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A cavity-backed coplanar waveguide slot antenna array

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Title:
A cavity-backed coplanar waveguide slot antenna array
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English
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Mcknight, James W
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University of South Florida
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Subjects / Keywords:
CPW slot
CPW-fed slot
Reflector
Bi-directional feed
Series feed
Beam-steering
C-band
Dissertations, Academic -- Electrical Engineering -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: In this thesis, a cavity-backed slot antenna array is designed for relatively wide instantaneous bandwidth, high gain and low sidelobes. The array consists of four, rectangular, slot elements, arranged side-by-side in a linear array and developed around 5GHz. Two feed points, at opposing sides of the printed array, each excite two of the slot elements through a series feed. This bidirectional feed presents symmetry to the design and prevents the tendency of beam-drift versus frequency as is common with many series-fed arrays. While being fed in-phase, the array will maintain boresight at broadside over the entire operating bandwidth. Also, the additional port allows for the potential introduction of a phase offset and, therefore, beam tilt. Finally, the printed array is designed to function within a quarter-wave, metallic cavity to achieve unidirectional radiation and improve gain.
Thesis:
Thesis (M.S.E.E.)--University of South Florida, 2009.
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Includes bibliographical references.
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by James W. Mcknight.
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Title from PDF of title page.
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Document formatted into pages; contains 98 pages.

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A Cavity-backed Coplanar Waveguide Slot Antenna Arr ay by James W. McKnight A thesis submitted in partial fulfillment of the requirements of the degree of Master of Science in Electrical Engineering College of Engineering University of South Florida Major Professor: Thomas M. Weller, Ph.D. Jing Wang, Ph.D. Kenneth Buckle, Ph.D. Date of Approval: October 14, 2009 Keywords: CPW slot, cpw-fed slot, reflector, bi-dir ectional feed, series feed, beamsteering, C-band Copyrighted 2009, James McKnight

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TABLE OF CONTENTS LIST OF TABLES iv LIST OF FIGURES v ABSTRACT ix CHAPTER 1 – INTRODUCTION 1.1 Overview 1 1.2 Motivation 1 1.3 Thesis Organization 3 1.4 Contributions 4 CHAPTER 2 – APERTURE AND SLOT ANTENNAS 2.1 Introduction 5 2.2 Planar Radiators 5 2.3 Existing Slot Antennas 6 2.4 Analysis of Radiators 10 2.4.1 Methods for Dipoles 10 2.4.2 Apertures and the Field Equivalence Princip le 12 2.5 Motivation for Using a CPW-fed Slot 16 2.6 Slot and Dipole Relations 20 2.7 Chapter Summary and Conclusions 22 CHAPTER 3 – THE SINGLE CPW-FED SLOT ELEMENT 3.1 Introduction 23 3.2 Slot Length 24 3.3 Feed Effects 29 3.4 Slot Width 31 3.5 Taper 33

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3.6 Slot Characteristics 35 3.6.1 Input Impedance 35 3.6.2 Radiation Pattern 37 3.7 Results and Comparison 41 3.8 Chapter Summary and Conclusions 48 CHAPTER 4 – THE FOUR-ELEMENT PLANAR ARRAY 4.1 Introduction 49 4.2 Array Analysis 50 4.3 Mutual Impedance 56 4.4 Feed Effects 58 4.4.1 Guided Wavelength 59 4.4.2 CPW Characteristic Impedance 60 4.5 Series Feed 62 4.5.1 Impedance Transformation 62 4.5.2 Feed Phase 64 4.6 Planar Array 66 4.7 Results and Comparison 69 4.8 Chapter Summary and Conclusions 76 CHAPTER 5 – CAVITY-BACKED PLANAR ARRAY 5.1 Introduction 77 5.2 Methods for Restoring Backside Radiation 77 5.2.1 Slots on Lenses 77 5.2.2 Grounded Substrates 78 5.2.3 Reflectors and Cavities 79 5.3 Design of Cavity-backed Array 79 5.4 Results and Comparison 85 5.5 Chapter Summary and Conclusions 90

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CHAPTER 6 – THESIS SUMMARY AND FUTURE WORK 6.1 Summary 92 6.2 Future Work and Recommendations 93 REFERENCES 96

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LIST OF TABLES Table 2.1 Comparison of Microstrip Patch and Slot A ntenna. 6 Table 3.1 3-dB beamwidth of Common-length Dipoles. 40 Table 4.1 Signal Width and Slot Dimensions for Give n Characteristic 61 Impedance. Table 5.1 Dimensions of Cavity-backed Array. 81

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LIST OF FIGURES Figure 1.1 Proposed Planar Array. 2 Figure 2.1 Slot Array in a Rectangular Waveguide as Pproposed by Orefice and 7 Elliot. Figure 2.2 Soliman’s Bow-tie Slot. 8 Figure 2.3 Hybrid Slot Array (a) and Log Periodic S lot Array (b). 9 Figure 2.4 Generic Rectangular Slot Excited by Coax 10 Figure 2.5 Monopole Subdivided into Infinitesimal S egments. 11 Figure 2.6 Huygens’s Field Equivalence Principle. 1 4 Figure 2.7 Illustration of Field Equivalence Princi ple for an Arbitrary Surface. 15 Figure 2.8 Slot Excited by Shorted Microstrip Feed. 17 Figure 2.9 Slot Excited by Effectively Shorted Micr ostrip Feed. 17 Figure 2.10 Various Microstrip Feeding Techniques f or the Slot. 18 Figure 2.11 CPW-fed Slot Antennas. 22 Figure 2.12 Slot (a) and Dipole Complement (b). 21 Figure 2.13 Radiated Fields from Slot in an Infinit e Ground Plane (a) and 21 Radiated Fields from Complimentary Dipole. Figure 3.1 Standard PCB (a), PCB with Backside Copp er Removed (b), Slot 23 Geometry Formed in Top Metallic Layer of PCB (c). Figure 3.2 Standing Current Distribution for Dipole s. 25

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Figure 3.3 Simulated Current Distribution for a CPS -fed Printed Dipole (a) and 26 CPW-fed Slot (b). Figure 3.4 Slot Length Adjusted (a) and Simulated F requency Shifts (b). 28 Figure 3.5 Conventional Dipole with Gap Feed Includ ed. 30 Figure 3.6 Simulated Signal Widths Effects on Slot Performance. 31 Figure 3.7 Return Loss Effects of Altering Slot Wid th. 32 Figure 3.8 Input Impedance vs. Slot Width. 33 Figure 3.9 Tapered (a) and Non-Tapered (b) Slot. 34 Figure 3.10 Return Loss for Tapered (green) vs. Non -Tapered (red) Slot. 34 Figure 3.11 Radiated Pattern of Center-fed, Wavelen gth-long Slot 38 with No Reflector. Figure 3.12 Radiated Pattern of Center-fed, Wavelen gth-long Slot with Finite 38 Reflector (a), and Infinite Reflector (b). Figure 3.13 Spherical Ccoordinate System for Slot S imulation. 39 Figure 3.14 3-dB Beamwidth for Wavelength-long Slot 40 Figure 3.15 Fabricated Rectangular Slot. 41 Figure 3.16 Comparison of Measured vs. Simulated Re turn Loss for 42 Rectangular Slot. Figure 3.17 Investigated Bowtie Styles. 43 Figure 3.18 Simulated Return Loss for Three Slots. 43 Figure 3.19 Fabricated Bow-tie Slots. 44 Figure 3.20 Comparison of Measured vs. Simulated Re turn Loss for 45 Bow-tie Slot.

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Figure 3.21 Comparison of Measured vs. Simulated Re turn Loss for 45 Rounded Bow-tie slot. Figure 3.22 Measured vs. Simulated E-Field Co-Polar ization Pattern. 46 Figure 3.23 Measured E-Field Co-polarization vs. Me asured E-Field 47 Cross-polarization. Figure 4.1 Basic Layout of Four-Element Linear Arra y. 50 Figure 4.2 Four-element Array of Point Sources with Uniform Spacing. 53 Figure 4.3 Radiation Intensity of Elements Spaced U niformly. 53 Figure 4.4 Four-element Array of Point Sources with Fixed Outer Spacing and Varied Inner Spacing. 55 Figure 4.5 Normalized Radiation Intensity of Four-e lement Array with Altered 55 Center Spacing. Figure 4.6 Layout for Mutual Impedance Measurements 57 Figure 4.7 Simulated Mutual Impedance. 58 Figure 4.8 Electric Field Lines for a Conventional CPW of Finite Dielectric 60 Thickness. Figure 4.9 Structure of CPW Feedline. 61 Figure 4.10 Impedance Transformation with Feedline. 63 Figure 4.11 Straight (a) and Meandered (b) CPW feed 65 Figure 4.12 Phase of S21 for Straight and Meandered Feed. 66 Figure 4.13 Quarter-wave Matching, 100 to 50 67 Figure 4.14 Full Array with Feed Offset. 68 Figure 4.15 Current Distribution of Full Array. 68

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Figure 4.16 Fabricated Printed Slot Array. 69 Figure 4.17 Return Loss for Port 1 of Planar Array. 70 Figure 4.18 Return Loss for Port 2 of Planar Array. 71 Figure 4.19 Simulated vs. Measured E-Co pattern. 72 Figure 4.20 Measured E-Co vs. Measured E-Cross. 73 Figure 4.21 Simulated vs. Measured H-Co Pattern. 74 Figure 4.22 Measured H-Co vs. Measured H-Cross. 75 Figure 5.1 Slot Antenna (a) and Loop Antenna (b) wi th Grounded Substrates. 74 Figure 5.2 Single Cavity-backed Slot. 80 Figure 5.3 Top View of Cavity-Backed Array in HFSS. 81 Figure 5.4 Plot of Current Distribution for Final C avity-backed Design. 82 Figure 5.5 Top View of E-field Vectors Surrounding the Cavity-backed Design. 83 Figure 5.6 Side View of E-field Vectors Surrounding the Cavity-backed Design. 84 Figure 5.7 E-Field Gain Over Multiple Frequencies. 84 Figure 5.8 Simulated vs. Measured Return Loss for C avity-Backed Array. 86 Figure 5.9 Simulated E-Co. vs. Measured E-Co. 87Figure 5.10 Measured ECo. vs. Measured E-Cross. 8 8Figure 5.11 Simulated H-Co. vs. Measured H-Co. 89Figure 5.12 Measured H-Co. vs. Measured H-Cross. 90 Figure 6.1 Proposed Omni-directional Structure. 94

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A Cavity-backed Coplanar Waveguide Slot Antenna Arr ay James McKnight ABSTRACT In this thesis, a cavity-backed slot antenna array is designed for relatively wide instantaneous bandwidth, high gain and low sidelobe s. The array consists of four, rectangular, slot elements, arranged side-by-side i n a linear array and developed around 5GHz. Two feed points, at opposing sides of the pr inted array, each excite two of the slot elements through a series feed. This bidirectional feed presents symmetry to the design and prevents the tendency of beam-drift versus freq uency as is common with many series-fed arrays. While being fed in-phase, the a rray will maintain boresight at broadside over the entire operating bandwidth. Als o, the additional port allows for the potential introduction of a phase offset and, there fore, beam tilt. Finally, the printed array is designed to function within a quarter-wave, meta llic cavity to achieve unidirectional radiation and improve gain.

