Fields and Waves I

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Fields and Waves I

• Lecture 21
• Waves in Lossy Media
• K. A. Connor
• Electrical, Computer, and Systems Engineering
  Department
• Rensselaer Polytechnic Institute, Troy, NY

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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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Overview of EM Waves

• EM Waves in Lossless Media
• Wave Equation
• General Solution (similarity to Transmission
  Lines)
• Lossless vs lossy materials (complex
  permittivity)
• Energy and Power
• EM Waves in Lossy Media
• Wave Polarization
• Reflection and Transmission at Normal Incidence
• Plane Waves at Oblique Incidence

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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 for a Conducting Medium

Homogenous wave equation for
Homogenous wave equation for
propagation constant is complex
Can also have this term in a lossy dielectric
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Propagation Constant
Phase constant
Attenuation constant
Np/m
(for a lossy medium)
rad/m
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Plane Waves
For plane waves we will have only z-dependence.
sing_bnd.m
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Solution of the Wave Equation
The Electric Field in phasor form (only x
component)
General solution of the differential equation for
a lossy medium
backward traveling in -z direction
forward traveling in z direction
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Intrinsic Impedance, ?c
The relationship between electric and magnetic
field phasors is the same but the intrinsic
impedance of lossy medium, ?c is different
If z is the direction of the propagation
intrinsic impedance
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Skin Depth, ds
shows how well an electromagnetic wave can
penetrate into a conducting medium
Skin Depth
m
Perfect dielectric s0 a0
ds8 Perfect Conductor s8 a8 ds0
Ulaby
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Low-Loss Dielectric
defined when e/eltlt1 practically if
e/elt10-2, the medium can be considered as a
low-loss dielectric
Np/m
Note that these two terms have the same function
but have different frequency dependence
rad/m
O
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Good Conductor
defined when e/egtgt1 practically if
e/egt100 , the medium can be considered as a
good conductor
Np/m
rad/m
O

• When 10-2 e/e 100, the medium is considered
  as a Quasi-Conductor.

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Example 1
Find , , , and of an electromagnetic
wave traveling through seawater (
) at 10 MHz and 100 GHz.
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Example 1 100 GHz
What features do you observe in this wave?
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Example 1 10 MHz
What features do you observe in this wave?
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Average Power Density
Average power density
W/m2
NOTE
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Average Power Density
If ?c is written in polar form
Average power density
W/m2
where
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Example 2
A 10 MHz wave that is polarized in the x
direction propagates in the z direction in
seawater. At z0, it has a power density of 10
W/m2 (Use the results of Example 1). a. Write
the electric and magnetic fields in phasor
form. b. Write the electric field in time domain
form. c. At what value of z will the power
density of the wave be 1 of its initial power?
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Example 2
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Example 2
Power Skin Depth (not usually called the skin
depth)
0.18 m
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Microwave Heating

• The power that is lost in a lossy medium turns
  into heat.
• We can, thus, heat materials with microwave
  energy or actually any kind of RF energy

http//www.amazon.com/exec/obidos/tg/detail/-/B000
22VY4C?vglancevitech-datameATVPDKIKX0DER
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Microwave Heating
To see how this works more completely, we need to
return to the Poynting vector and look at a more
thorough derivation.
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Microwave Heating
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Microwave Heating
Integrate this over a volume V defined by a
closed surface S
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Microwave Heating
Total power through S or total power leaving V
Ohmic Loss power lost to heating the material
Time rate of change of the stored electric and
magnetic field energy in the volume V
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Microwave Heating
Total power through S or total power leaving V
Ohmic Loss power lost to heating the material
Time rate of change of the stored electric and
magnetic field energy in the volume V
Thus, the Poynting Vector gives us a consistent
picture for power flow.
http//www.georgetown.edu/faculty/irvinem/CCT794/I
mages/
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Microwave Heating
Heating the material is, thus, determined from
or we can, equivalently, look at the heat
delivered per unit volume
where the second form is the usual expression
since microwave heating is almost always applied
to lossy dielectrics and not conductors.
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Microwave Heating
Finally, we are at the point where we can address
the heating that occurs in a microwave oven. Note
that, for phasor notation, one needs to do the
usual modification of these expressions to find
the average absorbed power.
If one looks through published papers, one finds
a lot of information on the dielectric properties
of food, since this information is important if
microwave ovens are to be designed
properly. General Tutorial http//www2.umist.ac.u
k/ucm/jmmd/mwh1.htm
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Microwave Heating
Typical values at room temperature
Note from the previous plots that losses go up
with temperature which produces an effect called
thermal runaway if heating remains at the same
location.
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Microwave Heating
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Microwave Heating
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Nuts have very different absorption properties
than pests.
Microwave Heating
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Fun with Microwaves???
http//www.gull.us/photos/misc/
http//margo.student.utwente.nl/el/microwave/
Note this experiment is almost always done by
some first year students who end up setting off
the smoke detectors in their dorms and ruining
their microwave ovens. It is probably best to
just look at the many examples of people doing
this and reporting their work online.
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Fun with Microwaves???
If you have too much time on your hands (this is
quite dangerous since it is possible to badly
burn yourself if you are not careful)
Superheating water with microwaves
http//howthingswork.virginia.edu/movies/shw512k.
rm Louis Bloomfield, University of Virginia
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Microwave Heating A Career Choice?
Ceralink is located in the RPI Tech Park Dr.
Holly S. Shulman Founder and President of
Ceralink Inc., Material Scientist Patricia
StricklandChief Operating Officer, Business
Manager Frank Shulman Chief Executive Officer
Morgana L. FallCeramic Engineer
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Microwave Heating A Career Choice?
http//www.globalsecurity.org/military/systems/mun
itions/hpm.htm
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Microwave Heating A Career Choice?
ELECTROMED 2005 Application of electric fields
for medical diagnostics and devices Bioeffects of
pulsed microwaves, millimeter waves, and
nonthermal plasmas Biological decontamination by
pulsed electric fields Plasma-based
sterilization Biomedical application of
plasmas Biophysical modeling and
simulations Electrobiochemical and
electrobiochemiluminescent sensing Electrobiomimet
ics Diagnostics and imaging techniques Effects of
gene and protein extraction and
expression Electroporation of cells and tissues
and their application