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Wave Incidence [Chapter 10 cont, Sadiku]

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Wave Incidence [Chapter 10 cont, Sadiku] Dr. Sandra Cruz-Pol Electrical and Computer Engineering Dept. UPR-Mayag ez – PowerPoint PPT presentation

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Title: Wave Incidence [Chapter 10 cont, Sadiku]


1
Wave Incidence Chapter 10 cont, Sadiku
  • Dr. Sandra Cruz-Pol
  • Electrical and Computer Engineering Dept.
  • UPR-Mayagüez

2
Ex. Light traveling in air encounters the water
another medium.
3
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?

4
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

5
Reflection at Normal Incidence
x
z
y
z0
Medium 2
Medium 1
6
Now in terms of equations
  • Incident wave

7
Reflected wave
  • Its traveling along z axis

8
Transmitted wave
9
The total fields
  • At medium 1 and medium 2
  • Tangential components must be continuous at the
    interface

10
Define
  • Reflection coefficient, G
  • Transmission coefficient, t
  • Note
  • 1 G t
  • Both are dimensionless and may be complex
  • 0G1

11
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
12
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

13
The EM field forms a Standing Wave on medium 1
E1
2Eio
z
Conducting material
14
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

15
Case 2
  • Medium 1 perfect dielectric s10
  • Medium 2 perfect dielectric s20

16
Standing waves due to reflection
E1
Lossless Medium 1
Eio (1G)
z
0
Lossless Medium 2
At every half-wavelength, everything repeats!

17
Case 3
  • Medium 1 perfect dielectric s10
  • Medium 2 perfect dielectric s20

18
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
19
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
20
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
21
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
22
Power Flow in Medium 1
  • The net average power density flowing in medium 1

23
Power Flow in Transmitted wave
  • The net average power density flowing in medium 2

24
Power in Lossy Media
  • where

25
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
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