Electromagnetics Vol. 2 PDF Download – Steven W. Ellingson (2020) BSEE

BSEE students in the second half of an engineering electromagnetics sequence can get “Electromagnetics, Volume 2” free from Virginia Tech. Steven W. Ellingson wrote it for third-year electrical engineering courses, and Virginia Tech Publishing released it in 2020 under a CC BY-SA 4.0 licence. It has 10 chapters and 3 appendices, with more than 40 worked examples inside the sections and a short reading list at the end of most sections.

Volume 1 is the first-semester book, covering fields, materials, basic waves and the first transmission-line theory. Volume 2 builds on it with wave propagation in lossy media and skin effect, reflection and refraction at boundaries, waveguides, microstrip and coaxial lines, optical fiber, radiation, and antennas. That makes it a strong match for the waves, transmission lines and antennas half of a BSEE course. Chapter 1 reviews Volume 1, so you can start here even if your first semester used another textbook.

Book Overview

Chapter List

Chapter 1: Preliminary Concepts

Difficulty: Easy · Key topics: SI units and prefixes, notation, coordinate systems, Maxwell’s equations, boundary conditions, constitutive parameters, uniform plane waves

This short opening chapter is a reset button, not new theory. It lists the SI units and prefixes used in electromagnetics, explains the notation (phasors carry a tilde), and sets out the Cartesian, cylindrical and spherical coordinate systems. Section 1.4 then condenses Volume 1: charge and current, electrostatics, magnetostatics, the boundary conditions between two materials, Faraday’s law and displacement current, static versus time-varying Maxwell equations, time-harmonic waves, and uniform plane waves. It closes with the usual material assumptions of homogeneity, isotropy, linearity and time-invariance.

Key Points:

• In the phasor domain, differentiation with respect to time becomes multiplication by jω, with ω = 2πf
• The time-varying Maxwell equations differ from the static ones in two places: Faraday’s law gains −∂B/∂t and Ampere’s law gains the displacement current ∂D/∂t
• Boundary conditions: tangential E and normal B are continuous; a jump in normal D needs surface charge, and a jump in tangential H needs surface current
• Lossless plane wave: phase velocity v_p = 1/√(με), wavelength λ = 2π/β, wave impedance η = √(μ/ε)
• E, H and the direction of propagation are mutually perpendicular, and power density is S = |E|²/(2η) when E is a peak value
• Ohm’s law for fields is J = σE; inside a perfect conductor E is essentially zero

Memory Tip: Treat the static-versus-time-varying table in Section 1.4 as a two-line cheat sheet. Only two terms change when fields vary in time, and they are the two that couple E and H into a wave.

Common Mistake: Skipping the chapter as “just review.” The notation conventions, especially that field amplitudes in the power formulas are peak values and not rms, are used in every later chapter.

Important Questions:

• What is the wave impedance of a medium, and what is its value in free space? η = √(μ/ε), the ratio of E to H in a plane wave. In free space it is about 377 Ω (120π Ω).
• Why is the displacement current needed? It lets a time-varying electric flux act as a source of magnetic field, so E and H become coupled and can sustain a propagating wave.

Chapter 2: Magnetostatics Redux

Difficulty: Medium · Key topics: Lorentz force, force on a current-carrying wire, torque on a current loop, motor principle, Biot-Savart law, magnetic field and work

Chapter 2 revisits magnetostatics with devices in mind. It starts with the Lorentz force, F = q(E + v × B), and the circling and drifting of charged particles in fields. The force on a wire follows from the same law: a closed loop in a uniform field feels no net force but can rotate, which is the simplest picture of an electric motor, and the chapter defines torque to describe it. Parallel wires attract or repel. The Biot-Savart law then gives the field of any steady current, including a circular loop. The last section shows that the magnetic field does no work, yet moving a conductor through it induces a potential.

Key Points:

• Lorentz force: F = q(E + v × B); the magnetic part is always perpendicular to the velocity
• Force on a straight wire segment in a uniform field: F = I l × B₀; the net force on a closed loop in a uniform field is zero
• Torque T = d × F, where d is the lever arm; its direction follows the right-hand rule and gives the sense of rotation
• Two long parallel wires exert a force per unit length of μ₀I₁I₂/(2πd); same-direction currents attract and opposite currents repel
• Biot-Savart law: dH = (I dl × R-hat)/(4πR²), with R-hat pointing from the source point to the field point; it is an inverse-square law valid only for steady currents
• The magnetic field does no work; a conductor of length l moving at speed v across a field B develops a potential of Bvl

Memory Tip: For parallel wires, think “same direction, they huddle”: currents flowing the same way attract, which is the opposite of the rule for like charges.

