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Simulation and design of lateral photo-dember emitters and a novel microwave antenna

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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
ProQuest Number: 10817106
All rights reserved
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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.
3
Dedicated to my mom, Manju Gulati
4
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.
1.1.
1.2.
1.3.
1.4.
1.5.
1.6.
INTRODUCTION ........................................................................... 18
Electrically Small Antennas ............................................................................... 18
Active and Passive Impedance Matching........................................................... 20
3-D Printed Antennas ......................................................................................... 22
Luneburg Lens Feeds ......................................................................................... 25
Mantle Cloaking of Elliptical Cylinders and Strips ........................................... 29
Thesis Outline .................................................................................................... 32
CHAPTER 2.
ELECTRICALLY SMALL HELICAL ANTENNA FOR HFBand COMMUNICATIONS: DESIGN AND FIELD EXPERIMENTS .................. 34
2.1.
2.2.
2.3.
HF-band long range communication .................................................................. 34
Uniform normal-mode ESHA (2m long) ........................................................... 35
Passive and active impedance matching networks ............................................. 38
2.3.1.
2.3.2.
2.3.3.
2.4.
Measurements..................................................................................................... 59
2.4.1.
2.4.2.
2.5.
Passive narrowband electronically tuned LC matching network ................ 38
Broadband Transformers ............................................................................ 41
Active broadband non-Foster matching circuit........................................... 54
Outdoor Field Measurements (Near-field).................................................. 59
Real Voice-Data Communication Measurements (Far-Field) .................... 61
Summary ............................................................................................................ 65
CHAPTER 3.
BROADBAND CONFORMAL DUAL-POLARIZED VIVALDI
ARRAY FOR FEEDING LUNEBURG LENS ........................................................... 67
3.1.
3.2.
Graded index 3-D Luneburg lens ....................................................................... 67
Feed network for 3-D printed Luneburg lens ..................................................... 70
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.3.
Introduction and Motivation ....................................................................... 70
Vivaldi Antenna Unit cell ........................................................................... 72
Planar dual-polarized 3 x 3 Vivaldi array ................................................... 77
Conformal dual-polarized Vivaldi feed array for lens (30 cm diameter) ... 80
Conformal dual-polarized Vivaldi feed array for lens (24 cm diameter) ... 86
Fabrication and Measurements........................................................................... 94
5
3.3.1.
3.3.2.
3.4.
Fabrication .................................................................................................. 94
Impedance Matching and Radiation Performance ...................................... 96
Summary .......................................................................................................... 104
CHAPTER 4.
3-D PRINTED CLOAKED MICROSTRIP ANTENNAS:
REDUCTION IN MUTUAL COUPLING ................................................................. 105
4.1.
4.2.
4.3.
4.4.
Introduction and Motivation............................................................................. 105
Cloaking of planar monopole antennas with reduced near-field coupling....... 107
Prototype Fabrication and Testing ................................................................... 115
Summary .......................................................................................................... 119
CHAPTER 5.
CONCLUSIONS AND FUTURE WORK .................................. 125
REFERENCES .............................................................................................................. 128
6
TABLE OF FIGURES
Figure 1 - 1 Overview of generalized additive manufacturing process [29]. ................... 23
Figure 1 - 2 (a) Radiated Far-field phase pattern φ() 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
7
Figure 2 - 17 Reactance behavior of negative capacitance and negative inductance (nonFoster) 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 nonFoster 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
8
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 Vpol. 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) Vslice 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 dualpolarized 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
9
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,
=5.9 with tan =0.05 for elliptical host spacer, and  = 2.7 with tan =0.01 for
10
polymer substrate material). The highlighted regions from the left to right corresponds to
region 1, region 1, and region 12) ....................................................................... 121
11
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
12
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
13
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
14
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
15
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 nearfield cloaked prototype is carried out using advanced 3D printing techniques.
17
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, highdirectional 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  ≪ 1, where  is the radius of
imaginary sphere confining the maximum dimension of the antenna, and  is the free space
wavenumber(2/). 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 ( = 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
 3 3
+
1

(1.1)
The 3-dB fractional bandwidth of an ESA is calculated as
3 =
1

(1.2)
Thus, the maximum fractional bandwidth for an ESA becomes
3, =
 3 3
≈ ()3 ,   ≪ 1.
1 +  2 2
(1.4)
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

 ln(1/|Γ |
(1.5)
where Γ 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
 =  
(1.6)
 =  
(1.7)
Where  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 gainbandwidth product remains constant
 x BW =   x
1

=
 

(1.8)
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 (≤ 2), 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.
21
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].
23
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]
24
Important material parameters, which depend on frequency of operation, include electric
permittivity (ɛ), metal conductivity (), permeability (), and loss tangent (tanδ).
In contrast to polymer printing, three main techniques for developing highprecision 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 offbody 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 doubleslot 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(), 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 
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:
=
 ⋅ 
2(1 −  )
(1.9)
where  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() 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
 =
2(1 −  ). 

