
Reflectarray Antennas
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Persons
PAYAM NAYERI, PhD, received his doctorate in electrical engineering from the University of Mississippi and holds a degree in applied physics. He is an Assistant Professor in the Electrical Engineering Department at Colorado School of Mines, USA.
FAN YANG, PhD, earned his doctorate in electrical engineering from the University of California at Los Angeles (UCLA), in 2002. He is a Professor in the Electronic Engineering Department, Tsinghua University, China.
ATEF Z. ELSHERBENI, PhD, is a Distinguished Chair Professor and Electrical Engineering Department Head at Colorado School of Mines, USA. He holds a doctorate in Electrical Engineering from Manitoba University, Canada.
Content
Foreword xiii
Preface xv
Acknowledgments xvii
1 Introduction to Reflectarray Antennas 1
1.1 Reflectarray Concept 1
1.2 Reflectarray Developments 2
1.3 Overview of this Book 5
References 7
2 Analysis and Design of Reflectarray Elements 9
2.1 Phase-Shift Distribution on the Reflectarray Aperture 9
2.2 Phase Tuning Approaches for Reflectarray Elements 13
2.2.1 Elements with Phase/Time-Delay Lines 14
2.2.2 Elements with Variable Sizes 15
2.2.3 Elements with Variable Rotation Angles 16
2.3 Element Analysis Methods 18
2.3.1 Periodic Boundary Conditions and Floquet Port Excitation 19
2.3.2 Metallic Waveguide Simulators 19
2.3.3 Analytical Circuit Models 21
2.3.4 Comparison of Element Analysis Techniques 22
2.3.4.1 Comparison between PBC and Metallic Waveguides 23
2.3.4.2 Comparison between PBC and the Circuit Model 24
2.4 Examples of Classic Reflectarray Elements 26
2.4.1 Rectangular Patch with Phase-Delay Lines 26
2.4.2 Variable Size Square Patch 30
2.4.3 Single Slot Ring Elements 33
2.5 Reflectarray Element Characteristics and Design Considerations 37
2.5.1 Frequency Behavior of Element Reflection Coefficients 37
2.5.2 Effects of Oblique Incidence Angles on Element Reflection Coefficients 37
2.5.3 Sources of Phase Error in Reflectarray Element Design 41
2.6 Reflectarray Element Measurements 43
References 46
3 System Design and Aperture Efficiency Analysis 49
3.1 A General Feed Model 49
3.1.1 Models of Linearly Polarized and Circularly Polarized Feeds 50
3.1.2 Balanced Feed Models 51
3.2 Aperture Efficiency 53
3.2.1 Spillover Efficiency 53
3.2.2 Illumination Efficiency 54
3.2.3 Effects of Aperture Shape on Efficiency 55
3.2.4 Effects of Feed Location on Efficiency 59
3.3 Aperture Blockage and Edge Diffraction 60
3.3.1 Aperture Blockage and Offset Systems 60
3.3.2 Edge Taper and Edge Diffraction 63
3.4 The Analogy between a Reflectarray and a Parabolic Reflector 70
3.4.1 The Offset System Configurations 71
3.4.2 Analogous Offset Reflector 72
3.4.2.1 Transformation from Reflector to Reflectarray System 72
3.4.2.2 Transformation from Reflectarray to Reflector System 75
3.4.3 Example of Analogous Offset Systems 76
References 77
4 Radiation Analysis Techniques 79
4.1 Array Theory Approach: The Robust Analysis Technique 80
4.1.1 Idealized Feed and Element Patterns 80
4.1.2 Element Excitations and Reflectarray Radiation Pattern 81
4.2 Aperture Field Approach: The Classical Analysis Technique 82
4.2.1 Complex Feed Patterns 82
4.2.2 Field Transformations from Feed to Aperture and Equivalent Surface Current 83
4.2.3 Near-Field to Far-Field Transforms and Reflectarray Radiation Pattern 85
4.3 Important Topics in Reflectarray Radiation Analysis 87
4.3.1 Principal Radiation Planes 87
4.3.2 Co- and Cross-Polarized Patterns 89
4.3.3 Antenna Directivity 90
