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Herausgeber: John Wiley & Sons
Kategorie: Wissenschaft und neue Technologien
Serie: Wiley - IEEE
Sprache: Englisch

Beschreibung

This book provides engineers with a comprehensive review of the state-of-the-art in reflectarray antenna research and development. The authors describe, in detail, design procedures for a wide range of applications, including broadband, multi-band, multi-beam, contour-beam, beam-scanning, and conformal reflectarray antennas. They provide sufficient coverage of basic reflectarray theory to fully understand reflectarray antenna design and analysis such that the readers can pursue reflectarray research on their own. Throughout the book numerous illustrative design examples including numerical and experimental results are provided.

Featuring in-depth theoretical analysis along with practical design examples, Reflectarray Antennas is an excellent text/reference for engineering graduate students, researchers, and engineers in the field of antennas. It belongs on the bookshelves of university libraries, research institutes, and industrial labs and research facilities.

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Leseprobe

Cover

Title Page

Foreword

Preface

Acknowledgments

1 Introduction to Reflectarray Antennas

1.1 Reflectarray Concept

1.2 Reflectarray Developments

1.3 Overview of this Book

References

2 Analysis and Design of Reflectarray Elements

2.1 Phase‐Shift Distribution on the Reflectarray Aperture

2.2 Phase Tuning Approaches for Reflectarray Elements

2.3 Element Analysis Methods

2.4 Examples of Classic Reflectarray Elements

2.5 Reflectarray Element Characteristics and Design Considerations

2.6 Reflectarray Element Measurements

References

3 System Design and Aperture Efficiency Analysis

3.1 A General Feed Model

3.2 Aperture Efficiency

3.3 Aperture Blockage and Edge Diffraction

3.4 The Analogy between a Reflectarray and a Parabolic Reflector

References

4 Radiation Analysis Techniques

4.1 Array Theory Approach: The Robust Analysis Technique

4.2 Aperture Field Approach: The Classical Analysis Technique

4.3 Important Topics in Reflectarray Radiation Analysis

4.4 Full‐Wave Simulation Approaches

4.5 Numerical Examples

References

5 Bandwidth of Reflectarray Antennas

5.1 Bandwidth Constraints in Reflectarray Antennas

5.2 Reflectarray Element Bandwidth

5.3 Reflectarray System Bandwidth

References

6 Reflectarray Design Examples

6.1 A Ku‐band Reflectarray Antenna: A Step‐by‐Step Design Example

6.2 A Circularly Polarized Reflectarray Antenna using an Element Rotation Technique

6.3 Bandwidth Comparison of Reflectarray Designs using Different Elements

References

7 Broadband and Multiband Reflectarray Antennas

7.1 Broadband Reflectarray Design Topologies

7.2 Phase Synthesis for Broadband Operation

7.3 Multiband Reflectarray Designs

References

8 Terahertz, Infrared, and Optical Reflectarray Antennas

8.1 Above Microwave Frequencies

8.2 Material Characteristics at Terahertz and Infrared Frequencies

8.3 Element Losses at Infrared Frequencies

8.4 Reflectarray Design Methodologies and Enabling Technologies

8.5 Future Trends

References

9 Multi‐Beam and Shaped‐Beam Reflectarray Antennas

9.1 Direct Design Approaches for Multi‐Beam Reflectarrays

9.2 Synthesis Design Approaches for Shaped‐ and Multi‐Beam Reflectarrays

9.3 Practical Reflectarray Designs

References

10 Beam‐Scanning Reflectarray Antennas

10.1 Beam‐Scanning Approaches for Reflectarray Antennas

10.2 Feed‐Tuning Techniques

10.3 Aperture Phase‐Tuning Techniques

10.4 Frontiers in Beam‐Scanning Reflectarray Research

References

11 Reflectarray Engineering and Emerging Applications

11.1 Advanced Reflectarray Geometries

11.2 Reflectarrays for Satellite Applications

11.3 Power Combining and Amplifying Reflectarrays

11.4 A Perspective on Reflectarray Antennas

References

Index

End User License Agreement

List of Tables

Chapter 03

Table 3.1 Design parameters for the offset reflectarray and reflector.

Chapter 05

Table 5.1 Summary of reflectarray element performances.

Table 5.2 Summary of phase ranges at 13.5 GHz and element bandwidth for the patch elements with different substrate thicknesses.

Table 5.3 Summary of phase ranges at 13.5 GHz and element bandwidth for the square loop elements with different substrate thicknesses.

Table 5.4 Summary of phase ranges at 13.5 GHz and element bandwidth for patch elements with different substrate thickness.

Table 5.5 Summary of phase ranges at 13.5 GHz and element bandwidth for the square loop elements with different trace widths.

Table 5.6 Summary of phase ranges at 13.5 GHz and element bandwidth for the cross‐dipole elements with different trace widths.

Table 5.7 Summary of directivity and bandwidth for reflectarray using the square patches.

Table 5.8 Summary of directivity and bandwidth for reflectarray using the square loops.

Table 5.9 Summary of directivity and bandwidth for reflectarray using the cross‐dipoles.

Chapter 06

Table 6.1 Design parameters for the offset reflectarray and reflector.

Chapter 07

Table 7.1 Phase range of reflectarray elements at 32 GHz.

Chapter 09

Table 9.1 Calculated radiation characteristics of the single‐ and quad‐beam reflectarrays.

Table 9.2 Design requirements of quad‐beam reflectarrays (beam directions and normalized gain levels).

Table 9.3 Measured gain of the asymmetric multi‐beam reflectarray prototype.

Table 9.4 Measured beam performance across the band for the prototype.

Chapter 10

Table 10.1 Measured gain of the beam‐scanning reflectarray prototypes.

Table 10.2 Key characteristics of some electronic devices used in reconfigurable reflectarrays.

Chapter 11

Table 11.1 Change in radiation performance of conformal cylindrical reflectarrays with D/

= 1.

List of Illustrations

Chapter 01

Figure 1.1 The geometry of an offset‐fed reflectarray antenna.

Figure 1.2 The first reflectarray antenna using waveguide technology.

Figure 1.3 The number of articles on reflectarray antennas published in IEEE. Data obtained from IEEE Xplore on April 1, 2016.

Figure 1.4 Organization of this reflectarray book.

Chapter 02

Figure 2.1 Typical geometry of a planar reflectarray antenna.

Figure 2.2 Typical geometrical parameters of a planar reflectarray antenna.

Figure 2.3 Grid layout of the unit‐cells of a reflectarray antenna with circular aperture.

Figure 2.4 Phases on the aperture with a centered feed and broadside beam: (a) spatial delay, (b) progressive phase, (c) phase distribution on the reflectarray antenna, and (d) phase distribution on the continuous aperture.

Figure 2.5 Phases on the aperture with an offset feed and an off‐broadside beam: (a) spatial delay, (b) progressive phase, (c) phase distribution on the reflectarray antenna, and (d) phase distribution on the continuous aperture.

Figure 2.6 Schematic models of reflectarray patch elements with attached phase/time‐delay lines of two different lengths.

Figure 2.7 Schematic models of variable size reflectarray square patch elements of two different sizes.

Figure 2.8 A typical S‐curve for variable size reflectarray elements.

