Profile Wide Scan Angle Phased Array Antenna

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DEVELOPMENT OF AN ULTRA-WIDEBAND LOW- PROFILE WIDE SCAN ANGLE PHASED ARRAY ANTENNA

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the

Degree Doctor of Philosophy in the Graduate School of

The Ohio State University

Henry H. Vo, B.S., M.S.

Graduate Program in Electrical and Computer Engineering

The Ohio State University

2015

Dissertation Committee:

Prof. Chi-Chih Chen, Advisor

Prof. John Volakis, Co-Advisor

Prof. Joel T. Johnson

Henry H. Vo

2015

Abstract

Coupling in phased arrays is a major issue. Mutual coupling causes both gain and bandwidth reduction. Such coupling arises from the presence of adjacent elements that produce scattering and losses during low-angle beam steering. The scattering effect is comprised of (1) structural scattering and (2) antenna-mode coupling and associated losses. Losses occur when the coupled energy received by adjacent elements is dissipated at the back-end loads, resulting in lower gain at wide scan angles. In addition, the interference from periodic nature of large arrays or feed networks may produce undesired scattering modes and traveling waves that limit the upper bound of the operational frequency and maximum scan angle in ultra-wideband (UWB) arrays. As a result, current ultra wideband (UWB) array designs typically have limited scanning to no more than 45° from normal.

In this dissertation, we examine the low angle scanning issues. These issues are verified via full-wave simulation. Our studies show that mutual coupling in the H-plane is stronger than in the E-plane, likely due to the dipole element pattern shape.

Another focus of this dissertation is the development of an UWB dual- polarization and low angle beam steering array based on the concept of tightly coupled

ii dipole arrays. For this array, we suppress/minimize mutual coupling by redesigning the antenna element, feed geometry, and array structure. Some key design parameters include

(1) the simple feed of tightly-coupled dipoles, (2) array height above ground plane, (3) dielectric superstrate, and (4) parasitic coupling ring. The common mode issue is avoided by retaining the ground plane height to less than λmid/4 and the array unit cell size to

0.45λhigh. The final design is also fabricatable on a low-cost PCB. The PCB uses (1) 0.35 mils thick copper corresponding to a standard ¼ oz. copper lamination, (2) 2 mils coupling slot width and plated-thru vias manufacturable using standard PCB process, and

(3) standard Roger RT/Ruroid 5880LZ substrate with dielectric constant of 1.96 and

Roger RT/Duroid 5880 superstrate with dielectric constant of 2.2.

An 18x18 prototype array is fabricated and measured to verify the final design.

The total array height of the fabricated prototype is 0.122λ at the lowest operating frequency. It is also demonstrated that the fabricated array is capable of scanning down to more than 60° in the E- and H-planes with impedance bandwidth of 2.62:1 subject to

VSWR ≤ 2. Good agreement was also observed between simulations and measurements.

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Dedication

Dedicated to my family

Acknowledgements

I dedicate this dissertation to my parents, my sisters, and my brothers, for their hard work and constant support throughout my education. Without their support, I would not have what I have today.

I am thankful to my advisor, Dr. Chi-Chih Chen for his support, encouragement, guidance, and endless patience throughout my time and work at the ElectroScience Lab

(ESL). I thank him for sharing of his expertise and teaching me the key points of antenna design, antenna miniaturization, and as well as antenna measurement. It is my honor to have such an outstanding advisor and to be his research group member. I would also like to thank my co-advisor, Dr. John Volakis for the advice and motivation I have received from him. Thanks Dr. Joel Johnson for his valuable suggestions on this dissertation and for his participating on all my examination committee.

Very special thanks go to Dr. Teh-Hong Lee for his friendship and providing me all the valuable information in antenna measurement. I would like to express my very special thanks to Patricia Toothman for her endless support, advice, and guidance.

Thanks to all my friends at ESL for their friendships and insightful discussions in research as well as in course-work.

Vita

December 31, 1974………………………….….…. Born – Quang Nam, Vietnam

2002……………………………………………….. B.S. Electrical Engineering, Cal Poly State University

2008……………………………………………..… M.S. Electrical Engineering, Cal Poly State University

2004-2006…………………………………………. Microwave Engineer, L-3 Com/Randtron Antenna Systems

2006-2009…………………………………………. R&D Engineer, Space Systems/Loral

2009-2011…………………………………………. Sr. R&D Engineer, Space Systems/Loral

2011-present………………………………………. Graduate Research Associate, The Ohio State University

Publications

H. H. Vo and C.C. Chen, “A Very Low-Profile UWB Phased Array Antenna Design for Supporting Wide Angle Beam Steering,” in review.

H. H. Vo and C.C. Chen, “Frequency and Scan Angle Limitations in UWB Phased Array,” European Conference on Antenna and Propagation (EUCAP), Hague, Netherlands, Apr. 2014.

H. H. Vo and C.C. Chen, “Causes of Low Scanning Angle Issues in Phased Array Antennas,” Antennas Measurement Technique Association (AMTA), Columbus, OH, Oct. 2013.

N. K. Host, H. H. Vo, and C.C. Chen, “Causes of Low Scanning Angle Issues in Phased Array Antennas,” Antennas and Propagation Society International Symposium, Orlando, FL, Jul. 2013.

Fields of Study

Major Field: Electrical and Computer Engineering

Studies in:

Electromagnetics

Microwave/Antenna Design and Measurement

RF Circuits

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Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgements ...... v

Vita...... vi

Table of Contents ...... viii

List of Tables ...... x

List of Figures ...... xi

Chapter 1: Introduction ...... 1

Chapter 2: Wide-Angle Scanning and Bandwidth Issues/Limitations of Phased Array Antennas .. 6

2.1 Mutual Coupling in Phased Arrays ...... 6

2.2 Low-Angle Scanning Issues ...... 7

2.2.1 Antenna Structure Mode Scattering Issue ...... 9

2.2.2 Absorption by Adjacent Elements ...... 11

2.2.3 Antenna Mode Scattering ...... 13

2.3 Bandwidth and Wide Scan Angle Limitations ...... 15

2.3.1 Lattice Scattering Mode in Scatter Array ...... 15

2.3.2 Lattice Scattering Mode in Phased Arrays ...... 18

Chapter 3: Development of Wide Scan Angle Phased Array ...... 26

3.1 Revisiting TCDA Operational Principles...... 27

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3.1.1 Ground Plane Effect in Ideal TCD Array ...... 28

3.2 Wide Scan Angle Array Design Procedure ...... 33

3.2.1 Tightly-Coupled Array Element Design ...... 33

3.2.2 Feeding Lines ...... 36

3.2.3 Effect of Array Height on Wide Scan Angle ...... 38

3.2.4 Effect of Element Pattern on Wide Scan Angle ...... 41

3.2.5 Effect of Mutual Coupling on Wide Scan Angle ...... 42

3.2.6 Effect of Parasitic Ring ...... 46

3.3 Design Parameter Tolerance Analysis ...... 48

3.3.1 Element-to-Element Coupling Slot Width Tolerance Study ...... 48

3.3.2 Bonding Layer Thickness Tolerance Study ...... 50

3.3.3 Feed-line Diameter Tolerance Study ...... 51

3.4 Summary ...... 53

Chapter 4: Prototype Measurement ...... 54

4.1 Finalized 18x18 Dual-Pol UWB Array Prototype Design ...... 54

4.2 Array Assembly ...... 57

4.3 Array Design Verification ...... 61

4.4 18x18 Array Prototype Measurement Results ...... 62

Chapter 5: Conclusion and Future Work ...... 75

Appendix A: Array Pattern Synthesis ...... 80

A.1 Finite Array Pattern Synthesis (Amplitude Distribution) ...... 83

A.1.1 Fast Array Pattern Synthesis using Element Patterns ...... 85

A.2 Array Patterns Synthesized Using PSO ...... 87

Bibliography ...... 91

List of Tables

Table 2.1: Predicted maximum bi-static RCS frequencies at a given look angle...... 17

Table A.1: Observed peak gain and SLL for different number edge elements attenuated by 10 dB...... 83

List of Figures

Figure 2.1. Transmitting (left) and receiving (right) mode coupling paths between two represented elements in array antenna...... 7

Figure 2.2. The four mechanisms associated with wide angle scanning...... 9

Figure 2.3. Infinite dipole arrays for back-scattering study: (a) Hertzian, (b) Narrow planar, (c) Wide planar, (d) Fat wire...... 10

Figure 2.4. Scattered field comparison of three infinite half-wavelength arrays. Hertzian dipole scattered field not shown on this plot since there is no structure scattering...... 11

Figure 2.5. Absorbed and reflected energy from adjacent elements...... 12

Figure 2.6. H-plane gain patterns of a 10-element 1D dipole array (Figure 2.5) for different scan angles (solid lines) and the envelope of total energy absorbed by the rest of array elements (dash- dot line) as a function of scan angle...... 13

Figure 2.7. Array realized peak gain vs. scan angle for three port impedance conditions. Impedance mismatch causes overall pattern and gain degradation...... 14

Figure 2.8. Scattering of infinite array of small PEC cylinders...... 16

Figure 2.9. Bi-static scattering patterns of scatter array of Figure 2.8a...... 18

Figure 2.10. A unit cell model of an infinite array of free-standing dipoles...... 19

Figure 2.11. Lattice modes at wide-angle scanning in phased array. (a): E-plane scanning, (b): H- plane scanning...... 19

Figure 2.12. Scattering of infinite array of dipoles...... 21

Figure 2.13. A unit cell model of an infinite array backed by a PEC ground plane and dielectric loading...... 22

Figure 2.14. Lattice modes in phased array backed by a PEC ground plane and no dielectric loading...... 24

Figure 2.15. Lattice modes in phased array backed by a PEC ground plane and dielectric loading...... 25

Figure 3.1. (a) Shorted circuit reactance of a lossless two wire transmission line, (b) Response of ground plane impedance in free space with different ground plane height “d”...... 28

Figure 3.2. Free-standing TCDA and its equivalent circuit and impedance response in Smith chart. Assume RAo is constant of 100 Ω and XAo varies from -200 to 200 Ω, and Z0 is 100 Ω...... 30

Figure 3.3. Ideal TCDA. (a) Impedance of free-standing array (blue dash-dot line), quarter wavelength PEC ground plane (black line), and array with PEC ground plane (red dash line). (b) Susceptance of ground plane alone (black solid line), array alone (blue dash-dot line), and resultant of ground plane plus array (red dash line). (c) Reflection coefficient of free-standing array (w/o ground plane) and with ground plane. Noted that Z0 is 100 Ω...... 31

