second peak is reduced and shifted lower in frequency. For t2 ≈ λc,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.

Z = 200Ω, Freq: 1−16 GHz j1 o

t =0 2

j0.5 j2 t =λ \10 200 2 c,g t =λ \6 2 c,g t =λ \4 150 2 c,g t =λ \3 2 c,g j0.2 100

) 50 Ω

0 0.2 0.5 1 2 0

Impdance ( −50 t =0 2 −j0.2 t =λ \10 −100 2 c,g t =λ \6 2 c,g t =λ \4 −150 2 c,g t =λ \3 −j0.5 −j2 2 c,g −200 2 4 6 8 10 12 14 16 −j1 Frequency (GHz) (a) (b)

Figure 3.18: TCDA with two-layer dielectric superstrate with ²1 = 2.2 of λc,g/4 thick- ◦ ness and ²2 = 1.4 of varying thickness, t2, scanned to θo = 0 ; (a) input impedance and (b) corresponding resistance (solid) and reactance (dash).

59 3.7 Summary

In this chapter, general miniaturization methods were discussed and multiple

TCDA implementations were presented. Specifically, in Section 3.2 we used equiva- lent 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 λL/30 using an

µr = 3. For µr > 3 an undesired TM210 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 (λL/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.

60 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 (8 - 12.5

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 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 60◦ 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 improve- ment [57]. The required even (Zeven) and odd (Zodd) mode coupled line impedances are 176.2 Ω and 30.2 Ω, respectively. However, the required coupled line separation g required is < 1 mil for a 25 mil thick Rogers 3206 microwave laminate. The small coupled line separation is beyond traditional fabrication capabilities and limits re- alization 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 Zeven = 104.6 Ω and Zodd = 39.7 Ω. The ring was then optimized to provide a return loss > 10 dB from 7.5 - 13 GHz or > 15 dB from 9 - 12.8 GHz and maintained a balanced output transmission |S21| > -0.75 dB from 8 - 12.5 GHz. See Fig. 4.1 for the final design layout and performance. Concurrently, the insertion loss is <

0.5 dB. The ring hybrid has a 50 Ω SMA coaxial cable input and two output ports that extend inside the ring, 180◦ out-of-phase from each other. As a result, the fields

62 add in series forming a 100 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 0.25 dB.

0

D −5 S Port 2 11 5mm S a 21 −10

w3 |S| (dB) 25mil w2 g2 −15 Port 1 w1 RO3206 −20 Ground Plane 7 8 9 10 11 12 13 Frequency (GHz) (a) (b)

Figure 4.1: Proposed wideband microstrip coupled line ring hybrid with balanced twin-wire output, a = 0.64516 mm, D = 0.88 mm, w1 = 38 mil, w2 = 20 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 (Za ≈ 200 Ω to 300 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 = 0.8128 mm, separation: D = 1.4 mm) was employed. The array and balun is printed on standard Rogers 3203 and

3206 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 matching (WAIM) superstrate [58] having a dielectric constant (εs) 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 <

-10 dB from 7.5 - 13 GHz, as illustrated in Fig. 4.2(b).

s

0

−5

−10 | (dB) Γ |

−15

−20 7 8 9 10 11 12 13 Frequency (GHz) (a) (b)

Figure 4.2: Non-symmetric tightly coupled dipole array unit cell with radome, inte- grated feed and matching network, the dimensions are: t1 = 1.75 mm, t2 = 0.75 mm, t3 = 1 mm, g = 7 mil, α = 85◦, a = 0.8128 mm, D = 1.4 mm, w1 = 30 mil, w2 = 20 mil, w3 = 17 mil, w4 = 24 mil, g2 = 3 mil, ²s = 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 8 - 12.5 GHz

(within 0.3 dB). Furthermore, the radiation efficiency is greater than 93% including all dielectric and copper conductor losses. Of importance is the remarkable scanning

64 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 60◦ in H-plane.

4 4 Boresight 2 3.5 E30 H30 E60 0 3 H60 E75 4πA/λ2 −2 2.5 dBi Realized Gain VSWR

−4 2

−6 1.5

−8 1 7 8 9 10 11 12 13 7 8 9 10 11 12 13 Frequency (GHz) Frequency (GHz) (a) (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 0.5” 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 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 100 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.