4.3.4 Antenna Efficiency and Gain 91
4.3.5 Spectral Transforms and Computational Speedup 94
4.4 Full-Wave Simulation Approaches 96
4.4.1 Constructed Aperture Currents Under Local-Periodicity Approximation 96
4.4.2 Complete Reflectarray Models 96
4.5 Numerical Examples 98
4.5.1 Comparison of the Array Theory and Aperture Field Analysis Techniques 98
4.5.1.1 Example 1: Reflectarray Antenna with a Broadside Beam 99
4.5.1.2 Example 2: Reflectarray Antenna with an Off-Broadside Beam 100
4.5.1.3 Comparison of Calculated Directivity versus Frequency 103
4.5.2 Consideration in the Array Theory Technique: Element Pattern Effect 105
4.5.3 Consideration in the Aperture Field Technique: Variations of Equivalence Principle 106
4.5.4 Comparisons with Full-Wave Technique 107
References 110
5 Bandwidth of Reflectarray Antennas 113
5.1 Bandwidth Constraints in Reflectarray Antennas 113
5.1.1 Frequency Behavior of Element Phase Error 113
5.1.2 Frequency Behavior of Spatial Phase Delay 115
5.1.3 Aperture Phase Error and Reflectarray Bandwidth Limitations 118
5.2 Reflectarray Element Bandwidth 121
5.2.1 Physics of Element Bandwidth Constraints 121
5.2.2 Parametric Studies on Element Bandwidth 122
5.3 Reflectarray System Bandwidth 135
5.3.1 Effect of Aperture Size on Reflectarray Bandwidth 135
5.3.2 Effects of Element on Reflectarray Bandwidth 140
References 144
6 Reflectarray Design Examples 147
6.1 A Ku-band Reflectarray Antenna: A Step-by-Step Design Example 147
6.1.1 Feed Antenna Characteristics 147
6.1.2 Reflectarray System Design 150
6.1.3 Reflectarray Element Design 153
6.1.4 Radiation Analysis 156
6.1.5 Fabrication and Measurements 159
6.2 A Circularly Polarized Reflectarray Antenna using an Element Rotation Technique 165
6.3 Bandwidth Comparison of Reflectarray Designs using Different Elements 169
References 176
7 Broadband and Multiband Reflectarray Antennas 179
7.1 Broadband Reflectarray Design Topologies 179
7.1.1 Multilayer Multi-Resonance Elements 179
7.1.2 Single-Layer Multi-Resonance Elements 181
7.1.3 Sub-Wavelength Elements 184
7.1.4 Reflectarrays Employing Single-Layer and Double-Layer Sub-Wavelength Elements 188
7.1.5 Broadband Design Methods for Large Reflectarrays 197
7.2 Phase Synthesis for Broadband Operation 197
7.2.1 A Phase Synthesized Broadband Reflectarray 200
7.2.2 A Dual-Frequency Broadband Reflectarray 203
7.3 Multiband Reflectarray Designs 206
7.3.1 A Single-Layer Dual-Band Circularly Polarized Reflectarray 210
7.3.2 A Single-Layer Tri-Band Reflectarray 213
References 221
8 Terahertz, Infrared, and Optical Reflectarray Antennas 227
8.1 Above Microwave Frequencies 227
8.2 Material Characteristics at Terahertz and Infrared Frequencies 228
8.2.1 Optical Measurements and Electromagnetic Parameters 228
8.2.2 Measured Properties of Conductors and Dielectric Materials 229
8.2.3 Calculating Drude Model Parameters for Conductors 229
8.3 Element Losses at Infrared Frequencies 234
8.3.1 Conductor Losses 234
8.3.1.1 Effect of Conductor Thickness 234
8.3.1.2 Effect of Complex Conductivity 237
8.3.2 Dielectric Losses 240
8.3.3 Effect of Losses on Reflection Properties of Elements 241
8.3.4 Circuit-Model Analysis 242
8.3.4.1 Circuit Theory and Loss Study 242
8.3.4.2 Zero-Pole Analysis of Element Performance 243
8.4 Reflectarray Design Methodologies and Enabling Technologies 245
8.4.1 Reflectarrays with Patch Elements 245
8.4.2 Dielectric Resonator Reflectarrays 248
8.4.3 Dielectric Reflectarrays 251
8.4.3.1 Dielectric Property and 3D Printing Technique 251
