Fundamentals of aperture antennas and arrays : from theory to design, fabrication and testing

This book is intended as an advanced text for courses in antennas, with a focus on the mature but vital background field of aperture antennas. The book is aimed at final year, MSc, PhD and Post-Doctoral students, as well as readers who are moving from academia into industry, beginning careers as wireless engineers, system designers, in R&D, or for practising engineers. It assumes the reader has undertaken an earlier course of study on Maxwell's equations, fields and waves. Some of these topics are summarised in the early few chapters in order to provide continuity and background for the remaining chapters. The aperture antennas covered include the main types of horns, reflectors and arrays as well as microstrip patches, reflectarrays and lenses. To provide more than a superficial treatment of arrays, the topic of mutual coupling is covered in greater detail than most similar books in the area. Also included is an introduction to arrays on non-planar surfaces, which is of importance for applications that involve curved surfaces such as in aerodynamics or for making aperture antennas unobtrusive. A chapter is included on some modern aperture antennas to illustrate design techniques beyond the most common types of aperture antennas described in the early chapters. This is to show where advances have recently been made and where they could be improved in the future. Also included are selected topics of a practical nature for aperture antennas, namely fabrication and measurement. Title Page 5 Copyright Page 6 Contents 9 Preface 15 Acknowledgement 17 Chapter 1 Introduction 19 References 24 Chapter 2 Background Theory 25 2.1 Maxwell ́s Equations for Time-Harmonic Fields 25 2.1.1 Field Representation in Terms of Axial Field Components in Source-Free Regions 27 2.1.2 Boundary Conditions 28 2.1.3 Poynting ́s Theorem 29 2.1.4 Reciprocity 29 2.1.5 Duality 31 2.1.6 Method of Images 31 2.1.7 Geometric Optics 31 2.2 Equivalent Sources 33 2.2.1 Aperture in a Ground Plane 35 2.2.2 Conformal Surfaces 35 2.3 Radiation 36 2.3.1 Near-Field 39 2.3.2 Far-Field 39 2.3.3 Mutual Coupling Between Infinitesimal Current Elements 41 2.4 Problems 44 References 45 Chapter 3 Fields Radiated by an Aperture 47 3.1 Radiation Equations 47 3.2 Near-Field Region 50 3.3 Fresnel Zone 50 3.4 Far-Field Region 51 3.4.1 Example of a Uniformly Illuminated Rectangular Aperture 56 3.5 Radiation Characteristics 58 3.5.1 Radiation Pattern 59 3.5.2 Half-Power Beamwidth 60 3.5.3 Front-to-Back Ratio 60 3.5.4 Polarization 60 3.5.5 Phase Centre 62 3.5.6 Antenna Gain and Directivity 62 3.5.7 Effective Aperture 64 3.5.8 Radiation Resistance 65 3.5.9 Input Impedance 65 3.5.10 Antenna as a Receiver 66 3.6 Aberrations 66 3.7 Power Coupling Theorem 68 3.8 Field Analysis by High-Frequency Methods 70 3.8.1 Asymptotic Physical Optics 71 3.8.1.1 Example: Scattering Radiation from Large Conducting Wire Loop 73 3.8.1.2 Special Case: APO in Two Dimensions 75 3.8.2 Geometrical Theory of Diffraction 79 3.9 Problems 85 References 88 Chapter 4 Waveguide and Horn Antennas 89 4.1 Introduction 89 4.2 Radiation from Rectangular Waveguide 90 4.3 Pyramidal Horn 92 4.3.1 Design of a Standard Gain Pyramidal Horn 97 4.3.2 Dielectric-Loaded Rectangular Horn 99 4.4 Circular Waveguides and Horns 103 4.4.1 Circular Waveguide 104 4.4.1.1 Matching at a Circular Aperture 108 4.4.2 Coaxial Waveguide 109 4.4.2.1 Matching of a Coaxial Aperture 113 4.4.2.2 Coaxial Apertures with an Extended Central Conductor 115 4.4.3 Conical Horn 119 4.4.4 Corrugated Radiators 123 4.4.5 Cross-Polarization 128 4.5 Advanced Horn Analysis Topics 132 4.5.1 Flange Effects 132 4.5.2 Mode Matching in Horns 133 4.5.3 Profiled Horns 141 4.5.3.1 Optimization 144 4.5.3.2 Parametric Profiles 144 4.6 Problems 149 References 151 Chapter 5 Microstrip Patch Antenna 155 5.1 Introduction 155 5.2 Microstrip Patch Aperture Model 156 5.3 Microstrip Patch on a Cylinder 161 5.4 Problems 164 References 165 Chapter 6 Reflector Antennas 167 6.1 Introduction 167 6.2 Radiation from a Paraboloidal Reflector 168 6.2.1 Geometric Optics Method for a Reflector 170 6.2.1.1 Dipole Feed 172 6.2.1.2 Circular Waveguides