Lectures on Electromagnetic Field Theory

1 Lectures onElectromagnetic Field TheoryWeng Cho CHEW1 Spring 2020, Purdue University1 Updated: May 2, 2020 ContentsPrefacexiAcknowledgementsxii1 Introduction, Maxwell s Importance of Electromagnetics .. Brief History of Electromagnetics .. Maxwell s Equations in Integral Form .. Static Electromagnetics .. s Law (Statics) .. FieldE(Statics) .. s Law (Statics) .. of Gauss s Law from Coulomb s Law (Statics) .. Homework Examples ..112 Maxwell s Equations, Differential Operator Gauss s Divergence Theorem .. s Law in Differential Operator Form .. Meaning of Divergence Operator .. Stokes s Theorem .. s Law in Differential Operator Form .. Meaning of Curl Operator .. Maxwell s Equations in Differential Operator Form .. Homework Examples ..223 Constitutive Relations, Wave Equation, Electrostatics, and Static Green Simple Constitutive Relations.

2 Emergence of Wave Phenomenon, Triumph of Maxwell s Equations.. Static Electromagnetics Revisted .. s Equation .. Green s Function .. s Equation ..30iiiElectromagnetic Field Homework Examples ..304 Magnetostatics, Boundary Conditions, and Jump Magnetostatics .. on Coulomb s Gauge .. Boundary Conditions 1D Poisson s Equation .. Boundary Conditions Maxwell s Equations .. s Law .. s Law .. s Law .. s Law for Magnetic Flux ..425 Biot-Savart law, Conductive Media Interface, Instantaneous Poynting Derivation of Biot-Savart Law .. Boundary Conditions Conductive Media Case .. Field Inside a Conductor .. Field Inside a Conductor .. Instantaneous Poynting s Theorem ..496 Time-Harmonic Fields, Complex Time-Harmonic Fields Linear Systems.

3 Fourier Transform Technique .. Complex Power ..577 More on Constitute Relations, Uniform Plane More on Constitutive Relations .. Frequency Dispersive Media .. Media .. Media .. Media .. and Biaxial Media .. Media .. Wave Phenomenon in the Frequency Domain .. Uniform Plane Waves in 3D ..668 Lossy Media, Lorentz Force Law, Drude-Lorentz-Sommerfeld Plane Waves in Lossy Conductive Media .. Lorentz Force Law .. Drude-Lorentz-Sommerfeld Model .. Dispersive Media .. Nanoparticles ..80 Contentsiii9 Waves in Gyrotropic Media, Gyrotropic Media .. Wave Polarization .. Polarization Case and Axial Ratio .. Polarization and Power Flow ..8810 Spin Angular Momentum, Complex Poynting s Theorem, Lossless Condi-tion, Energy Spin Angular Momentum and Cylindrical Vector Beam.

4 Complex Poynting s Theorem and Lossless Conditions .. Complex Poynting s Theorem .. Lossless Conditions .. Energy Density in Dispersive Media ..9511 Transmission Transmission Line Theory .. Time-Domain Analysis .. Frequency-Domain Analysis .. Lossy Transmission Line .. 10512 More on Transmission Terminated Transmission Lines .. Shorted Terminations .. Open terminations .. Smith Chart .. VSWR (Voltage Standing Wave Ratio) .. 11613 Multi-Junction Transmission Lines, Duality Multi-Junction Transmission Lines .. Single-Junction Transmission Lines .. Two-Junction Transmission Lines .. Stray Capacitance and Inductance .. Duality Principle .. Unusual Swaps .. Fictitious Magnetic Currents .. 12914 Reflection, Transmission, and Interesting Physical Reflection and Transmission Single Interface Case.

5 TE Polarization (Perpendicular or E Polarization)1.. TM Polarization (Parallel or H Polarization) .. Interesting Physical Phenomena .. Total Internal Reflection .. 1351 These polarizations are also variously know as thesandppolarizations, a descendent from the notationsfor acoustic waves wheresandpstand for shear and pressure waves Field Theory15 More on Interesting Physical More on Interesting Physical Phenomena, Homomorphism, Plane Waves, Trans-mission Lines .. Brewster Angle .. Surface Plasmon Polariton .. Homomorphism of Uniform Plane Waves and Transmission Lines Equations . TE or TEzWaves .. TM or TMzWaves .. 14816 Waves in Layered Waves in Layered Media .. Generalized Reflection Coefficient for Layered Media .. Phase Velocity and Group Velocity.

