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6.013

Electromagnetics and Applications

Undergraduate · Historical course

Spring 2009

Topics

  • Foundations, forces and fields, Gauss’s and Ampere’s laws (∫) for static fields
  • Vectors, •, ×, static field integral-solution examples: find E(r) for sphere, cylinder; Φ(r); H(r) for wire
  • Media, boundary conditions
  • Resistors, capacitors, devices as circuits, E relaxation τ = RC = ε/σ; if time, coaxial R
  • Review vector operators; Maxwell’s differential equations (t), E, H, uniform plane wave; sin (ωt)
  • Complex Maxwell’s equation, sinusoidal UPW, wave polarization
  • Poynting theorem derivation (time), UPW example (w e , w m , S(t))
  • Inductors, solenoidal; τ = L/R; vector operators; planar, cylindrical, spherical examples
  • Show w e = CV 2 /2, w m = LI 2 /2; toroidal inductors, inductors with gaps, transformers
  • Electric forces on e-beams, C plates, force from ∂w/∂z; generators and sensors
  • Magnetic forces: electron optics, motors and generators
  • Magnetic pressure, rotary wire and reluctance motors, forces on materials
  • Wave forces; E and H field relaxation; examples from L5-R7
  • Static Φ and fields, Laplace’s equation, separation of variables (x,y,z); inhomogeneous materials
  • Review: complex differential Maxwell’s equations (ω); UPW, polarization
  • Electromagnetic fields in media, uniaxial media, quarter-wave plate
  • Lossy media, skin depth, plasmas; fields, power, and energy
  • Boundary conditions, k•r, phase matching, non-uniform plane wave, Snell’s law
  • Boundary conditions, σ = ∞, perpendicular reflection from ε and σ = ∞; examples at angles
  • TE at planar boundary, TM by duality, Brewster’s angle
  • Derive v p , v g for 2 sines, plasma example, power and energy examples
  • Device and line delays; TEM parallel-plate line, telegraphers’ equation, Z o
  • TEM transients, graphical solution
  • Transients: Thevenin equivalents; L, C, diode loads; initial conditions; lossy TEM
  • Examples of transients: loads, initial conditions, analytic expressions
  • Architecture, generalized TEM line, Ζ(z), Γ(z), Ζ transformations
  • Gamma plane, Smith chart, VSWR
  • RLC resonators, series, parallel, ω o , ∆ω, α, Q L , Q I , Q E , coupling
  • Smith chart, single-stub tuning, Y n (z), λ/4 transformer
  • TEM resonators, w e (t), w m (t), Q, ∆ω, examples; |V(z,f)|
  • TE, TM parallel plate waveguide, k x , k y , E , H , v g , v p , cutoff, evanescence; waveguide movies
  • TE mn rectangular waveguide, cavity resonators, perturbations
  • TM waveguides, field sketches, Poynting vector; examples from L16
  • Conservation of energy, power, G(θ,φ), A e = Gλ 2 /4π, R r , V Th , RF links
  • RF link examples, bit rates, radar applications
  • Radiation by charges ρ, current J ; Φ and Ā; static, dynamic (t)
  • Radiation by current elements, Hertzian dipole, near and far fields; Biot-Savart
  • Wire antennas, wire arrays
  • Receiving antennas: V Th in dipoles and loops; d<<λ/2π, G = 4πA/λ 2
  • Mirrors, 2-dipole arrays with mirrors, ground reflections, propagation, thermal noise
  • Aperture antennas, diffraction
  • Link and antenna examples, phasor addition, radio astronomy, remote sensing
  • Optical fibers, applications, dielectric slab waveguide, fiber design
  • Waveguide dispersion (v g and v p in fiber waveguides), optical link examples
  • Lasers
  • Optical resonators, filters, multiplexers, interferometer/modulators, detectors
  • Acoustic waves, boundary conditions, reflections, antennas
  • Acoustic waveguides and resonators, resonator coupling
  • Course philosophy, resonator perturbations and speech generation

