Antenna Theory and Design

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1 Antenna Theory and Design SECOND EDITION Warren L. Stutzman Gary A. Thiele WILEY

2 Contents Chapter 1 Antenna Fundamentals and Definitions Introduction How Antennas Radiate Overview of Antennas Electromagnetic Fundamentals Solution of Maxwell's Equations for Radiation Problems The Ideal Dipole Radiation Patterns Radiation Pattern Basics Radiation from Line Currents Far-Field Conditions and Field Regions Steps in the Evaluation of Radiation Fields Radiation Pattern Definitions Radiation Pattern Parameters Directivity and Gain Antenna Impedance, Radiation Efficiency, and the Short Dipole Antenna Polarization 48 References 52 Problems 52 Chapter 2 Some Simple Radiating Systems and Antenna Practice Electrically Small Dipoles Dipoles Antennas Above a Perfect Ground Plane Image Theory Monopoles Small Loop Antennas Duality The Small Loop Antenna Antennas in Communication Systems Practical Considerations for Electrically Small Antennas 82 References 83 Problems 84 Chapter 3 Arrays The Array Factor for Linear Arrays Uniformly Excited, Equally Spaced Linear Arrays The Array Factor Expression Main Beam Scanning and Beamwidth The Ordinary Endfire Array The Hansen-Woodyard Endfire Array Pattern Multiplication Directivity of Uniformly Excited, Equally Spaced Linear Arrays Nonuniformly Excited, Equally Spaced Linear Arrays 116

3 xii Contents 3.6 Mutual Coupling Impedance Effects of Mutual Coupling Array Pattern Evaluation Including Mutual Coupling Multidimensional Arrays Phased Arrays and Array Feeding Techniques Scan Principles Feed Networks for Beam Scanning Scan Blindness Perspective on Arrays 136 References 136 Problems 137 Chapter 4 Line Sources 4.1 The Uniform Line Source Tapered Line Sources Fourier Transform Relations Between the Far-Field Pattern and the Source Distribution Superdirective Line Sources 159 References 163 Problems 163 Chapter 5 Resonant Antennas: Wires and Patches 5.1 Dipole Antennas Straight Wire Dipoles The Vee Dipole Folded Dipole Antennas Feeding Wire Antennas Yagi-Uda Antennas Corner Reflector Antennas Wire Antennas Above an Imperfect Ground Plane Pattern Effects of a Real Earth Ground Plane Ground Plane Construction Large Loop Antennas Microstrip Antennas Microstrip Patch Antennas Microstrip Arrays 216 References 218 Problems 219 Chapter 6 Broadband Antennas 6.1 Traveling-Wave Wire Antennas Helical Antennas Normal Mode Helix Antenna Axial Mode Helix Antenna Biconical Antennas Infinite Biconical Antenna Finite Biconical Antenna Discone Antenna Sleeve Antennas Sleeve Monopoles Sleeve Dipoles Principles of Frequency-Independent Antennas 250

4 Contents xüi 6.6 Spiral Antennas Equiangular Spiral Antenna Archimedean Spiral Antenna Conical Equiangular Spiral Antenna Related Configurations Log-Periodic Antennas 259 References 270 Problems 272 Chapter 7 Aperture Antennas Radiation from Apertures and Huygens' Principle Rectangular Apertures The Uniform Rectangular Aperture Tapered Rectangular Apertures Techniques for Evaluating Gain Directivity Gain and Efficiencies Simple Directivity Formulas Rectangular Horn Antennas Я-Plane Sectoral Horn Antenna Plane Sectoral Horn Antenna Pyramidal Horn Antenna Circular Apertures The Uniform Circular Aperture Tapered Circular Apertures Reflector Antennas Parabolic Reflector Antenna Principles Axisymmetric Parabolic Reflector Antenna Offset Parabolic Reflectors Dual Reflector Antennas Cross-Polarization and Scanning Properties of Reflector Antennas Gain Calculations for Reflector Antennas Other Reflector Antennas Feed Antennas for Reflectors Field Representations Matching the Feed to the Reflector A General Feed Model Feed Antennas Used in Practice 354 References 356 Problems 358 Chapter 8 Antenna Synthesis The Synthesis Problem Formulation of the Synthesis Problem Synthesis Principles Line Source Shaped Beam Synthesis Methods Fourier Transform Method Woodward-Lawson Sampling Method Linear Array Shaped Beam Synthesis Methods Fourier Series Method Woodward-Lawson Sampling Method Comparison of Shaped Beam Synthesis Methods 377

