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Fields and Waves. Lesson 5.2. PLANE WAVE PROPAGATION Lossless Media. 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. vector phasor.

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## Fields and Waves

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**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 vector phasor instantaneous field 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] [W] OR Average power density of the wave [W/m2]**Plane wave in a Lossless Medium**[W/m2] Do Problem 3

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