Figure 2.9 A 3D schematic model of a CP reflectarray element.

Figure 2.10 A schematic model of a CP reflectarray element showing the reference element with 0° phase shift (left) and the

rotated element with 2

phase shift (right).

Figure 2.11 A unit‐cell analysis setup: (a) 3D model in Ansys HFSS, (b) vector electric fields of the Floquet port excitation.

Figure 2.12 A metallic waveguide simulator: (a) 3D model in Ansys HFSS and (b) vector electric fields of the wave port excitation.

Figure 2.13 The circuit model for the unit‐cell of a reflectarray antenna.

Figure 2.14 The angle of incidence as a function of frequency in the standard X‐band waveguide.

Figure 2.15 Comparison between the reflection coefficients of an X‐band square patch reflectarray element using a waveguide simulator and a PBC model with Floquet port excitation: (a) phase, (b) magnitude.

Figure 2.16 Comparison between the reflection coefficients of an X‐band square patch reflectarray element using a circuit model and a PBC model with Flouqet port excitation: (a) phase, (b) magnitude.

Figure 2.17 A Ka‐band microstrip patch antenna array element: (a) 3D model of the element, (b) magnitude of reflection coefficient across the band.

Figure 2.18 A Ka‐band microstrip reflectarray element with attached phase‐delay line stubs modeled in Ansys HFSS.

Figure 2.19 Reflection coefficient of the Ka‐band microstrip reflectarray element as a function of the phase‐delay line length: (a) phase, (b) magnitude.

Figure 2.20 Magnitude of surface currents (|J

| in A/mm) on the unit‐cells: (a) inset‐fed microstrip patch element, (b) reflectarray element with open‐circuit stub.

Figure 2.21 Far‐field pattern for a reflectarray element with an open‐circuit stub.

Figure 2.22 A variable size Ka‐band microstrip reflectarray element modeled in Ansys HFSS.

Figure 2.23 Reflection coefficients of the Ka‐band microstripreflectarray element as a function of the patch width: (a) phase, (b) magnitude.

Figure 2.24 Total electric fields at a distance of 0.1 mm from the surface of the patch element: (a) |

|, (b) |

|, (c) |

|, (d) phase of

, (e) phase of

, and (f) phase of

. The unit for the magnitude plots is V/mm, and the unit for phase plots is degrees.

Figure 2.25 Phase of

: (a) incident fields, (b) scattered fields – amplitude of

, (c) incident fields, (d) scattered fields.

Figure 2.26 (a) Surface current magnitude (|

|) on the patch in A/mm, (b) Far‐field pattern.

Figure 2.27 (a) Design parameters for an SSR element. (b) SSR element modeled in Ansys HFSS.

Figure 2.28 Element rotation technique for SRR elements.

Figure 2.29 Magnitude of the reflection coefficient as a function of frequency for the SSR element.

Figure 2.30 Reflection phase as a function of rotation angle for the SSR element.

Figure 2.31 Reflection coefficients of the variable size square patch reflectarray element as a function of the patch width at three frequencies across the band: (a) phase, (b) magnitude.

Figure 2.32 Reflection coefficients of the variable size square patch reflectarray element as a function of the patch width for different angles of incidence with perpendicular polarization: (a) reflection phase for

= 0

, (b) (a) reflection magnitude for

= 0

, (c) reflection phase for

= 45

, (c) and (d) reflection magnitude for

= 45

Figure 2.33 Reflection coefficients of the variable size square patch reflectarray element as a function of the patch width for different angles of incidence with parallel polarization: (a) reflection phase for φ = 0

, (b) (a) reflection magnitude for φ = 0

, (c) reflection phase for φ = 45

, (c) and (d) reflection magnitude for φ = 45

Figure 2.34 The waveguide components for reflectarray element measurements.

Figure 2.35 Measurement setups for the reflectarray element.

Figure 2.36 Measured and simulated reflection coefficients for variable size reflectarray elements: (a) element phase, (b) element loss.

Chapter 03

Figure 3.1 Coordinate system of the reflectarray and feed system.

Figure 3.2 Radiation pattern of the cos

feed pattern model for different values of

Figure 3.3 Directivity of the cos

feed pattern model as a function of

Figure 3.4 Geometrical setup of the feed and the reflectarray aperture.

Figure 3.5 Aperture efficiency for a reflectarray with a rectangular aperture: (a) efficiency versus

, (b) normalized amplitude on the aperture for

= 4.5.

Figure 3.6 Aperture efficiency for a reflectarray with a square aperture: (a) efficiency versus

, (b) normalized amplitude on the aperture for

= 6.5.

Figure 3.7 Aperture efficiency for a reflectarray with a circular aperture: (a) efficiency versus

, (b) normalized amplitude on the aperture for

= 8.5.

Figure 3.8 Efficiency for a reflectarray with a front‐fed symmetric reflectarray: (a) aperture efficiency as a function of feed position and

, (b) efficiency as a function of feed position for

= 6.5.

Figure 3.9 Aperture blockage in front‐fed reflectarray systems: (a) symmetric, (b) offset.

Figure 3.10 Efficiency for an offset reflectarray with

= 6.5: (a) efficiency as a function of feed position for

offset

= 20°, (b) aperture efficiency as a function of feed position and

offset

Figure 3.11 Efficiency for an offset reflectarray as a function of feed beam pointing position on the aperture.

Figure 3.12 Amplitude distribution on the reflectarray aperture: (a) feed points to the geometrical center, (b) feed points to the optimum point.

Figure 3.13 Geometrical setup of a front‐fed symmetric reflectarray.

Figure 3.14 Aperture illumination and edge taper for a front‐fed symmetric reflectarray: (a) ET versus q for H

/D = 0.8, (b) normalized illumination on the aperture for

= 5.98 in dB scale.

Figure 3.15 Aperture illumination and edge taper for a front‐fed symmetric reflectarray: (a) ET versus H

for a fixed feed pattern (

= 7.4), (b) normalized illumination on the aperture for H

= 0.9 in dB scale.

Figure 3.16 Geometrical setup of an offset reflectarray system.

Figure 3.17 The side‐view of an offset reflectarray system showing the edge and feed subtended angles.

Figure 3.18 Illumination on the offset reflectarray aperture: (a) along

‐axis, (b) along

‐axis.

Figure 3.19 (a) Aperture illumination of an offset reflectarray. (b) ET as a function of polar angle on the reflectarray aperture.

Figure 3.20 The geometrical models and key parameters of the offset systems: (a) parabolic reflector, (b) reflectarray.

Figure 3.21 The analogous geometrical setup of the offset reflector and reflectarray systems.

Figure 3.22 The geometrical setup of the offset reflectarray in the reflector coordinates.

Figure 3.23 The main beam direction and geometrical setup of the offset reflectarray system.

Figure 3.24 (a) The parabolic reflector antenna model in FEKO. (b) The element phase distribution on the analogous reflectarray antenna aperture.

Chapter 04

Figure 4.1 Coordinate system of the reflectarray antenna for array theory analysis.

Figure 4.2 Flowchart of the transformations from feed to array coordinates.

Figure 4.3 Far‐field coordinate system for the reflectarray antenna.

