Novel Antennas, Matching Circuits, and Fabrication Techniques at HF and Microwave Frequencies

Item Type text; Electronic Thesis

Authors Gulati, Gitansh

Publisher The University of Arizona.

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Link to Item http://hdl.handle.net/10150/628481

NOVEL ANTENNAS, MATCHING NETWORKS, AND FABRICATION TECHNIQUES AT HF AND MICROWAVE FREQENCIES

by

Gitansh Gulati

______Copyright © Gitansh Gulati 2018

A Thesis Submitted to the Faculty of the

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

In Partial Fulfillment of the Requirements

For the Degree of

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF ARIZONA

2018

ACKNOWLEDGEMENT

First and foremost, I would like to express my sincere gratitude to my advisor Dr.

Hao Xin for his insightful guidance and support throughout my graduate research work and writing of this thesis. His immense knowledge and unique perspective on research encouraged me to understand things from theoretical as well as practical aspects. I would also like to thank my committee members, Prof. Kathleen Melde, and Prof. Siyang Cao, for their valuable comments and suggestions. In addition, I take the opportunity to thank

Prof. Ivan B. Djordjevic and Prof. Agustin Ochoa for their classes on advanced wireless communications and analog integrated circuits.

I owe many thanks to present and past group members and colleagues that I had pleasure to work with, Min Liang, Qi Tang, Noel Teku, Ahmed H. Abdelrahman, Kevin

Morris and Mingwei Yang. My special thanks to Min Liang for his constant supervision and support in most of the projects, especially 3D printing related projects. Thanks to Ryan

Willwater for extending his experience in advanced machining techniques. I also wish to thank all the members in the mmW Circuits and Antennas group.

I would extend my deepest gratitude to my parents, Gulshan Gulati and Manju

Gulati, my uncle, Girish Relhan and my brother, Tanish Gulati for their sacrifices, endless love, support, and encouragement.

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Dedicated to my mom, Manju Gulati

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TABLE OF CONTENTS

ACKNOWLEDGEMENT ...... 3 TABLE OF CONTENTS ...... 5 TABLE OF FIGURES ...... 7 TABLE OF TABLES ...... 12 LIST OF ABBREVIATIONS ...... 13 ABSTRACT ...... 16 CHAPTER 1. INTRODUCTION ...... 18 1.1. Electrically Small Antennas ...... 18 1.2. Active and Passive Impedance Matching ...... 20 1.3. 3-D Printed Antennas ...... 22 1.4. Luneburg Lens Feeds ...... 25 1.5. Mantle Cloaking of Elliptical Cylinders and Strips ...... 29 1.6. Thesis Outline ...... 32 CHAPTER 2. ELECTRICALLY SMALL HELICAL ANTENNA FOR HF- Band COMMUNICATIONS: DESIGN AND FIELD EXPERIMENTS ...... 34 2.1. HF-band long range communication ...... 34 2.2. Uniform normal-mode ESHA (2m long) ...... 35 2.3. Passive and active impedance matching networks ...... 38 2.3.1. Passive narrowband electronically tuned LC matching network ...... 38 2.3.2. Broadband Transformers ...... 41 2.3.3. Active broadband non-Foster matching circuit...... 54 2.4. Measurements...... 59 2.4.1. Outdoor Field Measurements (Near-field)...... 59 2.4.2. Real Voice-Data Communication Measurements (Far-Field) ...... 61 2.5. Summary ...... 65 CHAPTER 3. BROADBAND CONFORMAL DUAL-POLARIZED VIVALDI ARRAY FOR FEEDING LUNEBURG LENS ...... 67 3.1. Graded index 3-D Luneburg lens ...... 67 3.2. Feed network for 3-D printed Luneburg lens ...... 70 3.2.1 Introduction and Motivation ...... 70 3.2.2 Vivaldi Antenna Unit cell ...... 72 3.2.3 Planar dual-polarized 3 x 3 Vivaldi array ...... 77 3.2.4 Conformal dual-polarized Vivaldi feed array for lens (30 cm diameter) ... 80 3.2.5 Conformal dual-polarized Vivaldi feed array for lens (24 cm diameter) ... 86 3.3. Fabrication and Measurements...... 94

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3.3.1. Fabrication ...... 94 3.3.2. Impedance Matching and Radiation Performance ...... 96 3.4. Summary ...... 104 CHAPTER 4. 3-D PRINTED CLOAKED MICROSTRIP ANTENNAS: REDUCTION IN MUTUAL COUPLING ...... 105 4.1. Introduction and Motivation...... 105 4.2. Cloaking of planar monopole antennas with reduced near-field coupling...... 107 4.3. Prototype Fabrication and Testing ...... 115 4.4. Summary ...... 119 CHAPTER 5. CONCLUSIONS AND FUTURE WORK ...... 125 REFERENCES ...... 128

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TABLE OF FIGURES

Figure 1 - 1 Overview of generalized additive manufacturing process [29]...... 23 Figure 1 - 2 (a) Radiated Far-field phase pattern φ(휃) at distance r to determine the distance d to the phase center on z-axis, which is basically the center of radii of the phase front (dashed blue line). (b) geometry showing the mapping of far-field phase with phase front when phase center lies at the origin [46]...... 27 Figure 1 - 3 Geometries of cylindrical objects coated by mantle cloaks: (a) infinite dielectric cylinder with an ideal mantle cloak, (b) infinite conducting cylinder (PEC) with a conformal patch array, and (c) infinite dielectric cylinder with a conformal array of Jerusalem slots [72]...... 30

Figure 2 - 1 Pictorial representation of HF propagation via ground-wave, skywave and NVIS [80]...... 34 Figure 2 - 2 Fabricated prototype of electrically-small helical antenna (ESHA) with helix diameter 10 cm, pitch 17 cm, and 11.7 turns [86]...... 37 Figure 2 - 3 Input reflection coefficient of 2m long ESHA ...... 37 Figure 2 - 4 Measured (a) real and (b) imaginary part of input impedance of 2m ESHA over 0.4m x 0.2 m aluminum sheet located over the ground...... 38 Figure 2 - 5 (a) Structure of the proposed electronically tuned ESHA matched system, (b) schematic of switching network...... 39 Figure 2 - 6 Photograph of fabricated circuit (16 cm x 25 cm) with 6 independently tuned bands [86, 95]...... 40 Figure 2 - 7 Measured reflection coefficient of ESHA with switchable matching circuit prototype tuned independently at six HF-licensed bands...... 41 Figure 2 - 8 Equivalent circuit model of a wideband transformer [89]...... 43 Figure 2 - 9 Representation of complex permeability of Fair-rite material 61 in terms of equivalent resistance, reactance and total impedance [93]...... 46 Figure 2 - 10 Equivalent circuit model of an inductor wound on a ferrite core. Components with a D subscript are due to dimensional resonance, and with a C subscript are due to the wire wounded on the core [93]...... 47 Figure 2 - 11 Fabricated prototype of broadband transformer (ferrite type 43) [95]...... 49 Figure 2 - 12 Insertion-loss performance of fabricated 43 broadband transformer (ferrite type 43)...... 49 Figure 2 - 13 Extracted equivalent circuit model of fabricated 2:5 wideband TLT ...... 50 Figure 2 - 14 Performance agreement between measured and extracted equivalent circuit model for (a) return loss, (b) overall efficiency...... 51 Figure 2 - 15 Photograph of fabricated broadband transformer with (a) ferrite 52 material, (b) ferrite 61 material...... 52 Figure 2 - 16 ESHA matched system performance comparison with three fabricated broadband transformers with reference to (a) return loss, and (b) overall efficiency...... 53

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Figure 2 - 17 Reactance behavior of negative capacitance and negative inductance (non- Foster) compared with normal positive capacitance and inductance that obey Foster’s reactance theorem [100]...... 54 Figure 2 - 18 The schematic of different ways of realizing non-Foster elements: a) a cross-coupled pair of transistors; b) an operational amplifier with positive feedback; c) a negative resistor based NII (also named as j-transformation) [100]...... 55 Figure 2 - 19 Schematic of a 2m-long ESHA with non-Foster circuit (~ -40 pF) to cancel the large capacitive input reactance for broadband matching...... 55 Figure 2 - 20 The circuit schematic of the non-Foster matching network [100]...... 56 Figure 2 - 21 Photograph of fabricated circuit [86], [95], [100]...... 57 Figure 2 - 22 (a) Simulated and measured output impedance of the non-Foster circuit, and (b) the retrieved negative capacitance...... 58 Figure 2 - 23 The simulated and measured S11 of the ESHA w and w/o non-Foster broadband active matching network...... 58 Figure 2 - 24 (a) Test setup schematic with top view of test environment, (b) photographs depicting real-time testing of electrically-small helical antenna (ESHA) at receiver end with commercial antenna at transmitter end...... 60 Figure 2 - 25 The received power strength comparison of the electrically-small helical antenna matched system with broadband non-Foster matching, broadband transformer and narrowband electronically switched LC matching network...... 61 Figure 2 - 26 (a) Transmitter Configuration, (b) Receiver Configuration for voice-data communication measurement involving three matching prototypes...... 62 Figure 2 - 27 Pictorial depiction of locations observed for helical antenna with three different matching circuits...... 64 Figure 2 - 28 Estimated noise figure (NF) margin for ESHA matched system with non- Foster circuit for SNR improvement...... 65

Figure 3 - 1 Standard Luneburg Lens Cross-Section [107]...... 67 Figure 3 - 2 (a) Front view of Luneburg lens ANSYS HFSS prototype, (b) Pictorial view of thin-rods connecting all the discrete cubes together for a robust mechanical support structure [25]...... 69 Figure 3 - 3 Polymer jetting printed Luneburg lens (24 cm Diameter) ...... 70 Figure 3 - 4 Schematic of (a) multiple-beam Luneburg lens antenna, (b) scanned beam Luneburg lens antenna [114]...... 71 Figure 3 - 5 Schematic of exponentially-tapered Vivaldi unit element [129]...... 73 Figure 3 - 6 (a) Schematic of dual-polarized Vivaldi unit cell (b) Phase center determination for one element along z-axis with d ranging from 18 to 36 mm...... 75 Figure 3 - 7 Simulated return loss performance of different elements of a dual-polarized Vivaldi unit cell geometry...... 75 Figure 3 - 8 Phase center variation with frequency for one element of dual-polarized Vivaldi unit cell...... 76 Figure 3 - 9 (a) unit cell schematic for infinite-array simulation, (b) finite-array 3 x 3 schematic simulation...... 77

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Figure 3 - 10 Simulated reflection coefficient for dual-polarized planar Vivaldi...... 78 Figure 3 - 11 (a) Cross-sectional view, (b) bottom-view of dual-polarized 3 x 3 Vivaldi array (44.87 x 44.87 x 33.75 mm) with 12 H-pol. and 12 V-pol. elements [129]...... 79 Figure 3 - 12 (a) Return loss performance of a planar 3 x 3 dual-polarized all metal Vivaldi array fed using SMA connectors, (b) Simulated radiation patterns for V-pol. center element at different frequencies in both E and H planes...... 80 Figure 3 - 13 (a) Front view, (b) back view, (c) simulation setup of the conformal 53 element dual-polarized Vivaldi array for feeding 30 cm dia. Luneburg lens [129]...... 82 Figure 3 - 14 Simulated H-plane radiation patterns of Luneburg lens (30 cm dia.) fed with conformal Vivaldi array utilizing central (a) H-pol. element, (b) V-pol. element...... 83 Figure 3 - 15 Simulated E-plane multiple beams of Luneburg lens (30 cm dia.) for all V- pol. elements (middle slice 2) at 6 GHz (one elements is excited at a time with all other elements terminated in matched loads)...... 85 Figure 3 - 16 (a) Front view, (b) back view of the 60-element dual-polarized conformal Vivaldi array consisting of 4 x 9 H-pol. elements (colored grey) and 8 x 3 V-pol. elements (colored pink)...... 87 Figure 3 - 17 Simulated phase center variation with frequency for unit element of conformal dual-polarized Vivaldi array...... 88 Figure 3 - 18 Simulated (a) S11 (dB) of inner elements, (b) S11 (dB) for edge elements, and (c) isolation between vertical/horizontal elements...... 90 Figure 3 - 19 Simulation setup of Luneburg lens (24 cm diameter) in HFSS with conformal 60-element dual-polarized Vivaldi feed array...... 90 Figure 3 - 20 (a) Simulated H-plane radiation pattern for middle V-pol. element, and (b) middle H-pol element...... 91 Figure 3 - 21 Multiple beams emanating (E-plane radiation) from 24 cm diameter lens fed with 8 V-pol. elements of middle V-pol row/slice...... 93 Figure 3 - 22 3-D radiation plot depicting multiple-beam capabilities of lens fed with conformal dual-polarized Vivaldi array, excited with 13 elements one at a time with all other elements terminated in matched loads...... 93 Figure 3 - 23 Photograph of fabricated conformal aluminum dual-polarized Vivaldi array terminated with SMA connectors (a) front view, (b) back view...... 95 Figure 3 - 24 Measured return loss performance of feed array for all the elements in (a) H-slice 1, (b) H-slice 2, (c) H-slice 3, (d) H-slice 4, (e) V-slice 1, (f) V-slice 2, and (g) V- slice 3. (note: H-slices have 9 elements in a row, and V-slices have 8 elements in a row)...... 97 Figure 3 - 25 Measured isolation between coplanar and cross coupled elements of the conformal dual-polarized Vivaldi array...... 98 Figure 3 - 26 Photograph of 3D Luneburg lens (24 cm dia.) with conformal Vivaldi dual- polarized 60-element array...... 99 Figure 3 - 27 Measured gain patterns of lens antenna at 6 GHz excited for various array elements excited independently for (a) middle V-pol. elements and (b) middle H-pol. elements...... 100

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Figure 3 - 28 Measured and simulated gain (realized) patterns of lens antenna fed with middle V-pol. element at (a) 3 GHz, (b) 4 GHz, (c) 5 GHz, and (d) 6 GHz...... 102 Figure 3 - 29 Measured gain patterns at 3 – 6 GHz for lens antenna fed with middle (a) V-Pol. element, and (b) H-pol. element...... 103

Figure 4 - 1 Top view of the isolated microstrip-fed monopole (a) Antenna I, and (b) Antenna II, (c) bottom view depicting partial ground plane of antennas...... 108 Figure 4 - 2 Input reflection coefficients of Antenna I resonating at 0.92 GHz, and Antenna II resonating at 1.034 GHz...... 108 Figure 4 - 3 Linear gain patterns (3-D) for (a) Isolated antenna I at 0.92 GHz, and (b) isolated Antenna II at 1.034 GHz...... 109 Figure 4 - 4 Schematic (top view) of the uncloaked case with microstrip-fed monopole Antenna I (left) and Antenna II (right)...... 110 Figure 4 - 5 Linear gain patterns (3-D) of coupled but uncloaked case for (a) Antenna I, and (b) Antenna II...... 110 Figure 4 - 6 (a) Schematic (top view) of antenna I and antenna 2 in cloaked case, (b) cross-sectional view, metasurface cloak parameters for (c) antenna I, and (d) antenna II...... 111 Figure 4 - 7 S-parameters of two-microstrip fed monopole antennas (antenna I and antenna II) for cloaked and uncloaked case...... 112 Figure 4 - 8 Linear gain patterns (3-D) for cloaked case of (a) antenna I at 0.965 GHz, and (b) antenna II at 1.108 GHz...... 113 Figure 4 - 9 Linear gain patterns of antenna I at 0.965 GHz (a) in the E-plane, and (b) in the H-plane. Linear gain patterns of antenna II at 1.108 GHz (c) in the E-plane, and (d) in the H-plane...... 114 Figure 4 - 10 (a) Semi-elliptical Teflon mold under high intensity UV lamp (100 W), and (b) Cured semi-elliptical metasurface dielectric spacers for Antenna I & II...... 115 Figure 4 - 11 (a) 3-D printed (0.5 mm thick) semi-elliptical shell to aid metallization process, (b) photograph of fabricated semi-elliptical metasurface cloaks with metallic subwavelength strip inclusions developed using highly conductive spray coating technique to enclose antenna I and antenna II...... 116 Figure 4 - 12 (a) Embedded semi-elliptical metasurface cloaks in the 3D printed substrate, (b) picture showing the fabrication of planar monopole antennas I & II using double-sided adhesive copper tape and (c) back view of the fabricated prototype depicting partial ground plane...... 117 Figure 4 - 13 Measurement setup for testing s-parameters of fabricated near-filed cloaked prototype...... 118 Figure 4 - 14 Measured s-parameters of the fabricated near-field cloaked prototype (highlighted sections indicate the regions that depict cloaking behavior for antenna I and antenna II)...... 119 Figure 4 - 15 Simulated and measured s-parameters of the cloaked case (for simulation, 휖푐=5.9 with tan훿 =0.05 for elliptical host spacer, and 휖푟 = 2.7 with tan훿 =0.01 for

10 polymer substrate material). The highlighted regions from the left to right corresponds to region 푀1, region 푆1, and region 푀푆12) ...... 121

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TABLE OF TABLES

Table 1 - 1 Characteristics of the five basic categories of AM processes [21] ...... 24

Table 2 - 1 Extracted 2:5 TLT equivalent circuit parameters ...... 50 Table 2 - 2 Measured SNR comparison for matching circuits ...... 63

Table 3 - 1 Vivaldi unit cell geometry parameters ...... 73 Table 3 - 2 Simulated gain, HPBW and side-lobe level (30 cm lens) ...... 84 Table 3 - 3 Vivaldi unit cell geometry parameters ...... 87 Table 3 - 4 Simulated gain, HPBW and side-lobe level (24 cm lens) ...... 92

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LIST OF ABBREVIATIONS

1D, 2D, 3D One-, two-, three-dimensional

AM Additive Manufacturing

BAVA Balanced Antipodal Vivaldi Antenna

BLOS Beyond Line of Sight

BW Bandwidth

CAD Computer Aided Design

DGS Defected Ground Structures

EBG Electromagnetic Band Gap

EM Electromagnetic

ESA Electrically Small Antenna

ESHA Electrically Small Helical Antenna

FDTD Finite Difference Time Domain

FEBI Finite Element Boundary Integral

FEM Finite Element Method

GHz Gigahertz

GRIN Graded Index

HF High Frequency

HFSS High Frequency Simulation Software

HPBW Half Power Beam Width

LLM Layer Laminate Manufacturing

LOS Line of Sight

LPF Low Pass Filter

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LSB Low Side Band

MUF Maximum Usable Frequency

NDF Normalized Determinant Function

NF Noise Figure

NIC Negative Impedance Convertor

NII Negative Impedance Invertor

NMHA Normal Mode Helical Antenna

NVIS Near Vertical Incidence Sky-wave

OTH Over The Horizon

PEC Perfect Electric Conductor

PEP Peak Envelope Power

RF Radio Frequency

RFC Radio Frequency Choke

RFID Radio Frequency Identification

RMS Root Mean Square

RX Receiver

SA Spectrum Analyzer

SCS Scattering Cross Section

SMA SubMiniature Version A

SNR Signal-to-Noise Ratio

SSB Single Side Band

THz Terahertz

TM Transverse Magnetic

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TX Transmitter

UHF Ultra High Frequency

USB Upper Side Band

USRP Universal Software Radio Peripheral

UWB Ultra Wide Band

VHF Very High Frequency

VSWR Voltage Standing Wave Ratio

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ABSTRACT

This thesis focuses on the investigation of several novel antennas including electrically small antennas for HF communication system, as well as the applications of gradient index lens based broadband multiple-beam system, and electromagnetic cloak structures in printed technology.

