Fields and Waves

1
Fields and Waves
Lesson 5.2
PLANE WAVE PROPAGATION Lossless Media
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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
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Maxwells Equations in Phasor Domain
time domain
remember
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Complex Permittivity
complex permittivity
For lossless medium s0 e0 ec ee
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Wave Equations (charge free)

Homogenous wave equation for
propagation constant
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Plane Wave Propagation in Lossless Media
There are three constitutive parameters of the
medium s, e, µ
If the medium is nonconducting s0 a0 LOSSLESS
ec ee
Wavenumber k
(for a lossless medium)
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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
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Transverse Electromagnetic Wave
Spatial variation of and at t0
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Traveling waves
The Electric Field in phasor form (only x
component)
General solution of the differential equation
Amplitudes (constant)
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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
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Intrinsic impedance (?) 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

O
Phase velocity
m/s
wavelength
m
If the medium is vacuum up3x108 m/s, ?c377
O
Do Problem 2
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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
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Plane wave in a Lossless Medium
W/m2
Do Problem 3