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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley - IEEE
- Sprache: Englisch
Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell's equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems. Theory and Computation of Electromagnetic Fields, Second Edition: * Provides the foundation necessary for graduate students to learn and understand more advanced topics * Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates * Covers computational electromagnetics in both frequency and time domains * Includes new and updated homework problems and examples Theory and Computation of Electromagnetic Fields, Second Edition is written for advanced undergraduate and graduate level electrical engineering students. This book can also be used as a reference for professional engineers interested in learning about analysis and computation skills.
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Veröffentlichungsjahr: 2015
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Table of Contents
Cover
Title Page
Copyright
Preface
A Note about the second edition
Acknowledgments
Part I: Electromagnetic Field Theory
Chapter 1: Basic Electromagnetic Theory
1.1 Review of Vector Analysis
1.2 Maxwell's Equations in Terms of Total Charges and Currents
1.3 Constitutive Relations
1.4 Maxwell's Equations in Terms of Free Charges and Currents
1.5 Boundary Conditions
1.6 Energy, Power, and Poynting's Theorem
1.7 Time-Harmonic Fields
References
Problems
Chapter 2: Electromagnetic Radiation in Free Space
2.1 Scalar and Vector Potentials
2.2 Solution of Vector Potentials in Free Space
2.3 Electromagnetic Radiation in Free Space
2.4 Radiation by Surface Currents and Phased Arrays
References
Problems
Chapter 3: Electromagnetic Theorems and Principles
3.1 Uniqueness Theorem
3.2 Image Theory
3.3 Reciprocity Theorems
3.4 Equivalence Principles
3.5 Duality Principle
3.6 Aperture Radiation and Scattering
References
Problems
Chapter 4: Transmission Lines and Plane Waves
4.1 Transmission Line Theory
4.2 Wave Equations and General Solutions
4.3 Plane Waves Generated by a Current Sheet
4.4 Reflection and Transmission
4.5 Plane Waves in Anisotropic and Bi-Isotropic Media
References
Problems
Chapter 5: Fields and Waves in Rectangular Coordinates
5.1 Uniform Waveguides
5.2 Uniform Cavities
5.3 Partially Filled Waveguides and Dielectric Slab Waveguides
5.4 Field Excitation in Waveguides
5.5 Fields in Planar Layered Media
References
Problems
Chapter 6: Fields and Waves in Cylindrical Coordinates
6.1 Solution of Wave Equation
6.2 Circular and Coaxial Waveguides and Cavities
6.3 Circular Dielectric Waveguide
6.4 Wave Transformation and Scattering Analysis
6.5 Radiation by Infinitely Long Currents
References
Problems
Chapter 7: Fields and Waves in Spherical Coordinates
7.1 Solution of Wave Equation
7.2 Spherical Cavity
7.3 Biconical Antenna
7.4 Wave Transformation and Scattering Analysis
7.5 Addition Theorem and Radiation Analysis
References
Problems
Part II: Electromagnetic Field Computation
Chapter 8: The Finite Difference Method
8.1 Finite Differencing Formulas
8.2 One-Dimensional Analysis
8.3 Two-Dimensional Analysis
8.4 Yee's FDTD Scheme
8.5 Absorbing Boundary Conditions
8.6 Modeling of Dispersive Media
8.7 Wave Excitation and Far-Field Calculation
8.8 Summary
References
Problems
Chapter 9: The Finite Element Method
9.1 Introduction to the Finite Element Method
9.2 Finite Element Analysis of Scalar Fields
9.3 Finite Element Analysis of Vector Fields
9.4 Finite Element Analysis in the Time Domain
9.5 Discontinuous Galerkin Time-Domain Method
9.6 Absorbing Boundary Conditions
9.7 Some Numerical Aspects
9.8 Summary
References
Problems
Chapter 10: The Method of Moments
10.1 Introduction to the Method of Moments
10.2 Two-Dimensional Analysis
10.3 Three-Dimensional Analysis
10.4 Analysis of Periodic Structures
10.5 Analysis of Microstrip Antennas and Circuits
10.6 The Moment Method in the Time Domain
10.7 Summary
References
Problems
Chapter 11: Fast Algorithms and Hybrid Techniques
11.1 Introduction to Fast Algorithms
11.2 Conjugate Gradient–FFT Method
11.3 Adaptive Integral Method
11.4 Fast Multipole Method
11.5 Adaptive Cross-Approximation Algorithm
11.6 Introduction to Hybrid Techniques
11.7 Hybrid Finite Difference–Finite Element Method
11.8 Hybrid Finite Element–Boundary Integral Method
11.9 Summary
References
Problems
Chapter 12: Concluding Remarks on Computational Electromagnetics
12.1 Overview of Computational Electromagnetics
12.2 Applications of Computational Electromagnetics
12.3 Challenges in Computational Electromagnetics
References
Appendix A: Vector Identities, Integral Theorems, and Coordinate Transformation
A.1 Vector Identities
A.2 Integral Theorems
A.3 Coordinate Transformation
Appendix B: Bessel Functions
B.1 Definition
B.2 Series Expressions
B.3 Integral Representation
B.4 Asymptotic Expressions
B.5 Recurrence and Derivative Relations
B.6 Symmetry Relations
B.7 Wronskian Relation
B.8 Useful Integrals
Appendix C: Modified Bessel Functions
C.1 Definition
C.2 Series Expressions
C.3 Integral Representations
C.4 Asymptotic Expressions
C.5 Recurrence and Derivative Relations
C.6 Symmetry Relations
C.7 Wronskian Relation
C.8 Useful Integrals
Appendix D: Spherical Bessel Functions
D.1 Definition
D.2 Series Expressions
D.3 Asymptotic Expressions
D.4 Recurrence and Derivative Relations
D.5 Symmetry Relations
D.6 Wronskian Relation
D.7 Riccati–Bessel Functions
D.8 Modified Spherical Bessel Functions
Appendix E: Associated Legendre Polynomials
E.1 Definition
E.2 Series Expression
E.3 Special Values
E.4 Symmetry Relations
E.5 Recurrence and Derivative Relations
E.6 Orthogonal Relations
E.7 Fourier–Legendre Series
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Basic Electromagnetic Theory
Figure 1.1
Figure 1.2 Relationship between Maxwell's equations in integral and differential forms and boundary conditions.