Common Mistake: Believing a magnetic field can speed a charged particle up. It only changes the direction of motion; any change in energy has to come from an electric field or a mechanical force.

Important Questions:

• What is the net force on a rigid closed current loop in a uniform magnetic field? Zero translational force, because the integral of dl around the loop vanishes. The loop can still rotate, since the torque is generally not zero.
• When do you use the Biot-Savart law instead of Ampere’s law? When the current has too little symmetry for Ampere’s law, such as a single loop of current; Biot-Savart adds up the field of each current element.

Chapter 3: Wave Propagation in General Media

Difficulty: Hard · Key topics: Poynting’s theorem, Poynting vector, complex permittivity, loss tangent, propagation constant, decibels, poor and good conductors, skin depth

Chapter 3 is where loss enters the wave theory. Poynting’s theorem is derived as conservation of energy: power leaving a volume equals what is dissipated plus what is stored in electric and magnetic fields, and the Poynting vector gives the direction and density of power flow. The wave equation is then extended to lossy regions by adding conduction current, which produces complex permittivity and the loss tangent. Plane waves in lossy media get a complex propagation constant, so fields decay exponentially. After a short section on decibels, the chapter treats poor conductors, good conductors and skin depth.

Key Points:

• Electromagnetic energy can be transferred, stored in an electric field, stored in a magnetic field, or dissipated; Poynting’s theorem balances all four, and the Poynting vector is S = E × H
• Complex permittivity is ε_c = ε′ − jε″, with ε″ = σ/ω for conduction loss; the loss tangent is tan δ = σ/(ωε)
• The propagation constant is γ = α + jβ; fields fall off as e^−αz while β sets the phase
• Power ratios in decibels use 10 log₁₀; the attenuation rate in dB per metre is about 8.69α
• In a good conductor ε″/ε′ ≫ 1 and α ≈ β ≈ √(πfμσ), so transmission-line attenuation grows roughly as √f
• Skin depth δ_s = 1/α is the distance over which field magnitude falls to 1/e (about 0.368)

Memory Tip: In a good conductor α and β are equal, so over one skin depth the phase also advances by exactly one radian. A wave that has lost 63% of its amplitude has also turned through one radian.

Common Mistake: Using “loss” with one meaning. In a poor conductor (a dielectric) loss is field energy turned into current; in a good conductor it is power dissipated in the resistance of a material that is meant to carry current.

Important Questions:

• A cable has 100 W going in and 1 W coming out. What is the loss in dB? The power ratio is 0.01, so G = 10 log₁₀(0.01) = −20 dB, which is a loss of 20 dB.
• What is skin depth, and why does thin metal shield well at high frequency? It is the depth at which fields fall to 1/e, and it shrinks as 1/√f. At high frequency a thin sheet is many skin depths thick, so almost no field gets through.

Chapter 4: Current Flow in Imperfect Conductors

Difficulty: Medium · Key topics: skin effect, AC current distribution, wire impedance, equivalent inductance, dispersion in lines, surface impedance, sheet resistance

This chapter applies skin depth to real wires. At DC, the electric field is constant and current spreads evenly through a wire. At AC, the field is a wave that decays inside a good conductor, so in the perfect-conductor limit all current sits on the surface, and in a real conductor it is concentrated near the surface and falls off exponentially with depth. Integrating that current gives the impedance of a wire, whose reactance equals its resistance and can be modelled as an equivalent inductance. The chapter closes by defining surface impedance, a material property in ohms per square that is the basis of sheet resistance.

Key Points:

• DC resistance of a wire is R = l/(σA); a perfect conductor has zero impedance at every frequency
• In the AC case, current in a good conductor flows in a layer about one skin depth thick and decays as e^−z/δs
• The AC impedance of a wire has equal resistive and reactive parts, which is modelled by an equivalent inductance that matters in the kHz range and fades in importance as frequency rises
• Skin effect makes phase velocity in transmission lines frequency-dependent, so higher frequencies travel faster; this is chromatic dispersion
• Surface impedance Z_S = (1 + j)/(σδ_s) is a materials property in Ω per square; its real part is the sheet resistance

Memory Tip: At radio frequencies a solid wire acts like a hollow tube, so its resistance depends on circumference times skin depth and not on cross-sectional area.

