Skip to Chapter: 1, 2, 3, 4, 5, 6, 7, 8, 9
1-1
Use SI units for problem solving
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.
1-5
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
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.
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.
Demonstrate conservation of energy for high frequency circuits.
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.
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 the difference between conductors and dielectrics.
Define the electron drift velocity.
Define conduction current.
Describe a perfect dielectric.
Describe a perfect conductor.
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.
5-4
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 an 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.
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.
7-6
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.
8-3
Define index of refraction.
Determine the critical angle.
Determine the acceptance angle.
Explain the cause of modal dispersion.
Determine the usable data rate for a fiber.
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 elevation plane and azimuth plane.
Define the solid angle.
Determine the total power radiated by an antenna.
Determine the direction of maximum radiation of an antenna.
Define radiation lobes, main lobe, side lobes, and back lobes.
Define and determine beamwidth, half-power beamwidth, half-power angles and null beam-width.
Determine the pattern solid angle for an antenna.
Define and determine the directivity of an antenna.
Define and determine the radiation efficiency and gain of an antenna.
Calculate the radiation resistance and loss resistance.