8.4.3.2 Dielectric Reflectarray Design 253
8.4.3.3 Dielectric Reflectarray Prototypes and Measurements 259
8.5 Future Trends 261
References 264
9 Multi-Beam and Shaped-Beam Reflectarray Antennas 267
9.1 Direct Design Approaches for Multi-Beam Reflectarrays 268
9.1.1 Geometrical Aperture Division 268
9.1.2 Superposition of Aperture Fields 271
9.1.3 Comparison of Direct Design Approaches 272
9.2 Synthesis Design Approaches for Shaped- and Multi-Beam Reflectarrays 275
9.2.1 Basics of Synthesis Techniques 275
9.2.2 Local-Search Techniques 276
9.2.3 Global-Search Techniques 279
9.2.4 Full-Wave Optimization Design Approaches 280
9.3 Practical Reflectarray Designs 281
9.3.1 Single-Feed Reflectarray with Multiple Symmetric Beams 281
9.3.2 Feed Reflectarrays with Multiple Asymmetric Beams 286
9.3.3 Shaped-Beam Reflectarrays 294
9.3.4 Multi-Feed Multi-Beam Reflectarrays 297
References 300
10 Beam-Scanning Reflectarray Antennas 303
10.1 Beam-Scanning Approaches for Reflectarray Antennas 304
10.1.1 Design Methodologies 304
10.1.2 Classifications Based on Reflector Type 306
10.2 Feed-Tuning Techniques 307
10.2.1 Fully Illuminated Single-Reflector Configurations 307
10.2.1.1 Parabolic-Phase Apertures 307
10.2.1.2 Non-Parabolic-Phase Apertures 313
10.2.2 Partially Illuminated Single-Reflector Configurations 324
10.2.2.1 Parabolic Cylindrical-Phase Reflectarray Antennas (pcpra) 324
10.2.2.2 Parabolic Torus-Phase Reflectarray Antennas (PTPRA) 329
10.2.2.3 Spherical-Phase Reflectarray Antennas (SPRA) 331
10.2.3 Dual-Reflector Configurations 334
10.2.3.1 Parabolic Reflector/Reflectarray Antennas 334
10.2.3.2 Non-Parabolic Reflector/Reflectarray Antennas 336
10.2.4 Summary of Feed-Tuning Techniques 337
10.3 Aperture Phase-Tuning Techniques 339
10.3.1 Basics of Aperture Phase Tuning 339
10.3.2 Enabling Technologies 341
10.3.2.1 Mechanical Actuators/Motors 341
10.3.2.2 Electronic Devices 343
10.3.2.3 Functional Materials 352
10.4 Frontiers in Beam-Scanning Reflectarray Research 355
10.4.1 Active Reflectarrays 355
10.4.2 Comparison Between Analog and Digital Phase Control 355
10.4.3 Sub-Array Techniques 358
10.4.4 Hybrid Configurations 359
References 359
11 Reflectarray Engineering and Emerging Applications 367
11.1 Advanced Reflectarray Geometries 367
11.1.1 Conformal Reflectarrays 367
11.1.1.1 Analysis of Conformal Reflectarrays 367
11.1.1.2 Radiation Characteristics of Conformal Reflectarrays on Cylindrical Surfaces 369
11.1.2 Dual-Reflectarrays 375
11.2 Reflectarrays for Satellite Applications 379
11.2.1 An L-Band Reflectarray for the Beidou Satellite System 381
11.2.2 Reflectarrays Integrated with Solar Cells 384
11.3 Power Combining and Amplifying Reflectarrays 388
11.4 A Perspective on Reflectarray Antennas 393
11.4.1 Large-Aperture Planar Reflectarray Antennas 393
11.4.2 Reflectarray Antennas with Broad Bandwidth, Beam-Scanning Capability, and Low Cost 396
11.4.3 From Reflectarray Antennas to Transmitarray Antennas 396
References 397
Index 401
1
Introduction to Reflectarray Antennas
1.1 Reflectarray Concept