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CHAPTER 1 INTRODUCTION 1.1 Overview Among the current driving forces in wireless commun ications, there is a need for compact, efficient, inexpensive and reproducible an tennas. In some instances, particularly long-distance applications, radiators with directive, high-gain characteristics are necessary. This work proposes a cavity-backed slot array to that end. The array consists of four wavelength-long, rectangular slots which, in concert, will yield a high gain pattern and low sidelobes. Additionally, the array is excited with anti-symmetric feeds which will prevent beam drift over frequency. The bidirectional radiation array is placed within a metallic cavity to attain uni-direc tional radiation and further improve gain. 1.2 Motivation Slot antennas are known for their sturdy, planar st ructure and have long been a prominent part of wireless systems. Their structur e is complementary to the printed dipole and a single radiating slot will generate a linearly polarized, but broad, far-field pattern. Coplanar waveguide (CPW) feeds are a nat ural choice for printed slots as they allow the entirety of the design to be fabricated o n a single layer, in a single process.

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Often, an array of elements is employed to improve directionality and concentrate energy into a narrow pattern. The array is based on two array segments each composed of two slots and each with their own feed. When al l elements are fed in-phase, the array will produce a beam at broadside. However, because the design is based on dimensions that are proportional to the operational, center fr equency (fc), the beam may be sensitive to changes in frequency and drift away from broadsi de as the frequency moves away from fc. The symmetry of the array and opposing feeds cir cumvents this potential drawback and allows the beam stay fixed at broadsid e over a range of frequencies. A phase shifter, external to this device, could offse t the phase of one port, and allow the beam to be electronically tilted about broadside (F igure 1.1). Figure 1.1 Proposed Planar Array. The inherent bidirectional nature of the slot’s rad iation may be wasted if communication is only required in one direction. I f the antenna is mounted on a

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structure, that backside radiation would be radiati ng into the structure which could cause significant field cancellation. By properly positi oning a metallic reflector or cavity behind the slot, the backside radiation can be recu perated and added constructively to form a uni-directional and directive, major beam. 1.3 Thesis Organization This work is organized into six chapters. Chapter 1 introduces the work, its motivation and contributions. Chapter 2 is the bac kground/literature search and examines similar and/or contributing works including: rectan gular slots, printed slots and slot arrays. Also in this chapter, a theoretical analys is is presented for aperture antennas. Feeding the slot is of issue, so slot feeds are bri efly covered here too. Chapter 3 details the design of a wavelength-long rectangular slot element that the slot array is based around. Its various dimensions can be tuned to have strong resonance over a relatively wide bandwidth. Measured and sim ulated results for return loss and radiation pattern are given. Chapter 4 introduces the series-fed array of four elements. The array is built around the single slot developed in Chapter 3 in or der to increase the antenna gain. The chapter begins with an investigation of basic array theory to understand how the linear array will dictate the radiation pattern. Other de sign considerations are addressed here including: mutual impedance, the CPW feed effects a nd impedance matching. Finally, Chapter 5 incorporates the metallic cavit y. The array structure of Chapter 4 must be tuned to function properly within the cav ity. The design becomes more complicated with the addition of the cavity, so sim ulations are done in Ansoft’s HFSS.

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1.4 Contributions This work is intended as a proof of concept that a slot array can be designed to have high gain and a unidirectional radiation over a range of frequencies. To prevent the tendency of series-fed arrays to beam-drift over fr equency, an anti-symmetric will keep radiation fixed at broadside over the entire operat ing bandwidth. To the author’s knowledge, it is the only series-fed slot array tha t maintains broadside radiation versus frequency. The additional feed point will also all ow the introduction of a phase offset and, thus, beam-steering that is independent of fre quency. Furthermore, the array is made to function within a metallic cavity for uni-d irectional radiation, increased gain and negligible sidelobes and/or backside radiation. Th e design is built for operation in the Cband (around 5GHz) but can be scaled to other frequ encies.

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CHAPTER 2 APERTURE AND SLOT ANTENNAS 2.1 Introduction Planar antennas and, particularly, planar arrays ha ve garnered increasing popularity in space and radar communication systems remote sensing and radio astronomy. Their planar structure is inherently d urable and low-profile, making them an ideal candidate for aircrafts where they can be flu sh-mounted onto the hulls [1]. In this thesis, attention is focused on slot antennas and, specifically, CPW, series-fed slot arrays. Modern day slot antennas have their roots in rectan gular waveguides but have mostly shifted to the planar form. This chapter wi ll briefly address the assortment and evolution of slot radiators. Slots are a somewhat different breed of antennas, and, as such, a terse, theoretical analysis of the slot beh avior will be presented. Some attention will also be given to the available feeding techniq ues for the slot. 2.2 Planar Radiators While there are abounding variations in the family of planar radiators, most fall into one of two broader categories: patch antennas and slot antennas. Both slot and microstrip (patch) antennas are commonly formed in standard PCB substrates, making them relatively simple and cheap to produce. Each topology has its own advantages and

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n disadvantages, allowing the designer some flexibili ty. Table 2.1, below, gives a side-byside comparison of some of the more notable feature s of slot and microstrip radiators. Table 2.1 Comparison of Microstrip Patch and Slot Antenna Characteristic Microstrip Slot Analysis and design Easy Easy Fabrication Very Easy Very Easy Tolerance in Fabrication Critical Not very critical Profile Thin Thin Shape Flexibility Any Shape Limited Radiation Fields Unidirectional Unidirectional or Bidirectional Polarization Linear and Circular Linear and Circula r Bandwidth Narrow Wide Dual frequency operation Possible Possible Spurious radiation Moderate Low Isolation between radiating elements Fair Good Frequency scanning Easily possible Possible Cross-polarization level Low Very low End-fire antenna Not possible Possible The slot has some obvious advantages over the patch ; it is relatively insensitive to the fabrication process, it can be used for bidirec tional or unidirectional radiation and it is capable of wider bandwidths than the patch. It is the slot variety that will be explored in this work. 2.3 Existing Slots Antennas Even though the basic concepts behind radiating ape rtures were known in the late 17th century with the work done by Huygens, they were n ot extensively studied and developed until World War II [2]. With work like t hat done by Watson [3] and Stevenson [4], slots were first used in the walls o f rectangular waveguides to couple and radiate energy. Later, Orefice and Elliot [5] prov ed they could control antenna

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parameters like external mutual coupling, input imp edance and radiation pattern by adjusting the length, spacing and orientation of th e slot elements within a rectangular waveguide array (Figure 2.1). Figure 2.1 Slot Array in a Rectangular Waveguide as Proposed by Orefice and Elliot. Rectangular and circular waveguides still maintain some special-use applications today, but slots have mostly made the transformatio n to the planar form as the high-tech trends have called for low-profile, compact structu res. Rectangular slots, like those originally used in rectangular waveguides [5-8], ar e the most fundamental of slot shapes with only two adjustable dimensions. They are stil l employed in modern, planar designs. Yoshimura’s work [9] showed the rectangular slot co uld feasibly be fed with a microstrip and that a flat reflector behind the slot could sal vage backside radiation. In the same work, it was shown directionality could be further enhanced with an array of said elements. Nesic presented a printed, linear slot a rray excited by a CPW [10]. He noted that the CPW feed can be easily branched for a twodimension planar array. Bow-tie slots, like that introduced by Soliman et a l [16], are discernibly more complex than the rectangular slots, but with advant ages. Soliman showed that the bown r

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tie structures, shown in Figure impedance which can be easi pattern. Similar CPWfed ultra-wide bandwidths and/ slot, spiral slot and are compact Using these various slot configurations and feeding techniques, linear and planar slot arrays can be formed by feeding multi given to arrays formed from rectangular slots. The hybrid slot array by A. Bhobe are constructed around the rectangular slot CPW as Nesic first proposed nearly 60% demonstrating that the rectangular slot can be designed for tie structures, shown in Figure 2.2 can achieve very large bandwidths, have impedance which can be easi ly controlled and a dipole-like, linear ly polarized fed bow-tie antennas [12-18] use various techniques to obtain and/ or miniaturization. Other slot configurations like the annular slot, spiral slot and are compact but are not fit for this work. Figure 2.2 Soliman’s Bow-tie Slot. Using these various slot configurations and feeding techniques, linear and planar slot arrays can be formed by feeding multi ple structures systematically; attention will be given to arrays formed from rectangular slots. array (HSA) and logperiodic array (LPSA) designs by A. Bhobe are constructed around the rectangular slot element and center Nesic first proposed [19]. The HSA and LPSA designs achieved bandwidths of nearly 60% demonstrating that the rectangular slot can be designed for can achieve very large bandwidths, have an input ly polarized radiation use various techniques to obtain Other slot configurations like the annular Using these various slot configurations and feeding techniques, linear and planar ple structures systematically; attention will be periodic array (LPSA) designs (Figure 2.4) center -fed with achieved bandwidths of

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Figure 2.3 Hybrid Slot Array (a) and Log Periodic Slot Array (b). Kobayashi used CPW to feed 1-D and 2-D arrays of sl ots and showed that the gain of the major lobe could be significantly incre ased with additional elements, up to six, in a linear array. However, increasing from s ix to eight elements did not improve gain and most designs had low efficiency [20]. Hua ng, and others [21], similarly used a single, series CPW line to uniformly excite a linea r array of four elements which yielded a narrow, bidirectional E-beam at broadside. Their approach paid particular attention to the effects of mutual coupling and factored those e ffects into their design process. The Series-Feed Collinear Slot Array [22] used open-end ed and short-ended stubs to set the field distributions of six, series-fed slots. The arrays were capable of up to 20% bandwidths around 5GHz. They also showed that a fl at reflector could suppress backside radiation of the array (20dB down from the front) a nd significantly increase the peak gain. The Open-Ended Rampart Slot Array Antenna i s also fed with CPW and easily feeds the six elements of the array. Also based in the C-band, the array achieved up to 11% bandwidth with up to 9dBi of gain.

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2.4 Analysis of Radiators Slots are a form of horns, openended waveguides and lens/reflector antennas. antenna is simply an arbitrary hole or opening in a metal sheet or from which an e lectromagnetic categorically different from other antenna structur es in that the EM waves produced by apertures are controlled by the metal alone (Figure 2.5). proportions which will dictate the polarization of the EM field that can effectively r adiate thro field pattern, halfpower beamwidth and directivity and can be properly manipulated by prudent array de sign Figure 2.4.1 Methods for Dipoles I n terms of analysis, For struc tures like the wire, Radiators of aperture antenna, which include but are not limited to: slots, ended waveguides and lens/reflector antennas. In general, an aperture antenna is simply an arbitrary hole or opening in a metal sheet or screen through which or lectromagnetic (EM) field will radiate Aperture antennas are categorically different from other antenna structur es in that the EM waves produced by are controlled by the openings in a metal sheet, rather than the shape of the The shape and size of the aperture are frequency will dictate the center frequency of operation, input impedance polarization of the EM field that can effectively r adiate thro ugh it. As a result, the far power beamwidth and directivity are directly shaped by the opening and can be properly manipulated by prudent array de sign Figure 2.4 Generic Rectangular Slot Excited by Coax. Methods for Dipoles n terms of analysis, slots must be approached somewhat differently from patch tures like the wire, printed dipole and patch the radiation characteristics can be which include but are not limited to: slots, In general, an aperture screen through which or Aperture antennas are categorically different from other antenna structur es in that the EM waves produced by the shape of the are frequency -dependent of operation, input impedance and As a result, the far directly shaped by the opening must be approached somewhat differently from patch es. the radiation characteristics can be