Figure 1.3 A rectangular frame across a discontinuous interface.
Figure 1.4 A pillbox across a discontinuous interface.
Figure 1.5
Figure 1.6
Figure 1.7 Three concentric conducting spherical shells.
Figure 1.8 An infinitely long conductor with an offset hole
Figure 1.9 A dielectric slab inserted between two parallel plates.
Figure 1.10 A section of a rectangular waveguide.
Figure 1.11 A filament of electric current placed in a circular cavity.
Figure 1.12 An open rectangular waveguide radiating into free space.
Figure 1.13 A section of a coaxial waveguide.
Chapter 2: Electromagnetic Radiation in Free Space
Figure 2.1 Two approaches to calculating radiated fields from sources.
Figure 2.2 Radiation of an infinitesimal electric dipole in free space.
Figure 2.3 Field radiated by an infinitesimal dipole ( Am in a region. (a) Real part of (Vm). (b) Imaginary part of (Vm). (c) Real part of (Vm). (d) Imaginary part of (Vm). (e) Real part of (Vm). (f) Imaginary part of (Vm).
Figure 2.4 Radiation of a finite electric dipole in free space.
Figure 2.5 Far-field radiation patterns of finite electric dipoles of different lengths. (a) . (b) . (c) . (d) .
Figure 2.6 For a far-field observation point, and are practically parallel to each other.
Figure 2.7 Radiation of a circular electric current loop in free space.
Figure 2.8 A rectangular surface current coincident with the -plane.
Figure 2.9 Normalized radiated field of a surface current in the upper half-space. (a) and . (b) and .
Figure 2.10 Normalized radiated field of a uniformly distributed surface current in the upper half-space for two cases. (a) . (b) .
Figure 2.11 A rectangular phased array of dipoles in the -plane.
Figure 2.12 Normalized array factor in the upper half-space for two arrays with uniform excitation. (a) and . (b) and .
Figure 2.13 (a) Helmholtz coil. (b) Maxwell coil.
Figure 2.14 A small rectangular loop in the -plane.
Chapter 3: Electromagnetic Theorems and Principles
Figure 3.1 A volume with electric and magnetic current sources.
Figure 3.2 Image of a vertical electric dipole above a PEC ground plane. (a) Original problem. (b) Equivalent problem.
Figure 3.3 Variables and unit vectors associated with a field point at the -plane.
Figure 3.4 Image of a horizontal electric dipole above a PEC ground plane. (a) Original problem. (b) Equivalent problem.
Figure 3.5 Images of electric and magnetic dipoles above a PEC ground plane.
Figure 3.6 Images of electric and magnetic dipoles above a PMC ground plane.
Figure 3.7 Examples of image placement. (a) A vertical electric current element in a right-angled conducting wedge. (b) A horizontal electric current line in a -angled conducting wedge. (c) A tilted electric current element between two conducting planes. (There are an infinite number of images and only seven nearby images are shown.)
Figure 3.8 An electric current element placed tangentially on the surface of an electric conductor.
Figure 3.9 An antenna excited by an electric current element and a dipole placed at the observation point.
Figure 3.10 Illustration of the surface equivalence principle. (a) Original problem. (b) Equivalent problem for the exterior field.
Figure 3.11 Equivalent problems. (a) With a zero interior field. (b) With the interior region filled with perfect electric conductor. (c) With the interior region filled with perfect magnetic conductor.
Figure 3.12 Illustration of the physical equivalent for scattering by a conducting object. (a) Original problem. (b) Equivalent problem.
Figure 3.13 Illustration of the physical optics approximation.
Figure 3.14 Illustration of the induction theorem for scattering by a conducting object. (a) Original problem. (b) Equivalent problem.
Figure 3.15 Illustration of the induction theorem with an image theory approximation.
Figure 3.16 Equivalent problems for scattering by a dielectric object. (a) Original problem. (b) Equivalent problem for the exterior field. (c) Equivalent problem for the interior field.
Figure 3.17 Illustration of the induction theorem for scattering by a dielectric object. (a) Original problem. (b) Equivalent problem.
Figure 3.18 Radiation through an aperture in a conducting screen. (a) Original problem. (b) Equivalent half-space problem with an electric ground plane for the field in the right half-space. (c) Equivalent free-space problem for the field in the right half-space.
Figure 3.19 Radiation from a rectangular waveguide opening onto an infinitely large ground plane. (a) Geometry. (b) Radiation pattern.
Figure 3.20 Radiation through a virtual planar surface to the right half-space. (a) Original problem. (b) Equivalent free-space problem for the field in the right half-space.
Figure 3.21 Equivalent problems for the problem in Figure 3.20a. (a) Equivalent half-space problem with an electric ground plane for the field in the right half-space. (b) Equivalent free-space problem for the field in the right half-space.
Figure 3.22 Equivalent problems for the problem in Figure 3.20a. (a) Equivalent half-space problem with a magnetic ground plane for the field in the right half-space. (b) Equivalent free-space problem for the field in the right half-space.
Figure 3.23 Illustration of Babinet's principle. (a) A source radiating in free space. (b) The same source radiating through an aperture in a conducting screen. (c) The same source radiating in the presence of a magnetically conducting plate. (d) The dual source radiating in the presence of an electrically conducting plate in the dual medium.
Figure 3.24 Complementary structures. (a) An aperture antenna. (b) The complementary conducting flat plate antenna.
Figure 3.25 A circular current loop placed above a PEC ground plane and next to a vertical PMC ground plane.
Figure 3.26 An electric current element placed inside a metallic rectangular waveguide.
Figure 3.27 Two antennas in the presence of a conducting obstacle.
Figure 3.28 A cylindrical dipole antenna and its equivalent model.
Figure 3.29 A two-port network. (a) With current sources. (b) With voltage sources.