Modern-day wireless communication systems have developed interest in the field of low-profile broadband antennas. The design of electrically small antennas (ESA) presents numerous challenges, primarily due to inherently low impedance and narrow bandwidths. Improving these performance characteristics becomes even more challenging in the high frequency (HF) band due to longer wavelengths and corresponding antenna physical dimensions. In this thesis, we propose electrically-small vertically-polarized normal mode helical antenna (NMHA), about λ/50 at the lowest frequency of operation, to facilitate robust long-range HF-band communications (3 – 30 MHz). To overcome the potential issues related to electrically-small NMHA such as impedance matching, bandwidth and radiation efficiency, passive and active impedance matching techniques are investigated. Three types of matching networks are proposed, designed and experimentally demonstrated. These include passive narrowband electronically-switched LC matching network, broadband transformers and active non-Foster broadband matching circuit. In addition, performance of electrically-small helical antenna (ESHA) matched system in terms of received signal power strength, signal-to-noise ratio (SNR), and signal intelligibility is evaluated with the help of outdoor field test measurements.

Many potential areas of application such as satellite communication, air-traffic control, air-based tracking and surveillance, marine navigation, and automotive radar

16 require highly-directional wide-angle beam scanning with minimum pattern deformation and broadband behavior, in addition to lower-cost and weight considerations. In view of this, another area of concentration addressed by the thesis is towards the development of multiple-beam Luneburg lens antenna system. The additive manufactured 3D graded-index

Luneburg lens is employed for this application. Using the special property of a Luneburg lens that every point on the surface of the lens is the focal point of a plane wave incident from the opposite side, compact conformal dual-polarized all-metal Vivaldi feed array, with its phase center close to the lens surface, is proposed to realize the full potential of

Luneburg lens for practical wireless applications ranging from 3 – 6 GHz.

Lastly, this thesis discusses another interesting topic about electromagnetic invisibility and cloaking technology being applied to printed antennas in order to reduce mutual near-field coupling, based on the concept of mantle cloaking method. Two microstrip-fed monopole antennas placed in the near-field of each other, resonating at slightly different frequencies, become invisible to each other by cloaking the radiation part of each antenna. The cloak structure is realized by a conformal elliptical metasurface formed by confocal printed arrays of sub-wavelength periodic elements, partially embedded in the substrate. The existence of the metasurfaces leads to restoration of the radiation patterns of the antennas as if they were isolated. Finally, the fabrication of near- field cloaked prototype is carried out using advanced 3D printing techniques.

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Chapter 1. Introduction

This thesis explores several active research areas in the field of antennas and propagation for advanced wireless communication applications at microwave and HF frequencies. First, primary characteristics of electrically small antennas (ESA) are investigated for the design and implementation of robust long-range HF communication system. These include overall size limitations, lowest achievable operating frequency, gain, narrow bandwidth, polarization and impedance matching. Second, analysis and design of conformal dual-polarized feed array is studied for the development of broadband, high- directional Luneburg lens based antenna system with multiple-beam/scanned beam capabilities. Third, application of mantle cloaking in printed antennas is investigated to reduce mutual coupling between two closely spaced antennas, placed in the near-field of each other. Fabrication of the prototype is demonstrated using advanced 3D printing techniques.

1.1. Electrically Small Antennas

Advancement in modern communication systems has led to interests in the field of development of efficient and broadband antennas with a small form factor. An electrically small antenna (ESA) can be defined by the value of 푘푎 ≪ 1, where 푎 is the radius of imaginary sphere confining the maximum dimension of the antenna, and 푘 is the free space wavenumber(2휋/휆). The frequency dependent input impedance of the electrically small antenna is given by Z(ω) = R(ω) + j X(ω), where ω is the radian frequency, R(ω) is the antenna’s feed point resistance (contains both radiation and loss terms) and X(ω) is the antenna’s feed point reactance. A typical ESA behaves as either a lossy capacitor, a lossy inductor, or a combination of both, and its feedpoint impedance takes the form of a series

18 or parallel RLC circuit. An ESA has the major advantage of compactness as compared to half-wavelength dipole (푘푎 = 1.57). However, fundamental limitations derived by Wheeler and Chu on the small antenna performance governs design tradeoffs for impedance matching, bandwidth and radiation efficiency [1-3]. The radiation quality factor for a lossless ESA satisfies

1 1 푄 ≥ + (1.1) 푘3푎3 푘푎

The 3-dB fractional bandwidth of an ESA is calculated as

1 퐵푊 = (1.2) 3푑퐵 푄

Thus, the maximum fractional bandwidth for an ESA becomes

푘3푎3 퐵푊 = ≈ (푘푎)3, 푓표푟 푘푎 ≪ 1. (1.4) 3푑퐵,푚푎푥 1 + 푘2푎2

Consequently, reduction in the electrical size of antenna leads to significant increase in the minimum Q value, causing the fractional bandwidth of the antenna system to decrease accordingly. Further, by making antenna or matching circuit multi-resonant, the equation for bandwidth based on Q can be exceeded by maximizing the reflection coefficient within that band as governed by Bode-Fano limit [4]

1 휋 퐵 = (1.5) 푄 ln (1/|Γ푚푎푥 |

where Γ푚푎푥 is the maximum reflection coefficient in the matching bandwidth.

It is evident that the antenna fractional bandwidth can be increased with increase in losses,

19 but at a cost of the overall radiated power. In particular, the quality factor and gains for the lossy and the lossless systems are associated as follows

푄푙표푠푠푦 = 휂푟푎푑푄퐿표푠푠푙푒푠푠 (1.6)

퐺 = 휂푟푎푑퐷 (1.7)

Where 휂푟푎푑 is the radiation efficiency, D is the directivity of system and G is the gain.

Thus, when comparing lossy and losseless antenna systems, it can noticed that the gain- bandwidth product remains constant

1 퐷 퐺 x BW = 휂푟푎푑퐷 x = (1.8) 휂푟푎푑푄퐿표푠푠푙푒푠푠 푄퐿표푠푠푙푒푠푠

By understanding the effects of antenna size reduction on quality factor (Q), bandwidth, efficiency, and gain, an efficient matched ESA system can be developed.

1.2. Active and Passive Impedance Matching

In radio frequency (RF) applications such as transmitters, amplifiers, receivers and antennas, when a RF source is used to drive a load whose impedance varies with frequency, a task of vital importance is the design of impedance matching network to facilitate maximum power transfer between the two. However, a close match is generally attained only over a limited bandwidth, given by Bode-Fano upper bound [4-5]. This bound depends on the frequency characteristics of the load, and determines the highest achievable bandwidth by any passive matching network. The standard narrowband impedance matching techniques using reactive lumped circuit elements include L, T, and Π section matching, which may also include transformers with single and double-stub tuning of transmission lines [6-7]. Due to finite unloaded Q of passive L and C components involved,

20 this approach involves considerable loss.

A serious problem exists for input impedance matching of ESA over a wide frequency band as the reduction of electrical size of antenna leads to increase in the reactance. To compensate for the imaginary part of the complex input impedance of ESA over a wide bandwidth, it has been possible to construct compensating circuits to be switched on for use with the antenna. However, matching with lossless inductors and capacitors is useful only over small bandwidths, and a large number of different compensating circuits may be needed, each for a particular frequency band to cover the entire broadband. It is worth noting that one can achieve wideband matching by incorporating loss, but then the total efficiency of antenna system will be poor, resulting in significantly low gain for ESA. For transmitter antenna, this leads to increased output power, thus, directly contributing to the cost and complexity of the system.

Compared to lossy narrowband matching using reactive lumped circuit elements, a conventional ferromagnetic broadband transformers can be employed to perform impedance transformation with improved frequency response and efficiency across a wide operational bandwidth [8-9]. These type of broadband transformers are commonly employed for radio communication at high frequency (HF), very-high frequency (VHF) and lower ultra-high frequency (UHF) over long distances. They offer several advantages such as high output power usage (about 500 W peak-envelop-power (PEP)), low insertion loss (≤ 2푑퐵), low cost, ease-of-integration and design simplicity. It is important to consider that these transformers cannot conjugate match the reactive input impedance of the ESA. In contrast, they can be optimally designed to increase the overall efficiency of antenna matched system, discussed later in Chapter 2.

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Since the passive matching techniques for broadband matching of ESA are strongly limited by the gain-bandwidth constraint and overall power efficiency, active non-Foster matching has emerged as a potential research topic [10-15]. Most of the work in this area focuses on compensating the natural reactance of antenna over larger bandwidths, taking advantage of the negative-slope property of the reactance response in non-Foster elements.

Such circuits have already been widely investigated in the designs of voltage Controlled oscillators, active filters, amplifiers and more recently electrically small antennas [16-18].

Over the years, high-frequency (HF) communications, occurring over frequency range of 3 – 30 MHz, has enable radio enthusiasts to conduct long-range communications across the globe without the use of a satellite. One of the major challenges for an efficient on-the-move HF communications is the lack of low-profile antenna system with robust performance. Several configurations have been proposed in literature such as electronically switchable broadband loaded antenna for 10.5-30 MHz band [19], broadband bow-tie shaped HF antenna for 6-30 MHz band [20] but with antenna height not less than 15 m.

Chapter 2 discusses narrowband/broadband active and passive matching of electrically small antennas for HF communications in detail.

1.3. 3-D Printed Antennas

Additive manufacturing (AM), also known as “3D printing”, is an automated fabrication technique to build 3D objects directly from digital data. Recently, AM has exhibited impressive object making capability ranging from vehicles, housing parts, to entire building structures and complex 3D mechanical constructions. 3D printing technologies have incorporated several structural materials such as metal, polymer, ceramics, concrete and even biocompatible materials. Since any EM structure can be

22 viewed as a spatial distribution of EM properties, AM processes has the potential to spatially structure the EM property to create arbitrary EM materials. Compared to conventional manufacturing methods, AM approach has several advantages including: arbitrary complexity, digital manufacturing and waste reduction.

AM technology has been employed for the fabrication of various antennas.

Different types of antenna structures, working at frequencies from GHz to THz, have been realized in literature using different 3D printing techniques [21]. These include horn antennas [22], patch antennas [23], meander line antennas [24], gradient index (GRIN) lens antennas [25] and reflect-array antennas [26], made of different material such as all dielectric antenna [27], all metal antenna [28] and dielectric metal combined antenna [23], [25], [26].

Presently, there are several varieties of 3D printing techniques, following the basic AM procedure, for example, combining individually generated physical layers as shown in

Figure 1 - 1.

Figure 1 - 1 Overview of generalized additive manufacturing process [29].

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According to the methods of generating physical layers and bonding adjacent layers together to form an object, five basic categories of AM processes are commercially available [30], including selective sintering and melting, powder binder bonding, polymerization, extrusion and layer laminate manufacturing (LLM). Key aspects of these five processes are summarized in Table 1 - 1.

It is deemed vital to establish correlation between various printing qualities, for both polymer as well as metal, such as surface roughness, printing resolution, conductivity, thickness of deposited material, impact of material anisotropy, etc., with high frequency performance of 3D printed antennas. Some of the advantages of 3D printed antennas include: (1) significantly lightweight prototypes; (2) design flexibility to realize wide range of 3D geometries; (3) low-cost rapid prototyping of new designs [31-32]; (4) low heat and moisture absorption of the polymer base; (5) possibility to boost EM performance of deposited conductive layer via combination of different metals.

Although AM do enable innovative designs, several challenges in the development of new materials compatible with existing printing process still exist.

Table 1 - 1 Characteristics of the five basic categories of AM processes [21]

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Important material parameters, which depend on frequency of operation, include electric permittivity (ɛ), metal conductivity (휎), permeability (휇), and loss tangent (tanδ).

In contrast to polymer printing, three main techniques for developing high- precision metals are inkjet printing, aerosol jet printing and direct ink writing [33]. Another class of polymer-based dielectrics employed commonly to obtain optimal dielectric properties is UV-curable dielectrics which consist of chemical mixtures of oligomers (long molecules), monomers (short molecules), photo initiators and other fillers. Optimum dielectric curing conditions is necessary to minimize the occurrence of irregularities in post cured dielectric materials that include appropriate intensity (i.e. power) and wavelength of

UV light rays exposed, suitable cure temperature and duration of the process.

This work utilizes some of the aforementioned AM techniques for the fabrication and realization of 3D antennas, discussed in Chapter 3 and Chapter 4.

1.4. Luneburg Lens Feeds

Feeds are commonly used to supply energy to (or receive energy from) a secondary antenna, such as a reflector, lens, or beam waveguide. Modern-day applications of antennas with feeds include satellite communications, radar, radio telescopes, deep-space imaging and terrestrial microwave and millimeter-wave radio networks. Feeds can be characterized into four main categories: aperture, linear, travelling wave and compound antennas [34].

In lenses, as the feed network is placed behind the aperture, this topology eliminates aperture blockage and allows direct connection of the feed. Theoretically, the best performance in terms of maximum directivity and improved side-lobe level is attained when the phase center of the feed is aligned with the focal point of the lens [35].

25

Fundamentally, three main requirements for the design of high-performance feeds include: low cross polarization, phase center uniqueness and high antenna gain factor. In addition to principal plane amplitude patterns, phase patterns should also be equalized to unify the feed phase centers in the principal planes, thereby confining the aperture field of the feed to the focal plane field of the lens [36-37]. Luneburg lens feed sources are mostly rectangular open-ended waveguides, tapered slot antennas, patch antennas. Both linearly polarized and circularly polarized feed sources can be employed. Patch antennas offer advantages like low-profile form factor and conformal geometry with lens surface, but they may lead to significant spill-over losses due to broad radiation patterns, specifically for off- body fed lens. In addition, patch antennas cannot sustain high power, whereas open ended waveguides cannot achieve a single mode bandwidth of 2.5:1 [35]. Some of the previous works for integrated lens antennas at sub-millimeter wavelengths employing lens feed as double-slot antenna is reported in literature [38]. However, narrowband nature of double- slot antenna limits the inherent broadband capabilities of lens. Wideband feeds such as sinuous antenna [39], log-spiral or log-periodic antennas [40] have been investigated for lens applications in radio astronomy. However, they suffer from polarization stability with variation in frequency. To overcome this limitation, an alternate wideband planar feed that provide stable linearly-polarized radiation pattern with frequency along with stable phase center position is reported for millimeter applications [41]. Some other promising works include leaky slot line feed [42-43], square array of leaky slots [44], aperture-coupled microstrip-fed patch array [45].

