微波网络讲义

微波网络讲义46[1]1980[2]1980[3]1994[4]R.E.Collin()19812000411-11.11-11-3zzz1-11-2-3-4-5-6-7-8-9-10-11-1-21-2-3-4-5-6-7-8-9-764123891011512356894711-21-4a1-41.21.2.1-4Lr022=+∇LkLvv(1-1)µεω22=k()()zZyxLLt,vv=2222zt∂∂+∇=∇⇒TTTTTT(a)(b)1-311-30)(2222=++∇ZLkdzZdLZLttttrrr1-2022=+∇tcttLkLrr1-3ZdzZd222γ=1-4222γ+=kkc1-31-31-4zzBeAeZγγ+=−1-5γetjω,ezγ−zezγ-z1-5mm1-61-6Z0Z01Z02Z0mMmzεµxy11-41.2.2TEMTEMLaplaceTEM1VtErItHrttHIEVrr∝∝,2PPVI=}Re{*213Z00ZIV=1()()()()⎩⎨⎧==zIyxhHzVyxeEtt,,rrrr1-61ˆ=⋅×∫∫dszhesrr1-7s}Re{}ˆRe{*21*21VIdszHEPtst=⋅×=∫∫rr1-821-6erhr1-6)(zV)(zIerhr12AIIAVV=′=′,1-8}Re{'*21IVP′=123022ZAIVAIV==′′3wZwttZHE=rr1-931-61-90ZZhew=rr1-10herr×zˆ⎪⎪⎩⎪⎪⎨⎧×=×=ezZZhzhZZewwrrrrˆˆ001-110Z11-5[1-1]10TE10TEzWTExtzytexaSinZExHxHexaSinEyEyEγγππ−−⎟⎠⎞⎜⎝⎛−==⎟⎠⎞⎜⎝⎛==101010ˆˆˆˆZ10WTE=βωµ=221⎟⎠⎞⎜⎝⎛−aληTE10εµη=E10⎟⎠⎞⎜⎝⎛=xaASinyeπˆA1-6⎟⎠⎞⎜⎝⎛−=xaSinZAZxhWTEπ100ˆzzeAZEIeAEVγγ−−==0101012ˆ10200021020=⋅=⎟⎠⎞⎜⎝⎛=⋅×∫∫∫∫abZAZdxdyxaSinZAZdszheWTEabWTEsπ10202WTEZabAZ=AA=b2202110⎟⎠⎞⎜⎝⎛−==aabZabZWTEληzWTEzeZaEIebEVxaSinaxhxaSinbyeγγππ−−==⎟⎠⎞⎜⎝⎛−=⎟⎠⎞⎜⎝⎛=102,22ˆ,2ˆ1010TE10VmIm⎪⎪⎩⎪⎪⎨⎧=−====∫∫∫==aaWTEbyxzmbaxymZaEdxHdxJIbEdyEV00100102102π1-12TE1011-6102ˆ210WTEtstZabEdszHEP=⋅×=∫∫1-132)(0212⎟⎠⎞⎜⎝⎛−⋅==−aabIVZmmIVληπ1-1422)(0212⎟⎠⎞⎜⎝⎛−⋅==−aabPVZmPVλη1-15222)(0218⎟⎠⎞⎜⎝⎛−⋅==−aabIPZmIPληπ1-16⎪⎩⎪⎨⎧==IZiZVv001-171Maxwell⎩⎨⎧−=×∇=×∇HjEEjHωµωε1-18EH∇zzHzHHEzEEtztzt∂∂+∇=∇+=+=ˆˆˆ1-141-18()ZttHzHzzHˆˆ+×⎟⎠⎞⎜⎝⎛∂∂+∇=×∇()()tztttHzzHzH×∂∂+×∇+×∇=ˆˆ()ztEzEjˆ+=ωεzttEzjHˆωε=×∇1-20()()ttztEjHzzHzωε=×∂∂+×∇ˆˆ1-21(HE−→,EH→,εµ→,µε→,zttHzjEˆωµ−=×∇1-22()()ttztHjEzzEzωµ−=×∂∂+×∇ˆˆ1-231-201-22t∇1-231-2111-7()tttttHjEzzHjωµωε−=×∂∂+×∇×∇ˆ11-24()tttttEjHzzEjωεωµ−=×∂∂+×∇×∇−ˆ11-251-6()()IhjzVezIhjttωµωε−=∂∂×+×∇×∇ˆ11-26()()VejzIhzVejttωεωµ=∂∂×+×∇×∇−ˆ11-271-261-27he⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧⋅××∇×∇⋅+⋅−−=⋅××∇×∇⋅+⋅−=∫∫∫∫∫∫∫∫∫∫∫∫VdszhedseejdseejdzdIIdszhedshhjdshhjdzdVsssttsssttˆ1ˆ1ωµωεωεωµ(1-28zβγj=βjz−=∂∂1-111-261-27()()()()⎪⎪⎩⎪⎪⎨⎧=−⎟⎟⎠⎞⎜⎜⎝⎛−+×∇×∇−−=−+×∇×∇VejIjeZZVejIhjVjhZZIhjwttwttωεβωµωµβωε00113()⎪⎩⎪⎨⎧⎟⎟⎠⎞⎜⎜⎝⎛−=×∇×∇−=×∇×∇eZkehZkhwttwtt122ωµβωεβ1-291-71-8⎪⎪⎩⎪⎪⎨⎧=⋅=⋅∫∫∫∫swwsZZdseeZZdshh001-301-71-281-291-27⎪⎪⎩⎪⎪⎨⎧−=−=YVdzdIZIdzdV1-31111CjLjZωω+=221LjCjYωω+=11-8wZZL01µ=()wwZkZZCωεβε−=20102ZZCwε=ωµβµ−=202kZZLw1-311-71-7zTEMεµ=wZk=β∞=1C∞=2Lµε01ZL=02ZCµε=zTEβωµ=wZ∞=1Cωβ01ZL=βωµε02ZC=wcZkZL202µ=zTMωεβ=wZ021ZkZCcwε=βωµεwZL=102ZCωβ=∞=2LβjZY=0ZYZ=1.3T1-3bzzmmMaxwellβ0Z1L1C2L2C1L1C1L1C2L2C1L1C11-91-8zz1-811.1tjeωzeγ−zeγ+z-z1.21.311TM1.4βjZY=0ZYZ=1.5βαγj+=02Z01Z2l2l01Z1l01Z1N2N01Z02Z1l3l3l22-12.1——n2-1a1T2T···nT2-1bn(a)(b)2-1nnnµεσMaxwell2.21I2I···nI1V2V···nV⎪⎪⎩⎪⎪⎨⎧+⋅⋅⋅++=⋅⋅⋅⋅=⋅⋅⋅⋅+⋅⋅⋅++=+⋅⋅⋅++=nnnnnnnnnnIZIZIZVIZIZIZVIZIZIZV221122221212121211112-1⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡⋅⋅⋅⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡⋅⋅⋅nnnnnnnnIIIZZZZZZZZZVVV21212222111211212T1VnV2V2I1InI1TNnT2I2VMnV1I1VnIN22-2[][][]IZV=[]ZIViiiiIVZ=iI0i=12KniijiijIVZ=jI0jinji≠=,,,2,1,Ljji[]ZZIV⎪⎩⎪⎨⎧==iiiiiiZIiZVv002-2iZ0i[][][][][][][][]iziZZZdiagZZZZdiagIZZZZdiagVZZZdiagvonnnn=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⋅⋅⋅=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⋅⋅⋅=1,,1,11,,1,11111110201002010010100101LLdiag{}[z]ojiijijZZZz0=(2-3)ZZ[2-1]2-2TZ2-2TZ2-2TcaIZZIVZ+===011112cbIZZIVZ+===022221ccIZIZIIVZ====22021121ccIZIZIIVZ====110122121I2IbZaZcZ1V2V22-3Z2-3[][][]III′′=′=[][][][][][][][][]{}[]IZZIZIZVVV2121+=′′+′=′′+′=[][][]21ZZZ+=2-4ZZ2-32.3Y[][][]VYI=2-5YY0111132=⋅⋅⋅===nVVVVIY10211231=⋅⋅⋅===nVVVVIY2[y]ijjiijYZZy00=2-62-42-4[Y]YY[][][]21YYY+=[Z][Y][Z][Y][][]1−=YZ[][]1−=ZY2-7[]1Y[]2Y1I2I′1I′2I′1V′2V″1V″2V″1I″2I[]1Z[]2Z2V1V22-4[Z][Y]2-5a(b)(c)2-5a[]⎥⎦⎤⎢⎣⎡−−=−−−−1111ZZZZY[Y][Z]b[]⎥⎦⎤⎢⎣⎡=−−−−1111YYYYZ[Z][Y]c[Z][