Figure 3.30 An annular slot in an infinitely large perfectly conducting sheet in the -plane.
Figure 3.31 A narrow slot in an infinitely large conducting plane placed in the -plane.
Chapter 4: Transmission Lines and Plane Waves
Figure 4.1 Equivalent circuit of a segment of a transmission line.
Figure 4.2 Reflection by and transmission through a joint between two semi-infinite transmission lines.
Figure 4.3 Reflection on a transmission line terminated by an impedance load.
Figure 4.4 Transmission line excited by a distributed current source.
Figure 4.5 Locations of the poles of the integrand .
Figure 4.6 Locations of the two poles in the complex plane and the closed contour for integration.
Figure 4.7 Group velocity and phase velocity .
Figure 4.8 Direction of the electric field for a linear polarization.
Figure 4.9 Right- and left-hand elliptical polarizations.
Figure 4.10 General right- and left-hand elliptical polarizations.
Figure 4.11 Infinitely large current sheet in the -plane.
Figure 4.12 Plane wave incident normally on an interface.
Figure 4.13 Perpendicular polarized plane wave incident obliquely on an interface.
Figure 4.14 Parallel polarized plane wave incident obliquely on an interface.
Figure 4.15 Reflection and transmission coefficients for an interface between two dielectric media with and , respectively. (a) Perpendicular polarization. (b) Parallel polarization.
Figure 4.16
Figure 4.17
Figure 4.18 Plane wave transmitted into a left-handed medium.
Figure 4.19 Field produced by a point source refocused by a left-handed medium slab.
Figure 4.20
Figure 4.21 Transmission through a Polaroid.
Figure 4.22 Transmission through a quarter-wave plate.
Figure 4.23 Plane wave transmitted from air into a uniaxial medium.
Figure 4.24 Plane wave propagation in a uniaxial medium. (a) Ordinary wave. (b) Extraordinary wave.
Figure 4.25 Transmission through a gyrotropic medium—Faraday rotation.
Figure 4.26 Elliptically polarized wave rotating in the -plane and propagating in the -direction.
Figure 4.27
Figure 4.28 Dispersion diagram of a periodic array of dielectric slabs having a period length of , a thickness of , and a relative permittivity of , with waves propagating in the -direction. The shaded regions represent bandgaps.
Figure 4.29
Figure 4.30 Semi-infinite transmission line with a voltage source.
Figure 4.31 Finite transmission line with a current source.
Figure 4.32 Transmission line excited by a distributed voltage source.
Figure 4.33 Transmission line terminated by an impedance load.
Figure 4.34 An infinitely large current sheet placed in front of an infinitely large PEC plane.
Figure 4.35 Experimental setup of a Polaroid, a quarter-wave plate, and another Polaroid.
Figure 4.36 Experimental setup of a Polaroid, a quarter-wave plate, and a PEC reflector.
Figure 4.37 Plane wave reflection by a PEC-backed dielectric slab for parallel polarization.
Figure 4.38 Plane wave reflection by and transmission through a periodic dielectric slab.
Chapter 5: Fields and Waves in Rectangular Coordinates
Figure 5.1 Uniform waveguide of an arbitrary cross section.
Figure 5.2 Uniformly filled rectangular waveguide.
Figure 5.3 Cutoff frequency distribution for a 2:1 rectangular waveguide.
Figure 5.4 Transverse field distribution of the first 30 modes in a 2:1 rectangular waveguide.
Figure 5.5 Surface current on the wall of a rectangular waveguide for the TE
10
mode.
Figure 5.6 Ray picture of the TE
10
mode propagation in a rectangular waveguide.
Figure 5.7 Uniformly filled rectangular cavity.
Figure 5.8 Ray picture of the mode resonating in a rectangular cavity.
Figure 5.9 Material perturbation in a cavity. (a) Original cavity. (b) Perturbed cavity.
Figure 5.10 Geometry perturbation in a cavity. (a) Original cavity. (b) Perturbed cavity.
Figure 5.11 Rectangular waveguide filled with two homogeneous media.
Figure 5.12 Dispersion curves of the hybrid modes in a half-filled rectangular waveguide with , , and .
Figure 5.13 Ground-backed dielectric slab waveguide.
Figure 5.14 Dispersion curves of the first few modes in a ground-backed dielectric slab waveguide.
Figure 5.15 Ray picture of wave propagation in a dielectric slab waveguide backed by a ground plane.
Figure 5.16 Field excitation by a surface current source in a waveguide.
Figure 5.17 Rectangular waveguide excited by a current probe placed at and .
Figure 5.18 Field excitation by a volumetric current source in a waveguide.
Figure 5.19 Vertical electric dipole above a layered medium.
Figure 5.20 Horizontal electric dipole above a layered medium.
Figure 5.21 Dipoles on the top of a dielectric slab backed by a ground plane.
Figure 5.22 Dielectric slab waveguide.
Chapter 6: Fields and Waves in Cylindrical Coordinates
Figure 6.1 Uniformly filled circular waveguide.
Figure 6.2 Transverse field distribution of the first 30 modes in a circular waveguide.
Figure 6.3 Uniformly filled coaxial waveguide.
Figure 6.4 Uniformly filled circular cavity.
Figure 6.5 Circular dielectric waveguide. (a) Two-layered dielectric waveguide. (b) Simplified model.
Figure 6.6 Dispersion curves of the first several waveguide modes in a circular dielectric waveguide with and .
Figure 6.7 Illustration of the cylindrical wave transformation. The plots show the real part of the right-hand side of Equation (6.4.6) when the summation is evaluated from to . Clearly, a plane wave is formed in a region by increasing the number of terms in the summation. (a) . (b) . (c) . (d) . (e) . (f) .
Figure 6.8 Plane-wave scattering by a circular conducting cylinder.
Figure 6.9 Echo width of a circular conducting cylinder as a function of its normalized radius.
Figure 6.10 Scattering by a circular conducting cylinder with a radius of . (a) Snapshot of the scattered field . (b) Snapshot of the scattered field . (c) Snapshot of the total field . (d) Snapshot of the total field . (e) Scattering width for the TM case. (f) Scattering width for the TE case. The values of the fields are normalized by the magnitude of their respective incident fields.