Communicating over long distances had long been a dream for mankind until 1901 when Marconi demonstrated the first cross Atlantic wireless signal transmission. Since then, long distance communications have evolved to a degree where mankind can communicate wirelessly across the Solar System and beyond. Long distance communication requires large antennas in order to establish the wireless link between the transmitter and receiver. One of the most practical types of electrically large antennas are reflectors. While reflectors were originally built as optical devices [1], the discovery of electromagnetic waves by Maxwell, began a new era for communication with these antennas. The first experimental demonstration of wireless communication by Hertz in 1887, used a dipole-fed cylindrical parabolic antenna, which is believed to be the first reflector antenna operating at non-optical frequencies. Since then, reflectors have become the most widely used high-gain antenna in communications, radio astronomy, remote sensing, and radar [2].
An alternative approach to realization of a large antenna is by using several smaller antennas in the form of an array [3]. The first antenna array was built over 100 years ago [4]. In order to increase the directivity of a single monopole, Brown used two vertical antennas separated by half a wavelength and fed them out of phase [5]. He and several other notable scientists such as Marconi, Braun, and Adcock explored the unique characteristics of antenna array over the years [6]-[8]. Antenna array engineering evolved rapidly thereafter, particularly during the Second World War; however, it was the development of semiconductor technology in the 1960s and the printed circuit board technology in the 1970s that had the largest impact on their development. In particular the microstrip patch antenna proposed by Deschamps in 1953 [9] and later made practical by Munson in 1972 [10], revolutionized array engineering. Microstrip antenna arrays have since then played an important role in modern phased array systems.
While reflectors and arrays still compete for large aperture jobs in many types of systems, in the recent years, a new generation of high-gain antennas has emerged, which have attracted increasing interest from the antenna/electromagnetic community because of their low-profile, low-mass, and in many cases, low-cost features. This antenna is known as the reflectarray antenna [11]-[13]. The reflectarray antenna is a hybrid design, which combines many favorable features of reflectors and printed arrays, and as such can provide advantages over these two conventional antennas. The parabolic reflector is difficult to manufacture in many cases due to its curved surface that requires expensive custom molds and also become more difficult to manufacture at higher microwave frequencies. On the other hand, while antenna arrays offer the advantages of flexible design freedoms and versatile radiation performance, its feeding network suffers from the energy loss and design complexity, and the cost of the T/R modules [14] in active phased arrays becomes prohibitively high for many applications. As such, the reflectarray has fast been gaining attention as an alternative to these more mature technologies as it is able to mitigate the disadvantages associated with both of these high-gain antennas.
The reflectarray is an antenna with a flat reflecting surface consisting of hundreds of elements on its aperture and an illuminating feed antenna, as shown in Figure 1.1.
Figure 1.1 The geometry of an offset-fed reflectarray antenna.
The feed antenna spatially illuminates the aperture where the elements are designed to reflect the incident field with certain phase shifts in order to collimate the beam of the antenna in the desired direction and with the preferred shape. Its operation principle is similar in concept to reflector antennas with respect to the spatial illumination, and again similar in concept to antenna arrays with respect to phase synthesis and beam collimation.
