Modern Antenna Design

THOMAS A. MILLIGAN is Chief Engineer for Milligan & Associates, Inc., a consulting firm that offers wireless communications solutions. He previously was principal engineer at Lockheed Martin Astronautics, where he specialized in microwave antenna design and analysis. Mr. Milligan is the author of the first edition of Modern Antenna Design and coauthor of Antenna Engineering Using Physical Optics.

• Preface xv1 Properties of Antennas 11-1 Antenna Radiation 21-2 Gain 31-3 Effective Area 61-4 Path Loss 61-5 Radar Range Equation and Cross Section 71-6 Why Use an Antenna? 91-7 Directivity 101-8 Directivity Estimates 111-8.1 Pencil Beam 111-8.2 Butterfly or Omnidirectional Pattern 131-9 Beam Efficiency 161-10 Input-Impedance Mismatch Loss 171-11 Polarization 181-11.1 Circular Polarization Components 191-11.2 Huygens Source Polarization 211-11.3 Relations Between Bases 221-11.4 Antenna Polarization Response 231-11.5 Phase Response of Rotating Antennas 251-11.6 Partial Gain 261-11.7 Measurement of Circular Polarization Using Amplitude Only 261-12 Vector Effective Height 271-13 Antenna Factor 291-14 Mutual Coupling Between Antennas 291.15 Antenna Noise Temperature 301-16 Communication Link Budget and Radar Range 351-17 Multipath 361-18 Propagation Over Soil 371-19 Multipath Fading 39References 402 Radiation Structures and Numerical Methods 422-1 Auxiliary Vector Potentials 432-1.1 Radiation from Electric Currents 442-1.2 Radiation from Magnetic Currents 492-2 Apertures: Huygens Source Approximation 512-2.1 Near- and Far-Field Regions 552-2.2 Huygens Source 572-3 Boundary Conditions 572-4 Physical Optics 592-4.1 Radiated Fields Given Currents 592-4.2 Applying Physical Optics 602-4.3 Equivalent Currents 652-4.4 Reactance Theorem and Mutual Coupling 662-5 Method of Moments 672-5.1 Use of the Reactance Theorem for the Method of Moments 682-5.2 General Moments Method Approach 692-5.3 Thin-Wire Moment Method Codes 712-5.4 Surface and Volume Moment Method Codes 712-5.5 Examples of Moment Method Models 722-6 Finite-Difference Time-Domain Method 762-6.1 Implementation 762-6.2 Central Difference Derivative 772-6.3 Finite-Difference Maxwell’s Equations 772-6.4 Time Step for Stability 792-6.5 Numerical Dispersion and Stability 802-6.6 Computer Storage and Execution Times 802-6.7 Excitation 812-6.8 Waveguide Horn Example 832-7 Ray Optics and the Geometric Theory of Diffraction 842-7.1 Fermat’s Principle 852-7.2 H -Plane Pattern of a Dipole Located Over a Finite Strip 852-7.3 E-Plane Pattern of a Rectangular Horn 872-7.4 H -Plane Pattern of a Rectangular Horn 892-7.5 Amplitude Variations Along a Ray 902-7.6 Extra Phase Shift Through Caustics 932-7.7 Snell’s Laws and Reflection 932-7.8 Polarization Effects in Reflections 942-7.9 Reflection from a Curved Surface 942-7.10 Ray Tracing 962-7.11 Edge Diffraction 962-7.12 Slope Diffraction 982-7.13 Corner Diffraction 992-7.14 Equivalent Currents 992-7.15 Diffraction from Curved Surfaces 99References 1003 Arrays 1023-1 Two-Element Array 1043-2 Linear Array of N Elements 1093-3 Hansen and Woodyard End-Fire Array 1143-4 Phased Arrays 1153-5 Grating Lobes 1173-6 Multiple Beams 1183-7 Planar Array 1203-8 Grating Lobes in Planar Arrays 1253-9 Mutual Impedance 1273-10 Scan Blindness and Array Element Pattern 1273-11 Compensating Array Feeding for Mutual Coupling 1283-12 Array Gain 1293-13 Arrays Using Arbitrarily Oriented Elements 133References 1354 Aperture Distributions and Array Synthesis 1364-1 Amplitude Taper and Phase Error Efficiencies 1374-1.1 Separable Rectangular Aperture Distributions 1394-1.2 Circularly Symmetrical Distributions 1404-2 Simple Linear Distributions 1404-3 Taylor