Figure 3.4. Full-wave simulation TCDA. (a) Impedance of free-standing array (blue solid line) and array with PEC ground plane (red dash line). (b) Susceptance of ground plane alone (black solid line), array alone (blue solid line), and resultant of ground plane plus array (red dash line). (c) Reflection coefficient of free-standing array (w/o ground plane) and with ground plane. Noted that Z0 is 100 Ω...... 32

Figure 3.5. Initial design of a dual-polarized TCDA one quarter wavelength above ground plane at center frequency and its VSWR response at boresight. The antenna element is excited with a lumped port...... 35

Figure 3.6. Response of TCDA with actual feed line implemented...... 38

Figure 3.7. Reflection coefficient when the array is scanned at 60° in the E-plane with different ground plane height...... 40

Figure 3.8. The simulated VSWR vs. frequency under both E- and H-plane beam steering to 0°,

30°, 60°, and 75° for array height (above ground plane) of 0.18λd at center frequency...... 40

Figure 3.9. Vanishing E-plane pattern of a wire dipole due to symmetry (left) and maximum H- plane radiation direction (right)...... 41

Figure 3.10. E-plane scanned patterns (top right) of a 10-element collinear Hertzian dipole array (left) and the H-plane scanned patterns (bottom right) of a 10-element parallel Hertzian dipole

xii array (not shown). Note the loss of gain in E-plane scans during scanning due to dipole element pattern...... 42

Figure 3.11. Energy absorbed by other 9 elements in a 1x10 dipole array...... 43

Figure 3.12. Direction of radiated EM field on array of no superstrate (left) and with superstrate (right) on array surface...... 44

Figure 3.13. Effects of superstrate in the H-plane scan. (Left) without superstrate, more energy propagates along array plane. (Right) with 0.24λd thick superstrate, energy tends to propagate upward...... 45

Figure 3.14. Simulated VSWR vs. frequency in the E- and H-plane at scanned angles of 0°, 30°,

60°, and 75° for a ground plane height of 0.18λd at center frequency and a 0.24λd thick superstrate in front of the infinite array shown in Figure 3.6...... 45

Figure 3.15. Unit cell of the proposed low-profile dual-polarization UWB TCDA design which can be completely fabricated using standard PCB manufacturing process...... 47

Figure 3.16. Simulated VSWR vs. frequency in the E- and H-plane at scanned angles of 0°, 30°, 60°, and 75° for a TCDA design with parasitic ring placed on top of superstrate as shown in Figure 3.15...... 47

Figure 3.17. Element-to-element coupling slot width tolerance study. No significant effect on performance is observed from 1.5 to 2.5 mils slot width...... 49

Figure 3.18. Study of the tolerance of PCB bonding layer thickness. The bonding layer thickness of 3 mils with tolerance of ± 1mil. No significant effect on performance is observed...... 51

Figure 3.19. Study of the effects of the feed-line diameter...... 52

Figure 4.1. (a) Final design that can be entirely fabricated using PCB, (b) 2D block connector (left) formed by multiple 1D block connector (right)...... 55

Figure 4.2. (a) Front and back views of the 18x18 fabricated prototype array, (b) R65 connector blocks (top) and R65 to K cable (bottom)...... 56

Figure 4.3. Array element layout and tested elements (red highlighted)...... 58

Figure 4.4. (a) Assembly of the array test setup, (b) Array with the support of the test fixture, (c) Cables are secured by glue and styrofoam with green tape...... 60

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Figure 4.5. Radiation pattern measurement setup in the compact range...... 63

Figure 4.6. Measured antenna element |S11| without phase shifter; (top) E-elements, (bottom) H- elements ...... 64

Figure 4.7. (a) Simulated and measured element pattern in E- and H-plane at fc; (a) E-plane, (b) H-plane...... 65

Figure 4.8. 18x∞ array model analyzed in HFSS to obtain the predicted array gain and E- and H- plane scanned patterns of the prototype 18x18 array...... 67

Figure 4.9. Simulated and measured realized gain patterns at broadside; (a) Element gain pattern, (b) Array gain pattern...... 68

Figure 4.10. (a) Element layout in the 18x18 array, (b) Element numbers are re-labeled from 1 to 10, (c) E- and H-element in array unit cell...... 70

Figure 4.11. Simulated and measured coupling vs. frequency with element 7 excited; (a) E-plane element 1 to 3, (b) H-plane element 1 to 3, (c) E-plane element 4 to 6, (d) H-plane element 4 to 6, (e) E-plane element 7 to 10, (f) H-plane element 7 to 10...... 71

Figure 4.12. S-Parameter measurement setup; (a) Simulated |S| reference plane, (b) Measured |S| reference plane...... 72

Figure 4.13. R65 cable insertion loss vs. frequency...... 72

Figure 4.14. Normalized simulated and measured principal plane gain patterns for various scan angles; (a) E-plane 0.58fc, (b) H-plane 0.58fc, (c) E-plane fc, (d) H-plane fc, (e) E-plane 1.23fc, (f)

H-plane 1.23fc, ...... 73

Figure 5.1. Using multilayer superstrate to direct the array beam to a wider angle...... 78

Figure A.1. Near-field distributions of 10-element in E-plane at fc...... 82

Figure A.2. E-plane gain pattern of a 10x6 array at fc under different edge treatments...... 82

Figure A.3. 9x9 array which is used for array pattern synthesis. (a) 9x9 array with progressive phase between elements, (b) 9x9 array with amplitude excitations for SLL reduction...... 84

Figure A.4. Synthesized array pattern using Matlab as compared to full-wave simulated array pattern...... 87

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Figure A.5. Optimized array pattern from Matlab is verified in HFSS...... 89

Figure A.6. Optimized array patterns with scanned angles of 0°, 30°, and 60°...... 89

Figure A.7. 3D far-field plots for the cases of 0°, 30° before and after array synthesis...... 90

Chapter 1: Introduction

Phased array antennas are important in modern radars and communication applications in dynamic environments because of their fast beam steering and multiple target tracking capabilities [1-2]. For instance, they are widely used in ground-based multi-function military radar [3-4], airborne surveillance radar [5-6], spaceborne SAR

(synthetic aperture radar) [7-8], radio astronomy [9], and modern land mobile communication systems [10-12]. These advanced applications have been increasing the demands for better low-profile wideband phased array antennas for improves system performance as well as increased functionality.

The traditional phased array antenna design approach begins with designing a single array element to achieve a desired impedance bandwidth. This element is then replicated to make an array with a proper inter-element spacing, less than a half wavelength (at highest operating frequency) to avoid grating lobes [13]. However, at such spacing or less, strong coupling between elements is inevitable. This issue is worsened when the beam is scanned to low angles, i.e. close to the array plane. Such coupling effect can reduce bandwidth and limit the beam scanning range if it is not properly controlled. In additional, the presence of strong coupling between elements can also produce an undesirable lattice scattering mode in large periodic array structures, which limits the maximum operating frequency under wide-angle scanning conditions.

Therefore, designing a low profile UWB phased array antenna for wide scanning angle is still very challenging.

Many publications have discussed array bandwidth improvement [14-22]. A highly successful concept is current sheet or connected array by Munk [21-22]. This concept provides 4:1 bandwidth. But recently, Munk’s connected array was expanded to the tightly coupled dipole array (TCDA) concept [15, 18-20, 62] delivering more than

13:1 bandwidth. The TCDA design involves tightly coupled array elements placed less than a quarter of wavelength above the conducting ground plane which acts as a shunt inductance at the low frequency end and shunt capacitance at the high frequency end. The shunt reactance balances out the strong TCDA inter-element coupling reactance which acts as series capacitance at low frequency end and series inductance at high frequency end. However, such bandwidth is not guaranteed under wide scan angle conditions in most published ultra-wideband (UWB) TCDA designs. Therefore, previously published phased arrays were able to widen array bandwidth but array scanning capabilities were still limited.

When designing a phased array antenna, it is desirable to have an array that is able to scan all the way from broadside (0°) to horizon (90°). This will allow a radar to detect targets over larger look angles. A few publications discussed about widening array scanning [23-25]. In [23], a thin, high-k, dielectric slab is placed in the front and parallel to the array element to improve wide-angle impedance matching (WAIM) to reduce the variation of reflection coefficient with scan angle and polarization. The angle-dependent susceptance of the dielectric sheet with angle of incidence is utilized for compensating the angle-dependent impedance of the array element. It was shown in [23] that this

2 treatment allowed the array to scan from broadside up to 60° with maximum voltage standing wave ratio (VSWR) of 1.78. In [24], the wide scan angle is achieved by employing two sets of impedance matching circuits (one set connects element lines in the

E-plane and the other set connects in the H-plane) underneath the array element. These circuits introduce phased-dependent susceptance, to reduce element impedance mismatch over a wider range of scan angles. It was shown that these impedance matching circuits reduced the VSWR from 5 to 1.68 within 120° scan cone. However, the two mentioned methods in [23-24] only considered small bandwidth. In [25], several types of elements such as waveguide aperture elements or tapered-slot elements were investigated for wide- angle scanning arrays. However, these types of elements are bulky and tall. Therefore, they are not suitable for low profile applications.

There are various published design approaches for compensating the mutual coupling effect in array antennas. For instance, Gupta and Ksienski proposed the “Open-

Circuit Voltage” algorithm [26] where the N-element antenna array is treated as an N-port network. The mutual coupling between antenna elements is compensated via the calculated mutual impedance at the antenna terminals. However, this method can only be applied for transmitting arrays since the mutual impedance will be different when the array is receiving. Also, in practical situations, antenna elements are terminated with a load impedance and there are currents induced on the antenna terminal, while the method assumes all the antenna elements are open-circuited with no current flow. In [27], the calculated coupling coefficients between the array elements are formed into a matrix which can be used to compensate for the effects of mutual coupling. In order for this method to work, the element to element spacing must be larger than λ/2. It is also shown

3 that this method is not suitable for all planar array configurations. The effects of mutual coupling can be quantized and eliminated by the use of method of moment (MoM) [28].

However, this method requires the knowledge of the incident plane wave which is not available in practice.

Several other designs strive to minimize the mutual coupling or suppress surface waves under the element array using ground slits [29-30], electromagnetic band gap

(EBG) [31], or via-wall cavity structures [32]. However, the presence of these structures will create greater frequency-dependent and scan-dependent impedance and more structure scattering issues, and thus degrading the overall bandwidth and wide angle scanning performance. Furthermore, it is not practical to implement these structures due to the physical small size of the array unit cell at frequency above Ku band.