Common Mistake: Applying the DC formula R = l/(σA) with the full cross-section at RF. Only a thin outer layer carries current, so the real resistance is much higher.

Important Questions:

• Why can a hollow copper tube carry RF current almost as well as a solid rod of the same outer size? Because at high frequency the current sits within a skin depth of the surface, so the centre of a solid rod carries almost nothing.
• What is surface impedance and what are its units? It is the AC impedance of a conducting sheet per square, Z_S = (1 + j)/(σδ_s), written in ohms per square; it does not depend on length or width.

Chapter 5: Wave Reflection and Transmission

Difficulty: Hard · Key topics: normal incidence, material slab, half-wave and quarter-wave matching, TE and TM decomposition, oblique incidence, Snell’s law, Brewster’s angle, total internal reflection, evanescent waves

This is the longest chapter and covers what happens when a plane wave meets a boundary. It begins with normal incidence on one boundary, where the reflection coefficient comes from the two wave impedances, then moves to a slab between two media, with an equivalent impedance that behaves like a transmission-line input impedance, and conditions for total transmission. For oblique incidence, any wave is split into TE and TM parts and each is solved separately. The boundary conditions fix the angles of reflection and refraction, and the reflection coefficients lead to Brewster’s angle, total internal reflection and evanescent waves.

Key Points:

• Normal incidence: Γ = (η₂ − η₁)/(η₂ + η₁), the same form as a transmission-line reflection coefficient
• Total transmission through a slab with the same medium on both sides needs thickness d = mλ₂/2 (half-wave), where λ₂ is the wavelength inside the slab
• TE: E is transverse to the plane of incidence; TM: H is transverse to it; any incident wave is a sum of the two
• The angle of reflection equals the angle of incidence, and refraction follows Snell’s law, √(μ_r1ε_r1) sin ψ_i = √(μ_r2ε_r2) sin ψ_t
• Brewster’s angle is where the TM reflection coefficient is zero; for non-magnetic media tan ψ_B = √(ε_r2/ε_r1)
• Total internal reflection needs a wave going into a medium of lower permittivity at an angle beyond the critical angle, ψ_c = arcsin √(ε_r2/ε_r1) for non-magnetic media
• Beyond the critical angle the transmitted field is an evanescent wave: it decays exponentially away from the boundary and carries no power

Memory Tip: TE means the Electric field is Transverse to the plane of incidence, so it sticks out of the page; TM means the Magnetic field sticks out of the page.

Common Mistake: Looking for a critical angle when the wave goes from low to high permittivity, such as air into glass. Total internal reflection only happens when the second medium has the lower permittivity.

Important Questions:

• What is Brewster’s angle, and which polarisation does it affect? It is the angle of incidence at which the TM reflection coefficient is zero, so the reflected wave is purely TE. It is also called the polarizing angle.
• What does it mean that the field beyond the critical angle is evanescent? All incident power is reflected, and the field on the far side is a surface wave whose magnitude decays exponentially with distance and which stores no propagating power.

Chapter 6: Waveguides

Difficulty: Hard · Key topics: phase velocity, group velocity, parallel plate waveguide, TE and TM modes, TM0 mode, rectangular waveguide, cutoff frequency, propagation characteristics

Chapter 6 begins by separating phase velocity, the speed of a point of constant phase, from group velocity, the speed at which information travels. It then solves the parallel plate waveguide: the wave equation is split into TE and TM parts, giving discrete modes, each with a cutoff, plus the TM0 mode that has no cutoff and behaves like a plane wave between the plates. Section 6.7 shows how all field components of a unidirectional wave follow from the longitudinal ones. The rectangular waveguide is solved next, TM modes and then TE modes, ending with cutoff frequencies and the surprising velocity results.

