Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering

Transcription

1 Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering Second Edition Peter Russer ARTECH HOUSE BOSTON LONDON artechhouse.com

2 Contents Preface xvii Chapter 1 Introduction 1 References 6 Chapter 2 Basic Electromagnetics The Electromagnetic Field Concept Field Intensities Current and Flux Densities Constitutive Relations The Charge Density The Maxwell Puzzle The Integral Form of Maxwell's Equations The Electromagnetic Wave The Wave Equation The Polarization of Electromagnetic Waves KirchhofF's Laws Maxwell's Equations in Local Form Time-Harmonic Electromagnetic Fields Maxwell's Equations in the Frequency Domain Curvilinear Coordinates Boundary Conditions Problems 56 References 59 vii

3 Vltt Electromagnetics Chapter 3 Potentials and Waves The Electromagnetic Potentials The Helmholtz Equation Time-Harmonic Plane Waves Time-Harmonic Plane Waves in Lossless Medium Complex Waves TM and TE Fields and Waves Reflection and Transmission of Plane Waves Reflection and Diffraction of a TE Wave at a Plane Boundary Reflection and Diffraction of a TM Wave at a Plane Boundary Total Reflection Waves in Planar Layered Media Thin Conducting Sheets The Vector Wave Equation Circular Cylindrical Waves Excitation of a Cylindric Wave by a Uniform Current Filament Spherical Waves Problems 106 References 107 Chapter 4 Concepts, Methods, and Theorems Energy and Power Field Theoretic Formulation of Tellegen's Theorem Sources of the Electromagnetic Field The Uniqueness Theorem The Equivalence Principle Babinet's Principle Reciprocity The Lorentz Reciprocity Theorem The Reciprocity Theorem for Impressed Sources Green's Function The Integral Equation Method The Free-Space Green's Dyadic Form Green's Theorems The Scalar Green's Theorems Green's Theorems in Two Dimensions The Vector Green's Theorems Integral Formulation of the Equivalence Principle 141

4 Contents ix 4.13 The Sturm-Liouville Equation Spectral Representation of Green's Functions Problems 148 References 148 Chapter 5 Static and Quasistatic Fields Conditions for Static and Quasistatic Fields Static and Quasistatic Electric Fields Green's Function for the Static Electric Field Capacitance Static and Quasistatic Magnetic Fields Green's Function for the Static Magnetic Field Inductance The Laplace Equation Potential Separation Planes Three-Dimensional Laplace Equation in Cartesian Coordinates Conformal Mapping Field ofaneuipticcylindric Line Field ofacoaxial Line Parallel Wire Line The Schwarz-Christoffel Transformation The Coplanar Line The Coplanar Stripline The Stripline Problems 201 References 204 Chapter 6 Waves at the Surface of Conducting Media Transverse Magnetic Surface Waves Surface Currents Surface Current Losses 22" Induced Surface Currents Problems 227 References 228 Chapter 7 Transmission-Lines and Waveguides Introduction Phase and Group Velocity The Field Components Waveguides for Transverse Electromagnetic Waves 235

5 X Electromagnetics 7.5 Multiconductor Transmission-Lines Quasi-TEM Modes of Transmission-Lines Quasi-TEM Modes of Two-Conductor Transmission-Lines Quasi-TEM Modes of Multiconductor Transmission-Lines Planar Transmission-Lines The Microstrip Line Quasistatic Approximation for the Microstrip Line Coplanar Waveguide and Coplanar Stripline Hollow Waveguides TE Modes TM Modes Modal Expansions in Waveguides Rectangular Waveguides Transverse Electric Modes Transverse Magnetic Modes Power Flow in the Waveguide Orthogonality of the Waveguide Modes Generalized Currents and Voltages in Waveguides Attenuation Due to Conductor Losses Attenuation Due to Dielectric Losses Circular Cylindric Waveguides The Circular Waveguide Modes Power Flow and Attenuation in the TE 0 I Mode Radial Waveguides Radial Parallel Plate Waveguide Wedged Radial Parallel Plate Waveguide Spherical Waveguides Conical Waveguide Biconical Waveguide Dielectric Waveguides and Optical Fibers Homogeneous Planar Dielectric Waveguides Dielectric Slab with Single-Sided Metallization Circular Dielectric Waveguides with Step Index Profile Problems 329 References 333

6 Contents XI Chapter 8 The Transmission-Line Equations The Transmission-Line Concept Generalized Voltages and Currents Solution of the Transmission-Line Equations Wave Amplitudes Reflection Coefficient and Smith Chart Impedance Matching with Lumped Elements Impedance Matching with Stubs Solution of the Multiconductor Transmission-Line Equations Multimode Excitation of Uniform HoUow Waveguides The Transverse Field Equations Modal Field Representation Multimode Transmission-Line Equations for Hollow Waveguides Multimode Transmission-Line Equations of Lossless Waveguides without Internal Sources Green's Functions for Transmission-Lines Green's Function for the Transmission-Line with Matched Terminations Green's Function for the Transmission-Line with Arbitrary Linear Passive Terminations Problems 381 References 384 Chapter 9 Resonant Circuits and Resonators The Linear Passive One-Port The Reactance Theorem Resonant Circuits The Transmission-Line Resonator Cavity Resonators The Rectangular Cavity Resonator The Circular Cylindric Cavity Resonator Couplingof Resonant Circuits and Resonators The Loaded Quality Factor Termination of a Transmission-Line with a Resonant Circuit Inductive Couplingof Cavity Resonators Orthogonality of the Resonator Modes Excitation of Resonators by Internal Sources Problems 411