5 jdv Contents 8.4 Low Side-Lobe, Narrow Main Beam Synthesis Methods Dolph-Chebyshev Linear Array Method Taylor Line Source Method Perspective 390 References 390 Problems 391 Chapter 9 Antennas in Systems and Antenna Measurements Receiving Properties of Antennas Antenna Noise Temperature and Radiometry Radar Reciprocity and Antenna Measurements Pattern Measurement and Antenna Ranges Gain Measurement Gain Measurement of CP Antennas Gain Estimation Polarization Measurement Polarization Pattern Method Spinning Linear Method Dual-Linear Method Field Intensity Measurements 422 References 423 Problems 424 Chapter 10 СЕМ for Antennas: The Method of Moments Introduction to Computational Electromagnetics Introduction to the Method of Moments Pocklington's Integral Equation Integral Equations and Kirchhoff 's Network Equations Source Modeling Weighted Residuals and the Method of Moments Two Alternative Approaches to the Method of Moments Reaction Linear Algebra Formulation of MoM Formulation and Computational Considerations Other Expansion and Weighting Functions Other Electric Field Integral Equations for Wires Computer Time Considerations Toeplitz Matrices Block Toeplitz Matrices Compressed Matrices Validation Calculation of Antenna and Scatterer Characteristics The Wire Antenna or Scatterer as an iv-port Network Series Connections Parallel Connections Antenna Arrays The Linear Array The Circular Array Two-Dimensional Planar Array of Dipoles Summary Radar Cross Section of Antennas 472

6 Contents xv Modeling of Solid Surfaces Wire-Grid Model Continuous Surface Model Summary 487 References 487 Problems 488 Chapter 11 СБМ for Antennas: Finite Difference Time Domain Method Maxwell's Equations for the FD-TD Method Three-Dimensional Problem Formulation Two-Dimensional Problem Formulation One-Dimensional Problem Formulation Finite Differences and the Yee Algorithm Cell Size, Numerical Stability, and Dispersion Computer Algorithms and FD-TD Implementation Absorbing Boundary Conditions Source Conditions Source Functionality The Hard Source The Soft Source Total-Field/Scattered-Field Formulation Pure Scattered-Field Formulation Near Fields and Far Fields A Two-Dimensional Example: An -Plane Sectoral Horn Antenna Antenna Analysis and Applications Impedance, Efficiency, and Gain The Monopole over a PEC Ground Plane The Vivaldi Slotline Array Summary 542 References 542 Problems 543 Chapter 12 СЕМ for Antennas: High-Frequency Methods Geometrical Optics Wedge Diffraction Theory The Ray-Fixed Coordinate System A Uniform Theory of Wedge Diffraction Plane Analysis of Horn Antennas Cylindrical Parabolic Antenna Radiation by a Slot on a Finite Ground Plane Radiation by a Monopole on a Finite Ground Plane Equivalent Current Concepts A Multiple Diffraction Formulation Diffraction by Curved Surfaces Extension of Moment Methods Using the Geometrical Theory of Diffraction Physical Optics Method of Stationary Phase Physical Theory of Diffraction Cylindrical Parabolic Reflector Antenna-PTD Summary 612 References 613 Problems 614

7 xvi Contents Appendix A Tables of Commonly Used Frequencies 621 A.1 Radio Frequency Bands 621 A.2 Television Channel Frequencies 621 A.3 Mobile Telephone Bands 622 A.4 Radar Bands 622 Appendix В Data Material and Other Constants 623 B.l Conductivities of Good Conductors 623 B.2 Wire Data 623 B.3 Dielectric Constant: Permittivity 624 B.4 Permeability 624 B.5 Velocity of Light 624 B.6 Intrinsic Impedance of Free Space 624 Appendix С Vectors 625 C.l Unit Vector Representations 625 C.2 Vector Identities 625 C.3 Vector Differential Operators 626 Appendix D Trigonometric Relations 628 Appendix E Hyperbolic Relations 630 Appendix F Useful Mathematical Relations 631 F.l Dirac Delta Function 631 F.2 Binomial Theorem 631 F.3 Bessel Functions 631 F.4 Some Useful Integrals 632 Appendix G Computing Packages 633 G.l General Antenna Pagkage: APV 633 G.2 Array Plotting Package: PCARRPAT 633 G.3 Wire Antenna Code: WIRE 634 G.4 Parabolic Reflector Antenna Code: PRAC 634 G.5 Diffraction Codes 634 Appendix H Bibliography 636 Index 643

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