In summary, there is still a need for a low-profile wideband dual-polarization phased array antenna design that supports wide-angle scanning. This dissertation will present a novel UWB low-profile dual-polarized phased array antenna design which has reduced mutual coupling between array elements to improve scanning beyond 45° from broadside. This is accomplished by properly designing the antenna element, feed geometry, and array configurations. Some key design parameters include the tightly- coupled dipoles, extremely simple feed structures, array height above ground plane, and dielectric superstrate. The dissertation is organized as follows:

 Chapter 2 discusses the wide angle scanning and bandwidth issues, limitations in

phased array antennas. The mutual coupling mechanisms between elements in

array will be shown. The effects of mutual coupling as well as lattice scattering

onto the array bandwidth and gain pattern are presented. It is important to

characterize these effects since they limit the bandwidth and wide angle scanning

of the antenna array.

 Chapter 3 gives a brief overview of TCDA operational principles and a design

approach for wide angle scanning. This design is done for infinite arrays.

Therefore, edge effects are not accounted for. Key parameters of the antenna such

as feed-line, ground plane height, inter-element spacing, superstrate, and parasitic

coupling ring are investigated. Sensitivity analysis of antenna components is

performed prior to array prototype fabrication.

 In Chapter 4, the experimental measurements of an 18x18 dual-polarized

prototype array are presented. The array fabrication integrity is verified by

measuring the reflection coefficient of each antenna element. The measured

results are compared to the simulated results and the differences are discussed.

 Chapter 5 provides a summary of the dissertation, general conclusions, array

design as well as fabrication challenges, and a discussion for future work on

wideband, wide angle scan phased array.

 An optimization method on array tapering for side-lobe level (SLL) suppression is

performed and presented in Appendix A. The goal is to obtain low SLL while

minimize the reducing of the peak gain.

Chapter 2: Wide-Angle Scanning and Bandwidth Issues/Limitations of Phased Array Antennas

2.1 Mutual Coupling in Phased Arrays

It has been shown in [13, 26, 33-38] that the performance of phased array antennas is strongly affected by the “mutual coupling” between elements within the array. These coupling effects on the array performance depend upon (1) element type and its design parameters, (2) relative position of the elements, (3) feed of elements, and (4) scan angle.

Figure 2.1 explains the coupling mechanisms between the two antennas in proximity to each other. If one antenna (Ant. N) is excited (transmitting), a portion of the energy be coupled to the adjacent antenna (Ant. M). The amount of the coupled energy depends on the size, geometry, spacing, and orientation of elements. Such coupling arises from the presence of adjacent elements that introduces scattering and absorption effects during wide-angle beam steering. The scattering effect is composed of structure-mode scattering and antenna-mode scattering. The absorption effect happens when the EM energy received by an adjacent element is dissipated into the system. The coupling mechanisms shown in Figure 2.1 have also been mentioned in literatures [13, 33]. A list of the effects associated with the presence of adjacent elements is illustrated in Figure

2.2. To allow for an effective wide scan angle in phased array design, the main goal of

6 this chapter is to provide more insights into the causes of bandwidth and wide-angle scanning limitations.

Figure 2.1. Transmitting (left) and receiving (right) mode coupling paths between two represented elements in array antenna.

2.2 Low-Angle Scanning Issues

To avoid grating lobe issue, phased array elements are often packed closely with inter-element spacing less than half a wavelength. This naturally leads to strong coupling between elements. As illustrated in Figure 2.2, a portion of the energy coupled to the neighboring elements enters the system and manifests itself into so called “active

7 impedance” even though the element impedance actually remains unchanged. When the beam of an antenna array is steered to low angles, the electromagnetic energy illuminates neighboring elements increases, and the following four events illustrated in Figure 2.2 become more important.

1. A portion of electromagnetic (EM) energy continues propagating when there is no

obstruction from adjacent elements.

2. A portion of the EM energy is scattered by the structures of adjacent elements or

feeding structures, producing “structure mode” scattering. The strength of the

scattered fields depends on the size, orientation, composition, and geometry of these

structures.

3. A portion of EM energy received by the adjacent element propagates into its feed port

where it is partially reflected (due to mismatch between element and system) back out

to the antenna element and produce secondary radiation from this adjacent element.

This “antenna-mode scattering” interferes with the original array radiation.

4. A portion of energy intercepted by the adjacent element propagates through its feed

port into the system, and results in gain reduction at low-angle scanning due to this

system absorption. The amount of energy absorbed back by the system depends on

the impedance matching condition between the system and the element in the absence

of array at the given frequency. It is worthwhile to point out that this received energy

causes the power rerunning to the system to increase, and thus is often mistakenly

referred to as “active impedance” or “scan impedance” even though no impedance

changes occur during scanning.

Figure 2.2. The four mechanisms associated with wide angle scanning.

2.2.1 Antenna Structure Mode Scattering Issue

To demonstrate the element structure scattering effect during wide-angle scanning, four infinite arrays composed of Hertzian dipoles (zero cross section current source) and PEC half-wavelength dipoles with different element width or thickness were analyzed using a commercial full-wave EM simulation software High Frequency

Structure Simulation (HFSS) based on Floquet’s theorem for periodic boundary conditions (see Figure 2.3). All four arrays were analyzed in free-space without dielectric loading (substrate), feed lines, or ground plane backing. Figure 2.4 plots the computed unit-cell bi-static scattering patterns obtained when Figure 2.3(b), (c) and (d) arrays are illuminated by a grazing plane wave with electrical field polarized in parallel with

9 dipoles, i.e., θ = 90o. Note that all elements being terminated with a matched load, and therefore only structure-mode scattering is involved. Since Hertzian dipoles have zero cross sectional area, it does not produce any structure scattering, and thus is not included in Figure 2.4. It shows that the structure-mode scattered field intensity increases with the size of dipole element.

Figure 2.3. Infinite dipole arrays for back-scattering study: (a) Hertzian, (b) Narrow planar, (c) Wide planar, (d) Fat wire.

Figure 2.4. Scattered field comparison of three infinite half-wavelength arrays. Hertzian dipole scattered field not shown on this plot since there is no structure scattering.

2.2.2 Absorption by Adjacent Elements

A 10-element half wavelength dipole array was analyzed to demonstrate the effect of energy absorption and re-radiation (i.e. antenna-mode scattering) by adjacent elements.

As mentioned, when the impedance of the antenna element and the system are matched, the energy received will be absorbed by the system as illustrated in Figure 2.5, and results in radiation power reduction at wide-angle scanning. Note that the antenna impedance, ZA is 100 Ω, and the system impedance, ZS is 100 Ω for impedance matched condition.

Figure 2.6 plots the H-plane scanned gain patterns (solid lines) of a 10-element

1D dipole array for scanned angles from 0° (boresight) to 75° in 15° increments. As seen, while the peak gain decreases as the beam is steered to wide angle in the H-plane (dashed brown line); the total energy absorbed by all other 9 elements (dash-dot blue line) increases versus array scan angles. Therefore, it is obvious that most gain reduction at wide scan angles is caused by absorption of adjacent elements.

Figure 2.5. Absorbed and reflected energy from adjacent elements.

2.2.3 Antenna Mode Scattering

When there is an impedance mismatch between the antenna element and the system, a portion of received energy will be reflected back to the antenna and produce secondary radiation, i.e. antenna-mode scattering. To demonstrate this effect, the port impedance, i.e. system impedance (ZS in Figure 2.5) was changed from 100 Ω (matched condition) to 50 Ω and 150 Ω to produce different impedance matching conditions.

Figure 2.7 plots the envelope of peak gain for different scan angles (i.e. dashed brown line in Figure 2.6) and three different port impedance values. These envelope curves

13 were normalized to their broadside (0o) values. The results show that the decreasing rate of peak gain increases for the 50 Ω case and decreases for the 150 Ω case. The reason for this difference is due to destructive or constructive interference from the additional antenna-mode scattering as a result of additional reflection between antenna and system.

Whether the antenna-mode scattering is destructive or constructive depends on the sign of reflection coefficient and the length of feed line. Furthermore, the impedance mismatch causes overall pattern and gain degradation since less energy is delivered to the antenna element.

Figure 2.7. Array realized peak gain vs. scan angle for three port impedance conditions. Impedance mismatch causes overall pattern and gain degradation.

2.3 Bandwidth and Wide Scan Angle Limitations

With the collective scattering of the aforementioned structure-mode and antenna- mode scattering from periodic structures in phased array may generate lattice scattering modes when the beam is steered toward wide angles. These lattice scattering modes are generated as a result of in-phase or out-of-phase interferences of scattering from all periodic structures. As will be shown later, such lattice scattering modes limit the maximum operational frequency and wide scan angle of phased arrays.

2.3.1 Lattice Scattering Mode in Scatter Array

To investigate the lattice scattering modes produced by the periodic structures of phased arrays, the electromagnetic scattering from an infinite uniform array of small perfect electrical conducting (PEC) cylinders as shown in Figure 2.8(a) was studied. Each cylinder has a length of 2mm, diameter of 0.1mm, and array spacing of 5mm.

Figure 2.8(b) shows an incident plane wave with electrical field polarization parallel to the axis of cylinders and an incident angle of θ. The magnitude of total backscattered fields generated from this plane wave incidence should reach its maximum when direct scattering and high-order scattering other cylinders are in phase (see Figure

2.8(b) right figure). This occurs when the various components are in phase, implying the relation:

Figure 2.8. Scattering of infinite array of small PEC cylinders.

푀(푘푑 + 푘푑푠푖푛휃) = 2푁휋 (2.1)

where, k is the free-space wavenumber, d is the lattice (or array) spacing, M is the total scattering fields (M > 1 ϵ I ), N is the number of elements (N > 0 ϵ I ), and θ is the incident plane wave angle. From (2.1), the frequency at which the maximum back scattering occurs is given by

푁 푐 푓 = (2.2) 푀 푑(1+푠푖푛휃)

where, c is the speed of light in vacuum. Table 2.1 lists the lattice scatter mode frequencies predicted from (2.2) for different incident angles from 30° to 90° in 15° increments. To validate this prediction, full-wave simulations of this backscattering problem was performed using Ansoft HFSS, with periodic boundary conditions (PBC).

The resultant backscattered unit-cell radar cross section (RCS) is plotted in Figure 2.9 as a function of frequency for different incident angles. Observed that the frequencies which the maximum bi-static RCS occurred matched exactly to the lattice scatter frequencies predicted in Table 2.1 at its corresponding incident angle.

