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.

Table of Contents:
Preface xiii Acknowledgement xv 1 Introduction 1 References 6 2 Background Theory 7 2.1 Maxwell’s Equations for Time-Harmonic Fields 7 2.1.1 Field Representation in Terms of Axial Field Components in Source-Free Regions 9 2.1.2 Boundary Conditions 10 2.1.3 Poynting’s Theorem 11 2.1.4 Reciprocity 11 2.1.5 Duality 13 2.1.6 Method of Images 13 2.1.7 Geometric Optics 13 2.2 Equivalent Sources 15 2.2.1 Aperture in a Ground Plane 17 2.2.2 Conformal Surfaces 17 2.3 Radiation 18 2.3.1 Near-Field 21 2.3.2 Far-Field 21 2.3.3 Mutual Coupling Between Infinitesimal Current Elements 23 2.4 Problems 26 References 27 3 Fields Radiated by an Aperture 29 3.1 Radiation Equations 29 3.2 Near-Field Region 32 3.3 Fresnel Zone 32 3.4 Far-Field Region 33 3.4.1 Example of a Uniformly Illuminated Rectangular Aperture 38 3.5 Radiation Characteristics 40 3.5.1 Radiation Pattern 41 3.5.2 Half-Power Beamwidth 42 3.5.3 Front-to-Back Ratio 42 3.5.4 Polarization 42 3.5.5 Phase Centre 44 3.5.6 Antenna Gain and Directivity 44 3.5.7 Effective Aperture 46 3.5.8 Radiation Resistance 47 3.5.9 Input Impedance 47 3.5.10 Antenna as a Receiver 48 3.6 Aberrations 48 3.7 Power Coupling Theorem 50 3.8 Field Analysis by High-Frequency Methods 52 3.8.1 Asymptotic Physical Optics 53 3.8.1.1 Example: Scattering Radiation from Large Conducting Wire Loop 55 3.8.1.2 Special Case: APO in Two Dimensions 57 3.8.2 Geometrical Theory of Diffraction 61 3.9 Problems 67 References 70 4 Waveguide and Horn Antennas 71 4.1 Introduction 71 4.2 Radiation from Rectangular Waveguide 72 4.3 Pyramidal Horn 74 4.3.1 Design of a Standard Gain Pyramidal Horn 79 4.3.2 Dielectric-Loaded Rectangular Horn 81 4.4 Circular Waveguides and Horns 85 4.4.1 Circular Waveguide 86 4.4.1.1 Matching at a Circular Aperture 90 4.4.2 Coaxial Waveguide 91 4.4.2.1 Matching of a Coaxial Aperture 95 4.4.2.2 Coaxial Apertures with an Extended Central Conductor 97 4.4.3 Conical Horn 101 4.4.4 Corrugated Radiators 105 4.4.5 Cross-Polarization 110 4.5 Advanced Horn Analysis Topics 114 4.5.1 Flange Effects 114 4.5.2 Mode Matching in Horns 115 4.5.3 Profiled Horns 123 4.5.3.1 Optimization 126 4.5.3.2 Parametric Profiles 126 4.6 Problems 131 References 133 5 Microstrip Patch Antenna 137 5.1 Introduction 137 5.2 Microstrip Patch Aperture Model 138 5.3 Microstrip Patch on a Cylinder 143 5.4 Problems 146 References 147 6 Reflector Antennas 149 6.1 Introduction 149 6.2 Radiation from a Paraboloidal Reflector 150 6.2.1 Geometric Optics Method for a Reflector 152 6.2.1.1 Dipole Feed 154 6.2.1.2 Circular Waveguides and Horn Feeds 157 6.2.2 Edge Taper and Edge Illumination 160 6.2.3 Induced Current Method 162 6.2.3.1 Radiation from Symmetrical Reflectors with General Profile 164 6.2.3.2 Spherical Reflector 167 6.2.4 Receive-Mode Method 168 6.3 Focal Region Fields of a Paraboloidal Reflector 172 6.3.1 Asymptotic Representation of the Scattered Field 176 6.4 Blockage 181 6.5 Reflector Antenna Efficiency 183 6.6 Reflector Surface Errors 188 6.7 Offset-fed Parabolic Reflector 189 6.8 Cassegrain Antenna 196 6.8.1 Classical Cassegrain 196 6.8.2 Offset Cassegrain Antenna 198 6.9 Shaped Reflectors 202 6.9.1 Reflector Synthesis by Geometric Optics 203 6.9.2 Reflector Synthesis by Numerical Optimization 209 6.10 Problems 213 References 217 7 Arrays of Aperture Antennas 219 7.1 Introduction 219 7.2 Two-Dimensional Planar Arrays 219 7.2.1 Rectangular Planar Array 221 7.2.2 Hexagonal Array 223 7.3 Mutual Coupling in Aperture Antennas 228 7.3.1 Infinite