Guided waves 2014mk

Nguyễn Công Phương Engineering Electromagnetics Guided Waves & Radiation Contents I II III IV V VI VII VIII IX X XI XII XIII XIV XV Introduction Vector Analysis Coulomb’s Law & Electric Field Intensity Electric Flux Density, Gauss’ Law & Divergence Energy & Potential Current & Conductors Dielectrics & Capacitance Poisson’s & Laplace’s Equations The Steady Magnetic Field Magnetic Forces & Inductance Time – Varying Fields & Maxwell’s Equations Transmission Lines The Uniform Plane Wave Plane Wave Reflection & Dispersion Guided Waves & Radiation Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn Guided Waves & Radiation Transmission Line Fields Basic Waveguide Operation Plane Wave Analysis of the Parallel - Plate Waveguide Parallel - Plate Guide Analysis Using the Wave Equation Rectangular Waveguides Planar Dielectric Waveguides Optical Fiber Basic Antenna Principles Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn Transmission Line Fields (1) – + E E H H + Vs V0 − jβ z Esx ( z ) = = e d d I s V0 − jβ z H sy ( z ) = K sz = = e b bZ – + + ++ ++ + + –––– –– k + where Z0 = L / C ++ ++ + + –– –––– –– Vs ( z ) = V0e V I s ( z) = e − j β z Z0 I – I − jβ z → Pz = ∫ ∫ Re{E xs Hˆ ys }dxdy 0 V0 Vˆ0 = (bd ) d bZˆ b d V0 = = Re[Vs Iˆs ] 2Zˆ0 Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn Transmission Line Fields (2) C= t ε 'b d d σ σb G= C= ε' d L ≈ Lexternal = R= σ cδ b Conductor (σc) t Dielectric (σ, ε’, μ) b µd b L d µ Z0 = = C b ε' Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn Transmission Line Fields (3) 2πε ' C= ln(b / a) Dielectric (σ, ε’, μ) σ 2πσ G= C= ε' ln(b / a) µ b Lexternal = ln 2π a Rinternal Conductor (σc) a b c Cao tần 1 = , Rexternal = 2π aδσ c 2π bδσ c 1 1 R= +   2πδσ c  a b  Z0 = Lexternal = C 2π Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn µ b ln ε' a Transmission Line Fields (4) 2πε ' C= ln(b / a ) σ 2πσ G= C= ε' ln(b / a ) l Rinternal = = σ c S σ c (π a ) Rexternal = Dielectric (σ, ε’, μ) Conductor (σc) a b c Low frequency σ c [π ( c2 − b )]  1  + πσ c  a c − b2   µ  b 1 c2 c  L= ln + +  b − 3c + 2 ln   2 2π  a 4(c − b )  b   c −b R= Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn Transmission Line Fields (5) C= πε ' −1 cosh (d / 2a ) Lexternal G= ≈ πε ' ln(d / a ) (a ≪ d ) µ µ d −1 = cosh (d / a ) ≈ ln (a ≪ d ) π π a a Conductor (σc) Dielectric (σ, ε’, μ) a d High frequency σ πσ C= ε' cosh −1(d / a ) R= π aδσ c Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn Transmission Line Fields (5) C= G= L= R= πε ' cosh −1 (d / 2a ) πσ a Conductor (σc) Dielectric (σ, ε’, μ) d −1 cosh (d / 2a ) a Low frequency µ 1  −1 + cosh ( d / a )  π  π a 2σ c Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn Dẫn sóng & xạ Transmission Line Fields Basic Waveguide Operation Plane Wave Analysis of the Parallel - Plate Waveguide Parallel - Plate Guide Analysis Using the Wave Equation Rectangular Waveguides Planar Dielectric Waveguides Optical Fiber Basic Antenna Principles Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 10 Optical Fiber (9) Vc (11) = V 0,8 m =1, ℓ =1 = 2.405 → J ℓ −1(Vc ) = → V < Vc (11) = 2.405 0,6 → λ > λc = 0,4 2π a n12 − n22 2, 405 0,2 – 0,2 J ( βt ρ ) J1(βt ρ ) – 0,4 10 12 14 Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 16 53 Dẫn sóng & xạ Transmission Line Fields Basic Waveguide Operation Plane Wave Analysis of the Parallel - Plate Waveguide Parallel - Plate Guide Analysis Using the Wave Equation Rectangular Waveguides Planar Dielectric Waveguides Optical Fiber Basic Antenna Principles Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 54 z Basic Antenna Principles (1) I = I0 cos ωt A=∫ V µ [J ] µ[ I ]dL µ[ I ]d dv = ∫ = az 4π R 4π R 4π R   R  [I ] = I0 cos ω  t −    v  d I µ I d − jω R /v → Azs = e 4π R y x → [ I s ] = I0e − jω R /v Azs z µ I 0d  − jωr /v  Ars = Azs cos θ A = cos e θ  rs 4π R   Aθ s = − Azs sin θ →   A = − µ I 0d sin θ e − jωr /v A =  ϕs  θ s 4π R θ r Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn –Aθs Ars P(r, θ, φ) y 55 Basic Antenna Principles (2) µ I 0d cosθ e − jωr / v 4π R µI d Aθ s = − sin θ e− jωr /v 4π R Ars = Aϕ s = B s = µ H s = ∇× A s  ∂ ( Aϕ sin θ ) ∂Aθ ∇ ×A = −  r sin θ  ∂θ ∂ϕ   ∂Ar ∂(rAϕ )   ∂(rAθ ) ∂Ar a + − a + −  r   θ  r  sin θ ∂ϕ ∂r  r  ∂r ∂θ  ∂ ∂Ars  ( rAθ s ) −  Hϕ s = → µ r ∂r µ r ∂θ H = H = θs  rs → Hϕ s =   aϕ  I0d  ω 1 sin θ e− jωr /v  j +  4π  vr r  Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 56 Basic Antenna Principles (3) I0 d  ω  sin θ e − jω r /v  j +  4π  vr r  H rs = Hθ s = Hϕ s = ∂D ∇ ×H = → ∇ × H s = jωε Es ∂t  ∂ ( Hϕ sin θ ) ∂Hθ ∇×H = −  r sin θ  ∂θ ∂ϕ   Ers =  → E =  θ s   ∂Hr ∂ ( rHϕ )   ∂ (rHθ ) ∂H r a + − a + −  r   θ  r  sin θ ∂ϕ ∂r  r  ∂r ∂θ  ∂ ( Hϕ s sin θ ) jωε r sin θ ∂θ 1  1 ∂ −  (rHϕ s )  jωε  r  ∂θ   aϕ   I0d  − jω r /v  cos θ e +  Ers =  3 π jωε r    ε vr → I0d 1   − jωr /v  jω θ +  +  Eθ s = 4π sin e 3 jωε r   ε v r ε vr  Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 57 Basic Antenna Principles (4) Hϕ s = I0 d  ω  sin θ e − jω r /v  j +  4π  vr r  I0 d  − jω r /v  Ers = cos θ e +  3 2π jωε r   ε vr Eθ s I 0d 1  − jωr / v  jω = sin θ e +  + 3 4π jωε r   ε v r ε vr ω = 2π f , f λ = v, v = 1/ µε , η = µ /ε  I d 2π   Hϕ s = sin θ e − j 2π r/λ  j + 2 4π   λr r   I dη   − j 2π r /λ  →  Ers = cos θ e  + 3  π π r j r      E = I dη sin θ e − j 2π r/λ  j 2π + + λ   λ r r j 2π r   θs π    Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 58 Basic Antenna Principles (5) I0d  − j 2π r / λ  2π Hϕ s = sin θ e j + 2  4π  λr r  Ex: I 0d = 4π , θ = 90o , t = 0, f = 300 MHz, v = 3.108 m/s, λ = m  2π  − j 2π r → Hϕ s =  j + e  r r   2π  → Hϕ =  + cos{[arctg(2π r ) − 2π r ]}   r  r cos( a − b) = cos a cos b + sin a sin b cos[arctg( x)] = 1/ + x → Hϕ = r (cos 2π r + 2π r sin 2π r ) Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 59 Basic Antenna Principles (6) I0 d  2π  sin θ e − j 2π r /λ  j + 2 4π  λr r  Ex I 0d = 4π , θ = 90o , t = 0, f = 300MHz, v = 3.108 m/s, λ = m → H ϕ = (cos 2π r + 2π r sin 2π r ) r Hφ Hϕ s = Hφ r 102 101 Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 60 r z Basic Antenna Principles (7)  I d 2π   Hϕ s = sin θ e − j 2π r /λ  j + 2 4π   λr r   I dη   − j 2π r / λ  cosθ e  +  Ers = 3 π j 2π r   r   E = I dη sin θ e− j 2π r /λ  j 2π + + λ   λ r r j 2π r3   θs π    I0 d  − j 2π r /λ H = j sin θ e  ϕs 2λ r  → Eθ s = η Hϕ s → Ers =  I 0dη Eθ s = j sin θ e − j 2π r /λ 2λ r  d I y x z aφ θ φ y r x Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn ar aθ 61 Basic Antenna Principles (8) I 0d  − j 2π r /λ H = j sin θ e  ϕs 2λ r   E = j I0 dη sin θ e − j 2π r /λ  θ s 2λ r θ Eθ s Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 62 Basic Antenna Principles (9) I 0d Hϕ s = j sin θ e − j 2π r /λ λr I0 dη Eθ s = j sin θ e − j 2π r /λ 2λ r Eθ s = η Hϕs  Eθ = η Hϕ  → I 0d 2π r   H = − sin θ sin ω t −  ϕ   λ r λ    2π r   I 0d  2 Sr = Eθ Hϕ =  η sin θ sin  ωt −   λ r λ     ϕ =2π θ =π I d 2π r0  2π   2 η ω sin  t − S=∫ S r sin θ dθ dϕ =    ϕ =0 ∫θ =0 r λ r λ     I d π I d → Savr =   η = 40π    2λ r   2λ r  Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 63 z Basic Antenna Principles (10) Savr = Pavr  I 0d 40π   2λ r    d I y x = I Rradiation Rradiation Pavr 2d  = = 80π   I0 λ  Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 64 Basic Antenna Principles (11) d Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 65 Basic Antenna Principles (12) I Conductor Monopole I Image I Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 66 Contents I Introduction II Vector Analysis III Coulomb’s Law & Electric Field Intensity IV Electric Flux Density, Gauss’ Law & Divergence V Energy & Potential VI Current & Conductors VII Dielectrics & Capacitance VIII Poisson’s & Laplace’s Equations IX The Steady Magnetic Field X Magnetic Forces & Inductance XI Time – Varying Fields & Maxwell’s Equations XII The Uniform Plane Wave XIII Plane Wave Reflection & Dispersion XIV.Guided Waves & Radiation Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 67 ... Uniform Plane Wave Plane Wave Reflection & Dispersion Guided Waves & Radiation Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn Guided Waves & Radiation Transmission Line Fields Basic Waveguide... Fiber Basic Antenna Principles Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 10 Basic Waveguide Operation (1) z d x ε y Parallel-plate waveguide Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn... = ω µε ε y kl θ kl kx θ Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn 13 Basic Waveguide Operation (4) x E H H kl kx E kl z TM TE kl θ kx kl kx θ Guided Waves & Radiation - sites.google.com/site/ncpdhbkhn