ANTENNA THEORY
Contents
Preface
About the Companion Website
1 Antennas
1.1 Introduction
1.2 Types of Antennas
1.2.1 Wire Antennas
1.2.2 Aperture Antennas
1.2.3 Microstrip Antennas
1.2.4 Array Antennas
1.2.5 Reflector Antennas
1.2.6 Lens Antennas
1.3 Radiation Mechanism
1.3.1 Single Wire
1.3.2 Two-Wires
1.3.3 Dipole
1.3.4 Computer Animation-Visualization of Radiation Problems
1.4 Current Distribution on a Thin Wire Antenna
1.5 Historical Advancement
1.5.1 Antenna Elements
1.5.2 Methods of Analysis
1.5.3 Some Future Challenges
1.6 Multimedia
References
2 Fundamental Parameters and Figures-of-Merit of Antennas
2.1 Introduction
2.2 Radiation Pattern
2.2.1 Radiation Pattern Lobes
2.2.2 Isotropic, Directional, and Omnidirectional Patterns
2.2.3 Principal Patterns
2.2.4 Field Regions
2.2.5 Radian and Steradian
2.3 Radiation Power Density
2.4 Radiation Intensity
2.5 Beamwidth
2.6 Directivity
2.6.1 Directional Patterns
2.6.2 Omnidirectional Patterns
2.7 Numerical Techniques
2.8 Antenna Efficiency
2.9 Gain, Realized Gain
2.10 Beam Efficiency
2.11 Bandwidth
2.12 Polarization
2.12.1 Linear, Circular, and Elliptical Polarizations
2.12.2 Polarization Loss Factor and Efficiency
2.13 Input Impedance
2.14 Antenna Radiation Efficiency
2.15 Antenna Vector Effective Length and Equivalent Areas
2.15.1 Vector Effective Length
2.15.2 Antenna Equivalent Areas
2.16 Maximum Directivity and Maximum Effective Area
2.17 Friis Transmission Equation and Radar Range Equation
2.17.1 Friis Transmission Equation
2.17.2 Radar Range Equation
2.17.3 Antenna Radar Cross Section
2.18 Antenna Temperature
2.19 Multimedia
References
Problems
3 Radiation Integrals and Auxiliary Potential Functions
3.1 Introduction
3.2 The Vector Potential A for an Electric Current Source J
3.3 The Vector Potential F for A Magnetic Current Source M
3.4 Electric and Magnetic Fields for Electric (J) and Magnetic (M) Current Sources
3.5 Solution of the Inhomogeneous Vector Potential Wave Equation
3.6 Far-Field Radiation
3.7 Duality Theorem
3.8 Reciprocity and Reaction Theorems
3.8.1 Reciprocity for Two Antennas
3.8.2 Reciprocity for Antenna Radiation Patterns
References
Problems
4 Linear Wire Antennas
4.1 Introduction
4.2 Infinitesimal Dipole
4.2.1 Radiated Fields
4.2.2 Power Density and Radiation Resistance
4.2.3 Radian Distance and Radian Sphere
4.2.4 Near-Field (kr โช 1) Region
4.2.5 Intermediate-Field (kr > 1) Region
4.2.6 Far-Field (kr โซ 1) Region
4.2.7 Directivity
4.3 Small Dipole
4.4 Region Separation
4.4.1 Far-Field (Fraunhofer) Region
4.4.2 Radiating Near-Field (Fresnel) Region
4.4.3 Reactive Near-Field Region
4.5 Finite Length Dipole
4.5.1 Current Distribution
4.5.2 Radiated Fields: Element Factor, Space Factor, and Pattern Multiplication
4.5.3 Power Density, Radiation Intensity, and Radiation Resistance
4.5.4 Directivity
4.5.5 Input Resistance
4.5.6 Finite Feed Gap
4.6 Half-Wavelength Dipole
4.7 Linear Elements Near or On Infinite Perfect Electric Conductors (PEC), Perfect Magnetic Conductors (PMC) and Electromagnetic Band-Gap (EBG) Surfaces
4.7.1 Ground Planes: Electric and Magnetic
4.7.2 Image Theory
4.7.3 Vertical Electric Dipole
4.7.4 Approximate Formulas for Rapid Calculations and Design
4.7.5 Mobile Communication Devices and Antennas for Mobile Communication Systems
