Low-Profile Wideband Antennas Based on Tightly Coupled Dipole

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Low-Proﬁle Wideband Antennas Based on Tightly Coupled Dipole and Patch Elements

Dissertation

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Erdinc Irci, B.S., M.S.

Graduate Program in Electrical and Computer Engineering

The Ohio State University

2011

Dissertation Committee:

John L. Volakis, Advisor Kubilay Sertel, Co-advisor Robert J. Burkholder Fernando L. Teixeira c Copyright by

Erdinc Irci

2011 Abstract

There is strong interest to combine many antenna functionalities within a single,

wideband aperture. However, size restrictions and conformal installation requirements

are major obstacles to this goal (in terms of gain and bandwidth). Of particular

importance is bandwidth; which, as is well known, decreases when the antenna is

placed closer to the ground plane. Hence, recent eﬀorts on EBG and AMC ground

planes were aimed at mitigating this deterioration for low-proﬁle antennas.

In this dissertation, we propose a new class of tightly coupled arrays (TCAs) which

exhibit substantially broader bandwidth than a single patch antenna of the same size.

The enhancement is due to the cancellation of the ground plane inductance by the

capacitance of the TCA aperture. This concept of reactive impedance cancellation

was motivated by the ultrawideband (UWB) current sheet array (CSA) introduced by

Munk in 2003. We demonstrate that as broad as 7:1 UWB operation can be achieved

for an aperture as thin as λ/17 at the lowest frequency. This is a 40% larger wideband

performance and 35% thinner proﬁle as compared to the CSA.

Much of the dissertation’s focus is on adapting the conformal TCA concept to

small and very low-proﬁle ﬁnite arrays. Three particular designs are presented.

One is a 6×6 patch array occupying a λ/3 × λ/3 small aperture (mid-frequency is at 2.1 GHz). Remarkably, it is only λ/42 thick yet delivers 5.6% impedance bandwidth (|S11| < −10dB), 4.4dB realized gain (87% eﬃciency) and 23% gain

ii bandwidth (3dB drop). The second ﬁnite TCA consists of 4×2 patches and occupies a λ/3.2×λ/3.2 aperture on a λ/26 thick substrate (mid-frequency is at 2 GHz). This antenna delivers 17.3% impedance bandwidth, 4.8dB realized gain (95% eﬃciency) and 30% gain bandwidth. That is, more than twofold impedance bandwidth is delivered as compared to a single patch antenna of the same size on conventional or EBG substrate.

The third array being considered consists of 3×2 patches occupying a λ/3.2×λ/3.2 aperture and situated on a λ/22 thick substrate (mid-frequency is at 1.95 GHz).

Although of very low-proﬁle and of small size, this TCA achieves a 26% wideband performance with 4.5dB realized gain (97% eﬃciency) and 40% gain bandwidth.

It therefore covers DCS, PCS and UMTS bands (1.7 GHz – 2.2 GHz) for mobile communications. As compared to a conventional patch antenna that can cover the same frequency bands, the TCA is 85% smaller in size while also being 60% thinner.

This dissertation demonstrates that the tightly coupled array concept is quite versatile for miniaturization, bandwidth enhancement and applicability to a diverse range of next generation antennas.

iii Dedicated to my parents.

iv Acknowledgments

I would like to express my sincere gratitude to my advisor Prof. John L. Volakis and my co-advisor Dr. Kubilay Sertel for their continuous guidance, encouragement, patience and understanding. Their great vision and pursuit for excellence had always raised the bar. Therefore, this dissertation was a challenge to myself for reaching their high standards. I feel very honored, grateful and lucky to have worked with them. In these past four years, they had a huge impact on me, both professionally and personally, that I ﬁnd very invaluable.

I would like to thank Prof. Robert J. Burkholder and Prof. Fernando L. Teixeira for participating in my defense committee, reading and commenting on this dissertation and also for their helpful suggestions.

I would like to thank Jon Doane, Mustafa Kuloglu, Gokhan Mumcu and Ioannis

Tzanidis not only for their friendship but also for many fruitful technical discussions.

I also thank Ugur Olgun and Dr. Lanlin Zhang for their friendship and extensive help in fabricating my antenna prototypes. Additionally, I would like to thank all my friends at ESL: Elias Alwan, Nil Apaydin, Kenny Browne, Jae-Young Chung,

Stylianos Dosopoulos, Faruk Erkmen, Baris Guner, Justin Kasemodel, Gil-Young Lee,

Will Moulder, Hayrettin Odabasi, James Park, Tao Peng, Nathan Smith, Brandan

Strojny, Orbay Tuncay, Georgios Trichopoulos, Feng Wang, Salih Yarga and Jing

Zhao.

v Vita

February 10, 1982 ...... Born - Eskisehir, Turkey

2004 ...... B.S. Electrical and Electronics Eng. Bilkent University, Turkey 2007 ...... M.S. Electrical and Electronics Eng. Bilkent University, Turkey 2004-2007 ...... Grad. Research & Teaching Assistant Electrical and Electronics Eng., Bilkent University, Turkey 2007-present ...... Graduate Research Associate ElectroScience Laboratory, Electrical and Computer Eng., The Ohio State University, USA

Publications

Research Publications

E. Irci, K. Sertel and J. L. Volakis, “Antenna Miniaturization for Vehicular Platforms Using Printed Coupled Lines Emulating Magnetic Photonic Crystals,” Metamaterials, vol. 4, no. 2-3, pp. 127–138, Aug.-Sep. 2010.

N. Apaydin, E. Irci, G. Mumcu, K. Sertel and J. L. Volakis, “Miniature Antennas Based on Printed Coupled Lines Emulating Anisotropy,” Microwaves, Antennas & Propagation, IET, vol.4, no.8, pp.1039–1047, Aug. 2010.

E. Irci, K. Sertel and J. L. Volakis, “Miniature Printed Magnetic Photonic Crystal Antennas Embedded into Vehicular Platforms,” Applied Computational Electromag- netics Society Journal, vol. 26, no. 2, pp. 109–114, Feb. 2011.

vi E. Irci, K. Sertel and J. L. Volakis, “An Extremely Low-Proﬁle, Compact and Broad- band Tightly Coupled Patch Array,” Radio Science, submitted.

Conference Publications

E. Irci, K. Sertel and J. L. Volakis, “Unidirectional transmission characteristics of printed magnetic photonic crystals,” IEEE AP-S/URSI International Symposium, San Diego, CA, vol. APS, pp. 1–4, Jul. 5-11, 2008.

E. Irci, K. Sertel and J. L. Volakis, “Miniature Antenna Using Coupled Microstrip Lines Emulating Magnetic Photonic Crystals,” 2009 USNC/URSI Meeting, BDS1-7, Boulder, CO, Jan. 2009.

E. Irci, K. Sertel and J. L. Volakis, “Antenna Miniaturization Using Coupled Mi- crostrip Lines Emulating Magnetic Photonic Crystals,” 2009 IEEE AP-S/URSI In- ternational Symposium, Charleston, SC, vol. APS, pp. 1–4, Jul. 5-11, 2009.

K. Sertel, J. L. Volakis and E. Irci, “Small Wideband Antennas Based on Mag- netic Photonic Crystals,” 3rd International Congress on Advanced EM Materials in Microwaves and Optics, London, UK, 1-4 Sep. 2009.

E. Irci, K. Sertel and J. L. Volakis, “Miniature Printed Magnetic Photonic Crys- tal Antennas Embedded into Vehicular Platforms,” in Proceedings of the 26th In- ternational Review of Progress in Applied Computational Electromagnetics (Applied Computational Electromagnetics Society), Tampere, Finland, Apr. 2010.

E. Irci, K. Sertel and J. L. Volakis, “Miniature Multiband Microstrip Antenna De- sign via Dispersion Engineering,” 2010 URSI Radio Science Meeting, Toronto, ON, Canada, Jul. 2010.

E. Irci, K. Sertel and J. L. Volakis, “Ultrathin Miniature Antenna to Mitigate Plat- form Loading Eﬀects,” in Proc. 2010 IEEE Antennas and Propagation Soc. Int. Symp. Toronto, ON, Canada, pp. 1-4., Jul. 2010.

E. Irci, K. Sertel and J. L. Volakis, “An Extremely Low-Proﬁle, Compact and Broad- band Tightly Coupled Patch Array,” 2011 USNC/URSI Meeting, Boulder, CO, Jan. 2011.

E. Irci, K. Sertel and J. L. Volakis, “Bandwidth Enhancement of Low-Proﬁle Mi- crostrip Antennas Using Tightly Coupled Patch Arrays,” in Proc. 2011 IEEE An- tennas and Propagation Soc. Int. Symp., Spokane, WA, pp. 1-4., Jul. 2011.

vii Fields of Study

Major Field: Electrical and Computer Engineering

Studies in: Metamaterials and Photonic Crystals Dr. K. Sertel, Prof. J. L. Volakis Frequency Selective Surfaces Dr. K. Sertel, Prof. J. L. Volakis Ultrawideband Phased Arrays Dr. K. Sertel, Prof. J. L. Volakis Antenna Miniaturization Dr. K. Sertel, Prof. J. L. Volakis

viii Table of Contents

Page

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita ...... vi

List of Tables ...... xii

List of Figures ...... xiii

1. Introduction ...... 1

1.1 Ultrawideband Phased Array Antennas: Motivation, Challenges and Objectives ...... 1 1.2 Small, Low-Proﬁle and Broadband Antennas: Motivation, Chal- lenges and Objectives ...... 9 1.3 Contributions and Organization of the Dissertation ...... 14

2. A Low-Proﬁle and Ultrawideband Tightly Coupled Double-Legged Dipole Array ...... 18

2.1 Dipole Arrays in Free Space and Over a Ground Plane ...... 19 2.1.1 Dipole Arrays in Free Space: Wheeler’s Current Sheet Con- cept and its Realization Using Connected Dipoles ...... 19 2.1.2 Dipole Arrays over a Ground Plane: Munk’s Tightly Coupled Current Sheet Array ...... 23 2.2 Double-Legged Dipole Array Design ...... 26 2.2.1 Skewed Dipole Arrangement ...... 26 2.2.2 Regular Dipole Arrangement ...... 29

ix 2.2.3 Double-Legged Dipole Array ...... 31 2.2.4 Realization of the DLDA Using Overlapping Legs and Com- parisons to the CSA ...... 35 2.3 Concluding Remarks and Discussions ...... 37

3. An Extremely Low-Proﬁle, Compact and Broadband Tightly Coupled Patch Array ...... 40

3.1 Introduction ...... 41 3.2 Tightly Coupled Patch Array Design ...... 44 3.2.1 Unit Cell Design ...... 44 3.2.2 Finite Array Design ...... 48 3.3 Feeding Network Design ...... 55 3.4 Integrated Antenna Performance and Comparisons to Other Antennas 58 3.5 Experimental Veriﬁcation ...... 61 3.6 Concluding Remarks and Discussions ...... 63

4. Bandwidth Enhancement of Microstrip Patch Antennas Using Multiple Feeds and Patch Fragmentation ...... 64

4.1 Single Patch Antenna ...... 65 4.2 Single Patch Antenna with Multiple (1×2) Feeds ...... 66 4.3 Fragmented Patch Antenna with Multiple (2×1) Feeds ...... 69 4.4 Fragmented Patch Antenna with Multiple (2×2) Feeds ...... 71 4.5 Concluding Remarks and Discussions ...... 73

5. Bandwidth Enhancement of the TCPA by Combining Multiple Resonances 75

5.1 Tightly Coupled Patch Array Using Rectangular Patches ...... 76 5.1.1 Unit Cell Design ...... 77 5.1.2 Finite Array Design ...... 77 5.1.3 2×2 Feeding Network ...... 81 5.1.4 Integrated Antenna Performance and Comparisons to Other Antennas ...... 82 5.1.5 Experimental Verification of the TCPA with Rectangular Patches...... 84 5.2 Tightly Coupled Patch Array Using Rectangular Patches and Stubs 86 5.2.1 Unit Cell Design: 2D Periodic (Infinite Array) ...... 86 5.2.2 Unit Cell Design: 1D Periodic (Infinite × Finite) Array . . 87 5.2.3 Finite Array Design ...... 90 5.2.4 Integrated Antenna Performance and Comparisons to Other Antennas ...... 91

x 5.3 Concluding Remarks and Discussions ...... 94

6. Conclusions ...... 96

Bibliography ...... 102

xi List of Tables

Table Page

2.1 Comparison of the DLDA and the CSA with VSWR<2...... 34

xii List of Figures

Figure Page

1.1 Double-legged dipole array presented in this dissertation...... 8

1.2 Tightly coupled patch arrays presented in this dissertation...... 15

2.1 (a) Small section of an inﬁnite and planar dipole array. (b) Hypothet- ical rectangular waveguide supporting the TEM mode. (c) Equivalent transformer coupling the antenna with the waveguide...... 20

2.2 (a) Wheeler’s current sheet in free space. (b) Practical implementation of the electric current sheet using connected dipoles. (c) Equivalent circuit model for the connected dipoles in free space...... 22

2.3 Free space impedance of an inﬁnite, connected dipole array. Tran- sition from linear dipoles to bowties helps achieve a purely resistive impedance of 180Ω...... 22

2.4 (a) Linear connected dipole array over a ground plane. (b) Tightly coupled dipole array over a ground plane. (c) Equivalent circuit model. (d) Low-frequency impedance of dipole arrays. (e) Corresponding VSWRs of dipole arrays...... 24

2.5 Munk’s CSA with interdigital capacitors in dual-linear polarized setting. 26

2.6 Various arrangements of skewed dipole FSSs...... 27

2.7 Type 2 skewed dipole array...... 28

2.8 Impedance of the type 2 skewed dipole array in Fig. 2.7...... 29

2.9 Tightly coupled dipole array in regular arrangement...... 30

xiii 2.10 Impedance of the regular dipole array in Fig. 2.9...... 30

2.11 Double-legged dipole array geometry...... 31

2.12 Impedance of the DLDA in Fig. 2.11...... 32

2.13 VSWR of the DLDA in Fig. 2.11, with 190Ω system impedance. . . . 33

2.14 VSWR of the DLDA in Fig. 2.11, with 125Ω system impedance. . . . 34

2.15 (a) DLDA and, (b) CSA unit cells scaled to operate at 200 MHz and up. 35

2.16 VSWR of the DLDA and the CSA in Fig. 2.15...... 36

2.17 Same size apertures ﬁlled with (a) 4×4 CSA, (b) 10×10 DLDA elements. 37

3.1 Circuit model representations of FSSs. (a) Passive mode. (b) Radiat- ingmode...... 45

3.2 Tightly coupled patch array unit cell. (a) Top view. (b) Top view, shifted. (c) 3D view...... 46

3.3 TCPA unit cell input impedance and return loss. (a) Input impedance, (b) Return loss...... 47

3.4 Finite 6×6 TCPA array with 30 excited elements. (a) 3D view. (b) Top view. (c) Side view...... 49

3.5 Active return losses of: (a) 30 excited elements; (b) 18 excited elements, 12 terminated with 50Ω; (c) 18 excited elements, 12 terminated with 50Ω, plotted together...... 50

3.6 Finite 6×6 TCPA array with 18 excited elements. (a) 3D view. (b) Top view...... 51

3.7 Active return losses of: (a) 18 excited elements; (b) 18 excited elements, plotted together; (c) 16 excited elements, ports 9 and 12 terminated with 50Ω; (d) 16 excited elements, ports 9 and 12 terminated with 50Ω, plotted together...... 52

xiv 3.8 (a) Finite 6×6 TCPA array with 16 excited elements, top view. (b) Active return losses of 16 excited elements. (c) Active return losses of 16 excited elements, plotted together. (d) Active input impedances of 16 excited elements...... 53

3.9 Finite 6×6 TCPA array with 16 excited elements having optimized feed locations (distances in mm), 3D view. (b) Active input impedances of 16 excited elements. (c) Active return losses of 16 excited elements. (d) Active return losses of 16 excited elements, plotted together. . . . 54

3.10 Single stage miniature Wilkinson power divider. (a) Geometry. (b) Frequency response...... 56

3.11 Multiple-stage, 16-way, equal power division and feeding network. (a) Ge- ometry, 3D view. (b) Geometry, bottom view. (c) Frequency response. 57

3.12 Layouts of; (a) TCPA, (b) conventional patch antenna...... 59

3.13 Performance comparison of TCPA vs. conventional patch antenna. (a) Return losses. (b) Realized gains in broadside direction. (c) Radi- ation patterns in E-plane. (d) Radiation patterns in H-plane...... 60

3.14 Fabricated TCPA prototype. (a) Front view, (b) Back view...... 62

3.15 Measured return loss and realized gain of the TCPA prototype in Fig. 3.14. (a) Return loss, (b) Realized gain at broadside...... 62

4.1 Single patch antenna on ﬁnite-size substrate and ground plane. .... 65

4.2 Performance of single patch. (a) Input impedance, (b) Return loss. . 66

4.3 Surface currents on the patch...... 66

4.4 Patch antenna with 1×2 feeds...... 67

4.5 Performance of the 1×2 patch. (a) Input impedance, (b) Return loss. 67

4.6 Radiation mechanisms of single patch and 1×2 patch...... 68

4.7 Surface currents on the 1×2 patch. (a) Connected patch, (b) Frag- mented patch...... 68

xv 4.8 Connected patch antenna with 2×1 feeds. (a) Antenna layout, (b) Surface currents on the patch...... 69

4.9 Fragmented patch antenna with 2×1 feeds. (a) Antenna layout, (b) Sur- face currents on the patch...... 70

4.10 Performance of the 2×1 patch. (a) P2 input impedance, (b) P1 and P2 return losses: red, blue...... 70

4.11 Radiation mechanisms of single patch and 2×1 patch...... 71

4.12 Fragmented patch antenna with 2×2 feeds. (a) Antenna layout, (b) Sur- face currents on the patch...... 72

4.13 Performance of the 2×2 patch. (a) P2 input impedance, (b) P1 and P2 return losses: red, blue...... 72

5.1 TCPA unit cell with a rectangular patch that creates two resonances. (a) Top view and diﬀerent current paths on the patch corresponding to diﬀerent resonances. (b) Top view, shifted. (c) 3D view...... 76

