Updated 01/05/04
Skip to Chapter: 1, 2, 3, 4, 5, 6, 7, 8, 9
1-1
Use SI units for problem solving
1-2
Explain the physical meaning of Coulomb’s Law and the electric field.
Explain the physical meaning of charge conservation.
Explain the physical meaning of the principle of linear superposition.
Explain the polarization process and its effect on the electric field.
Explain the physical meaning of the Biot – Savart Law.
Explain the difference between static and dynamic fields.
1-3
Explain the physical meaning of a traveling wave.
Describe an undistorted traveling wave mathematically.
Describe a sinusoidal traveling wave in both lossless and lossy mediums mathematically.
Solve for the frequency, wavelength, amplitude, phase velocity and propagation constant of a sinusoidal traveling wave.
Use the concept of phase lead and lag to graph a traveling wave as a function of time or position.
1-4
Describe the electromagnetic spectrum.
1-5
Use complex numbers.
1-6
Use phasors.
2-1
Explain the impact of signal frequency and transmission line length on circuit models.
Describe the two basic types of transmission lines
2-2
Describe the lumped-element model for transmission lines.
Determine when to use the lumped element model.
2-3
Derive the telegrapher’s equations.
2-4
Define the complex propagation constant.
Use the wave equation to determine the voltage and current for a transmission line.
Define characteristic impedance.
2-5
Explain the difference between lossless and dispersionless transmission lines.
Define the reflection coefficient and find its range.
Define the standing wave ratio and find its range.
Determine the maximum and minimum amplitudes of a standing wave.
Determine the location of the maximum and minimum amplitudes of a standing wave along a transmission line.
Solve for the reflection coefficient, standing wave ratio, characteristic impedance and load impedance of a transmission line.
2-6
Define input impedance.
Solve for the input impedance along a transmission line.
2-7
Use short or open circuited transmission lines to create reactive elements.
Apply short and open circuit measurements to find characteristic impedance.
Explain the utility of a quarterwave transformer.
Design a quarterwave transformer.
Explain the utility of a matched transmission line.
2-8
Explain the difference between instantaneous and average power.
Determine the power delivered to a load impedance.
Determine the power reflected by a load impedance.
Determine the power incident on a load impedance.
2-9
Define the general reflection coefficient.
Explain the relationship between the general reflection coefficient and the input impedance for a Smith chart.
Solve for VSWR, impedance, admittance, reflection coefficient and the locations of voltage and current minimums and maximums using a Smith chart.
2-10
Use a quarter-wave transformer and Smith chart to solve an impedance mismatch.
Design a single stub tuner using a Smith chart.
2-11
Explain when the transient response of a transmission line must be considered.
Describe a pulse using step functions.
Explain the transient behavior of a step function qualitatively and mathematically.
Explain the transient behavior of a pulse qualitatively and mathematically.
Use bounce diagrams to determine the voltage as a function of time at a point along a transmission line.
Explain how a time domain reflectometer is used to determine faults along a transmission line.
3-1
Determine the magnitude of a vector.
Determine the directions of a unit vector.
Define base vectors for a coordinate system.
Add and subtract vectors.
Find distance and position vectors.
Find simple, dot and cross products of vectors.
Find scalar and vector triple products
3-2
Define an orthogonal coordinate system.
Explain the coordinates and their ranges for the cartesian, cylindrical and spherical coordinate systems.
Find the differential length, areas and volume for each coordinate system.
Integrate to find a length, volume or surface area using the differential length, volume or area respectively.
Find the position vector for each coordinate system.
3-3
Transform coordinates, unit vectors, vector components and vectors from one coordinate system to another.
3-4
Explain the difference between a scalar and vector field.
Define “del” or the gradient operator.
Define the gradient of a scalar field.
Explain qualitatively and mathematically why the gradient of a scalar field at a point is a vector whose magnitude is the maximum rate of change of the scalar field at that point and whose direction is the direction of the maximum rate of change from that point.
Define and find a directional derivative.
Find the gradient of a scalar field.
Use the gradient of a scalar field to find the function describing the scalar field.
3-5
Define flux density for a vector field.
Find the total flux crossing a closed surface..
Define the divergence of a vector field.
Find the divergence of a vector field at a point.
Explain the difference between a source and sink of flux.
Define a divergenceless field.
State the divergence theorem.
Use the divergence theorem to find the total flux crossing a closed surface.