4.7.6 Horizontal Electric Dipole
4.8 Ground Effects
4.8.1 Vertical Electric Dipole
4.8.2 Horizontal Electric Dipole
4.8.3 PEC, PMC and EBG Surfaces
4.8.4 Earth Curvature
4.9 Computer Codes
4.10 Multimedia
References
Problems
5 Loop Antennas
5.1 Introduction
5.2 Small Circular Loop
5.2.1 Radiated Fields
5.2.2 Small Loop and Infinitesimal Magnetic Dipole
5.2.3 Power Density and Radiation Resistance
5.2.4 Near-Field (kr โช 1) Region
5.2.5 Far-Field (kr โซ 1) Region
5.2.6 Radiation Intensity and Directivity
5.2.7 Equivalent Circuit
5.3 Circular Loop of Constant Current
5.3.1 Radiated Fields
5.3.2 Power Density, Radiation Intensity, Radiation Resistance, and Directivity
5.4 Circular Loop with Nonuniform Current
5.4.1 Arrays
5.4.2 Design Procedure
5.5 Ground and Earth Curvature Effects for Circular Loops
5.6 Polygonal Loop Antennas
5.7 Ferrite Loop
5.7.1 Radiation Resistance
5.7.2 Ferrite-Loaded Receiving Loop
5.8 Mobile Communication Systems Applications
5.9 Multimedia
References
Problems
6 Arrays: Linear, Planar, and Circular
6.1 Introduction
6.2 Two-Element Array
6.3 N-Element Linear Array: Uniform Amplitude and Spacing
6.3.1 Broadside Array
6.3.2 Ordinary End-Fire Array
6.3.3 Phased (Scanning) Array
6.3.4 Hansen-Woodyard End-Fire Array
6.4 N-Element Linear Array: Directivity
6.4.1 Broadside Array
6.4.2 Ordinary End-Fire Array
6.4.3 Hansen-Woodyard End-Fire Array
6.5 Design Procedure
6.6 N-Element Linear Array: Three-Dimensional Characteristics
6.6.1 N-Elements Along Z-Axis
6.6.2 N-Elements Along X- or Y-Axis
6.7 Rectangular-to-Polar Graphical Solution
6.8 N-Element Linear Array: Uniform Spacing, Nonuniform Amplitude
6.8.1 Array Factor
6.8.2 Binomial Array
6.8.3 Dolph-Tschebyscheff Array: Broadside
6.8.4 Tschebysheff Design: Scanning
6.9 Superdirectivity
6.9.1 Efficiency and Directivity
6.9.2 Designs with Constraints
6.10 Planar Array
6.10.1 Array Factor
6.10.2 Beamwidth
6.10.3 Directivity
6.11 Design Considerations
6.12 Circular Array
6.12.1 Array Factor
6.13 Multimedia
References
Problems
7 Antenna Synthesis and Continuous Sources
7.1 Introduction
7.2 Continuous Sources
7.2.1 Line-Source
7.2.2 Discretization of Continuous Sources
7.3 Schelkunoff Polynomial Method
7.4 Fourier Transform Method
7.4.1 Line-Source
7.4.2 Linear Array
7.5 Woodward-Lawson Method
7.5.1 Line-Source
7.5.2 Linear Array
7.6 Taylor Line-Source (Tschebyscheff-Error)
7.6.1 Design Procedure
7.7 Taylor Line-Source (One-Parameter)
7.8 Triangular, Cosine, and Cosine-Squared Amplitude Distributions
7.9 Line-Source Phase Distributions
7.10 Continuous Aperture Sources
7.10.1 Rectangular Aperture
7.10.2 Circular Aperture
7.11 Multimedia
References
Problems
8 Integral Equations, Moment Method, and Self and Mutual Impedances
8.1 Introduction
8.2 Integral Equation Method
8.2.1 Electrostatic Charge Distribution
8.2.2 Integral Equation
8.3 Finite Diameter Wires
8.3.1 Pocklingtonโs Integral Equation
8.3.2 Hallรฉnโs Integral Equation
8.3.3 Source Modeling
8.4 Moment Method Solution
8.4.1 Basis (Expansion) Functions
8.4.2 Weighting (Testing) Functions
8.5 Self-Impedance
8.5.1 Integral Equation-Moment Method
8.5.2 Induced EMF Method
8.6 Mutual Impedance Between Linear Elements
8.6.1 Integral Equation-Moment Method
8.6.2 Induced EMF Method
8.7 Mutual Coupling in Arrays