Figure 4.4 Coordinate rotations used for the reflectarray system: (a) rotation of

γ = φ

about the

‐axis with Z = Z′, (b) additional rotation of

β = θ

about the

´‐axis with Y′ = Y″.

Figure 4.5 Principal planes of the reflectarray antenna.

Figure 4.6 Principal planes of a reflectarray antenna in the angular coordinates with a main beam at the direction of (

26°,

= 40°).

Figure 4.7 Geometry of reflectarray patch elements modeled in Ansys HFSS.

Figure 4.8 Reflection phase versus patch width for the reflectarray elements.

Figure 4.9 Reflectarray design with a broadside beam: (a) Aperture taper, (b) Phase requirement on the aperture.

Figure 4.10 Reflectarray design with a broadside beam: (a) Mask of the reflectarray antenna, (b) Reflection phase of the elements on the reflectarray aperture.

Figure 4.11 Radiation pattern of the reflectarray with a broadside beam: (a)

‐plane, (b)

‐plane.

Figure 4.12 Radiation pattern of the reflectarray with a broadside beam: (a) co‐pol, (b) cross‐pol.

Figure 4.13 Reflectarray design with an off‐broadside beam: (a) Aperture taper, (b) Phase requirement on the aperture.

Figure 4.14 Reflectarray design with an off‐broadside beam: (a) Mask of the reflectarray antenna, (b) Reflection phase of the elements on the reflectarray aperture.

Figure 4.15 Incident electric fields on the reflectarray aperture: (a) |E

| (dB), (b) |E

| (dB), (c) phase of E

, (d) phase of E

Figure 4.16 Reflected electric fields on the reflectarray aperture: (a) phase of E

, (b) phase of E

Figure 4.17 Radiation pattern of the reflectarray with an off‐broadside beam: (a) P.P.1, (b) P.P.2.

Figure 4.18 Directivity versus frequency for the two reflectarray systems.

Figure 4.19 Radiation pattern of the reflectarray antenna and the effect of element pattern in P.P.1.

Figure 4.20 Radiation pattern of the reflectarray antenna and the effect of aperture currents in equivalence principle: (a) P.P.1, (b) P.P.1 zoomed view.

Figure 4.21 Reflectarray antenna simulated using FEKO, (a) top view of the reflectarray, (b) 3D radiation pattern of the reflectarray.

Figure 4.22 Radiation patterns of reflectarray antenna: (a) P.P.1, (b) P.P.2.

Figure 4.23 Phase shift on the reflectarray aperture, (a) ideal phase shift, (b) phase shift obtained by the reflectarray elements.

Figure 4.24 The progressive phase shift on the reflectarray aperture.

Chapter 05

Figure 5.1 A Ka‐band reflectarray variable‐size square patch element: (a) geometry, (b) reflection coefficients at 32 GHz.

Figure 5.2 (a) Reflection phase as a function of frequency for two patch widths. (b) Phase error as a function of frequency.

Figure 5.3 Cross sectional view of a reflectarray system and path delays.

Figure 5.4 Phase distribution on a reflectarray antenna aperture in degrees: (a) truncated to one phase cycle, (b) no truncation.

Figure 5.5 (a) Phase wraps on the aperture of the reflectarray. (b) Phase errors on the aperture of the reflectarray along the center

‐axis at an off‐center frequency with Δ

= −0.1

. A 180° out of phase is observed when

= 4.

Figure 5.6 The coordinate system of the reflectarray antenna.

Figure 5.7 Phase errors on the reflectarray aperture at off‐center frequencies: (a) 30 GHz, (b) 34 GHz.

Figure 5.8 Average phase error of the reflectarray antenna as a function of frequency.

Figure 5.9 (a) Phase curves obtained at different frequencies. (b) The definition for the upper and lower frequency limits in the definition of element bandwidth.

Figure 5.10 Geometrical models of variable‐size elements: (a) square patch, (b) square loop, and (c) cross‐dipole.

Figure 5.11 Phase curves obtained at 13.5 GHz for three different elements.

Figure 5.12 Current distributions at resonance dimensions for reflectarray elements: (a) patch, (b) loop, and (c) cross‐dipole.

Figure 5.13 Reflection phase curves of reflectarray elements at different frequencies: (a) patch, (b) loop, and (c) cross‐dipole.

Figure 5.14 Phase errors compared to the one obtained at center frequency for: (a) patch (b) loop (c) cross‐dipole.

Figure 5.15 Comparison of phase curves obtained at 13.5 GHz for patch elements with different substrate thicknesses.

Figure 5.16 Comparison of phase curves for the patch elements with different substrate thicknesses: (a) t = 0.79 mm, (b) t = 1.58 mm, and (c) t = 3.18 mm.

Figure 5.17 Comparison of phase differences for patch elements with different substrate thicknesses: (a) t = 0.79 mm, (b) t = 1.58 mm, and (c) t = 3.18 mm.

Figure 5.18 Comparison of phase curves obtained at 13.5 GHz for the square loop elements with different substrate thicknesses.

Figure 5.19 Comparison of phase curves for the square loop elements with different substrate thicknesses: (a) t = 0.79 mm, (b) t = 1.58 mm, and (c) t = 3.18 mm.

Figure 5.20 Comparison of phase differences for the square loop elements with different substrate thicknesses: (a) t = 0.79 mm, (b) t = 1.58 mm, and (c) t = 3.18 mm.

Figure 5.21 Comparison of phase curves obtained at 13.5 GHz for the cross‐dipole elements with different substrate thicknesses.

Figure 5.22 Comparison of phase curves for the cross‐dipole elements with different substrate thicknesses: (a) t = 0.79 mm, (b) t = 1.58 mm, and (c) t = 3.18 mm.

Figure 5.23 Comparison of phase differences for the cross‐dipole elements with different substrate thicknesses: (a) t = 0.79 mm, (b) t = 1.58 mm, and (c) t = 3.18 mm.

Figure 5.24 Comparison of phase curves for the square loop elements with trace width: (a)

= 0.5 mm, (b)

= 1 mm, and (c)

= 1.5 mm.

Figure 5.25 Comparison of phase differences for the square loop elements with trace width: (a) w = 0.5 mm, (b) w = 1 mm, and (c) w = 1.5 mm.

Figure 5.26 Comparison of phase curves for the cross‐dipole elements with trace width: (a)

= 0.5 mm, (b)

= 1 mm, and (c)

= 1.5 mm.

Figure 5.27 Comparison of phase differences for the cross‐dipole elements with trace width: (a)

= 0.5 mm, (b)

= 1 mm, and (c)

= 1.5 mm.

Figure 5.28 Directivity of the reflectarray antenna as a function of frequency for different aperture sizes.

Figure 5.29 Performance of a variable‐size square patch reflectarray using different substrate thickness: (a) Phase curves as a function of patch length, (b) directivity bandwidth of the reflectarray antenna with various thicknesses.

Figure 5.30 Performance of a variable‐size square loop reflectarray using different substrate thicknesses: (a) phase curves as a function of loop length, (b) directivity bandwidth of the reflectarray antenna with various thicknesses.