5.2 TCPA unit cell performance. (a) Input impedance. (b) Return loss. . 77

5.3 4×2 TCPA array with 8 excited elements illustrating the ﬁrst step of ﬁnite array design. (a) 3D view. (b) Top view...... 78

5.4 Active return losses and active input impedances of the excited elements in Fig. 5.3...... 78

5.5 Active return losses of the excited ports of the antenna shown in Fig. 5.3. 79

5.6 4×2 TCPA array with 4 excited elements. (a) 3D view. (b) Top view. 79

5.7 (a) Active return losses and active input impedances of the excited elements in Fig. 5.6. (b) Active return losses plotted together. .... 80

5.8 4×2 non-uniform TCPA array with 4 excited elements. (a) 3D view. (b) Top view...... 80

xvi 5.9 (a) Active return losses and active input impedances of the excited elements in Fig. 5.8. (b) Active return losses plotted together. .... 80

5.10 Single stage Wilkinson power divider. (a) Geometry. (b) Frequency response...... 81

5.11 Multiple-stage, 4-way, equal power division and feeding network. (a) Ge- ometry. (b) Reﬂection at input and output ports...... 82

5.12 Several microstrip antennas for performance comparisons...... 83

5.13 Return loss and realized gain comparison of the antennas in Fig. 5.12. (a) Return losses, (b) Realized gains at broadside...... 83

5.14 Fabricated prototype of the TCPA with rectangular patches. (a) Front view, (b) Bottom view...... 85

5.15 Measured return loss and realized gain of the TCPA prototype in Fig. 5.14. (a) Return loss, (b) Realized gain at broadside...... 85

5.16 2D periodic TCPA unit cell detailing the T-shaped patch and coaxial probe feed. (a) 3D view. (b) Top view...... 86

5.17 2D periodic TCPA unit cell performance. (a) Input impedance. (b) Re- turn loss...... 87

5.18 1D periodic TCPA unit cell corresponding to the inﬁnite×2 array. (a) 3D view. (b) Top view, d = 2.4 cm. (c) Top view, d = 1.8 cm. . . 88

5.19 Active input impedances for the 1D periodic unit cell in Fig. 5.18 and (a) d = 2.4 cm, (b) d = 1.8 cm, (c) d = 1.8 cm (zoomed). (d) Active return loss for d =1.8cm...... 89

5.20 Finite 3×2 TCPA array with 2 excited elements. (a) 3D view. (b) Top view...... 90

5.21 (a) Active input impedance; (b) Active input impedance, zoomed; (c) Active return loss; for the excited elements in Fig. 5.20...... 91

5.22 TCPA antenna layout illustrating the ﬁnalized array design with in- corporated feed. (a) 3D view. (b) Bottom view...... 92

xvii 5.23 Performance of the TCPA in Fig. 5.22. (a) Return loss. (b) Directivity and realized gain at broadside...... 92

5.24 Size and thickness comparison of the TCPA with an E-shaped patch that yields similar bandwidth...... 93

xviii Chapter 1: Introduction

1.1 Ultrawideband Phased Array Antennas: Motivation, Challenges and Objectives

Over the past decades, phased array antennas [1], [2] have become popular because they allow rapid beam steering electronically, rather than mechanically. Thus, the terms “phased array” and “electronically scanned array” (ESA) are often used synonymously. More recently, advances in solid-state technology led to “active electronically scanned arrays” (AESAs) that use active transmit/receive (T/R) modules at each radiating element [3], [4]. Compared to “passive” ESAs that use phase shifters connected to a single source, the T/R modules in AESAs not only provide phase shift- ing but also power ampliﬁcation, amplitude setting and low noise ampliﬁcation [4].

Either “passive” or “active”, these phased array antennas have found extensive usage in a diverse range of applications, mostly being military centric. For instance, phased array radars working at X-band are mainly used for targeting and tracking, with narrow pencil beams and high resolution. Especially, with proper frequency division and software deﬁned back-end, such radars can generate multiple beams.

Thus, in contrast to mechanically scanned antennas that can track a single target, these phased array radars can track multiple targets. As pointed out in [5], the

1 bandwidth requirement of such systems can be easily satisﬁed at X-band, because the center frequency is high. However, this convenience does not apply to most of other applications.

First example of wideband applications is long range surveillance and imaging. In this class of operation, the radar is expected to operate at long distances and possibly in bad weather conditions or must penetrate foliage camouﬂage. Eventually, these lead the radar to operate at low frequencies (large wavelengths), such as at VHF/UHF band. Obtaining high resolution with wide instantaneous bandwidth is much more diﬃcult in this case (e.g., as compared to X-band), due to the center frequency being very low [5]. In other words, phased array antennas with very high fractional bandwidth (or high-to-low operational frequency ratio) become indispensable.

Second major application area is electronic warfare (EW). The phased array antenna can be either in transmit mode as the jammer or in the receive mode as the target being jammed. For both scenarios, beam steering and adaptive beamforming capabilities are of signiﬁcance. More importantly, such EW systems typically need to cover a diverse electromagnetic spectrum ranging from VHF up to Ku bands. This implies the necessity for an ultrawideband (UWB) system.

As the third example, high-data-rate communication systems can be considered.

These usually come as an outcome of surveillance and imaging applications, where large chunks of data resulting from high resolution synthetic aperture radar images and radar cross section echos need to be sent in real time. Such high-data-rates also imply wideband performance.

It should be remarked that a similar need for wideband operation also exists for civilian applications; such as cellular communications, wireless networks and global

2 positioning. Currently, all these systems utilize diﬀerent bands scattered throughout the frequency spectrum. Some of them, like LTE and GSM, operate at as low as

700 MHz and 850/900 MHz. Other systems, like GPS, DCS and PCS, operate at L- band (1 GHz - 2 GHz); whereas UMTS, WLAN and WiMAX take up the S-band and lower half of the C-band (thus, from 2 GHz to 6 GHz). Hence, it becomes plausible to cover most of these applications with a small number of multi-functional antennas.

For portable and handheld devices, this is usually done using small-size multiband antennas [6]. For base stations and wireless access points, another choice would be to combine all frequency bands with a single aperture. For the applications summarized here, such antenna front-ends should cover 700 MHz - 6 GHz band. This implies 9:1 ultrawideband performance, which is very challenging to realize. However, this would make the system more robust to support rapidly changing and newly emerging wireless communication standards. As in the case of abovementioned military applications, phased array antennas could be possible candidates for realization. Especially, their beamforming capabilities and implementation of multi-input multi-output (MIMO) functionalities may result in unprecedented system performance.

Clearly, as elucidated above with several examples, there is a growing demand for ultrawideband phased array antennas. In early years of phased arrays, much emphasis was given to scanning capabilities, rather than bandwidth. These traditional arrays were usually comprised of dipoles, slots or microstrip patches [1] and resulted in narrowband performance. However, they were found sufficient for most X-band applications. With the emerging need for ultrawideband, the course of phased array design had changed in a way to utilize inherently wideband array elements. These include “Vivaldi” (flared notch, tapered slot) or “bunny-ear” (flared dipole) type of

3 elements [5], [7]. The former usually has λ/4 thickness (depth) at the lowest frequency of operation and can provide 10:1 bandwidth. The latter can achieve λ/8 depth, albeit with a reduced bandwidth of 4:1. Because these elements radiate like TEM horns, reducing their profile is difficult and their phase centers change with frequency. Also, since they are volumetric structures, their fabrication is not simple. These make such arrays less favorable. On the other hand, a planar array of “flower” elements can provide 2.6:1 bandwidth while being λ/8 thick over a ground plane [8].

In conclusion, realizing planar, ultrawideband and low-proﬁle arrays had remained a perennial challenge. This was mostly because traditional designs used half-wavelength dipoles, slots or patches that were highly resonant and thus narrowband. Arraying these elements was merely used as a tool for scanning and increasing antenna gain.

The mutual coupling between array elements was considered a phenomenon that degraded array performance and that needed to be prevented. However, a recent paradigm shift in array design is now making such traditional approaches obsolete.

This novel array design method is based on Wheeler’s “current sheet” concept [9].

In an earlier work [10], Wheeler perceived plane wave radiation from an inﬁnite array of antennas as a collection of radiation from each array element. Accordingly, each individual element was coupled to its own hypothetical TEM waveguide. This approach led to a simple derivation of radiation resistance for array elements. Later, in [9], Wheeler extended his work for the case of scanning in inﬁnite phased arrays.

In this scenario, each waveguide becomes oblique to the array plane, proportional to scan angle. This visualization extended the simple derivation of radiation resistance; in principal E- and H-planes as a function of scan angle.

4 A more important impact of [9] was its treatment of a phased array as an in-

finite, planar current sheet. In contrast to traditional arrays with highly resonant half-wavelength-long individual elements, the current sheet model represents smaller and closely spaced elements. Thus, in this case, the “fine structure” of elements can- not be resolved. This abstraction of phased arrays has two main implications. First, rather than element type, it is arraying (mutual coupling) and thus formed hypothetical waveguides that govern array radiation characteristics. This was verified in [11] with several numerical examples. Second, closely spaced array elements can support radiation at much lower frequencies than their stand-alone case (i.e., in the absence of array).

A simple realization of the current sheet concept is to interconnect array elements.

Therefore, this type of array is also referred to as a “connected array”. Early examples of this approach were presented by Baum [12] and Inagaki et. al. [13]; using

TEM horn and self complementary elements, respectively. In its simple form, the self complementary array in [13] is an array of connected “bowtie” dipoles and hence a planar version of the TEM horns in [12]. When freestanding, such connected self complementary arrays radiate bidirectionally and allow for a constant radiation resistance in a wide frequency range.

However, for most practical scenarios, arrays need to be placed above a host platform, such as a metallic ground plane. The impact of ground plane backing can be understood by referring to Wheeler’s hypothetical waveguides. In the presence of a ground plane, the waveguide underneath the array acts like a short-ended transmission line. When the array thickness is λ/4, the ground plane is seen as “open” and the array is similar to freestanding. At higher frequencies, ground plane eﬀect

5 becomes capacitive and when the thickness reaches λ/2, it shorts out the array. For

cubic latices (i.e., thickness equals square grid spacing), this doesn’t pose an extra

challenge because the array is already limited here due to onset of grating lobes (inter-

element spacing becomes λ/2). However, a more signiﬁcant challenge is observed at

low frequencies where array thickness is less than λ/4. In this case, ground plane eﬀect becomes inductive. This results in decreased resistance and increased inductive reactance for input impedance. In the DC limiting case (ω = 0), ground plane shorts out the array. In summary, for most practical arrays, it is the ground plane eﬀect at low frequencies that limits bandwidth performance.

A practical remedy to ground plane eﬀect was perceived by Munk after applying his profound knowledge on frequency selective surfaces (FSSs) [14]. Basically, Munk suggested adding capacitance between array elements to counteract ground plane inductance at low frequencies [7], [15]. In his case of dipole arrays, this capacitance can be formed at dipole tips using interdigital capacitors, overlapping arms or their proximities. Doing so, Munk showed that such dipole arrays can achieve 5:1 bandwidth with λ/10 thickness (at lowest operational frequency) on a ground plane [7], [15].

Thus, Munk’s dipole array emulated Wheeler’s electric current sheet on a ground plane and was referred to as current sheet array (CSA). Another terminology to emphasize coupling between array elements is to call such arrays “tightly coupled arrays”

(TCAs). This makes a distinction between “connected arrays”, which also emulate

Wheeler’s current sheet concept.

Although Munk’s CSA shows better performance compared to connected dipoles

[1], [16] or their Babinet equivalent long slot arrays [5], [17] on a ground plane, it still has some shortcomings. First, the intentional capacitance exactly cancels ground

6 plane inductance only at a single frequency. This is because frequency variation

of inter-element capacitance and ground plane inductance is opposite. Second, at

lower frequencies the inter-element capacitance dominates, which makes the array

“open-circuited” at DC. Thus, the low radiation resistance problem remains unsolved.

For these reasons, Munk’s approach was criticized by Hansen as “wrong physics”

[1], [18]. Instead of coupling capacitors, Hansen proposed using Non-Foster circuit

elements such as negative impedance converters (NICs) that could realize negative

inductance. Doing so, inductance due to ground plane would be counteracted by

NIC’s negative inductance for all frequencies. Although this idea is theoretically

plausible, the practicality and narrowband characteristics of NIC elements hinder its

usage.

As mentioned above, Munk’s CSA delivers 5:1 bandwidth and achieves λ/10 pro-

file. Remarkably, this performance is attained without using any substrates or superstrates. Thus, it doesn’t possess any material losses and can be easily scaled to other frequencies. However, there are still two important objectives (that also apply to other antennas in general): improving bandwidth and reducing profile. To address this first objective, Munk suggested using superstrates above the CSA [7], [15]. These superstrates not only channel more energy towards air (rather than ground plane) but also act as impedance transformers between the array and free space. Consequently, such superstrates were found to extend CSA bandwidth up to 9:1 [7]. Of course, this performance is obtained at the expense of increasing antenna profile, and thus neglects the second objective. An alternative method to fulfil both objectives (as suggested by

Hansen [1]) would be using magnetic substrates such as magneto-dielectrics, ferrites or metaferrites. However, such magnetic materials are usually band-limited, lossy and

7 heavy. Also, their electric permittivity is high. Thus, these substrates could generate higher order modes or surface wave modes that are uncalled for. These disadvantages hinder their utilization.

In conclusion, Wheeler’s current sheet concept has brought new breath to phased array design. Particularly for low-proﬁle ultrawideband arrays on ground planes,

Munk’s tight (i.e., capacitive) coupling approach is found useful. Recently, other novel designs have started emerging based on this approach. A striking example is the interwoven spiral array (ISPA) of Tzanidis et. al. [19]. This array achieves 10:1 bandwidth with λ/23 very low proﬁle, without using any substrates or superstrates.

However, as a result of spiral elements, it supports only circular polarization rather than linear or dual-linear polarization and its scanning capabilities are limited.

Therefore, one objective of this dissertation is to achieve bandwidth and proﬁle performance similar to ISPA while using dipole elements as in the case of CSA (to have polarization and scanning characteristics similar to CSA). For this, we propose a double-legged dipole array, depicted in Fig. 1.1. In essence, this array is a special

Figure 1.1: Double-legged dipole array presented in this dissertation.

8 collection of two diﬀerent dipole arrays. The ﬁrst array is simply a replica of Munk’s

CSA where each dipole is tightly coupled to other ones in adjacent unit cells. Dis- tinctively, the second array uses longer dipoles that couple to further unit cells rather than adjacent ones. This special arrangement of dipoles increases the aspect ratio of

Wheeler’s hypothetical waveguides. As a result, the second dipole array operates at much lower frequency while having higher radiation resistance, albeit with degraded bandwidth performance. As a remedy, each dipole in these two arrays is connected at their feeds (thus the double-legged dipole is formed). Essentially, this corresponds to connecting two arrays in parallel. Doing so, this new aperture creates multiple, well balanced resonances, thus concurrently achieving lower proﬁle and broader bandwidth as compared to the CSA.

1.2 Small, Low-Proﬁle and Broadband Antennas: Motivation, Challenges and Objectives

Previous section demonstrated the growing demand for UWB systems and presented antennas that can meet their requirements. As discussed, much progress has been made towards realizing smaller and thinner UWB apertures. However, even in the optimum case, such apertures end up being bulky. Nevertheless, they are found tolerable for larger aircrafts or vessels.

A more signiﬁcant challenge is related to realizing similar broadband systems on vehicles with limited real estate. Examples include unmanned aerial vehicles

(UAVs) and especially their miniature versions. For such airborne platforms, small and lightweight antennas are needed. In addition, decreasing antenna proﬁle is necessary to reduce aerodynamic drag and observability. A similar challenge also exists for ground vehicles, such as HMMWVs. In these multi-purpose vehicles, the hood, the

9 trunk and most of the roof are already occupied for other functions (e.g., weapons and

supplies). Thus, main concern becomes integration of antennas into the limited space

on platforms. That is, although large conducting surfaces are available, antennas need

to be placed at the edges of vehicle roof, doors, bumpers and window frames. To this

end, a traditional solution was to use quarter-wavelength-long monopole (whip) an-

tennas. This implies protruding antennas (especially at low frequencies) that increase

observability. Also, such monopoles are omnidirectional, narrowbanded and prone to

be damaged easily in the battleﬁeld.

For the reasons explained above, a recent objective is to replace protruding anten-

nas with small-size, low-proﬁle and conformal ones. In addition, such state-of-the-art

antennas are still required to deliver broad bandwidth, high gain, smooth radiation

pattern and polarization purity. However, gain and bandwidth of small antennas are

mainly constrained within their fundamental physical limits [20]–[24]. A detailed sur-

vey of these limits was recently presented in [25]. Basically, these works demonstrate

that antennas exhibit lower Q (i.e., increased bandwidth) when the stored electro-

magnetic energy diminishes within the spherical volume they occupy. Thus, antennas

approach their fundamental limits when they eﬀectively utilize a spherical volume. In

addition, using multiple arms increases their radiation resistance. Examples of such

antennas are spherical helix [26], spherical dipole [27], multiple-arm folded wire [28]

and spherical antennas with electromagnetically coupled planar elements [29].

The fundamental limits for Q mentioned above are deﬁned for the lowest order electric or magnetic dipoles (i.e., TM or TE modes) that exhibit linearly polarized, omnidirectional (doughnut shaped) radiation patterns with directivity of D=1.5. Re-

cent studies [30]–[33] show that various combinations of these elementary sources can

10 be harnessed for: i) decreasing Q by half, ii) increasing directivity by two, iii) achieving directional or bi-directional radiation patterns, iv) obtaining circular polarization.