3-6
Define the circulation of a vector field for a closed path.
Find the circulation of a vector field for a closed path.
Define the curl of a vector field.
Find the curl of a vector field at a point.
Describe a vector field where the circulation is zero.
State Stoke’s theorem.
Use Stoke’s theorem to find the circulation of a vector field for a closed path.
3-7
Define the Laplacian operator.
Apply the Laplacian operator for scalar and vector fields.
4-1
State Maxwell’s equations.
State the static case for Maxwell’s equations.
Explain in simple terms the physical phenomena modeled by Maxwell’s equations.
4-2
Define charge density for a volume, surface or line.
Find the total charge contained in a volume, on a surface, or along a line.
Define current density.
Find total current flowing through a surface.
4-3
State Coulomb’s law and define each term.
Use Coulomb’s law to find the electric field due to a charge, multiple charges, or a continuous charge distribution (a volume, surface or line of charge).
4-4
State Gauss’s law in differential and integral form.
Determine when it is appropriate to use Gauss’s law to find the electric field intensity or flux density.
Determine appropriate Gaussian surfaces.
Use Gauss’s law to find the electric field intensity or flux density.
4-5
Define the differential electric potential (differential voltage).
Use the differential electric potential to find the potential difference between two points.
Explain why a static electric field is conservative.
Use a reference potential point of infinity to find the electric potential at a point.
Determine the electric potential at a point due to a charge, multiple charges, or a continuous charge distribution.
Use the gradient of the electric potential to find the electric field intensity.
State and apply Poisson’s and Laplace’s equations.
4-6
State the electromagnetic constitutive parameters of a material.
Explain when a material is homogeneous and/or isotropic.
Explain the difference between conductors and dielectrics.
Define the electron drift velocity.
Define conduction current.
Describe a perfect dielectric.
Describe a perfect conductor.
Define a semiconductor.
4-7
Define electron and hole mobility.
Define the hole drift velocity.
Define the conduction current density.
Explain the point form of Ohm’s law.
Apply the point form of Ohm’s law to find current, current density and/or electric field.
Use current density and electric field intensity to find resistance.
Use electric field intensity and current density to find power dissipation.
4-8
Explain how polarization occurs in the presence of an external electric field and effects the net electric field in nonpolar materials.
Explain the relationship between electric flux density, electric field intensity and the electric polarization field.
Define electric susceptibility.
Describe dielectric breakdown.
4-9
Derive the boundary condition for the tangential component of the electric field intensity.
Derive the boundary condition for the normal component of the electric flux density.
Use boundary conditions to determine the electric field at the interface of two or more materials
4-10
Find the capacitance of two conducting bodies using the electric field intensity.
Explain the relationship between magnetic flux density and magnetic field intensity for most nonferromagnetic materials.
5-1
Explain the mathematical relationship that models the force acting on a moving charge in a magnetic field.
Derive the mathematical relationship that models the force acting on a current in a magnetic field.
Solve for the force or acceleration for a charged particle moving in a magnetic field.
Define the Lorentz force
Explain the differences between electric and magnetic forces.
5-2
State the Biot-Savart Law.
Use the Biot-Savart law to find the magnetic field generated by a current.
Use the Biot-Savart law to find the magnetic field generated by a surface or volume current density.
5-4
Explain the physical phenomena or property described by Gauss’s law for magnetism.
Derive Ampere’s circuital law from the differential form of Maxwell’s second equation.
Use Ampere’s law to find the magnetic field intensity.
5-5
Define the vector magnetic potential.
Define vector Poisson’s equation.
Explain when the vector magnetic potential may be the best choice for determining the magnetic flux density.
Define magnetic flux.
Use the magnetic flux density or the magnetic vector potential to find the magnetic flux.
5-7
Derive the boundary condition for the tangential component of the magnetic field intensity.
Derive the boundary condition for the normal component of the magnetic flux density.
Use boundary conditions to determine the magnetic field at the interface of two or more materials.
6-1
Explain under what circumstances a magnetic field can produce and electric field.
Define the electromotive force.
State Faraday’s law.
Explain how an emf may be generated in a closed conducting loop.
6-2
Explain and use Lenz’s law.
Use Faraday’s law to determine emf, magnetic flux density and current.
6-7
Define displacement current.
Solve to find the displacement current.
6-8
Explain the boundary conditions for time varying fields.
6-9
Explain the charge continuity equation.
Use the charge continuity equation to find current density.