6 Phase Velocity .. Group Velocity .. Wave Guidance in a Layered Media .. Transverse Resonance Condition .. 15517 Dielectric Generalized Transverse Resonance Condition .. Dielectric Waveguide .. TE Case .. TM Case .. A Note on Cut-Off of Dielectric Waveguides .. 16518 Hollow Hollow Waveguides .. Absence of TEM Mode in a Hollow Waveguide .. TE Case (Ez= 0,Hz6= 0) .. TM Case (Ez6= 0,Hz= 0) .. Rectangular Waveguides .. TE Modes (H Mode orHz6= 0 Mode) .. 17219 More on Hollow Rectangular Waveguides, Contd.. TM Modes (E Modes orEz6= 0 Modes) .. Bouncing Wave Picture .. Field Plots .. Circular Waveguides .. TE Case .. TM Case .. 181 Contentsv20 More on Waveguides and Transmission Circular Waveguides, Contd.

7 An Application of Circular Waveguide .. Remarks on Quasi-TEM Modes, Hybrid Modes, and Surface Plasmonic Modes Quasi-TEM Modes .. Hybrid Modes Inhomogeneously-Filled Waveguides .. Guidance of Modes .. Homomorphism of Waveguides and Transmission Lines .. TE Case .. TM Case .. Mode Conversion .. 19521 Cavity Resonators .. Transmission Line Model .. Cylindrical Waveguide Resonators .. Some Applications of Resonators .. Filters .. Electromagnetic Sources .. Frequency Sensor .. 20822 Quality Factor of Cavities, Mode The Quality Factor of a Cavity .. General Concepts .. Relation to the Pole Location .. Some Formulas forQfor a Metallic Cavity .. Example: TheQof TM110 Mode .. Mode Orthogonality and Matrix Eigenvalue Problem.

8 Matrix Eigenvalue Problem (EVP) .. Homomorphism with the Waveguide Mode Problem .. Proof of Orthogonality of Waveguide Modes .. 21623 Scalar and Vector Scalar and Vector Potentials for Time-Harmonic Fields .. Introduction .. Scalar and Vector Potentials for Statics, A Review .. Scalar and Vector Potentials for Electrodynamics .. More on Scalar and Vector Potentials .. When is Static Electromagnetic Theory Valid? .. Quasi-Static Electromagnetic Theory .. 22824 Circuit Theory Circuit Theory Revisited .. Kirchhoff Current Law .. Kirchhoff Voltage Law .. 230viElectromagnetic Field Inductor .. Capacitance .. Resistor .. Some Remarks .. Energy Storage Method for Inductor and Capacitor .. Finding Closed-Form Formulas for Inductance and Capacitance.

9 Importance of Circuit Theory in IC Design .. Decoupling Capacitors and Spiral Inductors .. 24125 Radiation by a Hertzian History .. Approximation by a Point Source .. Case I. Near Field , r 1 .. Case II. Far Field (Radiation Field ), r 1 .. Radiation, Power, and Directive Gain Patterns .. Radiation Resistance .. 25026 Radiation Radiation Fields or Far- Field Approximation .. Far- Field Approximation .. Locally Plane Wave Approximation .. Directive Gain Pattern Revisited .. 25827 Array Antennas, Fresnel Zone, Rayleigh Linear Array of Dipole Antennas .. Far- Field Approximation .. Radiation Pattern of an Array .. When is Far- Field Approximation Valid? .. Rayleigh Distance .. Near Zone, Fresnel Zone, and Far Zone.

10 27028 Different Types of Antennas Resonance Tunneling in Antenna .. Horn Antennas .. Quasi-Optical Antennas .. Small Antennas .. 28029 Uniqueness The Difference Solutions to Source-Free Maxwell s Equations .. Conditions for Uniqueness .. Isotropic Case .. General Anisotropic Case .. Hind Sight .. Connection to Poles of a Linear System .. Radiation from Antenna Sources and Radiation Condition .. 291 Contentsvii30 Reciprocity Mathematical Derivation .. Conditions for Reciprocity .. Application to a Two-Port Network and Circuit Theory .. Voltage Sources in Electromagnetics .. Hind Sight .. Transmit and Receive Patterns of an Antennna .. 30031 Equivalence Theorems, Huygens Equivalence Theorems or Equivalence Principles.