Thus, gain×bandwidth product of antennas can be increased by a factor of 2 or 4 by using multi-mode (i.e., multi-resonance) behavior. For instance, such bandwidth enhancement was demonstrated by Goubau’s multi-element monopole antenna [34].

Also, it is noted that a similar bandwidth enhancement could be obtained by using a simpler, single-element monopole that uses multi-section impedance matching [35].

This follows from Bode-Fano theory [36]–[38] that shows bandwidth enhancement via multi-section impedance matching. Thus, there are two equivalent approaches for bandwidth enhancement: i) designing a self-tuned, multi-mode antenna; ii) using a simpler antenna and designing an external multi-section impedance matching circuit.

Of course, the ﬁrst approach is more attractive, yet more challenging. Still, it implies spherical antennas to reach the fundamental limits.

Therefore, in addition to size reduction, another challenge relates to realizing thinner antennas without sacrificing bandwidth. This is mainly because the physical bounds for planar (thus low-profile) antennas are much more stringent than their spherical counterparts [39]. A good example to this phenomenon is the microstrip patch antenna [40]–[42] that gained ever increasing popularity due to its ease of design, fabrication and integration, also being cheap and lightweight. However, it shows narrowband performance. This can be understood better by considering the microstrip patch antenna as a parallel-plate capacitor. Decreasing patch profile implies increased capacitance, thus more stored energy and higher Q. Similarly, using a high permittivity substrate for size reduction also increases capacitance and Q. Thus, both of these result in narrow bandwidth.

11 Recently, several approaches have been proposed to enhance the poor bandwidth performance of patch antennas (see [42], [43] and references therein). Some of these were based on using advanced feeding methods such as proximity/aperture coupling or L-shaped/capacitive/inductive coaxial probe feeds. Some designs used slots or slits for creating multiple nearby resonances. Others were based on coplanar or stacked parasitic patches. In general, these methods allowed for improved bandwidth, albeit with increased antenna size and/or thickness. On the other hand, size reduction methods such as shorting pins/plates, meandering and slots/slits were also useful [44].

However, these degraded bandwidth, gain, radiation pattern and polarization. In conclusion, designing microstrip antennas usually results in an engineering compromise between the antenna size/thickness and its performance.

More recently, artificially engineered materials (i.e., metamaterials) have brought significant improvements over traditional methods described above. For instance, negative-refractive-index (NRI) [45] and composite right/left-handed (CRLH) [46] metamaterials allowed for novel dispersion modes to realize smaller guided-wave (e.g., coupler, filter, phase shifter) and radiated-wave (i.e., antenna) structures. Further- more, novel degenerate band edge (DBE) and magnetic photonic crystal (MPC) modes were created using layered anisotropic media and their printed circuit emulation [47]. Specifically, the wave slow-down phenomenon associated with these

DBE and MPC modes was harnessed for realizing a new class of small antennas [47]–

[49]. However, a common manifestation of dispersion engineering and miniaturization using these NRI, CRLH, DBE and MPC structures was also narrow bandwidth.

Another successful realization of metamaterials was the periodic mushroom-type electromagnetic band gap (EBG) structure, which formed a high impedance surface

12 (HIS) [50]. Such structures suppressed surface waves and mimicked perfect magnetic

conductors (PMCs). Hence, they formed an artiﬁcial magnetic conductor (AMC)

ground plane [50], [51]. In contrast to conventional metallic ground planes that gen-

erate an out-of-phase (180◦) reflection, the AMCs have an in-phase (0◦) reflection, albeit with limited bandwidth. Thus, the AMC reflected wave adds constructively with direct aperture radiation. This allowed for realizing low-profile antennas [50]–

[52], some with broadband but lossy performance (i.e., dissipated electric or electromagnetic energy) [53]–[55]. Suppression of surface waves also led to reduced mutual coupling between microstrip antennas [56].

Instead of utilizing mushroom-type structures as AMCs, in [57] return losses of low-profile wire antennas were enhanced by tailoring the EBG’s reflection phase. For this case, reflection phase was in the 90◦ ± 45◦ range and led to improved impedance

bandwidth when the EBG acted like neither perfect electric conductor (PEC) nor

PMC, but in their middle. Alternatively, metallic patches placed on metal-backed

high contrast dielectrics were employed in [58] to create reactive impedance substrates

(RISs) that could be tuned to operate anywhere between PEC and PMC ground

planes. Similar to [57], the impedance bandwidth and radiation performance of low-

proﬁle wire and patch antennas were improved when the RIS was neither PEC nor

PMC, but at an optimal reactive value in between.

Essentially, the periodic structures in previous eﬀorts are frequency selective sur-

faces (FSSs) [14], [59] in passive mode, which are employed as substrates or ground

planes to other radiating elements. The latter can be any element of choice; includ-

ing dipole, patch, spiral and their array versions. However, in this setup, the overall

antenna bandwidth is limited by the radiating element or the passive FSS, depending

13 on which one is smaller. Also, the radiator usually may not illuminate the FSS in such a manner (i.e., as a uniform plane wave) as to realize the ideal FSS reflection coefficient. Further, the FSS substrate implies significant thickness (in most cases

2/3 of overall thickness), which hinders reducing the antenna proﬁle.

The main distinction of this dissertation is to employ an FSS by itself as the radiating structure. In essence, this excited FSS is an array antenna and in terms of operation principles it has strong resemblance to UWB arrays. However, it is much smaller and thinner. Accordingly, its bandwidth performance is limited. Therefore, the proposed array resembles more to patch antennas. Yet, it achieves much broader bandwidth as compared to patches on conventional or EBG substrates with same overall size and thickness. Alternatively, this allows for thinner antennas while retaining previous bandwidth performance.

1.3 Contributions and Organization of the Dissertation

As outlined in above sections, this dissertation is aimed at profile reduction and bandwidth enhancement of planar antennas in general. Particularly, two classes of antennas are investigated: i) UWB phased arrays; ii) small, low-profile microstrip antennas. Traditionally, these two antenna groups were treated quite differently, since their bandwidth performance were not alike. On the contrary, one feature of this dissertation is to treat them equivalently. Thus, the current sheet and tightly coupled array concepts are applied for both classes. Specifically, the key contributions of this dissertation are:

1. Introduction of a new tightly coupled, double-legged dipole array (shown in

Fig. 1.1) that achieves 7:1 bandwidth with λlow/17 proﬁle (for VSWR<2) or 10:1

14 bandwidth with λlow/24 proﬁle (for VSWR<3) without using any substrates or

superstrates (thus lossless).

2. Design of a small (λ/3 × λ/3) and extremely low-proﬁle (λ/42) tightly coupled

square patch array [shown in Fig. 1.2(a)] with 5.6% impedance bandwidth,

4.4dB gain (87% eﬃciency) and 23% gain bandwidth (3dB drop).

3. Design of a small (λ/3.2 × λ/3.2) and very low-proﬁle (λ/26) tightly coupled

rectangular patch array [shown in Fig. 1.2(b)] having 17.3% impedance band-

width, 4.8dB gain (95% eﬃciency) and 30% gain bandwidth.

4. Design of a small (λ/3.2 × λ/3.2) and low-proﬁle (λ/22) tightly coupled patch

array [shown in Fig. 1.2(c)] having 26% impedance bandwidth, 4.5dB gain (97%

eﬃciency) and 40% gain bandwidth.

6.04 mm 3.44 mm (238 mil) (135 mil)

Hr = 25 Hr = 25 Hr = 10.2 Hr = 6.15 (a) (b)

7.14 mm (281 mil)

Hr = 25

Hr = 6.15 (c) Figure 1.2: Tightly coupled patch arrays presented in this dissertation.

15 The dissertation is organized as follows:

Chapter 2 starts by presenting the fundamental principles of Wheeler’s current sheet concept and its realization in free space using connected linear or bowtie dipoles.

Performance of these arrays in the presence of a ground plane is also considered.

Speciﬁcally, the inductive loading eﬀect of ground plane at low frequencies and thus degradation of bandwidth performance are explained. Munk’s remedy to this problem was to use capacitively coupled dipoles, and it is discussed here in detail. The rest of this chapter is devoted to presenting our novel double-legged dipole array. First, several new dipole arrangements and coupling schemes are discussed. Their advantages and disadvantages are presented. Then, bandwidth enhancement by combining two dipole array resonances are explained in details. As compared to Munk’s CSA, this novel array achieves about 40% more bandwidth ratio while also being 35% thinner.

Chapter 3 is devoted to realizing much thinner and smaller antennas. First, realization of the current sheet using tightly coupled patches and simple coaxial probe feeds is considered. This design is based on an inﬁnite array assumption. Therefore, truncation of the array and its treatment for retaining broadband performance is explained. Also, a compact and thin feed network is designed and integrated. A unique feature of this patch array is being extremely low-proﬁle. Performance comparison with a conventional patch antenna reveals more than twice impedance bandwidth and more than three times gain bandwidth performance.

Chapter 4 presents another explanation of the tightly coupled patch array. This is based on considering the patch array as a fragmented patch with multiple feeds.

Starting from a single patch, adding multiple feeds and their eﬀect on bandwidth are investigated. Necessary situations for patch fragmentation are found. As the key

16 conclusion, using multiple feeds (and patch fragmentation when necessary) indeed increases bandwidth. This is explained using cavity model of patch antennas and their radiating slots.

Chapter 5 is focused on realizing a broader bandwidth performance by using multiple resonances. For this reason, slightly thicker rectangular patch elements are used.

This patch array is compared against patch antennas on conventional or EBG substrates. For both cases, the patch array shows more than twice impedance bandwidth and also improved gain bandwidth.

Also in this chapter, another patch array based on rectangular elements is designed. In this design two patch resonances are brought very closely. In finite realization of this array, a challenge is related to strong surface wave modes inside the substrate. The treatment of these modes by adding small stubs is explained. Doing so, these surface wave modes could be controlled and pushed out of operating band of the array. The final form of this small and low-profile array enjoys a wideband performance. Comparison with a more conventional, E-shaped patch is also done.

It is revealed that the patch array achieves bandwidth performance similar to the

E-shaped patch, while being 85% smaller in area and also being 60% thinner. This illustrates its remarkable miniaturization performance.

Finally, Chapter 6 presents a summary of contributions, concluding remarks and discusses possible future work to improve current array performances.

17 Chapter 2: A Low-Proﬁle and Ultrawideband Tightly Coupled Double-Legged Dipole Array

This chapter presents a double-legged dipole array (DLDA) to realize a low-proﬁle and ultrawideband aperture over a ground plane. As in past approaches, this array also uses tight element coupling to counteract inductance formed due to the ground plane. However, past approaches were not adequate to address the decreased radiation resistance problem at low frequencies. As a remedy, our design uses double-legged dipoles that couple not only to adjacent unit cells but also to other ones further away.

Thus, a key aspect of the DLDA is to make use of diﬀerent radiation waveguides through diﬀerent dipole arrangements, without altering the feed grid.

Speciﬁcally, the proposed DLDA achieves 7:1 bandwidth with λlow/17 proﬁle (for

VSWR<2) or 10:1 bandwidth with λlow/24 proﬁle (for VSWR<3). As compared to previous tightly coupled dipole arrays, the DLDA allows for 40% larger bandwidth factor (i.e., high-to-low frequency ratio), while concurrently being 35% thinner. It is also noted that the DLDA does not utilize any magnetic/dielectric substrates or superstrates. Thus, its bandwidth enhancement or proﬁle reduction improvements are not due to any material loadings. As a result, the presented array does not possess any material losses and can be scaled easily to other frequencies.

18 In Section 2.1 below, we begin by explaining the radiation properties of arrays and the current sheet concept. Impact of ground plane backing on the antenna performance and possible remedies are discussed. Section 2.2 presents the DLDA antenna. Speciﬁcally, diﬀerent dipole arrangements and their radiation properties are presented. Comparisons to previous tightly coupled dipole arrays are made. Finally, conclusions are drawn in Section 2.3.

2.1 Dipole Arrays in Free Space and Over a Ground Plane

This section presents Wheeler’s current sheet concept as applied to arrays in free space. For this case, realization of the current sheet using connected dipole arrays is demonstrated. Next, these arrays are reconsidered over a ground plane. The impact of the ground plane on array bandwidth is discussed and Munk’s tightly coupled array concept is introduced.

2.1.1 Dipole Arrays in Free Space: Wheeler’s Current Sheet Concept and its Realization Using Connected Dipoles

A key understanding of plane wave radiation from an inﬁnite array of antennas is to consider it as a collection of radiation from each array element. For this, we refer to Fig. 2.1(a) that illustrates a planar dipole array. It is assumed that the array is of inﬁnite extend, at the boundary of a half space (i.e., backed by an open- circuit boundary) and inter-element spacing is less than λ. Also, a plane wave (either received or transmitted) normal to the array is considered. Of course, in transmit case, such a plane wave could be generated if all array elements are fed uniformly.

This also corresponds to the lowest order Floquet mode that radiates broadside. In either case, the currents formed on the dipole and application of image theory suggest

19 PEC PMC

(a) (b) (c) Figure 2.1: (a) Small section of an inﬁnite and planar dipole array. (b) Hypothet- ical rectangular waveguide supporting the TEM mode. (c) Equivalent transformer coupling the antenna with the waveguide. [10] hypothetical walls around each dipole, as shown in Fig. 2.1(a). Speciﬁcally, the walls perpendicular to the dipoles are perfect electric conductor (PEC) and the parallel ones are perfect magnetic conductor (PMC). Thus, each dipole can be thought to be sitting in a PEC/PMC waveguide as in Fig. 2.1(b) that supports a TEM mode

(i.e., plane wave). This waveguide (assumed to be ﬁlled with air) has a characteristic impedance of b Z Z , = 0 a (2.1)

where Z0 = 120π Ω is the free space impedance [10]. For a dipole of eﬀective height h located in the waveguide, as depicted in Fig. 2.1(c), the radiation resistance becomes h 2 b h 2 R Z Z . = b = 0 a b (2.2)

This is related to the amount of coupling between the waveguide and the dipole, that

was modeled as a transformer in [10]. Eqn. 2.2 has several implications. First, if the

eﬀective length of dipole is equal to waveguide height, its radiation resistance reduces

to that in Eqn. 2.1. Second, by changing the inter-element spacing between dipoles,

one can scale the ratio b/a to obtain diﬀerent radiation resistances.

20 Based on these observations, Wheeler conceived an inﬁnite phased array as a

planar current sheet [9]. Speciﬁcally, he considered small and densely spaced array

elements so that their “ﬁne structure” could not be resolved. This translates to

elements operating at much lower frequencies than their self (i.e., isolated) resonance.

In this case, the currents ﬂowing through array elements are almost constant. Thus,

the eﬀective length of dipoles become equal to the height of hypothetical waveguide

and one can use Eqn. 2.1 to calculate their radiation resistance. For the speciﬁc case

of square grid (i.e., b = a), the radiation resistance becomes R = Z0 = 120π Ω.

In [9], Wheeler also extended the results of [10] to include scanning. For the scan-

ning case, the hypothetical TEM waveguides become oblique to the array plane. Es-

sentially, scanning changes the width or height (thus, the aspect ratio) of waveguides

by a factor of cos θ, where θ is the scan angle. Therefore, the radiation resistance of

dipoles (electric current sheet) vary in proportion to cos θ for the H-plane and 1/ cos θ

in the E-plane.

One of the assumptions Wheeler made in [10] was half space. For the electric

current sheet (i.e., dipoles), this corresponds to placing an “open-circuit” beneath

the array, which is not realizable. However, the electric current sheet can be realized

in free space by connecting dipoles at their tips, as shown in Fig. 2.2(b). In this case,

there are two hypothetical waveguides: one above the array and the other below. Each

waveguide can be also considered as a transmission line with characteristic impedance

Z = Z0(b/a). Since the dipoles radiate bidirectionally into both these transmission lines, their radiation becomes R = Z/2=Z0(b/a)/2. If a square grid is used, the

radiation resistance is R = Z0/2=60π Ω.

21 (a) (b) (c) Figure 2.2: (a) Wheeler’s current sheet in free space. (b) Practical implementation of the electric current sheet using connected dipoles. (c) Equivalent circuit model for the connected dipoles in free space.

To validate our expectations from the simple current sheet model, several dipole arrays are considered, as shown in Fig. 2.3. As suggested by the current sheet model, when the currents on dipoles are close to uniform (which happens at very low frequencies), it becomes possible to achieve an almost resistive impedance of 60π = 188Ω, as shown in Fig. 2.3. However, the impedance of linear dipoles varies quickly as

Figure 2.3: Free space impedance of an inﬁnite, connected dipole array. Transition from linear dipoles to bowties helps achieve a purely resistive impedance of 180Ω.

22 one moves to higher frequencies. This is because these dipoles achieve self resonance

when their length are λ/2. A remedy to this problem is to adopt a bowtie shape for dipoles, rather than linear. As seen, the dipole impedance achieves a purely resistive

60π = 188Ω impedance when the ﬂare angle becomes 90◦. Indeed, this corresponds to a “self-complementary” antenna similar to that suggested by Inagaki et al. [13].

It is also remarked that for all these arrays, grating lobes start appearing when their inter-element spacing (and thus their length) reach λ/2. Therefore, even the bowtie array in free space has a high frequency limitation.

