Fields and Waves I

1
Fields and Waves I

• Lecture 23
• Reflection and Transmission at Normal Incidence
• K. A. Connor
• Electrical, Computer, and Systems Engineering
  Department
• Rensselaer Polytechnic Institute, Troy, NY

2
These Slides Were Prepared by Prof. Kenneth A.
Connor Using Original Materials Written Mostly by
the Following

• Kenneth A. Connor ECSE Department, Rensselaer
  Polytechnic Institute, Troy, NY
• J. Darryl Michael GE Global Research Center,
  Niskayuna, NY
• Thomas P. Crowley National Institute of
  Standards and Technology, Boulder, CO
• Sheppard J. Salon ECSE Department, Rensselaer
  Polytechnic Institute, Troy, NY
• Lale Ergene ITU Informatics Institute,
  Istanbul, Turkey
• Jeffrey Braunstein Chung-Ang University, Seoul,
  Korea

Materials from other sources are referenced where
they are used. Those listed as Ulaby are figures
from Ulabys textbook.
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(No Transcript)
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Figure References for Previous Slide
http//z.about.com/d/goamsterdam/1/0/V/2/-/-/canal
_reflection-1.jpg
http//www.alanbauer.com/
http//contrapunctus.net/league/photo/pcd0077/003.
php?fmtbase_jpegset1
http//www.indelibleinc.com/kubrick/films/2001/ima
ges.html
http//www.widerange.org/images/large/palaReflecti
on.jpg
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From H.G. Wells The Invisible ManSignet Classic,
2002
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Overview

• EM Waves in Lossless Media
• Wave Equation General Solution
• Energy and Power
• EM Waves in Lossy Media
• Skin Depth
• Approximate wave parameters
• Low Loss Dielectrics
• Good Conductors
• Power and Power Deposition
• Wave Polarization
• Linear, circular elliptical
• Reflection and Transmission at Normal Incidence
• Plane Waves at Oblique Incidence

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Normal incidence

MEDIUM 2 ?2
MEDIUM 1 ?1
incident plane wave
transmitted plane wave
reflected plane wave

• wave is normally incident on an infinite
  interface separating two different media
• impedance discontinuity
• similar to the transmission lines
• EM waves represented with rays or wavefronts

8
Step 1
As with transmission lines, the very first step
is to write down the general solution for the
electric and magnetic field waves in each of the
media in the problem. Part of writing down the
fields is to draw the little diagram with the
three mutually perpendicular vectors for each
component of the plane wave. Maybe the first
step should be to review the properties of
transmission line waves since we will be doing
identical analysis for uniform plane waves.
9
Lossless media

• two lossless, homogenous, dielectric media

MEDIUM 2 e2, µ2
MEDIUM 1 e1, µ1
.
.
.
.
.
z0
Incident wave
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Lossless media
transmitted wave
reflected wave
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Step 2
Next we write down the boundary conditions that
obtain for the waves we are to analyze. Note from
the diagram that both the electric and magnetic
fields have only tangential components. For a
conducting boundary the electric field must be
zero if it is only tangential. This is possible
by having the sign of the reflected wave be the
negative of the incident wave while their
magnitudes are the same. For a dielectric
boundary, both the electric and magnetic fields
must be continuous. That is, the field on one
side of the boundary (incident reflected) must
equal the field on the other side of the boundary
(transmitted).
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Boundary conditions
Tangential component of the electric field should
be continuous across the boundary Tangential
component of magnetic field should be continuous
(no current source)
Note that inc ref trans not inc ref trans
At the boundary (z0)
or
or
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Example 1
A 10 GHz plane wave has an electric field
magnitude of 100 V/m and propagates in the az
direction through a perfect dielectric with
9. E is in the ax direction. a. What are the
incident E and H phasors? b. At z 0, the
wave strikes a perfect conductor. What are the
reflected E and H phasors? c. Use the boundary
conditions to find the surface current density in
the conductor. d. Draw the standing wave
pattern for E and H (include numbers for
amplitude and position). e. Simulate this case
with sing_bnd.m by using a large imaginary
dielectric for region 2. f. Calculate the total E
and H. (phasor time domain form).
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Example 1
15
Example 1
16
Example 1
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Standardize notation
We now use the standardized notation of
reflection and transmission coefficients, just as
we did with transmission lines.
Ratio of the reflected wave magnitude to the
incident wave magnitude. (We use the electric
field by convention.)
Ratio of the transmitted wave magnitude to the
incident wave magnitude. (We use the electric
field by convention.)
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reflection and transmission coefficients
Normally incident
Normally incident
G and t are real for lossless dielectric media
Normally incident
For nonmagnetic media
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transmission line analogy

• One to one correspondence between the
  transmission line parameters
  and plane wave parameters
• incident and reflected waves create a standing
  wave pattern

Standing wave ratio

• if ?1 ?2 G0 S1
• ?2 0 (perfect conductor) G-1 S 8

• Smith chart can be used
• the max and min locations of the electric field
  intensity from the boundary are defined by the
  same expressions for the voltage max and min
  locations