Explain the relationship between the charge continuity equation and Kirchhoff’s current law.
6-11
Use Faraday’s law to find magnetic field intensity from electric field intensity.
Explain the difference between guided and unbounded mediums for electromagnetic wave propagation.
Describe the orientation of the electric and magnetic fields in coaxial cable.
7-1
Transform vector fields, charge and current density between the time and phasor domains.
State Maxwell’s equations in the phasor domain.
Derive how time derivatives are represented in the phasor domain.
Define the complex permittivity.
Define a charge free medium.
Derive the homogeneous wave equation for the electric and magnetic fields.
7-2
Define the wave number.
State the homogeneous wave equation for a lossless medium.
Define a uniform plane wave.
Prove that a uniform plane wave does not have field components in the direction of propagation.
Define the intrinsic impedance of a lossless medium.
Define the phase velocity and wavelength of an electromagnetic wave in a lossless medium.
Solve for the phase velocity and intrinsic impedance of free space.
Solve for the phase velocity, wavelength, frequency and wave number of an electromagnetic wave in a lossless medium.
Relate magnetic field intensity phasor and electric field intensity phasor for a uniform plane wave traveling in an arbitrary direction
Find electric field given the magnetic field and the reverse.
7-3
Qualitatively describe the polarization of a uniform plane wave.
Mathematically describe the polarization of a linearly or circularly polarized uniform plane wave using its modulus and inclination angle.
7-4
Define the attenuation constant and phase constant for a uniform plane wave traveling in a lossy medium.
Define the intrinsic impedance of a lossy medium.
Represent a uniform plane wave in a lossy medium in both the phasor and time domains.
Define skin depth and its connection to plane wave propagation in conductive and dielectric materials.
Define a ”low loss” dielectric.
Define a “good” conductor.
Determine the attenuation of a uniform plane wave traveling in a lossy medium.
7-5
Derive the current density for a semi-infinite good conductor.
Derive the internal and surface impedance for a good conductor.
Solve for the surface impedance of a transmission line.
Find the resistance pre unit length of a coax cable.
7-6
Define the Poynting vector.
Determine the total power flowing through an area.
Determine the average power density of a uniform plane wave in a lossless medium
8-1
Define a “ray”.
Qualitatively explain the reflection and transmission of a uniform plane wave in an unbounded medium at a boundary.
Mathematically describe the reflection and transmission of a uniform plane wave in an unbounded medium at a boundary.
Define the reflection and transmission coefficients.
Explain the analogous relationship between the plane-wave equations at normal incidence and the transmission line equations.
Use the analogous relationship between plane wave equations at normal incidence and transmission line equations to solve for reflection and transmission coefficients, SWR, locations of min and max field intensities.
Explain how power flow along a transmission line is analogous to the average power density flowing in an unbounded medium.
Solve for the average power density of incident, reflected and transmitted uniform plane waves.
8-2
State Snell’s Law of reflection.
State Snell’s Law of refraction.
Define index of refraction.
Explain the relationship between the index of refraction and the dielectric constant (relative permittivity).
Define the critical angle and total internal reflection.
8-3
Define the acceptance angle.
Explain why different modes may be present in a fiber optic cable.
Describe modal dispersion.
Define reciprocity, antenna radiation pattern, isotropic antenna, antenna polarization and antenna impedance.
Describe the two groups of radiation sources and give examples of each.
Define the far-field region.
Define antenna arrays and describe how they steer the radiation electronically.
9-1
Define the short dipole antenna
Derive the phasor retarded vector potential for a volume containing a phasor current distribution.
Define the spherical propagation factor.
Define the range, zenith and azimuth angles.
Find the magnetic and electric field phasors using retarded magnetic vector potentials.
Describe the far field approximation for a short dipole.
Define the normalized radiation intensity.
Use the normalized radiation intensity for find the average power density radiated by an antenna.
9-2
Define the solid angle.
Use the solid angle to find the total radiated power.
Define the elevation plane, azimuth plane and principal planes.
Define radiation lobe.
Explain the effect of main , side and back lobes.
Define the pattern solid angle.
Define beam width, half-power beam width, 3-dB beam width and null beam width.
Define the directivity of an antenna.
Solve for the direction of maximum radiation, beam solid angle, half power beamwidth and directivity of an antenna.
Define radiation efficiency and antenna gain.
Define radiation resistance and loss resistance.
Solve for antenna gain and efficiency.