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A vital resource that comprehensively covers advanced topics in applied electromagnetics for the professional
Electromagnetism (EM) is a highly abstract and complex subject that examines how exerting a force on charged particles is affected by the presence and motion of adjacent particles. The interdependence of the time varying electric and magnetic fields-one producing the other, and vice versa-has allowed researchers to consider them as a single coherent entity: the electromagnetic field. Under this umbrella, students can learn about numerous and varied topics, such as wireless propagation, satellite communications, microwave technology, EM techniques, antennas, and optics, among many others.
Fields and Waves in Electromagnetic Communications covers advanced topics in applied electromagnetics for the professional by offering a comprehensive textbook that covers the basics of EM to the most advanced topics such as the classical electron theory of matters, the mechanics model and macroscopic model. Specifically, the book provides a welcome all-in-one source on wireless and guided EM that deals in a wide range of subjects: transmission lines, impedance matching techniques, metallic waveguides, resonators, optical waveguides, optical fibres, antennas, antenna arrays, wireless systems, and electromagnetic compatibility (EMC), and more. The content is supported with innovative pedagogy, the most recent reports and working principles of relevant and contemporary technological developments including applications, specialist software tools, laboratory experiments, and innovative design projects.
Fields and Waves in Electromagnetic Communications readers will also find:
Fields and Waves in Electromagnetic Communications is an ideal textbook for graduate students and senior undergraduates studying telecommunication and wireless communication. It is also a useful resource for industry engineers and members of defense services. Moreover, the book is an excellent non-specialist engineering reference able to be used in other disciplines, such as biomedical engineering, mechatronics, computer science, materials engineering, civil and environmental engineering, physics, network engineering, and wireless services.
Nemai Chandra Karmakar, PhD, is the lead researcher at the Monash Microwave, Antenna, RFID and Sensor Laboratory (MMARS) at Monash University, Australia. He received his PhD in Information Technology and Electrical Engineering from the University of Queensland, Australia, in 1999. He is a pioneer in fully printable, chipless radio-frequency identification (RFID) tags and sensors, readers, signal processing, and smart antennas.
Preface xii
Acknowledgments xiv
About the Companion Website xvi
1 Uniform Plane Wave 1
1.1 Introduction to Uniform Plane Wave 1
1.2 Fundamental Concept of Wave Propagation 4
1.3 Plane Wave Concept 7
1.4 One Dimensional Wave Equation Concept 14
1.5 Wave Motion and Wave Front 17
1.6 Phase Velocity of UPW 19
1.7 Wave Impedance 23
1.8 Time Harmonic Field Wave Equations 25
1.8.1 Summary of Propagation Constant 29
1.9 Refractive Index of Medium and Dispersion 30
1.9.1 Summary of Wave Propagation in Lossless Medium 32
1.10 Time Harmonic Wave Solution 33
1.11 Poynting Theorem 35
1.12 Static Poynting Theorem 40
1.12.1 Poynting Theorem for a Wire 40
1.13 Energy Balance Equation in the Presence of a Generator: In-Flux and Out-Flow of Power 41
1.14 Time Harmonic Poynting Vector 43
1.15 Problems 48
2 Wave Propagation in Homogeneous, Nondispersive Lossy Media 55
2.1 Introduction 55
2.2 Wave Propagation in Lossy Media 57
2.3 Good Dielectric Medium 60
2.3.1 Wave Impedance of Good Dielectric 61
2.4 Low-Loss Dielectric Medium 62
2.4.1 Measurement Procedure of Relative Permittivity and Loss Tangent 65
2.4.2 Summary of Lossy Dielectric Materials 65
2.5 Wave Propagation in Good Conducting Medium 66