0 Measured: 1 excited Simulation: 1 excited Infinite Simulation −5 Simulation: 64 excited

−10 | (dB) Γ

Excited −15 Active |

−20

−25 7 8 9 10 11 12 13 14 Frequency (GHz) (a) (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 truncation and the resistive termination at the array surface. Specifically, the surface mount 100 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 = ±60◦ is due to the 12” finite ground plane used in mea- surements. The cross-polarization is approximately -10 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. 4.7.

We remark the array aperture without feed maintains a cross-polarized level 60 dB below co-polarized gain in the principal planes. The reduced cross-polarization unit cell geometry is depicted in Fig. 4.8.

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 8 - 12.5 GHz and cross polarization is < -20 dB, a 10 - 15 dB improvement over the previous probe location. Furthermore, the realized gain is within 0.3 dB of the maximum aperture directivity. With reduced probe coupling the array maintains an active VSWR < 2 for scanning up to 70◦ in the E-plane and 60◦ 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 50 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 Freq=8 GHz Freq=8 GHz 5 5

0 0

−5 −5

−10 −10

−15 −15 Realized Gain (dBi) Realized Gain (dBi) −20 −20

Measured:Co−Pol Measured:Co−Pol −25 Measured:Cross−Pol −25 Measured:Cross−Pol Simulated:Co−Pol Simulated:Co−Pol Simulated:Cross−Pol Simulated:Cross−Pol −30 −30 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 Theta (degrees) Theta (degrees) (a) (b)

Freq=10 GHz Freq=10 GHz 5 5

0 0

−5 −5

−10 −10

−15 −15 Realized Gain (dBi) Realized Gain (dBi) −20 −20

Measured:Co−Pol Measured:Co−Pol −25 Measured:Cross−Pol −25 Measured:Cross−Pol Simulated:Co−Pol Simulated:Co−Pol Simulated:Cross−Pol Simulated:Cross−Pol −30 −30 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 Theta (degrees) Theta (degrees) (c) (d)

Freq=12 GHz Freq=12 GHz 5 5

0 0

−5 −5

−10 −10

−15 −15 Realized Gain (dBi) Realized Gain (dBi) −20 −20

Measured:Co−Pol Measured:Co−Pol −25 Measured:Cross−Pol −25 Measured:Cross−Pol Simulated:Co−Pol Simulated:Co−Pol Simulated:Cross−Pol Simulated:Cross−Pol −30 −30 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 Theta (degrees) 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 100 Ω resistors; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 10 GHz, (d) H-plane at 10 GHz, (e) E-plane at 12 GHz, (f) H-plane at 12 GHz.

68 5

0

−5

−10

−15 Realized Gain (dBi) −20

Measured:Co−Pol −25 Measured:Cross−Pol Simulated:Co−Pol Simulated:Cross−Pol −30 7 8 9 10 11 12 13 14 ] Frequency (GHz)

Figure 4.6: Array (8x8) broadside gain vs. frequency when the center element is excited and all others are terminated using 100 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 Figure 4.8: Non-symmetric TCDA unit cell geometry with WAIM superstrate, in- tegrated microstrip balun and twin wire matching network interconnects, t1 = 1.75 mm, t2 = 0.75 mm, t3 = 1 mm, g = 7 mil, α = 85◦, a = 0.8128 mm, D = 1.4 mm, w1 = 48 mil, w2 = 20 mil, w3 = 17 mil, w4 = 14 mil, g2 = 3mil, ²s = 1.7.

5 4

0 Boresight 3.5 E45 H45 π λ2 −5 4 A/ E60 Realized Gain: Co−Pol 3 H60 −10 Realized Gain: Cross−Pol E70 Realized Gain: Cross−Pol [8]

dBi 2.5 −15

Active VSWR 2 −20

−25 1.5

−30 1 7 8 9 10 11 12 13 7 8 9 10 11 12 13 Frequency (GHz) Frequency (GHz) (a) (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.