One of the primary concerns in the development of Luneburg lens feeds is the stability of phase center with frequency. The phase center of an antenna is an imaginary

26 point from where the far field seems to emanate. Determination of the location of the antenna phase center is critical due to its simplification of the antenna as a point source and its effect on antenna gain and phase. The phase center can be derived directly from the shape of the radiated far field phase pattern φ(휃), and is mostly considered within a single plane with known far-field located at a distance r from a reference origin as demostrated in

Figure 1 - 2. The phase data is a series of data points, each consisting of a phase angle 휙 and an associated pattern rotation angle . Assuming the reference point to be at the center of the feed for symmetric radiating structures, the axial distance d from the reference point to the apparent phase center is calculated using:

훥휙 ⋅ 휆 푑 = (1.9) 2휋(1 − 푐표푠 휃) where 훥휙 is the change in phase from the on-axis phase. Once the distance to the phase center is determined, all phase data is adjusted so that the new reference point for the feed antenna pattern is the phase center.

Figure 1 - 2 (a) Radiated Far-field phase pattern φ(휽) at distance r to determine the distance d to the phase center on z-axis, which is basically the center of radii of the phase front (dashed blue line). (b) geometry showing the mapping of far-field phase with phase front when phase center lies at the origin [46].

27

2휋(1 − 푐표푠 휃). 푑 훥휙 = (1.10) 휆

Phase center location is calculated based on the optimum beamwidth of the feed antenna in principal planes. Due to different beamwdiths in E-plane and H-plane, there can be multiple phase centers, with respect to particular beamwidth chosen such as 3 dB beamwidth, 10 dB beamwidth, etc.. However, for low cross polarization they must be either coincident or very close to each other [47].

Conventional narrow-band antennas usually have a constant phase center in the operating frequency band. In contrast, it is difficult to achieve a stable phase center in case of broadband antennas as the beam width and frequency vary at the same time. Various analytical, experimental and numerical solutions are available for phase center determination [48-52].

Multiple beam antennas have been proposed for applications in terrestrial communication systems such as cellular mobile telephone systems [53] and dissemination of wideband services within a metropolitan area [54]. A multiple beam antenna provides several concurrent beams in space which enables a resource of a system, such as the available spectrum, to be adaptively shared amongst the available beams. The Luneburg lens antenna system allows for multiple highly-directive beams for beam steering [55]. It is beneficial when compared to a reflector or phased array, as it does not require mechanical steering or a complex phase-shifting beamforming network.

Although the phase centers of the waveguide and horn antennas are located close to the apertures, the unavailability of broadband (3- 6 GHz) waveguides, bulkiness and incapability of multi-beam steering structures have laid the motivation towards the

28 investigation of wide-bandwidth tapered-slot antenna array configurations with improved feed efficiency and uniform Luneburg lens aperture field illumination. In this work, determination of phase center of the proposed broadband Vivaldi feed antenna for both E- plane and H-plane is reported for optimal broadside beamwidth of feed antenna and phase error tolerance, discussed in detail in Chapter 3.

1.5. Mantle Cloaking of Elliptical Cylinders and Strips

Electromagnetic cloaking has always aroused interest in scientific community due to its capability to suppress bistatic scattering of the object, independent of the incident and observation angles. This technology delivers various remarkable applications which include camouflaging, non-invasive probing [56-57], near-filed imaging and low- interference communications [58-59]. Several techniques have been proposed for the investigation of cloak structures such as transformation optics [60-62], anomalous resonance method [63], plasmonic cloaking [64] and transmission-line networks [65-66].

In transformation optics, the geometrical path of light that minimizes the optical path can be curved in a desired fashion by generating a complex distribution of refractive indices.

In contrast, plasmonic cloaking utilizes unusual properties of bulk isotropic low or negative index materials to suppress the dominant scattering mode [67-69].

However, the aforementioned techniques possess fabrication issues since they depend on bulk volumetric metamaterials, which require the thickness to be comparable to the size of the cloaking object. In view of this, a different cloaking method based on mantle cloaking has been proposed in literature to accomplish EM invisibility for planar, cylindrical and spherical objects [70-73]. In this topology, dominant EM scattering mode is suppressed by creating anti-phase surface currents by employing infinitesimally thin

29 metasurfaces. Padooru et. al. [72] presents practical one-dimensional (1-D) and two- dimensional (2-D) cloaking structures based on analytical model that relies on scattering cancellation properties, characterized by an average surface reactance as shown in Figure

1 - 3.

The subwavelength metasurfaces are characterized by a homogeneous surface impedance (푍푠), thus relating 퐸푡푎푛 = 푍푠J, where 퐸푡푎푛 the macroscopic is surface tangential electric field, and J is the induced averaged electric surface current density.

Figure 1 - 3 Geometries of cylindrical objects coated by mantle cloaks: (a) infinite dielectric cylinder with an ideal mantle cloak, (b) infinite conducting cylinder (PEC) with a conformal patch array, and (c) infinite dielectric cylinder with a conformal array of Jerusalem slots [72].

30

Lorenz-Mie scattering theory [74-75] is applied to solve scattering problem using following boundary conditions: tangential components of electric and magnetic fields at the boundary of the core (휌 = 푎) should be continuous and (2) two-sided impedance boundary conditions at the boundary of the mantle cloak (휌 = 푎푐).

Tangential electric (퐸푡) and magnetic field (퐻푡) can be related to sheet impedance with the help of two-sided boundary conditions,

퐸 | + = 퐸 | − = 푍 (퐻 | + − 퐻| −) (1.11) 푡 푝=푎푐 푡 푝=푎푐 푠 푡 푝=푎푐 푝=푎푐

where 푍푠 is the surface impedance of the mantle cloak covering the cylinder. Based on the specific surface impedance value for respective geometry, bistatic scattering width can be reduced for all incident angles, thus rendering the object invisible for the operating frequency regime.

In regards to aforementioned concept, a graphene-based cloaking metasurface comprising a periodic array of graphene patches has been realized to achieve tunable scattering cancelation in the terahertz (THz) spectrum [76]. In extension to this, novel analytical approach for cloaking of dielectric and metallic elliptical cylinders comprising of a graphene monolayer and a nanostructured graphene metasurface is reported at low- terahertz frequencies [77]. This approach is aimed at investigating EM scattering problem for elliptical waves in terms of even and odd angular and radial Mathieu functions, along with the use of sheet impedance boundary conditions at the metasurface.

Inspired by the aforementioned analytical methods derived for investigating EM scattering problem for cloaking of 2D-elliptical objects [77], wherein infinitely long metallic cylinders and strips are cloaked by suitably designed confocal elliptically shaped

31 metasurfaces, Bernety et. al. [78] extended this technique to suppress mutual coupling between printed antennas. Practical realization of these elliptical-shaped cloaking structures is deemed vital to cater the full potential of this technique in printed antenna technology, which requires high performance, compactness, reliability and lightweight to be widely used in modern-day communication applications. In this work, we demonstrate the reduction in mutual coupling between two planar monopole antennas at microwave frequencies, placed in the near-field of each other, with the help of appropriately designed confocal metasurfaces with strip inclusions. Fabrication of the prototype is also carried out using advanced 3D printing techniques.

1.6. Thesis Outline

This thesis studies the potentials and challenges to overcome the bandwidth and efficiency limitations of electrically small antennas by utilizing active and passive matching networks; investigates the design of compact conformal antenna feed array to realize multi-beam capabilities of 3-D printed Luneburg lens; and implements elliptical metasurface cloaks to suppress mutual coupling in printed technology using advanced 3-D printing techniques.

Chapter 2 introduces electrically-small helical antenna (ESHA), about 휆/50 at the lowest frequency, for long range HF-band communications (3-30 MHz). To mitigate the issues associated with the proposed ESHA that include impedance matching, bandwidth, and radiation efficiency, theoretical design and experimental measurement of active and passive impedance matching networks are reported. These include electronically switched narrowband LC passive network, broadband transmission line transformer and active broadband non-Foster matching circuit. Further, outdoor field test measurements

32

(including real-voice data communications) are performed to analyze the performance of

ESHA matched system in terms of received signal power strength, approximate signal-to- noise ratio (SNR) and signal quality.

Chapter 3 proposes Vivaldi antenna based dual-polarized feed network design for

3-D printed Luneburg lens taking into consideration the effect of stable phase center requirement with the lens focal point. The feed network is realized in planar and conformal array configurations to demonstrate highly-directional multiple-beams emanating from the lens. Fabrication of proposed conformal dual-polarized Vivaldi array for feeding a 24 cm diameter lens is implemented using advanced machining techniques. Designs are simulated using the full wave EM package, ANSYS HFSS. Measurements are performed to analyze the performance of lens fed by the proposed feed network.

Chapter 4 discusses the potential of cloaking technology to reduce mutual coupling between printed antennas based on the concept of mantle cloaking. Two microstrip-fed monopole antennas, placed in near-field of each other, are covered with appropriately designed elliptical metasurfaces to mitigate and neutralize the effects of coupling, thus preserving their radiation patterns and impedance characteristics as if they were isolated.

The performance of the proposed structure is quantitatively characterized in terms of s- parermters and 3D/2D gain patterns using the full-wave EM simulation package, ANSYS

HFSS. Development and implementation of the proposed prototype is carried out using advanced 3-D printing techniques. Measured results are presented.

Finally, conclusions and future prospects are discussed in Chapter 5.

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Chapter 2. Electrically small helical antenna for HF-band communications: design and field experiments

2.1. HF-band long range communication

For decades, the high frequency (HF) band (3-30 MHz) has been recognized as the primary means of long-range wireless communications for science and broadcasting services by military, diplomatic, aeronautical, marine and amateur-radio enthusiasts. In the

HF region, propagation via direct wave, surface wave, near-vertical incidence sky wave

(NVIS) and sky wave provides a means of communication from line-of-sight (LOS) to beyond-line-of-sight (BLOS), and over-the-horizon (OTH) ranges [79]. Figure 2 - 1 shows various HF propagation modes. For this work, two primary propagation modes operated are skywave and ground-wave propagation. Ionosphere, composed of several ionized regions above the Earth’s surface, acts as a natural reflector for HF waves.

Figure 2 - 1 Pictorial representation of HF propagation via ground-wave, skywave and NVIS [80].

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However, daily and seasonal variations of the ionosphere geographically constantly affect the long-distance communications effectiveness. Therefore, the choice of carrier frequency is critical in real-time sky-wave propagation [81]. The maximum usable frequency (MUF) used to transmit over a particular path under given ionospheric conditions is the product of critical frequency and propagation factor, which is a function of transmission path length. MUF can be calculated as 푓푀푈퐹 = 푓표. sec 푖, where 푓표 is the critical frequency, 푖 is the angle if incidence, and sec 푖 being the propagation factor. In general, surface propagation can exist for ground ranges up to a few hundred kilometers with the longest ranges being over sea water and at the lowest HF frequencies, compared to ionospheric propagation that can extend to ground ranges exceeding 10,000 km with multiple hops.

2.2. Uniform normal-mode ESHA (2m long)

The helical antenna, introduced by John D. Kraus in 1946, is an antenna consisting of conducting wire wound in the form of a spring [82]. A helical antenna operates in two principle modes based on the far-field radiation pattern: the normal mode with the maximum radiation perpendicular to the helix axis; or the axial mode with the maximum radiation in the direction of the axis. In this work, normal-mode helix antenna (NMHA) is considered, where the helix diameter is much smaller than λ (typically ≤0.1λ), mounted vertically above a finite ground plane. The NMHA exhibits identical radiation pattern to that of a monopole antenna, however, resonates at a much shorter physical length in a narrow bandwidth. Subsequently, the NMHA is advantageous for applications in HF- communication, mobile and satellite communication, RFID and miniaturized medical implants [83-84].

35

The feed point input impedance of a NMHA is a complex function of its physical characteristics and there exist no clearly useful design formulas in the open literature [85].

Apart from physical measurements, well-defined input impedance is determined with the help of existing full-wave EM solvers based on finite difference time domain (FDTD) method or finite element method (FEM).

The design of helix for radiating element depend on three parameters, namely, the diameter d, the pitch angle 훼 and number of turns n. For normal-mode operation, the relation between these parameters follows

푠 훼 = tan−1 (2.1) 휋푑 where s is the spacing between the turns.

퐿 = √푠2 + (휋푑)2 (2.2)

휋푑 ≅ 퐾휆, 푤ℎ푒푟푒 퐾 < 0.5 (2.3)

The total length of the helix is given as,

푛퐿 = 푛휋푑 푠푒푐훼 (2.4)

To facilitate robust long-range HF-band communications (3-30 MHz), we propose the design of an electrically small vertically-polarized NMHA, resonant at 24.5 MHz, as shown in Figure 2 - 2. The antenna height H is 2 m, which is λ/50 at the lowest frequency.

The helix is wound around a PVC pipe with uniform pitch for mechanical support. The helix diameter, pitch, conductor thickness (i.e. helix wire diameter) and number of turns are optimized, using the commercial EM full-wave package ANSYS HFSS, to obtain a lowest self-resonance within the HF-band.

36

Figure 2 - 2 Fabricated prototype of electrically-small helical antenna (ESHA) with helix diameter 10 cm, pitch 17 cm, and 11.7 turns [86].

The simulated and measured input reflection coefficients (푆11) are plotted in Figure 2 - 3.

As discussed in section 1.2, as antennas become shorter (typically< 0.1휆), the radiation resistance decreases significantly, and the reactance and quality factor (푄) increases, thus affecting the impedance matching, bandwidth and radiation efficiency. Figure 2 - 4 depicts the measured input impedance of ESHA which indicates a large negative capacitive reactance below the resonant frequency.

Figure 2 - 3 Input reflection coefficient of 2m long ESHA 37

Figure 2 - 4 Measured (a) real and (b) imaginary part of input impedance of 2m ESHA over 0.4m x 0.2 m aluminum sheet located over the ground.

To overcome this issue, ESHA matched system is demonstrated employing narrowband electronically switchable passive matching network, broadband active non-Foster matching circuit, and wideband transformer matching network for amateur, maritime and broadcast applications.

2.3. Passive and active impedance matching networks

2.3.1. Passive narrowband electronically tuned LC matching network

With the objective of designing a reconfigurable electrically small antenna with low-angle omnidirectional transmission for long-range communications via the ionosphere, an electronically switched tuning network using high power PIN diodes is developed. The proposed prototype switches between six matching circuits, tuned at certain discrete frequencies along the HF-band as shown in Figure 2 - 5. To match the complex termination impedance of ESHA with maximum power transfer in the desired narrowband region of interest, lumped element T-section matching consisting of two inductors (L1, L2) and one capacitor (C1) is considered [7], [87-88]. The advantage of the three element networks, (T and π) compared to two-element matching (L-section) is that Q can be chosen

38 as an independent design parameter, thereby, offering some degree of choice of bandwidth.

Simple two element biasing network, consisting of DC blocking capacitor (1000 pF) and

RF chokes (i.e. 22 μH), is used to bias the pin diodes for each matching circuit independently (see Figure 2 - 5 (b)). Forward biasing pin diode requires 0.75 V and 50 mA such that it has 0.4 Ω in the ON stage and 6 kΩ in the OFF stage. A compensating resistor

(R=300 Ω) is connected in the bias current closed path to cancel any offset voltage fluctuations.

Figure 2 - 5 (a) Structure of the proposed electronically tuned ESHA matched system, (b) schematic of switching network.

39

A duroid 5880 substrate with 31 mil thickness is used in the fabrication. Figure 2 -

6 shows a photograph of the fabricated circuit with labeled LC components, pin diodes,

DC block capacitors and RF chokes (i.e. RFC). With an applied DC bias voltage of 15.96 volts, the measured voltage drop across the diode is 0.759 volts, enough to close the switch.

To be precise, for matching at discrete frequencies, pin diodes in each independent matching circuit path consumes about 0.814 W power. Figure 2 - 7 shows the measured reflection coefficient of the ESHA connected to the electronically reconfigurable matching circuit tuned at six discrete frequencies.

Figure 2 - 6 Photograph of fabricated circuit (16 cm x 25 cm) with 6 independently tuned bands [86, 95].

40

Figure 2 - 7 Measured reflection coefficient of ESHA with switchable matching circuit prototype tuned independently at six HF-licensed bands.

The reconfigurable instantaneous narrowband matching system has the advantage of filtering out-of-band interference and noise such that some of the circuitry in the receiver

(e.g. LPF) may not be needed. It is to be noted that this matching circuit is designed to match ESHA in receiver configuration. For transmit configuration, HF radios may require

TX power upto 100 W to establish long-range communications, which makes the circuit cost ineffective due to numerous lumped components involved. Outdoor field test measurements employing reconfigurable matching network are discussed in section 2.4.