1.2 Reflectarray Developments
The concept of reflectarray antennas was initially introduced in the early 1960s using short-ended waveguide elements with variable lengths [11]. The feed antenna illuminated the waveguides where the lengths of the shorted waveguides were designed such that the phase of the reradiated signals would form a collimated beam in the desired far-field direction. While the concept was very interesting, the bulky and heavy waveguide structure of this first reflectarray antenna was a major drawback. The experimental model of the waveguide reflectarray is shown in Figure 1.2.
Figure 1.2 The first reflectarray antenna using waveguide technology.
Source: Berry 1963 [11]. Reproduced with permission from IEEE.
Although some work on spiralphase reflectarrays was reported by Phelan in the mid-1970s [15], the reflectarray antenna did not receive much attention after that until the revolutionary breakthrough of printed microstrip antenna technology in the 1980s. Since then, research on reflectarray antennas has been on the rise, and several diversified applications such as multi-beam antennas for point-to-point communication, beam-scanning antennas for radar applications, and spatial power combining reflectarray systems have been demonstrated. In particular, over the past 10 years, an increased interest in reflectarray antenna research has been observed in both academic and industrial sectors of the antenna community, which is also propelled by advances in fabrication technologies as well as computational resources.
Since 2006, the IEEE Antennas and Propagation International Symposium (APS) has included sessions dedicated to reflectarray antennas in the general conference proceedings, and several sessions and special sessions have been held since then. Most notably a full-day special session on reflectarray antennas was held at the 2011 APS. Several hundred papers have been presented in these sessions, and many researchers are now interested in joining this active research area. In 2012, the International Journal of Antennas and Propagation published a special issue on Reflectarray Antennas: Analysis and Synthesis Techniques, which further stimulated the research interest in this area. A literature search on IEEE Xplore using the keyword "reflectarray" showed more than 1200 articles have been published in IEEE in this area, as shown in Figure 1.3. The majority of the articles, however, have been published in the recent years, and in particular, there has a notable increase in the number of papers over the last 10 years.
Figure 1.3 The number of articles on reflectarray antennas published in IEEE. Data obtained from IEEE Xplore on April 1, 2016.
The reflectarray antenna offers a multitude of capabilities that has encouraged continuous development and exciting applications in recent years. The elements of the reflectarray are designed to reflect the electromagnetic wave with a certain phase to compensate for the phase delay caused by the spatial feed. The phase shift of the elements is realized using various methods such as variable size elements, phase-delay lines, and element rotation techniques. The infinite array approach is used to calibrate the element phase versus element change [12]. Due to the very large number of elements involved in a reflectarray, full-wave simulation of the entire reflectarray antenna is still challenging. On the other hand, different theoretical models have been developed for the analysis of reflectarrays, such as the array theory formulation and the aperture field analysis technique, which show a good agreement with measured results. Moreover, implementing the spectral transform in these calculations allows for fast calculation of the radiation characteristics of the antenna, which is a considerable advantage for synthesis design problems using iterative procedures.
Single and multilayer reflectarrays have been designed to achieve broadband and multiband performance from microwave frequencies up to the THz range [16], [17]. Considerable improvements have been made to these designs over the years, and many practical designs have been demonstrated. One of the main challenges in reflectarray designs is improving the bandwidth of the antenna, which is the major drawback of printed resonator-type structures [18]. Different bandwidth improvement techniques such as using multilayer designs [19], [20], true time-delay lines [21], and sub-wavelength elements [22] have been studied and bandwidths of more than 20% have been reported.
Meanwhile, the direct control of the phase of every element in the array allows multi-beam performance with single or multiple feeds. The design of contoured beam reflectarrays is also a challenging field [23]. A phase-only synthesis process is used to obtain the required element phase shift from any given mask. Multi-feed multi-beam contoured beam designs have been demonstrated [24]; however, the performances of these designs are slightly inferior to the shaped-beam parabolic reflectors. Another advantage of reflectarrays is the ability of the antenna to scan the main beam to large angles off broadside. Beam-scanning reflectarrays are designed by using low-loss phase shifters integrated in every element of the array [25]. These...
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