70 4.5 64 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. 4.8. 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. 4.10

4.5.1 Scan Element Pattern

The array was mounted on a fiberglass pylon in the ElectroScience Laboratory compact range as depicted in Fig. 4.11. Fig. 4.12 displays the measured and simulated realized gain vs. frequency for a single element (number 29) excited with all others terminated using 50 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 10 GHz is shown in Fig. 4.13 and

Fig. 4.14, respectively. The cross-polarization is approximately -20 dB or lower over most of the principal plane scanning range, a 10 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 = 20◦ 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. 4.15. The error bars indicate the amount of pattern variation across the aperture and would

71 Element 8 Element 64

z y x

0.5” Radome Array PCB Element 1 Foam Balun PCB (a) (b)

(c) (d)

Figure 4.10: X-band 64 element linearly polarized array prototype; (a) with radome, (b) radome removed, (c) aperture removed displaying balun and twin-wire intercon- nects, (d) SMP input connects underneath ground plane.

72 y

x

Figure 4.11: Radiation pattern measurement setup with fiberglass support.

Element 29 Excited at Broadside 5

0

−5 Measured:Co−Pol −10 Measured:Cross−Pol Simulated:Co−Pol −15 Simulated:Cross−Pol

Realized Gain (dBi) −20

−25

−30 7 8 9 10 11 12 13 14 Frequency (GHz)

Figure 4.12: Finite array broadside realized gain with element 29 excited and remain- ing elements terminated in 50 Ω loads.

73 Freq=10 GHz, E−Plane 5

0

−5

−10 Measured: Co−Pol Measured: Cross−Pol Simulated: Co−Pol −15 Simulated: Cross−Pol

Realized Gain (dBi) −20

−25

−30 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees)

Figure 4.13: E-plane scan element pattern at 10 GHz with element 29 excited and remaining elements terminated in 50 Ω loads.

Freq=10 GHz, H−Plane 5

0

−5

−10 Measured: Co−Pol Measured: Cross−Pol Simulated: Co−Pol −15 Simulated: Cross−Pol

Realized Gain (dBi) −20

−25

−30 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees)

Figure 4.14: H-plane scan element pattern at 10 GHz with element 29 excited and remaining elements terminated in 50 Ω loads.

74 be zero if the array was infinite implying no truncation. As expected, the H-plane average SEP and standard deviation is symmetric around θ = 0◦. 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.

4.5.2 Mutual Coupling and Scan Impedance

Measuring the scan impedance of a UWB phased array is a challenging and te- dious 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 lat- tice. 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 be- tween 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 10 MHz to 18 GHz, IF bandwidth of 10 kHz and 3201 points was used. Fig. 4.16 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 Freq=8 GHz, E−Plane Freq=8 GHz, H−Plane 5 5

0 0

−5 −5

−10 −10

−15 −15

Realized Gain (dBi) −20 Realized Gain (dBi) −20

−25 −25

−30 −30 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees) Theta (degrees) (a) (b)

Freq=10 GHz, E−Plane Freq=10 GHz, H−Plane 5 5

0 0

−5 −5

−10 −10

−15 −15

Realized Gain (dBi) −20 Realized Gain (dBi) −20

−25 −25

−30 −30 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees) Theta (degrees) (c) (d)

Freq=12.5 GHz, E−Plane Freq=12.5 GHz, H−Plane 5 5

0 0

−5 −5

−10 −10

−15 −15

Realized Gain (dBi) −20 Realized Gain (dBi) −20

−25 −25

−30 −30 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees) Theta (degrees) (e) (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 10 GHz, (d) H-plane at 10 GHz, (e) E-plane at 12.5 GHz, (f) H-plane at 12.5 GHz. 76 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 cali- bration 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. 4.16 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 reflec- tions 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 B A C

D EF

(a) (a) (b)(b)

(c)

Figure 4.17: Measured reflection coefficient with the SMP cabled shorted; (a) fre- quency domain, (b) time-domain, (c) time-gated time-domain.

78 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 ex- tension capability using the copper tape short. The VNA auto port extension yields a low frequency (4.508 GHz) and high frequency (13.503 GHz) insertion loss of 237.32 mdB and 450.32 mdB, respectively. In addition, the delay through the cable and con- nectors was determined to be 804.956 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 806.5 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 0 dB line. The final insertion loss values was found to be 260 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 |S22| responses are compared in Fig. 4.19. 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 (a) (a)

(b) (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 cir- cuited manual amplitude port extension.