2.3.2. Broadband Transformers

Transformers are often used for wideband impedance transformation compared to narrowband matching which rely on “resonant-mode” lumped component circuits like L- sections, Pi-sections and T-sections. Broadband transformers with reasonable insertion loss (<2 dB) have been employed for 2 – 30 MHz broadband amplifiers [8-9]. Wideband

41 performance of a transformer is mainly determined by its coupling factor. In an ideal transformer, the voltage induced by changing flux in each winding is given as

푉 = 푛 휕∅⁄휕푡 (2.5) where n is the number of turns of winding under construction. As both the primary and secondary winding experience same flux coupling, the ratio of the primary to secondary voltage of transformer can be defined as

푉1⁄푉2 = 푛1⁄푛2 (2.6)

An ideal transformer is a perfectly linear device as the flux density of the core is independent of its permeability. Because ideal transformer has no losses (i.e. no reactive components), the instantaneous power dissipated in the load is equal to instantaneous power entering the transformer, such that

푣1푖1 = 푣2푖2 (2.7)

Using equation (2.6 and 2.7), primary and secondary impedances are related as

2 푍1 = 푉1⁄퐼1 = [푛1⁄푛2] . 푍2 (2.8)

In case of ideal transformers, the impedance ratio only depends on the turn ratio of transformer. In contrast, a practical transformer differs from ideal due to leakage flux

(contributing to leakage inductance), parasitic capacitances, finite magnetizing inductance, losses in windings (copper), core loss (hysteresis and eddy current losses), variation in relative permeability with signal level, dc current (saturation), and temperature dependent core effects. The overall performance of a practical transformer depends on the selection of the magnetic materials (suitable permeability of core material), conductor length or

42 number of turns of winding, and the method of construction. A complete equivalent model of a wide-band transformer is shown in Figure 2 - 8. The losses associated with the conductors in the primary and secondary windings are represented by series resistances R1 and R2, respectively.

Figure 2 - 8 Equivalent circuit model of a wideband transformer [89].

These resistances depict nonlinear behavior, increasing with frequency due to skin effect of the wire. However, for wide-band transformers employing ferromagnetic cores, contribution of this resistive loss in the overall transmission loss is negligible, due to significantly shorter length of wires. The hysteresis and eddy current losses caused by the ferromagnetic material are represented by the shunt resistance 푅푐. These kind of losses are significant in transformers that operate near the ferro-resonance region of the core material and tend to increase with 휔2or even 휔3. The flux in the transformer core that links the two windings is represented by mutual inductance M. The high frequency performance is limited by the leakage flux (i.e. the flux which is lost and does not contribute to mutual coupling), which in turn results in the primary and secondary leakage inductances 퐿푙1 and

퐿푙2. These leakage inductances are practically constant as the leakage flux paths are primarily in air. The capacitances associated with broadband transformers include

43 distributed primary capacitance (퐶11) resulting from the shunt capacitance of the primary winding, distributed secondary shunt capacitance (퐶22), and distributed inter-winding capacitance (퐶12). The mutual inductance M can be determined as a function of primary and secondary magnetizing inductances 퐿11 and 퐿22 by

1⁄2 푀 = 푘(퐿11퐿22) (2.9)

where k is the coupling factor of transformer, and 퐿11 and 퐿22 are related to leakage inductances as

퐿푙1 = 퐿11 − 푛푀 (2.10)

퐿푙2 = 퐿22 − 푀⁄푛 (2.11)

In general, value of n is usually taken to be the turn ratio of two windings of the transformer.

However, a more intuitive and better approach for it is

1 퐿 푛 = √ 11 (2.12) 푘 퐿22

It is to be noted that the magnetizing inductance (i.e. 퐿11) limits the low-frequency performance in practical transformer design, while the high-frequency performance is limited by leakage reactance (휔퐿푙2) [89-90]. For broadband transformer, the relative bandwidth of matched transformer is a function of coupling factor [91], given as

휔퐻⁄휔퐿 = 2/(1 − 푘) (2.13)

Among all the existing broadband transformer configurations, brass tube and bead topology is down-selected for matching of proposed ESHA with improved frequency response and efficiency across a wide operational bandwidth. In this configuration, two or 44 more stacked ferrite toroids are placed side by side and a brass (mon-magnetic) tube is passed through each toroidal cavity (see Figure 2 - 11). Both the tubes are connected at one end to form a single-turn primary. The secondary winding with n turns is wound inside the tubing which reduces leakage flux and improves coupling.

An important guideline in the design of broadband transformers, validated theoretically as well as experimentally in literature, is that the reactance of the secondary winding should be atleast four times the load impedance. This guideline is based on the mathematical reasoning that when the secondary inductive reactance is chosen to be atleast four times the load impedance magnitude, the input impedance predicted by the ideal transformer will be within 3% of its actual value, and with a phase error ≤ 14 degrees [92].

The next step is the selection of ferrite core material. At higher power levels, ferrite cores can experience magnetic flux density saturation which can introduce non-linear operation, and hence can give rise to harmonic generation and considerable loss in the transformer. Therefore, it is necessary to operate in regions where flux density remains well below the saturation level (see eqn. 2.16). The voltage across the input of the transformer carrying an rms current 퐼 and having an inductance 퐿 is given by

푑퐼 푉 = 퐿 = 푗휔퐿퐼 (2.14) 푑푡

Further, using the relation between inductance and magnetic flux, Φ = 퐿퐼

푉 = 푗휔훷 = 푗휔푛퐴퐵 (2.15) where 푛 is the number of turns in the primary, 퐴 is the cross-sectional area of the core in square meters, and 퐵 is the magnetic flux density. The maximum flux density is given as

45

푉_푚푎푥 퐵 = (2.16) 푚푎푥 휔푛푁퐴

where N is the number of cores in a stacked configuration.

Figure 2 - 9 shows the complex permeability of ferrite material in the form of equivalent resistance, reactance and total impedance. A more complete model of an inductor wound around on a ferrite core is shown in Figure 2 - 10. The capacitance (퐶푐) is the parasitic capacitance due to inductor winding. The inductance (퐿푐) corresponds to the core winding, and core loss due to hysteresis is denoted by 푅푐. The second parallel circuit in Figure 2 - 10 is governed by the dimensional resonance phenomenon, contributing to magnetic losses at resonance, as described by E.C. Snelling [94]. Dimensional resonance is same as in a cavity resonator.

Figure 2 - 9 Representation of complex permeability of Fair-rite material 61 in terms of equivalent resistance, reactance and total impedance [93].

46

For this work, NiZn ferrite materials with relative permeability values ranging from

125 to 800 are selected which have their dimensional resonances near 1 GHz, thus far away from region of interest.

Figure 2 - 10 Equivalent circuit model of an inductor wound on a ferrite core. Components with a D subscript are due to dimensional resonance, and with a C subscript are due to the wire wounded on the core [93].

Based on the aforementioned analysis and design guidelines, a broadband transformer is designed and fabricated to match ESHA with following requirements: 3-dB lower cutoff frequency of 3 MHz, 3-dB higher cutoff frequency of 30 MHz, load impedance of roughly 25 Ω, and source impedance of 50 Ω. The measured input impedance of ESHA depicts capacitive reactance below the resonant frequency, this makes the trivial design of broadband transformer difficult. Apart from impedance transformation, an efficient transformer design can compensate for the capacitive reactive part of antenna to some extent, thus, increasing the system efficiency compared to no matching case. In order to evaluate the performance of transformer broadband matching for ESHA, several transformer designs are evaluated in this work, investigating the performance in terms of loss, magnetic material (i.e. permeability), and inductive reactance. For construction

47 purposes, 0.76 mm thick brass tube with outer-diameter 12.7 mm is used as single-turn primary winding and 2.5 mm copper braided wire with 16 strands is used for secondary winding. Firstly, a broadband transformer design is taken into consideration with secondary winding reactance taken as eight times the load impedance of ESHA. Inductance of secondary winding required to achieve reactance of 200 ohm at lowest operating frequency is calculated as 10.61 μH. Fair-Rite ferrite core material 43 of relative permeability 800 is selected for the desired operation. The toroid model used is 5943000501 (퐴퐿=885 nH per turn) with an outer diameter 21 mm, inner diameter 13.2 mm, height 11.9 mm, effective path length 52 mm, and area of transversal section 46 푚푚2. The number of turns for the secondary required to produce optimum inductance with respective toroid is calculated as

퐿푠 2휋푟 퐿푆 푁푠 = √ = √ (2.17) 휇퐴 퐴퐿 where A is the area of transversal section of toroidal core, r is the mean radius of toroid, and 퐴퐿 is the inductance factor specified by the manufacturer. For high power applications, stacked toroidal cores are preferred compared to a binocular core. Also, number of turns can be reduced by selecting ferrite material with high permeability. It should be noted that the value of inductance factor (퐴퐿) can be increased to approximately n times by stacking n ferrite cores. Further, in order to maintain a relative bandwidth of 10:1, the coupling coefficient required (based on equation 2.13) is 0.8. This is accomplished using brass-tube bead topology with stacked cores, validated using numerical inductance matrix computation using ANSYS Maxwell magneto-static solver. Figure 2 - 11 shows the schematic of fabricated transformer with 2.5 turns secondary winding and one-turn primary winding (i.e. connected brass tube). Figure 2 - 12 depicts the performance of the fabricated

48 transformer (ferrite 43) in terms of insertion loss. To demonstrate the overall efficiency of matched ESHA system with fabricated broadband transformer, a two-port model of measured ESHA with simulated radiation efficiency is obtained [96].

Figure 2 - 11 Fabricated prototype of broadband transformer (ferrite type 43) [95].

Figure 2 - 12 Insertion-loss performance of fabricated 43 broadband transformer (ferrite type 43).

49

Further, a complete equivalent circuit model for the proposed transformer is developed with the help of measurement and full-wave EM simulation [89-91] as shown in Figure 2 - 13. Several parameters such as self and mutual inductances, flux leakage, and core loss can be approximated with the help of ANSYS Maxwell magneto-static/transient simulations. Table 2 - 1 gives the list of parametric values for the respective equivalent circuit model of the proposed transformer. Figure 2 - 14 shows the performance of ESHA matched system with fabricated transformer, and its extracted equivalent circuit model.

Both are observed to be in close agreement, thus validating the equivalent circuit model.

Figure 2 - 13 Extracted equivalent circuit model of fabricated broadband transformer (from ferrite material 43).

Table 2 - 1 Extracted equivalent circuit parameters

Parameter Symbol Value Primary series resistance (conductor losses) R1 24.24 Ω Secondary series resistance (conductor loses) R3 6.91 Ω Primary shunt capacitance C1 17.19 Pf Secondary shunt capacitance C2 5.32 pF Inter-winding capacitance C3 0.249 pF Shunt resistance (core losses) R2 989.56 Ω Primary leakage inductance L1 0.74 uH Secondary leakage inductance L3 0.41 uH Mutual inductance L 30.73 uH

50

Figure 2 - 14 Performance agreement between measured and extracted equivalent circuit model for (a) return loss, (b) overall efficiency.

Similarly, another broadband transformer is proposed with secondary winding reactance taken as four times the load impedance of ESHA. Secondary winding inductance required to achieve reactance of 100 ohm at lowest operating frequency is calculated as

5.31 μH. To achieve the respective inductance, low-permeability ferrite toroid (Fair-rite

5952020601) with inductance factor (퐴퐿= 151 nH/turn) is utilized to fabricate a broadband transformer with 2.42 secondary winding turns, comprising of six stacked pairs of toroidal cores (see Figure 2 - 15 (a)). Also, as specified by manufacturer, type 52 material has a loss factor (푡푎푛훿/휇) of 45e-6 (at 1 MHz) compared to 250e-6 for material 43.

51

Figure 2 - 15 Photograph of fabricated broadband transformer with (a) ferrite 52 material, (b) ferrite 61 material.

Furthermore, another broadband transformer configuration is investigated employing loss- loss and loss-permeability ferrite material (fair-rite type 61) with a loss factor of 30e-6 at

1 MHz. Fair-rite toroid model (5961000501) with inductance factor (퐴퐿= 135 nH/turn) is used. This broadband transformer consist of around 2.8 turns secondary winding passing through brass tubes surrounded by four stacked pairs of toroidal cores (see Figure 2 - 15

(b)). Figure 2 - 16 demonstrates the performance comparison in terms of return loss and total insertion loss of the matched ESHA with three different fabricated broadband transformers. Based on the desired sub-bands of operation within HF-band (3-30 MHz), one prototype outperforms the other. Even though the type 43 ferrite transformer exhibits better return loss compared to other two prototypes (i.e. type 52 and 61), its overall efficiency is poor compared to other configurations. It can be ascertained that improvement in reflection coefficient is due to loss introduced by matching network. In terms of overall

52 system insertion loss, ferrite 61 based transformer exhibits better performance beyond 7

MHz.

Figure 2 - 16 ESHA matched system performance comparison with three fabricated broadband transformers with reference to (a) return loss, and (b) overall efficiency.

However, for lower band ranging from 4 MHz to 7 MHz, ferrite 52 based transformer shows improvement in overall efficiency. Ferrite broadband transformers can be employed in high-power HF communications, primarily due to low-cost and simplicity. This work focuses to provide a reliable HF-communication over the entire HF-band, thus,

53 performance of ferrite 52 based broadband transformer matched system will further be evaluated with the help of radio communication measurements, discussed in section 2.4.

2.3.3. Active broadband non-Foster matching circuit

According to Foster’s reactance theorem, the reactance of a passive lossless network always monotonically increases with frequency [97]. Figure 2 - 17 shows that the reactance of conventional capacitor and inductor have positive 푑푋/푑휔. In contrast, negative capacitor and inductor show negative 푑푋/푑휔, thus, disobeying the Foster’s reactance theorem. These non-Foster elements, i.e. the negative capacitor or negative inductor, can be implemented with active devices. Non-Foster circuits can be employed to overcome the Chu’s limit [2] and achieve broadband electrically small antennas [14-15],

[18].

Figure 2 - 17 Reactance behavior of negative capacitance and negative inductance (non-Foster) compared with normal positive capacitance and inductance that obey Foster’s reactance theorem [100].

Negative-image modeling [18] is a common approach to realize non-Foster matching network for broadband matching of an electrically small antenna. These negative impedance converters (NICs) and invertors (NIIs) apply positive feedbacks to manipulate

54 the voltage-current relation at the output, hence, are easily prone to instability issues, making them quite challenging to implement in practical applications.

Figure 2 - 18 The schematic of different ways of realizing non-Foster elements: a) a cross-coupled pair of transistors; b) an operational amplifier with positive feedback; c) a negative resistor based NII (also named as j-transformation) [100].

Figure 2 - 19 Schematic of a 2m-long ESHA with non-Foster circuit (~ -40 pF) to cancel the large capacitive input reactance for broadband matching.

Three existing techniques commonly used in literature to realize NICs and NIIs are positive-feedback operational amplifier, cross-coupled pair of transistors (e.g., Linvill’s

NIC [98]), and negative resistor (Verman’s NII [99]) as shown in Figure 2 - 18. In order to achieve wideband matching of ESHA within the desired HF-band, a -40 pF negative

55 capacitor is proposed to cancel the large capacitive reactance of ESHA below the self- resonant frequency as shown in Figure 2 - 19.

Figure 2 - 20 The circuit schematic of the non-Foster matching network [100].

A stable negative capacitor (~ -40 pF) based on Linvill’s negative impedance converter (NIC) is designed, fabricated and tested [100-101]. Normalized determinant function (NDF) method [102-103] is used for the stability analysis of the non-foster matching network with multiple-feedback system (Figure 2 - 20). The proposed non-Foster circuit utilizes a floating Linvill’s negative impedance converter for transforming the internal positive capacitor (퐶푖푛푡) and resistor (푅푖푛푡) into their negative counterparts. The emitters of the cross-coupled transistors are biased using current source transistors. The transmission-lines in the feedback loop, despite being short, can make the circuit unstable due to oscillations. Therefore, small resistors (푅푠푡푏) are inserted into the cross-coupled feedback loops to stabilize the circuit.

Figure 2 - 21 shows the photograph of a fabricated circuit using stabilization resistance

(푅푠푡푏 = 10 Ω) and internal resistance (Rin = 5 Ω) to compensate loss.

56

Figure 2 - 21 Photograph of fabricated circuit [86], [95], [100].

The proposed non-Foster circuit is loaded with internal positive capacitor (퐶푖푛푡) of 39 pF. Figure 2 - 22 depicts the comparison of measured and simulated input impedance for the non-Foster circuit. Based on the measured reactance plot, a negative slope is observed as a function of frequency which denoted a wide-band negative capacitance (-42 pF at 15

MHz). The simulated and measured input reflection coefficients (푆11) of the helical antenna with and without non- Foster matching circuit are demonstrated in Figure 2 - 23. A good agreement between simulation and measurement is noticed except of a few MHz frequency shift. The non-Foster matching shows an improvement of 푆11 near 7 MHz. It is also observed that the reflection coefficient magnitude is greater than unity near 5 MHz. Even though we have improved return loss, but this does not guarantee improvement in overall gain. Improvement in reflection coefficient is also possible from the loss introduced by matching network. Thus, a field test must be conducted to examine the improvement of the received signal strength by employing non-Foster matched system.

57

Figure 2 - 22 (a) Simulated and measured output impedance of the non-Foster circuit, and (b) the retrieved negative capacitance.

Figure 2 - 23 The simulated and measured S11 of the ESHA w and w/o non-Foster broadband active matching network.

