EECE 557 Study Sheets

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VECTOR ARITHMETIC/COORDINATE SYSTEMS

Dot and cross product

rules for calculation; meaning
component of a vector
position and distance vectors

Coordinate systems
Conversion: between cartesian and cylindrical; between cylindrical and spherical

VECTOR CALCULUS

Line, surface, volume integrals
Del operator
Gradient: definition, use
Divergence: definition, use, divergence theorem
Curl: definition, use, Stoke's theorem
Scalar Laplacian: definition, use
Classification of vector fields

Divergenceless, solenoidal, source-free
Curl-free, irrotational, conservative

ELECTROSTATICS

Definition of electric field: force/unit charge
Source of electric field:

Coulomb's law: formulas for E, F from point, line, surface, volume charge
Superposition

Gauss' Law: integral form

definition/meaning of flux
finding D, E for symmetrical charge distributions

Gauss' Law: point form

meaning of divergence; how to calculate

Electric potential (voltage): compute V from E and vice versa

meaning of gradient of a vector

Flux lines and equipotentials: rules for drawing, meaning
Faraday's Law (static case)

meaning of conservative/curl-free field

Energy stored in electric field
Material properties: conductivity, permittivity
Conservation of charge/continuity of current equation

diffusion of charge in conductor, RC time constant
time for charge to reach equilibrium

Current, Ohm's Law
Resistance of simple geometries
Power dissipated by resistance
Dielectrics: dielectric polarization

meaning of permittivity; linearity/homogeneity/isotropy
dielectric breakdown
difference between E and D

Boundary conditions on E, D

dielectric/dielectric, conductor/dielectric

Capacitance: definition, how to compute
Resistance: definition, how to compute, relation to capacitance
Laplace's equation to find V, E, D for one-dimensional problems
Image method for finding E, V near conducting boundaries

MAGNETOSTATICS

Biot-Savart Law: Know that steady current creates magnetic field

know the derived formula for H due to a current segment--and how to use it.
be able to sketch the magnetic field/flux density for a given current geometry

Ampere's Law; Stokes' Theorem

compute H from I (or J) for symmetrical current distributions
verify Stokes' Theorem for a given vector field

Magnetic flux density: know the difference between B and H

know the integral definition of magnetic flux; flux thru open or closed surface
know the form of Maxwell's equations for static fields

Lorenz Force Law: F = Q(E + u x B) = ma

how much energy does B impart to a charged particle?
what is the path of a moving charge in a B field?
what is the direction of force between two currents?
what is the torque on a loop of current in a B field?

Inductance: definition, how to compute

calculate self inductance for simple geometries (internal, external)
calculate mutual inductance for simple geometries
energy stored in magnetic field

Magnetic materials and boundary conditions

be able to derive electric and magnetic boundary conditions
be able to calculate incidence/transmission angles
know the model of ferromagnetic domains
distinguish non-magnetic, ferromagnetic and ferrimagnetic materials
define permeability in plain English
Why are ferrimagnetic materials useful?
know hysteresis:

why is a narrow hysteresis loop desirable?
how is hysteresis related to permanent magnetism?
how is hysteresis useful (magnetic memory)
postulate a reason for saturation based on the domain model

superconductors exclude magnetic flux: how?

Magnetic circuits: know analogy with electric circuits

be able to solve for reluctance, flux, force and pressure

TIME-VARYING ELECTROMAGNETIC FIELDS

Faraday's Law

calculate induced emf due to a) moving conductors; b) changing B; c) both.
be able to predict direction of current flow: Lenz's Law

Displacement current--know complete Ampere's law

know continuity-of-current equation and its meaning
know definition of displacement current
calculate electric field from magnetic field using Ampere's Law
why was Maxwell's displacement current not easily verified?

Maxwell's Equations

write all 4 equations in both integral and point (differential) form
give a "translation" of each equation into plain English
in a given medium, find electric field from magnetic field and vice versa

Phasor notation
Conversion between time and frequency domains

ELECTROMAGNETIC WAVES--PLANE WAVES

Plane waves: solution to wave equation

expressions for E and H in lossless and lossy media
find E from H and vice versa
find magnitude, direction, wavelength of a wave given f and E or H

Plane waves in lossy media

intrinsic impedance
phase constant/wave number
attenuation constant/absorption coefficient, skin depth
propagation constant, loss tangent, loss angle
complex permittivity
wavelength, velocity
direction of propagation
simplifications for good conductors, good dielectrics
how to tell whether simplification is valid

Skin effect

definition of skin depth
calculate resistance of a geometry at a given frequency

Dielectric loss

how different from conductive loss?
physical explanation

Poynting vector

instantaneous and time-averaged power density
total power crossing a surface
meaning of Poynting vector (equivalent circuit)

Reflection/transmission at normal incidence:

reflection coefficient
input impedance
standing-wave ratio,
power transmitted/reflected
"transmission-line analogy" for layers of dielectrics

Reflection/transmission at oblique incidence:

Snell's Law
parallel and perpendicular polarization
power transmitted/reflected, conservation of power
Brewster angle: uses, why only parallel?

TRANSMISSION LINES

Equivalent Circuit

derivations of R, L, C, G from Maxwell's equations

Properties of waves on line: what do they mean, formulae

velocity, wavelength
characteristic impedance/admittance
propagation constant: attenuation and phase constants

Distortionless line: definition, usefulness
(T-lines and plane waves:) Meanings, formulae, usefulness of:

Reflection coefficient
Input impedance
Standing-wave ratio
Power transmitted/reflected

Matching methods: when used, why and how to compute specifications

quarter-wave transformer
stub match (single only)

Slotted line for measurement of load impedance
Smith Chart: Remember:

1) normalize/unnormalize
2) y or z?
3) towards generator (TG) or towards load (TL)?
how to read reflection coefficient, SWR on chart

Transients on transmission lines:

draw bounce diagram
plot v(t), i(t) at a point on the line

GUIDED WAVES

Differences between: TEM waves, plane waves, TM, TE waves

Examples of uses of each
Why no TEM in a waveguide?

Intrinsic impedance, velocity of TEM wave

relations between L, C, µ, epsilon, c, eta

TE/TM modes on waveguide

Why is single-mode preferred?
Which single mode is preferred, why?
Given frequency of operation, select possible a, b dimensions for guide
Cutoff frequency; why won't wave propagate at f < f_c
Power and loss in waveguide