Electromagnetics. Theory, Techniques, and Engineering Paradigms

Transcription

1 Electromagnetics Theory, Techniques, and Engineering Paradigms

2 The photograph on the cover represents the Cassini-Huygens spacecraft, a joint NASA-ESA-ASI deep-space mission to image the surface and study the atmosphere of Saturn and its moons, in particular Titan. The spacecraft will reach Saturn in the year 2004 and is equipped with a large number of electromagnetic sensors, operating in the microwave, infrared, and visible range. On top ofthe spacecraft is a 4-meter parabolic dish with a dichroic subreflector operating in the S, X, Ku, and Ka bands. As James Clark Maxwell wrote, We, that is, all the work we have done As waves in ether shall forever run In ever widening spheres through heaven Beyond the sun

3 Electromagnetics Theory, Techniques, and Engineering Paradigms Giorgio Franceschetti University of Naples Naples, Italy, and University of California at Los Angeles Los Angeles, California Springer Science+Business Media, LLC

4 Library of Congress Catalogtng-1n-Publ(cation Data Franceschett 1, Giorgio. Electromagnetics : theory, techniques, and engineering paradigms / Giorgio Franceschett 1. p. cm. Includes bibliographical references and index. ISBN Electromagnetics. 2. Electromagnetics Industrial applications. 3. Electromagnetic theory. I. Title. QC760.F dc CIP ISBN DOI / ISBN (ebook) Springer Science+Business Media New York 1997 Originally published by Plenum Press, New York in 1997 Softcover reprint of the hardcover 1st edition All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfdming, recording, or otherwise, without written permission from the Publisher

5 To Professors Gaetano Latmiral and Charles H. Papas who profoundly changed my way of thinking

6 Preface During the last twenty years the lifestyle of a large portion of the inhabitants of our planet has changed dramatically. This would never have been possible without the massive use of electronic and photonic technology, telecommunications, and computers. These disciplines are designed to code, transmit, detect, decode, and process signals and related information, and can be broadly addressed as information science and technology. In the sophisticated society in which we live and operate, this science is diffused transversely and plays a major role in almost every human activity. Information science and technology is the basis of a powerful industry that does not suffer the shortcomings of more traditional human enterprises. Information is a renewable source and its control and processing rely on software codes, which are a creation of the mind, and on related hardware, incredibly sophisticated but made out of simple, abundant materials. The rate of change and transformation of this industry is the highest mankind has ever experienced, and it requires not only the replacement of technologies but also a continuous updating of expertise to keep up with the rapid transformation. There is no doubt that this calls for a change in university training, to avoid students graduating at an already obsolete level. There appears to be an increasing consensus that university courses in applied science should concentrate on basic issues, so that the student can gain a very broad scientific background, a sort of hard core that will remain valid throughout herjhis professional career. Among others, one of the basic disciplines is electromagnetics, which plays an important role in telecommunications, solid-state physics, remote sensing, electromagnetic compatibility, health hazards, and safety standards, to list some of the most popular areas. This book is an attempt to filter out of this broad range of material those topics most often encountered, and it can be used to provide the student with a basic background in applied electromagnetics during a two-semester graduate course. vh

7 viii PREFACE The volume contains nine chapters. The first two are devoted to the essentials of electromagnetic theory. The next four, Chapters 3-6, introduce tools, methods, and procedures for studying electromagnetic fields. The last three present again all the material from the perspective of the user, the applied scientist, who must rely on simple, sound models for the design of electromagnetic components and systems. Knowledge of theory and related techniques is believed to be a most desirable prerequisite for the subsequent overview of the whole subject from an engineering standpoint. A few details about the contents of each chapter now follow. Chapter 1 presents electromagnetic theory: Maxwell's equations, energy theorems, constitutive relationships, strictly in the time-domain. Many existing books on applied electromagnetics prefer the steady-state sinusoidal approach, but it is my understanding that this somehow abstract presentation does not favor the physics. The time-domain is a much more natural environment; also, recent broadband applications of the electromagnetic field strongly suggest its study. Chapter 2 is ancillary to the first chapter. It presents simple solutions of Maxwell equations for propagation and radiation, always in the time domain. Space and time discontinuities are considered, as well as moving sources. The case studies examined in this chapter, together with the basic material presented in the first chapter, should provide the reader with a bit more than just a flavor of electromagnetic theory. Chapter 3 is the first devoted to techniques used in solving the electromagnetic equations. It exploits Maxwell equations in the transformed spaces: the frequency, wavenumber, and frequency-wavenumber domains. Constitutive relations in frequency and wavenumber space, pulse propagation in dispersive media, and transient radiation are discussed. In addition the field representation is introduced, including the important issues of plane-wave expansion and its asymptotic evaluation. Chapter 4 addresses the problem of narrowband signals, largely used in telecommunications. Phasor fields are treated, exploiting polarization and coherence of the field, and providing solutions for guided propagation in complex media and radiation from elementary sources, apertures, and arrays. Chapter 5 deals with electromagnetic equations in the high-frequency regime. The transition from the wave-field to the ray-field description is used to derive optical and quasi-optical solutions for the propagation and scattering problems. Both canonical (half-plane) and application-oriented (guided propagation, reflectors) cases are discussed. Chapter 6 introduces some of the numerical techniques that form the basis of the electromagnetic solver packages: the method of moments, as well as the finite element and finite difference methods. No attempt is made to generate numerical codes; a book cannot compete with specialized, commercially available packages. However, the basic information provided by the chapter is