8.7.1 Coupling in the Transmitting Mode
8.7.2 Coupling in the Receiving Mode
8.7.3 Mutual Coupling on Array Performance
8.7.4 Coupling in an Infinite Regular Array
8.7.5 Active Element Pattern in an Array
8.8 Multimedia
References
Problems
9 Broadband Dipoles and Matching Techniques
9.1 Introduction
9.2 Biconical Antenna
9.2.1 Radiated Fields
9.2.2 Input Impedance
9.3 Triangular Sheet, Flexible and Conformal Bow-Tie, and Wire Simulation
9.4 Vivaldi Antenna
9.5 Cylindrical Dipole
9.5.1 Bandwidth
9.5.2 Input Impedance
9.5.3 Resonance and Ground Plane Simulation
9.5.4 Radiation Patterns
9.5.5 Equivalent Radii
9.6 Folded Dipole
9.7 Discone and Conical Skirt Monopole
9.8 Matching Techniques
9.8.1 Stub-Matching
9.8.2 Quarter-Wavelength Transformer
9.8.3 Baluns and Transformers
9.9 Multimedia
References
Problems
10 Traveling Wave and Broadband Antennas
10.1 Introduction
10.2 Traveling Wave Antennas
10.2.1 Long Wire
10.2.2 V Antenna
10.2.3 Rhombic Antenna
10.3 Broadband Antennas
10.3.1 Helical Antenna
10.3.2 Electric-Magnetic Dipole
10.3.3 Yagi-Uda Array of Linear Elements
10.3.4 Yagi-Uda Array of Loops
10.4 Multimedia
References
Problems
11 Frequency Independent Antennas, Antenna Miniaturization, and Fractal Antennas
11.1 Introduction
11.2 Theory
11.3 Equiangular Spiral Antennas
11.3.1 Planar Spiral
11.3.2 Conical Spiral
11.4 Log-Periodic Antennas
11.4.1 Planar and Wire Surfaces
11.4.2 Dipole Array
11.4.3 Design of Dipole Array
11.5 Fundamental Limits of Electrically Small Antennas
11.6 Antenna Miniaturization
11.6.1 Monopole Antenna
11.6.2 Patch Antennas
11.6.3 Antenna Miniaturization Using Metamaterials
11.7 Fractal Antennas
11.8 Multimedia
References
Problems
12 Aperture Antennas
12.1 Introduction
12.2 Field Equivalence Principle: Huygensโ Principle
12.3 Radiation Equations
Summary
12.4 Directivity
12.5 Rectangular Apertures
12.5.1 Uniform Distribution on an Infinite Ground Plane
12.5.2 Uniform Distribution in Space
12.5.3 TE10-Mode Distribution on an Infinite Ground Plane
12.5.4 Beam Efficiency
12.6 Circular Apertures
12.6.1 Uniform Distribution on an Infinite Ground Plane
12.6.2 TE11-Mode Distribution on an Infinite Ground Plane
12.6.3 Beam Efficiency
12.7 Design Considerations
12.7.1 Rectangular Aperture
12.7.2 Circular Aperture
12.8 Babinetโs Principle
12.9 Fourier Transforms in Aperture Antenna Theory
12.9.1 Fourier Transforms-Spectral Domain
12.9.2 Radiated Fields
12.9.3 Asymptotic Evaluation of Radiated Field
12.9.4 Dielectric-Covered Apertures
12.9.5 Aperture Admittance
12.10 Ground Plane Edge Effects: The Geometrical Theory of Diffraction
12.11 Multimedia
References
Problems
13 Horn Antennas
13.1 Introduction
13.2 E-Plane Sectoral Horn
13.2.1 Aperture Fields
13.2.2 Radiated Fields
13.2.3 Directivity
13.3 H-Plane Sectoral Horn
13.3.1 Aperture Fields
13.3.2 Radiated Fields
13.3.3 Directivity
13.4 Pyramidal Horn
13.4.1 Aperture Fields, Equivalent, and Radiated Fields
13.4.2 Directivity
13.4.3 Design Procedure
13.5 Conical Horn
13.6 Corrugated Horn
13.7 Aperture-Matched Horns
13.8 Multimode Horns
13.9 Dielectric-Loaded Horns
13.10 Phase Center
13.11 Multimedia
References
Problems
14 Microstrip and Mobile Communications Antennas
14.1 Introduction
14.1.1 Basic Characteristics
14.1.2 Feeding Methods
14.1.3 Methods of Analysis
14.2 Rectangular Patch