2.6 Wave Impedance in Good Conductors 70
2.6.1 Practical Applications: Geophysics 72
2.7 Current Wave Equation in High Conductivity Materials 73
2.7.1 Current in a Conducting Sheet 74
2.7.2 Skin Effect and Internal Impedance 76
2.7.3 Sheet Resistance 79
2.7.4 High Frequency Effect 80
2.8 Sheet Resistance of a Wire and a Coaxial Line 84
2.9 Current Distribution on a Wire 85
2.9.1 Rayleigh Approximation of Finite Conductor Thickness 86
2.9.2 Internal Impedance of a Round Wire 87
2.10 Low Frequency Approximation 89
2.11 Skin-Effect Resistance and Inductance Ratios 90
2.12 Impedance of a Circular Tube and Coaxial Cable 91
2.13 Impedance of a Coaxial Cable 96
2.14 Impedance of Metallic-Coated Conductors and Laminates 98
2.15 1D Current Wave Equation in Multilayered Media 100
2.16 Boundary Conditions and Exact Solution of Surface Current of a Multilayered Medium 101
2.17 Design of Multi-Bit Chipless RFID Tags 103
2.18 Power Loss in Good Conductor 104
2.19 Practical Measurement of Sheet Resistance 106
2.19.1 Measurement of Sheet Resistance 109
2.19.1.1 Sheet Resistance Meter 110
2.20 Summary of Propagation in Conducting Media 112
2.21 Chapter Remarks 112
2.22 Problems 113
3 Uniform Plane Wave in Dispersive Media 117
3.1 Introduction 117
3.2 One-Dimensional Wave Equation 118
3.2.1 Field Solutions in Different Forms 122
3.2.2 Wave Motion 124
3.2.3 Phase Velocity 127
3.3 Dispersion of Media and Group Velocity 127
3.4 Dispersion in Digital Signal Processing and Information Theory 137
3.4.1 Group Velocity in Information Theory 137
3.4.2 Pulse Broadening in Dispersive Medium 139
3.5 Wave Impedance of Uniform Plane Wave 143
3.6 Polarization of Wave Fields 144
3.6.1 Linearly Polarized Waves 148
3.6.2 Circularly Polarized Waves 154
3.6.2.1 Practical Design of Circularly Polarized Wave 158
3.6.2.2 Applications of CP Waves 159
3.6.3 Elliptical Polarization 160
3.6.4 Polarization Loss Factor and Polarization Efficiency 166
3.6.4.1 Polarization Loss Factor 166
3.6.4.2 Polarization Efficiency 170
3.7 Specific Topics on Polarizations of Uniform Plane Wave 170
3.7.1 Magnetic Field in Plane Wave with Generic Polarization 171
3.7.2 Poynting Vector Calculation in Different Polarizations of Electromagnetic Fields 172
3.7.3 Elliptically Polarized Wave from Two Unequal Cross-Polar Circularly Polarized Wave 174
3.7.4 Effect of Medium Characteristics on Polarization-Anisotropic Medium 174
3.8 Chapter Remarks 177
3.9 Problems 178
4 Wave Propagation in Dispersive Media 181
4.1 Introduction 181
4.2 Dispersion in Materials 182
4.3 Classical Electron Theory and Dispersion in Material Media 184
4.4 Discrete Charged Particles in Static Electromagnetic Fields 185
4.5 Classical Mechanics Model of Matters 192
4.6 Motion of Charged Particle in Steady Electric and Magnetic Fields 195
4.7 Theory of Cyclotron 198
4.8 Analysis of Charged Particle in Time Harmonic Electric Field and Uniform Magnetic Field 200
4.9 Dispersion in Gaseous Media 203
4.10 Dispersion in Liquid and Solid Media 208
4.11 Ionic Dispersion in Liquid and Solid Media 210
4.12 Dispersion in Metals 214
4.12.1 Significance of Dispersion in Metals in Mixed Signal Electronics? 214
4.12.2 What Are Metals Made of: The Classical Electron Theory and Electromagnetic Wave Interaction? 216
4.13 Waves Propagation in Plasma 223
4.13.1 Electromagnetic Wave Interaction with Plasma 226
4.14 Wave Propagation in Plasma and Satellite Communications 235
4.14.1 Refractive Indices and Phase Velocities for RHCP and LHCP Cases 239
4.15 Waves in Dielectric Media 244
4.15.1 Classical Electron Theory of Dielectric 246
4.15.2 Macroscopic View of Dielectric 249
4.16 Microscopic View of Dielectric 252
4.16.1 Waves in Anisotropic Dielectric Medium 255
4.17 Problems 259
5 Reflection and Transmission of Uniform Plane Wave 263
5.1 Introduction 263
5.2 Electromagnetic Waves Analysis in the Context of Boundary Value Problems 267