Table 2.1: Predicted maximum bi-static RCS frequencies at a given look angle.

Figure 2.9. Bi-static scattering patterns of scatter array of Figure 2.8a.

2.3.2 Lattice Scattering Mode in Phased Arrays

To demonstrate the existence of the lattice scattering mode in phased array antennas, an infinite array of dipoles shown in Figure 2.10 with a unit-cell size of 5mm by 5mm was simulated using HFSS. The antenna element is excited via a lumped-port with matched port impedance of 100 Ω. Figure 2.11 plots the computed S11 magnitude as a function of frequency under different scan angles from 0° to 75° for the E- and H-plane.

Several local maxima of S11 values are observed above 30 GHz in both scanned planes.

Further examination of the frequencies where these local spikes occur reveals that the frequencies coincide well with the frequencies predicted in Table 2.1 and Figure 2.9.

Figure 2.11 also shows that the lattice mode scattering problem becomes more

18 pronounced at wide scan angles and at high frequencies. Furthermore, more ripples are observed in the H-plane scans (Figure 2.11(b)); hence, stronger mutual coupling in the H- plane than in the E-plane.

Figure 2.10. A unit cell model of an infinite array of free-standing dipoles.

continued (a)

Figure 2.11. Lattice modes at wide-angle scanning in phased array. (a): E-plane scanning, (b): H-plane scanning.

Figure 2.11 continued

(b)

It should be pointed out that the lattice modes in this case produce out-of-phase interference to the direct radiation from the source element, thus increasing S11. While the path difference based on (2.1) should produce an in-phase condition, this out-of-phase condition is caused by the additional phase reversal of the scattered fields from PEC dipole structures. As a result, equation (2.1) can be modified to include this effect as

푀(푘푑 + 푘푑푠푖푛휃) − (2푁 + 1)휋 = (2푁 + 1)휋 (2.3)

Notice that the (2푁 + 1)휋 on the left side of equation (2.3) is due to the phase reversal of the reflected fields. The right side of equation (2.3) is now (2N + 1)π instead

20 of 2Nπ, because the direct radiated fields and the scattered fields are 180° out of phase, resulting in high S11. The total fields can now be expressed as

푗(휙+휋) 퐸⃑ 푇표푡푎푙 = 퐴 + 퐵푒 (2.4)

where in equation (2.4), the first term is the direct radiated field and the second term is the scattered field, and both the phase terms are normalized to the wave directed reference plane. Also, the phase delay of the scattered field, ϕ is 2π. Figure 2.12 shows an infinite dipole array with its scattering characteristics which include direct radiation from the antenna element as well as scattered fields from adjacent elements. Since all the dipoles are connected to matched ports, the contribution from antenna-mode scattering in this case is not significant. Therefore, it can be concluded that such lattice scattering modes limit the frequency upper bound and the maximum scan angles of wideband phased array operations.

Figure 2.12. Scattering of infinite array of dipoles.

2.3.2.1 Effect of Ground Plane and Substrate on Lattice Scattering Mode

The array in Figure 2.10 is now backed by a PEC ground plane and dielectric loading as shown in Figure 2.13. There are two changes to the array, one is the presence of ground plane and the other is the dielectric loading (substrate). Let us examine the effect of each parameter on the array performance.

Figure 2.13. A unit cell model of an infinite array backed by a PEC ground plane and dielectric loading.

Again, we just focus on understanding the scattering properties of the array. First consider when the array is backed by a PEC ground plane and no dielectric loading. From the scattering point of view when a plane wave is incident upon the array, the wave that passes through the array keeps continuing its propagation until it sees the ground plane and is reflected. If the ground plane height is electrically large, the reflected fields will be

22 very weak and do not have much effect on the total scattered fields. Furthermore, the response of the array will be the same as in the case of the free standing array (as shown in Figure 2.11) if the ground plane height is infinite. When the ground plane height is electrically small, the phase delay term seen in equation (2.3) exists as well as an additional phase delay term from the reflected fields. This phase delay term will be a function of the ground plane height and the beam steering angle.

When the beam steers to wide angle, i.e. closer to the array plane, the wave is more concentrated along the array plane and there is not much reflected fields from the ground plane. As a result, the change in the lattice resonance frequency at wide-angle scanning is negligible. When the beam steers to a higher angle, i.e. closer to the normal of the array, the reflected fields will be stronger and the phase of the reflected fields is no longer negligible. The reflected fields are roughly 180° out of phase with the original scattered fields. In this case, the denominator of equation (2.2) will be smaller and the resonance will shift higher in frequency. Therefore, the lattice resonance frequencies for the array backed by a PEC ground plane (Figure 2.14) are higher than the lattice resonance frequencies of the array without PEC ground plane (Figure 2.11). For instance, at the scanned angles of 45° and 60°, the lattice resonance frequencies of the free- standing phased array are 35.15 GHz and 32.15 GHz. While for the array backed by a

PEC ground plane, these frequencies are 36.5 GHz and 33 GHz, respectively.

Figure 2.14. Lattice modes in phased array backed by a PEC ground plane and no dielectric loading.

Next, considering the array backed by a PEC ground plane and is loaded with dielectric substrate, the wavenumber from equation (2.3) is now the effective wavenumber between the vacuum and the substrate’s dielectric. Equation (2.2) can then be expressed as:

푁 푐 푓 = (2.5) 푀 휀 푑(1+푠푖푛휃) √ 푟푒푓푓

where, 휀푟푒푓푓 is the effective dielectric constant. As a result, the resonance frequency will get lower. In addition, surface waves will be more prone to propagate at wider scan angles. This will cause the lattice scattering to be stronger. Figure 2.15 demonstrates the

S11 responses of the array in Figure 2.13 while scanning in the E-plane. The H-plane scans are not shown since the lattice modes are the same in both scanned planes. As

24 observed, the lattice frequency modes are much lower and more pronounced as compared to the array without dielectric loaded as shown in Figure 2.14.

Figure 2.15. Lattice modes in phased array backed by a PEC ground plane and dielectric loading.

Chapter 3: Development of Wide Scan Angle Phased Array

According to the Wheeler–Chu limits [39-40], a small single antenna provides low gain and is difficult to steer its pattern. On the other hand, a large single antenna can produce high gain but is still difficult to steer its pattern. Phased array antennas composed of multiple radiating elements with phase shifters can provide high gain and are steerable.

Array beam pattern can also be shaped by applying different weightings among array elements. A TCDA is an array that has closely spaced dipole antenna elements [15, 18-

20, 62]. TCDA achieves wider bandwidth than conventional array antennas through the inter-element capacitive mutual coupling. The inter-element capacitive coupling is introduced at the ends of the dipole arms and is different from the conventional mutual coupling between elements. While the inter-element capacitive coupling is desirable for achieving wide bandwidth, conventional mutual coupling limits wide angle scanning

(WAS) in phased arrays, especially in the H-plane where strong mutual coupling occurs due to the dipole element pattern. The excitation of array element consists of an amplitude and a phase applying at each element input. In uniform spacing array with single beam, the phase shift between two successive elements is constant and is called phase-increment or progressive phase, β. The progressive phase value can be calculated based on the desired scanning angle and the operating frequency. That is, “β = kdsinθ”,

26 where k is the wave propagation constant, d is the element-to-element spacing, and θ is the beam angle. By varying β via the use of delay lines or phase shifters, the array beam can be steered to different directions. The operational principle of theoretical TCDA is discussed in section 3.1 and the remaining of the chapter discusses about the proposed systematic approach for designing an UWB low-profile dual-polarized TCDA that can support much wider beam steering angle compared to the existing TCDA designs.

Sensitivity analysis on key design parameters were also performed to access fabrication tolerance which is especially important for operating above Ku bands.

3.1 Revisiting TCDA Operational Principles

Traditional phased array antenna designs suffer from adverse effects of mutual coupling between elements [1, 2, 13, 41] on radiation pattern, polarization, and element impedance. The effect of mutual coupling is more serious if the element-to-element spacing is electrically small and is worsened when the beam is scanned to wide angle.

Conformal antennas are usually printed on substrates and are backed by a conducting ground plane, a necessary requirement for low-profile arrays to be mounted on a platform so that their performance will not be affected by the platforms. The presence of ground plane reduces the operating bandwidth of the array due to the shunt reactance effect introduced by the conducting ground plane. However, the connected array by Munk [21] produces 4:1 bandwidth whereas the more recent TCDA concept [18-

20] provides for 13:1 bandwidth and beyond.

3.1.1 Ground Plane Effect in Ideal TCD Array

Figure 3.1(a) shows a lossless two-wire transmission line with length “d”, characteristic impedance Z0, and a shorted termination (ground plane, ZL = 0). Since the line is lossless, the input impedance of the line is purely reactive as shown on the rim of the Smith chart (Figure 3.1(b) bottom). It is shown that when the distance “d” equals to a quarter of wavelength at the center frequency, the reactance becomes inductive at the low frequency end (i.e. below the center frequency) and capacitive at the high frequency end

(i.e. above the center frequency) as shown in Figure 3.1(b).

continued

Figure 3.1. (a) Shorted circuit reactance of a lossless two wire transmission line, (b) Response of ground plane impedance in free space with different ground plane height “d”.

Figure 3.1 continued

Figure 3.2 shows an ideal free-standing TCDA design with its equivalent circuit and impedance response plotted on Smith chart. In this case, the real part of the input impedance of the array is assumed to be 100 Ω and the reactance part is assumed to be varied from –j200 to +j200 Ω from 5 to 45 GHz. Note that the array reactance is capacitive below the center frequency band and becomes inductive above the center frequency band. Figure 3.3 demonstrates the impedance effect when the infinite array is

29 placed a quarter of wavelength (at the center frequency) above an infinite PEC ground plane. As seen, the bandwidth is enhanced from 1.73:1 (as for the free-standing array) to

4:1. Note the free-standing array equivalent circuits in Figure 3.2 and Figure 3.3 are adopted from [42, 61].

Figure 3.2. Free-standing TCDA and its equivalent circuit and impedance response in Smith chart. Assume RAo is constant of 100 Ω and XAo varies from -200 to 200 Ω, and Z0 is 100 Ω.

The ideal TCDA impedance bandwidth is validated by the full-wave simulation of an infinite free-standing dipole array. Each dipole is excited by a lumped-port with port impedance of 100 Ω and the array is positioned a quarter of wavelength (at the center frequency) above an infinite conducting ground plane. The array is under broadside beam condition and its reflection coefficient is plotted in Figure 3.4. It is observed that even though the obtained bandwidth is less than 4:1 which is due to the array not optimized for

31 maximum impedance bandwidth, its response is almost identical to the theoretical TCDA

(Figure 3.3).