80 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) (a) (b)(b)

(c)(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 Fig. 4.20 shows the simulated and measured mutual coupling across the aperture with element 29 excited (|Sn,29|, where n= 1:64) at 10 GHz. The E-plane mutual cou- pling to the nearest element is approximately 12 dB stronger than H-plane coupling at 10 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. 4.21-4.23. The agreement at 10 GHz is very good but diverges near the operational band edges. This is explained by examining the driven elements self reflection coefficient (|S29,29|) in Fig. 4.23(b). The measured reflection is 3 dB below simulation at 10 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).

XN Γii(θo, φo) = Sijaj (4.1) j=1

Where aj, kx and ky is defined as

−j(xj kx+yj ky) aj = |aj|e

82 kx = ko sin(θo) cos(φo)

ky = ko sin(θo) sin(φo).

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.

4.5.3 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 (S11, S22, etc.).

The measured principal plane beam scanning performance at low (8 GHz), middle

(10 GHz) and high (12.5 GHz) frequencies is displayed in Fig. 4.25. The aforemen- tioned E-plane truncation is evident in Fig. 4.25(a) where the beam splits scanning

◦ to θo = 60 . 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 (a) (b)

(c) (d)

(e) (f)

Figure 4.20: Mutual coupling across aperture with element 29 excited; (a) simulated 8 GHz, (b) measured 8 GHz, (c) simulated 10 GHz, (d) measured 10 GHz, (e) simulated 12.5 GHz, (f) measured at 12.5 GHz.

84 0 0

−5 −5 Measured S Measured S −10 1,29 −10 5,29 Measured S Measured S 2,29 6,29 −15 Measured S −15 Measured S 3,29 7,29 Measured S Measured S −20 4,29 −20 8,29 Simulated S Simulated S 1,29 5,29 |S| (dB) Simulated S |S| (dB) Simulated S −25 2,29 −25 6,29 Simulated S Simulated S 3,29 7,29 −30 Simulated S −30 Simulated S 4,29 8,29

−35 −35

−40 −40 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz) Frequency (GHz) (a) (b)

0 0

−5 −5 Measured S Measured S −10 9,29 −10 13,29 Measured S Measured S 10,29 14,29 −15 Measured S −15 Measured S 11,29 15,29 Measured S Measured S −20 12,29 −20 16,29 Simulated S Simulated S 9,29 13,29 |S| (dB) Simulated S |S| (dB) Simulated S −25 10,29 −25 14,29 Simulated S Simulated S 11,29 15,29 −30 Simulated S −30 Simulated S 12,29 16,29

−35 −35

−40 −40 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz) Frequency (GHz) (c) (d)

0 0

−5 −5 Measured S Measured S −10 17,29 −10 21,29 Measured S Measured S 18,29 22,29 −15 Measured S −15 Measured S 19,29 23,29 Measured S Measured S −20 20,29 −20 24,29 Simulated S Simulated S 17,29 21,29 |S| (dB) Simulated S |S| (dB) Simulated S −25 18,29 −25 22,29 Simulated S Simulated S 19,29 23,29 −30 Simulated S −30 Simulated S 20,29 24,29

−35 −35

−40 −40 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz) Frequency (GHz) (e) (f)

Figure 4.21: 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 - 20, (f) element 21 - 24.

85 0 0

−5 −5 Measured S Measured S −10 25,29 −10 29,29 Measured S Measured S 26,29 30,29 −15 Measured S −15 Measured S 27,29 31,29 Measured S Measured S −20 28,29 −20 32,29 Simulated S Simulated S 25,29 29,29 |S| (dB) Simulated S |S| (dB) Simulated S −25 26,29 −25 30,29 Simulated S Simulated S 27,29 31,29 −30 Simulated S −30 Simulated S 28,29 32,29

−35 −35

−40 −40 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz) Frequency (GHz) (a) (b)

0 0

−5 −5 Measured S Measured S −10 33,29 −10 37,29 Measured S Measured S 34,29 38,29 −15 Measured S −15 Measured S 35,29 39,29 Measured S Measured S −20 36,29 −20 40,29 Simulated S Simulated S 33,29 37,29 |S| (dB) Simulated S |S| (dB) Simulated S −25 34,29 −25 38,29 Simulated S Simulated S 35,29 39,29 −30 Simulated S −30 Simulated S 36,29 40,29