5.3 Reflection and Refraction at Plane Surface 271
5.4 Normal Incidence on a Perfect Conductor 272
5.5 Circularly Polarized Wave Incidence on a Conducting Surface 284
5.6 Normal Incidence at Dielectric Boundary 287
5.6.1 Calculation of Reflection and Transmission Coefficients 291
5.6.2 Calculation of Electromagnetic Power Density 293
5.7 Concept of Standing Waves 300
5.7.1 Trigonometric Analysis of Standing Wave 303
5.7.2 Time Domain Analysis of Standing Wave 307
5.7.3 Phasor Vector Analysis of Standing Wave 311
5.7.4 Transmission Line Analogy of Normal Incidence 317
5.8 Reflection from Multiple Layers 320
5.8.1 Effective Transmission and Reflection Analysis of Multilayered Dielectric Media Using Steady-State Boundary Conditions 322
5.8.2 Successive Transmission and Reflection Analysis of Multilayered Dielectric Media 327
5.8.3 Successive Transmission and Reflection Analysis Via ¿/4-Thick Dielectric Medium 329
5.8.4 Effective Transmission and Reflection Coefficients of Multilayered Dielectric Media 332
5.8.5 Reflection for a Large Number of Multiple Dielectric Media 336
5.9 Special Cases of Reflection from Multiple Layers 340
5.9.1 Reflection from a Dielectric Coated Good Conductor 341
5.9.2 ¿/2-Dielectric Window for Zero Reflection 343
5.9.3 Electrically Thin Dielectric Window 347
5.9.4 ¿/4-Dielectric Transformer Window 349
5.9.5 Reflection for 2-Ply Dielectric Window 354
5.9.6 Electromagnetic Absorber Design with a Thin Dielectric Window Placed (3¿ 0)/4 Distance from a Perfect Electric Conductor 356
5.9.7 Absorbers in Anechoic Chamber: Antenna Measurement 358
5.10 Final Remarks 359
5.11 Problems 360
6 Oblique Incidence of Uniform Plane Wave 371
6.1 Introduction 371
6.2 Methodologies Used in Oblique Incidence Theory 376
6.3 Coordinate System for Oblique Incidence Cases 378
6.4 Oblique Incidence on Conducting Boundary 387
6.5 TE Polarization on Conducting Boundary 390
6.5.1 Poynting Vector in TE Polarization 393
6.5.2 Phase Velocity Calculation 394
6.5.3 Waveguide Concept 396
6.5.4 Surface Current Calculation on Metallic Boundary 399
6.6 Parallel (TM) Polarization on Conducting Boundary 403
6.6.1 Surface Current and Induced Electric Charge Calculations on Metallic Boundary 407
6.7 Characteristic Wave Impedances 410
6.8 Oblique Incidence on Dielectric Boundary 410
6.8.1 Ray Trace Model of Generalized Oblique Incidence Field 411
6.9 Total Internal Reflection 413
> T c 415
6.10 TE Polarization of Oblique Incidence on Dielectric Boundary 421
6.10.1 Applications of Boundary Conditions at z = 0 426
6.10.2 Total Internal Reflection and Critical Angle ¿ c 428
6.10.3 Calculations of G TE and t TE 430
6.10.4 Effective Impedance Concept of TE Polarized Oblique Incidence 433
6.10.5 Total Internal Reflection in the Light of Impedance Concept 434
6.10.6 Special Cases of G TE 435
6.10.6.1 Reflection Coefficient G TE for Perfect Conductor 435
6.10.6.2 Both Medium Lossless and Non-magnetic Media 436
6.10.6.3 Critical Angle and Submarine Communications 436
6.10.6.4 TE Oblique Incidence on Multiple Dielectric Layers 437
6.10.7 Power Balance in TE Oblique Incidence 439
6.10.8 Equivalent Impedance Concept in Power Balance Equation 443
6.10.9 Summary of TE Polarized Oblique Incidence Case 444
6.11 TM Polarization Oblique Incidence 445
6.11.1 Field Analysis of TM Polarization Oblique Incidence 446
6.11.2 Applications of Boundary Conditions at z = 0 451
6.11.3 Calculations of G TM and t TM 453
6.11.4 Total Transmission and Brewster Angle ¿ B 456
6.11.5 Total Transmission for Arbitrary Polarized Signal at Plane Interface Between Dissimilar Perfect Dielectric 457
6.11.6 Brewster Angle and Wireless Communications 459
6.11.7 Chipless RFID Polarizer Exploits Brewster Angle 460
6.11.8 Effective Impedance Concept of TM Polarized Oblique Incidence 461
6.11.9 Total Transmission in the Light of Impedance Concept 462
6.11.10 Special Cases of G TM 464
