Fields and Waves I

1. Fields and Waves I Lecture 21 Waves in Lossy Media 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 Ulaby’s textbook. Fields and Waves I

3. 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 Fields and Waves I

4. Maxwell’s Equations in Phasor Domain time domain remember Fields and Waves I

5. Complex Permittivity complex permittivity For lossless medium σ=0 ε’’=0 εc =ε’=ε Fields and Waves I

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 Fields and Waves I

7. Propagation Constant Phase constant Attenuation constant [Np/m] (for a lossy medium) [rad/m] Fields and Waves I

8. Plane Waves For plane waves we will have only z-dependence. sing_bnd.m Fields and Waves I

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 backward traveling in -z direction forward traveling in +z direction Fields and Waves I

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 Fields and Waves I

11. Skin Depth, δs shows how well an electromagnetic wave can penetrate into a conducting medium Skin Depth [m] Perfect dielectric: σ=0 α=0 δs=∞ Perfect Conductor: σ=∞ α=∞ δs=0 Ulaby Fields and Waves I

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] Fields and Waves I

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”. Fields and Waves I

14. Example 1 Find , , , and of an electromagnetic wave traveling through seawater ( ) at 10 MHz and 100 GHz. Fields and Waves I

15. Example 1 – 100 GHz What features do you observe in this wave? Fields and Waves I

16. Example 1 – 10 MHz What features do you observe in this wave? Fields and Waves I

17. Average Power Density Average power density [W/m2] NOTE Fields and Waves I

18. Average Power Density If ηc is written in polar form Average power density [W/m2] where Fields and Waves I

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? Fields and Waves I

20. Example 2 Fields and Waves I

21. Example 2 Power Skin Depth (not usually called the skin depth) 0.18 m Fields and Waves I

22. 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/-/B00022VY4C?v=glance&vi=tech-data&me=ATVPDKIKX0DER Fields and Waves I

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. Fields and Waves I

24. Microwave Heating Fields and Waves I

25. Microwave Heating Integrate this over a volume V defined by a closed surface S: Fields and Waves I

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 Fields and Waves I

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. http://www.georgetown.edu/faculty/irvinem/CCT794/Images/ Fields and Waves I

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. Fields and Waves I

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: http://www2.umist.ac.uk/ucm/jmmd/mwh1.htm Fields and Waves I

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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. Fields and Waves I

33. Microwave Heating Fields and Waves I

34. Microwave Heating Fields and Waves I

35. Nuts have very different absorption properties than pests. Microwave Heating Fields and Waves I

36. 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. Fields and Waves I

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 http://howthingswork.virginia.edu/movies/shw512k.rm Louis Bloomfield, University of Virginia Fields and Waves I

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 StricklandChief Operating Officer, Business Manager Frank Shulman Chief Executive Officer Morgana L. FallCeramic Engineer Fields and Waves I

39. Microwave Heating – A Career Choice? http://www.globalsecurity.org/military/systems/munitions/hpm.htm Fields and Waves I

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 Fields and Waves I