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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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Lesson 5.2

PLANE WAVE PROPAGATION

Lossless Media

Lale T. Ergene

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

time domain

remember

complex permittivity

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

Homogenous wave equation for

propagation constant

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)

• 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

Spatial variation of and at t=0

The Electric Field in phasor form (only x component)

General solution of the differential equation

Amplitudes (constant)

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

• 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]

[W/m2]

Do Problem 3