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2.4. Measurements

2.4.1. Outdoor Field Measurements (Near-field)

The purpose of this experiment is to analyze the performance of the electrically- small helical antenna (ESHA) in terms of received signal power strength with proposed narrowband and broadband matching networks for HF-band communications. Figure 2 -

24 illustrates the complete experimental setup. A spectrum analyzer (SA) is connected to the receiver antenna (i.e. ESHA) under test to measure the received power and monitor the interference in the background. A continuous wave signal with output power 16 dBm is transmitted from the signal generator at the transmitter end. A commercial-off-the-shelf antenna (Alpha-EzMillitary) is used as transmitter antenna. The distance between TX and

RX antenna is fixed to be 54 m (about 0.5 to 5 λ from 3 to 30 MHz). Therefore, for some of the lower frequency bands, it is not in the far field. Buildings, nearby automobiles and metallic shelters may affect the field patterns and matching of the antennas at low frequency. However, the performance comparison results with three matching circuits would still be significant to estimate the received power improvement by one over the other.

59

Figure 2 - 24 (a) Test setup schematic with top view of test environment, (b) photographs depicting real-time testing of electrically-small helical antenna (ESHA) at receiver end with commercial antenna at transmitter end.

Figure 2 - 25 plots the received power spectrum for RX antenna (i.e. ESHA) with narrowband electronically switched LC matching network, broadband un-un transformer

(type 52), and active broadband non-Foster matching circuit. The large spectral fluctuation comes from the multipath interference. The performance of the reconfigurable matching circuit is found to be better than the transformer matching in bands at 14, 21 and 29 MHz with a minimum of 2-3 dB improvement.

Moreover, about 3-20 dB received signal power enhancement by non-Foster matching circuit is observed in a range of 3-21 MHz compared to other cases. Further, to assess the qualitative performance of the three independent matching networks, far-field voice data experiments are performed as discussed in the following section.

60

Figure 2 - 25 Received power strength comparison of the ESHA matched system with three test cases: broadband non-Foster matching, broadband transformer and narrowband electronically switched LC matching network (highlighted).

2.4.2. Real Voice-Data Communication Measurements (Far-Field)

The purpose of this experiment is to analyze the signal integrity and approximate

SNR for all three cases discussed earlier. The line of sight distance between the TX

(commercial AlphaEz antenna) and RX (ESHA) antenna is 650 m (about 6.5 to 65 λ from

3 to 30 MHz). The experiment setup is illustrated in Figure 2 - 26. At the transmitter side, voice signals (SSB modulation) are transmitted with 50 W power using a FLEX-6500 software-defined radio at licensed HF-band frequencies of 4.035 MHz, 7.021 MHz, 13.983

MHz, 17.615 MHz, 21.0175 MHz and 29.935 MHz.

The receiver setup is largely based on the setup proposed by Ettus Research [104].

It consists of the helical antenna, matching circuit, low pass filter and low noise amplifier,

61 all connected via coax cable. The low noise amplifier is then connected to a USRP N200 with a “BasicRX” daughterboard, which digitizes the signal and transmits it to a PC hosting

GNU Radio. A single side band (SSB) flow graph for GNU Radio, also from the Ettus application note, is used to process the incoming signal. The flow graph can be adjusted to operate as either an upper or lower side band (i.e. USB or LSB) receiver. It also creates a

GUI that allows a user to observe and tune to different frequencies on the spectrum. In most of the tests for all the bands and matching circuits, we were able to hear quite stable and clear voice signals. The measured SNR values for ESHA matched system with three different matching networks are listed in Table 2 - 2. It is observed that the transformer and reconfigurable LC matching networks have comparable performance.

Figure 2 - 26 (a) Transmitter Configuration, (b) Receiver Configuration for voice- data communication measurement involving three matching prototypes.

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Table 2 - 2 Measured SNR comparison for matching circuits Receiver: GNU software-defined radio (SNR dB) Broadband Narrowband Broadband Frequency Non-Foster Tunable LC Transformer (MHz) Matching Matching Matching 4.035 13 15 22.5 7.021 25 32 33 13.983 50 67 62 17.615 60 65 65 21.0175 60 62 65 29.935 58 57 64

It is interesting that although the non-Foster matching case has the highest received power as noticed in section 2.3.1, the SNR performance is not superior due to increased noise floor (noise figure of the active circuit) which is not considered in the design at this stage.

In addition, an experiment to test the receiver setup’s ability to relay long-range HF communications is performed with ESHA matched system in RX configuration (see Figure

2 - 26 (b)). Figure 2 - 27 shows the approximate locations that could be observed with the setup, where blue, black, and red paths represent the usage of the broadband transformer, broadband non-Foster matching, and reconfigurable LC circuit, respectively. These locations are reported by either hearing the user state it during the transmission or searching for their call signs in the FCC database. It is worth noting that the figures are not an accurate comparison of the ranges as data is collected at different instances, making it unable to authoritatively assert whether one matching circuit outperforms the others. Such a comparison also depends on the users’ activity of each instance as well. Thus, the figure is only indicative of general performance of matched ESHA system in receiving long-range communications.

63

Figure 2 - 27 Pictorial depiction of locations observed for helical antenna with three different matching circuits.

Our initial design of the non-Foster matching circuit did not consider the noise performance. It has been studied that the SNR improvement by a general matching circuit depends on the noise temperature of receiver system (Trx), the mismatch loss of the un- matched and matched antenna (휏푎 and 휏푚), and the gain of the matching circuit (Gm) [105].

Therefore, for a non-Foster matching circuit, the condition of SNR improvement is that the noise temperature Tm of the non-Foster circuit must be smaller than the margin,

휏푚 1 푇푚 < 푇푟푥 ( − ) (2.18) 휏푎 퐺푚

Based on Eq. (2-18), approximate calculation of required maximum noise figure margin for our helical antenna matching system (assuming 5 dB / 8 dB noise figure of receiver system) is carried out. It is estimated that the noise figure of the non-Foster circuit needs to be smaller than 10-40 dB (see Figure 2 - 28) to achieve SNR improvement [106-107]

64 which should be achievable. In practice, the noise temperature of the non-Foster circuit can be reduced by carefully selecting the transistors, biasing currents and circuit design.

Other types of circuit configuration of negative impedance converters or inverters can also be used to implement the non-Foster circuit.

50 NF = 5dB rx 40 NF = 8dB

C rx

I

N

r

o

f 30

e

n

i

g

r

a 20

m

F

N 10

0 0 5 10 15 20 25 30 Frequency (MHz) Figure 2 - 28 Estimated noise figure (NF) margin for ESHA matched system with non-Foster circuit for SNR improvement.

2.5. Summary

In this chapter, an electrically-small helical antenna (ESHA), about 2 m long, is proposed as a compact practical solution to long-range HF communications. The design, fabrication and testing of active and passive matching networks is carried out effectively for narrowband, and broadband matching of ESHA. Each of the three matching schemes has its own advantages and disadvantages. The non-Foster active matching has the benefit of broadband instantaneous matching as well as highest received power. However, since it is an active circuit incorporating transistors, care needs to be taken in designing non-

Foster matching circuit to maintain relatively low noise figure so that the system SNR

65 remains low. In contrast, transformer matching exhibits instantaneous broad bandwidth and improved performance in terms of signal-to-noise ratio. The reconfigurable narrowband LC matching circuit has the advantage of filtering out-of-band interference and noise so that some of the circuitry in the receiver (e.g., the LPF) may not be necessary.

Signal integrity and intelligibility has also been analyzed with the help of radio log measurements across the globe.

From the measurements and industry perspective, it can be asserted that broadband transformer can prove to be an excellent candidate in terms of instantaneous broadband capability, adequate power handling capability, circuit simplicity and cost. Also, efficient low-noise stable non-Foster matching can be employed to effectively cancel the negative reactance of electrically small antennas, thereby, providing significantly improved performance compared to non-matching case.

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Chapter 3. Broadband conformal dual-polarized Vivaldi array for feeding Luneburg lens

3.1. Graded index 3-D Luneburg lens

Electromagnetic (EM) structures with spatially-continuous variations in their refraction index (n) are known as graded index (GRIN) components. Compact effective

EM components can be adopted with small, continuous variation of index as compared to traditional discontinuous index changes [108]. Luneburg lens is a GRIN component which can be employed as antenna for wide-angle beam scanning due to its high gain, broadband behavior and multiple beam capability. It exhibits superior performance in contrast to conventional lenses made from non-varying materials. A plane wave incident on the lens focuses at diametrically opposite point on the surface of the lens as shown in Figure 3 - 1.

The refractive index (n) distribution of an ideal spherical Luneburg lens, made with non- magnetic material (휇푟 = 1) is given by Equation (3.1) [109]:

2 2 푛(푟) = 휀푟(푟) = 2 − (푟⁄푅) (3.1) where 휀푟 is the relative permittivity, 푅 is the radius of the lens and 푟 is the distance from the respective spatial point to the center of the sphere.

 Figure 3 - 1 Standard Luneburg Lens Cross-Section [110].

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From the manufacturing perspective, achieving continuously varying radial permittivity profile for a spherical lens is hardly possible. The discretized permittivity profile can be achieved in concentric onion-like spherical layers of thin molded hemispherical layers, which induces fabrication in terms of acceptable permittivity and shape accuracy. Moreover, care has to be taken to avoid air gaps during assembly of this lens [111-112]. Other methods have also been reported in literature for fabricating lenses, however, suffer from intrinsic and fabrication limitations [113-115].

To overcome the challenges associated with fabrication and cost, we employ additive manufacturing technique known as polymer-jetting rapid prototyping to realize a

3-D broadband Luneburg lens [116]. By controlling the filling ratio of a polymer / air based unit cell, the required graded index profile can be achieved. Based on the distance of each unit cell from the center of the sphere, effective permittivity of each unit cell is realized independently. Further, a 12 cm-diameter lens is designed, printed and characterized for

X-band (8.2 – 12.4 GHz) operation using commercially available rapid-prototyping machine [25]. Figure 3 - 2 shows the prototype of the 3D printed lens consisting of discrete polymer cubes with different sizes to control the constant dielectric distribution. Thin polymer rods are used to support the whole structure and connect all the cubes together

(see Figure 3 - 2 (b)). In addition, schematic of the cubic unit-cell with overall dimension of 5 mm and a dielectric cube with a variable dimension (b) is also depicted. Based on several fabrication and measurements, approx. average permittivity can be calculated from polymer filling ratio by the relation: -

휀푟 = 휀푝. 푓 + 휀표. (1 − 푓) (3.2)

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Figure 3 - 2 (a) Front view of Luneburg lens ANSYS HFSS prototype, (b) Pictorial view of thin-rods connecting all the discrete cubes together for a robust mechanical support structure [25].

where 휀푝 represents polymer material permittivity, and 푓 is the polymer filling ratio of the unit cell. The relation between spatial polymer cube size and the desired permittivity is extracted using fitted exponential function [108] as

푏 = 5.5593 − 590974푒−휀푟⁄0.07958 − 9.54823푒−휀푟⁄0.95537 (3.3)

The commercially available objet printer has a droplet size of 42 μm x 42 μm x 16 μm, which can enable fabrication of Luneburg lens below 100 GHz. Also, large structures with a size of up to 30 cm x 30 cm x 30 cm can be printed. In agreement to theory, the gain of the Luneburg lens antenna increases with the increasing of the lens diameter and the HPBW of the antenna decreases with the increasing of the diameter. In view of this, a 24 cm diameter Luneburg lens has been realized for a much broader frequency range from 4 GHz to 20 GHz which has been tested using an X-band and Ku-band waveguide [108], as shown in Figure 3 - 3. 69

Figure 3 - 3 Polymer jetting printed Luneburg lens (24 cm Diameter)

3.2. Feed network for 3-D printed Luneburg lens

3.2.1 Introduction and Motivation

Advanced wireless communication systems require high performance wide-angle beam scanning with minimum pattern deformation and broadband behavior. Many potential areas of application such as satellite communication, air-traffic control, air-based tracking and surveillance, marine navigation, and automotive radar would benefit from a lighter, lower-cost, electronically steered-beam antenna which removes the need for using a gimbal mechanism or phase shifters. The Luneburg lens antenna system has the potential for multi-beam highly-directive steering [109]. It has an advantage over conventional reflector or phased array system, as there is no requirement for mechanical steering or an integrated phase-shifting setup. In addition, conventional phased arrays suffer from beam pattern deformation for large scan angle (≥ ±60 degree in both azimuth and elevation planes), resulting in lower gain and higher side lobes.

70

Figure 3 - 4 Schematic of (a) multiple-beam Luneburg lens antenna, (b) scanned beam Luneburg lens antenna [117].

In contrast, Luneburg lens has the capability to produce highly directive beams with low sidelobe levels over broadband for entire 360 degree scan [118-119]. Figure 3 - 4 shows the basic geometry of a multiple beam, and a switched/scanned beam Luneburg lens antenna system. Theoretically, Luneburg lens reveals best performance in terms of maximum directivity and improved side lobe level when the phase center of the lens feed is aligned with the focal point of the Luneburg lens [117]. Hence, the feed antenna should have a stabilized phase center over the frequency range of interest.

In this chapter, miniaturized dual-polarized conformal Vivaldi array is proposed for feeding 3-D printed Luneburg lens to achieve highly-directive multiple-beams for practical wireless applications (3 – 6 GHz band). The constraints for the design of broadband feed array network for spherical Luneburg lens antenna include: (1) conformal geometry with phase center of each element coinciding with lens focal point, (2) linear-polarized

71 capability (both vertical and horizontal), (3) reduced backward radiation and (4) minimum

6 dB impedance bandwidth (for 3 – 6 GHz).

3.2.2 Vivaldi Antenna Unit cell

The flared-notch (Vivaldi), introduced by Gibson in 1979, is a widely known travelling-wave radiator in modern ultrawideband (UWB) phased arrays [120-122]. Due to its robust design, and economical manufacturability, it has been greatly employed to create inexpensive printed-technology large arrays [122-123]. Over the past 30 years, several variations to traditional flared-notch designs have been proposed such as balanced antipodal Vivaldi antenna (BAVA) [124], reduced-height BAVA [125], and the bunny ear

[126]. In contrast to PCB designs, all-metal flared notch radiators have also been widely utilized in different applications [127-129]. Further, tapered slot antennas have been investigated for their stabilized phase center over wide range of frequency. Based on the

Luneburg lens feeding requirements discussed in section 3.2.1, a compact all-metal dual- polarized flared-notch radiator array, also known as Vivaldi antenna array is engineered taking into account base design proposed by Kindt et al. [130] and Yan et al. [131].

The first step in the design procedure is to develop a Vivaldi unit cell in a dual- polarized configuration such that it exhibits a stable phase center close to its outer surface

(i.e. flared-end) over the desired frequency regime (3 – 6 GHz). According to Kindt’s design [58], the length and width of Vivaldi element at the highest desired operating frequency should be within four wavelengths and half a wavelength, respectively. The width of the element is restricted by the Nyquist sampling criteria to avoid undesirable grating lobes while the length-to-width ratio controls the total bandwidth.

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Figure 3 - 5 Schematic of exponentially-tapered Vivaldi unit element [132].

Table 3 - 1 Vivaldi unit cell geometry parameters Description Parameter Value (mm) Element length L 33.75 Element width W 13.5 Aperture width 퐴푊 9.13 Tapered slot width 푇푊 1.397 Feed slot width 퐹푊 0.627 Cavity-to-taper length 퐿퐹 4.40 Cavity width 퐶푊 2.89 Cavity length 퐶퐿 5.94 Cavity offset 퐶표 3.09 Feed offset 퐹표 1.65

Figure 3 - 5 shows the proposed design of an all-metal exponentially-tapered

Vivaldi unit element. The element, made of aluminum, is about 0.68 λ long, 0.27 λ wide and 0.09 λ thick at highest operating frequency (i.e. 6 GHz). The feed design consists of a direct coax-to-slot-line transition to reduce the design complexity and ease the fabrication process. Table 3 - 1 details the parameters of the unit cell. The coordinates of the exponentially-tapered antenna can be defined by following equations: -

푦 = 푐1 ∗ e푅푥 + c2 (3.4)

푅푥2 푅푥1 where, 푐1 = (푦2 − 푦1)⁄(푒 − 푒 ) (3.5)

푅푥2 푅푥1 푅푥2 푅푥1 푐2 = (푦1. 푒 − 푦2. 푒 )⁄(푒 − 푒 ) (3.6)

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The points (푥1, 푦1) and (푥2, 푦2) are the end points of the flare and R is the variable that controls the rate of opening. Based on the parameters listed for Vivaldi unit cell, tapered slot curve equations for left-side open (eqn. 3.7), and right-side open flaring (eqn. 3.8) are calculated as

푦 = −2.8335푒0.03푥 + 15.9342 (3.7)

푦 = 2.8337푒0.03푥 + 4.0625 (3.8)

Two crucial parameters that control lower-end bandwidth in this design are the size of the slot-line cavity and its position. Further, to counteract the effect of impedance reactance over the frequency band, slot-line region profile is adjusted. Symmetry in cavity fields should be maintained, if possible, by connecting the slot-line near the center of cavity.

