) 12 = 1+ j. = ε 2. = n 2 n 1. sinθ ic. mπ a. = 1+ j. cos mπ a x. H z. =±j ε 2. sin 2 θ i. cosθ t 1 [3.31] ε 2ε1. θ i. ε =1e jφ. tan φ sin 2.

Transcription

1 Mawell s Equatos (geeral deretal E B D ρ H J + D B 0 Mawell s Equatos (tme harmoc E jωb D ρ [.a] [.b] [.c] [.d] [.a] [.b] H J + D [.c] B 0 [.d] Mawell s Equatos (tegral E dl B ds [.] D ds ρdv V [.] D H dl J ds + ds [.3] B ds 0 [.4] Electromagetc Boudary odtos ˆ [ E E ] 0 [.] ˆ [ H H ] 0 [.3] ˆ H J [.4] ˆ [ D D ] ρ s [.5] ˆ [ B B ] 0 [.6] ˆ [ J J ] s [.7] Relecto & trasmsso (smple delectrc Γ E r0 η + [3.] T E t 0 E 0 + [3.3] Basc waves c β c ν p ω µ ε rε r ε o p.35 β π λ π ω µε ν p λ ν p µε ; η µ ε Uorm plae waves arbtrary drecto H( r k η ˆ E( r [.6] E( r ηk ˆ H( r Relecto & trasmsso (multple delectrcs Γ e η jβd ( η ( η ( +η ( η 3 e [3.7] ( +η ( η ( η ( η 3 e jβ d 4η T e η 3 e jβ d [3.8] ( e jβ d ( η 3 + ( + ( η η 3 ( ( 3 [3.9] η Z ( 3 + j ta β d d + jη 3 ta β d Γ e ρ e e jφ r Z ( d η η 3 [3.0] ( d 3 Z /0/ :00 PM /0/ :00 PM

2 Plae waves lossy materals α + jβ jωµ ( σ + jωε [.9] α ω µε + σ ωε [.0] β ω µε + σ ωε + [.] Lossy materals Polarato currets: ε c ε' jε" [p.46] taδ c σ e ε" ωε' ε' [p.48] oducto urrets: σ e σ +ωε" [p.48] taδ c σ + ωε" ωε' [p.48] Use taδ c stead o σ epresso or comple mpedace ωε µ µ µ η c ε e ε j σ ε ω + σ ( σωε 4 [.] ωε Good coductor appromatos α β ωµσ [p.54] δ α ωµσ πµσ [.6] η c µ jωµ ε j σ σ ωµ σ e j 45 [p.54] ωε Poytg Theorem V E J dv av ˆ E 0 η V µh + ε E dv ( E H ds [.3] [.3] av R e{ E H *} [.43] Arbtrarly drected uorm plae waves Er ( e jβ k ˆ r k ˆ ˆ β + y ˆ β y + ˆ β ω µε [.58] [p.97] Hr ( k η ˆ Er ( [.6] Relecto ad reracto o oblque waves at plaar delectrc teraces sθ ν p ε µ sθ t ν p ε µ (kow as ell s Law [3.9] Γ E r0 η cosθ η ε s θ t + ε [3.4] s θ T E t 0 E 0 [3.5] + ε s θ Γ E r0 η cosθ + + ε ε ε s θ t E 0 η + + ε [3.6] ε s θ ε T E t 0 ε cosθ ε η + + ε ε [3.7] s θ ε ε /0/ :00 PM /0/ :00 PM

3 Total teral relecto Parallel plate wavegude sθ c ε ε [3.9] or θ > θ c ±j ε ε s θ [3.3] Parallel-plate TE m modes: m0,±,±, s mπ a e mπ jωµ jωµa cos mπ a jωµ jωµ s mπ a e e [4.a] [4.b] [4.c] + j s θ ε Γ j s θ ε e jφ [3.3] ta φ s θ ε [p.9] ε cosθ + j s θ ε Γ ε cosθ j s θ ε e jφ [3.33] ta φ s θ ε ε Normal cdece o a lossy medum jω µε e jω µ σ jω η c Z s R s + jx s µ jωµ ε e ( jωµ σ + j δ σ σ + j σ δ [p.9] [3.39] [3.40] ε + j s θ ε Γ ε cosθ j s θ ε e jφ [3.33] Parallel-plate TM m modes: m0,±,±, 4 cos mπ a e jωε jωε cos mπ a e jmπ ωεa 4 s mπ a e Parallel-plate TEM mode 4 e jωε 4 e 0 Propagato costats cm mυ p a m a µε jβ m j ω µε mπ a α m j mπ a ω µε β [4.3a] [4.3b] [4.3c] [4.4a] [4.4b] [4.4c] [4.5] jβ c m, > c m [4.6] c m, < cm [4.4c] ta φ s θ ε ε [p.9] λ m π β m λ c m [4.8] υ pm ω β m υ p c m [4.8] /0/ :00 PM /0/ :00 PM

