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

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

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

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

Intrinsic Impedance, η c The relationship between electric and magnetic field phasors is the same but the intrinsic impedance of lossy medium, η c is different If +z is the direction of the propagation intrinsic impedance

Skin Depth, δ s shows how well an electromagnetic wave can penetrate into a conducting medium [m] Skin Depth Perfect dielectric: σ=0 α=0 δ s =∞ Perfect Conductor: σ=∞ α=∞ δ s =0

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][Ω]

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][Ω] When 10-2≤ ε’’/ε’ ≤100, the medium is considered as a “Quasi-Conductor”. Do Problem 1

Average Power Density [W/m 2 ] Average power density

Average Power Density [W/m 2 ] Average power density If η c is written in polar form where Do Problem 2