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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

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
• A 10GHz aircraft radar uses a narrow-beam
scanning antenna mounted on a gimbal behind a
• 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 no radome
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