Key Points:

• Phase velocity is v_p = ω/β; information travels at the group velocity, v_g = (dβ/dω)⁻¹
• Parallel plate modes are discrete; TM0 is the only mode with zero cutoff, so it exists at any plate spacing and is the model for microstrip
• In a rectangular waveguide of width a and height b, modes are labelled m and n; TM modes need both m and n at least 1, and TE modes can have one index zero but not both
• A mode propagates only above its cutoff, f_mn = [1/(2π√(με))] √[(mπ/a)² + (nπ/b)²]; below cutoff the field decays as e^−αz and carries no power
• Phase velocity in a propagating mode is above the free-space value, v_p = v_pu/√(1 − (f_mn/f)²), but group velocity is below it

Memory Tip: A waveguide is a high-pass filter. Below cutoff the wave dies away; above cutoff it travels, and the mode with the lowest cutoff, TE10 when a is larger than b, is the one that carries power first.

Common Mistake: Thinking a phase velocity above c breaks relativity. Phase velocity is only the speed of a point of constant phase; information moves at the group velocity, which stays below c.

Important Questions:

• What does it mean for a waveguide mode to be cut off? The operating frequency is below the mode’s cutoff frequency, so k_z is imaginary and the field decays exponentially along the guide instead of propagating.
• Which is the dominant mode of a rectangular waveguide with a > b, and why? TE10, because m = 1, n = 0 gives the lowest non-zero cutoff frequency when the wide side is a.

Chapter 7: Transmission Lines Redux

Difficulty: Medium · Key topics: parallel wire line, differential versus single-ended, microstrip, characteristic impedance, coaxial attenuation, power handling, why 50 ohms

Chapter 7 extends the transmission-line coverage from Volume 1. Section 7.1 treats parallel wire (twin lead) line, which is differential, cheap and low-loss up to about 100 MHz but not self-shielded. Section 7.2 studies microstrip: a trace over a ground plane on a dielectric operates below the cutoff of every mode except TM0, so its fields are close to TEM, and its characteristic impedance is estimated for wide, narrow and in-between traces. Sections 7.3 and 7.4 work out coaxial cable attenuation and the power limit set by dielectric breakdown. Section 7.5 uses both to explain why 50 Ω is standard.

Key Points:

• For a low-loss line, Z₀ ≈ √(L′/C′), with L′ and C′ the inductance and capacitance per unit length
• Twin lead is balanced (differential) and unshielded, with a phase velocity of roughly 0.8c to 0.9c; coax is single-ended and self-shielding
• Wide microstrip behaves like a parallel plate capacitor, giving Z₀ ≈ η₀h/(√ε_r W) for W much larger than h
• Coax attenuation is lowest for Z₀ between (60 Ω)/√ε_r and (77 Ω)/√ε_r, so 60 to 77 Ω for air-filled cable
• Power handling is limited by the breakdown field and is highest for an outer-to-inner radius ratio near 1.65, about 30 Ω for air-filled coax
• 50 Ω is a compromise between those two optima, not a law of nature; 75 Ω is a common second standard

Memory Tip: Remember the 50 Ω story as two arrows: lowest loss pulls toward about 77 Ω, highest power pulls toward about 30 Ω, and 50 Ω is the middle that suits both.

Common Mistake: Treating 50 Ω as special physics or assuming every coax cable has it. It is a convention chosen from trade-offs, and 75 Ω is a widely used second standard.

Important Questions:

• Why did engineers settle on 50 Ω as a standard impedance? It sits between the impedance that minimises coax attenuation (60 to 77 Ω in air) and the one that maximises power handling (about 30 Ω), and it also suits common antennas and PCB traces.
• How does parallel wire line differ from coaxial line? Parallel wire line is symmetric and differential, with exposed fields; coax is single-ended, and its outer conductor shields the fields.

Chapter 8: Optical Fiber

Difficulty: Easy · Key topics: core and cladding, total internal reflection, acceptance angle, modal dispersion, delay spread, data-rate limit

The shortest chapter, with three sections, puts Chapter 5 to work. Optical fiber is a core surrounded by cladding of lower permittivity, so light inside strikes the boundary beyond the critical angle and stays trapped. Because the fiber is about ten thousand wavelengths across, a light ray can be treated as a plane wave at a flat boundary. Section 8.2 turns the critical-angle condition into an acceptance angle, a cone of entry angles that the fiber will guide. Section 8.3 explains dispersion: different ray paths take different times, the delay spread grows with length, and that sets a ceiling on data rate.