6.11.10.1 Reflection Coefficient G TM for Perfect Conductor 464
6.11.10.2 Both Medium Lossless and Non-magnetic Media 464
6.11.10.3 Brewster Angle and Laser Beam with TM Polarization 464
6.11.10.4 Calculations of G eff for TM and TE Oblique Incidence on Multiple Dielectric Layer 465
6.11.11 Power Balance in TM Oblique Incidence 471
6.11.12 Equivalent Impedance Concept in Power Balance Equation 473
6.11.13 Summary of TM Polarized Oblique Incidence Cases 474
6.12 Problems 475
References 480
7 Incidence of Uniform Plane Wave in Lossy Media 481
7.1 Introduction 481
7.2 Applications 483
7.3 Normal Incidence on Imperfect Media 485
7.3.1 Normal Incidence on Imperfect Dielectric Boundary 493
7.3.1.1 Time Average Power Loss in Lossy Dielectric Medium 494
7.4 Applications of Normal Incidences on Lossy Dielectric Boundary 495
7.4.1 Microwave Biomedical Engineering 495
7.4.2 RF/Microwave Shielding for EMC Measures 497
7.5 Oblique Incidence in Lossy Medium 502
7.5.1 General Theory of Oblique Incidence from Air to Lossy Medium 502
7.5.2 Oblique Incidence and Propagation in Good Conductor 506
7.5.3 Oblique Incidence and Reflection from Lossy Medium 509
7.5.4 Oblique Incidence: Reflection from Good Conductor 510
7.5.5 Good Conductor to Good Conductor Interface 512
7.5.6 Oblique Incidence at the Interface of Two Lossy Medium with Real T I 512
7.5.7 Refraction for Two Conductive Media 515
7.6 Emerging Applications: Precision Agriculture 519
7.6.1 Wireless Sensor 521
7.6.2 Soil Models 522
7.6.3 TDR Technique in Soil Moisture Measurements 522
7.6.4 Sensor Design 524
7.6.5 Soil Moisture Remote Sensing Radiometer 524
7.6.6 Test Set Up 529
7.7 Chapter Summary 531
7.8 Problems 531
Acknowledgments 534
References 534
Appendix A Useful Electromagnetic Data 537
Index 542
With the emergence of new wireless technologies, electromagnetic wave propagation in nonconventional media has forced to revisit the classical electromagnetic theories in dynamic conditions. In this chapter, a few very important classical electromagnetic theories are examined in the light of wave propagations in time varying cases. The emerging applications are RF/microwave/millimeter-wave printed electronics on nonconventional materials, and study of propagation of electromagnetic waves in very complex composite media. The chapter first defines the uniform plane wave in the light of far field radiation from a dipole antenna followed by the uniform plane wave concept. Derivation of electromagnetic wave equations with the aid of Maxwell's equations and one-dimensional wave equation are presented next. The wave is characterized with its phase velocity meaning the velocity of wave propagation and the wave impedance, which is the function of the constitutive parameters of the medium. The above derivations are extended to the time harmonic field wave equation and the refractive index of medium and dispersion of medium. The time harmonic wave solution and polarization of the uniform plane wave are presented next. Finally, the energy balance equation which is called Poynting theorem is presented in detail for a few special cases followed by the conclusion of the chapter.
Maxwell unified all classical electromagnetic principles and laws into four potent equations. These equations are so universal that they can be used to characterize electromagnetic field wave equations for any frequency, for the static as well as the dynamic field conditions. In this regard, an electromagnetic field can be defined as: (i) every function that satisfies Maxwell's equations, which is finite, continuous,1 and single valued, and (ii) propagates through homogeneous, linear, and isotropic medium. In this chapter, we shall develop the uniform plane wave concept of the electromagnetic fields using Maxwell's equations for any frequency in a medium as stated above. In this chapter, we examine this aspect in depth.