(1.10)
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 Eplane 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 lowinterference 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 twodimensional (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 ( ), thus relating  =  J, where  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 ( = ) should be continuous and (2) two-sided
impedance boundary conditions at the boundary of the mantle cloak ( =  ).
Tangential electric ( ) and magnetic field ( ) can be related to sheet impedance with
the help of two-sided boundary conditions,
 |=+ =  |=− =  ( |=+ − |=− )
(1.11)
where  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 lowterahertz 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 /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-tonoise 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 sparermters 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.
33
Chapter 2.
2.1.
Electrically small helical antenna for HF-band
communications: design and field experiments
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].
34
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  =  . sec , where  is the
critical frequency,  is the angle if incidence, and sec  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 HFcommunication, 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  and number of turns n. For normal-mode operation, the relation
between these parameters follows
 = tan−1


(2.1)
where s is the spacing between the turns.
 = √ 2 + ()2
(2.2)
 ≅ , ℎ  < 0.5
(2.3)
The total length of the helix is given as,
 =  
(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 (11 ) are plotted in Figure 2 - 3.
As discussed in section 1.2, as antennas become shorter (typically< 0.1), the radiation
resistance decreases significantly, and the reactance and quality factor () 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 Lsections, 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
 =  ∅⁄
(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
1⁄2 = 1 ⁄2
(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
1 1 = 2 2
(2.7)
Using equation (2.6 and 2.7), primary and secondary impedances are related as
1 = 1⁄1 = [1 ⁄2 ]2 . 2
(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  . These kind of losses are
significant in transformers that operate near the ferro-resonance region of the core material
and tend to increase with 2 or even 3 . 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 1 and
2 . 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 (11 ) resulting from the shunt capacitance of the primary
winding, distributed secondary shunt capacitance (22 ), and distributed inter-winding
capacitance (12 ). The mutual inductance M can be determined as a function of primary
and secondary magnetizing inductances 11 and 22 by
 = (11 22 )1⁄2
(2.9)
where k is the coupling factor of transformer, and 11 and 22 are related to leakage
inductances as
1 = 11 − 
(2.10)
2 = 22 − ⁄
(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 11
√
 22
(2.12)
It is to be noted that the magnetizing inductance (i.e. 11 ) limits the low-frequency
performance in practical transformer design, while the high-frequency performance is
limited by leakage reactance (2 ) [89-90]. For broadband transformer, the relative
bandwidth of matched transformer is a function of coupling factor [91], given as
 ⁄ = 2/(1 − )
(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  and having an inductance  is given by
= 

= 

(2.14)
Further, using the relation between inductance and magnetic flux, Φ = 
 =  = 
(2.15)
where  is the number of turns in the primary,  is the cross-sectional area of the core in
square meters, and  is the magnetic flux density. The maximum flux density is given as
45
 =
_

(2.16)
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 ( ) is
the parasitic capacitance due to inductor winding. The inductance ( ) corresponds to the
core winding, and core loss due to hysteresis is denoted by  . 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 ( =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 2. The number of turns for the
secondary required to produce optimum inductance with respective toroid is calculated as
 2

 = √
=√


(2.17)
where A is the area of transversal section of toroidal core, r is the mean radius of toroid,
and  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 ( ) 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
Primary series resistance (conductor losses)
Secondary series resistance (conductor loses)
Primary shunt capacitance
Secondary shunt capacitance
Inter-winding capacitance
Shunt resistance (core losses)
Primary leakage inductance
Secondary leakage inductance
Mutual inductance
50
Symbol
R1
R3
C1
C2
C3
R2
L1
L3
L
Value
24.24 Ω
6.91 Ω
17.19 Pf
5.32 pF
0.249 pF
989.56 Ω
0.74 uH
0.41 uH
30.73 uH
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 ( = 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 (/) 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 lossloss 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 ( = 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 /. In contrast,
negative capacitor and inductor show negative /, 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 selfresonant 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 () and resistor () 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 () 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
( = 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 () 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 (11) 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 11 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.
58
2.4.
Measurements
2.4.1. Outdoor Field Measurements (Near-field)
The purpose of this experiment is to analyze the performance of the electricallysmall 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 voicedata communication measurement involving three matching prototypes.
62
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
13
15
22.5
4.035
25
32
33
7.021
50
67
62
13.983
60
65
65
17.615
60
62
65
21.0175
58
57
64
29.935
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 unmatched and matched antenna ( and  ), 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,

1
 <  ( −
)
 
(2.18)
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 margine for NIC
NFrx = 5dB
40
NFrx = 8dB
30
20
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 nonFoster 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.
66
Chapter 3.
3.1.
Broadband conformal dual-polarized Vivaldi
array for feeding Luneburg lens
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 nonmagnetic material ( = 1) is given by Equation (3.1) [109]:
()2 =  () = 2 − (⁄ )2
(3.1)
where  is the relative permittivity,  is the radius of the lens and  is the distance from
the respective spatial point to the center of the sphere.