Otherwise, feed point position can be optimized to partially cancel the resonances occurring due to shifted slot-line insertion relative to the cavity center. Figure 3 - 6 (a) shows the schematic of unit cell configuration of a dual-polarized all-metal Vivaldi antenna consisting of four independent structures interlocked together. To meet the phase center requirements for feeding Luneburg lens, and to maximize the number of elements surrounding lens, aperture width to depth ratio of Vivaldi dual-polarized unit cell configuration is optimized in accordance with other slot line-region parameters to achieve

3 – 6 GHz bandwidth (RL ≥ 6 dB). Figure 3 - 7 shows the simulated return loss performance of two horizontal-polarized (H-pol.) elements and two vertical-polarized (V- pol.) elements of the dual-polarized all-metal Vivaldi unit cell. Based on conical transmission-line theory, position of phase center for Vivaldi antenna can be located on the symmetry plane which shifts along the axis [133] (see Figure 3 - 6 (b)). For this work, distance to the phase center from a relative origin is calculated using slope method [134]. 74

Figure 3 - 6 (a) Schematic of dual-polarized Vivaldi unit cell (b) Phase center determination for one element along z-axis with d ranging from 18 to 36 mm.

Figure 3 - 7 Simulated return loss performance of different elements of a dual- polarized Vivaldi unit cell geometry.

Both the E-plane (XZ-plane) and H-plane (YZ-plane) variation of phase center position is studied for ±30 degree broadside with minimum phase tolerance of 5-10 degrees using far-field characteristics for peak-to-peak variation. The simulated phase

75 center variation with frequency for both E and H planes is shown in Figure 3 - 8. It is observed that the Vivaldi element is comparatively more stable in the H plane, varying within approx. 5 mm, but has a significant variation in the E-plane (about 8 mm), that agrees with the results reported in [135]. Min et. al. has evaluated the tolerance of feeding position on far-field pattern of Luneburg lens fed with X-band waveguide [108]. It was seen that the gain of lens antenna was almost same for waveguide positioned within 10 mm. However, relative side love levels may increase with the displacement of phase center from the focal point of lens. For the X-band waveguide fed lens, it was seen that the relative side-lobe level increased by 5 dB when the waveguide was displaced by 10 mm. Thus, the proposed Vivaldi feed geometry will be suitable for feeding Luneburg lens across H-plane

(YZ) with reasonably low relative side-lobe levels.

Figure 3 - 8 Phase center variation with frequency for one element of dual-polarized Vivaldi unit cell, where E-plane corresponds to XZ-plane and H-plane corresponds to YZ-plane.

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3.2.3 Planar dual-polarized 3 x 3 Vivaldi array

Until recently, computational methods for the accurate analysis of wideband

Vivaldi arrays were not employed for extensive parametric study. Now, with the availability of powerful computers, full-wave electromagnetic (EM) simulations is carried out to evaluate the proposed design prior to developing prototypes and to improvise performance, thereby investigating key design parameters. Further, modern analyses can anticipate irregularities that limit array performance such that they can be avoided with careful modifications of the antenna design. For this work, finite-element method (FEM) based full-wave EM simulation software, ANSYS HFSS is used to study the predicted theoretical performance of all-metal element design based on an infinite cell (Floquet) analysis [136]. In addition, finite array domain decomposition is carried out to accurately model the effects of mutual coupling and edge truncation in a finite array.

Figure 3 - 9 (a) unit cell schematic for infinite-array simulation, (b) finite-array 3 x 3 schematic simulation.

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Figure 3 - 10 Simulated reflection coefficient for dual-polarized planar Vivaldi.

Finite element boundary integral (FEBI) enhancements are used to precisely characterize finite array behavior. Figure 3 - 9 shows the simulation setup for both infinite, and finite dual-polarized all-metal Vivaldi planar array. It is well known that the infinite array approximation holds only for arrays that are large in terms of wavelengths [137]. The size of finite planar 3 x 3 dual-polarized Vivaldi array reported is about 0.81 λ x 0.81 λ at

6 GHz, which is significantly small to have a tight agreement between infinite and finite array simulations. Figure 3 - 10 shows the simulated return loss performance for the infinite, and finite array prototypes.

The aforementioned infinite/finite planar array simulations are carried out using lumped port excitation. In order to have a good agreement between simulated and proposed geometry, explicit array analysis is performed for 3 x 3 dual-polarized planar Vivaldi array fed with extended-Teflon SMA connectors (see Figure 3 - 11). It is noted that only one element is excited at a time in the simulation with all other elements terminated in 50 ohm loads for matching purposes.

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Figure 3 - 11 (a) Cross-sectional view, (b) bottom-view of dual-polarized 3 x 3 Vivaldi array (44.87 x 44.87 x 33.75 mm) with 12 H-pol. and 12 V-pol. elements [132].

To analyze the effect of truncation for finite dual-polarized array, it is necessary to anayze s-parameter performance of all the elements, particularly edge elements. Return loss performance for the proposed 3 x 3 planar Vivaldi array (fed with SMA connectors) is reported for cental and edge elements for both polarization (see Figure 3 - 12 (a)).

Radition performance investigaton is also necessary for minimum pattern distortion and high efficiency for integration with Luneburg lens.

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Figure 3 - 12 (a) Return loss performance of a planar 3 x 3 dual-polarized all metal Vivaldi array fed using SMA connectors, (b) Simulated radiation patterns for V-pol. center element at different frequencies in both E and H planes.

Radiation performance for both E-plane (XY plane) and H-plane (YZ plane) of the proposed 3 x 3 planar dual-polarized array for central V-pol. element is reported in Figure

3 - 12 (b).

3.2.4 Conformal dual-polarized Vivaldi feed array for lens (30 cm diameter)

High-directional, narrow beam radiation pattern with lower side lobe level is recommended for applications such as radar tracking and detection where jammer tries to interfere with side-lobe patterns, and telecommunication system where it is necessary to have maximum radiation in service region with shaped-pattern beam by base-station to increase frequency reuse factor and reduced pattern in the interference zone. Phased array technology is often employed to generate high gains and controllable antenna patterns.

However, there are challenges/limitations that still needs attention such as scan angle

80 limitation in azimuth as well as elevation plane, pattern deformation with different scan angles, stringent phase shifter requirements, high cost and complexity.

In this section, we demonstrate a multi-beam/scanned-beam prototype for the 3-D spherical Luneburg lens. In view of this, an array of all-metal dual-polarized Vivaldi antenna arranged in a manner to conform to a portion of the outside surface of Luneburg lens (30 cm dia.) is proposed based on the principle of planar dual-polarized Vivaldi array discussed in earlier section. It is an important criterion for single/multiple feeds to have their phase center close to the lens focal point, particularly within permissible limit. Figure

3 - 13 shows the design of proposed 53 element conformal dual-polarized Vivaldi-array consisting of 4 x 8 H-pol. elements and 3 x 7 V-pol. elements. H-pol. elements are rotated

10 degrees apart in horizontal plane to cover 72.5 degrees azimuth, and 5 degrees apart in vertical plane to cover 16.45 degrees elevation w.r.t. a 30 cm-diameter lens.

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Figure 3 - 13 (a) Front view, (b) back view, (c) simulation setup of the conformal 53 element dual-polarized Vivaldi array for feeding 30 cm dia. Luneburg lens [132].

Azimuth element spacing (i.e. angular rotational distance) is fixed to 10 degrees such that different elements along the horizontal plane can be excited to have multiple highly- directional narrow beams from 3 – 6 GHz.

Further, to evaluate the performance of 30 cm dia. Luneburg lens with the proposed conformal dual-polarized feed network, H-plane lens radiation performance for middle H- pol. element (colored red) and middle V-pol. element (colored green), as highlighted in

Figure 3 - 13 (b), is reported at discrete frequencies in Figure 3 - 14. Table 3 - 2 lists the radiation performance characteristics in terms of peak gain (dB), HPBW (deg.), and relative side-lobe levels at discrete frequencies. Both the gain and directivity increases with frequency due to increase in effective aperture size, as stated in literature.

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Figure 3 - 14 Simulated H-plane radiation patterns of Luneburg lens (30 cm dia.) fed with conformal Vivaldi array utilizing central (a) H-pol. element (XZ-plane at 흓 = ퟎ deg.), (b) V-pol. element (XY-plane at 휽 = 90 deg.).

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Table 3 - 2 Simulated gain, HPBW and side-lobe level (30 cm lens) Frequency V-pol. Element Excitation Relative Side-lobe Gain (dB) HPBW (deg) level (dB) 3 GHz 16.99 19.64 16.55 4 GHz 19.89 14.49 15.26 5 GHz 21.24 11.63 16.5 6 GHz 23.06 9.68 16.6

Frequency H-pol. Element Excitation Relative Side-lobe Gain (dB) HPBW (deg) level (dB) 3 GHz 15.42 19.44 14.46 4 GHz 18.38 14.72 16.1 5 GHz 20.91 11.67 17.21 6 GHz 23.41 9.43 15.8

The simulated gain of the (30 cm dia.) lens at 3 GHz for V-pol. and H-pol. element is 16.99 dB and 15.42 dB, respectively. At 6 GHz, the simulated gain for V-pol. and H- pol. element is 23.06 dB and 23.41 dB, respectively. The HPBW for V-pol. element decreases from 19.64 degrees at 3 GHz to 9.68 degrees at 6 GHz. For H-pol. element,

HPBW decreases from 19.44 at 3 GHz to 9.43 degrees at 6 GHz. It is also noticed that there is comparatively increased loss of the lens at higher frequencies, which can attributed to the material loss. A reasonable relative side-lobe levels, about 16 dB is observed for H- pol./V-pol. element at 6 GHz, which is about 4 dB lower than the lens simulated with waveguide WR-159. This is attributed to the displacement of phase center position from the aperture tip of the conformal array element.

Further, multiple beams (10 degrees apart) emanating from Luneburg lens (30 cm dia.) for all the V-pol. elements in the row/slice 2 (see Figure 3 - 13 (b)), excited one at a time with all other elements terminated in matched loads, are shown in Figure 3 - 15.

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Taking into consideration the effects of mutual coupling, simultaneous elements can also be excited, such that the active VSWR performance is within permissible limits. In this type of array, mutual coupling between collinear, parallel and cross-coupled elements needs to be investigated to employ the system for applications which require simultaneous multiple beams, both same and different frequencies. However, apart from reasonable relative side-lobe level performance, this 53 element conformal feed array cannot produce simultaneous beams for adjacent V-pol. column elements, and nearest diagonal V-pol and

H-pol elements, since the angular separation is significantly less than the HPBW (even at

6 GHz). Taking into account the shortcomings of this conformal dual-polarized feed network design in terms of performance and potential fabrication techniques, we propose a more robust conformal feed array prototype in the next section.

Figure 3 - 15 Simulated H-plane (XY-plane at theta ranging from 60 to 120 deg.) multiple beams of Luneburg lens (30 cm dia.) for all V-pol. elements (middle slice 2) at 6 GHz (one elements is excited at a time with all other elements terminated in matched loads). 85

Instead of 30 cm diameter Luneburg Lens, we use a 24 cm diameter 3D printed lens to showcase the performance of conformal feed array. This lens (24 cm dia.) is also a broadband lens fundamentally similar to the previous one, but has slightly lower lens gain due to decrease in the effective aperture size.

3.2.5 Conformal dual-polarized Vivaldi feed array for lens (24 cm diameter)

Based on the performance outcomes from the previous Vivaldi prototype, design optimizations are performed to meet the requirements for feeding Luneburg lens (24 cm dia.). Point source approximation is aimed at by decreasing the aperture-width and depth of Vivaldi element. Moreover, slot-line and cavity parameters are adjusted with respect to aperture changes to obtain reasonable matching. Table 3 - 3 lists the design parameters for the optimized Vivaldi unit element. In addition, arrangement of horizontal and vertical array elements conforming around the lens has also been reformed to have multiple beams in both azimuth as well as elevation plane. Based on the parameters listed for the modified

Vivaldi unit cell, tapered slot curve equation for left-side open (eqn. 3.9), and right-side open flaring (eqn. 3.10) are calculated as

푦 = −3.4365푒0.03푥 + 9.4524 (3.9)

푦 = 3.4365푒0.03푥 − 1.4524 (3.10)

Figure 3 - 16 shows the design of the proposed 60-element conformal dual-polarized

Vivaldi-array consisting of 4 x 9 H-pol. elements and 3 x 8 V-pol. elements. Both H-pol. and V-pol. elements are placed 10 degrees apart in azimuth and elevation plane, respectively. With respect to the 24 cm-diameter Luneburg lens, this prototype covers around 84 degrees in the horizontal plane and 32 degrees in the vertical plane.

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Table 3 - 3 Vivaldi unit cell geometry parameters Description Parameter Value (mm) Element length L 33 Element width W 8.8 Aperture width 퐴푊 6.6 Tapered slot width 푇푊 2.2 Feed slot width 퐹푊 0.825 Cavity-to-taper length 퐿퐹 4.125 Cavity width 퐶푊 2.75 Cavity length 퐶퐿 6.6 Cavity offset 퐶표 2.948 Feed offset 퐹표 2.066

Figure 3 - 16 (a) Front view, (b) back view of the 60-element dual-polarized conformal Vivaldi array consisting of 4 x 9 H-pol. elements (colored grey) and 8 x 3 V-pol. elements (colored pink).

To ease the fabrication process, the 3-D conformal prototype is developed into sections of horizontal and vertical slices which can be interlocked together. In lieu-of this, the angular

87 distance covered by vertical slices decreases from 32 degrees (for V-slice 4 located in center) to 25 degrees (for V-slice 1 located at edge), as seen in Figure 3 - 16 (a). It is to be noted that interlocking of horizontal and vertical slices requires the removal of metal part from the Vivaldi unit element with the introduction of airgaps, thus causing irregular variation in the feed point impedance for Vivaldi array elements located at the edges. Phase center position for the unit Vivaldi element of the conformal dual-polarized array is also determined for both E-plane and H-plane as shown in Figure 3 - 17. It is evident that the modified Vivaldi design exhibits stable phase center in both E/H-planes with position variation (≤ 4 mm).

In the HFSS simulation setup, all the SMA ports are 50-ohm wave-port, however, only one active port or the port of interest is excited with 1 W power while all other ports are terminated with matched loads. Figure 3 - 18 shows the simulated return loss performance for inner and edge elements of the proposed conformal dual-polarized Vivaldi array.

Figure 3 - 17 Simulated phase center variation with frequency for unit element of conformal dual-polarized Vivaldi array. 88

Due to significant impedance mismatch, edge elements should not be considered for the entire band from 3 – 6 GHz. Also, there can be a significant difference in incident power and accepted power for multi-port simulation due to power being coupled to different ports.

Therefore, it is desired to have minimal mutual coupling between the multiple ports despite being passive. For the proposed conformal dual-polarized array prototype, the isolation between adjacent H- pol. and V-pol. elements is found to be greater than 10 dB, considered reasonable for the desired application (see Figure 3 - 18 (c)). As every excited H/V-pol. element is surrounded by eight nearest V/H-pol. terminated elements, approx. 3 dB power is lost due to mutual coupling for the prototype, discussed in detail later.

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Figure 3 - 18 Simulated (a) S11 (dB) of inner elements, (b) S11 (dB) for edge elements, and (c) isolation between vertical/horizontal elements.

In order to evaluate the performance of 24 cm diameter Luneburg lens with the proposed conformal dual-polarized Vivaldi array, the entire lens structure is simulated using ANSYS HFSS. Figure 3 - 19 shows the schematic of simulation setup, where dielectric constant of the model region (polymer cubes) is set to 2.7 and tan 훿 (~0.01).

Figure 3 - 19 Simulation setup of Luneburg lens (24 cm diameter) in HFSS with conformal 60-element dual-polarized Vivaldi feed array.

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Figure 3 - 20 (a) Simulated H-plane radiation pattern for middle V-pol. element (XY-plane at 훉 = 92 deg.), and (b) middle H-pol. element (YZ-plane at 훟 =118 deg.).

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Table 3 - 4 Simulated gain, HPBW and side-lobe level (24 cm lens) Frequency V-pol. Element Excitation Relative Side-lobe Gain (dB) HPBW (deg) level (dB) 3 GHz 15.87 24.98 17.61 4 GHz 18.73 18.98 17.42 5 GHz 20.68 15.35 18.13 6 GHz 22.08 12.27 17.28

Frequency H-pol. Element Excitation Relative Side-lobe Gain (dB) HPBW (deg) level (dB) 3 GHz 14.78 26.75 16.35 4 GHz 18.25 18.74 16.83 5 GHz 20.49 15.32 18.02 6 GHz 22.03 12.66 19.92

Figure 3 - 20 plots the simulated H-plane radiation patterns for central H-pol. /V- pol. elements at different frequencies. It can be seen that the Luneburg lens works as a narrow beam antenna in a broad frequency band as predicted. Table 3 - 4 lists the radiation performance characteristics in terms of peak gain (dB), half-power beam width (HPBW), and relative side-lobe levels at discrete frequencies. The simulated gain of the (24 cm dia.) lens at 3 GHz for V-pol. and H-pol. element is 15.87 dB and 14.78 dB, respectively. At 6

GHz, the simulated gain for V-pol. and H-pol. element is 22.08 dB and 22.03 dB, respectively. The HPBW for V-pol. element decreases from 24.98 degrees at 3 GHz to

12.27 degrees at 6 GHz. For H-pol. element, HPBW decreases from 26.75 at 3 GHz to

12.66 degrees at 6 GHz. It can be observed that this modified conformal array outperforms the previous conformal Vivaldi-array (designed for 30 cm dia. lens) in terms of relative side-lobe levels. There is an improvement in relative side-lobe levels by approx. 1 – 3 dB at discrete frequencies. In addition, considerable improvement is also noticed in the undesired relative back-lobe levels.