−35 −35

−40 −40 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz) Frequency (GHz) (c) (d)

0 0

−5 −5 Measured S Measured S −10 41,29 −10 45,29 Measured S Measured S 42,29 46,29 −15 Measured S −15 Measured S 43,29 47,29 Measured S Measured S −20 44,29 −20 48,29 Simulated S Simulated S 41,29 45,29 |S| (dB) Simulated S |S| (dB) Simulated S −25 42,29 −25 46,29 Simulated S Simulated S 43,29 47,29 −30 Simulated S −30 Simulated S 44,29 48,29

−35 −35

−40 −40 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz) Frequency (GHz) (e) (f)

Figure 4.22: 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 - 40, (e) element 41 - 44, (f) element 45 - 48.

86 0 0

−5 −5 Measured S Measured S −10 49,29 −10 53,29 Measured S Measured S 50,29 54,29 −15 Measured S −15 Measured S 51,29 55,29 Measured S Measured S −20 52,29 −20 56,29 Simulated S Simulated S 49,29 53,29 |S| (dB) Simulated S |S| (dB) Simulated S −25 50,29 −25 54,29 Simulated S Simulated S 51,29 55,29 −30 Simulated S −30 Simulated S 52,29 56,29

−35 −35

−40 −40 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz) Frequency (GHz) (a) (b)

0 0

−5 −5 Measured S Measured S −10 57,29 −10 61,29 Measured S Measured S 58,29 62,29 −15 Measured S −15 Measured S 59,29 63,29 Measured S Measured S −20 60,29 −20 64,29 Simulated S Simulated S 57,29 61,29 |S| (dB) Simulated S |S| (dB) Simulated S −25 58,29 −25 62,29 Simulated S Simulated S 59,29 63,29 −30 Simulated S −30 Simulated S 60,29 64,29

−35 −35

−40 −40 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz) Frequency (GHz) (c) (d)

Figure 4.23: Measured and simulated mutual coupling vs. frequency with element 29 excited; (a) element 49 - 52, (b) element 53 - 56, (c) element 57 - 60, (d) element 61 - 64.

87 Element 29, Scanned to θ = 0°, φ = 0° 0 Measured Simulated −5

−10 | (dB) Γ

−15 Active |

−20

−25 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 Frequency (GHz)

Figure 4.24: Measured and simulated finite array element 29 active reflection coeffi- ◦ ◦ cient scanned to θo = 0 , φo = 0 .

cross-polarization level nearly 20 dB below the co-polarized component while scanning up to 60◦.

The E-plane measured and simulated radiation pattern while scanning to broad- side, 30◦ and 60◦ at 10 GHz is shown in Fig. 4.26. Similarly, the H-plane beam steering performance is displayed in Fig. 4.27. Good agreement between simulated and mea- sured scanning patterns in the principal planes and co-polarized and cross-polarized gain are observed. However, the measured cross-polarized component is stronger than simulation predicted, but remains 18 dB below the co-polarized component when scanned to 60◦ in the H-plane. The H-plane cross-polarization disagreement is a result of the fiberglass support which mounts to the H-plane sides (y-axis) of the array as depicted in Fig. 4.11.

88 Freq=8 GHz, E−Plane Freq=8 GHz, H−Plane 25 25

20 20

15 15

10 10

5 5

0 0

−5 −5 Realized Gain (dBi) Realized Gain (dBi) −10 −10

−15 −15

−20 −20 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees) Theta (degrees) (a) (b)

Freq=10 GHz, E−Plane Freq=10 GHz, H−Plane 25 25

20 20

15 15

10 10

5 5

0 0

−5 −5 Realized Gain (dBi) Realized Gain (dBi) −10 −10

−15 −15

−20 −20 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees) Theta (degrees) (c) (d)

Freq=12.5 GHz, E−Plane Freq=12.5 GHz, H−Plane 25 25

20 20

15 15

10 10

5 5

0 0

−5 −5 Realized Gain (dBi) Realized Gain (dBi) −10 −10

−15 −15

−20 −20 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees) Theta (degrees) (e) (f)