In solving the field wave equations, we need to deal with the complex phasor vector field quantities which are the functions of both space and time in double derivatives. In these situations, these vector functions are not easily solvable because of the following reasons: (i) no field solution is possible to get directly from scalar functions. Here, the functions are dependent on time and spatial coordinates, and (ii) the complexity of analyses of the vector functions increases as we move from one coordinate system to another coordinate system. As for example, the complexity of vector analysis of the electromagnetic fields increases as we move from the rectangular coordinate system to the cylindrical coordinate system to the spherical coordinate system. There are also other seven coordinate systems in the vector analysis with which the electromagnetic fields are resolvable, but we only confine ourselves in the three main coordinate systems. Also note that electromagnetic field propagation in bounded and unbounded media behave differently. In unbounded medium, the antenna radiates spherically, whereas in bounded structure such as rectangular metallic waveguide we solve electromagnetic field problems with the rectangular wave equations. In optical fibers, we analyze the electromagnetic fields using cylindrical coordinate systems. With the simplest one, the rectangular coordinate system, we shall develop the electromagnetic field wave theory in this coordinate system in the chapter. Then gradually we define field solutions for more complex coordinate systems in cylindrical and spherical coordinate systems. (iii) It is also not possible to solve 3D scalar wave equations in arbitrary coordinate systems by the use of separation of variable method.2 That is why, we keep our wave field analysis into simple configurations such as rectangular, circular, and spherical coordinate systems.3
Figure 1.2 illustrates how wireless communications networks established by the time varying electromagnetic field waves harness each and every device in the system for efficient wireless communications. As we have seen in the big picture of wireless communications shown in Figure 1.1, the wireless channel is established with the wave propagation. In this chapter, we shall study more details of the wireless channel augmented with the theory of uniform plane wave propagation. A brief description of the topics covered in the chapter are as follows:
Figure 1.1 Wireless communications networks showing how the electromagnetic waves harness each and every device in the system for efficient wireless communications.
In the definition of uniform plane waves in this chapter, the very beginning of the book, we already have given a very good understanding of the uniform plane wave. We have learned that in a uniform plane wave, the electric field E, the magnetic field H and, the Poynting vector P = E?×?H, which is also called the power flow density vector in (W/m2), are orthogonal to each other, and the wave propagates orthogonally with respect to the directions of the two fields.
After the proper definition of the uniform plane wave, we shall derive the electromagnetic plane wave equations. As we know, in a uniform plane wave the phase front is like a flat surface on which the phase of the signal is the same. From the derivation of the field wave equations, we shall now learn how to derive electromagnetic wave equations using simple differential equations. Uniform plane wave equation is a double derivative equation of both spatial and time coordinates. We shall see that the vector wave equation has two solutions, forward and reverse traveling wave fields.
Every plane wave has its intrinsic wave impedance which is defined as the ratio of electric field and the magnetic field intensities at any point in space. The wave impedance is a function of the constitutive parameters such as medium permittivity e (F/m), permeability µ (H/m), finite conductivity s (S/m), and angular frequency ? (rad/m). We shall define the intrinsic wave impedance of the lossless and lossy media in the chapter. You may recall the wave impedance of the plane wave in free space is 377 O.
The polarizations of uniform plane waves is a significant parameter that regulates the efficacy of electromagnetic communications. The polarization of the field wave is the spatial orientation of the electric field vector with respect to time. We shall learn more in details of various polarizations of the field waves and their significance in the wireless communications.
And finally, Poynting Theorem, that tells us the power flow density vector P = E?×?H (w/m2). Poynting Theorem is an energy balance equation that tells us that in a homogeneous, linear, and isotropic medium, the power input is equal to the electric and magnetic energy stored plus the power dissipated as the Ohmic loss as it propagates real power as the plane wave. The time average power is defined as
Finally, in this chapter, we shall solve many interesting problems as we go along with the theories on the uniform plane wave.
This chapter provides the very important concept of medium properties derived from the wave equation. There, we shall define the attenuation and phase constants, and the loss tangent for lossy medium. In defining those parameters, we shall go in deeper in defining the propagation of wave in good conductors and good dielectrics. These concepts are critically important in designing any practical RF and microwave circuits.
The aim of this chapter is to develop the concept of electromagnetic waves, and how they propagate in free space and in different complex media. It helps readers to understand the meaning of the polarization of plane waves and how introduction of a metallic or dielectric slab in their propagation paths affects their behaviors.4 The reader will also obtain the concept of 3D and 2D vector plots of electromagnetic field distributions in various conditions via some illustrations generated with Computer Simulation Technologies (CST) Microwave StudioT. A few practical examples and worked out problems of the plane wave propagation is also provided to enhance understanding in a real-world scenario.
In this section, we investigate the different aspects of plane waves: how they look like, how they behave when encountered with different obstacles such as buildings, walls inside a room, on the roads, and in the free space when wireless propagations happen. Recall Maxwell's two curl equations, Faraday's and Ampere's laws that tell us that for a plane wave to be generated, a source of time varying electromagnetic fields must exist. According to Ampere's circuital law:
In other words, if the electric field, E(t), varies at a point in space resulting in a time-varying electric flux density, D(t), it produces a time-varying magnetic field in the region around that point instantaneously. On the other hand, Faraday's law states...
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