# Chapter 7 Summary

# Concepts

- A spherical wave radiated by a source becomes approximately a uniform plane wave at large distances from the source.

- The electric and magnetic fields of a transverse electromagnetic (TEM) wave are orthogonal to each other, and both are perpendicular to the direction of wave travel.

- The magnitudes of the electric and magnetic fields of a TEM wave are related by the intrinsic impedance of the medium.

- Wave polarization describes the shape of the locus of the tip of the E vector at a given point in space as a function of time. The polarization state, which may be linear, circular, or elliptical, is governed by the ratio of the magnitudes of and the difference in phase between the two orthogonal components of the electric field vector.

- Media are classified as lossless, low-loss, quasi-conducting, or good conducting on the basis of the ratio ε′′/ε′=σ/ω ε.

- Unlike the dc case, where the current flowing through a wire is distributed uniformly across its cross section, the ac case has most of the current is concentrated along the outer perimeter of the wire.

- Power density carried by a plane EM wave traveling in an unbounded medium is akin to the power carried by the voltage/current wave on a transmission line.

# Mathematical and Physical Models

Complex Permittivity

ε c=ε′−j ε″ε′=ε ε″=σ ω

Lossless Medium

k=ω μ ε η=μ ε (Ω)u p=ω k=1 μ ε (m/s)λ=2 π k=u p f (m)

Wave Polarization

H˜=1 η k ˆ×E˜E˜=−η k ˆ×H˜

Maxwell’s Equations for Time-Harmonic Fields

∇⋅E˜=0∇×E˜=−j ω μ H˜∇⋅H˜=0∇×H˜=j ω ε c E˜

Lossy Medium

α=ω{ μ ε′2[ 1+(ε″ε′)2−1 ] }1/2 (Np/m)β=ω{ μ ε′2[ 1+(ε″ε′)2+1 ] }1/2 (rad/m)η c=μ ε c=μ ε′(1−j ε″ε′)−1/2 (Ω)δ s=1 α (m)

Power Density

S av=1 2 ℜ e[E˜×H˜*] (W/m 2)

# Important Terms

Provide definitions or explain the meaning of the following terms:

- attenuation constant α

- attenuation rate A

- auxiliary angle ψ 0

- average power density S av

- axial ratio

- circular polarization

- complex permittivity ε c

- dc and ac resistances

- elliptical polarization

- ellipticity angle χ

- good conductor

- guided wave

- homogeneous wave equation

- in phase

- inclination angle

- internal or surface impedance

- intrinsic impedance η

- LHC and RHC polarizations

- linear polarization

- lossy medium

- low-loss dielectric

- out of phase

- phase constant β

- phase velocity

- polarization state

- Poynting vector S

- propagation constant γ

- quasi-conductor

- rotation angle γ

- skin depth δ s

- spherical wave

- surface resistance R s

- TEM wave

- unbounded

- unbounded wave

- uniform plane wave

- wave polarization

- wavefront

- wavenumber k