MỘT SỐ CÔNG THỨC CƠ BẢN TRONG CÁC BÀI TẬP TRƯỜNG ĐIỆN TỪ gradϕ = G divA = G a1 + h12 ∂ϕ h1 ∂u1 h1h h G a + h13 ∂ϕ ∂u2 G a3 ∂ϕ ∂u3 G rotA =  ∂ (h h3A1 ) + ∂ (h1h3A2 ) + ∂ (h1h A3 )  ∂u ∂u  ∂u1  ∆ϕ = div(gradϕ ) = h1h h3   ( ∂ ∂u1 h h3 ∂ϕ h1 ∂u1 ) +  L α= ω µε ( ) σ 1+ G E =−gradϕ G G B = rotA ∆ϕ = − ρεV G G ∆A = −µJ ωε −1 ω µε β= G h 3a ∂ ∂u1 ∂ ∂u ∂ ∂u h1A1 h 2A h 3A Hệ h1 h2 h3 Đề 1 Trụ Cầu 1 r r rsinθ G G G G G G D = εE B = µH J = σ E dV = h1h h du1du2 du3 G G G G d A = h1du1a1 + h du2a + h 3du3a C= Q U µ0 =4π.10 L= Φ I −7 ( ) σ ωε (H/m) η= +1 G G P = (ε − ε )E V GG G G G Wm = 12 ∫ H.BdV = 12 L.I2 ρpS =−an(P1 −P) V∞ GG G γ = jωµ(σ+jωε) = α + jβ PJ = ∫ EJdV ρpV = −divP V G G β =−gradϕ =β.as GG We = 12 ∫ E.DdV = 12 C.U2 ε0 = 361π 10−9(F/m) 1+ G h 2a2 G G G ∆ A = grad(divA) − rot(rotA) G G G G dS =±h2h3du2du3a1 ± h1h3dudu 3a2 ± h1h2dudu 2a3 G G ∗ D v∫ s dS = q G G ∗ H v∫ d A = I h 1h h G h1a1 ∞ jωµ σ + jωε Uniform Plane Wave and Antenna: Hệ phương trình Maxwell Waveguide: (   E x = K12 −γ ∂∂Exz − jωµ ∂∂Hyz c ∂ E z ∂x G•  Gã G E = Hì a s    G G G G an × (H1 − H2 ) = Js G G G a n × (E1 − E ) = G G G a n (D1 − D2 ) = ρS G G G a n (B1 − B2 ) = G G G an (J1 − J2 ) = − ∂∂ρtS G G G rotH = J + ∂∂Dt G G rotE = − ∂∂Bt G divD = ρ V G divB = G divJ = − ∂∂ρtV ) 2  ∂2H z + ∂∂yE2z + K c2 E z = ∂x  = C cos H z  = H x jβC mπ Kc2 a  = H y jβC nπ K c2 b ( Pbx = v∫ S < Pr > dS R bx = 2Pbx / I x cos ) -jβz mπ a nπ b -jβz mπ a nπ b -jβz v − (f th /f ) λ mn = c − (f th /f ) α ( E x = − jβC K2 mπ a E y = − jβC K2 nπ b c ( = ω µ 2σ ) − jAIβ3sinθ 4πωε ( x sin nπ b mπ a 2π ∫ b −1 βr ∫0 ∫0 ) + β31r3 e-jβr j β2 r ) + β2jr2 + β31r3 e-jβr u n sin θ d θ d φ 4πu m ax Pbx = (  = 12 −γ ∂H z − jωε ∂E z H y ∂y ∂x K c    )dS α d = ) ω µ σ β ( ) +( ) = = K = ( ) +( ) = - β + ω µε β = β = ( ) −( ) −( ) f th = v2 nπ b -jβz nπ b -jβz m a mπ a c 2 n b ωth 2π nπ b ω mn  =0; E = η H    H z x TM y ; E y = − ηTM H x a ( Caùc thông số -jβz mπ a ) + β 21r e -jβr j βr 4πu nm ax π  >∫ C n g H t t d A  ∫ ( E x Hˆ y − E y Hˆ x  S ) ( y ) e cos ( x ) sin ( y ) e sin ( x ) cos ( y ) e mπ a P = 12 ηTE/TM ∫ w ( Kiểu sóng tới TMmn E z = Csin c λ D=  = 12 −γ ∂H z + jωε ∂E z H x ∂x ∂y K   ; E = −η H  E z =0; E x = ηTE H y y TE x v mn = ε = ε0(εr − j ωσε ) R0 = Re(η) ; L0 = Im(η) 2πa 2πaω ( E θ = δ =1/α m AIβ sinθ 4π  E r = − jA2Iβπωεcosθ λ = 2π/β  =0 + ∂∂yH2z + K c2 H z ) ( y ) e sin ( x ) cos ( y ) e cos ( x ) sin ( y ) e nπ b ∗ S Kiểu sóng tới TEmn mπ a  = H φ G G v = ω/β Pz = 12 ∫ Re{E× H}z dSz p •   E y = K12 −γ ∂∂Eyz + jωµ ∂∂Hxz c TĐT nguyên tố anten thẳng G•  G G•  H = 1η a s × E    2 mπ a v v λth 2 nπ b ηTE = ωµβ ; ηTM = ωεβ ; γ = jβ  |2 +|H  |2 dxdy |H x y  Lossless Transmission Line:  =U  e− jβz +U  e jβz = U  e jβd +U  e− jβd = U  cos(βz) − jZ I sin(βz) = U  cos(βd) + jZ I sin(βd) U t1 fx1 t2 fx2 1 2 I = U t1 e− jβz − U fx1 e jβz = Z Z  = U t2  +Z I U 02 dmax = 2βθ + k λ2  = U fx2  −Z I U 02  U t2 Z0    e jβd − UZfx2 e− jβd = − j UZ sin(βz) + I1cos(βz) = j UZ sin(βd) + I2cos(βd) Z(d ) = Z dmin = 2βθ + λ4 + k λ2 CuuDuongThanCong.com 1+ n − n Z2 + jZ0 tgβd Z0 + jZ2 tgβd =Z SWR = 11+− nn2 Umax = Ut2(1+n2) SWR − n = SWR +1 Umin = Ut2 (1− n2 ) Imax =  *}= (U )2 − (U )2 P = 12 Re{U.I t fx 2Z 2Z 0 https://fb.com/tailieudientucntt n = n2∠θ − 2βd n = ZZ2 +−ZZ0 = n2∠θ Umax Z0 Z0 = Imin = L0 vp = C0 ; Umin Z0 c εr µ r