PLANE WAVE PROPAGATION Fields and Waves Lesson 5.2 PLANE WAVE PROPAGATION Lossless Media Lale T. Ergene

Time Harmonic Fields EM wave propagation involves electric and magnetic fields having more than one component, each dependent on all three coordinates, in addition to time. e.g. Electric field instantaneous field vector phasor Valid for the other fields and their sources

Maxwell’s Equations in Phasor Domain time domain remember

Complex Permittivity complex permittivity For lossless medium σ=0 ε’’=0 εc =ε’=ε

Wave Equations (charge free) Homogenous wave equation for propagation constant

Plane Wave Propagation in Lossless Media There are three constitutive parameters of the medium: σ, ε, μ If the medium is nonconducting σ=0 α=0 LOSSLESS εc =ε’=ε Wavenumber k (for a lossless medium)

Transverse Electromagnetic Wave Electric and magnetic fields that are perpendicular to each other and to the direction of propagation They are uniform in planes perpendicular to the direction of propagation x At large distances from physical antennas and ground, the waves can be approximated as uniform plane waves Direction of propagation z y

Transverse Electromagnetic Wave Spatial variation of and at t=0

Traveling waves The Electric Field in phasor form (only x component) General solution of the differential equation Amplitudes (constant)

Uniform Plane waves In general, a uniform plane wave traveling in the +z direction, may have x and y components The relationship between them Do Problem 1

Intrinsic impedance (η) of a lossless medium Similar to the characteristic impedance (Z0) of a transmission line Defines the connection between electric and magnetic fields of an EM wave [Ω] Phase velocity [m/s] wavelength [m] If the medium is vacuum : up=3x108 [m/s], ηc=377 [Ω] Do Problem 2

Electromagnetic Power Density Poynting Vector , is defined [W/unit area] is along the propagation direction of the wave Total power [m/s] [W] OR [W] Average power density of the wave [W/m2]

Plane wave in a Lossless Medium [W/m2] Do Problem 3