3.2 Wide Scan Angle Array Design Procedure 3.2.1 Tightly-Coupled Array Element Design

The antenna elements commonly used in phased arrays include open-ended waveguides, tapered slots, patches, and dipoles. Among them, waveguide aperture elements can be scanned to very low angle, but are narrow band and bulky [13, 43-44].

Tapered slot elements provide good bandwidth but are relatively tall (~0.5λlow) [41, 45-

49]. Thus, both waveguide and tapered slot arrays are not suitable for low-profile applications. Patch arrays have relatively low profile but have very narrow bandwidth

[50-51]. Tightly-coupled dipole arrays (TCDA) placed a quarter of wavelength (at the center frequency) above a conducting ground plane can achieve an impedance bandwidth of as much as 13:1 at broadside. However, TCDAs can scan up to 45° from broadside with some reduction in bandwidth. Most practical low-profile phased array antennas require a ground plane backing so that the performance is less dependent on the host platforms. Hence, tightly-coupled dipole element is a good candidate for ultra-wideband, low-profile planar phased arrays. However, scanning down to 60° using the published

TCDAs comes with more significant reduction in bandwidth and higher VSWR.

Of important when designing a phased array antenna is array element size. The basic design principle is to have the element’s size and spacing between elements in an array must be no larger than a half-wavelength at highest frequency to avoid the effect of

33 grating lobe. By carefully taking all limitations and issues discussed in chapter 2 into consideration, a simulation model of the unit cell of an initial infinite dual-polarization

TCDA is designed and shown in top of Figure 3.5, where each dipole element is fed with a lumped port with a port impedance of 170 Ω. Notice the “X” shape slots between four adjacent dipole elements. These slots provide the coupling needed for this TCDA design to achieve wide bandwidth. The infinite array performance was analyzed based on this unit cell using HFSS which applies Floquet’s theorem of periodic boundaries. While this method accounts for the mutual coupling between the array elements, it does not include edge effects from elements in the case of finite arrays. The bottom plot of Figure 3.5 shows the VSWR response for broadside radiation, i.e. 0o scan angle, optimized for maximum impedance bandwidth based on the goal of VSWR < 2. This result shows an excellent bandwidth approximately 4.73:1.

3.2.2 Feeding Lines

Although the performance of the above infinite TCDA design looks impressive using theoretical lumped ports, its actual performance will be significantly changed after introducing realistic feeding structures. This will introduce additional scattering, coupling, and fabrication issues. In practical applications, an array antenna must be excited by a real feed line and a wideband array antenna needs to be fed by a wideband feed. The most well-known wideband feed is introduced by Marchand [52], which has larger bandwidth than other types of combiners and has been widely used since its introduction. Other baluns shown in [53] such as mast baluns, printed baluns, bypass baluns, or cutaway baluns also provide wideband and are popular in array antennas.

However, wideband baluns are often large and difficult to implement above Ku-band due to short wavelength. Therefore, due to the limitation on volumetric size of the unit cell and physical constraints on the feed lines, Figure 3.6 shows a TCDA design example with broader dipole geometry and feed structure, which is composed of two conducting pins for each dipole element. One of the dipole arms is connected to the top end of one of the pins, which is also shorted to the ground. The other dipole arm is connected to the other pin which is connected to the center conductor of the coaxial connector or cable below the ground plane. The conducting pins can be implemented using plated-thru vias or filled-holes in standard PCB fabrications. Therefore, the size of the pin is limited by the smallest filled holes or plated-thru vias which can be manufactured by current PCB fabrication process (around 0.3 to 0.65 mm). This design is similar to the feed approach adopted in [16] except that our design does not require additional shorting pins. This

36 allows us to mitigate the effects of scattered fields from the vias’ structures which degrade the overall array performance. Due to the physical constraints on the array unit cell size, eliminating the extra vias reduces fabrication complexity. The common mode resonance issue in our design is avoided by the reduction of ground plane height to less than λmid/4 and array unit cell size to 0.45λhigh. These are the key parameters of the design which make the array low profile and provide wide angle scanning. Observed in Figure

3.6 that the array with actual feed-line has a narrower bandwidth (3:1) as compared to the array which is fed by lumped ports as shown in Figure 3.5 (4.73:1).

Figure 3.6. Response of TCDA with actual feed line implemented.

3.2.3 Effect of Array Height on Wide Scan Angle

It is well known that TCDAs should be placed a quarter of a wavelength (at the center frequency) above the ground plane to maximize the operating impedance bandwidth. Normally when designing phased array antennas, the array element

38 impedance is chosen matched to the system impedance when the array’s beam is steered at broadside. However, when the beam is steered to lower angles the shunt reactance effect of ground plane changes significantly such that it can no longer balance out the reactance of the free-standing TCDA array, resulting in smaller impedance bandwidth.

Figure 3.7 demonstrates the effect of the ground plane height on the array impedance bandwidth for 60° beam in the E-plane. As seen, smaller height shows lower reflection coefficient, especially, at higher frequencies. Figure 3.7 also shows for larger height (λd/4) impedance bandwidth degrades as compared to broadside case in Figure 3.6.

Therefore, the benefit of placing the array a quarter of wavelength (at the center frequency) above the ground plane is only realized for the case of broadside radiation and is not observed when the array is scanned to wide angles. Hence, the array height needs to be properly chosen so that the array can be scanned to low angles with minimum degradation on impedance bandwidth. Although Figure 3.8 shows that the array height of

0.18λd has decent impedance bandwidth performance for 60° beam steering in the E- plane, its performance in the H-plane is still limited to 30° scan angles as shown in

Figure 3.8. This H-plane performance shortfall can be overcome with additional design features to be introduced in the next few sections.

Figure 3.7. Reflection coefficient when the array is scanned at 60° in the E-plane with different ground plane height.

Figure 3.8. The simulated VSWR vs. frequency under both E- and H-plane beam steering to 0°, 30°, 60°, and 75° for array height (above ground plane) of 0.18λd at center frequency.

3.2.4 Effect of Element Pattern on Wide Scan Angle

Figure 3.9 illustrates the current distribution of an ideal half wavelength Hertzian dipole with zero width (left) and its maximum radiation pattern (right). Notice that the pattern vanishes along the dipole axis due to perfect field cancellation as a result of rotational symmetry. This element pattern causes the beam peak magnitude of a collinear array of 10 Hertzian dipoles in the E-plane to decrease significantly when the array scans to wide angle as demonstrated in Figure 3.10 (top right). On the other hand, a dipole has a uniform pattern in the H-plane, resulting in constant beam peak magnitude of a linear array of 10 parallel Hertzian dipoles (not shown) during H-plane scanning as demonstrated in Figure 3.10 (bottom right).

Figure 3.9. Vanishing E-plane pattern of a wire dipole due to symmetry (left) and maximum H-plane radiation direction (right).

Figure 3.10. E-plane scanned patterns (top right) of a 10-element collinear Hertzian dipole array (left) and the H-plane scanned patterns (bottom right) of a 10-element parallel Hertzian dipole array (not shown). Note the loss of gain in E-plane scans during scanning due to dipole element pattern.

3.2.5 Effect of Mutual Coupling on Wide Scan Angle

Although Figure 3.10 shows a constant scanning beam magnitude in the H-plane for an array of theoretical Hertzian dipoles, in practical, actual array antenna element has to be connected to a feed line of a certain impedance value and connected to a RF system.

Therefore, the peak magnitude during H-plane scanning will not be constant as shown in

Figure 3.10. Rather, the magnitude will also decrease as scan angle increases due to the coupling effect. Figure 3.11 demonstrates this effect by examining the total energy

42 absorbed by the ports of the rest 9 elements as the 10-element dipole array fed with lumped ports for different scan angles from broadside at 0o to horizon at 90o. The port impedance in these simulations is 50 Ω. These simulated results indicate that as the scan angle increases, the amount of EM energy collected by other array elements via mutual coupling increases, thus causing far-field gain to drop. In fact, almost 90% the energy is absorbed by other array element when the beam is steered to 90o, i.e. array plane, in the

H-plane case. This also proves that the mutual coupling between elements is much stronger in the H-plane than in the E-plane.

Figure 3.11. Energy absorbed by other 9 elements in a 1x10 dipole array.

Magill and Wheeler showed that the mutual coupling that causes the wide angle scan limitation can be reduced or minimized by utilizing a dielectric superstrate [23] placed in front and parallel to the array antenna as illustrated in Figure 3.12. The presence

43 of this dielectric slab helps guiding the wave propagating upward, away from the array plane, and thus reducing element-to-element mutual coupling. However, this treatment has to be done carefully to keep the electrical thickness of the superstrate to minimal to avoid exciting surface waves which can lead to severe pattern degradation.

Figure 3.12. Direction of radiated EM field on array of no superstrate (left) and with superstrate (right) on array surface.

Figure 3.13 compares the near-field distributions of the electrical field magnitude at fc (center operating frequency) in the H-plane with and without a dielectric superstrate and a pattern beam steering angle of 60°. The superstrate thickness is 0.24휆푑, where 휆푑 is the wavelength in dielectric at the highest operating frequency. It is seen that more energy propagates along the array plane in the case without a superstrate. Figures 3.8 and

3.14 plot the simulated VSWR versus frequency for different scan angles in the E- and H- plane before and after adding superstrate, respectively. It is observed that there is a significant improved in the H-plane at wide angle scanning with the use of superstrate.

Note the TCDA element was re-optimized after adding the superstrate.

Figure 3.14. Simulated VSWR vs. frequency in the E- and H-plane at scanned angles of 0°, 30°, 60°, and 75° for a ground plane height of 0.18λd at center frequency and a 0.24λd thick superstrate in front of the infinite array shown in Figure 3.6.

3.2.6 Effect of Parasitic Ring

Although a thicker superstrate (>0.24λd) can further enhance the array scanning capability at wide angles, it increases overall height and could also support undesired surface waves which will severely affect the array impedance and patterns at higher frequencies. As demonstrated so far, wide angle beam steering is more challenging in the

H-plane than in the E-plane. To further improve the beam steering performance in the H- plane without using thick superstrate, a planar parasitic conducting ring was introduced on top of the superstrate surface directly above the tightly coupling slot between two adjacent dipoles as shown in Figure 3.15. This unique design helps suppressing the mutual coupling between adjacent elements as well as stabilizing impedance at wide scan angles. As demonstrated in Figure 3.16, the VSWR performance in the H-plane is improved, especially at 75o scan angle compared to the case without the parasitic ring as shown in Figure 3.14. This design can now support beam steering to at least 60° in both

E- and H-plane with an impedance bandwidth of 2.62:1 under the condition of VSWR <

Figure 3.15. Unit cell of the proposed low-profile dual-polarization UWB TCDA design which can be completely fabricated using standard PCB manufacturing process.