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determined once the current distribution throughout the metal can be known or approximated. The current distribution at any poin t on the structure is a function of space and time and can often be too complex and laborious to solve analytically. To simplify the problem, the actual current distribution can be regarded mathematically and conceptually as a collection of infinitesimal dipol e sources distributed over the surface where the current of each segment can be assumed co nstant. The radiated field from each of these small dipoles can be calculated using clos ed-form or numerical techniques. By taking their linear superposition or summation, the total field radiated from the structure can then be determined for any arbitrary point P in the far field. Figure 2.5 Monopole Subdivided into Infinitesimal Segments. An example of this technique is shown in Figure 2.6 for a simple monopole of negligible diameter. The monopole structure is sub divide into a number of infinitesimal point sources of length dz' Subdivisions that tend to zero length (or volume ) become more exact but, consequentially, more complicated. To be practically applied, the size of

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the segments must be specific to the structure and its relative size to wavelength proportions whereby the current per segment can be considered nearly uniform. n rr (1) (2) "n rr (3) # $%&' (%&') # +, -r.r/$%&' (%&'01234 5 (4) Equations 1-3 give the closed form solutions of in Eand H-Fields per linear division and are valid for the far field region of the monopole of Figure 2.6. The total far-field pattern can then be obtained by summing, or integrating, the contributions from all of the infinitesimal elements, as is given in E quation 4. This approximation is valid when the diameter of the wire is negligible, much l ess than the operating wavelength or independent of R and [1]. When the field approximation becomes multivariable dependent, the solution difficulty is significantly compounded. 2.4.2 Apertures and the Field Equivalence Principle An alternative method is in order for aperture ante nnas. In the absence of metal, no electric current flows through the slot itself. When energy is applied to the slot, the currents that flow in the metal sheet are not restr icted to the edges of the slot but, instead, spread throughout the sheet. Radiation, then, take s place from both sides of the sheet. In theory, the radiated field could be resolved by dir ectly solving the surface currents around the slot, as is done with dipole-like structures. Most slot approximations like Method of Moments (MOM) rely on the metal surrounding the slo t to be of infinite extent so image

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theory can be ushered in for simplification [2]. I n reality, though, this is not practically realizable. A more manageable pursuit would be to reduce the area to be solved for by evaluating the fields over the aperture itself, rat her than in the abundance of metal surrounding the aperture. The electric fields acro ss the slot can be replaced with equivalent magnetic currents down its length. Mag netic currents, though artificial, help to balance Maxwell’s equations and simplify the cal culations required to solve for the radiated field. If the exact field were known for every point on the face of the aperture, the radiated field could also be calculated exactly Still, the exact solutions are extremely difficult to obtain for apertures, so other approxi mate methods, like the field equivalence principle, are needed for simplification [23]. The field equivalence principle allows the actual s ources of an EM field within a region to be replaced by equivalent, yet fictitious sources that will produce the same fields within that region. The field equivalence p rinciple is an expansion on Huygens’ Principle which is a synthetic approximation of the fields over the aperture and considers the area of the aperture to be composed of individu al point sources [1]. Each of these sources can be viewed as a primary wavefront that s catters out radially and “ can be considered to be a new source of a secondary spheri cal wave and that a secondary wavefront can be constructed as the envelope of the se secondary spherical waves [24]” The equivalence principle is based on the uniquenes s theorem which states that “ a field in a lossy region is uniquely specified by the sources within the region plus the tangential components of the electric field over the boundary and the latter over the rest of the boundary. ”

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Together, the equivalence principle and uniqueness theorem can readily facilitate an approximate solution for any field on any surfac e. Thus, this technique can be used to recreate the fields exterior to some closed surface if the real sources creating those fields are fully contained within that boundary and the el ectric and magnetic currents on that boundary satisfy the necessary boundary conditions [1]. An example is demonstrated below. Figure 2.6 – Huygen’s Field Equivalence Principle. An arbitrary surface S in Figure 2.8(a) circumscribes a closed volume V1 which fully encapsulates the electric and magnetic source s J1 and M1 respectively; the region outside of S is source-free. The current sources within S produce electric fields E1 and magnetic fields H1 everywhere. The equivalence principle allows the sources lying inside the volume V1, to be replaced by equivalent fields which will ge nerate the same fields external to the surface S

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(a)Actual Problem (b) Equivalent Problem Figure 2.7 Illustration of Field Equivalence Prin ciple for an Arbitrary Surface. To accomplish this, the actual sources J1 and M1 are removed and an arbitrary E and H field is assumed to exist within V1, while E1 and H1 still remain in V2. For the two fields to exist on each side of the boundary S two equivalent current sources JS and MS must satisfy the boundary conditions of the tangent ial electric and magnetic field components [1] where The surface currents are assumed to be radiating in to an unbounded medium and will produce equivalent fields E1 and H1 only external to S Internal to S the tangential components of the E and H fields are only required to solve for the surface currents JS r # # $%& $%& r $%& # $%& # "r' (&)&* r') ($)$* 6 7 8 9 : ; < = > < ? @ 7 8 9 : ; A = > A ? n n

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n and MS, but are arbitrary and inconsequential nonetheless Love’s Equivalence principle further simplifies this approximation by assuming t hat there is a null field within S with only perfect conductors (electric or magnetic). Th en, E and H inside of S are identically zero and the surface currents will only produce ele ctric and magnetic fields outside of S The equivalent currents will then be reduced to: The above outlines techniques for solving the radia ting fields from an arbitrary surface. The field solutions are valid for both ne ar-field and far-field regions external to the surface S [1]. The ADS Momentum solver relies heavily on th ese principles and approximations to implement the Method of Moments f or the slot structures experimented with here. 2.5 Motivation for Using a CPW -fed Slot Antenna Various feeding techniques like stripline, microst rip and CPW are available for the slot [25]. Stripline, however, is often undes irable because its complex structure makes it more difficult to manufacture than microst rip and CPW. Stripline is also prone to higher-order propagation modes. Microstrip feeds work by coupling energy from the b ackside of the substrate, through the dielectric. In its simplest form, the feed line, usually of 50 characteristic impedance, is a conducting strip that lies perpendi cular to and centered on the slot it 6 7 8 9 : ; < = > < ? B C D E 8 9 : < = @ 7 > 8 9 : ; A = > A ? B F D E 8 9 : A =

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excites. The strip can be electrically shorted thr ough the dielectric to the slot’s edges (Figure 2.9). Alternatively, the microstrip can be terminated in an open-circuited stub by extending the microstrip feed beyond the slot a qua rter-wavelength, effectively shorting the line to the slot (Figure 2.10). Figure 2.8 Slot Excited by Shorted Microstrip Fee d. Figure 2.9 Slot Excited by Effectively Shorted Mi crostrip Feed. The impedance presented by the slot, as seen by the microstrip feedline, may not be evenly matched, resulting in reflections, power los s and reduced efficiency. As compiled in Bhartia, Bahl, et al, the input impedance of the slot can be adjusted with three different techniques. 1. The microstrip feed can be placed off-center 2.11(a ) +, -.

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2. The slot can remain center-fed but tilted from orth ogonal 2.11(b). 3. The feed can be reactively loaded by extending or s hortening the microstrip line 2.11(c). Figure 2.10 Various Microstrip Feeding Techniques for the Slot. While very common still, microstrip feeds require p rocessing to be done on, at least, two metal layers. Subsequently, these layer s must be accurately aligned during post-processing to function effectively. With CP W, the signal and ground lines share the metal conductor plane, atop the dielectric mate rial. The simplicity of this feeding technique is a natural choice for the slot because the slot and the feed share the same metal layer and can be processed simultaneously. C PW feeds are also known to have lower radiation leakage and less dispersion than mi crostrip lines [19]. Although it will +, +, -. +, -.

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not be exercised here, CPW feeds also facilitate th e parallel and series-connection of mounted (both active and passive) components, there by eliminating the need for vias. There are a multitude of CPW feed techniques availa ble for the planar slot antenna. A major issue concerning a CPW feed is th e need for a suitable transition between it and the slot. Originally proposed by N esic [10] 2.12(a), a center-fed, wavelength long slot may be the most straightforwar d. Current travels down the CPW feed and, upon reaching the slot, has two paths of equal impedance presented by the two slot portions. Upon its return to ground, the curr ent is equally split and creates a radiating E-field across the slot as it moves along the edges An off-set CPW feed (Figure 2.12(b)) can be used in a similar manner to the microstrip o ff-set for proper impedance matching of a full-wavelength long slot. Finally, a capacit ively-fed slot in Figure 2.12(c) and inductively-coupled slot Figure 2.12(d), each a hal f-wavelength long, serve as viable alternatives.

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! Figure 2.11 CPW -fed Slot Antennas. A downside of the CPW feed is its susceptibility to voltage difference between the two sides of the ground plane. To prevent this from occurring, air bridges are sometimes used to electrically tie the two ground p lanes together. 2.6 Slot and Dipole Relations Dipole antennas are readily understood and analyzed For this reason, the slot antenna is commonly characterized in terms of its d ipole-like behavior [27]. There has been much done in the endeavor of formulating these slot-dipole relations. Originally derived for applications in optics, Babinet’s princ iple describes how any field produced by an EM wave passing through an arbitrary aperture in a metal screen will effectively produce the same radiated pattern as the printed di pole which would perfectly fill that

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opening. Shown in Figure 2.13, if the metal sheet around the slot is of infinite extent, the radiated fields can be considered virtually identic al except that the electric and magnetic field vectors are orthogonally interchanged [28]. An additional consequence of the Eand Hvector orthogonality is that their respectiv e polarizations are also known to be orthogonally related. The dipole radiates an E-fie ld which aligns in the direction of its length. The E-field radiated by the slot, meanwhil e, is perpendicular to its length. Figure 2.12 – Slot (a) and Dipole Complement (b). Figure 2.13 – Radiated fields from Slot in an Infin ite Ground Plane (a) and Radiated Fields from Complimentary Dipole.

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This fact could be exploited in any design process. The time it takes for the Momentum solver to produce a solution for the given geometry is directly related to its planar footprint and solution frequency. The area required to physically describe the printed dipole is much reduced, relative to the equ ivalent slot and, therefore, requires much less time to be solved for. Many principles and solutions that apply to dipoles can also yield insight to the slot behavior. 2.7 Chapter Summary and Conclusions Slot antennas have been continually explored and de veloped in the last six decades and still continue to be an active area res earch today. Their planar form and simple but robust structure makes them desirable in a wide range of communication applications. Also, the slot’s ease of fabrication ability to be integrated with other electronic components and wide operating bandwidths gives the slot, in some instances, an advantage over patch radiators. The collection of works cited here have shown that the CPW line is a natural feed candidate for slot a ntennas and can effectively feed an array of slot elements. This work will pursue the development of the center-fed, wavelength-long slot in the following chapter.

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CHAPTER 3 THE SINGLE CPW -FED SLOT ELEMENT 3.1 Introduction In this chapter, the CPW center-fed, rectangular sl ot antenna is introduced. The individual slot element, while simple, is the basis of the four-element array investigated in this work and must be fully constru cted, characterized and understood before the array can be further developed. The CPW -fed slot, by definition, is an intentionally-leaky, uni-planar structure. The sl ot antenna can be easily fabricated with conventional PCB processes. With the backside copper-cladding removed in its entirety from the PCB substrate, the slot element i s formed by etching or milling away some pattern of copper-cladding on the top met allic layer (Figure 3.1). Figure 3.1 Standard PCB (a), PCB with Backside Co pper Removed (b), Slot Geometry Formed in Top Metallic Layer of PCB (c). /,, /,, 0 00

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There has been a substantial amount of work in the investigation of complex slot geometries to achieve, among other things, compact sizes and extremely wide bandwidths. However, the single slot element is no t the focus of this work. The individual slot geometry was intentionally kept sim ple with only a few adjustable dimensions so that it may be easily expanded into a linear array. To this end, a rectangular, center-fed slot was chosen for this pr oject. Its width and length can be adjusted to precisely set the resonant frequency an d match impedance to the driving port. Bow-tie slots could also be a substitute for the re ctangular slot and were given brief attention. Agilent’s ADS and Momentum software wer e used throughout the design process to construct, simulate and analyze the slot A combination of simulated and measured results for return loss and radiation patt ern will be given here. 3.2 Slot Length As given in Chapter 2.5, Babinet’s principal illust rates that the electric and magnetic fields for the printed slot and complement ary printed dipole and are orthogonally equivalent. On that premise, the curr ent distribution for a dipole is equal to and interchangeable with the voltage distribution a long the edges of the slot. The slot is long enough that its current and voltage distributi on is not uniform along its length. Therefore, adjustments in the length of the CPW slo t will setup the boundary conditions and determine how the voltage and current distribut e along the metal surrounding the slot. Ultimately, this distribution will establish the resonant frequency of the slot.