One-Parameter Linear Distribution 1444-4 Taylor n Line Distribution 1474-5 Taylor Line Distribution with Edge Nulls 1524-6 Elliott’s Method for Modified Taylor Distribution and Arbitrary Sidelobes 1554-7 Bayliss Line-Source Distribution 1584-8 Woodward Line-Source Synthesis 1624-9 Schelkunoff’s Unit-Circle Method 1644-10 Dolph–Chebyshev Linear Array 1704-11 Villeneuve Array Synthesis 1724-12 Zero Sampling of Continuous Distributions 1734-13 Fourier Series Shaped-Beam Array Synthesis 1754-14 Orchard Method of Array Synthesis 1784-15 Series-Fed Array and Traveling-Wave Feed Synthesis 1884-16 Circular Apertures 1914-17 Circular Gaussian Distribution 1944-18 Hansen Single-Parameter Circular Distribution 1954-19 Taylor Circular-Aperture Distribution 1964-20 Bayliss Circular-Aperture Distribution 2004-21 Planar Arrays 2024-22 Convolution Technique for Planar Arrays 2034-23 Aperture Blockage 2084-24 Quadratic Phase Error 2114-25 Beam Efficiency of Circular Apertures with Axisymmetric Distribution 214References 2155 Dipoles  Slots  and Loops 2175-1 Standing-Wave Currents 2185-2 Radiation Resistance (Conductance) 2205-3 Babinet–Booker Principle 2225-4 Dipoles Located Over a Ground Plane 2235-5 Dipole Mounted Over Finite Ground Planes 2255-6 Crossed Dipoles for Circular Polarization 2315-7 Super Turnstile or Batwing Antenna 2345-8 Corner Reflector 2375-9 Monopole 2425-10 Sleeve Antenna 2425-11 Cavity-Mounted Dipole Antenna 2455-12 Folded Dipole 2475-13 Shunt Feeding 2485-14 Discone Antenna 2495-15 Baluns 2515-15.1 Folded Balun 2525-15.2 Sleeve or Bazooka Baluns 2535-15.3 Split Coax Balun 2555-15.4 Half-Wavelength Balun 2565-15.5 Candelabra Balun 2565-15.6 Ferrite Core Baluns 2565-15.7 Ferrite Candelabra Balun 2585-15.8 Transformer Balun 2585-15.9 Split Tapered Coax Balun 2595-15.10 Natural Balun 2605-16 Small Loop 2605-17 Alford Loop 2615-18 Resonant Loop 2635-19 Quadrifilar Helix 2645-20 Cavity-Backed Slots 2665-21 Stripline Series Slots 2665-22 Shallow-Cavity Crossed-Slot Antenna 2695-23 Waveguide-Fed Slots 2705-24 Rectangular-Waveguide Wall Slots 2715-25 Circular-Waveguide Slots 2765-26 Waveguide Slot Arrays 2785-26.1 Nonresonant Array 2795-26.2 Resonant Array 2825-26.3 Improved Design Methods 282References 2836 Microstrip Antennas 2856-1 Microstrip Antenna Patterns 2876-2 Microstrip Patch Bandwidth and Surface-Wave Efficiency 2936-3 Rectangular Microstrip Patch Antenna 2996-4 Quarter-Wave Patch Antenna 3106-5 Circular Microstrip Patch 3136-6 Circularly Polarized Patch Antennas 3166-7 Compact Patches 3196-8 Directly Fed Stacked Patches 3236-9 Aperture-Coupled Stacked Patches 3256-10 Patch Antenna Feed Networks 3276-11 Series-Fed Array 3296-12 Microstrip Dipole 3306-13 Microstrip Franklin Array 3326-14 Microstrip Antenna Mechanical Properties 333References 3347 Horn Antennas 3367-1 Rectangular Horn (Pyramidal) 3377-1.1 Beamwidth 3417-1.2 Optimum Rectangular Horn 3437-1.3 Designing to Given Beamwidths 3467-1.4 Phase Center 3477-2 Circular-Aperture Horn 3487-2.1 Beamwidth 3507-2.2 Phase Center 3527-3 Circular (Conical) Corrugated Horn 3537-3.1 Scalar Horn 3577-3.2 Corrugation Design 3577-3.3 Choke Horns 3587-3.4 Rectangular Corrugated Horns 3597-4 Corrugated Ground Plane 3597-5 Gaussian Beam 3627-6 Ridged Waveguide Horns 3657-7 Box Horn 3727-8 T-Bar-Fed Slot Antenna 3747-9 Multimode Circular Horn 3767-10 Biconical Horn 376References 3788 Reflector Antennas 3808-1 Paraboloidal Reflector Geometry 3818-2 Paraboloidal Reflector Aperture Distribution Losses 3838-3 Approximate Spillover and Amplitude Taper Trade-offs 3858-4 Phase Error Losses and Axial Defocusing 3878-5 Astigmatism 3898-6 Feed Scanning 3908-7 Random Phase Errors 3938-8 Focal