Figure 6.11 Plane-wave scattering by a circular dielectric cylinder.
Figure 6.12 Scattering by a circular dielectric cylinder with a radius of and a relative permittivity of 4.0. (a) Snapshot of the scattered field . (b) Snapshot of the scattered field . (c) Snapshot of the total field . (d) Snapshot of the total field . (e) Scattering width for the TM case. (f) Scattering width for the TE case. The values of the fields are normalized by the magnitude of their respective incident fields.
Figure 6.13 Plane-wave scattering by a multilayer dielectric cylinder.
Figure 6.14 Plane-wave scattering by a multilayer dielectric cylinder containing a conducting cylinder inside the innermost layer.
Figure 6.15 Radiation by an infinitely long line current along the -axis.
Figure 6.16 Radiation by a cylindrical surface current.
Figure 6.17 Illustration of the addition theorem for the Hankel function. The plots show the real part of the right-hand side of Equation (6.5.32) in a region when the summation is evaluated from to . Clearly, an off-centered cylindrical wave is formed by increasing the number of terms in the summation. (a) . (b) . (c) . (d) . (e) . (f) .
Figure 6.18 Radiation by a cylindrical surface current in the presence of a conducting cylinder. (a) Three-dimensional view. (b) Cross-sectional view.
Figure 6.19 Radiation by an infinitely long line current in the presence of a conducting cylinder.
Figure 6.20 Radiation of an electric line current ( A) placed away from a conducting cylinder with a radius of . (a) Snapshot of the scattered field (Vm). (b) Snapshot of the total field (Vm).
Figure 6.21 Radiation by an infinitely long line current in the presence of a conducting wedge.
Figure 6.22 Snapshots of the field radiated by a line current in the presence of a -angled conducting wedge. (a) (Vm) produced by an electric current ( A) placed above the wedge. (b) (Am) produced by a magnetic current ( V) placed above the wedge. (c) (Vm) produced by an electric current ( A) placed above the wedge. (d) (Am) produced by a magnetic current ( V) placed above the wedge.
Figure 6.23 Field singularity (arbitrary unit) around the edge of a conducting wedge.
Figure 6.24 Radiation by an infinitesimally short dipole in the presence of a conducting cylinder.
Figure 6.25 Uniformly filled half-circular waveguide.
Figure 6.26 Uniformly filled circular waveguide with a conducting strip.
Figure 6.27 Infinitely long dielectric coated circular conducting cylinder.
Figure 6.28 Plane-wave scattering by a conducting half-cylinder placed on an infinitely large conducting ground.
Figure 6.29 Line current radiating in the presence of a conducting half-cylinder placed on an infinitely large conducting ground.
Figure 6.30 Shielded cylindrical surface current loaded with a dielectric cylinder.
Chapter 7: Fields and Waves in Spherical Coordinates
Figure 7.1 Uniformly filled spherical cavity.
Figure 7.2 Biconical antenna. (a) Infinitely long model. (b) Finite model. The dashed line shows a fictitious spherical surface coinciding with the top and bottom surfaces of the biconical antenna.
Figure 7.3 Radiation by a biconical antenna with an internal half-angle of in a region with a radius of . (a) Snapshot of the magnetic field of the TEM mode radiated by an infinitely long biconical antenna. (b) Snapshot of the magnetic field radiated by a truncated finite biconical antenna with .
Figure 7.4 Illustration of the spherical wave transformation. The plots show the real part of the right-hand side of Equation (7.4.11) when the summation is evaluated from to . Clearly, a plane wave is formed in a region by increasing the number of terms in the summation. (a) . (b) . (c) . (d) . (e) . (f) .
Figure 7.5 Plane-wave scattering by a conducting sphere.
Figure 7.6 Scattering by a conducting sphere with a radius of . (a) Snapshot of the scattered magnetic field in the E-plane. (b) Snapshot of the scattered electric field in the H-plane. (c) Snapshot of the total magnetic field in the E-plane. (d) Snapshot of the total electric field in the H-plane. (e) Magnitude of the total magnetic field in the E-plane. (f) Magnitude of the total electric field in the H-plane. The values of the fields are normalized by the magnitude of the incident electric field.
Figure 7.7 Bistatic RCS of a conducting sphere for the angle of incidence . (a) In the E-plane. (b) In the H-plane.
Figure 7.8 Monostatic RCS of a conducting sphere as a function of its normalized radius.
Figure 7.9 Plane-wave scattering by a dielectric sphere.
Figure 7.10 Scattering by a dielectric sphere with a radius of and a relative permittivity of 2.56. (a) Snapshot of the scattered magnetic field in the E-plane. (b) Snapshot of the scattered electric field in the H-plane. (c) Snapshot of the total magnetic field in the E-plane. (d) Snapshot of the total electric field in the H-plane. (e) Magnitude of the total magnetic field in the E-plane. (f) Magnitude of the total electric field in the H-plane. The values of the fields are normalized by the magnitude of the incident electric field.
Figure 7.11 Bistatic RCS of a dielectric sphere with a relative permittivity of 2.56 for the angle of incidence . (a) In the E-plane. (b) In the H-plane.
Figure 7.12 Monostatic RCS of a dielectric sphere with a relative permittivity of 2.56 as a function of its normalized radius.
Figure 7.13 Plane-wave scattering by a multilayer dielectric sphere.
Figure 7.14 Plane-wave scattering by a multilayer dielectric sphere containing a conducting core.
Figure 7.15 Point charge placed on the
z
-axis. The dashed line shows a fictitious spherical surface intersecting the point charge.
Figure 7.16 Illustration of the addition theorem for the spherical Hankel function. The plots show the real part of the right-hand side of Equation (7.5.14) in a region when the summation is evaluated from to . Clearly, an off-centered spherical wave is formed by increasing the number of terms in the summation. (a) . (b) . (c) . (d) . (e) . (f) .
Figure 7.17 Axisymmetric spherical surface current in free space.