2.1.2 Dipole Arrays over a Ground Plane: Munk’s Tightly Coupled Current Sheet Array

For most practical applications, arrays need to be placed over a host medium,

usually being a metallic ground plane. Fig. 2.4(a) depicts the case when linear con-

nected arrays discussed in previous section are placed at a height h = 7mm over the

ground plane. Their corresponding impedance is plotted in Fig. 2.4(d), together with

the free standing (i.e., w/o ground plane) case. As seen, the ground plane has an

important impact on the array impedance and this can be understood by referring

to the equivalent circuit model in Fig. 2.4(c). In the presence of a ground plane,

the waveguide underneath the array (with characteristic impedance of Z0 =2RA0) acts like a short-ended transmission line. Thus, the impedance seen looking into the

Z+ jZ πh/λ ground plane becomes 1 = 0 tan(2 ). As in free space case, the impedance Z− Z seen looking into the air is 1 = 0. For a more accurate model, the reactance due to dipoles is represented with the jXA term. For connected dipoles, this becomes

jXA = jωLd, where Ld represents the self dipole inductance. Therefore, the total

Z+//Z− jX impedance observed at the feed becomes 1 1 + A.

23 (a) (b) (c)

(d) (e) Figure 2.4: (a) Linear connected dipole array over a ground plane. (b) Tightly coupled dipole array over a ground plane. (c) Equivalent circuit model proposed in [15]. (d) Low-frequency impedance of dipole arrays. (e) Corresponding VSWRs of dipole arrays.

Z+ Z In the absence of a ground plane, the 1 term is simply 0 and resistive. However, Z+ in the presence of ground plane, the 1 term becomes reactive and adds in parallel to Z− Z− Z 1 . Therefore, although 1 = 0 term is always resistive, their parallel combination Z+ λ/ with 1 is not. Only exception is when the array thickness is 4 (or its multiple). In

this case, the ground plane is seen as “open-circuited”. At higher frequencies, ground

plane eﬀect becomes capacitive and when the thickness reaches λ/2, it shorts out

the array. For cubic latices, this doesn’t pose an extra challenge because the array

is already limited here due to onset of grating lobes (inter-element spacing becomes

λ/2). However, a more signiﬁcant challenge is observed at low frequencies where array

thickness is less than λ/4. In this case, ground plane eﬀect becomes inductive. Thus,

Z+ Z− parallel combination of 1 with 1 results in decreased resistance and increased

24 inductive reactance, see Fig. 2.4(d). In the DC limiting case (ω = 0), ground plane

shorts out the array. In summary, for most practical arrays, it is the ground plane

eﬀect at low frequencies that limits bandwidth performance. In the case of connected

dipoles, this limits its bandwidth performance to 2.5:1, as shown in Fig. 2.4(e).

A practical remedy to ground plane eﬀect was proposed by Munk [7], [15], who

suggested adding capacitance between array elements as in Fig. 2.4(b). In contrast

to simple connected dipoles with the jXA = jωLd reactive term, capacitively coupled dipoles have jXA = jωLd +1/(jω Cd), where Cd represents coupling capacitance between dipoles. As could be understood, this extra capacitive term dominates at low frequencies and counteracts the inductance due to the ground plane, as shown in

Fig. 2.4(d). Consequently, the array impedance becomes mostly resistive around the frequency this counteraction occurs. Doing so, the array bandwidth is extended to cover also lower frequencies [see Fig. 2.4(e)].

In dipole arrays, this capacitance can be formed at dipole tips using interdigital capacitors (as depicted in Fig. 2.5), or by overlapping dipole arms or their proximities.

Doing so, Munk showed that such dipole arrays can achieve 4.5:1 bandwidth with λ/10 thickness (at lowest operational frequency) while being very close to a ground plane

[7], [15]. Thus, Munk’s dipole array emulated Wheeler’s electric current sheet and was referred to as current sheet array (CSA). Another terminology to emphasize coupling between array elements is to call such arrays “tightly coupled arrays” (TCAs). This makes a distinction between “connected arrays”, which also emulate Wheeler’s current sheet concept.

Although Munk’s CSA resulted in signiﬁcant bandwidth improvement over connected arrays, it doesn’t address the small radiation resistance issue at low frequencies.

25 Figure 2.5: Munk’s CSA with interdigital capacitors in dual-linear polarized setting.

Inspection of Fig. 2.4(a) reveals that the resistance of CSA dipoles is even smaller than connected ones. As will be introduced shortly, the double-legged dipole array tackles this problem.

2.2 Double-Legged Dipole Array Design

This section presents a novel double-legged dipole array, which is formed by a combination of two diﬀerent dipole arrangements. First, these two arrangements and the corresponding dipole arrays are to be discussed. Next, the combined array performance is to be illustrated, also including comparisons to the CSA.

2.2.1 Skewed Dipole Arrangement

An intuitive way to conceiving tightly coupled array antennas is to treat them as frequency selective surfaces (FSSs) that are periodically excited over a ground plane.

Thus, one might expect that if the FSS is broadband, its excited array would also be

26 broadband. This idea led us to investigate broadband FSSs for possible utilization in

arrays. Among the ones listed in [14], two had exceptional bandwidth performance.

The ﬁrst one was skewed dipole FSS (or “Gangbuster” FSS as Munk named it) and

the second one was square spiral FSS. The latter supported our hypothesis after the

exceptional bandwidth performance of interwoven spiral array (ISPA) in [19].

Therefore, here we investigate the ﬁrst group, namely, skewed dipoles. As depicted

in Fig. 2.6, these skewed dipoles can be arranged in various ways. The “type n”

deﬁnition is made in a way that if one tip of the dipoles is at point (x, z), the other

tip is at (x + Dx,z + nDz). By increasing element type n, it is seen that dipole lengths are increased. Doing so, the fundamental resonance frequency of the FSS is lowered [14]. However, the inter-elemental spacings (i.e., Dx, Dz) are not changed.

Thus, the onset of grating lobes stays the same [14]. This is a key beneﬁt of skewed dipole arrangement.

(a) Type 2 (b) Type 3 (c) Type 4 Figure 2.6: Various arrangements of skewed dipole FSSs. [14]

27 To investigate their array performance, we chose skewed dipoles in type 2 ar-

rangement, as depicted in Fig. 2.7. The dipoles are fed at their centers and lumped

capacitors are distributed over the dipole legs. Speciﬁcally, the unit cell (inside black

box) size is 8.2mm × 8.2mm and the array thickness is 11.2mm. The capacitor with

C1 = 1pF capacitance is used for capacitive loading, whereas the one with C2 = 0.1pF capacitance provides the necessary inter-element coupling. The corresponding array impedance is plotted in Fig. 2.8. As seen, the resistance makes a peak of about 940Ω at 3.2 GHz. Compared to previous connected or tightly coupled dipole arrays, this resistance is excessive and can be explained by referring to the skewed unit cell in

Fig. 2.7. As seen, this unit cell (inside red box) is longer in the E-plane and narrower in the H-plane. As compared to a square grid, it is this aspect ratio that increases the characteristic impedance of waveguide by a factor of (1 + 22)/2 = 2.5. Thus, instead of 120π = 377Ω peak resistance, one would now expect 2.5×120π = 942Ω, and this is in agreement with Fig. 2.8. As a result of their increased waveguide impedance and longer length, such skewed dipoles resonate at lower frequencies, albeit with higher

8.2mm

C 8.2mm 1

Figure 2.7: Type 2 skewed dipole array.

28 and sharper resistance and reactance. Even if a high system impedance is selected,

their bandwidth is narrow. Therefore, although skewed dipoles show broadband FSS

performance, their bandwidth diminishes when used as arrays. This disproves our

initial hypothesis, which suggested that broadband FSSs would also result in broad-

band array antennas. Nevertheless, we make use of these skewed dipole elements to

our beneﬁt, as will be explained shortly.

1000 Real 900 Imaginary 800 700 600 500 400 300 ) Ω 200 100 0 Impedance ( −100 −200 −300 −400 −500 −600 −700

−800 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency (GHz) Figure 2.8: Impedance of the type 2 skewed dipole array in Fig. 2.7.

2.2.2 Regular Dipole Arrangement

This array (depicted in Fig. 2.9) is a replica of the CSA in the sense that each

dipole couples only to those in adjacent unit cells. In contrast to the CSA, the dipole

legs are made wider for capacitive loading. Also, a ﬂared transition from feed to

dipole legs is added. The lumped capacitor with C3 = 0.4pF capacitance provides the necessary inter-element coupling. As in skewed dipole case, this array uses a

29 square grid of 8.2mm × 8.2mm and it is 11.2mm thick. Its impedance is plotted in

Fig. 2.10 and this is found very similar to the one in Fig. 2.4(d). The main diﬀerence between two plots is observed for the frequencies where resistances make peaks, and this is attributed to diﬀerent thicknesses (11.2mm vs. 7mm) of the arrays.

8.2mm

C3 8.2mm

Figure 2.9: Tightly coupled dipole array in regular arrangement.

400 Real 350 Imaginary

300

250

200

150

100 )

Ω 50

−50 Impedance ( −100

−150

−200

−250

−300

−350

−400 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency (GHz) Figure 2.10: Impedance of the regular dipole array in Fig. 2.9.

30 2.2.3 Double-Legged Dipole Array

Z+ Z− As mentioned in Section 2.1.2, parallel combination of 1 (reactive) with 1

(resistive) decreased the total resistance. In double-legged dipole array (DLDA), we

exploit such impedance interaction to decrease the excessive resistance. For this,

the skewed rectangular dipoles and regular dipoles introduced above are connected

together at their feeds, as depicted in Fig. 2.11. This can be understood as connecting

the two arrays in parallel. Their grid spacing, thickness and capacitance values are

kept the same. The corresponding array impedance is plotted in Fig. 2.12. 11.2mm

8.2mm

C3 8.2mm

C1 C2

Figure 2.11: Double-legged dipole array geometry.

The ﬁrst resonance (determined from resistance peak) is mainly attributed to skewed dipole legs. As compared to their stand alone case, this peak resistance is decreased by 2.5 (becomes 380Ω) and is shifted to a slightly lower frequency (2.6 GHz).

The second resonance (with a slight peak of 175Ω at 6 GHz) is due to regular dipoles.

31 400 Real 350 Imaginary

300

250

200

150 )

Ω 100

0 Impedance (

−50

−100

−150

−200

−250

−300 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency (GHz)

Figure 2.12: Impedance of the DLDA in Fig. 2.11.

As compared to their stand alone case, peak resistance is decreased by 2. An additional third peak of 340Ω is also observed at 10.5 GHz. This peak did not exist in either skewed dipole or regular dipole case but appears here due to the increased total length of dipole element. Its high resistance behavior is due to the skewed legs (i.e., their higher resonance) and appearance at a lower frequency (i.e., before 12 GHz) with lowered resistance peak is due to addition of regular dipole legs.

In summary, proper connection of skewed dipole and regular dipole arrays enables creating an aperture with multiple resonances. The corresponding impedances of two arrays work together to decrease their excessive resistances and also to counteract their reactances. The lumped capacitance values are chosen in a way to achieve these two goals and maximize the bandwidth.

32 The corresponding VSWR performance of the DLDA is plotted in Figs. 2.13-2.14

with 190Ω and 125Ω system impedances, respectively. For the 190Ω case, DLDA

achieves 6.7:1 bandwidth with VSWR<2 and its thickness is λ/17 at the lowest op-

erational frequency. If VSWR<3 deﬁnition is chosen, its bandwidth becomes 9.2:1

while being λ/22 thick. This performance for VSWR<3 can be slightly improved if

125Ω system impedance is used instead. For this case, bandwidth increases to 9.5:1

and thickness becomes λ/24.

VSWR < 3 1.2 GHz − 11 GHz 9.2:1 BW 3 VSWR

VSWR < 2 1.56 GHz − 10.5 GHz 6.7:1 BW 2

1 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency (GHz)

Figure 2.13: VSWR of the DLDA in Fig. 2.11, with 190Ω system impedance.

Next, the DLDA is compared with the CSA in Table 2.1 (computed data in each case). For both arrays, the same 8.2mm × 8.2mm grid spacing was used. However,

the DLDA and the CSA thicknesses are diﬀerent (11.2mm and 7mm, respectively).

For a fair comparison, element sizes and thicknesses are given in terms of wavelengths.

It is observed that both arrays achieve their maximum bandwidth with similar system

33 5

VSWR < 3 1.1 GHz − 10.5 GHz 9.5:1 BW 3 VSWR

1 0 1 2 3 4 5 6 7 8 9 10 11 12 Frequency (GHz)

Figure 2.14: VSWR of the DLDA in Fig. 2.11, with 125Ω system impedance. impedances. However, the DLDA operates at much lower frequencies than the CSA, with broader bandwidth and smaller electrical thickness. Specifically, the DLDA achieves 40% more bandwidth ratio while concurrently being 35% thinner. Another important difference is between element sizes. Specifically, the DLDA elements are

60% smaller than the CSA’s at their lowest operational frequencies.

Table 2.1: Comparison of the DLDA and the CSA with VSWR<2 DLDA CSA System Impedance 190Ω 190Ω Operational Band (GHz) 1.56 - 10.5 3.8 - 17.8 Bandwidth 6.7:1 4.7:1 Element size (fhigh) λ/3.5 λ/2.1 Element size (flow) λ/23.4 λ/9.6 Thickness (fhigh) λ/2.6 λ/2.4 Thickness (flow) λ/17 λ/11

34 2.2.4 Realization of the DLDA Using Overlapping Legs and Comparisons to the CSA

In designing the DLDA unit cell in Fig. 2.11, lumped capacitors were used for easy tuning. One way to realize them is to use interdigital capacitors as in Fig. 2.5.

A simpler method is to use overlapping legs printed on diﬀerent sides of a thin dielectric sheet. In this case, the dimensions for realizing desired capacitance can be found easily using the C = εA/d formula. A more realistic DLDA unit cell using such overlapping legs is depicted in Fig. 2.15(a). This unit cell is an 8 times scaled up version of the one in Fig. 2.11, to operate from 200 MHz. The gap between overlapping legs used here is 0.08mm (3.15 mil), ﬁlled with air. Using a thin dielectric sheet would increase this distance in proportion to its relative permittivity, without distorting the array performance.

overlapping legs ) ” ) ” 14 cm 14 cm (5.5 9 cm 9 cm (3.5

(a) (b)

Figure 2.15: (a) DLDA and, (b) CSA unit cells scaled to operate at 200 MHz and up.

35 The CSA unit cell is also scaled up to operate from 200 MHz and it is shown in

Fig. 2.15(b). It is noted that both the DLDA and the CSA unit cells in Fig. 2.15 are

drawn to relative scale. Their corresponding VSWR curves are plotted in Fig. 2.16.

This scaled comparison shows the DLDA performance more clearly. Speciﬁcally, the

DLDAis2 thinner than the CSA and can operate up to 1.3 GHz, instead of 900 MHz.

3 VSWR

VSWR < 2 196 MHz − 1.286 GHz (6.6:1 BW) 2

VSWR < 2 CSA 196 MHz − 885 MHz (4.5:1 BW) DLDA 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Frequency (GHz)

Figure 2.16: VSWR of the DLDA and the CSA in Fig. 2.15.

Smaller element size of the DLDA also implies that more elements can be ﬁt in a

same-size aperture. This is illustrated in Fig. 2.17 with an example. As seen, while

the CSA can ﬁt 4×4 = 16 elements, the DLDA allows for 10×10 = 100 elements. This would give more degrees of freedom for realizing a ﬁnite array with various element excitation and termination schemes.

36 (a) (b) Figure 2.17: Same size apertures ﬁlled with (a) 4×4 CSA, (b) 10×10 DLDA elements.

2.3 Concluding Remarks and Discussions

This chapter presented the current sheet concept and its applications for realizing ultrawideband phased array antennas. A key aspect of this concept is to visualize the array as a collection of individual elements that couple to their hypothetical waveguides. As explained, this allows for simple derivations and equivalent circuit models to understand the array characteristics.

It was shown that, the current sheet can be realized by connecting array elements and this doesn’t pose much challenge when the array is free standing and radiating bidirectionally. However, the major challenge arises when the array is placed closely over a ground plane. As discussed, this is due to the reactive loading eﬀect of the ground plane. In addition to onset of grating lobes (when inter-element spacing becomes λ/2), the ground plane also limits the array at high frequencies when the array thickness reaches λ/2. Thus, the array is bounded at the high frequency end by whichever of these two that occurs earlier. As a result, array bandwidth can be

37 improved mainly by decreasing its lowest operational frequency. This also translates to realizing a lower-proﬁle array, since it is the thickness at lowest frequency that counts most.

However, as presented, there are two main challenges at low frequencies. First one is the excessive inductance due to the ground plane. Second one is the decreasing radiation resistance. It was shown that, the ﬁrst challenge can be circumvented by using tightly coupled elements. The intentionally formed capacitance counteracts the ground plane inductance, albeit in a narrowband region. Nevertheless, it was shown that this improves the array bandwidth and decreases the proﬁle substantially.

The second challenge, namely reduced radiation resistance, was not addressed suﬃciently in previous dipole arrays. In this chapter, we tackled this problem by introducing a double-legged dipole array (DLDA). A key aspect of this array is utilization of longer, skewed dipole legs to couple to others further away. The increased aspect ratio of hypothetical waveguides formed with these legs allows for creating a resonance at lower frequencies with high radiation resistance, albeit with narrow bandwidth. However, with proper combination of shorter dipole legs that couple to adjacent elements, this array achieves multiple, well-balanced resonances that can be matched in a broad frequency range. Speciﬁcally, the presented DLDA allows for

7:1 bandwidth with λlow/17 proﬁle (for VSWR<2). As compared to previous tightly coupled dipole arrays (such as CSA), the presented array has 40% more bandwidth ratio and also it is 35% thinner. It is also noted that this performance is obtained without using any substrates or superstrates which can introduce material losses. As a result, the array gain is comparable to its directivity and it can be easily scaled to other frequencies.

38 However, the DLDA setting also presents some disadvantages. Its multi-resonance behavior is supported by two dipole legs and at certain regions one of the legs con- tribute mainly to radiation. Also, these legs are not entirely parallel to each other.

That is, although the total polarization is linear, its direction is expected to rotate slightly throughout the operational band. In addition, the cross polarization levels are higher than simpler linear dipoles. Although dual linear polarization can be achieved by placing another 90◦ rotated array underneath, these arrays would also couple to each other.