Figure 3 - 1 Standard Luneburg Lens Cross-Section [110].
67
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:  =  .  +  . (1 − )
68
(3.2)
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  represents polymer material permittivity, and  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
 = 5.5593 − 590974 − ⁄0.07958 − 9.54823 − ⁄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 dualpolarized 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 dualpolarized 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.
72
Figure 3 - 5 Schematic of exponentially-tapered Vivaldi unit element [132].
Table 3 - 1 Vivaldi unit cell geometry parameters
Description
Element length
Element width
Aperture width
Tapered slot width
Feed slot width
Cavity-to-taper length
Cavity width
Cavity length
Cavity offset
Feed offset
Parameter
L
W








Value (mm)
33.75
13.5
9.13
1.397
0.627
4.40
2.89
5.94
3.09
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:  = 1 ∗ e + c2
where,
1 = (2 − 1 )⁄( 2 −  1 )
2 = (1 .  2 − 2 .  1 )⁄( 2 −  1 )
73
(3.4)
(3.5)
(3.6)
The points (1 , 1 ) and (2 , 2 ) 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
 = −2.8335 0.03 + 15.9342
(3.7)
 = 2.8337 0.03 + 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 (Vpol.) 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 dualpolarized 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.
76
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.
77
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.
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
[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.
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.
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.
81
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 highlydirectional 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 Hpol. 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.
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 (XZ-plane at
 =  deg.), (b) V-pol. element (XY-plane at  = 90 deg.).
83
Table 3 - 2 Simulated gain, HPBW and side-lobe level (30 cm lens)
Frequency
3 GHz
4 GHz
5 GHz
6 GHz
Frequency
3 GHz
4 GHz
5 GHz
6 GHz
V-pol. Element Excitation
Relative Side-lobe
Gain (dB) HPBW (deg)
level (dB)
16.99
19.64
16.55
19.89
14.49
15.26
21.24
11.63
16.5
23.06
9.68
16.6
H-pol. Element Excitation
Relative Side-lobe
Gain (dB) HPBW (deg)
level (dB)
15.42
19.44
14.46
18.38
14.72
16.1
20.91
11.67
17.21
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 Hpol. 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 Hpol./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.
84
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
 = −3.4365 0.03 + 9.4524
(3.9)
 = 3.4365 0.03 − 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.
86
Table 3 - 3 Vivaldi unit cell geometry parameters
Description
Element length
Element width
Aperture width
Tapered slot width
Feed slot width
Cavity-to-taper length
Cavity width
Cavity length
Cavity offset
Feed offset
Parameter
L
W








Value (mm)
33
8.8
6.6
2.2
0.825
4.125
2.75
6.6
2.948
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.
89
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  (~0.01).
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
(XY-plane at  = 92 deg.), and (b) middle H-pol. element (YZ-plane at  =118 deg.).
91
Table 3 - 4 Simulated gain, HPBW and side-lobe level (24 cm lens)
Frequency
3 GHz
4 GHz
5 GHz
6 GHz
Frequency
3 GHz
4 GHz
5 GHz
6 GHz
V-pol. Element Excitation
Relative Side-lobe
Gain (dB) HPBW (deg)
level (dB)
15.87
24.98
17.61
18.73
18.98
17.42
20.68
15.35
18.13
22.08
12.27
17.28
H-pol. Element Excitation
Relative Side-lobe
Gain (dB) HPBW (deg)
level (dB)
14.78
26.75
16.35
18.25
18.74
16.83
20.49
15.32
18.02
22.03
12.66
19.92
Figure 3 - 20 plots the simulated H-plane radiation patterns for central H-pol. /Vpol. 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.
92
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.
93
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.
96
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  at 3 GHz to 0.42  at 6 GHz. In contrast,
inter-element spacing between cross-elements (i.e. vertical and horizontal) ranges from
0.15  at 3 GHz to 0.3  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.
98
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.
101
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.
103
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 dualpolarized 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.
104
Chapter 4.
4.1.
3-D Printed cloaked microstrip antennas: reduction
of mutual coupling
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 bistatic 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⁄ ≥ 0.048⁄√ ). 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 ( = 2.7) is taken into account such
that
ℎ/2 < 0.048/√ (ℎ/2 = 0.017  0.048/√ = 0.029), where 2 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 1 = 0.92 GHz (Antenna I) and 2=1.034 GHz (Antenna II), each on the
substrate with  = 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.
107
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.
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.
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 1 , where 1 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.
110
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
( ) and (2) the permittivity of the dielectric spacer ( ). 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.
112
The optimum values for width of vertical metallic inclusions (ws ) on the elliptically
shaped metasurface cloaks obtained by numerical simulations is 1 = 0.1418 cm and
2 = 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.
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 Eplane, 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 ( = 5), a mixture of
Strontium titanate (3) 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.
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.
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
116
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.
117
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.
118
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).
119
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 remeasurement 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 ( ) 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
120
Figure 4 - 15, in which the regions of interest highlighted are region 1 (for cloaking
behavior seen by antenna I in measurement), region 1 (for cloaking behavior seen by
antenna I in simulation), and region 12 (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,  =5.9 with tan =0.05 for elliptical host spacer, and  = .  with
tan =0.01 for polymer substrate material). The highlighted regions from the left to
right corresponds to region  , region  , and region  )
121
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 (12 ). 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 semielliptical 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.
122
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.
124
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 /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 1520 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.
125
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.
126
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 firstorder 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.
127
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