1. Fields and Waves I Lecture 21 K. A. Connor Waves in Lossy Media
Electrical, Computer, and Systems Engineering Department
Rensselaer Polytechnic Institute, Troy, NY
Welcome to Fields and Waves I
Before I start, can those of you with pagers and cell phones please turn them off? Thanks.

2. J. Darryl Michael – GE Global Research Center, Niskayuna, NY
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 Ulaby’s textbook.
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3. EM Waves in Lossless Media
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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4. Maxwell’s Equations in Phasor Domain
time domain
remember
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5. Complex Permittivity complex permittivity
For lossless medium σ=0 ε’’= εc =ε’=ε
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6. 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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7. Propagation Constant Phase constant Attenuation constant [Np/m]
(for a lossy medium)
[rad/m]
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8. Plane Waves For plane waves we will have only z-dependence. sing_bnd.m
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9. Solution of the Wave Equation
The Electric Field in phasor form (only x component)
General solution of the differential equation for a lossy medium
forward traveling in +z direction
backward traveling in -z direction
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10. Intrinsic Impedance, ηc
The relationship between electric and magnetic field phasors is the same but the intrinsic impedance of lossy medium, ηc is different
If +z is the direction of the propagation
intrinsic impedance
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11. Skin Depth, δs
shows how well an electromagnetic wave can penetrate into a conducting medium
Skin Depth
[m]
Perfect dielectric:
σ= α= δs=∞
Perfect Conductor:
σ=∞ α=∞ δs=0
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Ulaby

12. Low-Loss Dielectric defined when ε’’/ε’<<1
practically if ε’’/ε’<10-2, 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]
[Ω]
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13. Good Conductor defined when ε’’/ε’>>1
practically if ε’’/ε’>100 , the medium can be considered as a good conductor
[Np/m]
[rad/m]
[Ω]
When 10-2≤ ε’’/ε’ ≤100, the medium is considered as a “Quasi-Conductor”.
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14. Example 1
Find , , , and of an electromagnetic wave traveling through seawater ( ) at 10 MHz and 100 GHz.
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15. Example 1 – 100 GHz What features do you observe in this wave?
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16. Example 1 – 10 MHz What features do you observe in this wave?
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17. Average Power Density Average power density [W/m2] NOTE
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18. Average Power Density If ηc is written in polar form
[W/m2]
where
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19. Example 2
A 10 MHz wave that is polarized in the x direction propagates in the +z direction in seawater. At z=0, 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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20. Example 2
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21. Example 2 Power Skin Depth (not usually called the skin depth) 0.18 m
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22. The power that is lost in a lossy medium turns into heat.
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
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23. 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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24. Microwave Heating
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25. Microwave Heating
Integrate this over a volume V defined by a closed surface S:
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26. 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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27. 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.
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28. 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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29. 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:
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32. 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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33. Microwave Heating
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34. Microwave Heating
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35. Nuts have very different absorption properties than pests.
Microwave Heating
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36. Fun with Microwaves??? http://www.gull.us/photos/misc/
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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37. 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
Louis Bloomfield, University of Virginia
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38. 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 Strickland Chief Operating Officer, Business Manager
Frank Shulman Chief Executive Officer
Morgana L. Fall Ceramic Engineer
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39. Microwave Heating – A Career Choice?
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40. 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
Electrobiomimetics
Diagnostics and imaging techniques
Effects of gene and protein extraction and expression
Electroporation of cells and tissues and their application
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