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Figure 3.2 Standing Current Distribution for Dipo les. Much like its dipole counterpart, the slot length w ill resonate at the common wavelength dimensions or multiples thereof. At res onance, dipoles of these discrete lengths will produce standing wave patterns, a depi ction of the current or voltage distribution along their lengths. Figure 3.2 illus trates the normalized standing current wave for dipoles of various lengths. These standin g current waves for the dipole are identical to the standing voltage waves of the slot where a current peak on the dipole correlates to a voltage peak across the slot. The length of the slot explored in this work was s et at a full wavelength ( g) and is center-fed, as proposed by Nesic [10]. Conceptu ally, the lowest impedance of the full wavelength-long, center-fed slot occurs at the feed (the slot’s center) and at the slot’s ends. Because the metal surrounding the slot is co nsidered to be perfectly conducting, -. -. -. -. 1+2 l/2 l/2 !3 !3 n !3 !3 3! ) 3! ) !3 ) !3n ) !3 ) !3

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n the electric field tangential to the slot is taken to be zero. Therefore, at the slot’s center and ends, the impedance is at its lowest and curren t at its maximum. With no resistance at the end of the slot, the voltage there is near z ero and grows until it reaches its maximum, a point one quarter-wavelength from the en d of the slot. For a given center frequency, the slot length of one wavelength could roughly be determined by: GH2 IJK L MnNN where g is the guided wavelength, fc is the center frequency of resonance, c is the speed of light and eff is the effective permittivity surrounding the tran smitted signal. The precise length, then, was determined empirically th rough simulations in ADS. Figure 3.3 Simulated Current Distribution for a C PS-fed Printed Dipole (a) and CPW -fed Slot (b). (9) (a) (b)

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Figure 3.3(a) shows the current distribution for a matched, wavelength-long, printed dipole. The current behaves as predicted, closely corresponding to the curves depicted in Figure 3.2. The densest current accumu lates along the center of the two slot segments. Current density falls off gradually as i t gets closer to the end where it eventually vanishes. Conversely, the current distr ibution for a printed slot antenna is shown in Figure 3.3(b). The current for the slot i s inverted from that of the dipole and is distributed throughout the finite metal sheet surro unding it. It is somewhat incidental to show how the current distribution aligns with the e xpected model; however, it is a powerful means of determining whether the elements in the subsequent series-fed array are operating in-phase. When fed in-phase, current will synchronously rise and fall on the slots’ edges; this will be apparent by plotting the current distribution. The overall length of the slot, end to end, is no t simply a function of the radiating section of the slot, but is also a factor of the feed and taper dimensions. To focus on the effects caused by the radiating, recta ngular aperture, the slot length, for these purposes, will be with respect to the dimension l in Figure 3.4(a). Feed and taper effects will be addressed in subsequent sections.

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Figure 3.4 – Slot Length Adjusted (a) and Simulated Frequency Shifts (b). The curves of Figure 3.4 depict how variations in t he slot lengths translate into shifts in the center frequency of resonance. A zer o-crossing in the phase of S11 is indicative of resonance; the slot can be set to res onate at nearly any frequency by adjusting its length. It was noted that a 10% vari ation in the slot length ( l ) corresponds to a shift of about 9.44% in the center, resonant freq uency. l/2 l/2 l/2=19.875mm l/2=15.875mm l/2=21.875mm l/2=17.875mm l/2=23.875mm S11 45

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3.3 Feed Effects The current and/or voltage distributions given in F igure 3.2 are ideal in the sense that they are based on an ideal feed that does not disturb the field distribution. When a practical feed is introduced, however, some perturb ations occur, forcing the fields to arrange differently. The impedance of the device, then, is altered accordingly, if only slightly. Most close-form expressions for antenna analysis as sumes the feed gap( s ) for conventional dipole antennas (Figure 3.5) to be neg ligible, if not identically zero. To account for feed effects of a real feed, the curren t distribution of a simple dipole can be altered to include an additional, “quadrature term” [1]. Equations 10 and 11 include the term, preceded by the coefficient ( p ), which factors in the feed radius (equivalent to slot width) and feed gap (equivalent to CPW signal width ). The value of p decreases as these dimensions become smaller, thus reducing the weight of the second term. +, -r.r/ +EO*PQ% >R5ST+E*UVW P/ >UVW, X/5YZ[\!] ]X&^ +, -r.r/ +EO*PQ% SR5ST+E*UVW P/ >UVW, X/5YZ[\>X&^] ]! (10) (11)

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! Figure 3.5 Conventional Dipole with Gap Feed Incl uded. Equations 10 and 11 are merely approximate methods of determining how current distributions are disrupted by the feed. To accura tely determine these effects, a numerical technique, like MOM, must be employed. F igure 3.6 relates the influence signal width and slot width have on the slot perfor mance. s l/2 l/2

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Figure 3.6 – Simulated Signal Widths Effects on Slo t Performance. Signal width has a direct and apparent effect on th e frequency of resonance. The effect is similar to what would be expected for a d ipole. An increase of 1mm in signal width increases the resonant frequency by ~ 75MHz. 3.4 Slot W idth While the slot length, taper and feed will set the boundary conditions and, in turn, the frequency of resonance, the width of the slot d ominantly controls the impedance of the slot. By increasing or decreasing slot width, the resulting capacitance formed by the electric field across the slot is proportionally an d respectively lowered or raised. This capacitance directly controls the slot’s input impe dance and increase when the width is increased. Similarly, decreasing slot width will l ower input impedance. Thus, slot width can be tuned to match the slot element to the drivi ng source. s = 2mm s = 3 mm s = 4 mm s = 5 mm s = 6 mm s 45 S11

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Figure 3.7 shows how adjustments in the width of th e slot can be better matched to the source for a deeper and wider resonance. A slot was designed with the proper length to resonate at a center frequency of 5GHz. Its width was adjusted to match the 50 port driving it. Figure 3.7 – Return Loss Effects of Altering Slot W idth. For the given feed dimensions and slot length, the slot has a width which will be best matched to the source impedance. Away from th at width, the match and slot performance will be proportionally degraded due to mismatches and reflections. Precise slot width, too, was determined experimentally in s imulations. The narrow slot of 2.61mm (6.5% g) was not resonating well (with a return loss < 10 dB). But, as the slot was incrementally widened, its impedance increased and approached that of the driving port and energy began to couple more effectively in to the device. The 5.11mm (12.84% g) wide slot was matched almost perfectly where almos t all of the inserted power is w 6 S11 w=2.61mm w=3.11mm w=3.61mm w=4.11mm w=5.11mm w=4.61mm w=5.61mm w=6.11mm

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being radiated from the element. Beyond 5.11mm, ad ditional increases in slot width caused the slot performance to degrade again, and a t a similar rate. Figure 3.8 Input Impedance vs. Slot Width. Inspecting the real input impedance directly gives a good depiction as to how slot width will control the input impedance. At 5GHz, a narrow slot of 2.61mm will produce a relatively stable input impedance of ~25 across the entire 2 GHz band. Each half millimeter increase in width returns ~5 of impedance at the ports. 3.5 Taper Throughout the design process, the slot width was c ontinually adjusted for impedance matching. When the slot parameters are v aried, the slot width must be appropriately adjusted to match its impedance to th at of the port. If the feed of the slot Zin 7 w=2.61mm w=3.11mm w=3.61mm w=4.11mm w=4.61mm w=5.11mm w=5.61mm w=6.11mm

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is taken to be where the CPW feed line and the slot s intersects, it can be seen that by altering the slot width, the feed point of the slot is also shifted. In order to isolate these effects, the feed of the slot (at its center) was g iven a taper, allowing the slot width to be modified independent of other physical parameters. Figure 3.9 – Tapered (a) and Non-Tapered (b) Slot Figure 3.10 – Tapered (green) vs. Non-Tapered (re d) Slot. 6 450 S11 S11 tapered non tapered non tapered tapered

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The effect of the taper is shown in Figure 3.10. T wo slots of identical, overall length, width and feeds, differ only by the taper a t their base (Figure 3.9). The tapered, rectangular slot radiates near 5GHz. Without the t aper, there is an apparent shift of ~500MHz (10%) in the resonant frequency; the slot w ithout a taper is radiating near 4.5GHz. The taper was 2mm or about 4.3% of the tot al slot length, and was intentionally kept small relative to the size of the slot in orde r to minimize its effect. The taper shortens the effective length of the slot by reduci ng the area where current can setup along it edges and adequately radiate across its wi dth. 3.6 Slot Characteristics 3.6.1 Input Impedance The input impedance of any antenna has an important role in the design process. Indeed, antennas will radiate well and have wide ba ndwidths strictly because the input impedance they produce is closely matched to the im pedance of the port driving them. The slot has complex impedance, composed of both a resistive and reactive component. The total impedance has many contributions includin g: the impedance mismatches and reflections due to transitions and turns, dielectri c losses, impedance shifts from the feed and radiation resistance. The power lost through radiation ( Rr) appears as an ohmic loss and can be considered as such in determining the to tal impedance presented by the antenna. All other losses are generally lumped tog ether into a term RL. Then, the impedance of the antenna is given by _`_S_a (12)

PAGE 46

n where: _\bbc[\0cbd0[Zce0bc0b _aX[\0cbd0[Zce0bc0b That is, the total real resistance at the driving p ort RA is the resistance due to radiation and all additional losses of the antenna. It is desired that the bulk of the input impedance be the resistance due to radiation, for t he losses to be minimized. An ideal antenna would be lossless, in which case, the input impedance at resonance is identical to the radiation resistance. Efficiency is a figure o f merit which demonstrates the antenna’s ability to radiate and is directly derived from the input resistance. Efficiency, is given as 02f))$g and shows that as all other losses tend to zero, th e antenna efficiency will become 100%. Conversely, as the losses increase for a matched an tenna, the efficiency will drop, consequentially reducing the amount of input power which is being properly radiated. The slot is said to be resonating when the input im pedance becomes purely real, or the reactive component goes to zero. This behav ior can be observed readily when the imaginary part of the return loss (S11) has a zero-crossing. Even though the impedance o f the slot may be purely real, it may not be radiatin g well if it is not properly matched to its driving source. The antenna is said to be radiatin g well when the magnitude of the return loss is greater than 10dB (S11 -10dB). In order for energy to be properly couple d into the device and minimize reflections (maximize power transfer), it is important for the slot (13)

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and source to be impedance matched. Consequently, poorly matched elements will result in low gain and low efficiency. 3.6.2 Radiation Pattern When properly matched, the slot will have the abili ty to take the electrical signal from the driving source and effectively transform i t into a transmitted EM wave. A wellmatched slot was simulated in Momentum and its 3-D radiation pattern plotted at the center frequency. In Figure 3.11, a single radiati ng slot produces the typical “doughnut” radiation pattern that is nearly identical to that of its complementary dipole. This fact remains despite the presence of the large, metal sh eet surrounding the slot. The electric field intensity can exist near the surface of the c onducting plane because the electric fields lines are perpendicular to the surface. The electric fields, however, cannot occupy the plane itself, causing a thinly sliced negation or perturbation in the 3-D pattern [28]. Poynting’s vector is used to determine the pattern of radiated power and dictates that the dipole and slot do not radiate power evenly in all directions; they are anisotropic by nature. For these elements, radiation is at a maxi mum at broadside and rapidly decays in the direction of the slot’s ends. Figure 3.11 Radiated Pattern of Center-fed, Wavel ength-long Slot with No Reflector.