Key Points:

• Guiding needs a core index above the cladding index, n_f > n_c, where n = √ε_r
• The core-cladding boundary reflects totally when the angle of incidence is at least arcsin(n_c/n_f)
• The acceptance angle defines a cone; light entering outside it is not trapped
• The shortest path runs along the axis and the longest bounces at the threshold angle, giving delay spread τ = l(n_f/c)(n_f/n_c − 1)
• To avoid pulse overlap, τ must be smaller than T − t_on, so the maximum data rate falls in proportion to fiber length, even if the fiber is lossless
• Repeaters or single-mode fiber reduce the dispersion problem

Memory Tip: Picture runners on a long track, some taking the straight line and others zig-zagging. The longer the track, the more the pack spreads out, and the further apart you must space the starts.

Common Mistake: Assuming loss is the only thing that limits a fiber link. Modal dispersion limits the data rate of multimode fiber even when the fiber has no loss at all.

Important Questions:

• What condition must the core and cladding satisfy for light to be guided? The core must have a higher index (permittivity) than the cladding, and rays must meet the boundary at or beyond the critical angle.
• Why does the maximum data rate of multimode fiber fall as the cable gets longer? Delay spread grows linearly with length, so pulses smear and overlap unless they are spaced further apart.

Chapter 9: Radiation

Difficulty: Hard · Key topics: current moment, magnetic vector potential, Lorenz gauge, Hertzian dipole, far-field approximation, electrically-short dipole, half-wave dipole, surface and volume currents

Chapter 9 asks what field a given current distribution produces. It starts informally with a current moment, a tiny current element at a point, then takes the rigorous route: magnetic vector potential reduces Maxwell’s equations to one inhomogeneous wave equation with the current as source. Its point-source solution is a spherical wave, and superposition extends it to any line current. The Hertzian dipole is the building block and gives a simple far field. The chapter applies this to the electrically-short dipole, to a thin straight filament, and to the half-wave dipole, and ends by showing that surface and volume currents need only a change of variable.

Key Points:

• The basic radiating source is a current moment I dl (units A·m); I dl, J_s ds and J dv all describe the same moment
• Magnetic vector potential A satisfies a wave equation with source −μJ; for a point source A = μ I dl e^−γr/(4πr)
• The recipe is current to A, then H = (1/μ)∇ × A, then E from Ampere’s law
• Far field means r much larger than both the source size and λ; the field is a spherical wave with a factor e^−jβr/r
• The Hertzian dipole field has a sin θ pattern: zero along the current axis, strongest broadside to it
• Electrically-short dipole: L much less than λ/2 with triangular current. Half-wave dipole: L = λ/2 with a cosine-shaped current that is zero at the ends

Memory Tip: Remember the chain J, A, H, E: start from the current, find the potential, take its curl for H, and get E last.

Common Mistake: Mixing up the Hertzian dipole, which has uniform current along its length, with the electrically-short dipole, which has triangular current. They give different radiation resistance, by a factor of 4.

Important Questions:

• What is the far-field approximation, and what does the radiated field look like? It applies when r is much greater than the source size and the wavelength. The field is a spherical wave: phase e^−jβr, magnitude falling as 1/r.
• Why does a short dipole radiate nothing along its own axis? The far field is proportional to sin θ, where θ is measured from the current direction, so it is zero when θ = 0 or 180 degrees.

Chapter 10: Antennas

Difficulty: Hard · Key topics: how antennas radiate, radiation resistance, radiation efficiency, directivity and gain, radiation pattern, reception model, reciprocity, effective aperture, Friis equation

The final chapter turns radiation theory into engineering models. It first explains why an ideal transmission line does not radiate while a bent end does. For transmission, the electrically-short dipole is modelled as an impedance with radiation resistance, loss resistance and reactance, and the chapter defines radiation efficiency, directivity, gain and the radiation pattern. For reception it builds a Thevenin equivalent circuit, proved with reciprocity and a derivation of the induced potential. It ends with effective aperture and the Friis transmission equation for a complete radio link.

