6.013 | Spring 2009 | Undergraduate

# Electromagnetics and Applications

## Calendar

The calendar below provides information on the course’s lecture (L) and recitation (R) sessions.

UPW = uniform plane wave
TE = transverse electric
TM = transverse magnetic
TEM = transverse electromagnetic
VSWR = voltage standing wave ratio

SES # TOPICS DEMOS KEY DATES
Foundations
L1 Foundations, forces and fields, Gauss’s and Ampere’s laws (∫) for static fields Balloons Problem set 1 out
R1 Vectors, •, ×, static field integral-solution examples: find E(r) for sphere, cylinder; Φ(r); H(r) for wire
L2 Media, boundary conditions Boomer
R2 Resistors, capacitors, devices as circuits, E relaxation τ = RC = ε/σ; if time, coaxial R
L3 Review vector operators; Maxwell’s differential equations (t), E, H, uniform plane wave; sin (ωt) UPW movie Problem set 2 out
R3 Complex Maxwell’s equation, sinusoidal UPW, wave polarization Slinky
L4 Poynting theorem derivation (time), UPW example (we, wm, S(t)) Helmholtz
R4 Inductors, solenoidal; τ = L/R; vector operators; planar, cylindrical, spherical examples
R5 Show we = CV2/2, wm = LI2/2; toroidal inductors, inductors with gaps, transformers   Problem set 3 out
Forces, motors, generators, and MEMS
L5 Electric forces on e-beams, C plates, force from ∂w/∂z; generators and sensors
R6 Magnetic forces: electron optics, motors and generators
L6 Magnetic pressure, rotary wire and reluctance motors, forces on materials Motor Problem set 4 out
R7 Wave forces; E and H field relaxation; examples from L5-R7
L7 Static Φ and fields, Laplace’s equation, separation of variables (x,y,z); inhomogeneous materials Scooter
R8 Review: complex differential Maxwell’s equations (ω); UPW, polarization
Waves in media and at boundaries
L8 Electromagnetic fields in media, uniaxial media, quarter-wave plate Stressed media Problem set 5 out
R9 Lossy media, skin depth, plasmas; fields, power, and energy Wave movie
L9 Boundary conditions, k•r, phase matching, non-uniform plane wave, Snell’s law Prism
R10 Review for quiz 1
Quiz 1
R11 Boundary conditions, σ = ∞, perpendicular reflection from ε and σ = ∞; examples at angles
L10 TE at planar boundary, TM by duality, Brewster’s angle Brewster’s angle
R12 Derive vp, vg for 2 sines, plasma example, power and energy examples Dispersion video
Limits to computation speed
L11 Device and line delays; TEM parallel-plate line, telegraphers’ equation, Zo Fluorescent Problem set 6 out
R13 TEM transients, graphical solution
L12 Transients: Thevenin equivalents; L, C, diode loads; initial conditions; lossy TEM Transient movies
R14 Examples of transients: loads, initial conditions, analytic expressions
RF/microwave guidance and filtering
L13 Architecture, generalized TEM line, Ζ(z), Γ(z), Ζ transformations VSWR, slotted Problem set 7 out
R15 Gamma plane, Smith chart, VSWR
L14 RLC resonators, series, parallel, ωo, ∆ω, α, QL, QI, QE, coupling
R16 Smith chart, single-stub tuning, Yn(z), λ/4 transformer
L15 TEM resonators, we(t), wm(t), Q, ∆ω, examples; |V(z,f)| Coupled resonator video Problem set 8 out
R17 TE, TM parallel plate waveguide, kx, ky, E, H, vg, vp, cutoff, evanescence; waveguide movies
L16 TEmn rectangular waveguide, cavity resonators, perturbations Cavity resonator perturbation
R18 TM waveguides, field sketches, Poynting vector; examples from L16
Wireless communications
L17 Conservation of energy, power, G(θ,φ), Ae= Gλ2/4π, Rr, VTh, RF links   Problem set 9 out
R19 Review for quiz 2
Quiz 2
R20 RF link examples, bit rates, radar applications
R21 Radiation by charges ρ, current J; Φ and Ā; static, dynamic (t)   Problem set 10 out
L18 Radiation by current elements, Hertzian dipole, near and far fields; Biot-Savart Dipole video
R22 Wire antennas, wire arrays
L19 Receiving antennas: VTh in dipoles and loops; d<<λ/2π, G = 4πA/λ2 Yagi antenna Problem set 11 out
R23 Mirrors, 2-dipole arrays with mirrors, ground reflections, propagation, thermal noise
L20 Aperture antennas, diffraction Laser diffraction
R24 Link and antenna examples, phasor addition, radio astronomy, remote sensing
Optical communications
L21 Optical fibers, applications, dielectric slab waveguide, fiber design μW fiber Problem set 12 out
R25 Waveguide dispersion (vg and vp in fiber waveguides), optical link examples
L22 Lasers Simulated 3-level laser
R26 Optical resonators, filters, multiplexers, interferometer/modulators, detectors
Acoustics
L23 Acoustic waves, boundary conditions, reflections, antennas p, u(x,z,t) movie; keys
R27 Acoustic waveguides and resonators, resonator coupling
L24 Course philosophy, resonator perturbations and speech generation Acoustic resonator

## Course Info

Spring 2009
##### Learning Resource Types
Problem Sets with Solutions
Demonstration Videos
Exams with Solutions
Lecture Notes
Online Textbook