Inter-University Electronics Series, Vol. 7 ANTENNA THEORY part 2 Robert E. Collin Division of Electrical Sciences and Applied Physics Case Western Reserve University Cleveland, Ohio Francis J. Zucker Air Force Cambridge Research Laboratories L. G. Hanscom Field Bedford, Massachusetts McGraw-Hill Book Company New York St. Louis San Francisco London Sydney Toronto Mexico Panama
Foreword Preface v vii CONTENTS CHAPTER 16 WAVE FRONTS, RAYS, AND FOCAL SURFACES F. Sheppard Holt 16.1 Introduction 1 16.2 The Eikonal and the Eikonal Equation 2 16.3 Geometrical Optics as a Zero-wavelength Approximation 4 16.4 Fermat's Principle and Snell's Laws 6 16.5 Phase Analysis and Phase Synthesis 8 16.6 Power Flow in Ray Tubes 10 16.7 Power Distribution in the Aperture 11 16.8 Power Distribution in the Focal Region 13 16.9 Power Distribution in the Far Field 15 16.10 Reflection from a Conducting Surf ace 17 16.11 Ray Collimation and Off-focus Feeding 19 16.12 Congruences and the Equal-path-length Law 21 16.13 Focal Surfaces 23 16.14 General Comments on Focal Surfaces 28 Appendix A: Principal Normal Radii of Curvature, Principal Directions, Principal Planes, and Lines of Curvature 30 Appendix В: Geometrical Optics Power Flow in a Source-free, Nonconducting, Isotropic, Homogeneous Medium 31 Problems 33 References 34 CHAPTER 17 REFLECTOR С J. Sletten 17.1 Importance of Reflector Antennas 36 17.2 Types of Reflector Antennas and Their Primary Uses 36 17.3 The Paraboloid with Source at the Focus 37 17.4 The Wide-angle or Off-focus Characteristics of Paraboloids 55 17.5 Techniques for Compound Primary-feed Designs 64 17.6 Spherical Reflector 69 17.7 Cylindrical Reflector Antennas 83 17.8 Parabolic Torus Antennas 86 17.9 Stepped Reflector Antennas 89 17.10 Multiplate Antenna 92 17.11 The Corner Reflector Antenna 96 Problems 101 References 101 xi
Xll CONTENTS CHAPTER 18 LENS John Brown 18.1 Introduction 104 18.2 Artificial Dielectrics 104 18.3 Design of Homogeneous Lenses 117 18.4 Lenses for Beam-scanning Applications 121 18.5 Extension of Scanning Analysis 126 18.6 Nonhomogeneous Lenses 131 18.7 Configuration Lenses 136 18.8 Discussion 144 Problems 145 References 149 CHAPTER 19 GENERAL CHARACTERISTICS OF TRAVELING-WAVE Alexander Hessel 19.1 Introduction 151 19.2 Modal Properties of Uniform Traveling-wave Structures 155 19.3 The Dispersion Relation for Shielded Waveguides 156 19.4 Guided Waves on Planar Open Structures 162 19.5 The Excitation Problem in Traveling-wave Structures 168 19.6 Characteristics of Specific Guided Waves 177 19.7 Guided Waves on Periodically Loaded Traveling-wave Structures 184 19.8 The Brillouin Diagram and Mode Coupling in Closed Periodic Structures 191 19.9 Guided Waves on Radiating, Periodically Loaded, Traveling-wave Structures Kinematic Properties 195 19.10 Spectral Properties of Spatial Harmonics 203 19.11 Guided Waves in Radiating, Periodically Loaded, Traveling-wave Structures Dynamic Properties 209 19.12 Examples of Brillouin Diagrams of Periodically Loaded, Radiating, Travelingwave Structures 225 Appendix A: Review of Modal Formalism 235 Appendix В: The Square Root Function in the Complex k z Plane 238 Appendix C: The Transformation к г = k 0 sin w 241 Appendix D: The Spectral Representation of the Field of a Magnetic Line Source above an Inductive Surface Reactance Plane 242 Appendix E: Some Properties of the Dispersion Relation of Lossless, Planar, Periodic, Open, Traveling-wave Structures 246 Appendix F: The principal Branch of Solutions of the Dispersion Relation for SM RS at ßod = Sir 248 Problems 250 References 255