3.3 Design Parameter Tolerance Analysis

This section discusses about the findings of tolerance analysis conducted on key design parameters to gain better understanding of the effects of the imperfections of manufactured components or the misalignments in assembled products on the product performance before fabrication of the final array design. The tolerance study conducted include

1. element-to-element coupling slot width,

2. bonding layer thickness between array board and superstrate, and

3. feed-line (i.e. plated through via or filled hole) diameter.

Since the proposed array is for high frequency (> Ku band) applications and involves TCDA elements for maximum bandwidth, all the parts are physically small and are in proximity to each other. Hence, any small dimension variation could have a significant impact on the overall performance. Therefore, conducting design tolerance analysis is necessary prior to fabrication.

3.3.1 Element-to-Element Coupling Slot Width Tolerance Study

The coupling slot plays an important role in TCDA design since it provides the necessary coupling reactance which acts as series capacitance to counteract the shunt inductance introduced by the backing ground plane at low frequency end. A smaller slot width produces stronger coupling, and thus leading to a wider bandwidth. However,

48 fabricating such a small slot involves some uncertainty in mean width and edge straightness. Therefore, slot width tolerance is the most important issue for the proposed array design. Since our design calls for 2 mills slot width and the smallest slot width for standard PCB fabrication is limited to 1.5 mils, we compare the simulated S11 performance between the slot widths of 1.5 mils, 2 mils, and 2.5 mils under beam steering conditions, as shown in Figure 3.17. It is observed that these three cases have similar performance. From these results, we can conclude that the slot width can vary from 1.5 mils to 2.5 mils without affecting bandwidth and scanning performance.

Figure 3.17. Element-to-element coupling slot width tolerance study. No significant effect on performance is observed from 1.5 to 2.5 mils slot width.

3.3.2 Bonding Layer Thickness Tolerance Study

The bonding layer (Bondply 2929) was recommended by the PCB manufacturer for bonding the antenna board which containing planary array elements, feed vias, and a superstrate which serves as a wide angle impedance matching in the H-plane as well as array’s radome. The bonding process is usually done by applying heat and pressure to activate the bonding action. Although the process is controlled by computer to build up the heat and the pressure correctly, the resultant thickness could still vary slightly around

3 mils. To better understand the impact of the variation of bonding layer thickness on array performance, we conducted simulations for bonding layer thickness of 2 mils, 3 mils, and 4 mils, respectively. Figure 3.18 compares the simulated results of S11 under different beam steering conditions in the E-plane and H-plane. These results indicate that our design can tolerate at least ± 1mil variation in the bonding layer thickness.

Figure 3.18. Study of the tolerance of PCB bonding layer thickness. The bonding layer thickness of 3 mils with tolerance of ± 1mil. No significant effect on performance is observed.

3.3.3 Feed-line Diameter Tolerance Study

Our TCDA design uses two metal pins as feeding lines for connecting array elements to coaxial connectors. The feed-lines can be implemented with plated-thru via hole or solder filled holes. The feed-lines’ diameter of our design is 17 mils. In order to study the effect of possible variation of such diameter on antenna performance, simulations were conducted for diameter of 16 mils, 17 mils and 18 mils, respectively. As shown in Figure 3.19, the simulated S11 results under different beam steering conditions

51 in the E-plane and H-plane are compared for the mentioned three vias’ diameters. These results show that the diameter of feed line has significant effect on impedance matching condition. Specifically, at 60° scan angle in the E-plane, the 18-mil diameter via has slightly better performance at high frequency end. On the other hand, the 16-mil diameter via has a better performance at high frequency end in the H-plane scan. As a result, we concluded that the feed-line diameter needs to be 17 mils ± 0.5mils.

Figure 3.19. Study of the effects of the feed-line diameter.

3.4 Summary

In this chapter, an UWB low-profile dual-polarization phased array antenna was designed using the tightly coupled dipole array concept. The array was fed by a very simple unbalanced feed line adopted in [16]. The reduction of array ground plane height to less than λmid/4 and array unit cell size to 0.45λhigh solved the common mode resonance caused by the unbalanced feed line as well as prevented the lattice scattering issue appear in the upper operational frequency end. Furthermore, the reduction in ground plane height allows the array to scan to lower angles. The low angle scanning issue discussed in chapter 2 caused by strong mutual coupling between elements was overcome by introducing a dielectric superstrate on top of the radiating elements. This superstrate directs the EM energy propagates upward, away from the array elements; thus, reducing the antenna mode scattering and absorption effects of adjacent elements. The mutual coupling between elements was further reduced by placing the parasitic ring on top of the superstrate. With the utilization of superstrate and parasitic coupling ring on top of array elements, the array was capable of scanning up to 60° in the E- and H-plane with impedance bandwidth of 2.62:1. Fabrication tolerances of several key design parameters were studied before fabricating the prototype array. These studies showed that the effect of typical PCB fabrication tolerances on the antennas’ performance was minimal and acceptable.

Chapter 4: Prototype Measurement

4.1 Finalized 18x18 Dual-Pol UWB Array Prototype Design

The main objective of this chapter is to validate the proposed dual-polarization

UWB array design using measured results from a smaller 18x18 prototype array. The final unit-cell design specifications adopted for fabricating the 18 by 18 array (324 total elements in one polarization) is again shown in Figure 4.1(a). Figure 4.1(b) shows the custom-designed connector blocks to be soldered onto the back of the array. Figure 4.2 shows a fabricated 18x18 array based on the Figure 4.1(a) design which also takes the adhesive bonding layer between the array layer and the superstrate into consideration.

This choice of 18 by 18 elements was made so that it is large enough to allow for studying mutual coupling and accommodating three edge elements, and small enough to fabricate and test economically. The thickness of copper is approximately 0.35 mils, corresponding to standard ¼ oz. copper lamination. The width of the coupling slots between elements is 2 mils, smallest manufacturable width using standard PCB processes. The substrate and superstrate are made of standard PCB materials: Roger

RT/Duroid 5880LZ and Roger RT/Duroid 5880, respectively. The front and back views of the fabricated 18x18 prototype array are shown in Figure 4.2(a).

(a)

(b)

Figure 4.1. (a) Final design that can be entirely fabricated using PCB, (b) 2D block connector (left) formed by multiple 1D block connector (right).

The picture on the right hand side of Figure 4.2(b) shows some RF cables connected to block connectors. Each connector is a 50 Ω snapped-on R65 coaxial connector type. During measurements, a short section of R65-to-K coaxial cable was used for connecting the array to RF instruments. The special custom made 18-connector blocks configuration also adds mechanical strength to the array. During fabrication, these connector blocks were automatically picked up, placed, and soldered on to the bottom of the antenna using the standard flow soldering process. The array fabrication integrity was verified by measuring the reflection coefficient of each antenna element.

continued (a)

Figure 4.2. (a) Front and back views of the 18x18 fabricated prototype array, (b) R65 connector blocks (top) and R65 to K cable (bottom).

Figure 4.2 continued

(b)

4.2 Array Assembly

Figure 4.3 shows the array element layout and designation as well as the selected testing elements (highlighted in red) for array performance validation. Due to the limited number R65-to-K cables, the element-to-element coupling and element pattern of the elements shown in “red” in Figure 4.3 were measured. Note that these red and green regions were chosen strategically to include all possible coupling scenarios. This allows the effects from edge elements, corner elements, and center elements to be included in the synthesized array gain patterns. For each measurement, one of the elements in the red area is excited, and the surrounding elements (including the elements in green area and the non-excited elements in red area) are terminated with matched loads as illustrated in

Figure 4.4(a). This setup maintains at least two terminated elements around the element under test. The array truncation effect can also be evaluated with this measurement setup.

Figure 4.3. Array element layout and tested elements (red highlighted).

Figure 4.4(a) shows the assembly of the antenna array with test cables. The R65 connector blocks were soldered onto the back of the antenna array (as seen in Figure 4.2).

The cable’s R65 end (R65 female) is connected to the R65 connector and the cable’s K- connector end is connected to a 50 Ω termination (for the non-excited elements) or to a testing cable (for excited element) through a 2.92mm (K connector) to 3.5mm (SMA connector) adapter for connecting to a vector network analyzer.

Figure 4.4(b) shows the assembled array with the measurement support fixture.

Due to the weight of the K-connectors and 50 Ω terminations, cables connected to the non-excited elements (Figure 4.3 green area) are taped to the test fixture and cables connected to the excited elements (Figure 4.3 red area) are secured between two styrofoam pieces to prevent them from bending (Figure 4.4(c) right hand side). It was discovered that the snapped-on connection between the cable and the block connector is relatively weak and can come loose too easily. Therefore, these connections are further secured by applying glue to each cable-connector interface and also around the cable block as seen in the left picture of Figure 4.4(c). This ensures that good connections between cables and array due to rotating of the rotor during measurement. Good connections were verified by measuring reflection coefficient at the end of each connected cable before taking the time-consuming pattern measurements.

(a)

(b) continued

Figure 4.4. (a) Assembly of the array test setup, (b) Array with the support of the test fixture, (c) Cables are secured by glue and styrofoam with green tape.

Figure 4.4 continued

(c)

4.3 Array Design Verification

The fabricated prototype array measurements are used to validate the proposed full-wave simulated design. The measurements are conducted in an anechoic chamber.

The anechoic chamber minimizes the reflected waves from nearby objects and the ground. This allows the simulated and anechoic chamber measurements to similar set up conditions.

The fabricated prototype array S-parameters include the reflection coefficient at each element input and the coupling between elements. These were measured using vector network analyzer. The radiation pattern and gain measurements were conducted

61 with a standard gain horn antenna as the system transmitter and the prototype array was mounted on a rotating positioner to serve as the receiver. The positioner was set to rotate in the range from -90° to +90° to cover the designed array scan range from -75° to +75°.

Another standard gain horn that has known gain relative to an isotropic radiator over the rated bandwidth is used as a reference antenna to calibrate out the system losses such as the path loss and the cable loss. The far-field magnitude and phase data of each tested element are collected versus scanned angles and the realized gain and radiation patterns were synthesized by the combination of the measured element patterns. The measured S- parameters and realized gain and radiation patterns are compared with the results from the simulated model and the antenna design is verified by the comparison between the measured and simulated results.