Figure 4.25: Measured principal plane co-polarized (—) and cross-polarized (- - -) ◦ ◦ ◦ realized gain beam scanning performance from θo = -60 to 60 in 10 increments; (a) E-plane at 8 GHz, (b) H-plane at 8 GHz, (c) E-plane at 10 GHz, (d) H-plane at 10 GHz, (e) E-plane at 12.5 GHz, (f) H-plane at 12.5 GHz. 89 Freq=10 GHz, E−Plane 30 Measured: Co−Pol 25 Measured: Cross−Pol Simulated: Co−Pol 20 Simulated: Cross−Pol 15

10

5

0

−5 Realized Gain (dBi) −10

−15

−20 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees)

Figure 4.26: Finite array E-plane radiation pattern at 10 GHz scanned to θo = ◦ ◦ ◦ ◦ 0 , 30 , 60 , φo = 0 .

Freq=10 GHz, H−Plane 30 Measured: Co−Pol 25 Measured: Cross−Pol Simulated: Co−Pol 20 Simulated: Cross−Pol 15

10

5

0

−5 Realized Gain (dBi) −10

−15

−20 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 Theta (degrees)

Figure 4.27: Finite array H-plane radiation pattern at 10 GHz scanned to θo = ◦ ◦ ◦ ◦ 0 , 30 , 60 , φo = 90 .

90 The measured and simulated broadside array gain is compared to the maximum theoretical directivity in Fig. 4.28. The simulated realized gain is higher than the theoretical limit above 11 GHz due to the finite ground plane diffraction adding in phase. Similarly, below 11 GHz the gain is slightly lower than the limit because the diffraction combines destructively. Further, we remark the area used in calculation was determined using the TCDA elements physical aperture area and not the PCB area which extends past to accommodate mechanical mounting.

Fully Excited 8x8 Array at Broadside 25

20

15 4πA/λ2 10 Measured: Co−Pol Measured: Cross−Pol 5 Simulated: Co−Pol 0 Simulated: Cross−Pol

−5 Realized Gain (dBi) −10

−15

−20 7 8 9 10 11 12 13 14 Frequency (GHz)

Figure 4.28: Finite array broadside realized gain as a function of frequency with all elements excited.

4.6 Summary

A novel non-symmetric tightly coupled dipole array with integrated balun and matching network was presented. The conformal array is placed λ/7 over a ground plane at the lowest frequency of operation (8 GHz). The array relied on a new non- symmetric dipole element offering several degrees of freedom to allow cancelation of

91 the inductance caused by the ground plane. A wideband ring hybrid was proposed for unbalanced to balanced conversion and is printed directly on the ground plane, maintaining the array’s low-profile height and simple layered planar PCB construc- tion. A impedance matching 136 Ω twin wire transmission line connects the feed and aperture. We remark that the actual array bandwidth is much larger, and at this time is limited by the feed design. The developed conformal array is capable of scanning up to 70◦ in E-plane and 60◦ in H-plane with an active VSWR < 2 from 8 - 12.5

GHz (1.6:1). A small finite 8 × 8 array was fabricated and verified experimentally.

Good agreement between simulation and measurement was confirmed over multiple scan angles.

92 CHAPTER 5

CONCLUSION AND FUTURE WORK

Wideband, low-profile and planar phased arrays have recently been the subject of extensive research. In this dissertation, we focused on the development and real- ization of a wideband, wide-angle scanning and low-profile conformal aperture using a TCDA. Specifically, in Chapter 2 we investigated various phased array antennas and demonstrated that TCDAs become increasingly wideband when placed above a ground plane. Key to achieving wideband performance is cancelation of the ground plane inductance using interelement capacitive mutual coupling. Further, realistic

TCDA balun feed arrangements were presented and important design considerations were discussed such as size restriction, impedance matching, and common mode sup- pression.

Multiple methods for increasing series inductance and shunt capacitance using reactive and material treatments were presented in Chapter 3. Initially, inductive loading was examined using volumetric meandering. Such meandering can be im- plemented using plated vias and traditional PCB manufacturing, thus maintaining the arrays low-cost and planar assembly. For additional inductive loading, ferrite substrates (between the array and ground plane) were examined to improve TCDA bandwidth (up to 7:1). Concurrently, ferrites reduce array thickness to λL/30 with

93 µr = 3. However, aggressive miniaturization (µr > 3) excites an undesired ferrite resonant mode. As such, rectangular resonant cavity analysis was used to model and predict the TM210 ferrite mode frequency. If the mode is suppressed, TCDAs become extremely wideband (8.2:1) and very low-profile (λL/56) using a ferrite substrate with

µr = 7. In addition, we also studied capacitive reactive loading by controlling the mutual capacitance between neighboring elements using a novel non-symmetric ele- ment. The additional degrees of freedom provided by the non-symmetric element were presented to control input impedance and miniaturize the element. For practicality, we next considered dielectric superstrates for array protection. In doing so, a design guideline for determining single and dual layer dielectric substrates was developed to increase low frequency resistance and reduce impedance variation over a broad range of frequencies.