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Still, the end goal for this work is to produce a s ingle, directive, uni-directional major lobe. Without a reflector, the single slot h as directivity of 3.826 dBi. To redirect or regain power that would otherwise be lost throug h backside radiation, a flat, metallic reflector can be placed behind the slot at a conven tional distance of one quarterwavelength ( /4). A slot with a finite reflector is shown in Fi gure 3.12(a). Figure 3.12 Radiated Pattern of Center-fed, Wavel ength-long Slot with Finite Reflector (a), and Infinite reflector (b). The arrangement will partially suppress backside ra diation and increase directivity to 4.841 dBi. To fully capture all bac kside radiation, a reflector of infinite size would be necessary but is nevertheless impractical. Figure 3.12(b) shows the halfdoughnut pattern, a theoretical consequence of an i nfinite reflector placed behind the slot. The pattern has virtually zero backside radiation w ith an improved directivity of 6.313dBi.

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Figure 3.13 Spherical Coordinate System for Slot Simulation. The length of the slot is directly related to its 3 -dB beamwidth. The 3dB beamwidth, or half-power beamwidth (HPBW), is a fig ure of merit for the major lobe of the antenna. The rate at which the intensity falls off is representative of the power density of the beam and describes its ability to fo cus energy in a given direction. With the slot oriented as shown in Figure 3.13, the 2-D plot of Figure 8 represents a slice of the total radiated field as seen at =0, and swept about At broadside ( =0, 180) the radiation is most intense and gradually reduces, ev entually into a null, away from broadside, at the slots’ ends.

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! Table 3.1 The 3-dB Beamwidth of Common-length Dip oles l<< 3-dB beamwidth = 90 l= /4 3-dB beamwidth = 87 l= /2 3-dB beamwidth = 78 l=3 /4 3-dB beamwidth = 64 l= 3-dB beamwidth = 47.8 An antenna can radiate well at many different wavel ength proportions, but its half-power beamwidth is established with the length of the device; Balanis [1] presents some for standard-length dipoles in Table 3.1. The table shows that longer dipoles have the narrower beamwidths at broadside. Figure 3.14 – 3-dB Beamwidth for Wavelength-long Sl ot. The simulated slot has a half-power beamwidth of ab out 46, nearly identical to the mathematical prediction for a wavelength-long d ipole in Table 3.1. Wavelength-long slots and dipoles are capable of narrower HPBW than those of shorter lengths. As the

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length increases beyond one wavelength ( l > ), however, the number of sidelobes begins to increase [1]. 3.7 Results and Comparison Based on the design procedures and considerations g iven above, a rectangular slot was designed and fabricated to operate around 5GHz. Shown in Figure 3.15, the slot was milled into the Rogers 4003C substrate. A coax-toCPW connector was used to feed the slot and make measurements. Figure 3.15 – Fabricated Rectangular Slot.

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Figure 3.16 – Comparison of Measured vs. Simulated Return Loss for Rectangular Slot. Figure 3.16 shows the return loss of the measured a nd simulated rectangular slot. The simulated and fabricated versions behave simila rly, but the center frequency of the fabricated slot is slightly off 5GHz and suffers fr om ~2.3% less BW. As a viable alternative to the rectangular slot, bo w-tie slots were also considered during the design process. Bow-tie slots have been shown to be capable of very wide bandwidths and could be easily incorporated into th is array design. The rectangular slots can be flared at their ends like that of Figure 3.1 7(a) or flared and rounded 3.17(b). In the latter case, the design allows the current to flow around the slot more freely with fewer abrupt turns and transitions, theoretically increas ing bandwidth. 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Freqeuncy (GHz) -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0S 1 1 M a g n i t u d e ( d B ) Legend Rectangular Slot (Meas)Rectangular Slot (Sim)

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Figure 3.17 Investigated Bowtie Styles. Figure 3.18 – Simulated Return Loss for Three Slots 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Freqeuncy (GHz) -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0S 1 1 M a g n i t u d e ( d B ) Legend Rectangular Slot (Sim)Bow-tie Slot (Sim)Rounded Bow-tie (Sim)

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The simulated bow-tie slot has a 25.36% bandwidth a nd the simulated, rounded bow-tie has 32.4%, 4% and 10.8% more respectively t han the rectangular slot. Both were fabricated (Figure 3.19) and measured. Figure 3.19 – Fabricated Bow-tie Slots.

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Figure 3.20 – Comparison of Measured vs. Simulated Return Loss for Bow-tie slot. Figure 3.21 – Comparison of Measured vs. Simulated Return Loss for Rounded Bow-tie slot. 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Freqeuncy (GHz) -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5S 1 1 M a g n i t u d e ( d B ) Legend Bow-tie Slot (Meas)Bow-tie Slot (Sim) 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Freqeuncy (GHz) -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5S 1 1 M a g n i t u d e ( d B ) Legend Rounded Bow-tie(Meas)Rounded Bow-tie(Sim)

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n Neither of the measured slots have a resonance as d eep as their simulated counterpart. Still, both resonate well near the ce nter frequency and have wider bandwidths. Figure 3.22 –Measured vs. Simulated E-Field Co-pola rization Pattern. 0 45 90 135 180 225 270 315 -40 -40 -30 -30 -20 -20 -10 -10 -50 -50 Legend E-Field Co-Pol (Sim)E-Field Co-Pol (Meas)

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Figure 3.23 –Measured E-Field Co-polarization vs. M easured E-Field Cross-polarization. 0 45 90 135 180 225 270 315 -20 -15 -15 -10 -10 -5 -5 Legend E-Field Cross-Pol (Meas) E-Field Co-Pol (Meas)

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3.8 Chapter Summary and Conclusions A printed, rectangular slot structure was developed extensively investigated, and shown to be a simple and reliable radiator. The re sults given here demonstrate that these devices can be made to radiate well by adjusting th e slot length, width and feed dimensions. The design process of the slot antenna as described above is straightforward and reproducible for many frequencies and PCB platf orms. It does, however, require software-simulated iterations for fine-tuning. A s ingle, rectangular slot can radiate over a >20% bandwidth around 5GHz and additional bandwidth can be attained with bow-tie and rounded bow-tie variations; measured and simula ted results closely align. All three will produce a “doughnut” radiation pattern with a relatively narrow beamwidth. A quarter-wave finite reflector positioned behind the slot was shown in simulation to improve the directivity by ~1dB, while an infinite reflector improved directivity by ~2.5dB.

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CHAPTER 4 THE FOUR-ELEMENT PLANAR ARRAY 4.1 Introduction In the previous chapter, the development and charac teristics of a single slot antenna were presented. The radiating element coul d be designed and easily tuned to function over a wide bandwidth. The radiation pat tern for the individual element was, however, shown to be very broad, and thus, to have low gain. Many applications, like long-distance communications, require antennas to h ave low sidelobe and high gain characteristics. One simple and convenient solutio n is to employ several, often identical, antennas into an array. Together, the radiating el ements can be configured to achieve directional radiation patterns and high gain. A li near array of four elements, capable of forming a directive beam, will also be to that end. This chapter is focused on the design of the design of the slot array and the connecting CPW between them. The array is composed of four slot elements arranged as two pairs of bidirectional, series-fed segments (Fi gure 4.1). Prior to designing the array in simulations, a precursory analysis of array theo ry was performed to predict the far field behavior of the four elements. Simulated and measu red results of return loss and radiation pattern for the functional array will be presented here.

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! The planar (linear) array employed in this design i s composed of four slot elements which provide a directive and steerable ma jor beam. Figure 4.1 Basic Layout of Four-Element Linear Ar ray. 4.2 Array Analysis The initial aim of this work was to produce a uni-d irectional antenna from a bidirectional planar, slot array. Each planar segmen t consists of a four-element slot array. Two feeds, arranged bi-directionally, will excite t he each of the series-fed segments (Figure 30). The array was designed to produce a d irective major lobe at broadside which is both narrow in phi but broad in theta. Wh en an offset phased is introduced into one of the segments, the beam can be tilted off bro adside. The radiation pattern of linear arrays can be descr ibed by and controlled by the relative spacing of the elements in the array, the amplitude and phase of each element or some combination of the three. However, there is a direct trade-off between the r /48 4$/ /48

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directivity of the major lobe, and the amount of po wer lost in side-lobe radiation. As the major beam at broadside is gradually “squeezed” by adjusting element spacing, the array will beget sidelobes. The design will intend to ke ep gain high and sidelobe levels low. Prior to examining the slot layout in simulation, a parametric analysis was done to investigate the effects of element spacing, amplitu de and feed-phase of the four-element, linear array. This mathematical approach is an ide al interpretation of the destructive and constructive effects of four, infinitesimal point-s ources radiating in freespace. The analysis neglects some actual contributing factors including: equal power distribution, current distribution and coupling, but is meant to be a precursory exercise to demonstrate how the individual elements in the array will gover n the total radiated pattern. Mathsoft’s MathCAD was used to plot the radiation i ntensity of the four infinitesimal dipoles arranged in a linear array. U sing simple array theory (Equations 14 and 15), the pattern produced by the linear array c an be calculated from the array factor, and, in turn, by the radiation intensity. The radi ation of each element can be fully described by its amplitude ( a1, a2), feed phase ( 1, 2) and physical, freespace separation ( dc do) from the geometric center of the array. hi / j=Kk(lKmKnoKpq7 /KklK rSj'Kk(lKmKnsKpq7 /Kk(lK rS j'Kk(lKmKnsKpq7, /Kk(lK rSj=Kk(lKmKnoKpq7, /KklK r (14)

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t / B hi /B /', B hi u! /B /' Figure 4.2 shows the four point sources arranged in a linear array and radiating with equal amounts of power. The normalized radiat ion patterns of the array, plotted with Equations 14 and 15, are shown with incrementa l, uniform spacing of d between all of the elements; distances are given in terms of th e freespace wavelength of the 5GHz center frequency. The patterns show that closely-spaced elements prod uce broad, bi-directional major lobes at broadside (90 and 270). Increasin g the spacing between the elements makes the major lobe more directive (Figure 4.3). However, this does not come without consequence. As energy is increasingly focused at broadside, radiation will also grow in the sidelobes. (15)

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Figure 4.2 – Four-element Array of Point Sources wi th Uniform Spacing. Figure 4.3 Radiation Intensity of Elements Spaced Uniformly. In this work, the two inner elements are linked to their respective, neigboring, outer elements by a series feed. This CPW feed bet ween them will restrict their relative movement in freespace. To account for this limitat ion, the outer element spacing d of '-. '-. '-. '-.n 9

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Figure 33 was fixed at 0 /2(freespace wavelengths), while the inner spacing d1 between the pairs was altered to see its effects on the rad iation pattern. As was similarly shown in the uniformly spaced array, increasing the distanc e d1 between the two pairs will directly control the directivity of the major lobe and size of the sidelobes. A center spacing of d1= 0 /4 has a relatively directive major beam and no det ectable, extraneous lobes. Extending the spacing further causes the major lobe to narrow at broadside but sidelobes grow considerably.