14.2.1 Transmission-Line Model
14.2.2 Cavity Model
14.2.3 Directivity
14.3 Circular Patch
14.3.1 Electric and Magnetic FieldsโTMzmnp
14.3.2 Resonant Frequencies
14.3.3 Design
14.3.4 Equivalent Current Densities and Fields Radiated
14.3.5 Conductance and Directivity
14.3.6 Resonant Input Resistance
14.4 Quality Factor, Bandwidth, and Efficiency
14.5 Input Impedance
14.6 Coupling
14.7 Circular Polarization
14.8 Arrays and Feed Networks
14.9 Antennas for Mobile Communications
14.9.1 Planar Inverted-F Antenna (PIFA)
14.9.2 Slot Antenna
14.9.3 Inverted-F Antenna (IFA)
14.9.4 Multiband Antennas for Mobile Units
14.10 Dielectric Resonator Antennas
14.10.1 Basic DRA Geometries
14.10.2 Methods of Analysis and Design
14.10.3 Cavity Model Resonant Frequencies (TE and TM Modes)
14.10.4 Hybrid Modes: Resonant Frequencies and Quality Factors
14.10.5 Radiated Fields
14.11 Multimedia
References
Problems
15 Reflector Antennas
15.1 Introduction
15.2 Plane Reflector
15.3 Corner Reflector
15.3.1 90โฆ Corner Reflector
15.3.2 Other Corner Reflectors
15.4 Parabolic Reflector
15.4.1 Front-Fed Parabolic Reflector
15.4.2 Cassegrain Reflectors
15.5 Spherical Reflector
15.6 Multimedia
References
Problems
16 Smart Antennas
16.1 Introduction
16.2 Smart-Antenna Analogy
16.3 Cellular Radio Systems Evolution
16.3.1 Omnidirectional Systems
16.3.2 Smart-Antenna Systems
16.4 Signal Propagation
16.5 Smart Antennasโ Benefits
16.6 Smart Antennasโ Drawbacks
16.7 Antenna
16.7.1 Array Design
16.7.2 Linear Array
16.7.3 Planar Array
16.8 Antenna Beamforming
16.8.1 Overview of Direction-Of-Arrival (DOA) Algorithms
16.8.2 Adaptive Beamforming
16.8.3 Mutual Coupling
16.8.4 Optimal Beamforming Techniques
16.9 Mobile Ad hoc Networks (MANETs)
16.9.1 Overview of Mobile Ad hoc NETworks (MANETs)
16.9.2 MANETs Employing Smart-Antenna Systems
16.10 Smart-Antenna System Design, Simulation, and Results
16.10.1 Design Process
16.10.2 Single ElementโMicrostrip Patch Design
16.10.3 Rectangular Patch
16.10.4 Array Design
16.10.5 4 ร 4 Planar Array versus 8 ร 8 Planar Array
16.10.6 Adaptive Beamforming
16.11 Beamforming, Diversity Combining, Rayleigh-Fading, and Trellis-Coded Modulation
16.12 Other Geometries
16.13 Multimedia
References
Problems
17 Antenna Measurements
17.1 Introduction
17.2 Antenna Ranges
17.2.1 Reflection Ranges
17.2.2 Free-Space Ranges
17.2.3 Compact Ranges
17.2.4 Near-Field/Far-Field Methods
17.3 Radiation Patterns
17.3.1 Instrumentation
17.3.2 Amplitude Pattern
17.3.3 Phase Measurements
17.4 Gain Measurements
17.4.1 Realized-Gain Measurements
17.4.2 Gain-Transfer (Gain-Comparison) Measurements
17.5 Directivity Measurements
17.6 Radiation Efficiency
17.7 Impedance Measurements
17.8 Current Measurements
17.9 Polarization Measurements
17.10 Scale Model Measurements
17.10.1 Gain (Amplitude) Measurements, Simulations and Comparisons
17.10.2 Echo Area (RCS) Measurements, Simulations and Comparisons
References
Appendix I: f(x) =sin(x)/x
Appendix II: fN(x) =|sin(Nx)/N sin(x)| N = 1, 3, 5, 10, 20
Appendix III: Cosine and Sine Integrals
Appendix IV: Fresnel Integrals
Appendix V: Bessel Functions
Appendix VI: Identities
Appendix VII: Vector Analysis
Appendix VIII: Method of Stationary Phase
Appendix IX: Television, Radio, Telephone, and Radar Frequency Spectrums
Index
EULA