Figure 5.31 Performance of a variable‐size cross‐dipole reflectarray using different substrate thicknesses: (a) phase curves as a function of dipole length, (b) directivity bandwidth of the reflectarray antenna with various thicknesses.

Figure 5.32 Directivity as a function of frequency for reflectarrays using different elements.

Chapter 06

Figure 6.1 The LB 62–15 pyramidal horn antenna from A‐INFO.

Figure 6.2 The feed horn antenna model in ANSYS HFSS.

Figure 6.3 The electric field magnitude inside the horn antenna at 14.25 GHz: (a) E‐plane, (b) H‐plane.

Figure 6.4 Electric fields on the aperture of the horn antenna: (a) |E

| (V/m), (b) |E

| (V/m), (c) phase of E

(degrees), and (d) phase of E

(degrees).

Figure 6.5 A 3D pattern of the horn antenna.

Figure 6.6 Normalized and cosine‐

model of the radiation patterns of the horn antenna.

Figure 6.7 Reflectarray aperture efficiency as a function of focal point to aperture distance.

Figure 6.8 (a) Illumination on the reflectarray aperture. (b) Edge taper as a function of aperture azimuth angle.

Figure 6.9 Geometrical setup of the reflectarray and reflector in the reflector coordinate system.

Figure 6.10 (a) Grid layout of the array. (b) Required phase shift on the reflectarray aperture.

Figure 6.11 Reflectarray element simulation model.

Figure 6.12 Reflection coefficients of the element at 14.25 GHz: (a) phase, (b) magnitude.

Figure 6.13 Mask plot of the reflectarray antenna.

Figure 6.14 (a) Quantized phase distribution on the aperture. (b) Quantization phase errors on the aperture.

Figure 6.15 Radiation pattern of the reflectarray antenna in the principal planes: (a) P.P.1, (b) P.P.2.

Figure 6.16 Comparison of the radiation pattern of the reflectarray antenna at 14.25 GHz using ideal and patch elements: (a) P.P.1, (b) P.P.2.

Figure 6.17 Radiation pattern of the reflectarray at 14.25 GHz in the

‐plane: (a) contour plot, (b) 3D pattern.

Figure 6.18 Images of the reflectarray antenna in ANSYS HFSS: (a) top view without the feed, (b) 3D view with the feed horn.

Figure 6.19 A 3D radiation pattern of the reflectarray antenna at 14.25 GHz obtained using ANSYS HFSS.

Figure 6.20 Comparison of the radiation patterns of the reflectarray antenna at 14.25 GHz obtained using two different approaches: (a) P.P.1, (b) P.P.2.

Figure 6.21 Photo of the reflectarray antenna under test.

Figure 6.22 Electric fields sampled by the near‐field scanner at 14.25 GHz: (a) |E

| in dB, (b) phase of E

in degrees, (c) |E

| in dB, (d) phase of E

in degrees.

Figure 6.23 Measured radiation pattern of the reflectarray at 14.25 GHz in the

‐plane: (a) contour plot, (b) 3D pattern.

Figure 6.24 Comparison between the measured and simulated radiation pattern of the reflectarray antenna at 14.25 GHz: (a) P.P.1, (b) P.P.2.

Figure 6.25 Measured performance of the reflectarray antenna as a function of frequency: (a) gain, (b) aperture efficiency.

Figure 6.26 Photograph of the Ka‐band feed horn antenna.

Figure 6.27 Measured far‐field patterns of the Ka‐band circularly polarized horn antenna.

Figure 6.28 The SRR element along with the design parameters.

Figure 6.29 Magnitudes of co‐ and cross‐polarized element reflection coefficients as a function of frequency. (b) Effects of incident angle on the reflection coefficient magnitudes as a function of frequency.

Figure 6.30 Fabricated circularly polarized reflectarray antenna: (a) array prototype, (b) reflectarray system.

Figure 6.31 Comparison between measured and simulated radiation patterns of the reflectarray antenna at 32 GHz: (a) P.P.1, (b) P.P.2.

Figure 6.32 Geometrical models of variable size elements: (a) square patch, (b) square loop, and (c) cross dipole.

Figure 6.33 Coordinate setup for the reflectarray test.

Figure 6.34 The measurement setup for far‐field pattern measurement.

Figure 6.35 Photographs of fabricated reflectarray prototypes using variable size elements: (a) square patch, (b) cross dipole, and (c) square loop.

Figure 6.36 Comparison of the measured and simulated E‐plane patterns at 13.5 GHz for reflectarrays using different elements: (a) square patch, (b) cross dipole, and (c) square loop.

Figure 6.37 Comparison of the measured and simulated H‐plane patterns at 13.5 GHz for reflectarrays using different elements: (a) square patch, (b) cross dipole, and (c) square loop.

Figure 6.38 Measured E‐plane radiation patterns of the reflectarrays at 13.5 GHz with different elements: (a) square patch, (b) cross dipole, and (c) square loop.

Figure 6.39 Measured H‐plane radiation patterns of the reflectarrays at 13.5 GHz with different elements: (a) square patch, (b) cross dipole, and (c) square loop.

Figure 6.40 The measured performance of reflectarrays consisting of different element shapes as a function of frequency: (a) gain, (b) efficiency.

Chapter 07

Figure 7.1 (a) Single‐layer reflectarray with patches of variable size. (b) Reflection phase as a function of patch size.

Figure 7.2 (a) Double‐layer reflectarray with patches of variable size. (b) Reflection phase as a function of patch size.

Figure 7.3 (a) A two‐layer reflectarray prototype. (b) Measured radiation pattern of the antenna across the band.

Figure 7.4 Geometries of double‐square and double‐circular rings.

Figure 7.5 Phase response of the double‐ring elements as a function of outer ring size: (a) double‐square, (b) double‐circle.

Figure 7.6 (a) Configurations of composite substrates. (b) Phase responses of double‐circular rings and double‐square rings compared to that of the stacked two‐layer square patches.

Figure 7.7 Reflection coefficients versus patch size at the center frequency 32 GHz for λ/2, λ/3, and λ/4 unit‐cells with normal incidence: (a) phase, (b) magnitude.

Figure 7.8 (a) Reflection phases versus frequency for 0° and 90° elements for λ/2, λ/3, and λ/4 unit‐cells. (b) Phase errors for a 90° relative phase difference versus frequency for λ/2, λ/3, and λ/4 unit‐cells.

Figure 7.9 Absolute value of weighted phase error on the reflectarray aperture: (a) λ/2 elements – 30 GHz, (b) λ/2 elements – 34 GHz, (c) λ/4 elements – 30 GHz, (d) λ/4 elements – 34 GHz.

Figure 7.10 Photographs of the fabricated arrays: (a) λ/2 array with 848 square patches, (b) λ/3 array with 1941 square patches.

Figure 7.11 Photographs of the fabricated arrays: (a) λ/2 array with 848 square patches, (b) λ/3 array with 1941 square patches.

Figure 7.12 Measured and simulated radiation patterns of the reflectarray antennas at 32 GHz in the vertical plane.

Figure 7.13 Measured gain and aperture efficiency versus frequency for the prototypes: (a) λ/2 array, (b) λ/3 array.

Figure 7.14 Comparison between the measured gain versus frequency for the λ/2 and λ/3 array.