Periodic Arrays 230 7.3.2 Finite Arrays 235 7.3.3 Mutual Impedance and Scattering Matrix Representation 239 7.3.4 Analysis of Arrays of Aperture Antennas by Integral Equation Methods 242 7.3.4.1 Moment Method Approach 245 7.3.4.2 Mode Matching in Arrays 247 7.3.5 Mutual Coupling Analysis in Waveguide Apertures 249 7.3.5.1 Rectangular Waveguide Arrays 249 7.3.5.2 Self-Admittance of TE10 Mode 253 7.3.5.3 Arrays of Circular and Coaxial Waveguides 257 7.3.5.4 Self-Admittance of TE11 Mode in Circular Waveguide 262 7.3.5.5 Mutual Coupling in Other Geometries 266 7.3.5.6 Waveguide-Fed Slot Arrays 269 7.3.5.7 Arrays of Microstrip Patches 273 7.3.5.8 A Numerical Formulation of Coupling in Arbitrary Shaped Apertures 278 7.3.6 An Asymptotic Expression for Mutual Admittance 281 7.3.7 Radiation from Finite Arrays with Mutual Coupling 284 7.4 Techniques for Minimizing Effects of Mutual Coupling 286 7.4.1 Element Spacing 286 7.4.2 Aperture Field Taper 287 7.4.3 Electromagnetic Fences 287 7.4.4 Mutual Coupling Compensation 287 7.4.5 Power Pattern Synthesis Including the Effect of Mutual Coupling 289 7.5 Low-Sidelobe Arrays and Shaped Beams 289 7.6 Problems 300 References 302 8 Conformal Arrays of Aperture Antennas 307 8.1 Introduction 307 8.2 Radiation from a Conformal Aperture Array 308 8.2.1 Waveguide with E-Field Polarized in Circumferential Direction 308 8.2.2 Waveguide with E-Polarized in Axial Direction 315 8.2.3 Historical Overview of Asymptotic Solutions for Conformal Surfaces 317 8.3 Mutual Coupling in Conformal Arrays 319 8.3.1 Asymptotic Solution for Surface Dyadic 322 8.4 Coupling in a Concave Array: Periodic Solution 325 8.5 Problems 331 References 331 9 Reflectarrays and Other Aperture Antennas 335 9.1 Introduction 335 9.2 Basic Theory of Reflectarrays 337 9.3 Extensions to the Basic Theory 341 9.4 Other Aperture Antennas 344 9.4.1 Lenses 344 9.4.2 Fabry–Pérot Resonator Antennas 352 9.5 Problems 354 References 356 10 Aperture Antennas in Application 357 10.1 Fabrication 357 10.1.1 Machining 357 10.1.2 Printing 358 10.1.3 Mould Formation 358 10.1.4 Electroforming 358 10.1.5 Lightweight Construction 358 10.1.6 Pressing and Stretch Forming of Reflector Surfaces 359 10.1.7 Assembly and Alignment 360 10.2 Measurement and Testing 361 10.2.1 Far-Field Measurement 361 10.2.2 Near-Field Measurement 364 10.2.3 Intermediate-Field Measurement 369 10.3 Modern Aperture Antennas 371 10.3.1 Compact Low-Sidelobe Horns 371 10.3.2 Multibeam Earth Station 375 10.3.3 Radio Telescopes 379 10.4 Problems 387 References 388 Appendix A: Useful Identities 391 A.1 Vector Identities 391 A.2 Geometric Identities 392 A.3 Transverse Representation of the Electromagnetic Field 393 A.4 Useful Functions 394 References 394 Appendix B: Bessel Functions 395 B.1 Properties 395 B.2 Computation of Bessel Functions 400 References 401 Appendix C: Proof of Stationary Behaviour of Mutual Impedance 403 Appendix D: Free-Space Dyadic Magnetic Green’s Function 405 Reference 406 Appendix E: Complex Fresnel Integrals 407 References 409 Appendix F: Properties of Hankel Transform Functions 411 References 412 Appendix G: Properties of Fock Functions for Convex Surfaces 413 G.1 Surface Fock Functions 413 G.1.1 Soft Surface Functions (m > 0) 414 G.1.2 Hard Surface Fock Functions (m < 0) 415 G.2 Acoustic Fock Functions 417 G.2.1 Soft Acoustic Fock Function 418 G.2.2 Hard Acoustic Fock Function 419 References 421 Index 423

About the Author :
Trevor S. Bird PhD, FTSE, Principal Antengenuity, Adjunct Professor Macquarie University & Honorary CSIRO Fellow, Australia.