Another main difference of DLDA from the CSA is its smaller grid spacing. Of course, this allows for fitting more elements into same size apertures. This presents several advantages, as well as disadvantages. The advantage stems from truncation of the infinite array. Usually, finite tightly coupled arrays need resistive, open- or short- circuited terminations around the excited region (i.e., in the periphery of the array).

Having more elements inside the same aperture would bring additional degrees of freedom for treating the ﬁnite array. Also, the “hot” (i.e., excited) region can be made larger. However, as is evident, there are more elements to feed and the space is much more limited for placing integrated feeds. These would bring additional burdens for feeding. Typical for almost all ultrawideband phased arrays, this DLDA would also need baluns and impedance transformers in pace with its bandwidth.

These challenges related to ﬁnite realization and feeding of ultrawideband arrays are beyond the scope of this dissertation and they are investigated separately in [60].

The rest of this dissertation is focused on realization of current sheet and tightly coupled array concepts for much smaller and lower-proﬁle arrays. Finite array and feeding aspects of the tightly coupled arrays will be discussed mainly for these arrays.

39 Chapter 3: An Extremely Low-Proﬁle, Compact and Broadband Tightly Coupled Patch Array

In this chapter, a tightly coupled patch array (TCPA) design concept is intro-

duced to realize small-size, extremely low-proﬁle planar antennas with broadband

performance. Past approaches have used frequency selective surfaces (FSSs) as part

of the substrate or ground plane (i.e., in passive mode) for also realizing low-proﬁle

antennas. In contrast, the proposed TCPA employs an FSS aperture as the radi-

ating structure (i.e., array antenna). A key aspect of the TCPA is the exploitation

of diﬀerences in FSSs when operating in radiating and passive modes. Tight ele-

ment coupling and periodic excitation are the key aspects for achieving broadband

operation. Speciﬁcally, a small-size, ﬁnite array is designed along with a very thin

and compact feeding network. The designed TCPA resonated at 2.07 GHz with

5.6% impedance bandwidth (|S11| < −10dB), 4.4 dB realized gain (86% eﬃciency)

and 23% gain bandwidth (3dB drop). Of importance is that, the overall aperture

dimensions were only λ0/3 × λ0/3 and λ0/42 thick (including feeding network) at the mid-frequency of operation. A preliminary TCPA antenna prototype was fabricated and tested. Both simulated and measured data showed enhanced bandwidth as compared to the conventional microstrip patch antennas of the same size and thickness. However, as common for such extremely low-proﬁle microstrip antennas, the

40 conductivity losses were increased. Thus, the measured efficiency of the first TCPA prototype was significantly affected.

3.1 Introduction

As outlined in Chapter 1, recent studies on electromagnetic band gap structures brought significant novelties. These can be grouped in three main categories. First one is based on the band gap associated with EGBs. This leads to suppression of surface waves and also reducing mutual coupling between antennas. Second one is associated with the EBG’s high impedance characteristics and it is exploited for realizing high impedance surfaces or artificial magnetic conductors. Such surfaces provide in-phase reflection (as compared to out-of-phase for metallic ground planes) and they are utilized for realizing low-profile antennas. However, antennas on such

AMCs still suffer from narrow bandwidth, because the reflected wave doubles their input impedance and causes difficulty in matching. The third category is based on reflection characteristics of the EBG and it is found more useful for enhancing antenna bandwidth. In this case, the EBG provides a reactive loading to the antenna. Thus, it operates as a frequency selective surface rather than a band gap structure. Usually, dipole or patch antennas were placed above such FSSs. Of course, this increases the total antenna profile. Also, antenna bandwidth is still limited due to inherent narrowband behavior of the dipole or patch radiator.

In this chapter, we present an alternative methodology to realize very low-proﬁle and small size microstrip antennas. The resulting design achieves broad bandwidth, high gain and good radiation performance. This is accomplished by using the FSS itself as the radiating aperture (i.e., operating the FSS as array antenna). This

41 approach was ﬁrst envisioned in [15] in the form of a current sheet array (CSA).

The tightly coupled patch array (TCPA) proposed here was therefore inspired from the CSA functionality. However, there are several diﬀerences between the CSA and

TCPA. Among them:

1. The CSA is an ultrawideband (UWB) antenna demonstrated to reach 5:1 impe-

dance bandwidth (for VSWR<2) without any dielectric substrates or super-

strates, even though it is λ0/10 thick at the lowest operational frequency. On

the contrary, the TCPA employs a high contrast dielectric substrate for minia-

turization and achieves λ0/50 proﬁle (at the mid-band of operation). Thus, its

bandwidth is much narrower as a consequence of the much thinner proﬁle.

2. In CSA design, dielectric materials are suggested as superstrates rather than

substrates, to improve the bandwidth up to 9:1 and to obtain better scan ca-

pability [7]. In TCPA, the opposite is done for achieving a very low-proﬁle. In

addition, only broadside radiation is considered.

3. The CSA uses dipole elements with interdigital ﬁngers or overlapping arms to

introduce the necessary inter-element capacitance. The dipole elements are pre-

ferred for their UWB performance and achieving dual-linear polarization. For

the TCPA, patch elements are employed for their better bandwidth performance

in low-proﬁle microstrip antennas. In this case, the inter-element capacitance

is obtained by the close proximity of the patches (and the reason the aperture

is referred to as the TCPA). For the current design, single linear polarization is

considered.

42 4. The dipole arms in the CSA are excited using two out-of-phase coaxial ca-

bles. This arrangement introduces the well-known common modes at the feed

structure. Thus, a balun is necessary between the balanced dipole arms and

the unbalanced coaxial cables. These diﬃculties are overcome in the TCPA ar-

rangement using standard SMA coaxial probes to excite the patches. The probe

feeds are brought towards patch edges to enable adjacent patch excitation to

form the current sheet.

5. In ﬁnite realizations of the CSA, only elements towards the center are excited.

The other elements towards the edges are terminated with resistors in an ef-

fort to suppress edge diﬀractions that deteriorate the radiation pattern and the

impedance bandwidth of excited elements. However, radiation eﬃciency is typ-

ically reduced down to as low as 30% at the lowest operational frequency. For

the TCPA, we also excite elements selectively. However, the passive elements

are left open-circuited for improved eﬃciency. In fact, the radiation eﬃciency

reaches 97% while most of the loss is coming from the feeding network, reducing

eﬃciency to 86%.

Below, in Section 3.2, we begin by explaining the operational principle of the

TCPA. We describe the unit cell and provide a step-by-step realization of the ﬁnite size TCPA. Section 3.3 presents the thin and compact microstrip feeding network for exciting the TCPA. In Section 3.4, the TCPA is compared with a conventional patch antenna. Next, in Section 3.5, measured results for a fabricated TCPA prototype are given. Conclusions are drawn in Section 3.6.

43 3.2 Tightly Coupled Patch Array Design

This section details the TCPA design, ﬁrst assuming an inﬁnite array setting.

Then, realization of a ﬁnite array is considered with special emphasis on selecting

which elements to excite and choices for terminating the unexcited ones.

3.2.1 Unit Cell Design

FSSs have been typically constructed using closely spaced dipoles, while other

element types are also possible [14]. In this regard, patch elements can be also viewed

as a special case of dipoles (i.e., fat dipoles). For understanding, we can represent

the FSSs using equivalent circuits, as depicted in Fig. 3.1. Speciﬁcally, each dipole

can be represented by an inductor of inductance Ld. Also, the coupling between dipoles can be represented by a series capacitance, Cd. Such an FSS resonates at √ ω0 =1/ LdCd. At frequencies lower than this resonance, the FSS becomes capacitive.

For HIS, AMC and EBG applications, such FSSs are placed on grounded dielectric slabs, as illustrated in Fig. 3.1(a). For the fundamental mode and principle E- and

H-planes, the grounded dielectric slab of thickness h can be considered as a shorted transmission line. Thus, the impedance seen looking into the substrate, from the FSS

+ + plane, becomes Z = jZd tan(βdh). Obviously, Z is inductive for thin substrates.

The resulting circuit model is shown in Fig. 3.1(a). As pointed out in [61], although

below the FSS resonance Cd term dominates over Ld, this series inductance should be still included in the model. In this case, the resonance frequency of the FSS on grounded dielectric slab becomes ω0 =1/ (Ld + Lgp)Cd, where Lgp represents the inductance due to ground plane. One important conclusion in [61] was, in contrast to what would be expected from the easier parallel-LC model that neglects the Ld term,

44 increasing capacitance Cd does not decrease the HIS bandwidth of FSS on ground plane. On the contrary, tightly coupled patches were shown to deliver much broader bandwidth than cross-type elements [61].

+ + Ld Cd Z = j Zd tan(Edh) Z = j Zd tan(Edh)

Ld Ld Z0, E0 Zd, Ed Z0 Lgp Z0, E0 Zd, Ed Z0 Lgp Z0 Lgp C C d d feed

h h Zin (a) (b) Figure 3.1: Circuit model representations of FSSs. (a) Passive mode. (b) Radiating mode.

As noted earlier, past designs for low-proﬁle antennas employed FSSs as sub-

strates or ground planes underneath the main radiator (e.g., dipole, patch). This

main radiator is usually capacitive below its natural resonance. The FSS on ground

plane, which is inductive below its own resonance, was therefore used for cancelling

the capacitance of the main radiator [58]. As would be expected, this arrangement

required FSSs with suﬃcient thickness to provide the necessary inductance. In several

works [57], [58], [62] it was observed that thickness of the FSS itself constitutes at

least 2/3 of the overall antenna thickness. Clearly, this is an important hindrance to

achieve very low-proﬁles.

Indeed, similar cancellation of inductance by capacitance is also employed in the

CSA [15], whose unit cell shown in Fig. 3.1(b). In essence, the CSA is an FSS on a

ground plane, where the FSS itself is the radiator. Dipoles in this otherwise passive

FSS are excited periodically at their centers. Capacitances are introduced intention-

ally at the tips of neighboring dipole arms. Similar to the low-proﬁle antennas on

passive FSSs, this capacitance serves to cancel the inductance due to the ground

45 plane, determining the lowest frequency of operation for the CSA. Consequently, the

CSA can achieve a 4.5:1 UWB performance, while maintaining a low-proﬁle of λ0/10.

In addition, the simple circuit models shown in Fig. 3.1(b) are quite accurate for calculating the input impedance.

In fact, the TCPA concept is mainly inspired by the impressive wideband and low- profile performance of the CSA. TCPA is intended to bring the benefits of such an array to the area of miniature microstrip antennas. Eventually, the goal is to achieve a small size, very low-profile (both physically and electrically), yet broadband and high gain microstrip antenna. For this, we considered tightly coupled patch elements on a grounded high contrast dielectric substrate (εr = 25, tanδ = 0.001; obtainable from

Trans-Tech Inc. or TCI Ceramics), as illustrated in Fig. 3.2. The HIS performance

of such patches were already found to be very broadband in the passive FSS mode

[61]. The high contrast dielectric substrate is preferred for miniaturizing the patch

elements, therefore to be able to ﬁt as many elements in a small ﬁnite volume. When

7.5 mm radiation boundary

3 mm y 7.5 mm x

(a)

0.5 mm

2.8 mm

y substrate ground plane x (Hr = 25) coaxial feed (b) (c) Figure 3.2: Tightly coupled patch array unit cell. (a) Top view. (b) Top view, shifted. (c) 3D view. 46 tightly packed on this high contrast dielectric, close proximity of patch elements

also create enough capacitance (1.3pF using the formulas given in [58]) to cancel

the inductance due to the ground plane. This capacitance also acts as capacitive

loading for additional miniaturization. For excitation, standard SMA probes feeds

are used (probe radius: 25 mil, coaxial feed radius: 80 mil, ﬁlled with εr = 2 material).

Each patch is excited periodically, at a point towards its edge. Diﬀerent from CSA, capacitive coupling and excitation sections of the unit cell are very close to each other.

Since the probe feed is very close to the edge, its coaxial section exceeds the bounds of unit cell. To avoid this, the unit cell is shifted so that the feed stays in the middle, as shown in Figs. 3.2(b)-(c). This structure is simulated in Ansoft HFSS v12.1 by applying the periodic boundary conditions depicted in Fig. 3.2(c). This implies an inﬁnite array excited periodically and uniformly.

Active input impedance and return loss obtained from the inﬁnite TCPA are shown in Fig. 3.3. Although the unit cell is very small and extremely low-proﬁle

(λ0/20×λ0/20×λ0/57 or λg/4×λg/4×λg/11.4 at 1.88 GHz), it has a broad impedance

bandwidth (7.3% for |S11| < −10 dB). This can be attributed to periodically exciting

D E Figure 3.3: TCPA unit cell input impedance and return loss. (a) Input impedance, (b) Return loss. 47 each unit cell, as in the case of CSA. Indeed, for such an array, the evanescent waves

around one unit cell can only extend up to half way into next unit cells [15]. If the same

unit cell was to be used stand alone (in the absence of FSS array), these evanescent

waves would extend into inﬁnity [15]. Therefore, the TCPA has less evanescent waves,

implying less stored energy (thus, lower Q) and broader bandwidth. In addition, it

should be remarked that the TCPA element has very small periodicity. As in the

case of tightly placed Gangbuster dipoles [14], or other unit cells in passive FSS

mode [63], smaller periodicity also helps achieving broader bandwidth. This is again

because the evanescent waves around each unit cell shrink to smaller physical space,

hence decreasing stored energy and Q.

3.2.2 Finite Array Design

For the ﬁnite array realization, we considered a small size (4.8cm × 4.8cm × 2.8mm)

grounded dielectric substrate as shown in Fig. 3.4(a). Within this small area, the sub-

strate can host 6×6 = 36 TCPA unit cells. The leftmost column of the array was left unexcited due to the close proximity of the coax feeds to the edge. Thus, the remaining 30 ports are excited uniformly, as shown in Fig. 3.4(b). A close inspection reveals that, each feed also capacitively excites the neighboring patch to its left, as illustrated in Fig. 3.4(c). In this manner, two adjacent patches can be considered as the arms of a fat dipole, fed at the center. Therefore, a current sheet is formed on the

TCPA aperture, ﬂowing through the overlapping arms of these hypothetical dipoles.

Next, active return losses of the 30 uniformly-excited elements are computed, as depicted in Fig. 3.5(a). Due to the symmetry in the array, only results for upper half of the array are shown (which is also implied for the rest of the results in this

48 P1 P2 P3 P4 P5 2.8 mm P6 P7 P8 P9 P10

P11 P12 P13 P14 P15

P16 P17 P18 P19 P20

P21 P22 P23 P24 P25

P26 P27 P28 P29 P30 D E + – + – + – + – + – + –

F Figure 3.4: Finite 6×6 TCPA array with 30 excited elements. (a) 3D view. (b) Top view. (c) Side view. manuscript). From Fig. 3.5(a), it is observed that all elements, except those on the two rightmost columns, resonate around 2 GHz, which is close to 1.88 GHz

(expected from infinite array). The elements on the two rightmost columns resonate at slightly higher frequencies. This is a classical manifestation of truncating the substrate in finite arrays. Such finite edges cause wave bounces and diffractions from the dielectric/air boundaries. Since the elements on these two columns were found to be “problematic”, we next consider the case where these elements are not excited.

Although these elements are not excited, the coaxial probes were kept in place, thus these ports are terminated with 50Ω impedances. The new active return losses for the remaining 18 excited elements are shown in Fig. 3.5(b). Fig. 3.5(c) shows these return losses plotted on top of each other. It can be observed that for this case, all

18 excited elements resonate at 2 GHz. A comparison of return losses in Fig. 3.5(a) and Fig. 3.5(b) together revealed that the response for these 18 elements change only slightly.

49 D E

F Figure 3.5: Active return losses of: (a) 30 excited elements; (b) 18 excited elements, 12 terminated with 50Ω; (c) 18 excited elements, 12 terminated with 50Ω, plotted together.

Although Fig. 3.5(c) shows great promise, it should be remarked that the probe feeds with 50Ω termination impedances would dissipate the power delivered to them.

Evidently, this decreases the antenna eﬃciency signiﬁcantly. Moreover, such resistive antenna loads are not desired for high power applications. In addition, although unexcited, probe feeds need to be connected to these patches, which is uncalled for.

In the next step, we considered leaving the unexcited ports as open-circuited (parasitic patches), rather than terminating with 50Ω loads. The new geometry and numbering of ports are shown in Fig. 3.6. Active return losses corresponding to this case are

50 P1 P2 P3

P4 P5 P6

P7 P8 P9

P10 P11 P12

P13 P14 P15

P16 P17 P18 D E Figure 3.6: Finite 6×6 TCPA array with 18 excited elements. (a) 3D view. (b) Top view. shown in Fig. 3.7(a) for each individual port; and in Fig. 3.7(b) for all ports together.

It is observed that only ports 6, 9 (and their symmetric ones 12, 15) resonate at a slightly higher frequency. As done previously, we next terminate two of these ports

(9 and 12) with 50Ω loads. The resulting active return losses for the remaining 16 excited ports are shown in Figs. 3.7(c)-(d). Again, all remaining excited ports now resonate at the same frequency, i.e., 2 GHz.

As the next step, the process explained above is repeated by considering only 16 excited elements, while the rest are left open. The new TCPA geometry is shown in Fig. 3.8(a). Similar to previous observations, active return losses for these ports

[shown in Figs. 3.8(b)-(c)] indicate that only 2 of the excited ports (now 6 and 13, were 6 and 15 in previous) resonate at a slightly higher frequency. These two ports can be also considered to be terminated or left open, and the process for choosing which elements to excite can be carried out in this manner until acceptable performance is achieved. However, we opted to discontinue such design iterations at this point. As the main reason, it can be remarked that the total number of excitations are now

51 (a) (b)

(c) (d) Figure 3.7: Active return losses of: (a) 18 excited elements; (b) 18 excited elements, plotted together; (c) 16 excited elements, ports 9 and 12 terminated with 50Ω; (d) 16 excited elements, ports 9 and 12 terminated with 50Ω, plotted together.

