3 Derivation of Greens theorem for Efield a

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3 Derivation of Green’s theorem for E-field (a는 임의의 상수 벡터. ) (Vector Green’s

3 Derivation of Green’s theorem for E-field (a는 임의의 상수 벡터. ) (Vector Green’s identity) 전자파 연구실

5 Green’s theorem with free space kernel : G 0 Infinite free space ;

5 Green’s theorem with free space kernel : G 0 Infinite free space ; for free space Free space Green function을 이용하여 만든 Green’s theorem식. 전자파 연구실

Derivation of free space dyadic Green’s function 6 Aperture안테나의 radiated E field를 구하기 위한

Derivation of free space dyadic Green’s function 6 Aperture안테나의 radiated E field를 구하기 위한 Green function. 전자파 연구실

Dyadic Green’s function for half space – PEC : G 1 8 ; for

Dyadic Green’s function for half space – PEC : G 1 8 ; for half space 전기장의 접선 성분을 0으로 만 들기 위한 Green function들. t는 지면과 평행한 성분, n은 지 면에 수직인 성분. ; image current Perfect electric conductor 전자파 연구실

Half space Green function with sources on PEC 9 Non-zero Perfect electric conductor Green’s

Half space Green function with sources on PEC 9 Non-zero Perfect electric conductor Green’s theorem 에서는 tangential current만 중요함. 전자파 연구실

Dyadic Green’s function for half space – PMC : G 2 10 ; for

Dyadic Green’s function for half space – PMC : G 2 10 ; for half space 전기장의 접선 성분을 0으로 만 들기 위한 Green function들. t는 지면과 평행한 성분, n은 지 면에 수직인 성분. ; image current Perfect magnetic conductor Non-zero 전자파 연구실

Image current for magnetic current 11 전기장은 자기장을 1번 미분한 양이므 로 대칭성이 반대임.

Image current for magnetic current 11 전기장은 자기장을 1번 미분한 양이므 로 대칭성이 반대임. Perfect electric conductor Perfect magnetic conductor 전자파 연구실

Summary – image current Perfect electric conductor Perfect magnetic conductor The equivalent currents contain

Summary – image current Perfect electric conductor Perfect magnetic conductor The equivalent currents contain only tangential components. 12 Perfect electric conductor Perfect magnetic conductor 전자파 연구실

Dyadic Green’s function for half space – PEC : G 1 For PEC J+Ji

Dyadic Green’s function for half space – PEC : G 1 For PEC J+Ji (tangential components only) become zero. Tangential 전류의 image current는 (-)부호를 붙여야 하므로, 13 Infinite half space Perfect Electric conductor Incident field가 도체 면을 통해 들어오는 경우, 도체 면에서 R 1=R 2이므로 면 적분은 전자파 연구실

Integral for half space (PEC) Dyadic Green’s function 14 전자파 연구실

Integral for half space (PEC) Dyadic Green’s function 14 전자파 연구실

Far field pattern by surface integral (Equivalence principle. ) 15 Aperture 하나의 계산 test

Far field pattern by surface integral (Equivalence principle. ) 15 Aperture 하나의 계산 test main lobe Aperture의 크기가 동일하고 위상만 다르 므로, 하나의 aperture에 해당하는 E-field 를 r, , 에 대해 look-up table로 만들고 나 머지 aperture들은 이 결과를 이용한다. 전자파 연구실

E-field approximation : Fourier transform, Fresnel diffraction 19 : Fresnel diffraction 전자파 연구실

E-field approximation : Fourier transform, Fresnel diffraction 19 : Fresnel diffraction 전자파 연구실

20 Fraunhofer diffraction : Fourier transform 전자파 연구실

20 Fraunhofer diffraction : Fourier transform 전자파 연구실

Diffraction of half plane 21 PEC Cornu’s spiral 전자파 연구실

Diffraction of half plane 21 PEC Cornu’s spiral 전자파 연구실

Radiation from open-ended coaxial cable PEC 23 PMC Free space 전자파 연구실

Radiation from open-ended coaxial cable PEC 23 PMC Free space 전자파 연구실

Integral equation for scattering 24 EFIE Electric field integral equation MFIE Magnetic field integral

Integral equation for scattering 24 EFIE Electric field integral equation MFIE Magnetic field integral equation PEC S 전자파 연구실

Discretization : Method of moment 25 양변에 weighting function Wm을 곱하고 적분. Volume current

Discretization : Method of moment 25 양변에 weighting function Wm을 곱하고 적분. Volume current segment junction 전자파 연구실

Wire antenna 26 전자파 연구실

Wire antenna 26 전자파 연구실

Thin wire antenna approximation 27 E-field by antenna segment 전자파 연구실

Thin wire antenna approximation 27 E-field by antenna segment 전자파 연구실

28 Derivation Cross-section EMLAB 전자파 연구실

28 Derivation Cross-section EMLAB 전자파 연구실

Approximation of the integrand 29 EMLAB 전자파 연구실

Approximation of the integrand 29 EMLAB 전자파 연구실

30 Pocklington’s integral equation Hallen’s integral equation Constraint : 전자파 연구실

30 Pocklington’s integral equation Hallen’s integral equation Constraint : 전자파 연구실

Pocklington’s Equation 31 전자파 연구실

Pocklington’s Equation 31 전자파 연구실

Mixed potential formulation (Harrington’s) 32 전자파 연구실

Mixed potential formulation (Harrington’s) 32 전자파 연구실

33 With pulse basis function, 전자파 연구실

33 With pulse basis function, 전자파 연구실

EFIE 34 EMLAB 전자파 연구실

EFIE 34 EMLAB 전자파 연구실

Moment method : Impedance matrix 35 EMLAB 전자파 연구실

Moment method : Impedance matrix 35 EMLAB 전자파 연구실

Calculation of a singular surface integral 36 EMLAB Source position 전자파 연구실

Calculation of a singular surface integral 36 EMLAB Source position 전자파 연구실

Impedance matrix : pulse basis functions 37 EMLAB For pulse basis functions 전자파 연구실

Impedance matrix : pulse basis functions 37 EMLAB For pulse basis functions 전자파 연구실

Thin wire antenna 38 EMLAB Self term : Distant term : 전자파 연구실

Thin wire antenna 38 EMLAB Self term : Distant term : 전자파 연구실

Impedance matrix – thin wire, pulse basis 39 Self term : Distant term :

Impedance matrix – thin wire, pulse basis 39 Self term : Distant term : EMLAB 전자파 연구실

40 Derivation Cross-section EMLAB 전자파 연구실

40 Derivation Cross-section EMLAB 전자파 연구실

Approximation of the integrand 41 EMLAB 전자파 연구실

Approximation of the integrand 41 EMLAB 전자파 연구실

Surface integral term 42 EMLAB 전자파 연구실

Surface integral term 42 EMLAB 전자파 연구실

Wire antenna - self impedance 44 EMLAB 전자파 연구실

Wire antenna - self impedance 44 EMLAB 전자파 연구실

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