Plane Fields 3968-9 Feed Mismatch Due to the Reflector 3978-10 Front-to-Back Ratio 3998-11 Offset-Fed Reflector 3998-12 Reflections from Conic Sections 4058-13 Dual-Reflector Antennas 4088-13.1 Feed Blockage 4108-13.2 Diffraction Loss 4138-13.3 Cassegrain Tolerances 4148-14 Feed and Subreflector Support Strut Radiation 4168-15 Gain/Noise Temperature of a Dual Reflector 4218-16 Displaced-Axis Dual Reflector 4218-17 Offset-Fed Dual Reflector 4248-18 Horn Reflector and Dragonian Dual Reflector 4278-19 Spherical Reflector 4298-20 Shaped Reflectors 4328-20.1 Cylindrical Reflector Synthesis 4338-20.2 Circularly Symmetrical Reflector Synthesis 4348-20.3 Doubly Curved Reflector for Shaped Beams 4378-20.4 Dual Shaped Reflectors 4398-21 Optimization Synthesis of Shaped and Multiple-Beam Reflectors 442References 4439 Lens Antennas 4479-1 Single Refracting Surface Lenses 4489-2 Zoned Lenses 4519-3 General Two-Surface Lenses 4549-4 Single-Surface or Contact Lenses 4599-5 Metal Plate Lenses 4619-6 Surface Mismatch and Dielectric Losses 4639-7 Feed Scanning of a Hyperboloidal Lens 4649-8 Dual-Surface Lenses 4659-8.1 Coma-Free Axisymmetric Dielectric Lens 4669-8.2 Specified Aperture Distribution Axisymmetric Dielectric Lens 4689-9 Bootlace Lens 4709-10 Luneburg Lens 472References 47210 Traveling-Wave Antennas 47410-1 General Traveling Waves 47510-1.1 Slow Wave 47810-1.2 Fast Waves (Leaky Wave Structure) 48010-2 Long Wire Antennas 48110-2.1 Beverage Antenna 48110-2.2 V Antenna 48210-2.3 Rhombic Antenna 48310-3 Yagi–Uda Antennas 48510-3.1 Multiple-Feed Yagi–Uda Antennas 49210-3.2 Resonant Loop Yagi–Uda Antennas 49510-4 Corrugated Rod (Cigar) Antenna 49710-5 Dielectric Rod (Polyrod) Antenna 49910-6 Helical Wire Antenna 50210-6.1 Helical Modes 50310-6.2 Axial Mode 50410-6.3 Feed of a Helical Antenna 50610-6.4 Long Helical Antenna 50710-6.5 Short Helical Antenna 50810-7 Short Backfire Antenna 50910-8 Tapered Slot Antennas 51210-9 Leaky Wave Structures 516References 51811 Frequency-Independent Antennas 521Spiral Antennas 52211-1 Modal Expansion of Antenna Patterns 52411-2 Archimedean Spiral 52611-3 Equiangular Spiral 52711-4 Pattern Analysis of Spiral Antennas 53011-5 Spiral Construction and Feeding 53511-5.1 Spiral Construction 53511-5.2 Balun Feed 53611-5.3 Infinite Balun 53811-5.4 Beamformer and Coaxial Line Feed 53811-6 Spiral and Beamformer Measurements 53811-7 Feed Network and Antenna Interaction 54011-8 Modulated Arm Width Spiral 54111-9 Conical Log Spiral Antenna 54311-10 Mode 2 Conical Log Spiral Antenna 54911-11 Feeding Conical Log Spirals 550Log-Periodic Antennas 55011-12 Log-Periodic Dipole Antenna 55111-12.1 Feeding a Log-Periodic Dipole Antenna 55611-12.2 Phase Center 55811-12.3 Elevation Angle 55911-12.4 Arrays of Log-Periodic Dipole Antennas 56011-13 Other Log-Periodic Types 56111-14 Log-Periodic Antenna Feeding Paraboloidal Reflector 56311-15 V Log-periodic Array 56711-16 Cavity-Backed Planar Log-Periodic Antennas 569References 57112 Phased Arrays 57312-1 Fixed Phase Shifters (Phasers) 57412-2 Quantization Lobes 57812-3 Array Errors 58012-4 Nonuniform and Random Element Existence Arrays 58212-4.1 Linear Space Tapered Array 58212-4.2 Circular Space Tapered Array 58412-4.3 Statistically Thinned Array 58712-5 Array Element Pattern 58812-6 Feed Networks 59012-6.1 Corporate Feed 59012-6.2 Series Feed 59212-6.3 Variable Power Divider and Phase Shifter 59212-6.4 Butler Matrix 59412-6.5 Space Feeding 59612-6.6 Tapered Feed Network with Uniform-Amplitude Subarrays 59712-7 Pattern Null Formation in Arbitrary Array 59912-8 Phased Array Application to Communication Systems 60112-9 Near-Field Measurements on Phased Arrays 602References 604Index 607