Key Points:

• Antenna impedance is Z_A = R_rad + R_loss + jX_A, and radiation efficiency is R_rad/(R_rad + R_loss)
• For an electrically-short dipole R_rad ≈ 20π²(L/λ)², which is very small, and the reactance is large and negative, so impedance matching is needed
• Directivity D = S/S_ave; gain equals directivity times radiation efficiency; the short dipole has a maximum directivity of 1.5 (about 1.76 dB)
• A receiving antenna is a Thevenin source V_OC = E · l_e in series with Z_A, where l_e is the effective length, and it must be co-polarized with the wave
• Reciprocity relates what an antenna does when transmitting to what it does when receiving
• Effective aperture A_e = λ²G/(4π); Friis equation: P_R = P_T G_T G_R [λ/(4πR)]²

Memory Tip: Read the Friis equation as three factors: what you send (P_T G_T), how well you catch it (G_R), and how thinly it has spread over the distance, [λ/(4πR)]².

Common Mistake: Using the Friis equation without checking its assumptions. It needs free-space conditions, co-polarized antennas and a conjugate-matched receiver; any mismatch or polarization loss comes on top.

Important Questions:

• Why can’t a short dipole be connected directly to a typical transmission line? Its radiation resistance is tiny and its reactance is large and capacitive, so most power would reflect back. A matching network, for example a series inductor, is needed.
• State the Friis transmission equation and its assumptions. P_R = P_T G_T G_R [λ/(4πR)]², assuming free space, co-polarized antennas and a conjugate-matched receiver.

Appendices A–C: Material Parameters, Mathematical Formulas and Physical Constants

Appendix · Difficulty: Easy · Key topics: permittivity, permeability, conductivity, trigonometry, vector operators, vector identities, physical constants

The appendices are reference sheets repeated from Volume 1 with a few additions. Appendix A gives typical values and ranges of relative permittivity, relative permeability and conductivity for common materials, with notes on how they vary with frequency and temperature. Appendix B collects trigonometric and hyperbolic identities and lists the gradient, divergence, curl and Laplacian in Cartesian, cylindrical and spherical coordinates, followed by vector identities. Appendix C lists the physical constants used in the text. They are meant for looking things up while solving problems, not for reading straight through.

Key Points:

• Gases and vacuum have relative permittivity very close to 1; liquid water is roughly 72 to 81; dry soil is about 2.5 to 3.5
• Nearly all materials have relative permeability close to 1; the exceptions are ferromagnetic metals and ferrites
• Conductivity depends on frequency and temperature; copper, gold and aluminum are all in the 10⁷ S/m range
• Appendix B gives each vector operator in all three coordinate systems, which Chapters 6, 9 and 10 rely on

Memory Tip: Before an exam, try writing the Laplacian and curl in spherical coordinates from memory, then check against Appendix B; Chapters 9 and 10 use these constantly.

Common Mistake: Treating the table values as exact. The book itself says permittivity and conductivity vary with frequency, temperature and composition, so use the numbers given in your problem.

Important Questions:

• Which common materials have a relative permeability very different from 1? Mostly ferromagnetic metals such as iron, and ferrites; nearly every other material is close to the free-space value.
• Why does a conductivity value from a table need care? Conductivity changes with frequency and temperature, so tabulated values are representative figures, not precise constants.

Download Electromagnetics Vol. 2 PDF (Free)

This book is free from its official source, Virginia Tech’s VTechWorks repository. Click the button below to open the official page for Electromagnetics, Volume 2, where you can download the PDF.

How to Study This Book

This is the second half of a two-book sequence. The author’s own preface names Electromagnetics Volume 1 (Ellingson, 2018) as the presumed first-semester text, but says its exact topics and order are not an essential prerequisite, so a different first-semester book works too. Volume 1 is a separate book. What you do need is electric circuits and linear systems from second year, plus complex numbers, trigonometry, vector calculus, partial differential equations and multivariable calculus. Use Section 1.4 as your checklist: if any equation in it looks unfamiliar, go back to your first-semester notes before Chapter 3.

Chapter 2 stands on its own and can be read before or after the rest. Chapters 3 and 4 are one chain about loss. Do not skip Sections 3.3 to 3.6, because the complex permittivity and the propagation constant γ = α + jβ are what Sections 3.10 to 3.12 and Chapter 4 build on. Chapters 5 to 7 mostly assume lossless media, and loss returns with coaxial attenuation in Section 7.3.