CONTENTS xiii CHAPTER 20 LEAKY-WAVE Т. Tamir 20.1 Introduction 259 20.2 The Field of a Leaky-wave Distribution 262 20.3 Radiation-pattern Calculations 268 20.4 The Complex-angle Plane w and Its Relation to the Leaky-wave Field 273 20.5 Control of Aperture Distribution 277 20.6 Determination of the Complex Wave Number k z 279 20.7 Specific Antenna Structures 289 Problems 295 References 295 CHAPTER 21 SURFACE-WAVE Francis J. Zucker 21.1 Introduction to Surface Waves 298 21.2 How Does a Surface-wave Antenna Radiate? 304 21.3 Surface-wave Excitation 313 21.4 Discontinuities and Tapers 325 21.5 Surface-wave Structures 331 Appendix: Saddle-point Integration 338 Problems 341 References 343 CHAPTER 22 LOG-PERIODIC R. Mittra 22.1 Historical Introduction 349 22.2 Principle of Scaling and Application to Log-periodic Design 350 22.3 Application of k-ß Diagrams to Log-periodic Antenna Analysis 357 22.4 Other Approaches to the Analysis of Log-periodic Structures 361 22.5 Transient Response of Log-periodic Antennas 378 Appendix A: Solution of Equations for P(ct) and Q(a) Appearing in Sec. 22.4-d 380 Appendix В: The Expressions for the Far Field of a Conical Spiral Antenna 382 Problems 383 References 384 CHAPTER 23 CHARACTERISTICS OF OVER LOSSY EARTH James R. Wait 23.1 Fields of Elementary Dipoles over a Homogeneous Half Space 386 23.2 Radiation Resistance and Impedance Increments Resulting from the Presence of the Homogeneous Half Space 392
xiv CONTENTS 23.3 Characteristics of a Thin Linear Antenna over the Conducting Half Space 401 23.4 Linear Antenna over a Solid Metal Disk Which Is Lying on the Half Space 405 23.5 Radial Wire Ground Systems 414 23.6 Influence of the Ground Plane on Antenna Patterns 424 23.7 Conclusions 435 References 435 CHAPTER 24 ELECTROMAGNETIC FIELDS OF SOURCES IN LOSSY MEDIA James R. Wait 24.1 Introduction 438 24.2 The Infinitesimal Radiating Sources in a Lossy Medium 442 24.3 The Finite Current Element 458 24.4 The Horizontally Stratified Earth 461 24.5 Electric Dipole inside a Two-layer Earth 476 24.6 The Infinite Wire over the Three-layer Earth 482 24.7 Grounded Wires on the Homogeneous Earth 492 24.8 Self-impedance of Circuits in a Dissipative Medium 495 Appendix A: Plane Wave Transient Propagation 502 Appendix В: Evaluation of Integrals 505 References 506 CHAPTER 25 IN PLASMA James R. Wait 25.1 Introduction and Basic Considerations 515 25.2 Radiation from a Current Distribution in an Isotropic Electron Plasma 518 25.3 Application to a Cylindrical Antenna 520 25.4 The Cylindrical Shell Model 526 25.5 Collected Results 529 25.6 Boundary-value Approaches to Antennas in Plasma Media 532 25.7 Influence of the DC Magnetic Field 548 25.8 Concluding Remarks 551 References 553 CHAPTER 26 THE ANTENNA AS A SPATIAL FILTER 26.1 Introduction 557 26.2 Spatial Frequency Analysis 557 A. C. Schell
CONTENTS XV 26.3 The Distinction between Coherence and Incoherence 560 26.4 The Incoherent Source Antenna Transfer Function 561 26.5 Different Antenna Types and Their Spatial Frequency Responses 563 26.6 Optimizing System Performance 565 26.7 Optimizing Incoherent Source Transfer Functions 567 26.8 Data Processing 570 26.9 Angular Resolution Enhancement 574 Problems 577 References 578 CHAPTER 27 SIGNAL-PROCESSING A. A. Ksienski 27.1 Introduction 580 27.2 Definition and Description of Multiplicative Arrays 583 27.3 Response of Linear and Nonlinear Multiplicative Antennas to General Source Distributions 586 27.4 Performance of Multiplicative Arrays in the Presence of Noise 596 27.5 Multiple Correlation Arrays 608 27.6 Aperture Synthesis 608 27.7 Applications of Multiplicative Arrays 611 27.8 Pattern Multiplication by Two-way Mode of Operation 616 27.9 Definition and Description of Synthetic Array Radar 620 27.10 Synthetic Array Pattern 622 27.11 Parametric Design Considerations of Synthetic Array Radar 624 27.12 Unfocused Synthetic Arrays 627 27.13 Focused Synthetic Arrays 630 27.14 Recording and Optical Processing in Synthetic Array Radar 631 27.15 The Optical Properties of the Records 634 27.16 Performance Degrading Factors of Synthetic Array Radar 635 27.17 Detection Methods 643 Problems 650 References 651 CHAPTER 28 LARGE ANTENNA SYSTEMS Merrill I. Skolnik 28.1 Introduction 655 28.2 Limitations to Antenna Size 657 28.3 Large Antennas Examples 665 Problems 673 References 673 Bibliography 675 Index 677