8 PREFACE ix in favor of numerical-technique understanding and usage, allowing a less blind use of electromagnetic solvers. Chapters 7-9 are devoted to propagation, radiation, and scattering from the application point of view. All the material previously treated is revisited and organized from a different perspective: simple models are employed, leading to equivalent circuits and (possibly scalar) performance parameters, to be used in the design of electromagnetic components and systems. Propagation (Chapter 7) is rephrased in terms of transmission line models and equivalent circuits of microwave junctions, and covers waveguides, striplines, fibers, and related circuits. Radiation (Chapter 8) is described in terms of simple transmitting and receiving parameters such as the gain and effective area, and covers wire antennas, apertures, reflectors, and arrays. Wave techniques as well as ray techniques (where appropriate) are exploited. Sampling techniques for efficient computation of the radiated field are presented as a first step in the synthesis problem. Cavities and scattering (Chapter 9) are studied by means of equivalent circuits, modal expansion, and statistical tools in the case of rough surfaces. All the chapters are organized in a number of sections and subsections, the latter developing details and case studies. This arrangement compares favorably with the conventional setup in which the exercises at the end of each chapter are often either simply numerical or so difficult as to scare the reader rather than interest him. A summary and very few references are added to each chapter, the aim being to stimulate curiosity and introduce the reader to a wider scientific arena. In the modern world of simply accessible large databases, exhaustive references can be obtained at the touch of one's fingers on any particular issue, and no conventional book can match this. Accordingly, the mission of the book and its inherent philosophy have been focused on providing the reader with the ability to select appropriate keywords in order to explore the available huge databases, and with the basic grammar to read, understand, and profit from the retrieved material. This has been the object in writing this book. Giorgio Franceschetti

9 Contents CHAPTER 1. Fundamentals 1.1. Maxwell Equations The Current Density Equation The Independence of Maxwell Equations The Lentz-Neumann Law Polarization and Magnetization Field Sources Source Power Constitutive Relationships Nonlinear Media Linear Anisotropic Media Anisotropic Media Classification Linear Dispersive Media. I Linear Dispersive Media. II Chiral Media Fields at Space and Time Boundaries 1.3. Energy and Momentum Electromagnetic Energy for Nonlinear Media Poynting's Theorem for Anisotropic Media Poynting's Theorem for Dispersive Media Lossless and Lossy Media The Radiation Pressure Initial and Boundary Conditions Electric and Magnetic Perfect Conductors The Radiation Condition The Edge Condition 1.5. Symmetry Properties Image Theory XI

10 xii CONTENTS The Duality Theorem for Inhomogeneous Media Summary and Selected References 42 References CHAPTER 2. Elementary Solutions 2.1. Plane Waves Lossy Media Anisotropic Media Plane Waves at Discontinuity Boundaries Conductive Media Bounded Waves Radiation from Prescribed Sources Elementary Sources Magnetic Sources Free-Space Green's Functions Vector and Scalar Potentials Radiation from Moving Sources 2.4. Summary and Selected References References CHAPTER 3. Spectral Domains 3.1. Preliminary Considerations Distributions and Dirac Functions The Frequency Domain Properties of Transformed Fields and Related Quantities Conductive Media Polar Dielectrics Magnetized Plasma Plane-Wave Propagation in Dispersive Media Plane-Wave Propagation in a Plasma Medium Plane-Wave Propagation in a Conductive Medium Plane Wave at a (Space) Discontinuity Boundary Radiation in Dispersive Media Scalar Green's Function Evaluation The Wavenumber Domain

11 CONTENTS Radiation from Prescribed Sources 3.4. The Wavenumber-Frequency Domain Space Dispersive Media. Compressible Plasma Radiation in Isotropic Homogeneous Media The Resonant Wave Solution Guided-Wave Representation The Field Representation Fields and the Plane-Wave Spectrum Relationship Asymptotic Evaluation of the Far Field Radiation from Apertures Gaussian Beams Summary and Selected References References xiii CHAPTER 4. Narrowband Signals and Phasor Fields 4.1. Narrowband Signals Phasor Evaluation Linear Operations on Phasors Response of a Linear Time-Invariant Circuit to a Narrowband Signal Quadratic Averages Power and Phasors Bandlimited Signals Almost Bandlimited Signals 4.2. Complex Vectors Scalar Product for Complex Vectors and Some of Their Properties Polarization States Stokes Parameters and the Poincare Sphere Field Coherence Maxwell Equations in Ph as or Form Poynting's Theorem The Energy Theorem Uniqueness Image Theory Duality Transformation Reciprocity The Equivalence Theorem Plane-Wave Propagation