Figure 7.15 Geometry of single‐layer and double‐layer reflectarray phasing elements.

Figure 7.16 Absolute value of weighted phase error on the reflectarray aperture for double‐layer designs: (a) λ/2 elements – 30 GHz, (b) λ/2 elements – 34 GHz, (c) λ/4 elements – 30 GHz, (d) λ/4 elements – 34 GHz.

Figure 7.17 Average phase error of the reflectarray antenna as a function of frequency for single and double‐layer elements.

Figure 7.18 Gain vs frequency for single and double‐layer reflectarrays using λ/2 and λ/4 elements.

Figure 7.19 True‐time delay reflectarray elements: (a) Aperture couple element. (b) Simulated and measured phases for the reflectarray element.

Figure 7.20 Multi‐panel reflectarray configurations.

Figure 7.21 (a) Geometry of the reflectarray element. (b) Element reflection phase as a function of ring length.

Figure 7.22 Computed gain using the dual‐frequency phase synthesis approach.

Figure 7.23 Graphical illustration of the proposed phase synthesis approach: (a) before and (b) after the optimization of the reference phases Δ

and Δ

Figure 7.24 Photographs of the fabricated reflectarrays designed using (a) the single‐frequency approach, (b) the dual‐frequency approach, and (c) the improved dual‐frequency approach in [40].

Figure 7.25 (a) Photograph of the measurement setup of the reflectarray, feeding horn, and the supporting structure. (b) Measured gain performances of the three reflectarrays designed using different phase synthesis approaches.

Figure 7.26 Geometry of the triple resonance phasing element.

Figure 7.27 The coverage areas of two type of elements on the phase plane.

Figure 7.28 A 3D model of the reflectarray antenna.

Figure 7.29 (a) Radiation patterns at the two design frequencies. (b) Gain and aperture efficiency as a function of frequency.

Figure 7.30 Dual‐band reflectarrays: (a) low frequency layer above high frequency, (b) high frequency layer above low frequency.

Figure 7.31 FSS‐backed reflectarray antenna element.

Figure 7.32 A six‐band reflectarray element configuration: (a) top layer, (b) bottom layer, (c) side view.

Figure 7.33 Geometry of the dual‐band reflectarray element.

Figure 7.34 Co‐polarization reflection coefficient at 20 GHz: (a) phase, (b) magnitude. Co‐polarization reflection coefficient at 30 GHz: (c) phase, (d) magnitude.

Figure 7.35 Radiation patterns at 20 GHz: (a) offset plane, (b) orthogonal plane.

Figure 7.36 Radiation patterns at 30 GHz: (a) offset plane, (b) orthogonal plane.

Figure 7.37 The measured gain and aperture efficiency versus frequency bands of interest: (a) 19~21.5 GHz, (b) 29~31.5 GHz.

Figure 7.38 Geometry of a single‐layer tri‐band reflectarray.

Figure 7.39 (a) Geometry of the Ka‐band element. (b) Reflection phase as a function of frequency.

Figure 7.40 (a) Geometry of the C‐band element. (b) Reflection phase as a function of frequency.

Figure 7.41 (a) Geometry of the C‐band element. (b) Reflection phase as a function of frequency.

Figure 7.42 Element geometries of the (a) Ka band, (b) X band, (c) C band, with (d) the arrangement of the sub‐arrays.

Figure 7.43 Element performance of (a) Ka band, (b) X band, and (c) C band.

Figure 7.44 Element phase compensation schemes for the (a) Ka band, (b) X band, and (c) C band.

Figure 7.45 The fabricated prototype (a) reflectarray aperture, (b) local details, and (c) the reflectarray system with a C/X band feed horn.

Figure 7.46 Measured far‐field patterns of the reflectarray at (a) Ka band (32 GHZ, LHCP), (b) X band (8.4 GHZ, RHCP), and (c) C band (7.1 GHz, Eθ).

Chapter 08

Figure 8.1 The electromagnetic spectrum [5].

Figure 8.2 Measured properties of conductors at infrared: (a) index of refraction, (b) conductivity.

Figure 8.3 Measured properties of dielectrics at infrared: (a) index of refraction, (b) relative permittivity and loss tangent.

Figure 8.4 Comparison between the measured properties and the Drude model for gold.

Figure 8.5 Reflection coefficients for infrared reflectarray elements with a zero‐thickness patch: (a) magnitude, (b) phase.

Figure 8.6 Reflection coefficients for infrared reflectarray elements with a 100‐nm thick patch modeled with only the real part of conductivity (non‐dispersive): (a) magnitude, (b) phase.

Figure 8.7 Reflection coefficients for infrared reflectarray elements with a 100‐nm thick patch using the Drude model for conductors: (a) magnitude (HFSS), (b) phase (HFSS), (c) magnitude (CST), (d) phase (CST).

Figure 8.8 Comparison of reflection coefficients for infrared reflectarray elements with a 100‐nm thick patch using the Drude model for conductors: (a) magnitude for the large‐conductivity case, (b) phase for the large‐loss case, (c) magnitude for the small‐conductivity case, (d) phase for the small‐conductivity case.

Figure 8.9 Reflection coefficients for infrared reflectarray elements with various values of dielectric loss tangent: (a) reflection magnitude and (b) reflection phase.

Figure 8.10 Comparison between circuit‐model and full‐wave simulations for low‐loss and high‐loss cases: (a) reflection magnitudes, (b) reflection phases.

Figure 8.11 The positions of poles and zeros in the S‐plane, and the corresponding phase versus frequency: (a) lossless case (R → ∞), (b) high‐loss case (R <

Figure 8.12 (a) Layout of the IR reflectarray. (b) Fabricated IR reflectarray prototype and a zoomed image of one patch strip.

Figure 8.13 Interferograms of reference flat and both fabricated reflectarrays. (a) Bare substrate. (b) Array #1. (c) Array #2.

Figure 8.14 Comparison of measured and modeled reflection phase for the IR reflectarray elements.

Figure 8.15 Variable‐size elements for THz reflectarrays: (a) variable‐size square patch, (b) variable‐size square DR.

Figure 8.16 Reflection coefficients of the variable‐size elements for THz reflectarrays: (a) phase, (b) magnitude.

Figure 8.17 The THz time‐domain spectrometer system at University of Arizona.

Figure 8.18 Measured dielectric properties of the polymer material.

Figure 8.19 Photo of the polymer‐jetting rapid prototyping machine.

Figure 8.20 Schematic view of the dielectric reflectarray in [26].

Figure 8.21 Reflection coefficients of the dielectric reflectarray elements at 100 GHz.

Figure 8.22 Aperture phase distributions for the dielectric reflectarrays: (a) design for minimum phase wraps (Design 1), (b) design for minimum element loss (Design 2), (c) 1‐bit design (Design 3).

Figure 8.23 Three 3D models of dielectric reflectarrays in Ansys HFSS: (a) Design 1, (b) Design 2, (c) Design 3.

Figure 8.24 Simulated gain patterns of the dielectric reflectarrays at 100 GHz.

Figure 8.25 (a) Aperture phase for a dielectric reflectarray with a lattice size of λ/10 and (b) 3D model.

