Fields and Waves

1. Fields and Waves Lesson 5.3 PLANE WAVE PROPAGATION Lossy Media Lale T. Ergene

2. Wave Equations for a Conducting Medium Homogenous wave equation for Homogenous wave equation for ; propagation constant is complex

3. Propagation Constant Phase constant Attenuation constant [Np/m] (for a lossy medium) [rad/m]

4. 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

5. 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

6. 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

7. 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] [rad/m] [Ω]

8. 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”. • Do Problem 1

9. Average Power Density Average power density [W/m2]

10. Average Power Density If ηc is written in polar form Average power density [W/m2] where Do Problem 2