Nonhomogeneous media dispersion EM LAB 2 1 3

Nonhomogeneous media의 경우 dispersion 이란? EM LAB 이정한 2

1. 3 Electromagnetic Energy and Power Flow Time-average, electric field energy (lossless, isotropic, not dispersion) Time-average, magnetic field energy (lossless, isotropic, not dispersion) EM LAB 이정한 3

R L V C I EM LAB 이정한 5

< Thomson’s Theorem > The charge reside on conducting bodies and give rise to the electric field E will distribute themselves in such a way that the energy function We is minimized 0 EM LAB 이정한 7

Example : Coaxial cable EM LAB 이정한 9

< A Variational Theorem > EM LAB 이정한 10

< Derivation of Expression for Stored Energy > EM LAB 이정한 11

0 0 EM LAB 이정한 12

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1. 4 Boundary Condition And Field Behavior In Source Regions EM LAB 이정한 15

Case 1) General case EM LAB 이정한 16

Case 1) J=D=0 that is, a surface charge density does not exist on the boundary S EM LAB 이정한 17

Case 2) a surface charge density exist on the boundary S ( D=0, J is not zero ) n Closed surface S C n 1 EM LAB 이정한 18

ex) At a perfectly conducting boundary conditions EM LAB 이정한 19

Case 3) Diffraction problem 가상 전류 EM LAB 이정한 21

Case 4) n Open surface S C n 1 Js: a current sheet of density flowing toward the boundary C 전하가 쌓임 EM LAB 이정한 22

Case 5) A sheet of current filaments Media 1 Media 2 EM LAB 이정한 23

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Singular Behavior at a Dielectric Corner EM LAB 이정한 28

Singular Behavior at a Dielectric Corner EM LAB 이정한 29

1. 6 The Wave Equation lamellar + solenoidal EM LAB 이정한 31

1. 7 Auxiliary Potential Functions EM LAB 이정한 32

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Inhomogeneous 의 경우, magnetic & electric Hertzian potential function이 미분형태로 더 복잡해진다. EM LAB 이정한 37

1. 8 Some Field Equivalence Principles - What’s the Field Equivalence Principles ? - What kind of the Field Equivalence Principles we will study? • Love’s field equivalence theorem • Schelkunoff’s field equivalence principles • Babinet’s principle • The Schwarz reflection principle • Method of images EM LAB 이정한 38

1) Love’s Theorem EM LAB 이정한 41

2) Schelkunoff’s Field Equivalence Principles By image method same EM LAB 이정한 42

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3) Babinet’s principle Duality principle of electromagnetic field & Babinet’s priciple Perfectly conducting disk Perfectly conducting screen (magnetic wall) (electric wall) Aperture EM LAB 이정한 44

Z<0 Z=0 Z>0 Odd + Even mode Ei Hi Odd mode Even mode EM LAB 이정한 45

<Aperture> Even Odd Even Electric wall <Disk> Magnetic wall EM LAB 이정한 46

odd even odd even EM LAB 이정한 47

even odd odd even odd EM LAB 이정한 49

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Z<0 Z>0 EM LAB 이정한 51

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Z>0 Z<0 Anti-symmetric Z<0 Z>0 EM LAB 이정한 54

4) The Schwarz Reflection Principle 5) Method of images EM LAB 이정한 55

1. 9 Integration of the inhomogeneous Helmholtz equation S 0 Vo P(x, y, z) , R=0 EM LAB 이정한 56

r 0 a Vo EM LAB 이정한 57

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n Open surface S C n 1 Js: a current sheet of density flowing toward the boundary C 전하가 쌓임 EM LAB 이정한 59

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1. 10 Lorentz Reciprocity Theorem EM LAB 이정한 61

Lorentz reciprocity theorem 은 많은 경우에 적용가능함. • A volume bounded by perfectly conducting S Reyleigh-Carson reciprocity theorem • source-free volume • no magnetic current sources. • etc EM LAB 이정한 62