4 oducto losses α ctem R s ηa ηa cm R s α ctem ηa R α ctm s m ηa ωµ o σ c m c m Delectrc losses α d ω µε' ε" ε' ω c m ω [4.] [4.3] [4.4] [4.7] For parallel plate TE modes the total power through the gude s b a β P av mπ ωµ s a ddy β ab [p.77] 4ωµ 0 0 For the parallel plate TEM (TM 0 mode the total power through the gude s P av 4 ba [p.77] Delectrc slab wavegude TM Modes The o-ero eld compoets are,,ad For -d/ ( o s( β + e cos( β [4.34] where the trasverse propagato costat s gve by β ω µ d β h d [4.35] For -d/ ( a e α d (, d a e α ( + d, d [4.36] where the trasverse atteuato costat s gve by α β ω µ 0 h 0 or α β ω µ 0 [4.37] The cuto requeces are gve by ( m m,3,5,...odd TMm d µ d m,4,6...eve [4.45] TE Modes The o-ero eld compoets are,,ad For -d/ ( o s( β + e cos β where the trasverse propagato costat β ω µ d β h d For -d/ ( a e α d (, d a e α ( + d, d where the trasverse propagato costat ( [4.46] α β ω µ 0 h 0 or α β ω µ 0 [4.37] For Odd TM Modes: α ta β d β For Eve TM Modes: α β cot d β For ALL TM Modes: α ω ( µ d β The cuto requeces are gve by ( m m,3,5,...odd TEm d µ d m,4,6...eve [4.40] [4.44] [4.4] [4.49] /0/ :00 PM /0/ :00 PM

5 Delectrc covered groud plae TEm ( m m,3,5,...odd _ TM m [4.50] d µ d m,4,6...eve _TE m Delectrc slab wavegude ray theory taθ β β [p.306] Detaled eample o odd TM Modes or slab delectrc wavegude: ree space above the gude For d/ ( 0 s β d e α ( d [4.39a] ( jβ α 0 s β d e α ( d [4.39b] y ( jω 0 s β d e α ( d [4.39c] α For d/ ( 0 s β ( jβ β 0 cos β 0 ( jω β ( [4.39d] ( [4.39e] 0 cos( β [4.39] For -d/ ( 0 s β d e α ( + d ( jβ α 0 s β d e α ( +d y ( jω 0 s β d e α ( +d α [4.39g] [4.39h] [4.39] Rectagular wavegudes: TM modes s mπ a s π b y e jβ m jβ m mπ h a cos mπ a s π b y jβ m π mπ s h b a π cos b y jωε π mπ s h b a cos π b y jωε mπ h a cos mπ a s π b y Z TM m 0 η c m Rectagular wavegudes: TE modes cos mπ a cos π b y e jβ m e jβ m e jβ m e jβ m jβ m mπ mπ s h a a cos π b y jβ m h π b cos mπ a s π b y jωµ h π b cos mπ a s π b y jωµ mπ mπ s h a a cos π b y Z TE m η c m For both TM ad TE modes: h ω µε where h m ω c m µε mπ a mπ a mπ a + π b + π b + π b e jβ m e jβ m e jβ m e jβ m e jβ m β m ω µε mπ a π b β c m [5.3a] [5.3b] [5.3c] [5.3d] [5.3e] [5.6] [5.a] [5.b] [5.c] [5.d] [5.e] [5.] ω µε [5.4] [5.5] [5.6] /0/ :00 PM /0/ :00 PM

6 Domat T mode: cos π a e jβ 0 jβ 0a π s π a e jβ 0 jωµa s π π a e jβ 0 0 β 0 α cte0 ω µε π a π λ + b c0 R a s ηb c 0 λ 0 π β 0 c0 Z TE0 a µε λ λ a π a η aµ c 0 4a µε [5.3a] [5.3b] [5.3c] [5.3d] [5.3e] [5.9] [5.3] [5.4] [5.4] rcular wavegudes: TM modes where 0 t a r cos φ l [5.46a] E r jaβ TM l t t J ' l l a r cos φ l [5.46b] E φ ja β TM l t t l a r s φ l [5.46c] H r jωεa t t l r a r s φ l [5.46d] H φ jωεa t t J ' l l a r cos φ l [5.46e] where β TM l ω µε t l a [5.44] t l ctml [5.45] πa µε rcular wavegudes: TE modes where 0 s a r cos ( φ e jβ l [5.48a] H r jaβ TE l s l H φ ja β TE l s l r E r ja ωµ s l r J E φ jaωµ s J ' l s l J ' a r s l J a r s l a r s l a r cos ( φ e jβ l [5.48b] s ( φ e jβ l [5.48c] s ( φ e jβ l [5.48d] cos ( φ e jβ l [5.48e] where β TEl ω µε s l a s ctel l πa µε [p.359] [p.359] /0/ :00 PM /0/ :00 PM

7 Table 5. lth roots (t l o J (.0 l Table 5.3 lth roots (s l o J (.0 l /0/ :00 PM