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Figure 4.4 – Four-element Array of Point Sources wi th Fixed Outer Spacing and Varied Inner Spacing. Figure 4.5 – Normalized Radiation Intensity of Four -element Array with Altered Center Spacing. '-. '-. '-. '-.n 9

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n The array analysis shows that the directivity of th e major lobe at broadside can be drastically increased by spacing the elements far a part, but is eventually restricted by the growth of grating lobes. A uniform spacing of d = /4 yields two major lobes (front and back) with no detectable sidelobes. As spacing is increased, the major lobes become narrower, but the sidelobes grow significantly. 4.3 Mutual Impedance The array analysis is useful in understanding how t he four-element array will shape the far-field pattern, but having the element s in close proximity will inevitably give rise to mutual affects. In addition to the couplin g from the radiated fields, all of the slots will also share the ground plane. This will alter the current distribution and, thus, input impedance. Mutual impedance plays an important ro le in antenna performance because it is the driving port impedance that must be match ed. The mutual impedance of two side-by-side dipoles is given as v=,wxyz{/|r}r v==Sv='Q}~}r R v',wxyz{/|~}~ v''Sv'=Q}r}~ R Each element creates its own self-impedance (Z11 and Z22), but also experiences some additional impedance from the neighboring element(s ) (Z12 and Z21). Mutual impedance is quite complex to analyze mathematically, so MOM was used to directly measure the effects of two slots as a function of their freespa ce separation. (18) (19)

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Figure 4.6 – Layout of Mutual Impedance Measurement s Two slots were arranged as shown in Figure 4.6. Ea ch slot had already been previously matched to a 50 port. The mutual impedance, then, is the variatio n (from 50 ) in either of the slot’s input impedance after the y have been simulated together. The simulated, mutual affects are plotted in Figure 4.7. As would be expected, coupling is stronger for smaller spacing between the two slo ts and decays as the spacing increases. The highest, simulated, mutual impedance was -17 at d=0.08 0. d

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Figure 4.7 – Simulated Mutual Impedance 4.4 Feed Effects The array theory uses ideal elements to examine the radiated far field, but to practically feed all four elements, some feedline must be place d between them. The dimensions of the feed, up to now, were somewhat insignificant. In the des ign of the single slot given in Chapter 3, the feed effects could be negated by shifting the refer ence plane to the base of the slot. These effects, though, are real and must be factored into any prud ent array design. Expanding the single slot into the two-element series-fed array of two slots, the CPW feed must be extended some distance away, where the second can be affixed. The charac teristic impedance, and therefore feed dimensions, of the line was determined first; the s lot was subsequently built around it. The feed is pivotal to the proper functioning of the array a nd its effects are addressed here. Once element spacing is decided, the mutual impedance can be cor rected by tuning the slots back to 50. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Distance(d/ l ll l 0 ) -20 -15 -10 -5 0 5 10R e a l M u t u a l I m p e d a n c e ( W ( W ( W ( W )

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4.4.1 Guided W avelength The electric field lines of the traveling, slow-wav e are evenly split between the air above and substrate below as it is transmitted thro ugh the CPW line. In theory, a substrate of infinite thickness has half of the EM field lines contained within the substrate below and the other half within the air above. Thu s, the effective permittivity ( eff) is taken to be the average of the two: €€ =S '^ ‚S '^ The guided wavelength ( g), then, is the scaled freespace wavelength and is given as ƒ U „K L €€ where c is the speed of light and f is the frequency of interest. A substrate of infinite thickness is implausible, but the same ass umptions will apply for relatively thick substrates where most of the lower field lines are still contained within the substrate (Figure 4.8). (20) (21)

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n! Figure 4.8 Electric Field Lines for a Conventiona l CPW of Finite Dielectric Thickness 4.4.2 CPW Characteristic Impedance The conventional CPW structure is on a single diele ctric substrate and without a ground plane on the backside of the dielectric. It s few variable dimensions can be adjusted to set the desired, characteristic impedan ce of the line. These features are: the signal(S), gap widths ( w ), substrate height ( h ) and substrate permittivity ( r) of the CPW, and are sufficient to fully describe its characteri stic impedance (Figure 4.7). The proximity of the signal line to the ground plane wi ll dominate the capacitance of the line and, in turn, the line’s characteristic impedance.

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n Figure 4.9 – Structure of CPW Feedline While all line impedances are theoretically possibl e, extremely high and low characteristic impedances are difficult to achieve as they require that the signal width( s ) to become very large or gap width ( w ) to become very small. Some consideration must also be given to feasible fabrication dimensions in cluding: minimum milling features, connector sizes, and overall footprint. For the re lative dimensions and scale of this design, characteristic line impedances between 30 and 75 were practical. Table 4.1 Signal Width and Slot Dimensions for Gi ven Characteristic Impedance. Characteristic Impedance=25 Characteristic Impedance=50 Characteristic Impedance=100 W-Width(mm) S-Signal(mm) W-Width(mm) S-Signal(mm) W -Width(mm) S-Signal(mm) 0.10 168.745 0.10 1.133 0.10 0.082 0.25 168.809 0.25 3.530 0.25 0.220 0.50 168.805 0.50 9.719 0.50 0.463

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n Table 4.1 shows how the characteristic impedance of a line will drastically alter its dimensions. For a line of 25 characteristic impedance, a signal width of 168mm is required, nearly 400% larger than the slots themsel ves. At the other end of the scale, a line of 100 characteristic impedance has a very narrow signal width and large gap width. 4.5 Series Feed 4.5.1 Impedance Transformation The design was aimed to evenly match the series-fed slot elements to radiate power evenly. For this to happen, the CPW feed be tween the two slots should not alter the input impedance of the second slot. vwx, … / vEv†S‡KvEKˆj8 … / vES‡Kv†Kˆj8 … / The addition of this feed-line transforms the input impedance of the single slot as given by Equation 22 which says that the impedance looking into the feed line ( Zin ) at some distance of feed away ( d ) is described by: the input impedance of the singl e slot ( ZL), the characteristic impedance of the transmission line ( Z0) and the propagation constant ( given in degrees/mm). Unless the feed is used fo r impedance matching, its characteristic impedance should be equal to the inp ut impedance of the slot itself. Figure 4.6 demonstrates how impedance matching can be acco mplished with the feedline. (22)

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n Figure 4.10 – Impedance Transformation with Feedlin e. In accordance with Equation 22, feeds of three diff erent line impedances (with assumed identical propagation constants) are used t o feed a 50 load. At the load ( l=0 ), all three lines produce equal input impedance, iden tical to the load. Moving away from the load along the line, their effects become prono unced. The 50 line is matched to the load and will never alter the impedance, only phase The 70.7 and 25 lines have a variable effect on the impedance which is a functio n of the feed length. At odd multiples of a quarter guided-wavelength (n g/4, n=1, 3, 5... ) the impedance transformation is the most significant where vwx vE 'v† (23)

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n The lines have no effect at even multiples of a qua rter wavelength (n g/4, n=0,2, 4...) ; the input impedance is identical to the load impeda nce. Between these two extremes, any input impedance can be achieved by choosing the cor responding feed length. 4.5.2 Feed Phase The characteristic impedance of the CPW line will b e chosen to match the impedance of the slot (50 ). Therefore, the impedance will not (ideally) be shifted at any distance away from the radiating element. The length, however, will shift the phase of the transmitted signal. To ensure that the slot s are being fed in-phase, the electrical length between any two similar points on the slots should be some multiple of a guided wavelength (n g, where n=1,2,3.. ). That is to say, the electric path around the sl ot will account for some change in phase of the signal. Us ually the path around the slot accounts for exactly a whole wavelength, and, therefore, the feed itself will also be one full cycle in length. The CPW feed, then, will be set so that the voltage will rise and fall across along the slots’ edges in concert. That way, their combined radiation effects are the constructive formation of a single, bi-directional beam at broadside. The length of this feed will set the freespace sepa ration of the slots and may not align with the preferred freespace separation as de termined in the array analysis. Also, the series-fed is a limitation in the spatial econo my of the overall array. To reduce the overall footprint of the array and/or allow flexibi lity of spacing between the series-fed elements to improve gain or reduce sidelobes, the f eed can be meandered.

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n The phase of the feed can be verified by removing the slot from the end of the CPW line and replacing it with a port. The phase o f the transmitted signal, S21, will exhibit a zero-crossing for each full rotation. Figure 4.11 – Straight (a) and M e andered (b) CPW Feed. (a) (b) Port 1 Port 2 Port 2 Port 1

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nn Figure 4.12 – Phase of S21 for Straight and Meandered Feed. The 0 phase crossings of S21 in Figure 4.8 are an indication that the signal fed into port 1 is in phase with that received at port 2. Both the straight and meandered CPW feeds are of equal length and exhibit this behavior thus verifying that the meandered feed will not alter the phase of the signal and can be u sed to properly feed the array. When port 2 is replaced with a second slot, the elements will be operating in phase. 4.6 Planar Array To construct the series-fed segments, two slots are placed half of a freespace wavelength apart ( d= 0 /2 ) and with a 50 CPW feed at their center; the feed dimensions are determined by ADS’ Linecalc. The slot lengths and widths are adjusted until a strong resonance around 5GHz is achieved by matching the s lots to the feed and nullifying the effects mutual impedance. A meandered 50 line of a one guided wavelength ( g) is 4 4.5 5 5.5 6Frequency (GHz) -80 -60 -40 -20 0 20 40 60 80S 2 1 P h a s e ( d e g ) Legend Straight FeedMeandered Feed

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n then used to adjoin the two slots. The summation o f the two 50 slots yields a 100 impedance at the input. Employing impedance matchi ng with the feed that is before the array, a 70.7 quarter-wavelength line is used to convert the 100 impedance back to the desired, nominal 50 (Figure 4.9). The signal width was kept fixed at 4mm while gap width was increased to achieve the higher chara cteristic impedance. Figure 4.13 – Quarter-wave Matching, 100 to 50 The two-element array is now matched for a 50 input; mirroring it about itself will give the full planar array; the two inner slot s were kept at half a freespace wavelength ( 0/2). The 70.7 impedance line was again reduced back to the 50 impedance and extended away for the connectors to b e mounted. To compensate for the direction of the feed, an additional 50 line of 180 was added to one of the segments (Figure 4.13). This phase offset would otherwise b e provided by a phase shifter, peripheral to this work. 100 50 70.7 g/4 0/2 0/2

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n Figure 4.14 – Full Array with Feed Offset To verify that the slots are operating in-phase, th e current distribution is again plotted in Figure 4.14. The plot shows that all fo ur slots are simultaneously experiencing strong current distribution along their edges, indi cative of in-phase resonance for the wavelength-long elements. Figure 4.15 – Current Distribution of Full Array. g/2 (180 phase delay)

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n If the elements are not radiating in-phase, cancell ation and unwanted nulls could occur in the radiated far field. The symmetry of t he design helps to abate any minor length or impedance differences that may arise. The array is fed bi-directionally at each of its en d by two separate ports. Nominally, the ports will be 180 out of phase (to account for the direction of the feed) and the major beam will be fixed at broadside. A p hase shifter, external to this design, can provide continuous phase control of one of the feeds. As the phase between the elements is progressively changed, the major lobe c an be swept off broadside. The amount of possible tilt is, again, limited by the r apid growth of sidelobes. 4.7 Results and Comparison Figure 4.15 shows the fabricated planar array with soldered connectors. The board was milled into a 60mil, Rogers 4003C ( r=3.55) board. Measured and simulated RL plots (Figures 4.17 and 4.18) roughly align, but the apparent shift is likely caused by an imperfect impedance match between the CPW line a nd the coax-to-CPW connector. Figure 4.16 – Fabricated Printed-slot Array.