In Chapter 4, a novel non-symmetric tightly coupled dipole array with integrated balun and matching network was presented and verified experimentally. The array is capable of scanning up to 70◦ in E-plane and 60◦ in H-plane with an active VSWR <

2 from 8 - 12.5 GHz (1.6:1). A cross-polarization level 20 dB below the co-polarized component over most of the scanning range is also maintained. The conformal array is placed λ/7 over a ground plane at the lowest frequency of operation (8 GHz). The array relied on a new non-symmetric dipole element fed using a modified wideband ring hybrid. The ring hybrid uses microstrip coupled lines to improve bandwidth and is printed directly on the ground plane, maintaining the array’s low-profile height and simple layered planar PCB construction. A small finite 8 × 8 array was fabricated and verified experimentally. Good agreement between simulation and measurement was confirmed over multiple scan angles.

94 This dissertation presented conceptually new broadband inductive and capacitive miniaturization techniques, as well as polarization properties of linear and dual linear polarized TCDAs. Further, practical balanced feed approaches were investigated and a small 64 element X-band array with wide-angle scanning and low cross-polarization was designed and experimentally demonstrated to verify the presented concepts. The key contributions of this dissertation are:

• Demonstrated using equivalent circuits and full wave simulations that tightly

coupled dipole arrays exhibit capacitive mutual coupling that cancels the in-

ductive ground plane loading over large bandwidths.

• Introduced a new non-symmetric element to independently control TCDA in-

put impedance. The additional design parameters offered by the non-symmetric

element were used to achieve miniaturization and increase bandwidth. In addi-

tion, magnetic and dielectric materials were shown to improve bandwidth and

reduce the array profile.

• Proposed multiple wideband feed designs incorporating unbalanced to balanced

conversion. This critical achievement allowed for impedance matching while

concurrently avoiding common mode excitations and maintaining the array’s

low-profile.

• Designed, fabricated and experimentally verified a wideband planar 64 element

X-band. The array was shown to scan up to a remarkable 70◦ in E-plane and

60◦ in H-plane with an active VSWR < 2 from 8 - 12.5 GHz (1.6:1 or 44%).

These results are believed to be the best reported in terms of array height and

wide-angle scanning over a wide bandwidth fed using unbalanced 50 Ω inputs.

95 This is a significant achievement compared to other arrays which typically scan

up 45◦. The extreme low-profile nature of the proposed array and layered PCB

construction is certainly a key feature to maintain low-cost and reduce weight.

Continued efforts are necessary for improved performance and functionality. First, the hybrid ring currently limits the array’s bandwidth and is suitable only for linear polarization. Wideband unbalanced to balanced conversion is always challenging, especially if one does not want to increase the array height or limit power handling capability. Furthermore, interconnect design with shielding amendable to layered

PCB fabrication is important to suppress or shift the common mode above the array’s operating frequency range and maintain low-cost. The array presented in Chapter 4 avoided common modes by reducing the unit cell size to 8 mm or .33λH . Therefore, the required number of transmit/receive modules to populate a given aperture size is increased and subsequently the cost. This is a serious limitation of the current design and further work is needed to remove common modes while maintaining a

λH /2 unit cell size, provide dual linear polarization and retain wide-angle scanning over extremely large bandwidths (4:1 and above).

In this dissertation, the ferrite loading study was not comprehensive in scope or practicality. Only ideal lossless ferrite material with constant permeability versus frequency were presented as a proof of concept. In addition, suppression of the undesired TM210 ferrite resonant cavity mode was not performed. Therefore, a more rigorous analysis using realistic frequency varying ferrite properties over multiple scan angles and mode suppression or mitigation is necessary.

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