and Horn Feeds 175 6.2.2 Edge Taper and Edge Illumination 178 6.2.3 Induced Current Method 180 6.2.3.1 Radiation from Symmetrical Reflectors with General Profile 182 6.2.3.2 Spherical Reflector 185 6.2.4 Receive-Mode Method 186 6.3 Focal Region Fields of a Paraboloidal Reflector 190 6.3.1 Asymptotic Representation of the Scattered Field 194 6.4 Blockage 199 6.5 Reflector Antenna Efficiency 201 6.6 Reflector Surface Errors 206 6.7 Offset-fed Parabolic Reflector 207 6.8 Cassegrain Antenna 214 6.8.1 Classical Cassegrain 214 6.8.2 Offset Cassegrain Antenna 216 6.9 Shaped Reflectors 220 6.9.1 Reflector Synthesis by Geometric Optics 221 6.9.2 Reflector Synthesis by Numerical Optimization 227 6.10 Problems 231 References 235 Chapter 7 Arrays of Aperture Antennas 237 7.1 Introduction 237 7.2 Two-Dimensional Planar Arrays 237 7.2.1 Rectangular Planar Array 239 7.2.2 Hexagonal Array 241 7.3 Mutual Coupling in Aperture Antennas 246 7.3.1 Infinite Periodic Arrays 248 7.3.2 Finite Arrays 253 7.3.3 Mutual Impedance and Scattering Matrix Representation 257 7.3.4 Analysis of Arrays of Aperture Antennas by Integral Equation Methods 260 7.3.4.1 Moment Method Approach 263 7.3.4.2 Mode Matching in Arrays 265 7.3.5 Mutual Coupling Analysis in Waveguide Apertures 267 7.3.5.1 Rectangular Waveguide Arrays 267 7.3.5.2 Self-Admittance of TE10 Mode 271 7.3.5.3 Arrays of Circular and Coaxial Waveguides 275 7.3.5.4 Self-Admittance of TE11 Mode in Circular Waveguide 280 7.3.5.5 Mutual Coupling in Other Geometries 284 7.3.5.6 Waveguide-Fed Slot Arrays 287 7.3.5.7 Arrays of Microstrip Patches 291 7.3.5.8 A Numerical Formulation of Coupling in Arbitrary Shaped Apertures 296 7.3.6 An Asymptotic Expression for Mutual Admittance 299 7.3.7 Radiation from Finite Arrays with Mutual Coupling 302 7.4 Techniques for Minimizing Effects of Mutual Coupling 304 7.4.1 Element Spacing 304 7.4.2 Aperture Field Taper 305 7.4.3 Electromagnetic Fences 305 7.4.4 Mutual Coupling Compensation 305 7.4.5 Power Pattern Synthesis Including the Effect of Mutual Coupling 307 7.5 Low-Sidelobe Arrays and Shaped Beams 307 7.6 Problems 318 References 320 Chapter 8 Conformal Arrays of Aperture Antennas 325 8.1 Introduction 325 8.2 Radiation from a Conformal Aperture Array 326 8.2.1 Waveguide with E-Field Polarized in Circumferential Direction 326 8.2.2 Waveguide with E-Polarized in Axial Direction 333 8.2.3 Historical Overview of Asymptotic Solutions for Conformal Surfaces 335 8.3 Mutual Coupling in Conformal Arrays 337 8.3.1 Asymptotic Solution for Surface Dyadic 340 8.4 Coupling in a Concave Array: Periodic Solution 343 8.5 Problems 349 References 349 Chapter 9 Reflectarrays and Other Aperture Antennas 353 9.1 Introduction 353 9.2 Basic Theory of Reflectarrays 355 9.3 Extensions to the Basic Theory 359 9.4 Other Aperture Antennas 362 9.4.1 Lenses 362 9.4.2 Fabry–Pérot Resonator Antennas 370 9.5 Problems 372 References 374 Chapter 10 Aperture Antennas in Application 375 10.1 Fabrication 375 10.1.1 Machining 375 10.1.2 Printing 376 10.1.3 Mould Formation 376 10.1.4 Electroforming 376 10.1.5 Lightweight Construction 376 10.1.6 Pressing and Stretch Forming of Reflector Surfaces 377 10.1.7 Assembly and Alignment 378 10.2 Measurement and Testing 379 10.2.1 Far-Field Measurement 379 10.2.2 Near-Field Measurement 382 10.2.3 Intermediate-Field Measurement 387 10.3 Modern Aperture Antennas 389 10.3.1 Compact Low-Sidelobe Horns 389 10.3.2 Multibeam Earth Station 393 10.3.3 Radio Telescopes 397 10.4 Problems 405 References 406 Appendix A Useful Identities 409 A.1 Vector Identities 409 A.2 Geometric Identities 410 A.3 Transverse Representation of the Electromagnetic Field 411 A.4 Useful Functions 412 References 412 Appendix B Bessel Functions 413 B.1 Properties 424 B.2 Computation of Bessel Functions 418 References 419 Appendix C Proof of Stationary Behaviour of Mutual Impedance 421 Appendix D Free-Space Dyadic Magnetic Green ́s Function 423 Reference 424 Appendix E Complex Fresnel Integrals 425 References 427 Appendix F Properties of Hankel Transform Functions 429 References 430 Appendix G Properties of Fock Functions for Convex Surfaces 431 G.1 Surface Fock Functions 431 G.1.1 Soft Surface Functions (m>0) 432 G.1.2 Hard Surface Fock Functions (m