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! Figure 4.17 – Return Loss for Port 1 of Planar Arra y. 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Freqeuncy (GHz) -30 -25 -20 -15 -10 -5S 1 1 ( d B ) Legend Planar Array Port 1(Meas)Planar Array Port 1 (Sim)

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Figure 4.18 – Return Loss for Port 2 of Planar Arra y. Both plots demonstrate a bandwidth greater than 28% The return loss stays well above the 10dB mark below 4GHz lower limit that has been examined throughout the design process, but the additional bandwidth is of little consequence to this work. 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6Freqeuncy (GHz) -30 -25 -20 -15 -10 -5S 2 2 M a g n i t u d e ( d B ) Legend Planar Array Port 2 (Meas) Planar Array Port 2 (Sim)

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Figure 4.19 – Simulated vs. Measured E-Co Pattern. 0 45 90 135 180 225 270 315 -30 -25 -25 -20 -20 -15 -15 -10 -10 -5 -5 Legend E-Field Co-Pol (Sim) E-Field Co-Pol (Meas)

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Figure 4.20 –Measured E-Co vs. Measured E-Cross. The E-field co-polarization cut of Figure 4.19 demo nstrates a directive major lobe at broadside for both simulated and measured patter ns. The measured sidelobe levels were ~12dB down from the major beam and about 5 dB higher than simulated. It should be noted that the measured array also produced a na rrower major beam which would, 0 45 90 135 180 225 270 315 -25 -20 -20 -15 -15 -10 -10 -5 -5 Legend E-Field Co-Pol (Meas) E-Field Cross-Pol (Meas)

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understandably, result in higher sidelobe levels, a s predicted by the array model. The measured E-field cross-polarization (Figure 4.20) i s, at its peak, much lower (~18dB down) than the maximum co-polarization in the E-pla ne. Figure 4.21 – Simulated vs. Measured H-Co Pattern. 0 45 90 135 180 225 270 315 -30 -25 -25 -20 -20 -15 -15 -10 -10 -5 -5 Legend H-Field Co-Pol (Sim) H-Field Co-Pol (Meas)

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Figure 4.22 Measured H-Co vs. Measured H-Cross. The measured H-field radiation patterns are shown i n Figures 4.21 and 4.22. Plots of measured and simulated co-pol patterns are nearly identical in shape and beamwidth. Cross polarization levels in the H-plan e also stay more than 17dB down from the peak co-polarization levels. Deep nulls a re apparent in the plane of the array for the simulated patterns because the infinitely long metal sheets assumed in Momentum prevent the radiation of parallel waves. 0 45 90 135 180 225 270 315 -35 -30 -30 -25 -25 -20 -20 -15 -15 -10 -10 -5 -5 Legend H-Field Cross-Pol (Meas) H-Field Co-Pol (Meas)

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n 4.8 Chapter Summary and Conclusions A four-element slot array was designed based on the rectangular slot of Chapter 3. A mathematical array analysis helped determine how array spacing would shape the farfield radiation pattern. Momentum was used to show that there is a strong relationship between slot spacing and mutual impedance that must be considered in the array design. The signal and gap widths of the series, CPW feed w ere designed to avoid any impedance transformation at center frequency and its length w as set so that the slots were radiating in-phase. The slots were individually tuned for 50 input impedance around the CPW feed, combined in-series and then reduced back to 5 0 with a quarter-wave matching line. The measured return loss varied slightly fr om the simulated return loss, most likely this can be attributed to the connector. Measured and simulated pattern measurements also showed close alignment, with measured cross-po larization significantly lower than co-polarization measurements in both E and H planes

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CHAPTER 5 CAVITY-BACKED PLANAR ARRAY The CPW-fed slot inherently radiates bidirectional and, for this reason, has had little use as a conventional, uni-directional radia tor. There are several approaches to restrict radiation to above the groundplane and rec over that power so that it may be constructively added to the fields in the opposing half-space. Lenses, grounded substrates and metallic reflectors were considered. 5.2 Methods for Restoring Backside Radiation 5.2.1 Slots on Lens Dielectric lenses in direct contact with the radiat ing ground plane are one method to attain uni-directional radiation. A high-dielec tric lens can be placed as a superstrate atop the ground plane. The original, thin substrat e and air on the backside of the ground plane will have much lower effective permittivity t han thick dielectric lens on the opposite side. The superstrate, therefore, will co ntain most of the field, causing most of the power to be radiated through the lens and great ly reduce radiation in the backside. The shape of the lens will tend to focus the field. Lenses can be used to impedance match between inter faces and their construction is typically extremely durable. They do, however, have many drawbacks. Fields that

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travel through thicker portions of the lens may suf fer from considerable more power loss if the lens is dissipative [28]. Sometimes lenses are made from many dielectric layers, making them difficult and expensive to produce. Th e efficiency of lenses is low because unwanted reflections occur on both the front and re ar surfaces. Also, they are usually multiples wavelengths thick and only reasonable for higher frequencies where the wavelength is small. 5.2.2 Grounded Substrates The CPW-fed rectangular slot and loop antennas (Fig ure 5.1) have grounded substrates, making them inherently unidirectional. These structures often require many dielectric layers of varying permittivity to preven t parallel plate TEM modes between the two metal sheets [25]. Both the slot and loop desi gns had low radiation efficiencies, 36% and 54%, respectively. Figure 5.1 Slot Antenna (a) and Loop Antenna (b).

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5.2.3 Reflectors and Cavities Probably the simplest and cost-effective method for achieving uni-directinal radiation is a metallic reflector placed behind the array. When positioned a quarterwavelength away from the array, the flat reflector will reflect most backside radiation. The quarter-wave spacing of the reflector is pivota l in its functioning and will ensure that the reflected power will be wholly added to that po wer radiated in the front side. In addition to the quarter-wave, finite, metal plat e, the cavity has walls which will fully enclose the backside of the array and help pr event backside radiation leakage. In theory, a properly designed cavity could double the gain of the antenna. The cavity can also be loaded with a dielectric to further shrink the size (depth) of the total assembly, but will come at the expense of reduced bandwidth and e fficiency. An air-filled cavity will be pursued here as it is the simplest. 5.3 Design of Cavity-backed Array Most of the design, up this point was carried out i n Agilent’s ADS. However, because of the increased complexity that this cavit y-backing introduces, Ansoft’s HFSS was used for the full and final design. The additi on of the cavity does not leave the array performance unaffected and the change in CAD tools required that some design features be changed. The close proximity of the metallic cavity structur e causes parallel-plate capacitance between itself and the ground plane of the array. The increased capacitance will decrease the characteristic impedance of the s lot dimensions. Through certain design

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! modifications, the cavity effects can be corrected. The meandered feed was mitered at its bends to mitigate parasitics. The freespace separa tion used in the planar array was preserved here so that any improvements in gain cou ld be considered a product of the cavity addition. An approach similar to that used for the planar array was used for the cavity-backed array. First, a single slot was tune d to be matched to the driving port and function within the cavity. These dimensions were verified to have strong resonance centered at fc and transferred to the full array. Freespace sepa ration was set for the four elements and the meandered feed was altered until t he elements were radiating in phase. All dimensions were tuned until matched to the driv ing port. The layout of the final array is shown in Figure 5.3 with the relevant dimensions in Table 5.1. Figure 5.2 – Single Cavity-backed Slot

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Figure 5.3 – Top View of Cavity-backed Array in HFS S. Table 5.1 – Dimensions of Cavity-backed Array Dimension Length/width(mm) Dimension Length/width(mm) l1 14.5 s1 23 l2 8.75 w1 0.75 l3 7.93 w2 2 l4 10 w3 5.2 l5 21 w4 0.26 l6 6.12 w3 l 2 l 3 l 1 l4 w2w3w3w3 l4 l 3 l4l1 l5 l5 l5l5w4w1 s1 w2 l6 w4

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Figure 5.4 –Plot of Current Distribution for Final Cavity-backed Design. Once more, the current plot in Figure 5.4 ensures t hat electrical length between the slots is one wavelength and the slots are excit ed in phase. The current distribution shown here indicates that the all four slots are ra diating together and with nearly equal power.

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Figure 5.5 –Top View of E-field Vectors Surrounding the Cavity-backed Design. Looking from above, the arrows of Figure 5.5 are re presentative of the E-field vectors surrounding the cavity-backed array. The f ields above the array are linearly (horizontally) polarized along the direction of the slot’s width and are strongest in the array’s geometric center. The field vectors will a lways be horizontally polarized, but will flip directions (left-to-right or right-to-left) de pending on the upward or downward cycle of the sinusoidal source. The field is also shown to exist far beyond the structure. Figure 5.6 shows that some fields also exist behind the cavity. The fields can be seen coupling from the front around to the back. The ca vity appears to be effective in highly suppressing radiation in the backside.

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Figure 5.6 –Side View of E-field Vectors Surroundin g the Cavity-backed Design. To verify that the array symmetry and dual feeds wi ll prevent beam-drift across frequencies, the gain of the array was plotted at c enter frequency and other, nearby frequencies. Figure 5.7 – E-Field Gain Over Multiple Frequencies -10.00 0.00 10.00 90 60 30 0 -30 -60 -90 -120 -150 -180 150 120

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The plots in Figure 5.7 corroborate this point. It should be noted that the major lobe of this array remains at broadside for all plo tted frequencies (100MHz steps between 4.6-5.4GHz). The gain will degrade, though, in pr oportion to the departure in frequency away from fc. 5.4 Results and Comparison The design was again milled into a 60mil Rogers 400 3C board ( r=3.55) and placed into an aluminum cavity. The cavity was des igned such that the groundplane of the array was flush with the top of the cavity In F igure 5.8, the simulated RL bandwidth is ~360MHz BW (7.2%) and greater than 1.17GHz (23.4 %) for the measured. In actuality, the RL for the measured design was > 10d B beyond 7GHz, but attention was kept at the established band of interest. The fa bricated and simulated arrays both have deep resonances near 5GHz, but, otherwise, their RL features do not have much correspondence.

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n Figure 5.8 –Simulated vs. Measured Return Loss for Cavity-Backed Array

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Figure 5.9 Simulated E-Co. vs. Measured E-Co. The gain of the simulated, cavity-backed antenna wa s 14.575dBi with sidelobes that were 14dB down. Measured gain was more than 3 dB lower at 11dBi with sidelobes still about 14dB down. The E-field co-polarization plots in Figure 5.9 are largely in accordance, less the apparent anomaly in part of th e major lobe. Rather than including the delay line in the design, one attached post-pro cessing. The delay (including a 50 milled line and various coax connectors) was likely the cause of this discrepancy. 0 45 90 135 180 225 270 315 -35 -30 -30 -25 -25 -20 -20 -15 -15 -10 -10 -5 -5 Legend E-Field Co-pol(Meas)E-Field Co-pol(Sim)

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Figure 5.10 Simulated H-Co. vs. Measured H-Co. H-field co-polarization cuts demonstrate closer ali gnment and nearly identical beamwidths. Impedance or phase errors exposed in t he E-plane (Figure 5.9) would be difficult to detect in the H-field. The array is only capable of beam-tilt in the E-plane, along the axis that the elements lay along. The w idth of the beam in the H-plane is set by the length of the slots and should never tilt. 0 45 90 135 180 225 270 315 -35 -30 -30 -25 -25 -20 -20 -15 -15 -10 -10 -5 -5 Legend H-Field Co-pol(Meas)H-Field Co-pol(Sim)

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Figure 5.11 – Measured E-Co. vs. Measured E-Cross. Both co-polarization plots show that backside radia tion is ~18dB down from the major lobe. Figures 5.11 and 5.12 exhibit the arra y’s extremely low cross-polarization levels for both E and H-planes. 0 45 90 135 180 225 270 315 -25 -25 -20 -20 -15 -15 -10 -10 -5 -5 -30 -30 Legend E-Field Co-pol(Meas)E-Field Cross-pol(Meas)

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! Figure 5.12 – Measured H-Co. vs. Measured H-Cross. 5.5 Chapter Summary and Conclusions Through a straightforward design approach, a four-e lement slot array was tuned to function well within a metallic cavity. Some appr oximate assumptions could be made in the early design stages, but the complexity of the structure necessitates a 3-D solver like HFSS for reliable characterization. The array yiel ded a directive lobe at broadside, but 0 45 90 135 180 225 270 315 -35 -30 -30 -25 -25 -20 -20 -15 -15 -10 -10 -5 -5

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did suffer from some deformation; likely an inciden tal artifact of the phase-delay network on one of the ports. The broad lobe in the H-plane for measured and simulated arrays were in close agreement. Backside radiation levels were shown to be greatly suppressed, a direct benefactor to the frontside gain. And, th e 8dBi of measured gain for the planar array (Chapter 4) was increased, as anticipated, by 3dB with the installation of the cavity.