4.4 18x18 Array Prototype Measurement Results

The far-field gain patterns in the E- and H-plane were measured in the

ElectroScience Laboratory’s Compact Range. The pattern measurement setup is shown in

Figure 4.5. As mentioned, the reflection coefficient |S11| of each antenna element in both polarizations (V- and H-polarization) is measured and shown in Figure 4.6 for initial array assembly verification. As seen, the low |S11| value serves an indication of good cable connection.

Figure 4.5. Radiation pattern measurement setup in the compact range.

Figure 4.6. Measured antenna element |S11| without phase shifter; (top) E-elements, (bottom) H-elements

Figure 4.7 shows one of the center element radiation patterns in both principal planes (top: E-plane and bottom: H-plane) at the center frequency (fc). It is observed that

64 the measured and simulated patterns are generally in good agreement in both E- and H- plane. Notice that the measured H-plane element pattern has more fluctuations than the

E-plane. These fluctuations are due to the scattered fields from the edges of the finite prototype array [21, 42]. Also, the electric field is vertically polarized and parallel to the feed lines in the E-plane, whereas in the H-plane the electric field is horizontally polarized and is not suppressed by the feed lines. As a result, stronger scattered fields in the H-plane create more ripples and more loss at low scan angles as seen in Figure 4.7.

The cross polarized fields in both E- and H-plane agree well between measured and simulated patterns in terms of magnitude level and pattern shape.

continued

Figure 4.7. (a) Simulated and measured element pattern in E- and H-plane at fc; (a) E- plane, (b) H-plane.

Figure 4.7 continued

Note that the simulated gain and beam steering patterns presented in this chapter were obtained from a semi-infinite array with 18 by infinite array elements as shown in

Figure 4.8. The array consists of 18 dual-polarized elements in the finite dimension, whereas in the infinite dimension a periodic boundary condition is utilized. This setup reduces the scattering effects from the ground plane and edge elements. Hence, less fluctuation is observed as compared to the measured data. The simulated 18x18 array broadside gain (Figure 4.9(b)) is then predicted by multiply the full-wave simulated gain obtained from the 1x18 array gain by a factor of 18, and the later normalized simulated beam steering patterns (Figure 4.14) are obtained from the simulated 1x18 array along the finite array dimension.

Figure 4.8. 18x∞ array model analyzed in HFSS to obtain the predicted array gain and E- and H-plane scanned patterns of the prototype 18x18 array.

The broadside realized gains of the center element alone and of the array as a function of frequency are shown in Figure 4.9. The measured element patterns in Figure

4.3 were used to generate the element patterns of all 18x18 elements. Note that some elements patterns can be generated from element patterns of other elements based on symmetry. The array scanning patterns were then synthesized by combining weighted element patterns with equal amplitude weightings and proper progressive phase weightings for a desired beam steering angle as will be discussed in Appendix A. Note that the highest frequency in this data stops at 1.23fc instead of the designed 1.45fc due to the upper frequency limit of our measurement equipment. The measured and simulated realized gain levels of the array at broadside are also compared to the theoretical

67 directivity in Figure 4.9(b) based on aperture size. It can be seen that the simulated realized data agree with the theoretical directivity, indicating good aperture efficiency of our design. However, the measured realized gain is on average of 1 dB lower with approximately 3 dB peak-to-peak fluctuations and 5 dB at lower frequency end. This is due to inconsistencies in the reference gain data of the reference antenna used for gain calibration as well as the effect of scattering interference such as edge diffraction from the array ground plane. The measured gain level of the cross-polarized component is higher than the simulation result, but the level is still about 18 dB below the co-polarized component in the frequency ranges from 0.67fc to 1.23fc and 10 dB at 0.6fc. This higher measured cross-pol was limited by the cross-pol level of the transmitting antenna in the measurement setup.

continued

Figure 4.9. Simulated and measured realized gain patterns at broadside; (a) Element gain pattern, (b) Array gain pattern.

Figure 4.9 continued

To show the element to element mutual couplings, the measured elements in

Figure 4.3 are re-labeled from 1 through 10 as shown in Figure 4.10(b) for the convenience of the following discussions. Note that element #1 is an edge element. Since the array is dual-polarization; that is, there are two antenna elements in each unit cell.

Therefore, additional letter “E” or “H” is used to indicate its polarization accordingly as shown in Figure 4.10(c).

Figure 4.10. (a) Element layout in the 18x18 array, (b) Element numbers are re-labeled from 1 to 10, (c) E- and H-element in array unit cell.

The simulated and measured mutual coupling versus frequency for the measured elements in Figure 4.10(b) and (c) are shown in Figure 4.11. It is observed that the mutual coupling response between elements is similar in the E- and H-plane. For the closest adjacent element (S6,7 or S8,7 and element 7 is excited), it is seen that the measured coupling level is about 5 to 6 dB lower than the simulated level (red curves in Figure

4.11(e), (f) . However, this is due to the losses of the R65 cables and test adapters used in the measurement as illustrated in Figure 4.12. While the simulated coupling is obtained at the end of the R65 connector block (Figure 4.12(a)), the measured coupling is obtained at the end of the R65-to-K cable as shown in Figure 4.12(b). The loss of this additional cable is about 2 to 3 dB as shown in Figure 4.13.

Figure 4.11. Simulated and measured coupling vs. frequency with element 7 excited; (a) E-plane element 1 to 3, (b) H-plane element 1 to 3, (c) E-plane element 4 to 6, (d) H- plane element 4 to 6, (e) E-plane element 7 to 10, (f) H-plane element 7 to 10.

Figure 4.12. S-Parameter measurement setup; (a) Simulated |S| reference plane, (b) Measured |S| reference plane.

Figure 4.13. R65 cable insertion loss vs. frequency.

The normalized simulated and measured radiation patterns at frequencies of

0.58fc, fc, and 1.23fc in the E- and H-plane are shown in Figure 4.14. The synthesize beam is steered from -75° to +75° in 15° increments. The measured side-lobe level is about -13 dB at broadside and rises up to -9.4 dB at 75°. The measured cross-pol component remains 19 dB below co-pol at broadside and 13 dB below co-pol at 75°. A very good agreement between simulated and measured patterns is observed in Figure 4.14.

continued

Figure 4.14. Normalized simulated and measured principal plane gain patterns for various scan angles; (a) E-plane 0.58fc, (b) H-plane 0.58fc, (c) E-plane fc, (d) H-plane fc, (e) E- plane 1.23fc, (f) H-plane 1.23fc,

Figure 4.14 continued

Chapter 5: Conclusion and Future Work

The subject of this dissertation was to develop of a novel ultra-wideband low- profile phased array antenna design that can support wide-angle scanning. The proposed array designs focused on the K to Q bands and a dual-linear polarized array was developed with a 2.62:1 bandwidth. The designed array achieved scanning up to 70° in both E- and H-plane while maintaining good impedance matching with VSWR ≤ 2. Such an exceptional performance was achieved by properly controlling and mitigating the strong mutual coupling among array elements when scanning to low angles. We have demonstrated how such mutual coupling limits the operational bandwidth and beam scanning range. Our study also showed that strong mutual coupling in the H-plane resulted in more undesired absorption and scattering by adjacent elements as a result of stronger mutual coupling as compared to the E-plane. We also demonstrated how the lattice scattering problem associated with the periodic structures in phased array antennas is related to the frequency upper bound under wide angle scanning conditions.

In chapter 3, we presented a systematic procedure of designing the proposed low- profile, dual-polarized, wideband phased array antenna design starting with an UWB element design based on TCDA concept. However, this approach is not applicable to wide scan angle where the ground plane effect is significantly different from broadside.

This problem was overcome by reducing the ground plane height to 0.18λd at center frequency instead of the 0.25λd adopted in conventional phased array designs. The strong mutual coupling in the H-plane was minimized by placing a dielectric superstrate that is

0.24λd in thickness at highest frequency. This superstrate directs more EM energy upward and away from the array plane, and thus reducing the scattering and absorption effects of adjacent elements. The thickness of the superstrate was kept as small as possible to suppress surface waves. It was also found that the introduction of superstrate lowered the operational frequency at low frequencies, as well as the antenna impedance due to dielectric loading effects. Therefore, a novel parasitic conducting ring was introduced on top of the superstrate directly above the TCDA’s inter-element coupling slots. The parasitic conducting ring helps suppress the mutual coupling between adjacent elements without using thick superstrate. As a result, surface wave propagation is suppressed and array impedance does not vary unreasonably as the beam is scanned at low angles.

The fabrication tolerances of several key design parameters were studied to determine the allowable dimensional tolerance for each key design feature prior to fabricating the final prototype array. It was determined that typical PCB fabrication tolerances on antenna performance were minimal and acceptable.

The developed design was validated with measured results obtained using a fabricated 18x18 prototype array and presented in chapter 4. To simplify simulation, the simulated scanned patterns are obtained from a numerical model of a semi-infinite array

(18x∞ array). The array fabrication and assembling quality was first verified by comparison of measured and simulated reflection coefficient data for each antenna element. Due to high operating frequencies (above Ku band), the array unit cell was

76 physically small making its fabrication and testing a challenge. For instance, the original optimized design with a smaller coupling slot width for stronger inter-element coupling had better scanning performances but could not be adopted due to the minimum slot width that can be manufactured using standard PCB fabrication process. As a result, a 2- mil gap was adopted in the final design and had to compensate coupling using a wider element. Similarly, the plated-thru via hole required an annular ring that also limits how close the feed lines can be positioned. In addition, the close proximity of array elements complicates the connections and soldering required for feeding. Even with these tremendous design and fabrication challenges, we successfully demonstrated that the fabricated array can scan to 60° in the E- and H-plane with an impedance bandwidth of more than 2.5:1 for VSWR better than 2:1. The final designed array was of low profile; with a total array height of 0.122λ at the lowest frequency of operation. The radiation pattern side-lobe level (SLL) was found to be about -13 dB at broadside and -9.4 dB at

75°. Cross-polarized component was 19 dB below the co-polarized one at broadside and

13 dB below at 75°.

The SLL of the array pattern can be reduced by applying appropriate magnitude weightings to the edge elements of the array. By using one of the optimization methods introduced by Kennedy and Eberhart [57], Particle Swarm Optimization (PSO), a set of amplitudes were obtained for edge elements in a 9 by 9 array. The optimized pattern peak gain was 1.2 dB lower as compared to the peak gain with uniform distribution. Doing so, the SLL was lowered by 11 dB.

