Wave Incidence [Chapter 10 cont, Sadiku]

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Wave IncidenceChapter 10 cont, Sadiku

• Dr. Sandra Cruz-Pol
• Electrical and Computer Engineering Dept.
• UPR-Mayagüez

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Ex. Light traveling in air encounters the water
another medium.
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Wave incidence

• For many applications, such as fiber optics,
  line power transmission, its necessary to know
  what happens to a wave when it meets a different
  medium.
• How much is transmitted?
• How much is reflected back?

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We will look at

• Normal incidence
• Wave arrives at 0o from normal
• Standing waves
• Oblique incidence
• Wave arrives at another angle
• Snells Law and Critical angle
• Parallel or Perpendicular
• Brewster angle

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Reflection at Normal Incidence
x
z
y
z0
Medium 2
Medium 1
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Now in terms of equations

• Incident wave

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Reflected wave

• Its traveling along z axis

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Transmitted wave
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The total fields

• At medium 1 and medium 2
• Tangential components must be continuous at the
  interface

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Define

• Reflection coefficient, G
• Transmission coefficient, t

• Note
• 1 G t
• Both are dimensionless and may be complex
• 0G1

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PE 10.8

• A 5GHz uniform plane wave Eis 10e-jbz ax in free
  space is incident normally on a large plane,
  lossless dielectric slab (zgt0) having e 4eo and
  mmo.
• Find
• the reflected wave Ers and
• the transmitted wave Ets.

Answer -3.33 ejb1z x V/m, 6.67 e-jb2z x V/m
where b2 2b1 200 p/3
SEE http//www.acs.psu.edu/drussell/Demos/reflect/
reflect.html
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Case 1

• Medium 1 perfect dielectric, s10
• Medium 2 perfect conductor, s28
• Halla impedancias intrínseca.
• Reflección,
• Transmisión
• y campos
• http//www.phy.ntnu.edu.tw/java/waveSuperposition/
  waveSuperposition.html

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The EM field forms aStanding Wave on medium 1
E1
2Eio
z
Conducting material
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Standing Wave Applets

• http//www.phy.ntnu.edu.tw/java/waveSuperposition/
  waveSuperposition.html
• http//www.ngsir.netfirms.com/englishhtm/StatWave.
  htm
• http//www.physics.smu.edu/olness/www/03fall1320/
  applet/pipe-waves.html
• http//www.walter-fendt.de/ph14e/stwaverefl.htm

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Case 2

• Medium 1 perfect dielectric s10
• Medium 2 perfect dielectric s20

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Standing waves due to reflection
E1
Lossless Medium 1
Eio (1G)
z
0
Lossless Medium 2
At every half-wavelength, everything repeats!

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Case 3

• Medium 1 perfect dielectric s10
• Medium 2 perfect dielectric s20

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Standing waves due to reflection
E1
Lossless Medium 1
Eio (1G)
Eio (1-G)
z
0
Lossless Medium 2
At every half-wavelength, all em properties repeat
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Standing Wave Ratio, s

• Measures the amount of reflections, the more
  reflections, the larger the standing wave that is
  formed.
• The ratio of E1max to E1min
• or

Ideally s1 (0 dB) No reflections
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PE 10.9

• The plane wave E50 sin (wt 5x) ay V/m in a
  lossless medium (m4mo, eeo) encounters a lossy
  medium (mmo, e4eo, s0.1 mhos/m) normal to the
  x-axis at x0. Find
• G
• t
• s
• Er
• Et
• http//www.walter-fendt.de/ph14e/stwaverefl.htm

?Answers 0.8186
exp(j171o) 0.23 exp(j33.56o) 10.03 40.93 sin
(wt 5x 171o) y 11.5 e -6.02x sin (wt - 7.83x
33.6o) y V/m
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Ex. Antenna Radome

• A 10GHz aircraft radar uses a narrow-beam
  scanning antenna mounted on a gimbal behind a
  dielectric radome.
• Even though the radome shape is far from planar,
  it is approximately planar over the narrow extent
  of the radar beam.
• If the radome material is a lossless dielectric
  with mr1 and er9, choose its thickness d such
  that the radome appears transparent to the radar
  beam.
• Mechanical integrity requires d to be greater
  that 2.3 cm.

Antenna with radome
Antenna with no radome
Answer l/2.5cm, d2.5cm
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Power Flow in Medium 1

• The net average power density flowing in medium 1

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Power Flow in Transmitted wave

• The net average power density flowing in medium 2

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Power in Lossy Media

• where

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We will look at

• Normal incidence
• Wave arrives at 90o from the surface
• Standing waves
• Oblique incidence (lossless)
• Wave arrives at an angle
• Snells Law and Critical angle
• Parallel or Perpendicular
• Brewster angle