Figure 7.18 Field radiated by a circular current loop having a uniform current of 1 A and a radius of . (a) Snapshot of . (b) Magnitude of .
Figure 7.19 Magnetic field lines of a spherical surface current with .
Figure 7.20 Spherical surface current loaded with a sphere. (a) A conducting core. (b) A dielectric core.
Figure 7.21 Field radiated by a circular current loop having a uniform current of 1 A and a radius of in the presence of a conducting sphere with a radius of . (a) Snapshot of . (b) Magnitude of .
Figure 7.22 Spherical surface current radiating in the presence of an infinitely long conducting cone.
Figure 7.23 Field singularity (arbitrary unit) around the tip of a conducting cone.
Figure 7.24 Electric dipole on the top of a conducting sphere.
Figure 7.25 Hemispherical cavity. (a) Horizontally placed. (b) Vertically placed.
Figure 7.26 Infinitely long conducting cone as a nonuniform circular waveguide. (a) For waves propagating along the positive -axis. (b) For waves propagating along the negative -axis.
Figure 7.27 Infinitely long horn as a nonuniform waveguide.
Figure 7.28 Finite circular horn antenna. The dashed line shows a fictitious spherical surface coinciding with the opening of the horn.
Figure 7.29 Slotted infinitely long conducting cone.
Chapter 8: The Finite Difference Method
Figure 8.1 Finite difference approximation.
Figure 8.2 Uniformly divided one-dimensional domain.
Figure 8.3 Finite difference mesh of a two-dimensional domain.
Figure 8.4 Numerical phase error in degrees per wavelength as a function of the wave propagation direction.
Figure 8.5 (a) Finite difference mesh for Yee's FDTD algorithm. (b) Assignment of the field components on an FDTD cell.
Figure 8.6 FDTD discretization of a three-dimensional domain. (a) A computational domain discretized into many rectangular cells. (b) Assignment of the field components on an FDTD cell for Yee's FDTD algorithm.
Figure 8.7 Variation of the numerical phase error in degrees per wavelength as a function of the wave propagation direction for two mesh densities. (a) . (b) .
Figure 8.8 Plane wave incident on the
yz
-plane.
Figure 8.9 Illustration of the computational domain truncated by absorbing and Neumann boundaries for the problem of a line source radiating in front of an infinitely large conducting plane.
Figure 8.10 Snapshots of the electric field radiated by the line current radiating in front of an infinitely large conducting plane.
Figure 8.11 Plane wave incident on the interface between the upper and lower half-spaces.
Figure 8.12 Computational domain truncated using the conductor-backed PMLs.
Figure 8.13 Axial, sagittal, and coronal slices of the head model used in the FDTD calculation. (
Source
: After Chen et al. [12], Copyright ©1998 IEEE.)
Figure 8.14 SAR (W/Kg) distribution in the axial, sagittal, and coronal slices at 256 MHz. (
Source
: Chen et al. [12], Copyright ©1998 IEEE.)
Figure 8.15 Magnetic field (A/m) distribution in the axial, sagittal, and coronal slices at 256 MHz. (
Source
: Chen et al. [12], Copyright ©1998 IEEE.)
Figure 8.16 Typical setup for FDTD simulation of scattering problems. A total/scattered field interface is introduced as a Huygens’ surface to excite the incident field in the total-field region. A near-to-far-field transformation is employed to calculate far fields based on the near fields on the surface.
Figure 8.17 Scattering of a TM-polarized, modulated Gaussian pulse by a square conducting cylinder. (a) Snapshot of the scattered electric field. (b) Snapshot of the total electric field.
Figure 8.18 (a) Shielded microstrip line. (b) Dielectric loaded waveguide.
Chapter 9: The Finite Element Method
Figure 9.1 One-dimensional domain subdivided into linear elements.
Figure 9.2 One-dimensional linear basis functions.
Figure 9.3 Finite element mesh with (a) triangular elements and (b) tetrahedral elements (only the surface mesh is shown here for clarity).
Figure 9.4 Linear triangular element.
Figure 9.5 Basis function for linear triangular elements.
Figure 9.6 Finite element mesh with elements and nodes numbered.
Figure 9.7 Two-dimensional model of a shielded 16-element birdcage coil loaded with the human head.
Figure 9.8 Magnitude of the magnetic field inside the loaded birdcage coil at four different frequencies. (
Source
: Jin and Chen [10], Copyright ©1997 ISMRM.)
Figure 9.9 Magnitude of the scattered magnetic field for a plane wave incident from the left to right and scattered by a conducting airfoil.
Figure 9.10 Snapshot of the radiated field by a two-dimensional waveguide-fed horn antenna excited by the first mode.
Figure 9.11 Vector basis function for a linear triangular element.
Figure 9.12 Vector basis function for linear triangular elements.
Figure 9.13 Finite element mesh with elements, nodes, and edges numbered.
Figure 9.14 Dispersion characteristics of an insulated image guide. (a) Geometry (, , , , , and ). (b) Dispersion curves.
Figure 9.15 Transmission coefficient of a cylindrical cavity resonator. (a) Geometry. (b) Calculation versus measurement. (
Source
: Liu et al. [11], Copyright ©2002 Wiley.)
Figure 9.16 S-parameters for an overlap-gap-coupled microstrip filter. (a) Top and side view of the geometry (, , , mm, mm, mm, mm, mm, mm, mm, mm, mm. (b) . (c) . (
Source
: Lee and Jin [12], Copyright ©2007 IEEE.)
Figure 9.17 Scattering by a metallic sphere having a radius of . (a) Magnitude of the scattered electric field in the E-plane. (b) Magnitude of the scattered electric field in the H-plane. (c) Magnitude of the total electric field in the E-plane. (d) Magnitude of the total electric field in the H-plane. The values of the fields are normalized by the magnitude of the incident electric field.
Figure 9.18 Bistatic RCS of a metallic sphere having a radius of .
Figure 9.19 Microstrip patch antenna recessed in a ground plane. The antenna is fed by a coaxial line, which is modeled as an electric current probe.