Further investigations are necessary to improve array performance. For example, the impedance bandwidth is much wider if the array is fed by a wideband balun [15, 18-

20, 62, 63]. However, this is a most challenging part of the design since low loss and wideband baluns are often large and difficult to implement at high frequencies such as Ku band or higher.

Extension of the dielectric technique used in Chapter 3 would serve well as a next step for mutual coupling reduction in arrays. Also, use of a multilayer superstrate is another related research topic of interest to direct the array beam to wider scanned angles.

Figure 5.1(b) shows a technique for realizing a multilayer superstrate that can be used on top of the array. With this technique, wider scan angles can be obtained as compared to the single layer design in Figure 5.1(a) (휽2 > 휽1). For the beam to steer to wider angles, toward the array plane, the permittivity of the layer closer to the array surface should larger than the one closer to the air interface. That is, 휺r1 > 휺r2 > 휺r3 > 휺r4. Further, changes from one layer to other must be small to ensure higher bandwidths.

Figure 5.1. Using multilayer superstrate to direct the array beam to a wider angle.

Use of substrate with high dielectric constant can result in more energy to be trapped within the substrate under the array element. This will lower the efficiencies due to less energy being delivered to the antenna and more losses in the substrate. Also, narrowing the bandwidth due to energy absorption by adjacent elements and result in high reflection coefficient. This problem is more serious with larger substrate thickness and dielectric permittivity. To overcome this drawback, the effective dielectric permittivity of the material can be reduced by a periodic inclusion of air cylinders in the homogeneous substrate. It is important to note that with the reduction in the effective dielectric permittivity of substrate material, the physical size of the array unit cell size will increase. This also increases the overall directivity of the array as the effective area radiating aperture is also increased. Therefore, using perforated substrates in the design is an interested method to improve the overall array performance.

Appendix A: Array Pattern Synthesis

This section is focused on finalizing the array aperture termination design for controlling the side lobe level (SLL) of the array pattern. The main objective is to find appropriate magnitude weightings of the edge elements to yield a desired radiation pattern with SLL below -20 dB at all frequencies and beam steering angles up to 70°.

The SLL (in absolute units) of the array pattern is the ratio of the highest side lobe peak to the main lobe peak. In dB units, SLL can be expressed as

|퐹(푆퐿퐿)| 푆퐿퐿 = 20푙표푔 푑퐵 |퐹(푚푎푥)|

where |F(max)| is the maxima of the major lobe (main lobe) and |F(SLL)| is the highest side lobe of the pattern.

It is well known that the excitation of an array aperture needs to be tapered near its edges in order to reduce the undesired SLL. A uniformly excited array aperture without edge tapering treatment produces a SLL of approximately -13 dB, much higher than the desired -20 dB below the peak of main beam. Since edge tapering reduces effective aperture size, and thus reducing gain, it is desirable to minimize the fraction of aperture to be tapered. The best edge tapering strategy and the minimum fraction of aperture edge tapering depends on the mutual coupling between array elements. A

80 stronger mutual coupling implies a larger fraction of aperture edge needs to be tapered down, and results more gain loss for a given overall aperture size.

To better understand the effects of edge element tapering, several array sizes have been studied. Figure A.1 shows the near-field distributions of a 10x6 array in the E-plane

(along 10 elements direction) at fc (center frequency) under different edge treatments. The top three plots are for the cases where 3 edge elements (on each side), 2 edge elements, and 1 edge element are terminated with matched loads (50 Ω). The fourth plot is for uniform excitation without edge treatment. The bottom plot is for the configuration where two edge elements (on each side) are excited like the uniform case, but each is attenuated by 10 dB. Judging from how fast the field magnitude decreases in the lateral direction at each end, the 50 Ω termination cases do not show smoother magnitude decaying compared to the uniform case. On the other hand, the 10 dB attenuator treatment case exhibits a more gradual field tapering off at each end, and therefore should have lower

SLL. This speculation is confirmed by the corresponding far-field gain patterns shown in

Figure A.2 where the reduction of SLL for the 50 Ω termination cases is small. For the two edge elements (each side) attenuated by 10 dB case, the SLL is reduced down to -21 dB. In this case, the peaks gain only drops approximately 0.9 dB, which is quite acceptable. Table A.1 compares the observed peak gain and SLL between 0 (uniform case), 1, and 2 edge elements attenuated by 10 dB attenuators. It shows that a minimum of two edge elements is needed using a -10 dB attenuation approach in order to suppress the SLL to below -20 dB.

Figure A.1. Near-field distributions of 10-element in E-plane at fc.

Figure A.2. E-plane gain pattern of a 10x6 array at fc under different edge treatments.

Table A.1: Observed peak gain and SLL for different number edge elements attenuated by 10 dB.

A.1 Finite Array Pattern Synthesis (Amplitude Distribution)

In array pattern synthesis, there are several well-known analytical techniques such as Binomial [54], Taylor [55], or Dolph-Tschebyscheff [56] methods that are used to evaluate the side lobe level of the array. Binomial arrays have very low level minor lobes, wide beamwidth, and low directivity. Taylor arrays produce the first few side lobes (near the main beam) at equal level and tapering far outside lobes with decaying envelop. The problem with Taylor array is the high level of close-in side lobes. Dolph-Tschebyscheff is a compromise between uniform and binomial arrays. However, it is only applicable to uniform spaced linear arrays with isotropic elements. There are some limitations of the above methods as such the arrays are simple; the effects of mutual coupling and scattering between adjacent elements are not taken into account. Such coupling and scattering have detrimental effects on the final total pattern of the array. The effects

83 become more pronounced as the array’s beam steers to low angles. In this section, we synthesize the SLL of the array pattern by adopting the information of the array element’s pattern from the full-wave simulation which already included the effects of mutual coupling and structure’s scattering such as antenna element and feed lines. The total pattern will then computed using Matlab and SLL of the pattern will be optimized.

Figure A.3(a) shows a 9x9 array with proper progressive phase between array elements (for array beam steering) and Figure A.3(b) shows a 9x9 array with amplitude weightings (Am1, Am2, Am3) which will be applied on the 3-edge elements of the 9x9 array for side lobe reduction. The center elements will have uniform amplitude excitations (Am4).

continued (a) Figure A.3. 9x9 array which is used for array pattern synthesis. (a) 9x9 array with progressive phase between elements, (b) 9x9 array with amplitude excitations for SLL reduction.

Figure A.3 continued

(b)

A.1.1 Fast Array Pattern Synthesis using Element Patterns

After the array in Figure A.3 is simulated in HFSS, each element in the array is excited independently with magnitude of 1W, 0 degree phase and the total E-plane pattern of each element is exported to files. The element patterns without beam steering are then imported into Matlab and the total array E-plane pattern is calculated from the combination of all element patterns as

푀 퐸퐴푟푟푎푦(휃, 휙) = ∑푚=1 퐴푚퐸푚 (휃, 휙) (A.1)

The array pattern under beam steering condition can be synthesized from element patterns by adding a progressive phase to element patterns (Am)

푀 푗∠퐴푚 퐸퐴푟푟푎푦(휃, 휙) = ∑푚=1[|퐴푚|푒 퐸푚 (휃, 휙)] (A.2)

The array far-field pattern is calculated from this E-field pattern as

2 4휋푈(휃,휙) 2휋|퐸퐴푟푟푎푦(휃,휙)| 퐺퐴푟푟푎푦(휃, 휙) = = (A.3) 푃푖푛푐 휂푃푖푛푐

where, η is the free space impedance and Pinc is the total incident power applied to the array.

The scanned array pattern can be rapidly calculated in Matlab using the element patterns which were exported from HFSS. Figure A.4 compares the array pattern synthesized from Matlab using (A.1) and the array pattern obtained from full-wave simulation HFSS at fc for broadside beam steering case. Notice that the two patterns are matched very well in the range of ±50° which included the first and highest side lobe of the pattern. The small discrepancy at low angles between the two patterns is due to the meshing refinement of the array elements and boundary conditions.

Figure A.4. Synthesized array pattern using Matlab as compared to full-wave simulated array pattern.

A.2 Array Patterns Synthesized Using PSO

Particle swarm optimization (PSO) is an optimization algorithm which is developed by Kennedy and Eberhart in 1995 [57]. The process behind the algorithm was inspired by the social behavior of animals, such as bird flocking or fish schooling while looking for food. More details of this algorithm can be found in [58-60].

Using the above fast array pattern synthesis approach, one can optimize the magnitude tapering design for minimizing SLL very quickly without running full-wave simulations. To start with the initial pattern synthesis, the edge elements Am1, Am2, and

Am3 of the 9x9 array in Figure A.3 are applied with a range of amplitude weightings that have attenuation values from 0 to -30 dB. The weighting of center elements (Am4) of the

87 array is set to 0 dB (1 W). The progressive phase was applied to each element for beam steering and gain patterns were computed using (A.2).

In non-uniform arrays, there is a compromise between the SLL and directivity.

Therefore, after the gain and SLL for all the iterations are determined, a set of array coefficients that yield the best attainable SLL and directivity for all the frequencies and scan angles will be chosen. Those array coefficients will be applied back into HFSS for pattern verification. Figure A.5 shows the patterns for uniform distribution and optimized distribution cases at fc and 0° scanned angle. The optimized amplitudes of Am1, Am2, and

Am3 are 0.045 (-13.5 dB), 0.06 (-12.2 dB), and 0.41 (-3.9 dB), respectively. The peak gain of the optimized pattern has 1.2 dB lower compared to the peak gain of the uniform distribution pattern. However, the SLL of the optimized pattern is 11 dB better. Figure

A.5 is also included the optimized pattern verification between Matlab and HFSS. The pattern from Matlab has peak gain of 18.4 dBi and SLL of -24.2 dB while for pattern from HFSS, they are 18.2 dBi and -24.0 dB, respectively. Figure A.6 shows the optimized patterns for the scan angles of 0°, 30°, and 60°. The patterns at boresight angle matched very well to each other as mentioned from the above. However, when the beam steers to low angles, there is more disagreement between the two patterns in the other scanned direction of the beam. This is due to the effect of the “lattice scattering” modes from HFSS results. Figure A.7 shows the 3-D far-field plots before and after array synthesized for the cases of 0° and 30° at fc. The optimized 3-D far-field plot shows a significant improved in SLL.

Figure A.5. Optimized array pattern from Matlab is verified in HFSS.

Figure A.6. Optimized array patterns with scanned angles of 0°, 30°, and 60°.

Figure A.7. 3D far-field plots for the cases of 0°, 30° before and after array synthesis.

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