Figure 8.26 Effect of lattice size on the radiation performance of dielectric reflectarrays.

Figure 8.27 Top view of the fabricated dielectric reflectarray prototypes: (a) Design 1, (b) Design 2, (c) Design 3. The back side is gold plated.

Figure 8.28 Comparison of measured and simulated radiation patterns of the dielectric reflectarrays at 100 GHz: (a) Design 1, (b) Design 2, (c) Design 3.

Figure 8.29 Measured gains versus frequency for the dielectric reflectarray prototypes.

Figure 8.30 (a) Geometrical model of the liquid crystal reflectarray element. (b) Reflection coefficients as a function of relative permittivity.

Chapter 09

Figure 9.1 Radiation pattern of the double‐beam reflectarray antenna designed with the geometrical approach: (a) 2D contour plot, (b) 3D pattern.

Figure 9.2 Radiation pattern of the quad‐beam reflectarray antenna designed with the geometrical approach: (a) 2D contour plot, (b) 3D pattern.

Figure 9.3 (a) Amplitude distribution from equation (9.4). (b) Practical amplitude distribution. (c) Ideal amplitude distribution.

Figure 9.4 A 3D radiation pattern of the multi‐beam reflectarray antennas designed with the superposition approach: (a) double‐beam, (b) quad‐beam.

Figure 9.5 Normalized radiation patterns of the single‐ and quad‐beam designs.

Figure 9.6 Schematic model of alternating projections on two intersecting sets M and R.

Figure 9.7 Flowchart of the APM optimization.

Figure 9.8 A 2D view of the mask model for the quad‐beam reflectarray in the

‐plane.

Figure 9.9 A flowchart of the PSO algorithm.

Figure 9.10 Convergence curves of the APM optimization for different SLL requirements.

Figure 9.11 Radiation pattern of the optimized quad‐beam reflectarray at 32 GHz.

Figure 9.12 (a) Optimized phase distribution of the reflectarray elements. (b) Fabricated quad‐beam reflectarray.

Figure 9.13 Measured and simulated co‐polarized radiation patterns of the quad‐beam reflectarray antenna: (a)

= 45° plane, (b)

= 135° plane.

Figure 9.14 Measured gain and efficiency of the quad‐beam reflectarray antenna.

Figure 9.15 Measured radiation patterns of the reflectarray antenna across the 1 dB gain band in the

= 45° plane.

Figure 9.16 Upper bound mask (

) for an asymmetric multi‐beam reflectarray antenna.

Figure 9.17 Convergence curves of the PSO for multi‐beam reflectarray antenna design.

Figure 9.18 Optimized phase distributions for quad‐beam reflectarrays: (a) Case I, (b) Case II, (c) Case III, and (d) Case IV.

Figure 9.19 Radiation patterns of optimized multi‐beam reflectarrays: (a) Case I, (b) Case II, (c) Case III, and (d) Case IV.

Figure 9.20 An asymmetric quad‐beam reflectarray antenna designed using the APM method, which does not satisfy the design requirements: (a) phase distribution, (b) radiation pattern.

Figure 9.21 Phase distribution on the reflectarray aperture using variable size square patch elements.

Figure 9.22 Fabricated single‐feed reflectarray antenna with asymmetric multi‐beam: (a) array, (b) reflectarray system.

Figure 9.23 Radiation pattern of the asymmetric quad‐beam reflectarray prototype at 32 GHz: (a) simulated result, (b) measured result.

Figure 9.24 Measured gain and efficiency of the asymmetric quad‐beam reflectarray antenna prototype.

Figure 9.25 Measured radiation patterns of the asymmetric quad‐beam reflectarray prototype at off‐center frequencies: (a) 31 GHz, (b) 33 GHz.

Figure 9.26 Shaped‐beam reflectarray: (a) fabricated prototype, (b) measured radiation patterns.

Figure 9.27 Radiation patterns at central and extreme frequencies for the reflectarray optimized in the 12.8–14.2 GHz band. (a) 12.8 GHz. (b) 13.5 GHz. (c) 14.2 GHz.

Figure 9.28 Shaped‐beam reflectarray antenna in the DTU‐ESA spherical near‐field antenna test facility.

Figure 9.29 Simulated (solid lines) and measured (dotted lines) radiation patterns of the manufactured breadboard for both H‐ and V‐polarizations at 10 GHz. (a) H‐polarization, co‐polar; (b) H‐polarization, cross‐polar; (c) V‐polarization, co‐polar; and (d) V‐polarization, cross‐polar.

Figure 9.30 Simulations (co‐polar and cross‐polar in solid and dashed lines, respectively) and measurements (co‐polar and cross‐polar in dash‐dot and dotted lines, respectively) at the central frequency (25.5 GHz). Central beam in H‐polarization (a) and (c) and lateral beam in V‐polarization (b) and (d). Main cuts in azimuth (a) and (b) and elevation (c) and (d). Minimum required gain in solid line.

Chapter 10

Figure 10.1 Design methodologies for beam‐scanning reflectarray antennas.

Figure 10.2 Feed displacement paths for reflectarray antennas: (a) axial displacement, (b) lateral displacement.

Figure 10.3 Effect of axial displacement of the feed on the phase distribution on the aperture: (a) Ideal phase shift, (b) corresponding phase error.

Figure 10.4 Effect of axial displacement of the feed on the radiation performance of reflectarray antennas: (a) F/D = 0.4 (

= 1.447), (b) F/D = 0.7 (

= 4.586), (c) F/D = 1.0 (

= 9.318), (d) normalized gain versus axial displacement.

Figure 10.5 Effect of lateral displacement of the feed on the radiation performance of reflectarray antennas: (a) F/D = 0.4 (q = 1.447), (b) F/D = 0.7 (q = 4.586), (c) F/D = 1.0 (q = 9.318), and (d) normalized gain loss versus bmws.

Figure 10.6 Different paths for feed displacement: (a) lateral movement, (b) circular arc movement.

Figure 10.7 Coordinate system for the bifocal reflectarray antenna.

Figure 10.8 Phase distribution on the reflectarray antenna aperture: (a) conventional parabolic design, (b) bifocal design.

Figure 10.9 Scanned gain patterns of reflectarray antennas: (a) parabolic‐type, (b) bifocal‐type.

Figure 10.10 Shaped far‐field mask used for the optimization.

Figure 10.11 Convergence curves for the single‐objective (PSO) and multi‐objective (MOPSO) optimizations.

Figure 10.12 Phase distribution on the aperture of the optimized reflectarray antennas: (a) PSO design, (b) MOPSO design.

Figure 10.13 Scanned gain patterns of the optimized beam‐scanning reflectarray antennas: (a) PSO, (b) MOPSO.

Figure 10.14 Simulated gain versus scan angle for reflectarray antennas.

Figure 10.15 Fabricated reflectarray prototypes: (a) parabolic design, (b) bifocal design, (c) PSO design, and (d) MOPSO design.

Figure 10.16 Fabricated mechanical beam‐scanning reflectarray prototype.

Figure 10.17 Scanned gain pattern of the fabricated beam‐scanning reflectarray antennas: (a) parabolic‐type design, (b) bifocal design, (c) PSO design, and (d) MOPSO design.