Figure 9.20 Input impedance of a loaded microstrip patch antenna. (a) Resistance. (b) Reactance. (
Source
: Jiao and Jin [15], Copyright ©2002 Wiley.)
Figure 9.21 Two-arm logarithmic spiral antenna. (a) Geometry of the arms. (b) Enlarged feed region. (c) Input impedance. (
Source
: Lou and Jin [16], Copyright ©2005 IEEE.)
Figure 9.22 Mutual coupling simulation for a microstrip antenna array. (a) Layout of the geometry. (b) Scattering parameters as a function of frequency from 1 to 3 GHz (The graph on the th row and th column shows . The lines represent the FETD results, and the circles represent the results calculated by the DGTD-central flux algorithm.
Figure 9.23 Monostatic RCS of a metallic cube of side length . (
Source
: Chatterjee et al. [31], Copyright ©1993 IEEE.)
Figure 9.24 Plane wave incident on the surface of an anisotropic medium.
Figure 9.25 VV-polarized monostatic RCS of a metallic double ogive at 9 GHz. (
Source
: After Greenwood and Jin [36], Copyright ©1999 IEEE.)
Chapter 10: The Method of Moments
Figure 10.1 (a) A piece of metallic conductor charged to potential . (b) Discretization of the surface into small surface patches.
Figure 10.2 Two-dimensional object in free space.
Figure 10.3 (a) Deformed such that resides inside . (b) Deformed such that resides outside .
Figure 10.4 Contour divided into short segments.
Figure 10.5 Scattering by a circular conducting cylinder with a radius of . The incident wave propagates from the left to right. The left and right columns show the results for the TM and TE polarizations, respectively. (a) Magnitude of the induced surface current density . (b) Magnitude of the induced surface current density . (c) Magnitude of the scattered field . (d) Magnitude of the scattered field . (e) Magnitude of the total field . (f) Magnitude of the total field . The values of the fields are normalized by the magnitude of their respective incident fields.
Figure 10.6 Scattering by a square conducting cylinder with a cross section of . The incident wave propagates from the left to right. The left and right columns show the results for the TM and TE polarizations, respectively. (a) Magnitude of the induced surface current density . (b) Magnitude of the induced surface current density . (c) Magnitude of the scattered field . (d) Magnitude of the scattered field . (e) Magnitude of the total field . (f) Magnitude of the total field . The values of the fields are normalized by the magnitude of their respective incident fields.
Figure 10.7 Bistatic scattering width for square conducting cylinders having a cross section of and , respectively, with the angle of incidence . (a) TM polarization. (b) TE polarization.
Figure 10.8 Illustration of triangular basis functions .
Figure 10.9 Three-dimensional object in free space.
Figure 10.10 (a) Deformed such that resides inside . (b) Deformed such that resides outside .
Figure 10.11 (a) A conducting wire carrying current . (b) Discretization of a wire and the triangular basis functions .
Figure 10.12 (a) Delta-gap voltage source. (b) Magnetic frill current source.
Figure 10.13 Geometry of a 2.0-m wire antenna with a bend at the feed point.
Figure 10.14 Input admittance versus frequency for a 2.0-m wire antenna with a bend at the feed point.
Figure 10.15 Current distribution on the bent wire antenna at 75, 150, and 225 MHz. (a) Magnitude. (b) Phase.
Figure 10.16 (a) Two triangles joined at a common edge. (b) Vector plot of the RWG function.
Figure 10.17 A quadrature point divides a triangle into three subtriangles. (b) Each subtriangle is mapped into the -plane as a right-angled triangle.
Figure 10.18 Triangular mesh of an almond.
Figure 10.19 Snapshot of the induced surface electric current density on a 9.936-inch-long conducting almond with a 10-GHz plane wave incident horizontally from an azimuth angle of away from the tip. (a) Vertical polarization. (b) Horizontal polarization.
Figure 10.20 Monostatic RCS of a 9.936-inch-long conducting almond at 10 GHz. (a) VV polarization. (b) HH polarization.
Figure 10.21 Bistatic RCS of a two-layer dielectric sphere at 1.2 GHz (The inner sphere has a radius of 0.9 m and a relative permittivity of , and the outer layer has a radius of 1.0 m and a relative permittivity of ). (
Source
: After Donepudi et al. [22], Copyright © 2003 IEEE.)
Figure 10.22 Illustration of rooftop functions.
Figure 10.23 Specular reflection and transmission coefficients of a circular patch infinite array on a top of an infinitely large dielectric slab. (a) Reflection coefficient. (b) Transmission coefficient. Solid lines: TM incidence. Dashed lines: TE incidence. (
Source
: Jin and Volakis [27], Copyright © 1990 IEEE.)
Figure 10.24 (a) Geometry of a missile-like object. (b) HH- and VV-polarized bistatic RCS for the head-on incidence at 1.0 GHz.
Figure 10.25 Surface electric current radiating in the presence of a grounded substrate.
Figure 10.26 Integration contours and in the complex -plane.
Figure 10.27 S-parameters for a microstrip double stub. (a) Geometry (, mm, the line width is 0.122 mm, the stub length is 2.921 mm, and the spacing between the two stubs is 0.757 mm). (b) S-parameters. (
Source
: Ling et al. [47], Copyright © 1999 IEEE.)
Figure 10.28 E-plane radiation pattern of a series-fed microstrip antenna array at 9.42 GHz. (a) Geometry (the antenna array is printed on a substrate of relative permittivity and thickness mm). (b) Normalized radiated power. (
Source
: Ling and Jin [46], Copyright © 1997 Wiley.)
Figure 10.29 (a) Piecewise quadratic function. (b) Shifted quadratic B-spline function.
Figure 10.30 Monostatic RCS of a two-layer dielectric sphere whose inner layer (core) has a radius of 0.8 m and a relative permittivity of 1.5 and whose outer layer has a radius of 1.0 m and a relative permittivity of 2.0.
Figure 10.31 Rectangular cavity fed by a coaxial waveguide whose inner conductor is extended into the cavity and terminated by a 47 resistor. (a) Geometry. (b) Power delivered into the cavity. (
Source
: After Bagci et al. [58], Copyright © 2007 IEEE.)