16, which happens to be a power of 2. This makes the feeding network design (to be discussed in the next section) much easier.

One critical observation from Figs. 3.5, 3.7 and 3.8 was the poor impedance matching for some of the ports. Although most ports resonated at around 2 GHz, inves- tigation of the return losses revealed that their input impedances were not exactly

50Ω. In Fig. 3.8(d), real and imaginary parts of the input impedance for each excited port are also shown, which corresponds to the geometry in Fig. 3.8(a). Indeed, real

52 P1 P2 P3

P4 P5 P6

P7 P8

P9 P10

P11 P12 P13

P14 P15 P16 (a) (b)

(c) (d) Figure 3.8: (a) Finite 6×6 TCPA array with 16 excited elements, top view. (b) Active return losses of 16 excited elements. (c) Active return losses of 16 excited elements, plotted together. (d) Active input impedances of 16 excited elements. parts of the input impedance for ports 4, 5, 7, 8, 9, 10, 11 and 12 were much higher than expected (in the orders of 90Ω-110Ω). Ports 3 and 16, on the other hand, were observed to be close to 40Ω. As explained earlier, such disruptions stemmed from truncation of the ﬁnite array. Fortunately, real part of the input impedance for each excited port can be decreased or increased simply by moving the probe feed closer to or away from center of the patch, respectively. To avoid creating other modes and cross polarization, the feeds are only moved along the y-axis (shown in Fig. 3.2).

(a) (b)

(c) (d) Figure 3.9: Finite 6×6 TCPA array with 16 excited elements having optimized feed locations (distances in mm), 3D view. (b) Active input impedances of 16 excited elements. (c) Active return losses of 16 excited elements. (d) Active return losses of 16 excited elements, plotted together.

Indeed, after a few iterative steps of concurrent ﬁne tuning, the feed positions shown in Fig. 3.9(a) were found optimal for best impedance matching. Fig. 3.9(b) shows the new input impedances for excited elements. It can be observed that real parts of input impedances are close to 50Ω for all patches, at their resonant frequencies. Cor- responding return losses are given in Figs. 3.9(c)-(d), which indicate that resonance frequencies of the excited patches move to slightly higher frequencies. While each

54 patch has about 7.2% impedance bandwidth, their resonance frequencies are not exactly overlapping. These patches continuously cover an 8.8% band, centered around

2.07 GHz. The overlapping band, where they all have |S11| < −10 dB, is about 5.8%.

Thus, if the patches are to be excited using the same signal source, (possibly making use of a feeding network), the overall impedance bandwidth would be close to 5.8%.

Clearly, the resonance frequencies of all patches can be optimized to overlap exactly, by adjusting the size of each individual patch. In this case, the overall impedance bandwidth can be increased to 7.2%. However, this option is left as future work. In summary, the geometry and results in Fig. 3.9 constitute the final version of the finite size TCPA designed here. We remark that, at 2.07 GHz, this TCPA has the electrical size of λ0/3 × λ0/3 × λ0/52. Yet, this extremely thin TCPA design achieves a realized gain of 5 dB (97% efficiency).

3.3 Feeding Network Design

The TCPA designed in Section 3.2 utilizes standard 50Ω SMA probes. Therefore, it is quite possible to feed it using an external feeding network. Since the TCPA has 16 ports, there are various ways of forming such a feeding network. The easiest option would be to use a 16-way equal power divider. Alternatively, one can use

8-way, 4-way or 2-way power dividers and combine them to form a multi-stage power divider. However, such external power dividers are usually bulky, expensive and more importantly, they can have high insertion losses. To avoid these, in this section we design a compact microstrip feeding network, which is also very thin. This network employs four stages of 2-way equal power dividers (i.e., Wilkinson power divider).

55 A major diﬃculty associated with the feeding network is the limited space un-

der the antenna. Due to small size of patch elements, miniaturized dividers are

called for. A design guideline for realizing such miniature dividers was given in [64],

where the λg/4 sections of the Wilkinson divider were miniaturized via meandering.

This design is adopted for 2.07 GHz center frequency and its corresponding layout is shown in Fig. 3.10(a). As the substrate, a 25 mil thick Rogers RO3010 (εr = 10.2, tanδ = 0.0023) is used. Correspondingly, widths of the microstrip lines with 50Ω and

70.7Ω characteristic impedances are 22 mil and 9 mil, respectively. Of course, using a higher permittivity dielectric substrate would help miniaturization. However, in that case the microstrip lines need to be much narrower. Clearly this is not desirable, since such very narrow microstrip lines would create diﬃculties in fabrication.

The narrowest microstrip line employed here is 9 mil, which can be fabricated using standard milling or screen printing techniques.

8 mm

P20.4 mm P3 22 mil 40 mil 175 mil 20 mil

22 mil 9 mil 8 mm 100:chip resistor P1

22 mil 25 mil Hr = 10.2

(a) (b) Figure 3.10: Single stage miniature Wilkinson power divider. (a) Geometry. (b) Frequency response.

56 Since the substrate is very thin, and microstrip lines are narrow, conductivity losses become important. To take into their eﬀects, metallizations on both sides of the substrate are modeled as 3D copper plates with 35 μm thickness (1oz cladding).

A small size (0.4mm × 0.2mm) chip resistor from Panasonic ERJXGN series is also employed for improving isolation. The transmission, isolation and reﬂection performance of this divider is shown in Fig. 3.10(b). It is observed that the isolation and reﬂection levels are good across the whole band. Insertion loss is around 3.1 dB, which is only 0.1 dB higher than the theoretical value (3dB). Thus, after four stages of such dividers, a total of 0.4dB insertion loss (in addition to 12dB theoretical) can be expected.

25 mil

P1 (input port)

output ports (to antenna) (a) (b)

(c) Figure 3.11: Multiple-stage, 16-way, equal power division and feeding network. (a) Geometry, 3D view. (b) Geometry, bottom view. (c) Frequency response. 57 The desired 16-way power divider network is formed by cascading 4 stages of

Wilkinson power dividers designed above. Input/output ports of the network are included as standard SMA probes. One necessary requirement for the TCPA is having uniform excitations. Therefore, microstrip line sections from input port to all output ports are adjusted to be the same length. As in Wilkinson divider case, metallizations are modeled as 35 μm thick copper plates. Layout of the ﬁnal feeding network is shown in Figs. 3.11(a)-(b). Reﬂection seen at the input port is given in Fig. 3.11(c), which exhibits the required broadband performance. In addition, transmissions from the input port to each of the output ports are examined. It is found that the insertion loss is 0.5dB ± 0.7dB (in addition to 12dB theoretical, after 4 stages of equal power split). The phase variations are ±6◦.

3.4 Integrated Antenna Performance and Comparisons to Other Antennas

In this section, integrated performance of the TCPA (i.e., array + feed) is evalu- ated by comparing it to a conventional patch antenna having same overall dimensions.

First, the array part of the TCPA designed in Section 3.2 is combined with the feeding network designed in Section 3.3. This is done by removing the SMA probes underneath the array and above the feeding network ground planes and directly combining the two. Thus, the array and the feed network utilize the same ground plane, while the circular holes with 80 mil radius (which were opened to host coaxial feeds) remain intact. Then, the microstrip lines of the feeding network are connected to the patches using vias (with 25 mil radius, same as probe feeds). The layout of the TCPA in its

ﬁnal form is shown in Fig. 3.12(a). In the HFSS model, all metallic parts are copper,

58 3.44 mm 3.44 mm (135 mil) (135 mil)

Hr =25 Hr =25 Hr = 10.2 (a) (b) Figure 3.12: Layouts of; (a) TCPA, (b) conventional patch antenna. including patches, vias, ground plane and the microstrip lines. Therefore, all conductivity and dielectric losses are accounted for. Total thickness of the TCPA including its feeding network becomes 135 mil. The computed impedance bandwidth of this

TCPA prototype is 5.6% at 2.07 GHz. This is very close to the 5.8% bandwidth previously expected from Fig. 3.8(d). However, due to insertion losses in its feeding network (0.6dB), its realized gain drops to 4.4dB, reducing its eﬃciency from 97% to

86%. It is noted that the small amplitude and phase misbalances in the feed did not aﬀect the radiation pattern appreciably. At 2.07 GHz, the overall dimensions of the

TCPA are λ0/3 × λ0/3 × λ0/42, which is an extremely thin antenna.

For comparison purposes, several conventional patch antennas were considered.

The aim was to ﬁnd an antenna having the same overall dimensions with the TCPA, while providing the broadest impedance bandwidth. Since the TCPA utilizes almost all of its substrate, a seemingly logical choice would be to use a large patch, ex- tending to the limits of the substrate. However, to be able to resonate at the same frequency with the TCPA, such a patch needs to be placed on a low contrast dielectric substrate. For ﬁxed physical thickness, this would make the substrate electrically thinner (with respect to guided wavelength). Thus, such large patch antennas on low contrast substrates have very narrow bandwidths (about 0.5%). Another choice was

59 connecting the excited patches of the TCPA, forming a U-shaped patch. In addition, using parasitic patches around this U-shaped patch (as was in the case of TCPA) was also considered. Neither of these approaches could exceed 1% bandwidth. The best impedance bandwidth was obtained, however, using a rectangular patch on high contrast dielectric substrate (εr = 25). Layout of this antenna is shown in Fig. 3.12(b).

This rectangular patch could create two resonances and was matched to 50Ω in between. However, since the substrate is thin, the resonances are very narrowband. This reduces the impedance bandwidth signiﬁcantly. The broadest impedance bandwidth

(a) (b)

(c) (d) Figure 3.13: Performance comparison of TCPA vs. conventional patch antenna. (a) Return losses. (b) Realized gains in broadside direction. (c) Radiation patterns in E-plane. (d) Radiation patterns in H-plane.

60 obtained after optimization was 2.5% at 2.07 GHz. Fig. 3.13(a) compares the input impedance of the TCPA and this conventional patch. Realized gain of the patch antenna was as high as 5.16 dB, however, decreased very sharply with frequency.

The realized gains in broadside direction are compared in Fig. 3.13(b), where it is revealed that TCPA can also maintain a very broad gain bandwidth. This is mainly because TCPA creates a current sheet on the antenna aperture which doesn’t ﬂuctu- ate abruptly with frequency. The radiation patterns of the TCPA and conventional patch were found to be very similar, as shown in Figs. 3.13(c)-(d). This similarity also applies to their cross polarization levels.

3.5 Experimental Veriﬁcation

A TCPA prototype was built and tested at The Ohio State University Electro-

Science Laboratory and is shown in Fig. 3.14. The patch array was screen-printed using a silver ink (Heraeus C 1076 SD). The feeding network was fabricated using a milling machine with small (0.4mm × 0.2mm) chip resistors (Panasonic ERJXGN) soldered to improve isolation. The measured return loss gave 4.2% bandwidth at

2.13GHz (with a small frequency shift and little less than the 5.6% computed) and is shown in Fig. 3.15(a). This diﬀerence is likely due to a possible air gap formed between the ground plane and array substrate and the sensitivity of probe feed positions. The latter could have caused a slight non-overlap of the individual patch resonances.

The broadside realized gain of the fabricated TCPA prototype was measured in the anechoic chamber. From Fig. 3.15(b), we observe a peak realized gain of 1.6dB

(50% eﬃciency) at 2.15GHz. This is 3dB smaller than the computed gain with the

61 (a) (b) Figure 3.14: Fabricated TCPA prototype. (a) Front view, (b) Back view. diﬀerence attributed to conductivity losses in the feeding network, soldering and silver ink. This prototype had very thin silver cladding (12 μm) with imperfect surface roughness to augment conductivity losses. We remark that such conductivity losses would be also present for the conventional patch.

(a) (b) Figure 3.15: Measured return loss and realized gain of the TCPA prototype in Fig. 3.14. (a) Return loss, (b) Realized gain at broadside.

62 3.6 Concluding Remarks and Discussions

A small-size and low-profile antenna array was designed using tightly coupled patch elements. Due to its small periodicity and tight placement, these patches serve as a broadband frequency selective surface. Rather than using a secondary radiating element (typically placed above), this FSS itself was used as the main radiator. While the former method is employed very commonly in the open literature for realizing low-profile antennas, the latter enabled achieving much reduced profile with more enhanced impedance and realized gain bandwidths as compared to conventional patch antennas. This much broadband performance was mainly due to small periodicity and periodic excitation of the FSS, which helped reducing the stored electromagnetic energy underneath the antenna. In essence, this created an effective current sheet on the antenna aperture that doesn’t fluctuate abruptly with frequency and utilizes the whole substrate as efficiently as possible. Finally, the TCPA can be also considered as a fragmented (or segmented) patch with multiple selective feeds. For conventional patches, radiation occurs from the radiating slots (magnetic line currents). For the patch array, the magnetic currents are between adjacent patches to represent the slots formed among the patches. In this context, the TCPA demonstrates the advantages of using such fragmented patches instead of a single and connected patch with a single feed. This is explained in details in the next chapter.

63 Chapter 4: Bandwidth Enhancement of Microstrip Patch Antennas Using Multiple Feeds and Patch Fragmentation

The tightly coupled patch array in Chapter 3 can be visualized as a large, fragmented patch with multiple selective feeds. This array was designed first using an infinite array setting. Subsequently, the effects of finite truncation were treated using selective, fine-tuned excitations. This chapter investigates similar operation without resorting to the periodic structure. Instead, our study starts with a conventional, single patch with a single feed. By introducing multiple feeds to the patch (and by fragmenting it when necessary), it is shown that antenna bandwidth can be enhanced substantially. This is mainly due to the radiating magnetic current slots formed among fragmented patches and their lower Q. Also, utilization of multiple feeds and patch fragmentation corresponds to increasing patch size in the transverse dimensions while keeping antenna thickness the same. This is equivalent to creating an anisotropic dielectric substrate that speeds up the wave laterally. As would be understood, this is in contrast to footprint miniaturization via emulation of anisotropy and wave slow-down [47] that results in narrow bandwidth.

64 4.1 Single Patch Antenna

First, we considered a single patch antenna with a single feed shown in Fig. 4.1 on a 4.8cm × 4.8cm × 6mm dielectric substrate, having permittivity εr = 10.2. The ground plane placed underneath was as large as the substrate (i.e., 4.8cm × 4.8cm).

As shown in Fig. 4.1, patch size was 3.7cm × 1.95cm and a coaxial feed was placed

7mm away from the patch center. In this setup, the patch created two resonances shown in Fig. 4.2(a). Using a standard 50Ω SMA coaxial probe feed, this single patch delivered 6.9% impedance bandwidth at 1.9 GHz and its return loss is plotted in Fig. 4.2(b). Surface currents on the patch are also shown in Fig. 4.3. For all examples considered in this chapter, substrate and ground plane sizes, as well as substrate properties, were kept the same. The aim is to design patch antennas (with variable patch sizes) that are all matched to 50Ω about the same frequency (i.e., 1.9

GHz).

1.95cm

4.8cm

4.8cm 6mm

7mm 3.7cm

Figure 4.1: Single patch antenna on ﬁnite-size substrate and ground plane.

(a) (b) Figure 4.2: Performance of single patch. (a) Input impedance, (b) Return loss.

Figure 4.3: Surface currents on the patch.

4.2 Single Patch Antenna with Multiple (1×2) Feeds

As investigated in Chapter 3, here we also considered using multiple feeds. Instead of a single probe feed, two feeds were utilized to excite the patch, similar to shown in Fig. 4.4. When the patch size was kept the same, having two feeds instead of a single feed didn’t change the bandwidth signiﬁcantly. Still, feed location needed to be optimized for ﬁnding best positions for 50Ω matching. However, having two

66 1.9cm

5mm P1 8.5mm 4.3cm

Figure 4.4: Patch antenna with 1×2 feeds. feeds instead of one brought another degree of freedom. By increasing the length of the patch, while moving the feeds away from the patch center, 50Ω matching was obtained at almost the same frequency as the single feed case.

The resonances created by this patch are shown in Fig. 4.5(a), and the corresponding return loss is plotted in Fig. 4.5(b). This longer patch with two feeds had

8.5% bandwidth. Thus, the bandwidth was increased by 23%, while the substrate and ground plane sizes were kept the same. This is mainly because the patch, in this

(a) (b) Figure 4.5: Performance of the 1×2 patch. (a) Input impedance, (b) Return loss. 67 case, has longer apertures for radiation, as illustrated in Fig. 4.6. Surface currents on the patch are also given in Fig. 4.7(a).

Figure 4.6: Radiation mechanisms of single patch and 1×2 patch.

D E Figure 4.7: Surface currents on the 1×2 patch. (a) Connected patch, (b) Fragmented patch.

As an important observation from Fig. 4.7(a), currents between the feeds ﬂows parallel to the shorter edge of the patch. This is reasonable, because both feeds are uniform and act like even-mode sources. As a result, creating a small gap at the center of the patch, similar to what is shown in Fig. 4.7(b), didn’t change the resonance frequency or bandwidth of the patch. Thus, this example revealed two important ﬁndings: i) having multiple feeds in 1×2 setup allows increasing patch antenna size and increases bandwidth; ii) in this setup, fragmenting the patch into two is not necessarily needed.

68 4.3 Fragmented Patch Antenna with Multiple (2×1) Feeds

In this example, we again consider two feeds, however in a 2×1 setting. First, we refer to Fig. 4.8(a), where a large patch is used. At 1.95 GHz, this patch had the surface currents shown in Fig. 4.8(b). As seen, the currents had much longer path in this setup. Thus, this patch had its ﬁrst resonance at a much lower frequency. Now, consider the case in Fig. 4.9(a) where a 0.1mm slot is created close to patch center.