Figure 10.18 Illustration of a (a) parabolic cylindrical reflector, and (b) parabolic cylindrical reflectarray.

Figure 10.19 Compensation phase distribution of the parabolic cylindrical reflectarrays: (a) conventional, (b) optimized.

Figure 10.20 Photographs of the fabricated parabolic cylindrical reflectarrays: (a) conventional, (b) optimized, and (c) photograph of the waveguide slot array antenna.

Figure 10.21 Measured radiation patterns of the conventional design at 0°, 15°, and 30° scan angles in the (a) H‐plane and (b) E‐plane.

Figure 10.22 Measured radiation patterns of the optimized design at 0°, 15°, and 30° scan angles in the (a) H‐plane and (b) E‐plane.

Figure 10.23 (a) Image of a parabolic torus reflector antenna. (b) Geometrical setup of the PTPRA in the parabolic (

) plane.

Figure 10.24 The aperture phase distribution on the PTPRA.

Figure 10.25 Feed displacement path for the PTPRA.

Figure 10.26 Scanned patterns of the PTPRA when the feed is moved along the focal arc of the reflector.

Figure 10.27 The cross‐sectional geometry of a spherical‐phase reflectarray antenna.

Figure 10.28 Phase error over the aperture of a spherical‐phase reflectarray antenna.

Figure 10.29 Scanned patterns for the spherical‐phase reflectarray antenna.

Figure 10.30 Dual‐band beam‐scanning dual‐reflectarray antenna with the reflectarray as the main reflector: (a) image of the dual‐reflectarray antenna, (b) scanned beam in the X band, (c) scanned beam in the Ka band.

Figure 10.31 A 94 GHz beam‐scanning dual‐reflectarray antennas with the reflectarray as sub‐reflector. (a) Image of the dual‐reflectarray antenna. (b) Measured and simulated radiation patterns of dual‐reflector antenna with three flat metal sub‐reflectors in the azimuth plane at 94 GHz.

Figure 10.32 Bifocal dual‐reflectarray antenna for 27° scan coverage: (a) prototype, (b) measured scanned beam patterns.

Figure 10.33 Spherical reflector antenna with sub‐reflectarray: (a) PO current distribution on the main reflector, (b) scanned beam patterns.

Figure 10.34 Phase‐tuning approaches for reconfigurable reflectarray elements: (a) tunable size elements, (b) tunable delay‐line elements, and (c) tunable rotated elements.

Figure 10.35 (a) The concept of mechanically rotated elements. (b) A mechanically beam‐scanning reflectarray prototype demonstrating a scan range of 10°.

Figure 10.36 A CP beam‐scanning reflectarray using micromotors.

Figure 10.37 Mechanically actuated beam‐scanning/switching reflectarrays: (a) Electrostatic actuators for reflectarray patch elements. (b) Surface translation.

Figure 10.38 A 25,600 element electronic beam‐scanning reflectarray antenna using PIN diodes demonstrating 50° scan coverage in both elevation and azimuth planes.

Figure 10.39 Electronic beam‐scanning reflectarray elements using PIN diodes. (a) Exploded view of the elementary cell in [75] where phase control is implemented at the sub‐array level. (b) Expanded view of a reflectarray element based on gathered patches aperture‐coupled to a common delay line, using a PIN diode as electronic control switch.

Figure 10.40 Electronic element rotation technique for beam‐scanning reflectarray antennas: (a) schematic, (b) element prototype.

Figure 10.41 Beam‐scanning reflectarray elements using MEMS switches: (a) Variable length slot configuration. (b) Aperture‐coupled patch configuration.

Figure 10.42 A beam‐scanning reflectarray antenna using MEMS demonstrating a scan range from 0° to 40° off‐broadside: (a) element model, (b) 100 element prototype.

Figure 10.43 Reconfigurable reflectarray elements using digitally switched MEMS capacitors.

Figure 10.44 Beam‐scanning reflectarray element using a tunable MEMS device: (a) schematic model of the MEMS capacitor, (b) element prototype.

Figure 10.45 Electronic beam‐scanning reflectarray antennas using varactor diodes. (a) A 70‐element prototype demonstrating a 100° azimuth scan coverage. (b) A 30‐element prototype demonstrating 2D beam‐scanning.

Figure 10.46 Liquid crystal beam‐scanning reflectarray antennas. (a) A Ka‐band prototype demonstrating a 40° scan coverage. (b) A 256 element 77 GHz prototype.

Figure 10.47 Liquid crystal reflectarray prototype.

Figure 10.48 A 19‐GHz beam‐scanning reflectarray antenna using thin‐film ferroelectric phase shifters.

Figure 10.49 Active reflectarray prototypes. (a) A fixed beam design. (b) A reconfigurable design.

Figure 10.50 Comparison of reflectarray radiation pattern with digital and analog phase control: (a) broadside beam, (b) scanned beam.

Figure 10.51 Scan‐loss performance of reflectarrays with digital and analog phase control.

Figure 10.52 A reflectarray prototype with reduced number of control bits: (a) reflectarray and feed horn, (b) phase shifting layer.

Chapter 11

Figure 11.1 Coordinate system for a conformal reflectarray antenna.

Figure 11.2 Cross‐section of the conformal cylindrical reflectarray systems.

Figure 11.3 Radiation patterns of cylindrical reflectarrays: (a) concave, (b) convex.

Figure 11.4 Normalized HPBW in the curvature plane as a function of cylinder radius.

Figure 11.5 Normalized SLL in the curvature plane as a function of cylinder radius.

Figure 11.6 Normalized gain versus frequency for the reflectarray antennas.

Figure 11.7 Gain bandwidth of the reflectarray antennas as a function of cylinder radius.

Figure 11.8 Dual‐reflector/reflectarray configurations: (a) reflectarray as the primary reflector, (b) reflectarray as the sub‐reflector, (c) reflectarray as both the primary and sub‐reflector.

Figure 11.9 Photograph of a 77 GHz dual‐reflectarray using a hyperboloidal sub‐reflector.

Figure 11.10 Schematic model of a sub‐reflectarray/parabolic reflector configuration.

Figure 11.11 (a) Concept of sub‐reflectarray compensation. (b) Compensated far‐field pattern using sub‐reflectarray compensation.

Figure 11.12 Top view of the antenna configuration.

Figure 11.13 A Cassegrain dual‐reflectarray antenna.

Figure 11.14 Measured radiation patterns of the antenna: (a) elevation, (b) azimuth.

Figure 11.15 The model of the GEO satellite in Earth’s orbit.

Figure 11.16 Schematic view of the L‐band reflectarray.

Figure 11.17 Zoomed view of a small section of the L‐band reflectarray.

Figure 11.18 Feed antenna for the L‐band reflectarray and measured radiation patterns.

Figure 11.19 Photos of the L‐band reflectarray antenna system designed for the Beidou navigation satellite system.

Figure 11.20 Constellation diagram for the L‐band signal received by the reflectarray.

Figure 11.21 (a) Photograph of an octagonal solar cell. (b) Multi‐layered structure of the solar cell with integrated reflectarray elements.

Figure 11.22 (a) Top view of the crossed‐dipole elements with grid electrodes. (b) Simulated phase and magnitude responses of the elements as a function of dipole length.