7 XU Electromagnetics References 412 Chapter 10 Passive Microwave Circuits Linear Multiports Source-Free Linear Multiports Impedance and Admittance Representations The Chain Matrix The Scattering Matrix The Transmission Matrix Tellegen's Theorem Connection Networks Tellegen's Theorem for Discretized Fields The Power Properties Reciprocal Multiports Elementary Two-Ports Signal Flow Graphs Lumped Element Equivalent Circuits Foster Representation of Reactance Multiports Cauer Representation of Radiating Structures Obstacles in Waveguides The Symmetry Properties of Waveguide Junctions Symmetrie Three-Port Waveguide Junctions Symmetrie Four-Port Waveguide Junctions Problems 463 References 466 Chapter 11 Periodic Structures and Filters Periodic Electromagnetic Structures TE Modes in Rectangular Periodic Waveguides Sinusoidal Variation of the Permittivity Wave Parameter Theory of Two-Ports Lumped Low-Pass Filter Prototypes The Butterworth Prototype The Chebyshev Prototype Ladder Filter Networks Butterworth Ladder Networks Chebyshev Ladder Networks Frequency Transformation Low-Pass to High-Pass Transformation Low-Pass to Band-Pass Transformation Low-Pass to Band-Stop Transformation 495

8 Contents xm 11.6 Transmission-Line with Periodic Load Plane Wave Scattering by Periodic Structures Scattering of TE Waves by Periodic Structures Scattering of TM Waves by Periodic Structures Metamaterials Problems 515 References 517 Chapter 12 Radiation from Dipoles The Hertzian Dipole Aperiodic Spherical Waves Vertically Oriented Electric Dipole over Lossy Half-Space The Far-Field of the Vertical Dipole over Ground The Surface Wave Horizontally Oriented Electric Dipole over Lossy Half-Space Problems 544 References 545 Chapter 13 Antennas Introduction Linear Antennas The Integral Equation for the Linear Antenna The Impedanceof the Linear Antenna The Loop Antenna Receiving Antennas The Hertzian Dipole as Receiving Antenna The Loop Antenna as Receiving Antenna The Linear Dipole Antenna as Receiving Antenna Gain and Effective Antenna Aperture Antenna Arrays Linear Antenna Arrays Circular Antenna Arrays Aperture Antennas Radiating Apertures Hörn Antennas Gain and Effective Area of Aperture Antennas Mirror and Lens Antennas Slot Antennas Microstrip Antennas Planar Rectangular Patch Antenna 593

9 XIV Electromagnetics Broadband Antennas Problems 597 References 601 Chapter 14 Numerical Electromagnetics Introduction The Methodof Moments The Transmission-Line Matrix Method The Mode Matching Method 617 References 623 Appendix A Vectors and Differential Forms 627 A.l Vectors 627 A.2 Differential Forms 631 A.2.1 Products of Exterior Differential Forms 632 A.2.2 The Contraction 633 A.2.3 The Exterior Derivative 634 A.2.4 The Laplace Operator 635 A.3 Stokes' Theorem 636 A.4 Curvilinear Coordinates 640 A.4.1 General Cylindrical Coordinates 646 A.4.2 Circular Cylindric Coordinates 647 A.4.3 Spherical Coordinates 650 A.4.4 Twisted Forms 653 A.4.5 Integration of Differential Forms by Pullback 653 A.5 Double Differential Forms 654 A.6 Relations between Exterior Calculus and Conventional Vector Notation 656 A.6.1 Differential Operators 656 A.6.2 Maxwell's Equations 656 References 657 Appendix B Special Functions 659 B.l Ordinary Bessel Functions 659 B.2 Modified Bessel Functions 662 B.3 Spherical Bessel Functions 665 B.4 Legendre Polynomials 667 B.5 Spherical Harmonics 670 References 672

10 Contents xv Appendix C Linear Algebra C.l Unitary Vector Space C.2 Diagonalization of a Matrix C.3 Matrix Functions C.4 The Hubert Space C.4.1 Linear Operators in Hubert Space C.4.2 Function Spaces C.4.3 Function Spaces with Biorthogonal Basis References Appendix D Fourier Series and Fourier Transform D.l The Fourier Series D.2 The Fourier Integral D.3 The Delta Distribution References Appendix E Complex Integration E.l Analytic Functions E.2 The Residue Theorem E.3 The Saddle-Point Method References List of Symbols 711 About the Author 717 Index 719