Chapter 11: Fast Algorithms and Hybrid Techniques
Figure 11.1 Computational complexity of a few hypothetical numerical schemes. (a) Computation time versus the number of unknowns. (b) Memory requirement versus the number of unknowns.
Figure 11.2 Arbitrarily shaped plate (a circular plate is shown in the figure) placed in a uniform rectangular mesh and modeled as a collection of small rectangular cells. The original plate is shown by the dashed line, and the staircase approximation is shown by the thick solid line.
Figure 11.3 Radiation by a corporate-fed microstrip antenna array having elements. (a) Geometry and current distribution (, mm, mm, mm, mm, mm, mm, mm, mm, mm). (b) Radiation patterns at GHz. (
Source
: After Wang et al. [10], Copyright © 1998 IEEE.)
Figure 11.4 Magnitude of the total electric field inside a two-layer dielectric sphere along the -, -, and -axes. The inner layer has a radius m and , the outer layer has a radius m and , and the frequency is 100 MHz. The solid line represents the Mie series solution and the dash-dot line represents the numerical solution. (
Source
: Wang and Jin [17], Copyright © 1998 IEEE.)
Figure 11.5 Staircase model of a human head and SAR (W/kg) at 256 MHz calculated using a grid under the excitation of a plane wave incident from the top. (a) Axial view. (b) Sagittal view. (c) Coronal view. (d) SAR in the axial slice. (e) SAR in the sagittal slice. (f) SAR in the coronal slice. (
Source
: Wang and Jin [17], Copyright © 1998 IEEE.)
Figure 11.6 Translation of RWG basis functions on a triangular mesh to point sources on rectangular grids. The highlighted triangular basis function on the left is approximated by nine delta functions. The one on the right is approximated by 16 delta functions.
Figure 11.7 Memory requirement versus the number of unknowns. (
Source
: Ling et al. [19], Copyright © 1998 EMW Publishing.)
Figure 11.8 CPU time versus the number of unknowns. (a) Matrix fill. (b) Matrix solve per iteration. (
Source
: Ling et al. [19], Copyright © 1998 EMW Publishing.)
Figure 11.9 Geometry of a combined triangle/half-circle plate. (a) Without a narrow slot. (b) With a narrow slot.
Figure 11.10 HH-polarized monostatic RCS of a combined triangle/half-circle plate at . (a) Without a narrow slot. (b) With a narrow slot. (
Source
: Ling et al. [19], Copyright © 1998 EMW Publishing.)
Figure 11.11 Monostatic RCS of 1.0-m-long almond at 300 MHz. (
Source
: Wang et al. [22], Copyright © 1998 Wiley.)
Figure 11.12 Monostatic RCS of 1.0-m-long almond at 757 MHz. (
Source
: Wang et al. [22], Copyright © 1998 Wiley.)
Figure 11.13 Monostatic RCS of a inches wing at 300 MHz. (
Source
: Wang et al. [22], Copyright © 1998 Wiley.)
Figure 11.14 Basis functions divided into groups so that the far-field interactions can be computed rapidly, whereas the near-field interactions are calculated directly.
Figure 11.15 Vector expressed as a sum of three vectors: , , and .
Figure 11.16 Vector expressed as a sum of three vectors: , , and , where denotes the center of group and denotes the center of group .
Figure 11.17 Practical subdivision of basis functions into groups and illustration of the far- and near-field interactions.
Figure 11.18 Telephone communication network. (a) Direct connections (for clarity only four telephones are connected to all other telephones). (b) Connections via hubs. (c) Connections using two layers of hubs.
Figure 11.19 Subdivision of basis functions into multilevel groups for the implementation of the multilevel fast multipole algorithm.
Figure 11.20 Multilevel aggregation and disaggregation processes. (a) Aggregation. (b) Disaggregation.
Figure 11.21 RMS error in the H-plane bistatic RCS of a 9-diameter sphere versus the number of unknowns per square wavelength. (
Source
: Donepudi et al. [38], Copyright © 2001 IEEE.)
Figure 11.22 E-plane bistatic RCS pattern of a conducting sphere having a diameter of 72. (
Source
: Donepudi et al. [38], Copyright © 2001 IEEE.)
Figure 11.23 Surface current on a car induced by the radiation of a Hertzian dipole at 1.0 GHz. (
Source
: Song et al. [44], Copyright © 1998 IEEE.)
Figure 11.24 Surface current on an airplane induced by an incident plane wave at 2 GHz. The plane wave is incident from the nose and is vertically polarized. (
Source
: Song et al. [44], Copyright © 1998 IEEE.)
Figure 11.25 Maximum rank of the submatrices in the moment-method matrix for a conducting sphere. (
Source
: Zhao et al. [58], Copyright © 2005 IEEE.)
Figure 11.26 Computational complexity of the ACA algorithm applied to the moment-method matrix for a conducting sphere. (a) Memory requirement. (b) Computation time. (
Source
: Zhao et al. [58], Copyright © 2005 IEEE.)
Figure 11.27 Computation time and memory requirements versus the number of unknowns in the ACA algorithm applied to dielectric spheres with radius from to . (a) Memory requirement. (b) Matrix assembly time. (c) Solution time per iteration.
Figure 11.28 Comparison of the errors in the bistatic RCS calculations using the direct moment method and the ACA algorithm for a dielectric sphere with radius . (a) VV polarization. (b) HH polarization.
Figure 11.29 Two rectangular elements with electric fields assigned at the edges and the magnetic fields assigned at the centers.
Figure 11.30 Directly interfacing a conformal unstructured mesh with a uniform rectangular mesh.
Figure 11.31 Interface between an explicit and structured FDTD grid and an implicit and unstructured FETD grid. Data exchange from the FDTD grid to the FETD grid occurs on the thick solid line, whereas data exchange from the FETD grid to the FDTD grid occurs on the thick dashed lines. (
Source
: Modified after Jin and Riley [92], Copyright © 2009 Wiley.)