Figure 11.23 Prototype of a Ka‐band reflectarray antenna integrated with solar cells.

Figure 11.24 Measured and simulated radiation patterns of the reflectarray.

Figure 11.25 (a) Measurement setup. (b) Calculated output power and light transmittance for a separation distance of 200 mm.

Figure 11.26 The feed array configuration for the power combining reflectarray.

Figure 11.27 The 37‐element power combining reflectarray.

Figure 11.28 A two‐feed single‐beam reflectarray antenna: (a) geometry of the system, (b) photograph of the layout.

Figure 11.29 (a) Configuration of a single unit‐cell amplifier. (b) The layout of the 137‐element active reflectarray.

Figure 11.30 Performance comparison between the spatial combiner using passive and active reflectarrays.

Figure 11.31 A 3‐m Ka‐band inflatable reflectarray antenna.

Figure 11.32 Reflectarrays for solar sail applications. Image is from [51].

Figure 11.33 The 500‐m radio telescope being assembled in China. Image is from [53].

Figure 11.34 The Ivanpah solar power facility from [54].

Figure 11.35 Geometries of: (a) a transmitarray antenna, and (b) a reflectarray antenna.

Guide

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Reflectarray Antennas: Theory, Designs, and Applications

Payam Nayeri

Colorado School of MinesUSA

Fan Yang

Tsinghua UniversityChina

Atef Z. Elsherbeni

Colorado School of MinesUSA

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Payam Nayeri, Fan Yang, and Atef Z. Elsherbeni to be identified as the authors of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication data applied for

ISBN: 978‐1‐118‐84676‐6

Cover design by WileyCover images: (Background) © Andrey Prokhorov/Gettyimages; (Foreground) Courtesy of Payam Nayeri, Fan Yang, and Atef Z. Elsherbeni

To my parents who I am eternally grateful for their love, support, and encouragement throughout my career

Payam Nayeri

To my colleagues and students, and to my family

Fan Yang

To my wife, Magda, daughters, Dalia and Donia, son, Tamer, and the memory of my parents

Atef Z. Elsherbeni

Foreword

Although the concept of the reflectarray antenna was first introduced in 1963, the vast interest in it did not come about until in the late 1980s with the development of low‐profile microstrip antennas. From the word reflectarray, it can be deduced that this is an antenna that combines the unique features of a parabolic reflector and a phased array. Thus, a low‐profile reflectarray consists of an array of microstrip elements that are provided with a set of pre‐adjusted phases to form a focused beam when illuminated by a feed, in a similar way to a parabolic reflector. The array elements can be printed onto either a flat surface or a slightly curved surface and have been demonstrated to have the ability to produce a high‐gain pencil beam, a contour‐shaped beam, multiple beams, or an electronically scanned beam. Because the array elements in a reflectarray are not physically interconnected, it can produce a high‐gain beam with relatively high efficiency similar to that produced by a parabolic reflector. There were several pioneers that initiated the study of printed reflectarrays during the late 1980s. I thought about the idea of a reflectarray due to my earlier work experiences with microstrip antennas and frequency selective surfaces (FSS). At certain resonant frequencies, the FSS can only reflect as a nearly perfect conductor since all elements are identical. It cannot cause the reflected waves to form a phase‐coherent beam. However, if each FSS element is designed differently with appropriate phase delay, a coherent beam can then be formed and a printed reflectarray is consequently formed.

This book gives a comprehensive presentation of reflectarray antennas. Chapter 1 is a general overview of the operating principles as well as the developmental history of reflectarray antennas. Chapters 2 through 5 provide very complete and detailed design and analysis techniques, including the important element characterization and selection, radiation efficiency analysis and system design, various radiation analysis approaches and tradeoffs, and the most critical bandwidth issues and analysis. Chapter 6 gives a few specific design examples; in particular, a Ku‐band step‐by‐step design example and a circularly polarized reflectarray design. It is well known that the bandwidth limitation generally presents critical issues in reflectarray design. Chapter 7 is devoted to broadband solutions by presenting several bandwidth widening techniques and multiband approaches. The Terahertz, infrared, and optical frequencies have been found to be the frontier of research and application for antennas. Reflectarray antennas have also found applications in these extremely high frequency areas and are presented in Chapter 8, where the critical issues of material characterization and element loss are discussed. Low‐loss dielectric resonators, used as elements, are also presented in this chapter. A single reflectarray antenna can not only be designed to produce a high‐gain pencil beam, but, due to its many array elements, also has the ability to generate a specifically contour‐shaped beam as well as multiple beams. Chapter 9 gives a thorough presentation of the design approaches, which include direct design approaches and synthesis design approaches for a single reflectarray to radiate a contour‐shaped beam or multiple beams. Chapter 10 engages in discussion about a reflectarray’s beam scanning capability and design approaches. One of the key advantages of the reflectarray is its ability to achieve fast electronic beam scanning by implanting a low‐loss phase shifter into each of its elements without the need for expensive transmit/receive modules and high‐loss power division network. Thus, the reflectarray, owing to the hybrid nature of reflector and array, can behave like an efficient high‐gain parabolic reflector and a relatively low‐cost phased array. Finally, Chapter 11 discusses several emerging and future applications of reflectarray antennas, such as a reflectarray conformally mounted on curved surfaces, satellite applications, integration with solar cells, amplifying reflectarrays, dual‐reflectarrays, very large aperture applications, and so on.

By comparing this book with the very first reflectarray book published by the Wiley‐IEEE Press (Huang and Encinar) in 2008, this book not only gives more updated information, but also gives more detailed analysis and design presentations. The authors of that 2008 book also presented their own pioneering contribution in the areas such as broadband design using sub‐wavelength patch elements, a special phase synthesis approach, and single as well as multilayer approaches. In particular, a single layer design with tri‐band circular polarization performance was achieved. It was a cooperative effort that fulfilled my contractual request from the Jet Propulsion Laboratory while the authors were teaching at the University of Mississippi. A unique split‐square ring element was also used to achieve excellent circular polarization for this single‐layer multiband reflectarray. In that book, the authors presented their own contributions in the area of Terahertz and infrared reflectarray applications. In addition, the synthesis technique for a single reflectarray to achieve multiple beams and specifically shaped beams was presented as well. The electronic beam scanning capability of the reflectarray was also fully discussed with several well‐presented new design approaches.

This book is well organized and has significant amount of information in design and analysis with many practical application results augmented with adequate number of references to help the readers to comprehend. Undoubtedly, I believe this book is not only well suited as a university text book but also is an excellent source of design and analysis information for antenna engineers for many years to come.

Dr. John HuangPrinciple Engineer, retiree ofThe Spacecraft antenna research groupJet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, California, USA

Preface

High‐gain antennas are an essential part of long‐distance wireless communications, radar, and remote sensing systems, which vary with frequency, coverage, resolution, and flexibility of operation. The conventional choices for antennas in these systems were typically reflectors, lenses, or arrays. In recent years, however, a new generation of high‐gain antennas has emerged that combines the favorable features of both printed arrays and reflector antennas and creates a high‐gain antenna with low‐profile, low‐mass, and low‐cost features. This antenna is known as the reflectarray.

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