This slot fragments the patch into two patches with similar size, each being excited with its own feed. Current distribution along the patches in this setup is shown in

Fig. 4.9(b).

3.3cm

P1 P2 3.3cm 6mm 7.25mm

D E Figure 4.8: Connected patch antenna with 2×1 feeds. (a) Antenna layout, (b) Surface currents on the patch.

As would be observed, this distribution is signiﬁcantly diﬀerent from the one in

Fig. 4.8(b). Active input impedances and return losses of the patches are plotted

in Fig. 4.10(a) and Fig. 4.10(b), respectively. Although both patches are narrower

and slightly shorter than the original patch in Fig. 4.1, they resonate at about the

69 1.55cm 1.65cm

P1 P2 3.3cm 6mm 7.25mm

1mm

D E Figure 4.9: Fragmented patch antenna with 2×1 feeds. (a) Antenna layout, (b) Sur- face currents on the patch. same frequencies. This is due to the strong coupling between the patches. In this example, the feed on the left (P1) is found very diﬃcult to match to 50Ω. However, the feed on the right (P2) can be matched easily and has 8.7% bandwidth. This is 26% broader than the single patch case in Section 4.1. This superior bandwidth performance can be explained by following the radiation mechanism of the array.

(a) (b) Figure 4.10: Performance of the 2×1 patch. (a) P2 input impedance, (b) P1 and P2 return losses: red, blue.

70 D E

Figure 4.11: Radiation mechanisms of single patch and 2×1 patch.

Typically, a simple patch antenna has two radiating magnetic currents (as explained by the cavity model, [41]), illustrated in Fig. 4.11(a). When two patches are spaced closely, fringing fields flow from one patch to another (instead of going to ground plane). Thus, one of the vertical magnetic currents on each patch is replaced by a horizontal one (formed on the slot among patches) as shown in Fig. 4.11(b). This slot significantly lowers antenna quality (thus increases bandwidth) [65]. Here, it should be remarked that there are still two vertical magnetic currents, see Fig. 4.11(b). These vertical currents can be replaced with horizontal ones if parasitic patches are also used at each side of the array. This would not only increase the bandwidth, but also enable better impedance matching of the port to the left (P1). Such examples are considered in Chapter 5.

4.4 Fragmented Patch Antenna with Multiple (2×2) Feeds

This example investigates a combined case of Section 4.2 and Section 4.3. Individ-

ual patch sizes and feed locations were adjusted for obtaining the broadest bandwidth

at about the same frequency with previous examples. Corresponding antenna geom-

etry and surface currents are shown in Fig. 4.12(a) and Fig. 4.12(b), respectively.

Active input impedance and active return loss for only upper half of the antenna are

71 plotted in Fig. 4.13 (due to symmetry). As in Section 4.3, only feeds on the right

could be matched to 50Ω. In this case, these feeds had 15.1% bandwidth. Remark-

ably, this is 119% broader than the single antenna case and 74% broader than the

cases in both Section 4.2 and Section 4.3.

1.6cm 1.7cm

P1 P2 6.5mm 6mm 4.75mm 4.2cm

P3 P4

1mm (a) (b) Figure 4.12: Fragmented patch antenna with 2×2 feeds. (a) Antenna layout, (b) Sur- face currents on the patch.

(a) (b) Figure 4.13: Performance of the 2×2 patch. (a) P2 input impedance, (b) P1 and P2 return losses: red, blue.

72 4.5 Concluding Remarks and Discussions

In this chapter, several linearly polarized patch antennas with multiple feeds were

considered. Based on presented results, the following conclusions can be made. If

multiple feeds are placed in a direction orthogonal to polarization (as in Section 4.2),

patch size can be increased in this direction. This allows having longer radiating slots

and increasing bandwidth. For this case, fragmenting the patch is not necessary.

In contrast, using multiple feeds along polarization direction (as in Section 4.3)

is useful only if the patch is also fragmented in the same direction. Doing so, a slot

is created among patches that radiates more eﬃciently. Instead of vertical radiating

slots on patch edges, this horizontal slot (in essence a magnetic current) has lower Q,

thus broader bandwidth. This behavior would be especially useful for realizing low-

proﬁle antennas. In conventional patches, lower proﬁle results in smaller radiation

apertures. More importantly, due to the increased capacitance between patch and

ground plane, such antennas have high Q (diminishing bandwidth). On the other hand, horizontal magnetic currents on slots can be realized in close proximity of the ground plane without much sacriﬁce in bandwidth. This is mainly because such horizontal magnetic currents do not get cancelled by their image due to the ground plane.

For the fragmented antenna examples in Section 4.3 and Section 4.4, a common observation was the improved bandwidth performance of the feed in proximity of the slot. Other feeds close to patch edges remained “problematic”. A remedy to this can be using parasitic patches on both sides of the fragmented patch. In other words, this forms a larger fragmented patch with only elements around the center being excited.

This would allow impedance matching for all feeds and also would yield additionally

73 improved bandwidth. Examples of this kind of arrays will be shown in the next chapter.

In essence, the presented fragmented patch antennas with multiple feeds enable utilizing the small-size substrate more efficiently. In conventional patch antennas, the patch covers only a small portion of the aperture. Reducing the substrate and ground plane sizes decreases the bandwidth significantly. Therefore, these are kept relatively large. One approach to utilize the most of substrate might be using lower permittivity dielectrics. Doing so, the patch can be made larger. However, this decreases the electrical thickness of the patch (in terms of guided wavelength), which is the most significant reason for narrow bandwidth. In contrast, using higher permittivity dielectrics increases electrical thickness (for same physical dimensions). However, the patch needs to be made very small in this case. The fragmented patch with multiple feeds combines the preferable properties of these two approaches. In other words, the patch can be made large in the lateral direction while concurrently being thick

(electrically). Thus, the fragmented patch realizes a uniaxial dielectric tensor having ⎡ ⎤ ε ε 0 ⎢ xx xy ⎥ εeﬀ = ⎣ εyx εyy 0 ⎦ (4.1) 00εzz where εxx,εyy <εzz. Doing so, a current sheet is formed on the whole substrate aperture. The fragmented patch antennas outlined in this section closely resemble the long slot array [17], which is the dual of Munk’s Current Sheet Array (CSA) antenna [15]. Inspired by the CSA concept and following similar design methodology, in the next chapter we present a practical approach for realizing such fragmented patch antennas having multiple feeds.

74 Chapter 5: Bandwidth Enhancement of the TCPA by Combining Multiple Resonances

Chapter 3 presented an extremely low-proﬁle tightly coupled patch array (TCPA)

antenna with 6×6 square patches. This antenna delivered 5.6% impedance band-

width, which is more than two times broader as compared to conventional patches

of the same thickness. However, this bandwidth performance is inadequate for many

wideband applications and needs to be improved. For this, a convenient method is to

use rectangular patches that create two resonances. By combining these resonances,

much broader bandwidth can be obtained. This was demonstrated in Chapter 4 with

several examples. It was shown that multiple feeds and patch fragmentation could

be also used for rectangular patches to enhance bandwidth. However, designing such

antennas (especially with parasitic elements) while selecting which elements to feed,

tuning individual element sizes and adjusting feed locations all concurrently is quite

diﬃcult. This is because there are too many degrees of freedom and making an initial

guess is not very feasible. To overcome this, in this chapter we again follow a de-

sign methodology similar to that presented in Chapter 3. In summary, this approach

starts from an inﬁnite array and arrives at a truncated, ﬁnite-size version.

In Section 5.1 we present a TCPA with 4×2 rectangular patches that achieves a small size (λ0/3.2 × λ0/3.2) and very low proﬁle (λ0/26). This array allows for

75 17.3% impedance bandwidth, 4.8dB gain (95% eﬃciency) and 30% gain bandwidth.

Section 5.2 presents another array that uses 3×2 connected rectangular patches with the addition of small microstrip stubs. This array also attains a small size (λ0/3.2 ×

λ0/3.2) and it is also low-proﬁle (λ0/22). In addition, it allows for a broader 26% impedance bandwidth, 4.5dB gain (97% eﬃciency) and 40% gain bandwidth. Finally, conclusions are drawn in Section 5.3.

5.1 Tightly Coupled Patch Array Using Rectangular Patches

This section details the TCPA design, ﬁrst assuming an inﬁnite array setting.

Then, realization of a ﬁnite array is considered with special emphasis on selecting which elements to excite, ﬁne tuning individual element sizes and feed positions for broadest bandwidth.

radiation boundary

7.5 mm 4.5 mm

3.5 mm 5.4 mm y y 2.3 cm x x ground plane substrate coaxial feed (Hr = 25) (a) (b) (c) Figure 5.1: TCPA unit cell with a rectangular patch that creates two resonances. (a) Top view and diﬀerent current paths on the patch corresponding to diﬀerent resonances. (b) Top view, shifted. (c) 3D view.

76 5.1.1 Unit Cell Design

The TCPA design starts by designing the unit cell of the array as shown in Fig. 5.1.

A high contrast dielectric substrate (εr =25, tan δ =0.001) was used to fit more elements into a small-size finite array. A rectangular patch element was used and fed towards its edge using a coaxial probe. This rectangular patch created two resonances due to different current paths as depicted in Fig. 5.2(a) and was matched to 50Ω between these resonances. The corresponding return loss is shown in Fig. 5.2(b).

It is seen that this unit cell (in inﬁnite array setting) provides 18.6% bandwidth

(with |S11| < −10dB) at 1.88 GHz. This bandwidth performance is truly impressive, considering that the unit cell is only λ0/30 thick.

(a) (b) Figure 5.2: TCPA unit cell performance. (a) Input impedance. (b) Return loss.

5.1.2 Finite Array Design

For the ﬁnite array realization, we considered a small size (4.8cm × 4.8cm), 5.4mm thick substrate that can host 4×2 TCPA unit cells. As in Chapter 3, our study started by exciting all elements, see Fig. 5.3. The corresponding active return losses and active input impedances are plotted in Fig. 5.4 for only upper half of the array

77 5.4 mm P1 P2 P3 P4

P5 P6 P7 P8

(a) (b) Figure 5.3: 4×2 TCPA array with 8 excited elements illustrating the ﬁrst step of ﬁnite array design. (a) 3D view. (b) Top view.

(due to symmetry). Fig. 5.5 shows the active return losses plotted together. As seen, the 2×2 elements in the center almost mimicked the inﬁnite array performance in

Fig. 5.2, albeit their ﬁrst resonance being sharper. This was because the ﬁrst mode had currents predominantly along the x-axis and truncation of the array more severely

aﬀected them.

Figure 5.4: Active return losses and active input impedances of the excited elements in Fig. 5.3.

78 P4

Figure 5.5: Active return losses of the excited ports of the antenna shown in Fig. 5.3.

Next, we considered the case where only the 2×2 elements in the center excited.

The remaining elements were left open-ended (i.e., parasitic) as shown in Fig. 5.6.

Fig. 5.7 plots the corresponding active return losses and active input impedances for excited elements. As could be observed, port 1 (and port 3) performance was similar to that of inﬁnite array (see Fig. 5.2). To also improve the matching of port 2 (and port 4), the array elements had to be individually resized and their feeding locations had to be ﬁne tuned, as shown in Fig. 5.8. Doing so, all ports had similar and well-matched returns losses, as given in Fig. 5.9.

5.4 mm P1 P2

P3 P4

(a) (b) Figure 5.6: 4×2 TCPA array with 4 excited elements. (a) 3D view. (b) Top view.

79 P2

(a) (b) Figure 5.7: (a) Active return losses and active input impedances of the excited elements in Fig. 5.6. (b) Active return losses plotted together.

5.4 mm P1 P2

P3 P4

(a) (b) Figure 5.8: 4×2 non-uniform TCPA array with 4 excited elements. (a) 3D view. (b) Top view.

P1 P2

(a) (b) Figure 5.9: (a) Active return losses and active input impedances of the excited elements in Fig. 5.8. (b) Active return losses plotted together.

80 5.1.3 2×2 Feeding Network

The 6×6 TCPA in Chapter 3 had 16 excited elements conﬁned in a small space.

As could be understood, this required highly miniaturized power dividers and the

resultant feeding network was considerably complicated. Particularly, the miniatur-

ized dividers required quite narrow microstrip lines, and very small chip resistors had

to be used. These had brought signiﬁcant challenges in realization of the feed and

resulted in signiﬁcantly reduced eﬃciency.

Fortunately, the newer TCPA has only 2×2 elements to feed and the real estate for feeding is relatively large. To alleviate the fabrication challenges mentioned above, we chose to use a 25 mil thick substrate with εr =6.15 (rather than εr =10.2), and the new Wilkinson power divider is depicted in Fig. 5.10(a). This divider provided good isolation and reﬂection and had only 0.1dB insertion loss (in addition to 3 dB theoretical), see Fig. 5.10(b).

12.4 mm

P2 1 mm P3 39 mil 50 mil 165 mil 30 mil

40 mil 15 mil 12 mm 100:chip resistor P1

25 mil 39 mil Hr = 6.15

(a) (b) Figure 5.10: Single stage Wilkinson power divider. (a) Geometry. (b) Frequency response.

81 P2 P3

P4 P5

(a) (b) Figure 5.11: Multiple-stage, 4-way, equal power division and feeding network. (a) Ge- ometry. (b) Reﬂection at input and output ports.

Next, a 4-way feeding network was designed based on the divider in Fig. 5.10(a) and it is shown in Fig. 5.11(a). This 2-stage feed had 0.2dB insertion loss (in addition to 6dB theoretical) and its input/output ports had good reﬂection, as given in

Fig. 5.11(b).

5.1.4 Integrated Antenna Performance and Comparisons to Other Antennas

The ﬁnal TCPA was obtained by assembling the array and feeding network using vias, as shown in Fig. 5.12(a). Thus, the array and feeding network utilized the same ground plane sandwiched between the two substrates. The TCPA had an overall size of 4.8cm × 4.8cm × 6.04mm, including its feeding network. The corresponding return loss is plotted in Fig. 5.13(a) showing 17.3% impedance bandwidth centered at 1.95 GHz. At this frequency, the TCPA dimensions correspond to λ0/3.3 × λ0/3.3

× λ0/25.5 with the TCPA thickness over the ground plane being λ0/28.5.

For comparison, we considered a patch antenna on a reactive impedance substrate

(RIS) [58] as depicted in Fig. 5.12(b). The RIS patches were placed 4mm away from

82 6.04 mm 6mm (238 mil) (236 mil)

= 25 Hr Hr = 6 Hr = 6.15 Hr = 25 (a) Tightly Coupled Patch Array (b) Patch on Reactive Impedance Substrate

6mm (236 mil)

Hr = 25

(c) Patch on Conventional Substrate Figure 5.12: Several microstrip antennas for performance comparisons. the ground plane and the excited one was 2mm above the RIS. The overall dimensions of this antenna were almost the same as the TCPA. Similarly to the TCPA, the rectangular patch had two resonances. From Fig. 5.13(a) we observe that the patch

(a) (b) Figure 5.13: Return loss and realized gain comparison of the antennas in Fig. 5.12. (a) Return losses, (b) Realized gains at broadside.

83 on RIS had a 7.7% impedance bandwidth at 1.88 GHz. This result was obtained using

Ansoft’s HFSS v12 and is slightly larger than reported [58] (5% FDTD simulation,

6.7% measured).

A second patch antenna on a conventional substrate was next considered for comparison, shown in Fig. 5.12(c). This antenna also used a substrate of εr = 25 and had the same overall dimensions. Again the rectangular patch had two resonances and delivered a 6.7% impedance bandwidth at 1.9 GHz, see Fig. 5.13(a).

It can be concluded that the RIS slightly increases the impedance bandwidth.

However, the TCPA allows for more than twice the bandwidth as compared to using either conventional or EBG-like substrates (RIS in this case).

The realized gain of these antennas (at broadside, θ =0◦) is shown in Fig. 5.13(b).

As expected, the 0.2dB insertion loss in the feeding network decreased the TPCA realized gain from 5dB down to 4.8dB at 1.95 GHz, yielding 94% eﬃciency. The other two antennas had 4.7dB realized gain (97% eﬃciency) at about 1.9 GHz. The radiation patterns of all 3 antennas were found almost identical, shown at the inset of

Fig. 5.13(b). The front-to-back ratio was 6dB for these antennas and all were linearly polarized.

5.1.5 Experimental Veriﬁcation of the TCPA with Rectan- gular Patches

A TCPA prototype was built and tested, similarly to the one in Chapter 3. The patch array was screen-printed using a silver ink (Heraeus C 1076 SD). A feeding network was also fabricated using a milling machine with 1mm × 0.5mm chip resistors

(Panasonic ERJ-2RKF1000X) soldered to improve isolation. The fabricated prototype is shown in Fig. 5.14. The measured return loss was 12% bandwidth at 2GHz

(a) (b) Figure 5.14: Fabricated prototype of the TCPA with rectangular patches. (a) Front view, (b) Bottom view.

(little less than the 17.3% computed) and is shown in Fig. 5.15(a). This diﬀerence is likely due to a possible air gap formed between the ground plane and array substrate and the sensitivity of probe feed positions. The latter could have caused a slight non-overlap of the individual patch resonances.

(a) (b) Figure 5.15: Measured return loss and realized gain of the TCPA prototype in Fig. 5.14. (a) Return loss, (b) Realized gain at broadside.

The broadside realized gain of the fabricated TCPA prototype was measured in the anechoic chamber. From Fig. 5.15(b), we observe a peak realized gain of 3.8dB

(75% eﬃciency) at 2GHz. This is 1dB smaller than the computed gain with the

85 diﬀerence attributed to conductivity losses due to the feed, silver ink and soldering.

This prototype had very thin silver cladding to increase such conductivity losses.

