Fields and Waves

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# Fields and Waves - PowerPoint PPT Presentation

Fields and Waves. Lesson 5.2. PLANE WAVE PROPAGATION Lossless Media. Time Harmonic Fields. EM wave propagation involves electric and magnetic fields having more than one component, each dependent on all three coordinates, in addition to time. . e.g. Electric field. vector phasor.

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Fields and Waves

Lesson 5.2

PLANE WAVE PROPAGATION

Lossless Media

Lale T. Ergene

Time Harmonic Fields

EM wave propagation involves electric and magnetic fields having more than one component, each dependent on all three coordinates, in addition to time.

e.g. Electric field

vector phasor

instantaneous field

Valid for the other fields and their sources

Complex Permittivity

complex permittivity

For lossless medium σ=0 ε’’=0 εc =ε’=ε

Wave Equations (charge free)

Homogenous wave equation for

propagation constant

Plane Wave Propagation in Lossless Media

There are three constitutive parameters of the medium: σ, ε, μ

If the medium is nonconducting σ=0 α=0 LOSSLESS

εc =ε’=ε

Wavenumber k

(for a lossless medium)

Transverse Electromagnetic Wave

• Electric and magnetic fields that are perpendicular to each other and to the direction of propagation
• They are uniform in planes perpendicular to the direction of propagation

x

• At large distances from physical antennas and ground, the waves can be approximated as uniform plane waves

Direction of propagation

z

y

Transverse Electromagnetic Wave

Spatial variation of and at t=0

Traveling waves

The Electric Field in phasor form (only x component)

General solution of the differential equation

Amplitudes (constant)

Uniform Plane waves

In general, a uniform plane wave traveling in the +z direction, may have x and y components

The relationship between them

Do Problem 1

Intrinsic impedance (η) of a lossless medium

• Similar to the characteristic impedance (Z0) of a transmission line
• Defines the connection between electric and magnetic fields of
• an EM wave

[Ω]

Phase velocity

[m/s]

wavelength

[m]

If the medium is vacuum : up=3x108 [m/s], ηc=377 [Ω]

Do Problem 2

Electromagnetic Power Density

• Poynting Vector , is defined

[W/unit area]

is along the propagation direction of the wave

Total power

[m/s]

[W]

[W]

OR

Average power density of the wave

[W/m2]