Y]2.42-6A⎥⎦⎤⎢⎣⎡−⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡222221121111IVAAAAIV2-811A21A12A21AA2-6AAA2-7A[]⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡22111IVAIV[]⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡−33222IVAIV···[]⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡−++11nnnnnIVAIV[][][][]⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡++++11112111nnnnnIVAIVAAAIVL[][][][]nAAAAL21=2-9AA2-71:nZY1+−nInI−3I−2I−1V1I1A2A3AnALL2V3VnV1+nV1I2I−[A]1V2V22-52-2[a]02012222020112120201212101021111ZZAaZZAaZZAaZZAa==⎪⎩⎪⎨⎧==2-10ZA[]21222221122121211111det1ZZAZZAZAZZA==⎪⎪⎩⎪⎪⎨⎧==2-1121122211]det[ZZZZZ−=Z[2-2]2-8Γ[A][a]2-8Γ⎪⎩⎪⎨⎧′−=⎟⎠⎞⎜⎝⎛′−+′=11111IIIZVV()⎪⎩⎪⎨⎧−+=′−=′22121IYVIVV[]⎥⎦⎤⎢⎣⎡=1011ZA[]⎥⎦⎤⎢⎣⎡=1012YA[][][]⎥⎦⎤⎢⎣⎡+==!121YZZYAAA[]()⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡+=02010201020101021ZZZZYZZZZZZYa2.5()()⎪⎩⎪⎨⎧−=−=+=+=−+−−+−VVZBeAeZIVVBeAeVzzzz0011γγγγ(2-12)−+VV,abZ2I−′−1I1I1V′1V2VY22-6()()⎪⎪⎩⎪⎪⎨⎧−=−⋅=+=+=−+−+baVVZZibaVVZv00011(2-13)s⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡nnnnnnnnaaasssssssssbbbMLLLLLLLM2121222211121121(2-14)[][][]asb=s0111132=====naaaabsL1102112431=====naaaaabsL221s()s()sZYsszs(2-13)[][][][][][][][][]⎪⎩⎪⎨⎧−=+==baibavizv[][]{}[][][]{}[]azbz11−=+[][][]{}[][]{}[]azzb111−+=−zs[][][]{}[][]{}111−+=−zzs(2-15)[1]1111+−==Γzzssy[][][]{}[][]{}yys−+=−111(2-16)sa()222112112122211211211222111222211211112112222222211211222112111122aaaasaaaaaaaasaaaaaaaasaaaaaaaas+++=+++−=+++−−+=+++−−+=(2-17)ssyz,a22-72I1I1V2V01Z02Zs[2-3]θs.⎪⎩⎪⎨⎧==−−1221aebaebjjθθ[]⎥⎦⎤⎢⎣⎡=−−00θθjjees2-9[2-4]s⎩⎨⎧=−=2121VVII()()0222201111,ZbaIZbaI−=−=()()0222201211,ZbaVZbaV+=+=2-10()()()()⎪⎩⎪⎨⎧+−=+−−=−2202210122012102baZbaZbaZbaZ⎥⎦⎤⎢⎣⎡⎥⎥⎦⎤⎢⎢⎣⎡−=⎥⎦⎤⎢⎣⎡⎥⎥⎦⎤⎢⎢⎣⎡21020101022102010102aaZZZZbbZZZZ⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−−+=⎥⎦⎤⎢⎣⎡