Figure 11.32 Metallic double ogive. (a) Geometry. (b) Surface current density for a sinusoidal plane wave excitation at 30 GHz. (
Source
: Jin and Riley [92], Copyright © 2009 Wiley.)
Figure 11.33 Monostatic RCS of the metallic double ogive at 9 GHz. (a) VV polarization. (b) HH polarization. (
Source
: Jin and Riley [92], Copyright © 2009 Wiley.)
Figure 11.34 Computational domain truncated by a surface that tightly encloses the object to be analyzed. (
Source
: Jin and Riley [92], Copyright © 2009 Wiley.)
Figure 11.35 Monostatic RCS of a cylinder consisting of a conductor and two different dielectric materials. (a) Geometry. (b) -polarized RCS at 0.3 GHz. (
Source
: Donepudi et al. [40], Copyright © 2003 IEEE.)
Figure 11.36 A 1.0-inch-thick trapezoidal conducting plate with its edges coated by 2.0-inch-wide lossy dielectric having . (
Source
: Donepudi et al. [40], Copyright © 2003 IEEE.)
Figure 11.37 Monostatic RCS of the coated trapezoidal plate in the -plane at 1.0 GHz. (a) VV polarization. (b) HH polarization. (
Source
: Donepudi et al. [40], Copyright © 2003 IEEE.)
Figure 11.38 An open conducting cavity having a dimension of 5 m 5 m 10 m made of 0.1-m-thick conductors with its interior surface coated by a 0.1-m-thick lossy dielectric with . Shown in the Figure is the thickness of the conducting wall and the thickness of the coating is not shown for the sake of clarity. (
Source
: Donepudi et al. [40], Copyright © 2003 IEEE.)
Figure 11.39 Monostatic RCS of the coated rectangular cavity in the -plane at 0.3 GHz. (a) polarization. (b) polarization. (
Source
: Donepudi et al. [40], Copyright © 2003 IEEE.)
Chapter 12: Concluding Remarks on Computational Electromagnetics
Figure 12.1 Because of the large variety of electromagnetic-related engineering problems, a large number of numerical and asymptotic methods have been developed to solve Maxwell's equations.
Figure 12.2 Because of the predictive power of Maxwell's equations and the pervasiveness of electromagnetic phenomena in modern technologies, computational electromagnetics can impact many scientific and technological areas. (Expanded from Chew et al. [38].)
Figure 12.3 Range profile of an aircraft. (a) VV polarization. (b) HH polarization. (
Source
: Yilmaz et al. [113], Copyright ©2004 IEEE.)
Figure 12.4 Inverse synthetic aperture radar image of an aircraft at from nose-on. (a) Calculation. (b) Measurement. (
Source
: Wang and Ling [133], Copyright ©2002 IEEE.)
Figure 12.5 Bandpass rectangular waveguide filter. (a) Geometry. (b) Transmission frequency response.
Figure 12.6 Field distribution in a waveguide filter at a few frequencies. (a) 41 GHz. (b) 41.4 GHz. (c) 42 GHz. (d) 43 GHz.
Figure 12.7 Typical electromagnetic compatibility problem: coupling of external field into an interior system.
Figure 12.8 Mutual coupling between antennas. (a) Geometrical model of an airplane with an eight-element log-periodic monopole array mounted on the wing and a single monopole antenna mounted on the fuselage. (b) Ratio of the power received by the array to the power delivered to the monopole antenna. (
Source
: Bagci et al. [115], Copyright ©2007 IEEE.)
Figure 12.9 Photonic crystal cavity with nine holes in the – direction. (a) Geometry. The dielectric slab has a refractive index of and a thickness of , where denotes the lattice constant. The regular holes have a radius of , and the modified holes have a radius of . (b) Energy stored in the cavity. The locations of the energy peaks correspond to the resonant frequencies of the resonant modes. (
Source
: Li and Jin [147], Copyright ©2008 Wiley.)
Figure 12.10 Normalized magnitude of the electric field at the midplane. (a) Doubly degenerate dipole modes. (b) Nondegenerate hexapole mode. (c) Doubly degenerate quadrupole modes. (d) Nondegenerate monopole mode. (
Source
: Li and Jin [147], Copyright ©2008 Wiley.)
Figure 12.11 Photonic crystal waveguide. (a) Top view of the geometry. (b) A snap shot of the field distribution. (
Source
: Li and Jin [146], Copyright ©2007 OSA.)
Figure 12.12 Electromagnetic hyperthermia using an annular phased array of applicators at 85 MHz. (a) Cross section of the human trunk with seven targeted regions. (b) Steady-state temperature optimized based on the specific absorption rate for region A. (c) Steady-state temperature optimized based on the temperature for region A. (d) Steady-state temperature optimized based on the temperature for region B. (
Source
: Kowalski and Jin [158], Copyright ©2000 IEEE.)
Figure 12.13 Basic steps to solve a practical engineering problem by numerical analysis.
Figure 12.14 Computational electromagnetics is a highly interdisciplinary field that combines physics, mathematics, and computer science to support advanced engineering applications.
Appendix B: Bessel Functions
Figure B.1 Cylindrical Bessel functions with an integer order. (a) Bessel functions of the first kind . (b) Bessel functions of the second kind .
Appendix C: Modified Bessel Functions
Figure C.1 Modified Bessel functions of the first and second kind, and .
Appendix D: Spherical Bessel Functions
Figure D.1 Spherical Bessel functions with an integer order. (a) Spherical Bessel functions of the first kind . (b) Spherical Bessel functions of the second kind .
Figure D.2 Riccati–Bessel functions of an integer order. (a) Riccati–Bessel functions of the first kind . (b) Riccati–Bessel functions of the second kind .
Appendix E: Associated Legendre Polynomials
Figure E.1 The first few Legendre polynomials and . (a) as a function of . (b) as a function of .
Figure E.2 The first few Legendre functions of the second kind and . (a) as a function of . (b) as a function of .
Theory and Computation of Electromagnetic Fields
Second Edition
Jian-Ming Jin
Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign
Copyright © 2015 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.