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Example 2
The same wave as in example 1 strikes a
dielectric-air boundary at z0 as shown below. a.
Find the reflection and transmission
coefficients. b. What are the reflected and
transmitted electric field phasors? c. What are
the reflected and transmitted H phasors? What is
Ht/Hi? d. What is the standing wave ratio in
the dielectric? Sketch the standing wave pattern
for E and H. Run sing_bnd.m for this problem.
e. What is the average power density of the
incident, reflected, and transmitted waves?
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Example 2
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Example 2
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Power flow in lossless media
The average power density flowing in medium 1
The average power density flowing in medium 2
For lossless media
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General Solution
Ei Er
Et
Hi Hr
Ht
Boundary
What quantities can be specified or
calculated? Magnitude of incident E, dielectric
properties of each region, intrinsic impedance of
each region, frequency, wavelength, incident
power, reflected power, transmitted power,
transmission coefficient, reflection coefficient,
standing wave ratio
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Lossless Transmission Lines
Uniform Plane Waves in Lossless Media
Total voltage and current
Total fields
Phase velocity
Propagation constant
Characteristic/Intrinsic impedance
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Lossless Transmission Lines
Uniform Plane Waves in Lossless Media
Generalized Reflection Coefficient
Total again
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Lossless Transmission Lines
Uniform Plane Waves in Lossless Media
Line or Wave Impedance
Also
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Lossless Transmission Lines
Uniform Plane Waves in Lossless Media
At another location z
Continuity of Z(z) at a boundary between two
regions
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Lossless Transmission Lines
Uniform Plane Waves in Lossless Media
Input impedance
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Multiple Boundaries
If A is incident, each reflection produces the
additional waves shown.
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Multiple Boundaries
The waves take the usual general form in each
region.
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Radomes
http//igscb.jpl.nasa.gov/network/site/areq.html
http//www.cmmacs.ernet.in/nal/picts/
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Radomes
http//www.air-and-space.com/200320Miramar20Airs
how20statics20page202.htm
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http//www.hiaper.ucar.edu/photo_gallery/031802.ht
ml
Radomes
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http//en.wikipedia.org/wiki/FileNavy-Radome.jpg
Radomes
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Radomes
http//www.collegeem.qc.ca/ena/avionique/photos/an
tennes/radar.htm
http//www.radome.net/nws.html
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Example 3
A 10 GHz radar transmitter is used in the
configuration shown below. Note that the
radome-outside air boundary is identical to the
boundary examined in example 2.
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Example 3
a. What is E/H at the z0 boundary of example
2? (equivalent to the region 2-3 boundary in
this problem). Compare it with the value in air.
b. Now refer to the full radome problem.
Where can you put the left boundary so that
E/H in the radome matches that in the air on
the left? For mechanical reasons, the radome
must be more than 2 cm thick. c. What is
for this value of d? d. What is if d is 0.2
mm thinner than designed?
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Example 3
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Summary of the radome problem
Thus, since regions 1 and 3 are the same, the
input impedance gives a perfect match and no
reflection occurs.
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Another common multiple boundary application
The radome is a half wavelength thick. We can
also use a layer one quarter wavelength thick to
eliminate reflections from a lens (at least at a
particular frequency).
Thus, since the input impedance is the same as
the intrinsic impedance of region 1, we again
have a perfect match and no reflection occurs.
42
Anti-Reflection Coating
http//hyperphysics.phy-astr.gsu.edu/hbase/phyopt/
antiref.htmlc3
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Anti-Reflection Coating
AR coatings are similar to the coatings found on
microscopes and camera lenses. They consist of
several layers of metal oxides applied to the
front and back lens surfaces. Because of the
layering effect, AR coatings sometimes have a
hint of green or purple color, depending on the
individual manufacturer's formula.
For an experiment at Oberlin, the coated lens was
optimized for the middle of the visible spectrum
so red and blue are reflected to form violet
http//www.oberlin.edu/physics/catalog/demonstrati
ons/optics/coatedlens.html
http//news.thomasnet.com/fullstory/23211/1782
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Multiple vs Single Layer Coating
From left to right a lens without coating, single
coated and multicoated. From the first to the
third image the light transmission improved from
96 to 99.5
http//www.astrosurf.org/lombry/reports-coating.ht
m
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Multiple vs Single Layer Coating
The principle of coatings is to reduce the light
reflecting on the glass surface. If the coating
has a quarter wavelength thickness and the glass
yields an index of refraction higher than the one
of the coating the two reflections are in phase
opposition and cancel. For one multicoated
surface the transmission can increase up to 3.5.
Single
Multiple
http//www.kenrockwell.com/tech/lenstech.htm
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Anti-Reflection Coating
One of the characteristics of an AR coating is
the colour of the residual 1 reflection on the
lens - sometimes called the bloom. On modern
broadband Reflection Free lenses it can be tuned
to be either a soft green or blue without
compromising the quality of the anti-reflection
properties. The AR bloom should not be confused
with a permanent lens tint. An AR bloom is almost
imperceptible and can only be seen when holding
the lens up to sunlight or artificial light.
http//www.siltint.com/Ophthalmic_products/technic
al.htm
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Question
From the point of view of an EE, CSE or EPE, what
are we doing when we eliminate reflections?
Impedance Matching
A great deal of what we do as engineers is really
impedance matching. When impedances match, we
usually have the optimum operating conditions we
seek.
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Boundary between lossy media

• two lossy media

MEDIUM 2 e2, µ2, s2
MEDIUM 1 e1, µ1, s1
.
.
.
.
.
z0
Medium 1
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Boundary between lossy media

Medium 2
.
G and t are real for lossless dielectric media