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Figure 3 - 21 Multiple beams emanating (H-plane at theta ranging from 62 deg. to 132 deg. in intervals of 10 degree) from 24 cm diameter lens fed with 8 V-pol. elements of middle V-pol row/slice.

Figure 3 - 22 3-D radiation plot depicting multiple-beam capabilities of lens fed with conformal dual-polarized Vivaldi array, excited with 13 elements one at a time with all other elements terminated in matched loads.

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Further, multiple beams (10 degrees apart) emanating from Luneburg lens (24 cm dia.) for all the V-pol. elements in the middle row, excited one at a time, are shown in

Figure 3 - 21. In addition, a 3-D representation of lens fed with the proposed array depicting multiple beams excited by 13 elements independently is shown in Figure 3 - 22.

3.3. Fabrication and Measurements

3.3.1. Fabrication

The fabrication of the conformal all-metal dual-polarized Vivaldi array, designed for 24-cm diameter lens, is carried out using advanced machining techniques. Each element of the array is designed to interlock with each other, and is cut using a standard waterjet cutting process. The waterjet cutting process uses a stream of very high pressure water (325 MPa) mixed with abrasive to cut the material, in this case aluminum plate.

Waterjet cutting is known for its accuracy and precision, enabling thin slots to be cut from the material rapidly, thereby, reducing manufacturing cost by an order of magnitude compared to conventional machining process.

Due to process and machine limitations, the edges of the part cut with waterjet process should be perpendicular to the surface of the raw material. Owing to the spherical nature of the array and the flat construction of each individual element, the elements interface with each other at angles which vary by several degrees from perpendicular. The design accommodates this by widening the interlocking slots on each element by the projected deviation across the thickness of the material, considering both the width of the interfacing part and the angular offset, ensuring no interference with assembly.

Once the elements are cut, and prior to assembly, the holes for the electrical feedthroughs are drilled using a fixture to locate the element and a standard milling machine. Finally,

94 the elements are assembled and welded at the intersecting points with a Gas Tungsten Arc

Welding process to secure the completed conformal array. Further, extended Teflon 4-hole flange SMA connectors (p/n: Amphenol 132144) are inserted into the drilled feedthroughs and soldered at the backplane to ensure rigidity. Figure 3 - 23 shows the fabricated prototype of the conformal dual-polarized 60-element Vivaldi array. All the ports, apart from the excited port, are terminated with 50 ohms female SMA loads. The terminated ports are an intrinsic part of impedance matching, however, may also contribute to loss due to mutual coupling.

Figure 3 - 23 Photograph of fabricated conformal aluminum dual-polarized Vivaldi array terminated with SMA connectors (a) front view, (b) back view. 95

3.3.2. Impedance Matching and Radiation Performance

To evaluate the matching performance of the fabricated array considering fabrication and assembly tolerances, return loss testing for all the 60 elements is performed.

Measured S11 (dB) plots are grouped into rows (i.e. H-slices) and columns (i.e. V-slices) for better understanding and representation. Figure 3 - 24 illustrates the measured return loss matching where 9 elements of H-pol. row/slice are grouped together, and 8 elements of V-pol. column/slice are grouped together. In addition to return loss measurements, it is also important to characterize isolation between nearby elements which can contribute to significant loss due to mutual coupling.

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Figure 3 - 24 Measured return loss performance of feed array for all the elements in (a) H-slice 1, (b) H-slice 2, (c) H-slice 3, (d) H-slice 4, (e) V-slice 1, (f) V-slice 2, and (g) V-slice 3. (note: H-slices have 9 elements in a row, and V-slices have 8 elements in a row).

There are three mechanisms responsible for the mutual coupling that include: 1) the direct space coupling between array elements; 2) the indirect coupling caused by the scattering from nearby objects; and 3) the feed network to interconnect elements in the array. Although the elements for the proposed array are excited independently for the present scenario, still this case is different from the isolated antenna (i.e. unit cell)

97 performance. The effect of mutual coupling becomes strong when the inter-element spacing is smaller than half-wavelengths. For the proposed conformal dual-polarized

Vivaldi array, inter-element spacing between coplanar elements (i.e. vertical-vertical and horizontal-horizontal elements) ranges from 0.21 휆 at 3 GHz to 0.42 휆 at 6 GHz. In contrast, inter-element spacing between cross-elements (i.e. vertical and horizontal) ranges from

0.15 휆 at 3 GHz to 0.3 휆 at 6 GHz. Figure 3 - 25 depicts the measured coplanar and cross isolation between the nearby elements of the array in central portion. It is worth noting that a single excited element is surrounded by eight nearest terminated elements, particularly four cross-coupled elements, two collinear elements, and two parallel elements. These 8 elements contribute to loss in the accepted power due to mutual coupling in an isolated case (i.e. where one array element is excited and all other elements are terminated), approximately ranging anywhere between 2.5 dB at 6 GHz to 6 dB at 3 GHz, depending on the location of the element in the array.

Figure 3 - 25 Measured isolation between coplanar and cross coupled elements of the conformal dual-polarized Vivaldi array.

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Figure 3 - 26 Photograph of 3D Luneburg lens (24 cm dia.) with conformal Vivaldi dual-polarized 60-element array.

Next, antenna radiation patterns for 3D printed Luneburg lens (24 cm dia.) are measured using an Agilent vector network analyzer (PNA E8361A) in an anechoic chamber. In the experiment, the Luneburg lens is fed by proposed dual-polarization conformal Vivaldi array mounted on the surface of the lens as shown in Figure 3 - 26.

Radiation pattern measurements for 8 V-pol. elements and 4 H-pol. elements located at 0 degree elevation are reported. The measured gain patterns of 8 V-pol. elements at 6 GHz are shown in Figure 3 - 27 (a). Similarly, the measured gain patterns of 4 H-pol. elements at 6 GHz, oriented perpendicular to previous configuration such that elements are in azimuth plane at 0 degree elevation, are reported in Figure 3 - 27 (b). The measured maximum gain of the Luneburg lens is 17.19 dB and the HPBW is 12.5 degrees at 6 GHz,

99 agreeing well with the simulation results. The measured relative side lobe is about 16.2 dB for middle V-pol. element and about 21 dB for middle H-pol. element.

Figure 3 - 27 Measured H-plane gain patterns of lens antenna at 6 GHz for 10 degree apart (a) middle V-pol. elements and (b) middle H-pol. elements, where one element is excited at a time. 100

In addition, Figure 3 - 28 illustrates the comparison between simulated realized gain and measured gain patterns at discrete frequencies from 3 – 6 GHz for lens antenna excited with central V-pol. element of the array. The agreement between the simulation and measurement results is reasonable. The somewhat smaller gain (i.e. 0.32 dB at 3 GHz, 0.96 dB at 4 GHz, 0.75 dB at 5 GHz and 1.2 dB at 6 GHz) of the measured data is probably caused by the machining and welding tolerances of the aluminum feed array. The gain of the Luneburg lens increases with the increase of frequency, and the HPBW decreases with the increase of frequency, as expected.

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Figure 3 - 28 Measured and simulated H-plane gain (realized) patterns of lens antenna fed with middle V-pol. element at (a) 3 GHz, (b) 4 GHz, (c) 5 GHz, and (d) 6 GHz.

Figure 3 - 29 depicts the measured directional beams around 0 degree at all frequencies for both V-pol. and H-pol. element, indicating that this Luneburg lens works well as a directional antenna in a broad frequency band. It can be seen that for lens fed with middle V-pol. element, the measured gain ranges from 7.65 dB at 3 GHz to 17.19 dB at 6

GHz and HPBW decreases from 24 degrees at 3 GHz to 12.5 degrees at 6 GHz. Similarly, for lens fed with H-pol. element, the measured gain ranges from 6.5 dB at 3 GHz to 17.18

102 dB at 6 GHz and HPBW decreases from 23.8 degrees at 3 GHz to 12.7 degrees at 6 GHz.

Figure 3 - 29 Measured H-plane gain patterns at 3 – 6 GHz for lens antenna fed with middle (a) V-Pol. element, and (b) H-pol. element.

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3.4. Summary

In this chapter, a highly-directional multiple-beam broadband antenna system for 3

- 6 GHz practical wireless communications is proposed and demonstrated. This system comprises of 3D-printed graded index Luneburg lens integrated with conformal dual- polarized all-metal Vivaldi feed array. The lens (24 cm diameter) is printed using rapid polymer jetting technique while the feed array is fabricated using advanced machining techniques. Good agreement between measurement and simulation is achieved for antenna parameters such as realized gain, HPBW and relative side-lobe level. Measurement results show that the average gain of this lens antenna is from 7 dB (at 3 GHz) to 17.17 dB (at 6

GHz). The measured average HPBW is about 23.9 degrees (at 3 GHz) to 12.6 degrees (at

6 GHz).

From the industry perspective, this cost-effective lens-based antenna system can be used in communication and sensing applications with the integration of electronically switched network, thus leveraging the multi-beam capabilities of the broadband lens. Also, the proposed system can operated in mixed cases, where different elements can be excited at different frequencies. However, care needs to be taken to include the effect of mutual coupling for all cases. When multiple elements are excited simultaneously, it is recommended to analyze the array performance is terms of active s-parameters.

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Chapter 4. 3-D Printed cloaked microstrip antennas: reduction of mutual coupling

4.1. Introduction and Motivation

Cloaking technology has always been an active research area in the field of non- invasive probing, camouflaging and imaging. Another interesting application of cloaking technology is the reduction of mutual coupling between antennas [59]. Lowering destructive mutual coupling levels for multiple antennas installed in compact and complex structures is always deemed vital for antenna applications. In this regard, metamaterials have been utilized extensively to provide electromagnetic cloaking by suppressing both bi- static and total scattering cross-sections (SCS) of the object [61], [63], [66], [69], [138].

However, these techniques are difficult to realize in real-time scenario as they mostly depend on bulk volumetric metamaterials.

One of the major challenges associated with design of antenna cloaking structure is the capability to reduce coupling without affecting electromagnetic performance of antenna. In view-of-this, plasmonic and mantle cloaking methods have been applied to short, half-wavelength dipoles, thereby preserving the matching and radiation characteristics of the antennas [58], [139-140].

Modern wireless communications demands high performance, miniaturization, lightweight and reliability. To meet these requirements, microstrip antennas are commonly used in congested electromagnetic environments, thus giving rise to increase mutual coupling levels between closely spaced antennas. The sources of these unwanted coupling effects in planar microstrip antennas include: (1) near-field coupling, (2) far-field coupling and (3) surface-wave coupling [68]. Near-field coupling occurs when an antenna is located

105 in the near-field (Fresnel region) of another antenna, where EM fields are reactive and decrease with distance. Generally, this type of coupling is more prominent in adjacent patch array elements using low-permittivity substrates, where the guided substrate wavelength becomes very close to free space, for center-to-center spacing between the patches close to antenna dimensions, thereby degrading the radiation performance of antennas [141]. In contrast, the far-field coupling arises due to the radiation energy being absorbed by the antenna located in the far-field (Fraunhofer Region) of another antenna. Applications using thin grounded dielectric substrate, usually involving power interaction between antennas, experience this kind of coupling. Apart from these, surface-wave coupling is encountered typically when the substrate thickness is large (ℎ⁄휆표 ≥ 0.048⁄√휖푟). Several techniques have been studied in literature to reduce mutual-coupling between printed antennas such as mushroom-like electromagnetic bandgap structures (EBG) [142-143], defected-ground structures (DGS) [144-145], field-cancellation approach [146] and insertion of parasitic elements [147]. Despite numerous techniques and design, an efficient reliable method for reduction of mutual coupling without affecting antenna performance is still challenging.

In this chapter, we propose the implementation of novel technique introduced by

Bernety et al. [78] to suppress the electromagnetic interaction between microstrip antennas at microwave frequencies, and overcome the mutual coupling on the basis of the eminent mantle cloaking method [72], [148]. Inspired by the cloaking of 2-D elliptical objects discussed in [77], two planar monopole antennas with different resonant frequencies become invisible to each other when covered with proposed conformal elliptical metasurfaces, formed by printed arrays of sub-wavelength periodic elements, partially

106 embedded in the substrate. Both near-field and far-field mutual-coupling can be reduced with the help of this cloaking structure without affecting antenna performance.

4.2. Cloaking of planar monopole antennas with reduced near-field coupling

In this section, we present the methodology to reduce the mutual coupling between two microstrip-fed monopole antennas, achieved by confocal elliptically shaped metasurfaces, based on the concept of mantle cloaking. Firstly, radiation pattern and reflection coefficient of two isolated planar monople antennas, resonating at slightly different frequencies, is studied. Then, these two planar antennas are placed close to each other (i.e. in the near-field zone) without any cloaking structures such that they exhibit significant coupling. Finally, cloaked case is investigated, wherein these antennas are covered by suitably designed elliptical metasurfaces to mitigate and neutralize the effects of coupling, thereby restoring the radiation patterns and impedance characteristics of the antennas as if they were isolated.

For this work, a low-permittivity substrate (휖푟 = 2.7) is taken into account such that ℎ/휆2 < 0.048/√휖푟 (ℎ/휆2 = 0.017 푎푛푑 0.048/√휖푟 = 0.029), where 휆2 is the wavelength of the antenna with the higher frequency. Therefore, we can neglect the effect of surface-wave coupling on the resulting mutual coupling as it is weakly excited.

Figure 4 - 1 demonstrates two isolated microstrip-fed monopole antennas resonating at 푓1 = 0.92 GHz (Antenna I) and 푓2=1.034 GHz (Antenna II), each on the substrate with 휖푟 = 2.7 and ℎ = 4.725 mm along with partial ground structure, with the parameters: L = 21 cm, W = 18.9 cm, L1 = 11.4 cm, L2 = 10.44 cm, m = 1.2 cm, s = 5.85 cm and G = 5.1 cm.

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Figure 4 - 1 Top view of the isolated microstrip-fed monopole (a) Antenna I, and (b) Antenna II, (c) bottom view depicting partial ground plane of antennas.

Figure 4 - 2 Input reflection coefficients of Antenna I resonating at 0.92 GHz, and Antenna II resonating at 1.034 GHz.

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Figure 4 - 3 Linear gain patterns (3-D) for (a) Isolated antenna I at 0.92 GHz, and (b) isolated Antenna II at 1.034 GHz.

Full- wave EM simulation package, ANSYS HFSS is used to analyze the structure. Figure

4 - 2 and Figure 4 - 3 show the simulated reflection coefficients and 3-D linear radiation plots for the two-isolated planar monopole antennas.

Further, the two microstrip-fed monopole antennas are placed in the near-field of each other (separated by a distance d = 0.147 휆1, where 휆1 is the wavelength related to

Antenna I) to analyze the coupling effect in the uncloaked case as shown in Figure 4 - 4. It is observed that the presence of each antenna changes the radiation pattern of the other one drastically as shown in Figure 4 - 5.

In the final step, elliptically shaped metasurfaces with metallic strip inclusions are used to cover the aforementioned antennas to reduce mutual coupling, thereby preserving the radiation patterns as if they were isolated. This type of mantle cloaks (i.e. elliptical shaped metasurfaces with metallic strip inclusions) are inspired by the analytical method

109 used for cloaking infinitely long metallic elliptical cylinders and strips, where the cloaking object is supposed to be under a transverse magnetic (TM) plane-wave excitation [77].

Figure 4 - 4 Schematic (top view) of the uncloaked case with microstrip-fed monopole Antenna I (left) and Antenna II (right).

Figure 4 - 5 Linear gain patterns (3-D) of coupled but uncloaked case for (a) Antenna I, and (b) Antenna II.

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The metasurface cloak should be conformal and confocal with respect to the object to achieve effective EM invisibility based on solving the scattering problem in elliptical coordinates and also, by the application of sheet impedance boundary conditions at the metasurface. The elliptical metasurface cloaks are designed such that the antennas become invisible to each other without altering their impedance matching at respective resonance frequencies, thus depicting performance similar to the isolated case. The schematic of cloaked prototype is shown in Figure 4 - 6.

In order to investigate the optimized cloak design for antenna I, the first step is the determination of number of vertical strips of the cloak structure (N), based on which we can have a specific value for periodicity (D) as per dielectric spacer perimeter.