Readings

Fall 2005

Topics

  • Review of vector and integral calculus; cartesian, cylindrical, and spherical coordinate systems; e j(ωt-kz) complex notation; gradient, curl, and divergence
  • Simple problems using superposition and integral forms of Gauss’ and Ampere’s laws with simple spatial distributions of volume charge density and volume current density
  • Derive boundary conditions; apply boundary conditions to surface charge and surface current problems
  • Boundary condition problems, e.g., perfectly conducting sphere or cylinder surrounding point or line charge or line current
  • Problem solutions using differential form of Maxwell’s equations: surface and volume charged or current carrying planar layer, cylinder and sphere
  • The electric field, electric scalar potential, and the gradient; Poisson’s and Laplace’s equations; potential of point charge; Coulomb superposition integral
  • The electric dipole (potential and electric field); simple problems using the Coulomb superposition integral (line charge, ring of line charge, disk of surface charge)
  • Method of images
  • Method of images problems with planes, cylinders, and spheres
  • Conservation of charge boundary condition; maxwell capacitor; magnetic dipoles and circuits; reluctance
  • Wave equation; Poynting’s theorem
  • Oblique incidence on a perfect conductor; transverse magnetic (TM) waves with oblique incidence on lossless media described by ε and µ; reflection and transmission; transverse electric (TE) waves with oblique incidence on lossless media
  • Lasers; applications to optics: polarization by reflection; totally reflecting prisms; fiber optics-straight light pipe, bent fiber
  • Lasers; optical devices
  • Transmission line sinusoidal steady state problems with short circuit, open circuit, and loaded ends; short-line limits as circuit approximations to capacitors and inductors
  • Impedance and VSWR problems using the Smith chart; single-stub tuner
  • Reflections from ends; driven and initial value problems
  • Rectangular waveguides; TM and TE modes; cut-off
  • Cavity resonators; group and phase velocity; dispersion relations; lasers
  • Force problems in capacitive and inductive systems
  • Ohm’s law for moving media; Faraday’s disk (homopolar generator); torque; equivalent circuit
  • Torque-speed characteristics of rotating machines
  • Radiation by charges and currents; setting the gauge; Lorentz gauge; superposition integral solutions for scalar and vector potentials; radiation from a point electric dipole; receiving antenna properties
  • Electric and magnetic fields from a point electric dipole; far-field solution; radiation resistance; effective dipole length; antenna gain
  • Transmitting and receiving antennas; wireless and optical communications
  • Wireless and optical communication problems
  • Acoustic waves
  • Acoustic wave boundary value problems
  • Course review

Readings

  • Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy . Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207. For figures and demos (out of print but available as a free online textbook .) ↗
    Listed reading
  • The table below provides the reading assignments for the course. The required readings are taken from the textbook Electromagnetics and Applications by D. H. Staelin. These readings are listed without an abbreviation in the table. The related reading sections for video demonstrations during the course are abbreviated as H/M. The entire contents of H/M can be found in Supplemental Resources > Electromagnetic Fields and Energy . ↗
    Listed reading
  • H/M = Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy . Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207.
    Listed reading
  • SES #: R1 · TOPICS: Review of vector and integral calculus; cartesian, cylindrical, and spherical coordinate systems; e j(ωt-kz) complex notation; gradient, curl, and divergence · READINGS: 1.2-1.5, appendices B, C
    Reading assignment
  • SES #: L2 · TOPICS: Derive boundary conditions; apply boundary conditions to surface charge and surface current problems · READINGS: 2.1
    Reading assignment
  • SES #: L4 · TOPICS: The electric field, electric scalar potential, and the gradient; Poisson’s and Laplace’s equations; potential of point charge; Coulomb superposition integral · READINGS: 2.2
    Reading assignment
  • SES #: L5 · TOPICS: Method of images · READINGS: 2.7
    Reading assignment
  • SES #: L8 · TOPICS: Wave equation; Poynting’s theorem · READINGS: 1.3.2, 1.4, 1.6
    Reading assignment
  • SES #: L9 · TOPICS: Oblique incidence on a perfect conductor; transverse magnetic (TM) waves with oblique incidence on lossless media described by ε and µ; reflection and transmission; transverse electric (TE) waves with oblique incidence on lossless media · READINGS: 5.3
    Reading assignment
  • SES #: R10 · TOPICS: Lasers; applications to optics: polarization by reflection; totally reflecting prisms; fiber optics-straight light pipe, bent fiber · READINGS: 11.3.2
    Reading assignment
  • SES #: R12 · TOPICS: Transmission line sinusoidal steady state problems with short circuit, open circuit, and loaded ends; short-line limits as circuit approximations to capacitors and inductors · READINGS: 5.2
    Reading assignment
  • Demo: V(z,t), I(z,t) movies
    Listed reading
  • SES #: R14 · TOPICS: Impedance and VSWR problems using the smith chart; single-stub tuner · READINGS: 5.2.4, 10.6.4
    Reading assignment
  • SES #: L13 · TOPICS: Reflections from ends; driven and initial value problems · READINGS: 5.2.1, 5.2.2, 9.2
    Reading assignment
  • SES #: L14 · TOPICS: Rectangular waveguides; TM and TE modes; cut-off · READINGS: 5.4.1, 5.4.3
    Reading assignment
  • SES #: R17 · TOPICS: Cavity resonators; group and phase velocity; dispersion relations; lasers · READINGS: 5.4.4, 10.7
    Reading assignment
  • SES #: R18 · TOPICS: Force problems in capacitive and inductive systems · READINGS: 8.1, 8.3
    Reading assignment
  • Film: Synchronous Machines
    Listed reading
  • SES #: L19 · TOPICS: Radiation by charges and currents; setting the gauge; Lorentz gauge; superposition integral solutions for scalar and vector potentials; radiation from a point electric dipole; receiving antenna properties · READINGS: 6.1.3, 6.2, 6.3
    Reading assignment
  • SES #: R22 · TOPICS: Electric and magnetic fields from a point electric dipole; far-field solution; radiation resistance; effective dipole length; antenna gain · READINGS: 6.3
    Reading assignment
  • SES #: L21 · TOPICS: Transmitting and receiving antennas; wireless and optical communications · READINGS: 10.1
    Reading assignment
  • SES #: L22 · TOPICS: Acoustic waves · READINGS: 12.1-12.3
    Reading assignment
  • SES #: R25 · TOPICS: Acoustic wave boundary value problems · READINGS: 12.4
    Reading assignment
Sources