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ELEG413lec3 - ELEG 413 Lecture#3 Mark Mirotznik Ph.D...

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ELEG 413 Lecture #3 Mark Mirotznik, Ph.D. Associate Professor The University of Delaware Email: [email protected]
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Classification of Materials 1. Homogenous or Inhomogenous: If the material properties are independent of spatial location then the material is homogenous, otherwise it is called inhomogenous 2. Isotropic or Anisotropic: If the material properties are independent of the polarization of the applied field then the material is isotropic, otherwise it is called anisotropic. 3. Linear or non-Linear: If the material properties are independent on the magnitude and phase of the electric and magnetic fields, otherwise it is called non-linear ) , , ( z y x ε Inhomogenous E D E E E D D D z y x zz zy zx yz yy yx xz xy xx z y x ε ε ε ε ε ε ε ε ε ε = = anisotropic ... 3 3 2 1 + + + + = E E E E D o o χ χ χ ε
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Classification of Materials - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + t=t1 t=t2 t=t 3 t=t 4 t=t 5 t=t 6 A material’s atoms or molecules attempt to keep up with a changing electric field. This results in two things: (1) friction causes energy loss via heat and (2) the dynamic response of the molecules will be a function of the frequency of the applied field (i.e. frequency dependant material properties) 4. Dispersive or non-dispersive: If the material properties are independent of frequency then the material is non-dispersive, otherwise it is called dispersive
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Electric Properties of Materials Frequency Behavior (Complex Permittivity) 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ = = + + = × - = × B D J J D j H B j E c i ρ ϖ ϖ E J H B E D s c o ~ ~ ~ ~ ~ ) ( ~ * σ μ ϖ ε = = = 0 ) ~ ( ~ ) ~ ( ~ ~ ~ ~ ~ ~ * * = = + + = × - = × H E E J E j H H j E s i o ρ ε σ ε ϖ μ ϖ ) ( ) ( ) ( * ϖ ε ϖ ε ϖ ε - = j is called the complex permittivity 0 ) ~ ( ~ ) ~ ( ~ ~ ~ ) ( ~ ~ ~ * = = + + - = × - = × H E E J E j j H H j E s i o ρ ε σ ε ε ϖ μ ϖ loss term Dielectric constant 0 ) ~ ( ~ ) ~ ( ~ ~ ) ( ~ ~ ~ * = = + = × - = × H E J E j H H j E i eff o ρ ε ϖ ε ϖ μ ϖ ϖ σ ϖ ε ϖ ε ϖ ε s eff j j - - = ) ( ) ( ) (
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Frequency Behavior of Sea Water
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Electric Properties of Materials Frequency Behavior (Complex Permittivity) 0 ) ~ ( ~ ) ~ ( ~ ) ( ~ ~ ~ ~ ~ * = = + + + = × - = × H E E J E j H H j E s i o ρ ε ε ϖ σ ε ϖ μ ϖ 0 ) ~ ( ~ ) ~ ( ~ ~ ~ ) ( ~ ~ ~ * = = + + - = × - = × H E E J E j j H H j E s i o ρ ε σ ε ε ϖ μ ϖ 0 ) ~ ( ~ ) ~ ( ~ ~ ~ ~ ~ ~ * = = + + = × - = × H E E J E j H H j E eff i o ρ ε σ ε ϖ μ ϖ ε ϖ σ σ σ ϖ σ + = + = s a s eff ) ( 0 ) ~ ( ~ ) ~ ( ~ ~ ~ ~ ~ ~ * = = + + = × - = × H E J J J H H j E eff i d o ρ ε μ ϖ E J J E j J eff eff i d ~ ~ ~ ~ ~ σ ε ϖ = = Displacement current Source current Effective electric conduction current
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Electric Properties of Materials Frequency Behavior (Complex Permittivity) 0 ) ~ ( ~ ) ~ ( ~ ~ ~ ~ ~ ~ * = = + + = × - = × H E E J E j H H j E eff i o ρ ε σ ε ϖ μ ϖ ε ϖ σ σ σ ϖ σ + = + = s a s eff ) ( 0 ) ~ ( ~ ) ~ ( ~ ~ ) 1 ( ~ ~ ~ * = = + - = × - = × H E J E j j H H j E i eff o ρ ε ε ϖ σ ε ϖ μ ϖ 0 ) ~ ( ~ ) ~ ( ~ ~ )) tan( 1 ( ~ ~ ~ * = = + - = × - = × H E J E j j H H j E i eff o ρ ε δ ε ϖ μ ϖ 0 ) ~ ( ~ ) ~ ( ~ ~ ~ ~ ~ * =
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