Figure 4 - 6 (a) Schematic (top view) of antenna I and antenna 2 in cloaked case, (b) cross-sectional view, metasurface cloak parameters for (c) antenna I, and (d) antenna II. 111

It should be noted that N can be chosen randomly based on effective cloaking exhibited for each value of N [69]. Thereafter, two primary parameters are optimized to tune the properties of the metasurface along with antennas in order to achieve cloaking at f2 and maintaining resonance conditions at f1, which include (1) the widths of the vertical strips

(푤푠) and (2) the permittivity of the dielectric spacer (휖푐). In general, antenna I is loaded by the elliptical-metasurface cloaking structure at its resonant frequency such that the incoming EM wave from antenna II cannot see antenna I, similar to isolated case.

According to the design procedure discussed, to achieve an appropriate cloak design for the isolated microstrip-fed monopole antennas, the total number of vertical strips

(N) is chosen to be 10. Based on this value, periodicity for cloaks is calculated as D = 0.38 cm according to the perimeter of the dielectric spacer (ϵc = 5) with a = 0.73 cm and b =

0.31 cm.

Figure 4 - 7 S-parameters of two-microstrip fed monopole antennas (antenna I and antenna II) for cloaked and uncloaked case.

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The optimum values for width of vertical metallic inclusions (ws) on the elliptically shaped metasurface cloaks obtained by numerical simulations is 푤1 = 0.1418 cm and

푤2 = 0.1217 cm. The value of parameters R1 and R2 obtained is 6.075 cm and 6.96 cm, respectively. Also, it is noted that the lengths of the planar monopole antennas for cloaked case needs to be slightly optimized in order to accommodate the shift in frequency, L1 =

11.175 cm, and L2 = 12.06 cm. Figure 4 - 7 shows the s-parameters of the cloaked, uncloaked and isolate case for a qualitative comparison. It is clearly evident that mutual coupling (S12) has reduced to 17.6 dB at f1 = 0.965 GHz, and reduced to 18 dB at f2 = 1.108

GHz. It should be noted that the specific frequencies are selected based on their radiation pattern behavior similarity to the isolated case. Figure 4 - 8 demonstrates the 3-D linear gain patterns of the cloaked antennas. In addition, to have qualitative comparison, 2-D linear gain patterns for all three cases (i.e. isolated, uncloaked and cloaked) for antenna I at 0.965 GHz and antenna II at 1.108 GHz are plotted in Figure 4 - 9.

Figure 4 - 8 Linear gain patterns (3-D) for cloaked case of (a) antenna I at 0.965 GHz, and (b) antenna II at 1.108 GHz.

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Figure 4 - 9 Linear gain patterns of antenna I at 0.965 GHz (a) in the E-plane, and (b) in the H-plane. Linear gain patterns of antenna II at 1.108 GHz (c) in the E- plane, and (d) in the H-plane.

The plotted radiation patterns imply that by covering the radiating parts of each antenna by its respective properly designed cloak leads to the preservation of the radiation patterns of the antennas and recovering their input impedance characteristics. It is worth noting that these simulated results are based on first-order ideal lossless analysis for the three cases discussed (i.e. isolated, uncloaked and cloaked). 114

4.3. Prototype Fabrication and Testing

The realization and fabrication of the proposed narrowband microstrip-fed monopole antennas prototype integrated with elliptical metasurface cloaks is performed using advanced 3D printing techniques. Development of elliptical structure is accomplished with a two-fold strategy, wherein metasurface cloaks with strip inclusions are realized in a semi-elliptical fashion and then united to form the complete geometry.

First, the substrate dielectric material of low dielectric permittivity (r = 2.7) and height (h

= 0.4725 cm) with semi-elliptical carvings for embedding metasurface cloaks is 3D printed using rapid polymer jetting technique using commercially available Objet printer (Eden

350). Secondly, for the development of elliptical dielectric spacers (휖푐 = 5), a mixture of

Strontium titanate (푆푟푇푖푂3) powder and ultraviolet (UV) curable resin is prepared in a suitable volumetric ratio.

Second, this semi-solid solution is poured in a semi-elliptical teflon mold where it is cured under high intensity UV lamp (~100 W) as shown in Figure 4 - 10 (a).

Figure 4 - 10 (a) Semi-elliptical Teflon mold under high intensity UV lamp (100 W), and (b) Cured semi-elliptical metasurface dielectric spacers for Antenna I & II.

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Figure 4 - 11 (a) 3-D printed (0.5 mm thick) semi-elliptical shell to aid metallization process, (b) photograph of fabricated semi-elliptical metasurface cloaks with metallic subwavelength strip inclusions developed using highly conductive spray coating technique to enclose antenna I and antenna II.

It is worth noting that the solution is cured in multiple layers due to the limitation of UV light penetrability, thus consuming approximately 3 hours for one sample. The photographs of the prepared semi-elliptical samples are shown in Figure 4 - 10 (b).

Once the samples are prepared, the next step is to develop thin metallic subwavelength periodic inclusions over the cured semi-elliptical dielectric spacer using highly conductive nickel spray coating technique. Nickel conductive coating is a one-part durable acrylic lacquer pigmented with a highly conductive nickel flake. It utilizes a solvent based system with no heated curing necessary. The cured coating is smooth, hard and abrasion resistant. Due to its strong adhesion to acrylic, ABS, polycarbonate and other injection molded plastics, this is deemed appropriate choice for the metallization process in this case. 3-D printed thin semi-elliptical polymer shells are used for ensuring accuracy and precision in the spray metallization process as shown in Figure 4 - 11 (a). Under ambient pressure and temperature, deposited metal layer thickness can vary from 20 nm to

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7-10 μm depending on the number of spray coats, with a volume resistivity of about 0.004

Ω.cm. Figure 4 - 11 (b) shows the fabricated semi-elliptical metasurface cloaks for antenna

I and antenna II.

Figure 4 - 12 (a) Embedded semi-elliptical metasurface cloaks in the 3D printed substrate, (b) picture showing the fabrication of planar monopole antennas I & II using double-sided adhesive copper tape and (c) back view of the fabricated prototype depicting partial ground plane.

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Third, planar monopole antennas and partial ground plane are fabricated with thin copper tape (~1.4 mil thick) to ease the process. Also, it is to be noted that SMA connectors were soldered to planar antennas (i.e. copper tape) before attaching it to the substrate to protect it from melting. Also, prior to copper tape bonding, 3D printed semi-elliptical metasurface cloaks for respective antenna I and II should be embedded correctly in the substrate as shown in Figure 4 - 12.

Finally, microstrip-fed planar monopole antennas are covered on the top with the remaining semi-elliptical metasurface cloaks to form the confocal elliptically shaped cloaks around the radiating part of the monopole antennas in order to supress mutual coupling as discussed in earleir sections.

Figure 4 - 13 Measurement setup for testing s-parameters of fabricated near-filed cloaked prototype.

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Figure 4 - 13 shows s-parameters measurement setup of the fabricated prototype using Agilent network analyzer (E8361A PNA) calibrated with a step size of 250 KHz for accuracy. Figure 4 - 14 depicts the measured s-parameters with frequency regions highlighted that illustrate the performance of cloaked antennas. In an ideal (lossless) cloaked situation, as stated earlier (see Figure 4 - 7), the s-parameters of two uncloaked planar monopole antennas, placed in the near field of each other, are optimized by covering them with suitably designed confocal elliptically shaped metasurfaces, such that they do not interefere with each other in the regions of mutual coupling reduction. From the measurement results, it is observed that the mutual coupling is reduced to 17.4 dB at f1 =

0.827 GHz, and reduced to 16.26 dB at f2 = 1.015 GHz.

Figure 4 - 14 Measured s-parameters of the fabricated near-field cloaked prototype (highlighted sections indicate the regions that depict cloaking behavior for antenna I and antenna II).

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However, this reduction in mutual coupling (as seen in the measured plots) does not guarantee full restoration of radiation characteristics of the cloaked antennas. This is attributed to the fact that the measured S22 at f1 = 0.827 GHz is -5.2 dB and measured S11 at f2 = 1.015 GHz is -9.09 dB, which ideally should be close to 0 dB to effectively cloak one antenna from the other, thus, preserving their radiation patterns and recovering their input impedance characteristics. Moreover, there is a significant deviation of measured results (for the fabricated prototype) from the ideal cloaked simulation case, which prompts to the investigation of fabrication tolerances.

Several reasons for the aforementioned deviation in the measurement results compared to simulation can be dielectric loss in the cured host semi-elliptical spacers and polymer substrate material, shift in permittivity values of the UV cured semi-solid solution, conductor losses and surface roughness. In view-of-this, the first step taken is the re- measurement of dielectric constant and loss tangent of the UV-cured sample (prepared by mixing Strontium titanate and epoxy resin in weighted fraction). Effective permittivity is extracted from the measured s-parameters of the sample. The measured dielectric constant (휖푐) comes out to be 5.9 and the loss tangent, about 0.05. In addition, the measured loss tangent of the 3D-printed substrate material is about 0.01. The volume conductivity of the nickel spray paint is approximated as 2.5e4 Siemens/m, based on the manufacturer datasheet (MG Chemicals, super shield conductive nickel coating, 841).

In the next step, full-wave simulation of the cloaked prototype (see Figure 4 - 6) is carried out incorporating the measured permittivity and loss tangent values, along with finite conductivity values (i.e. copper and nickel) for the conductors. For a qualitative analysis, both simulated and measured s-parameters for the cloaked case are shown in

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Figure 4 - 15, in which the regions of interest highlighted are region 푀1 (for cloaking behavior seen by antenna I in measurement), region 푆1 (for cloaking behavior seen by antenna I in simulation), and region 푀푆12 (for cloaking behavior seen by antenna II in both measurement and simulation). It is clearly evident from the simulated results that one of the primary reasons for the deviation of cloaking behavior from the ideal lossless situation is due to significant loss and higher permittivity of the UV cured semi-elliptical host dielectric spacer material. Based on this simulation of cloaked case, it can be asserted that the measured s-parameters are seen to be in the reasonable agreement with the simulated results.

Figure 4 - 15 Simulated and measured s-parameters of the cloaked case (for simulation, 흐풄=5.9 with tan휹 =0.05 for elliptical host spacer, and 흐풓 = ퟐ. ퟕ with tan휹 =0.01 for polymer substrate material). The highlighted regions from the left to right corresponds to region 푴ퟏ, region 푺ퟏ, and region 푴푺ퟏퟐ)

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It is observed that the first measured S22 resonance for antenna II at 0.757 GHz (i.e. -18.6 dB) is shifted by 0.023 GHz compared to the simulated S22, at 0.78 GHz (-17.2 dB). Also, the first measured S21 minima at f1 = 0.827 GHz (i.e. -17.4 dB) is shifted by 0.073 GHz compared to the simulated S21 minima, occurring at 0.9 GHz (i.e. -16.81 dB). For antenna

II, both the simulated and measured regions of interest are in agreement, depicted by region (푀푆12). For both simulated and measured, second resonance S21 minima lies at f2

= 1.015 GHz (i.e. -16.26 dB). However, the measured S11 value (dB) at second S21 minima (at f2 = 1.015 GHz) is about 5 dB lower compared to simulated S11 value (i.e. -

4.06 dB).

These differences that still persist between the measured and simulated cloaked case (considering material deviations) are assumed due to variation in UV-cured sample developed from the mixture of Strontium titanate nanoparticles and epoxy resin host in weighted fractions. Numerous reasons associated with this kind of variation can be the morphology of the nanoparticles and composites, as well as the thermal conduction characteristics and electrical properties of the composites. Another possibility can be discontinuous elliptical structure. This means that the metasurface cloaks with strip inclusions are realized in a semi-elliptical fashion and then united to form the complete geometry. This can cause microscopic air gaps to exist between the two united semi- elliptical metasurfaces with planar microstrip antenna placed between them. Apart from this, variation in thickness of the deposited metal layer using spray painting and its surface roughness also contribute to some extent, which has not been characterized for simulation results reported. The effect of surface roughness for this application is minimal as we operate at low microwave frequencies.

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4.4. Summary

In this chapter, cloaking technique based on the mantle-cloaking method has been applied to two nearby planar antennas to suppress the mutual near-field coupling such that both the antennas can work independently of each other. Even though there is no definitive analytical solution found in literature for cloaking finite-length objects, the approach is inspired by cloaking of infinite long metallic strips, where even and odd Mathieu functions can be employed to analyze the scattered elliptical fields. Confocal elliptical shaped metasurface cloaks with metallic strip inclusions have been implemented to cover planar monopole antennas, thereby improving their matching characteristics and preserving the radiation patterns as if they are isolated. The mutual scattering parameter (S12) is reduced to 17.6 dB at f1 = 0.965 GHz, and reduced to 18 dB at f2 = 1.108 GHz for antenna I and antenna II, respectively.

Fabrication of the cloaked prototype has also been attempted with the help of advanced 3D printing techniques where the entire prototype is developed in sections and then integrated to form the complete structure as discussed in detail in section 4.3. The measurement results are in reasonable agreement with the simulation results as reported, with simulation carried out taking into account true permittivity and loss tangent values for the dielectric materials employed in the fabrication.

In order to realize the full potential of cloaking technology in printed antennas, investigation of fabrication techniques with controlled manufacturing processes and permissible material tolerances is deemed essential. Novel fabrication techniques can be applied with careful addressing of some important issues such as acceptable variations for manufacturing parameters, process deviations, geometry distortions, porosity and cracking

123 of dielectrics, and metallization thickness and surface roughness, contributing to overall loss.

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Chapter 5. Conclusions and Future Work

This dissertation discusses the theoretical limits and practical matching of electrically-small antennas at HF band; advancement in 3D-printed components and additive manufacturing; requirements of high-performance antenna feeds along with procedure to determine phase center; and EM invisibility based on mantle cloaking of elliptical cylinders and strips.

First, the design and fabrication of compact ESHA (about 휆/50 at lowest frequency) is reported to facilitate static and mobile long-distance HF communications within the 3 – 30 MHz band. Passive and active impedance matching networks are designed, fabricated and tested to improve the matching bandwidth of the proposed ESHA for both instantaneous narrowband-switched and broadband applications. These include electronically switched narrowband LC matching circuit, broadband transformers, and broadband active non-Foster circuit. Practical factors that control the impedance bandwidth capability and overall efficiency of the transformer have been analyzed with the help of equivalent circuit modelling including ferrite material characteristics. Further, taking into account stability, device parasitics, DC biasing, transmission lines effect and load impedance, design of a stable -40 pF non-Foster circuit is achieved for broadband matching of the proposed ESHA. The results show that the non-Foster matched ESHA received 15-

20 dB more signal power from 3 to 14 MHz than the other two passive matching cases.

However, despite highest received signal strength, non-foster circuit yielded lower SNR

(about 5-10 dB difference) compared to the broadband passive transformer for far-field real voice-data measurements.

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In future works, non-Foster matching circuit needs to be developed for practical communication applications employing electrically small antennas taking into account several factors, in addition to stability, that include power capacity and DC-power consumption for transmit configuration, and noise figure margin for receiver configuration.

Furthermore, transmission line transformer matching can be investigated to achieve 20:1 bandwidth with minimum insertion loss (≤0.5 dB) and reasonable VSWR performance

(3:1) for matching electrically small antennas by employing internal lumped/distributed capacitance to compensate shunt inductance, thereby reducing the impedance mismatch

[149].

Next, a conformal dual-polarized all-metal Vivaldi array is synthesized to realize high-directional multiple beam capability of additive manufactured 3D Luneburg lens for practical wireless applications covering 3 – 6 GHz band. Good agreements have been achieved for lens fed with array comprising of vertical and horizontal polarized elements.

Independent multiple beams are realized by exciting different elements separated by their

HPBW at operating frequency. Also, this allows the feed array to function in mixed cases where different elements can operate at different frequencies. One of the major challenges associated with the proposed dual-polarized conformal array to operate in mixed cases, where single/multiple elements can be excited simultaneously, is the reduction of mutual coupling. This issue becomes more prominent at lower frequencies, where inter-element spacing is less than half-wavelengths. In addition to independent multiple-beams, the proposed array can be engineered to achieve electronic beam scanning by controlling the phase and amplitude of different elements [118]. This can be accomplished by carefully studying the effect of active impedance seen by various elements at respective scan angles.

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Finally, we have implemented the design of near-field cloaked planar antennas utilizing conformal elliptical metasurfaces with printed arrays of sub-wavelength periodic elements to suppress mutual near-field coupling between two microstrip-fed monopole antennas. It has been shown using full-wave EM simulation package (i.e. HFSS) that by covering each antenna with suitably designed confocal elliptically shaped metasurface cloak, partially embedded in the substrate, the near-field coupling between the antennas has been reduced to about 17.6 dB. Thus, the two antennas placed in the near-field of each other operate as if they were isolated due to the improved matching characteristics and preserve their individual radiation patterns. Development of the prototype has been carried using advanced 3D printing techniques such as rapid polymer jetting and pressure controlled conductive spray painting. The measured results deviate from the ideal first- order simulations (i.e. lossless scenario) due to increased losses and permittivity values obtained for the UV curable dielectrics. Novel 3D fabrication techniques need to be considered addressing important issues such as acceptable variations for manufacturing parameters, process deviations, geometry distortions, porosity and cracking of dielectrics, and metallization thickness and surface roughness, contributing to overall loss.

In the future work, larger arrays with more than two antennas will be studied to utilize the mantle cloaking concept in a number of practical applications.

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