5.2 Tightly Coupled Patch Array Using Rectangular Patches and Stubs

In this section, we reconsidered utilizing rectangular patches for creating two res-

onances. As distinct from previous section, both resonances were loosely matched to

50Ω. Doing so, two dips were obtained in the return loss and this yielded superior

impedance bandwidth. However, as will be explained shortly, realization of the ﬁnite

array was more stringent due to truncation eﬀects. To resolve these, we added a

transition step from an inﬁnite array to a ﬁnite array, namely, 1D periodic unit cell

for an infinite×finite array. Also for treating truncation effects, this array used small microstrip stubs attached to the rectangular patches.

5.2.1 Unit Cell Design: 2D Periodic (Inﬁnite Array)

This TCPA design also started by considering an inﬁnite array. In contrast to the

design in Section 5.1, the rectangular patch was made narrower and the probe feed

was moved away from the patch center, see Fig. 5.16. Also, a short microstrip stub

3.2 mm …

6.35 mm 91 mil 2.9 mm … y … 160 mil x

substrate ground plane

(Hr = 25) 4.6 mm coaxial feed … (a) (b) Figure 5.16: 2D periodic TCPA unit cell detailing the T-shaped patch and coaxial probe feed. (a) 3D view. (b) Top view. 86

(a) (b) Figure 5.17: 2D periodic TCPA unit cell performance. (a) Input impedance. (b) Re- turn loss.

had to be added to the left of the patch for hosting the feed. Thus, the resulting

element resembles a T-shaped patch. The corresponding input impedance and return

loss is plotted in Fig. 5.17. As seen, the two resonances had about 75Ω peak resistance

and two closely spaced dips were created in the return loss. Doing so, 36% bandwidth

was obtained while the array was only λ0/22.5 thick. This bandwidth performance was found exceptionally good for covering digital communication system (DCS; 1710-

1880 MHz), personal communication system (PCS; 1850-1990 MHz), universal mobile telecommunication system (UMTS; 1920-2170 MHz) and wireless local area network

(WLAN; 2400-2484 MHz) bands continuously.

5.2.2 Unit Cell Design: 1D Periodic (Inﬁnite × Finite) Array

To make the transition from inﬁnite array to a ﬁnite array easier, we considered

an infinite×finite array first. For this, two unit cells of Fig. 5.16 were cascaded in the x-direction and periodicity was applied in the y-direction (according to the coordinate system previously defined in Fig 5.16). The corresponding 1D unit cell for the infinite×2 array is depicted in Fig. 5.18. As seen, a longer patch was formed by

87 7.3 mm P1 P1 P1

………… = 2.4 cm = 1.8 cm d P2 d

P2 P2

(a) (b) (c) Figure 5.18: 1D periodic TCPA unit cell corresponding to the infinite×2 array. (a) 3D view. (b) Top view, d = 2.4 cm. (c) Top view, d = 1.8 cm. connecting two individual patches. Originally, the two feeds were positioned along the center of their individual patches, as in Fig. 5.18(b). The corresponding active input impedance (by exciting two feeds uniformly) is plotted in Fig. 5.19(a). It could be observed that the first resonance (about 1.6 GHz) shows a sharp resonance with high resistance. A similar effect was previously observed for the TCPA in Section 5.1 and was attributed to x-directed currents. To resolve this, here we considered bringing the two feeds closer, as shown in Fig. 5.18(c). The corresponding active return loss is plotted in Fig. 5.19(b). As seen from Fig. 5.19(b), the first resonance in Fig. 5.19(a) splits into two: one sharp resonance at 1.2 GHz, and a regular resonance (predicted previously from the 2D unit cell) at 1.75 GHz. The former is attributed to x-directed

TM0 surface wave mode that launches from the feed, attaches to the patch, reﬂects

from the patch edge and arrives back to the feed. The latter is a regular patch mode

that dominantly depends on the patch length. When the feeds are at the centers of

individual patches, the path lengths for these two resonances are the same. Therefore,

88 the two resonances overlap at the same frequency. As the feeds are moved towards

the center, the path for surface wave resonance is increased. Thus, this undesired

mode is shifted to lower frequencies. Doing so, the peak resistance of patch resonance

at 1.75 GHz was decreased to 85Ω, as seen in Fig. 5.19(c), and 25% bandwidth was

obtained, as given in Fig. 5.19(d). Indeed, these unit cell dimensions were scaled and

ﬁne-tuned to continuously cover DCS, PCS and UMTS bands (i.e., 1710-2170 MHz).

(a) (b)

(c) (d) Figure 5.19: Active input impedances for the 1D periodic unit cell in Fig. 5.18 and (a) d = 2.4 cm, (b) d = 1.8 cm, (c) d = 1.8 cm (zoomed). (d) Active return loss for d = 1.8 cm.

89 5.2.3 Finite Array Design

Similarly to Section 5.1, we ﬁrst considered a 4×2 array with 2×2 excited elements

(not shown here). However, matching excited elements all together was found very diﬃcult in this case. To facilitate this, we considered exciting only one column of patches (i.e., 1×2). Also, one parasitic column was placed to both sides of the excited one, as shown in Fig. 5.20. Thus, the resulting TCPA was formed essentially by 3×2

(connected) rectangular patches. The active input impedance of excited elements is plotted in Fig. 5.21(a). As seen, there are three sharp resonances below 1.5 GHz. The

first one (at 1.2 GHz) is reminiscent from Fig. 5.19(b) and it is attributed to a surface wavemodeinx-direction. The two new resonances appearing at about 1.45 GHz are due to similar phenomenon in the y-direction. If the 1D unit cell in Fig. 5.18(c) is used directly, one of these resonances appear at about 1.6 GHz. The stubs to the right of each patch were added intentionally to push this resonance to 1.45 GHz. Doing so, the first regular patch resonance was not affected appreciably [see Fig. 5.21(b)].

However, the addition of small stubs created an additional resonance. This resonance was indeed pushed up to 2.22 GHz (i.e., outside of operational band) by decreasing

2.1 mm 2.1 mm 1.7 mm 1.7 mm

6.5 mm 1.7 mm P1 1.7 mm 4.2 mm 4.2 mm

3.2 mm 4.2 mm P2

3.2 mm 2.1 mm (a) (b)

Figure 5.20: Finite 3×2 TCPA array with 2 excited elements. (a) 3D view. (b) Top view.

(a) (b)

(c) Figure 5.21: (a) Active input impedance; (b) Active input impedance, zoomed; (c) Ac- tive return loss; for the excited elements in Fig. 5.20. stub lengths. In other words, the stub lengths and widths were adjusted in a way to move the undesired resonances away from the patch resonances. Doing so, this

TCPA allowed for 25% bandwidth, as shown in Fig. 5.21(c).

5.2.4 Integrated Antenna Performance and Comparisons to Other Antennas

This TCPA antenna was much easier to feed because it had only two excited elements. Therefore, the Wilkinson divider in Fig. 5.10(a) was scaled for the new operational band and it was integrated with the array, as shown in Fig. 5.22. Since

91 7.14 mm (281 mil)

Hr = 25 H = 6.15 r (a) (b) Figure 5.22: TCPA antenna layout illustrating the ﬁnalized array design with incor- porated feed. (a) 3D view. (b) Bottom view.

(a) (b) Figure 5.23: Performance of the TCPA in Fig. 5.22. (a) Return loss. (b) Directivity and realized gain at broadside. one divider section was used, the insertion loss due to the feed was only 0.1dB. The return loss of the antenna is plotted in Fig. 5.23(a). As seen, this return loss curve is almost similar to the one in Fig. 5.21(c) and allows for 26% bandwidth to continuously cover DCS, PCS and UMTS bands (i.e., 1710-2170 MHz).

Fig. 5.23(b) plots the directivity and the realized gain at broadside (θ =0◦). The radiation patterns at diﬀerent frequencies are also plotted as insets of Fig. 5.23(b).

As seen, the realized gain increases from 3.5dB up to 5dB in the 1.7 GHz - 2.2 GHz

92 band. The resonance due to the stubs at 2.22 GHz creates a small dip in the broadside

gain by tilting the main beam 45◦. However, the peak gain of this beam at θ =45◦

is about 5dB. Despite this small dip, the broadside gain bandwidth (determined by

3dB drop) of this antenna is 40%. It is noted that this antenna is always linearly

polarized in the y-direction, for all frequencies.

For comparison, we chose the E-shaped patch antenna presented in [66] which also creates two closely spaced resonances with constant linear polarization. This patch was scaled to operate at the same frequency band as the TCPA and is shown in Fig. 5.24. To illustrate the size and thickness comparison more clearly, the TCPA is also shown with the same relative scale.

The E-shaped patch in Fig. 5.24 allowed for 31% bandwidth (slightly larger than that of the TCPA), albeit with larger footprint size (λ0/1.7 × λ0/2.7) and thickness

17 mm (669 mil)

7.14 mm (281 mil)

17 mm (669 mil) 7.14 mm (281 mil)

Figure 5.24: Size and thickness comparison of the TCPA with an E-shaped patch that yields similar bandwidth.

93 (λ0/9). Also, for proper bandwidth performance, this patch needed a large ground plane (λ0/1.2 × λ0/1.4). As a result of the large ground plane, this patch had 8dB

to 9dB directivity and realized gain. The TCPA dimensions (including the feed

substrate) correspond to λ0/3.2 × λ0/3.2 × λ0/22. Thus, the TCPA is 85% smaller in area and it is also 60% smaller.

5.3 Concluding Remarks and Discussions

This chapter presented two novel antennas based on tightly coupled array and

current sheet concepts. As compared to the TCPA previously presented in Chap-

ter 3, these antennas were about 2 times thicker, however, they provided 3 to 4 times

broader bandwidth. These superior bandwidth performances were achieved by adapt-

ing rectangular patches for combining two resonances together. Inevitable for such

operation, the antenna thicknesses had to be increased. However, as evident from

presented comparisons, these TCPAs still performed better than patch antennas on

conventional substrates or EBGs. Speciﬁcally, the TCPA in Section 5.1 allowed for 2

times broader bandwidth with little compromise in gain. Alternatively, the TCPA in

Section 5.2 demonstrated the miniaturization performance of the TCPA as compared

to conventional patches. Although much smaller and thinner, this TCPA achieved

almost similar bandwidth performance. However, its directivity and gain were less, as

limited by the small aperture size. It is also remarked that the TCPAs in this chapter

had fewer elements to feed. This alleviated the design complexity and insertion losses

due to the feed.

In conclusion, this chapter demonstrated that the TCPA concept is quite versatile

to be applied with diﬀerent elements types, with diﬀerent excitation or truncation

94 schemes. As a common observation, at least one column of parasitic elements had to be used in both sides of the excited elements to ensure proper operation that can be predicted from inﬁnite array setting. Indeed, truncation of the inﬁnite array posed some extra challenges, but these were treated by properly adding parasitic elements, changing feed positions and adding small microstrip stubs.

95 Chapter 6: Conclusions

The current sheet concept has recently been the focus of extensive research for realizing ultrawideband phased arrays. In particular, tightly coupled arrays (TCAs) exploit capacitive coupling to counteract inductive loading when arrays are placed in close proximity over ground planes. These two approaches together serve to enhance the bandwidth and reduce the proﬁle of UWB arrays. This dissertation investigated possible ways to improve the bandwidth and thickness performance of such UWB arrays. More importantly, this dissertation exploited the current sheet and TCA concepts for realizing very small-size and low-proﬁle broadband antennas.

Earlier studies have focused on these two classes of problems differently. One aspect of this dissertation is to borrow ideas from narrowband and ultrawideband antennas and use them together. For instance, multiple resonances have been exploited for enhancing the bandwidth of small and narrowband antennas. This dissertation follows a similar principle to enhance UWB array bandwidth. On the other hand, tightly coupled arrays have been primarily used for UWB arrays. But, their application to small-size and very low-profile antennas is done here for the first time. We remark that the TCA on thin substrates is closely related to electromagnetic band gap, reactive impedance substrate and frequency selective surface structures used as substrates. In this respect, this dissertation provides a novel method to employ such

96 structures as the radiating aperture (rather than just use them as substrates). The new contributions can be summarized as follows:

1. Demonstration of bandwidth enhancement and proﬁle reduction through mul-

tiple resonances with novel UWB arrays

2. Introduction of tightly coupled arrays to small and very low-proﬁle antennas

for bandwidth enhancement

3. Truncation methods for realizing ﬁnite-size, small apertures

4. Compact and low-loss feeds for small array excitation

5. Design, fabrication and veriﬁcation of small, low-proﬁle antennas with enhanced

bandwidth

6. Bandwidth enhancement demonstration in microstrip antennas via multiple

feeds and patch fragmentation

Specifically, Chapter 2 summarized the current sheet and tightly coupled array concepts as applied to ultrawideband phased arrays. In particular, impact of the ground plane on array bandwidth was discussed. The benefits of tight element coupling were presented to circumvent ground plane effects. One shortcoming of previous tightly coupled dipole arrays was low radiation resistance at low frequencies.

This problem was tackled by introducing different dipole arrangements and coupling mechanisms. A double legged dipole array that combined multiple resonances was also proposed for bandwidth enhancement and profile reduction. More specifically, this array achieved 7:1 bandwidth with λlow/17 profile (for VSWR<2). As compared

97 to previous tightly coupled dipole arrays, this new dipole arrangement allowed for a

40% larger bandwidth ratio with 35% thinner proﬁle.

Chapter 3 presented applications of the tightly coupled array concept aimed at realizing small-size and extremely low-profile microstrip antennas. In particular, a realization of the current sheet with tightly coupled patch elements and standard coaxial probe feeds was presented. A step-by-step design methodology was formed to make the transition from an infinite array to a small finite array. In this respect, selective excitation of array elements and simplistic termination of unexcited ones was investigated. It was found that elements around the array center could mimic infinite array performance only when elements at the array edges were used parasiti- cally. A compact and thin feed network was also designed for excitation. Specifically, the size of this antenna was λ0/3 × λ0/3 × λ0/42 and it delivered 5.6% impedance bandwidth, 4.4dB realized gain (87% efficiency) and 23% gain bandwidth (computed values). As compared to a conventional patch antenna, the new array of the same size had two times greater impedance bandwidth and three times greater gain bandwidth.

A prototype of this array was also fabricated and tested. A major challenge was feed network losses and also the conductivity loss due to the silver ink that was used for screen printing the patches on the ceramic substrate. This resulted in an unforeseen decrease in antenna gain (1.6dB) and eﬃciency (50%). The measured antenna bandwidth was 4.2% and this was in good agreement with the computed value. Clearly, better fabrication methods can be employed to overcome the feed and printing loss issues.

98 Chapter 4 considered an analysis and understanding of the bandwidth enhance-

ments provided by the tightly coupled patch arrays. This chapter started by consid-

ering a single patch antenna and then introduced multiple feeds. Patch fragmentation

was found necessary if multiple feeds were used along the polarization direction. Es-

sentially, the multiple feeds and patch fragmentation served to increase the lateral

aperture size by creating slots among the patches. It was also noted that the band-

width enhancement was due to the longer radiation slots and the replacement of

vertical slots with horizontal ones. Parasitic patches were also found important for

matching the excited elements.

Chapter 5 presented two additional patch arrays that achieved broader bandwidth

by combining two resonances of the rectangular patches. Speciﬁcally, the ﬁrst array

was λ0/3.2×λ0/3.2×λ0/26 in size and allowed for 17.3% impedance bandwidth, 4.8dB

gain (95% eﬃciency) and 30% gain bandwidth (computed values). The fabricated

prototype had 12% impedance bandwidth and 3.8dB gain (75% eﬃciency). This

decrease in gain and eﬃciency can be also attributed to the losses due to the feed.

The second array presented in Chapter 5 also used rectangular patches. In addition,

it employed small microstrip stubs to push undesired modes due to surface waves

out of its operational band. This array was also small and of low-proﬁle, being

λ0/3.2 × λ0/3.2 × λ0/22. Yet, it allowed for 26% impedance bandwidth, 4.5dB gain

(97% eﬃciency) and 40% gain bandwidth (computed values). A prototype of this array is being fabricated.

This dissertation clearly demonstrates that the current sheet and tightly coupled array concepts, when combined, can realize smaller and lower-proﬁle antennas. In terms of gain and radiation pattern, the presented antennas are similar to conventional

99 microstrip patch antennas. However, their bandwidth are about twofold broader. The latter, of course, translates to smaller and lower-proﬁle antennas. In the past, much thicker antennas had to be used to realize the same bandwidth. It was also found that patch antennas on EBG structures were only slightly beneﬁcial for enhancing bandwidth. The arrays presented here can be thought of as radiating EBG structures.

In this respect, this dissertation demonstrated that exciting the EBG directly achieves more than twofold broader bandwidth than exciting a primary radiator over the EBG.

Of course, designing and exciting the presented arrays was more challenging as compared to conventional, single-element patches. For some applications, use of a microstrip feed network underneath the array is not desirable. A better solution would be to use a stripline feed. Doing so, the array can be placed on almost any platform.

Another challenge relates to miniaturizing array elements to realize small antennas.

In our case, this required use of high permittivity ceramic substrates; but these are not suitable for milling or etching. Thus, we employed screen printing techniques to realize the antenna structure. In turn, this approach resulted in conductivity losses due to the employed silver ink. A better solution would be to use commercially available ceramic/polymer composite substrates having slightly lower permittivities but cladded with copper. These can be milled or etched more easily to reduce conductivity losses. However, this would come as a compromise in antenna size.

Finally, the presented arrays used simple coaxial probe feeds for design and realization ease. As common for conventional antennas, more advanced feeding methods such as L-shaped probes and aperture/proximity coupling could be employed to enhance bandwidth further. Speciﬁcally, proximity or aperture coupling by a microstrip line underneath the array could enable the excitation of many elements (with some

100 progressive phase shift). This approach could alleviate the complexity stemming from power division to many individual elements. With proper unit cell phase ad- justments, the latter feeding arrangement could be quite eﬀective in reducing feed losses and complexity. Since inter-element distances are quite small in terms of free space wavelength, beam tilting would not be appreciable due to the phase variations in the feed design.

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