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CHAPTER 6 THESIS SUMMARY AND FUTURE WORK 6.1 Summary This work demonstrated that a series-fed slot array with dual, anti-symmetric feeds can be designed to function within a metal ca vity with improved gain. The fourelement structure generates a single major lobe at broadside with 11 dB of gain and sidelobes which are14 dB down. Dual feeds, one at each end of the array, are pivotal in prohibiting beam-drift against frequency and were s hown to function as expected. Each component of the antenna was considered theoretical ly as a starting point, then analyzed experimentally in software simulations. Finally, e ach step of the design was fabricated, measured and compared to its simulations. The array was first constructed around a wavelength -long, rectangular slot. Each slot was designed to radiate with a center frequenc y of 5GHz and ~20% BW. To improve gain, a linear array of four such elements was capable of ~8dBi of gain and a bandwidth of +28%. That array was tuned to operate within a metallic cavity for an improved gain of ~11dBi. Keeping with modern trends, the CPW-fed, slot array presents an efficient, lowprofile and inexpensive approach for attaining bi-d irectional or uni-directional radiation, improved gain performance and radiation fixed at br oadside over a range of frequencies.

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This work seeks to make its small contribution to t he bigger body of concurrent research. There is, no doubt, much room for improvement with this design. Suggestions are in 6.2. 6.2 Future Work and Recommendations Throughout the process of developing this project, many questions arose. Entangled with these questions are many plausible s olutions, only a few of which could be fully explored. The author could go on ad infit um in suggesting future work or citing useful enhancements for this project. A few of the more pertinent modifications will be named below. The gain of the array could most readily be improve d by expanding the array with additional elements. The series-fed structure is such that more elements could be simultaneously fed if the impedance of the lines wa s set to match their respective impedances. For increased the bandwidth, the bowtie slot showed promising potential. It and other slot designs should be investigated fu rther for bandwidth improvements. To implement the scanning capabilities of this work a phase shifter and/or powersplitting network is necessary. Phase shifters can be constructed in a number of ways but must address, in varying degrees, some issues like: 1.) Ability to change rapidly 2.) High peak and average power handling 3.) Low loss 4.) Insensitive to temperature changes 5.) Small in size and weight

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Common to phase phase shifters are potential candidates. discrete phase values while the ferrite shifters are analog and are drive n b external H-field. Ultimately, the combination of many planar segments like that could be arranged around a cylinder to form an om Figure 6.1 – Linear Array with phase shifter (a), Each panel would make up a portion or slice of the total far field pattern. Coupled with a phase shifting network, each directi ve beam could scan vertically (as picture in Figure 6.1(b)). lean, or pitch. The panels could be electronically steered to compe nsate for the movement of the vessel and keep radiation fixed in a particular direction. Common to phase d arrays for radar applications, diode phase shifters and ferrite phase shifters are potential candidates. The diodeflavored are digital devices which have while the ferrite shifters are analog and are drive n b Ultimately, the combination of many planar segments like that designed here could be arranged around a cylinder to form an om nidirectional pattern (Figure 6 Linear Array with phase shifter (a), Omni-directional Structure (b) Each panel would make up a portion or slice of the total far field pattern. Coupled with a phase shifting network, each directi ve beam could scan vertically (as picture in Figure 6.1(b)). This concept is ideal for moving objects that are The panels could be electronically steered to compe nsate for the movement of the vessel and keep radiation fixed in a particular direction. arrays for radar applications, diode phase shifters and ferrite flavored are digital devices which have while the ferrite shifters are analog and are drive n b y applying an designed here directional pattern (Figure 6 .2). Structure (b) Each panel would make up a portion or slice of the total far field pattern. Coupled with a phase shifting network, each directi ve beam could scan vertically (as objects that are prone to tilt, The panels could be electronically steered to compe nsate for the movement of the vessel and keep radiation fixed in a particular direction. Additionally,

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the design pattern allows each panel to be individu ally turned “on” or “off”, thus preventing any transmission or reception in a parti cular direction. This feature would be propitious in combating jamming attempts as the seg ment(s) undergoing jamming could be intentionally disabled.

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n REFERENCES [1] Constantine A. Balanis, Antenna Theory Analysis and Design, 3rd ed., John Wiley& Sons, Inc., Hoboken, New Jersey, 2005. [2] W.L. Stutzman, G.A. Thiele, Antenna Theory and Design, John Wiley and Sons, New York City, New York, 1981. [3] W.H. Watson, The Physical Principles of Waveguide Transmission and Antenna Systems, Clarendon Press, Oxford, 1947. [4] A.F. Stevenson, “Theory of Slots in Rectangula r Waveguides,” J. Appl. Phys., Jan. 1948, pp: 24-38. [5] M. Orefice, “ Design of waveguide-fed series slot arrays,” IEEE P roceedings, Vol.129, Pt. H, No. 4, Aug. 1982, pp: 165-169. [ 6] L. Goldstone, A. Oliner, “Leaky-Wave Antennas I: Rectangular Waveguides," Antennas and Propagation, IRE Transactions on Vol. 7, Iss. 4, Oct. 1959, pp: 307-319. [ 7] F. J. Paoloni, “A Cavity-Backed Resonant Slot Ar ray-Theory and Measurement,” Antennas and Propagation, IEEE Transa ctions on, Vol. AP-28, No. 2, March 1980, pp 259-263 [ 8] Increased-bandwidth Resonant Slot Aarray with Bi directional Radiation Pattern, Electronics Letters Sept. 1974, Vol. 10 No 19, pp:396-397. [9] Y. Yoshimura, “ A Microstripline Slot Antenna,” Microwave Theory an d Techniques, IEEE Transactions on, Vol. 20, Iss. 11, Nov. 1972, pp:760-762. [10] A. Nesic “Slotted Antenna Array Excited by a Coplanar Waveguide,” Electronics Letters, Vol. 18, No. 6, March 1982, pp : 275-276. [11] E.A. Soliman,et al., “ Bow-tie Slot Antenna Fed by CPW,” Electron. Lett., Vol 35, 1999, pp: 514-515. [12] Y.D Lin, S.N. Tsai, “Coplanar Waveguide-Fed U niplanar Bow-Tie Antenna,” Antennas and Propagation, IEEE Transactions on, Vol 45, No. 2, Feb 1997, pp:305-306.

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[13] M. Nedil, T.A. Denidni, L. Talbi, “A New Backto-Back Slot Bow-Tie Antenna for Millimeter-Wave Applications,” IEEE CCECE Cana dian Conference, Vol. 3, May 2003, pp: 1433-1436. [14] C.H.Lee, S.-Y. Chen, P. Hsu, “Compact Modified Bow-tie Slot Antenna Fed by CPW for Ultra-wideband Applications,” IEEE AP-S Int ernational Symposium and URSI Radio Science Meeting, Jun. 2009. [15] L. Marantis, P. Brennan,“A CPW-Fed Bow-tie Sl ot Antenna with Tuning Stub,” Antennas & Propagation Conference, March 2008, pp:3 89-392. [16] S.-Y Chen, P. Hsu, “A Modified Bow-tie Slot A ntenna Fed by a Coplanar Waveguide,” Antennas and Propagation, IEEE Transact ions on, Vol. 1, June 2004, pp:799-802. [17] S.-H. Wi, J.-M. Kim, et al., “Bow-tie-shaped Meander Slot Antenna for 5 GHz Application,” Antennas and Propagation, IEEE Transa ctions on, Vol. 2, 2002, pp:456-459. [18] Y.-L. Chen, C.-L. Ruan, L.Peng, “A Novel Ultr a-wideband Bow-tie Slot Antenna in Wireless Communication,” Progress In Electromagn etics Research Letters, Vol. 1, 2008, pp:101–108. [19] A. Bhobe, “ Wide-Band Slot Antennas with CPW Feed Lines: Hybrid and LogPeriodic Designs,” Antennas and Propagation, IEEE T ransactions on, Vol.52, No.10, Oct. 2004, pp: 2545-2554. [20] H. Kobayashi, “ Slot Array Antennas Fed by Coplanar Waveguide for M illimeter Wave Radiation,” Microwave Theory and Techniques, I EEE Transactions on, Vol.46, No. 6, 1998, pp: 800-805. [21] T.F. Huang, S.W. Lu, P. Hsu,“Analysis and Des ign of Coplanar Waveguide-Fed Slot Antenna Array,” Antennas and Propagation, IEEE Transactions on, Vol. 47, No. 10, Oct. 1999, pp:1560-1565. [22] S.Y. Chen, I.C. Lan, P. Hsu, “In-Line SeriesFeed Collinear Slot Array Fed by a Coplanar Waveguide,” Antennas and Propagation, ,” I EEE Transactions on,Vol. 55, No. 6, June 2007, pp:1739-1744. [23] R.E. Collin, Antenna Theory Part 1, 3rd ed., McGraw-Hill, Inc., Hoboken, New York, 1969 [24] C. Huygens, “Traite de la Lumiere, Leyde,” 16 90. Translated into English by S.P. Thompson, London, 1912, reprinted by The University of Chicago Press.

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[25] R. Garg, P. Bhartia, I. Bahl, A. Ittipiboon, Microstrip Antenna Design Handbook Artech House, Norwood, MA, 2001, Ch 7. [26] Robert E. Collin, Antenna Theory Vol. 7 McGraw-Hill Book Company, Hoboken, New York, 2005. [27] L.V. Blake, Antennas Norwood, Artech House, MA 1984.


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A cavity-backed coplanar waveguide slot antenna array
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ABSTRACT: In this thesis, a cavity-backed slot antenna array is designed for relatively wide instantaneous bandwidth, high gain and low sidelobes. The array consists of four, rectangular, slot elements, arranged side-by-side in a linear array and developed around 5GHz. Two feed points, at opposing sides of the printed array, each excite two of the slot elements through a series feed. This bidirectional feed presents symmetry to the design and prevents the tendency of beam-drift versus frequency as is common with many series-fed arrays. While being fed in-phase, the array will maintain boresight at broadside over the entire operating bandwidth. Also, the additional port allows for the potential introduction of a phase offset and, therefore, beam tilt. Finally, the printed array is designed to function within a quarter-wave, metallic cavity to achieve unidirectional radiation and improve gain.
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