1. ECE 305 Electromagnetic Theory
Fall 2016
ECE 305 Electromagnetic Theory
Part 4: Waves and Applications
Chapter 9 Electromagnetic Wave Propagation
Qiliang Li
Dept. of Electrical and Computer Engineering, George Mason University, Fairfax, VA

2. §10.1 Introduction

3. §10.1 Introduction
In general, waves are means of transporting energy or information. This chapter solve EM waves in the following materials

4. §10.2 Waves in General A wave is a function of both space and time!
If it is harmonic (or sinusoidal), time dependent: ejwt
One dimensional scale wave

6. §10.2 Waves in General The solution of harmonic wave:
The imaginary part:
Harmonic ejwt
Amplitude?
Phase
Phase constant or Wave number

8. FIGURE 10.2 Plot of E(z, t) = A sin(ωt – βz) at time (a) t = 0, (b) t = T/4, (c) t = T/2; P moves in the +z-direction with velocity u.

10. Example 10.1

11. §10.3 Wave Propagation in Lossy Dielectrics
For Charge free:

13. Let:

14. FIGURE 10.5 An E-field with an x-component travelling in the +z-direction at times t = 0 and t = Δt; arrows indicate instantaneous values of E.

15. Similarly,

16. E and H are out of phase by θη
In summary
E and H are out of phase by θη or

17. Current ratio

18. Example 10.2
Hint:

19. §10.4 Plane Waves in Lossless Dielectrics

20. §10.5 Plane Waves in Free Space

21. E and H

22. §10.6 Plane Waves in Good Conductors
45o is because

23. Skin depth or penetration depth: wave amplitude decreases to a factor e-1

24. For a good conductor

25. Surface or skin resistance
Example 10.3

27. Work on it by yourself …

28. §10.7 Wave Polarization

29. §10.8 Power and The Poynting Vector
Poynting vector P represents the instantaneous power density vector associated with EM field at a given point

30. §10.9 Reflection of a Plane Wave at Normal Incidence