12 xiv CONTENTS Propagation of a Gaussian Wavepacket in a Plasma Medium Information Scrambling through a Dispersive Channel Plane-Wave Propagation in a Magnetized Plasma Guided Propagation Oblique Incidence on a Dielectric Half-Space Guided Propagation along a Dielectric Slab Propagation inside a Parallel-Plate Guide Guided Propagation along Cylindrical Structures Radiation from Prescribed Sources The Elementary Electric Dipole The Elementary Magnetic Dipole The Elementary Huygens Source Radiation from Planar Sources Radiation from Linear Arrays Summary and Selected References 225 References CHAPTER 5. High-Frequency Fields 5.1. Asymptotic Form of Maxwell Equations The Transport Equation Rays in a Homogeneous Medium Ray Propagation in a Layered Medium Polarization Change along a Ray Ray Properties Reflector Antennas Lens Antennas Guided Propagation The Ray Coordinate System High-Frequency Propagation in a Homogeneous Environment Ray Amplitude at Reflection Boundaries: The Two-Dimensional Case Ray Amplitude at Reflection Boundaries: The Three-Dimensional Case Asymptotic Form of Field Representations Scattering by a Conducting Half-Plane The Edge Ray Transition Functions The Slope Diffraction Coefficient 277

13 CONTENTS The Lateral Ray The Creeping Ray Summary and Selected References References xv CHAPTER 6. The Numerical Domain 6.1. General Considerations Matrix Equations Matrix Inversion Eigenvalue Computation Matrix Condition 6.2. The Method of Moments The Electromagnetic Field Integral Equations Scattering by a Metal Strip The Finite Element Method Elements and Element Bases Guided-Wave Propagation Absorbing Boundary Conditions 6.4. The Finite Difference Method Stability and Numerical Dispersion FDM in the Frequency Domain 6.5. Summary and Selected References References CHAPTER 7. Engineering Topics: Propagation 7.1. General Considerations Transmission Lines The Telegraphists' Equations Reflection Coefficient and Impedance Matching Multisection Transmission Lines Nonuniform Transmission Lines Multiconductor Transmission Lines Transmission Line Generators Equivalent Transmission Lines: Two-Dimensional Structures Multilayer Propagation Transverse Resonance

14 xvi CONTENTS Propagation along a Grounded Slab Equivalent Transmission Lines: Three-Dimensional Structures The Rectangular Waveguide The Circular Waveguide The Coaxial Cable Mode Orthogonality and Power Flux Waveguide Excitation Waveguide Losses The Inhomogeneous Rectangular Waveguide The Fiber Planar Guiding Configurations The Effective Dielectric Constant 7.6. Equivalent Circuits Computation of Matrix Entries Junction Matrix Properties Shift of Port Position The Three-Port Junction The Four-Port Junction The Directional Coupler Periodic Structures Obstacles in Waveguides 7.7. Summary and Selected References References CHAPTER 8. Engineering Topics: Radiation 8.1. Transmitting and Receiving Antennas Reciprocity Theory and Antennas 8.2. Parameters of the Transmitting Antenna The Radiation Parameters of the Elementary Loop Antenna The Radiation Parameters of the Elementary Huygens Source Input Resistance of Elementary Antennas Antenna Beamwidth Mechanical Forces on Antennas Parameters of the Receiving Antenna Power and Polarization Matching The Radio Link Equation Effective Area of Elementary Antennas

15 CONTENTS xviii Noise Temperature of the Antenna Wire Antennas Short Antennas The Half-Wave Dipole Antenna The Traveling-Wave Antenna Mutual Impedance Aperture Antennas The Rectangular Aperture The Circular Aperture The Patch Antenna Reflector Antennas The Parabolic Dish Computation of the Reflector Radiation Diagram via the Current Integration Method Computation of the Reflector Radiation Diagram via Optical Techniques Arrays Array with Uniform Excitation Array with Tapered Excitation The Binomial Array Sum and Difference Patterns Summary and Selected References 499 References CHAPTER 9. Engineering Topics: Scattering 9.1. Interior Resonance The Parallelepiped Cavity The Loaded Coaxial Cavity Multimode Cavities Open Cavities Energy Decay in the Cavity Equivalent Circuit of the Cavity 9.2. Exterior Resonance Cylindrical Coordinates Spherical Coordinates Exterior Scattering via Asymptotic Techniques Rough Surfaces Scattering by a Planar Rough Surface Summary and Selected References References

16 XVIII CONTENTS APPENDIXES A. Vector Analysis..... B. Dyadic Analysis..... C. Useful Integrals and Series D. Special Functions and Asymptotic Evaluations INDEX

17 Electromagnetics Theory, Techniques, and Engineering Paradigms