Chapter 5 should be read in order. Read 5.1 first, because every later reflection coefficient is a variation on it; 5.2 and 5.3 then add the slab. For oblique incidence, 5.5 sets up the TE and TM decomposition, and the book itself recommends doing the TE case (5.6) before the TM case (5.7). Sections 5.8 to 5.12 turn those results into Snell’s law, Brewster’s angle and total internal reflection. If your course is short on time, protect 5.1, 5.5 to 5.8 and 5.11.

Chapter 6 is the most equation-heavy chapter. Read 6.1 on phase and group velocity, then treat the parallel plate guide (6.2 to 6.6) as a warm-up for the rectangular guide (6.7 to 6.10), which repeats the same pattern with two mode indices. If the derivations feel long, focus on the results in 6.10: cutoff frequency, phase velocity and group velocity. Chapter 7 is mostly independent; Section 7.5 (“Why 50 Ohms?”) makes a good first read because it explains why the earlier sections matter. Chapter 8 has only three sections and needs only Section 5.11, so it is a one-evening chapter.

Chapters 9 and 10 form the antenna block. Work through 9.1 to 9.5 before opening Chapter 10. Sections 9.2 and 9.3 are heavy derivations, but their results are short: remember the vector-potential solution and the far-field expression from 9.4. Within Chapter 10, Sections 10.1 to 10.8 are the transmit side (efficiency, impedance, directivity, pattern). Sections 10.9 to 10.12 are the receive side; 10.9 is an informal first pass and 10.11 to 10.12 give the rigorous version using reciprocity. Sections 10.13 and 10.14 bring everything together in effective aperture and the Friis equation.

Know what the book does not do. It stays with single-element analysis, so there are no antenna arrays, no horn or patch antenna design, no circular waveguides, no cavity resonators and no Smith chart. The PDF has no end-of-chapter problems; practice comes from the more than 40 worked examples inside the sections, and the official page lists problem sets and a solution manual as separate files. Because the book is assembled from reusable modules, a few cross-references say a section “may appear in a different volume”; that is the module system, not a missing page.

The official page offers two PDF versions: a standard PDF and a screen-reader-friendly PDF with the same content. Either works for study. Keep the Wikipedia “Additional Reading” links at the end of most sections for second explanations of the same idea.

Used In These Programs

This book is used for the Electromagnetic Waves course in: BS Electrical Engineering. Browse all Electromagnetics books or all Engineering category books.

Who Should Read This

Electromagnetics Volume 2 is written for BSEE students in the second electromagnetics course of a two-semester sequence, usually in the third year, and also suits telecommunications and RF-focused electrical programs. It is a good fit if you are taking a course on electromagnetic waves, transmission lines, waveguides and antennas, and it works as a free reference next to another textbook. It is not a first introduction to electric and magnetic fields. If your calculus-level electricity and magnetism feels shaky, the University Physics Volume 2 page covers electricity, magnetism and electromagnetic waves and is a useful refresher, and Calculus Volume 3 covers the vector calculus used from Chapter 2 onward. The book will also help physics students who want the engineering side of waves and antennas. It is less suited to readers who need a full treatment of antenna arrays or microwave circuit design.

Applicable Universities

This book is useful for students at Pakistani universities offering BS Electrical Engineering, including UET Lahore, UET Taxila, NUST, COMSATS, NED, GIKI, FAST, and other HEC-recognized institutions, wherever a second-semester course in electromagnetic waves, transmission lines and antennas is part of the degree.

FAQs

Related Books

• University Physics Volume 2 – OpenStax (electricity, magnetism and electromagnetic waves at calculus level)
• University Physics Volume 1 – OpenStax (the wave ideas of superposition, wavelength and frequency)
• University Physics Volume 3 – OpenStax (optics, reflection, refraction and interference)
• Calculus Volume 3 – OpenStax (the vector calculus behind div, curl and line integrals)

Electromagnetics, Volume 2 gives BSEE students a free route from lossy waves and skin effect through waveguides and transmission lines to antennas and the Friis equation. Browse more Engineering books or Physics books for the rest of your semester.

Electromagnetics, Volume 2, by Steven W. Ellingson. Virginia Tech Publishing, 2020. Copyright 2020 Steven W. Ellingson. Free under a Creative Commons Attribution-ShareAlike 4.0 licence (CC BY-SA 4.0). DOI: https://doi.org/10.21061/electromagnetics-vol-2 . Official source: https://vtechworks.lib.vt.edu/handle/10919/93253