b7 Transmission lines 2 -comm theorem

8/9/2019 b7 Transmission lines 2 -comm theorem

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' 41o1- ,L tM f .-' ' s " -+ t ! - "- e{a- f r:

Transmnission{nesIn many communicationssystenN, it is oftennecessaryo: inierconnectpoints that arelome li'lrlltc apan from each olhcr. The',n ionnectionetween transmittcrand its an-rennas a lypical \amfleol this. I f lhc tre-quencys high enough. ucha distancemay\rellbecome n appreciable rallion of lhcwavclcngLhcing propagared. t rhen be-comesecessaryo consider hc Properties f' the nierconnectilgwircs, sincc thcse nolongei ehave s short circuits. It will bocomcelidenl hal thesite, separation nd generallayour f tfie sysrem f rvires ecomes ignifi-caniunder theseconditions.

We will analyzewirc systems hichhave ropcriicsh.ricanaffect ignal harac-{eristics. hediscussionill beginwith ur-damentalsndgoon o study uch ropcrties'as he chancteristit impeddnoef transmis-sior lines.The Smiti cfidrtand ts applica-iionswill bestudicd extandexamplesivenof themanyproblemshatcanbesolved iihits aid.Finally,hechapterooks t thevarious hAnsrnission-lineomponentsn com-mon use, notabfystlrs, ilircctionalcauplercand balatrce-to-unfufurnce ronsformers(baluns).

OBIECTIVES{lpanNory etitlg ht nuterial in Chatter 7, the studeht ,ill he uble o:Underotondhc thcory of tranlnrissionines n general.Calculate hecharactedsticmpedance f a transmissionine.Defin he terhs rranrlirg wayer,standing-wawntio (SWR),andnotnelizdtioh lDeterminche equirctnenlsor impedance atching.Analyzehe prope(iesof impedance atching tubs.Becomehmillar with thc Smithcharl and ts use.

BASICPRINCIPLESlines in the conlext fthis book) rc consideredo be nrpedance-match-designedo deliverpower RF) rorn hc transnittero theantenna, ndmoiimum ignal rort the antennao the receivcr. rom sucha broaddefinirion, ny

IB5


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tr66ELECTriOl.iraoMt lllNICAltON StSTtn{S

n,)co.q l lnba:n.e ri cl 'XCtJRI i - l ' l ransmis$i{ ,n in.s.

1r ) i i re r r lL3in led, ,e

slstenroj lvirescan be consjdereds ornrnrg neor lnore lar$issim hres. i Lhepfopertiesf theserresmustbe aker ntoaacornt.lre inesnighr aswcllb{ :araDgedlll somc irnple, onstanrar{crn. his lill nrakehe propLyrics ucheasiofocatcu:lalc.and r will alsomake hcn con(ant br any ypeofrransmissi{nrine.Alt pmcLicaltransmissionincs arcarr ngcd n solncuniformpatLern.his sinrpljfies alcularions,ruduic, (, . ,LdndurJf.r.rr -r 'n\cniuJr

7"1,l Fundanrentals of Troflsmission LinesThcrcarc wo typcs l coDrnronlyscd ransmisxionincs. hcpa rllel-wircba,uuceqlline is slrown n Figurc7-lb, and thc coaxial unbalanccd)ine in Figurc7-td.The p4rullel-wireine s employed hcrcbalanoedropcflics le equiredrorjn$tance.io connecting foldcd-dinlc antennno a TV rcccivcrof I rr]or?ri.r nrennato an IF transmitter. he coaxial ine s l|scdwhenunbalmccd rcpetiesarcneedcd,as n tbe nterconnectioDl A broadcast.ansmittero itrigrounded ntenn&. t s ahoemphyod.alUHF andmicrowavc'rcquencies,o avoid he isk ol radiatio0romLhetran$mi$sionine t$cl f .A)rysystem f conductorss ikell lo rldirle RF euergyl thoc(nrductorepam.tionappr(racheshalf-vr'avelengtht heoperutingfequency. his s iar nro|c ikety 0occur n aparallel-wircine han n a coaxialire, whose utcroonducn)ruuoundsho

CHz, cithof wavcguidcs r coaxial incsore sed. (lctcndiogon rhe cquirenrcntsapplication, hcrcas avcguidcsrcnol nonnally sod cbw 1GHz, nd coa)dallircsarenot nonnally sedabove B CHzDescriptioD Within eachbrcadgrorpingor type o1 tr.$s:nissionmc thcre s mastonishing ariely of dillcrcrt kinds, dictatedby variousapflicatjons.A bro{sedrough a manulaclurcr'sal.Llog ill graphicallyllustratehis point. It irvatirbshows,as docsT,thle 7l for a numberof hres. the different brms of linesconncctors.ogcLh$with thcir chaructcristics,alnrgs udapplicrtions.-iriei ni irigid or ilc/-iblc, ai f spa.od of filled wirh (l i crcnLdiclcc{fics. with smo{)rhor co 'rgaledconductorsas he .:ircunrsraoces narrt. DjffercnLdinnrelers nd pro|)crtl.s r


3/37

F

g4:L1'l !'"t!+ larlllli{'n[ll; ':l'll'"; ,. ',,,ir:* : 1;t:i,',,,''., ]i'R|. i ] rni ] i !16]In j i l ]


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ELECTROI]ICCONIMUNICAiON SYSTEMS

|IGURE 7-2 Gcternt e{iuit:rlen{ ircuit of transdission ine'

nressures rlv) use{lasa mcans l keeping ut uoistureAs thc powet rarNmittedsi'."t""t"a- - .*, n",f''"crcss-seclionalimensionsf lhocable Forexa ple'rigid

oir"fJ*"t i. "o*inl "oppercablewith anouter imrete'of22 5 m.haspeak owe-r

.r i ' ." . , of l " lhis n. reJ.c' o400L$,cr :,noL'rcr ' iurncte l 8 n mm rrd oIrfu' tor n zr0-rrnr urer iomLlcr 'r wi l l bc 'hown \ l t r l re.nDcr ] l " : ' : i t i : 'k"hoigedofong it t ttt" outerdiametel, oensure

consta|t a]ueof All ne

Eouilalrnt circuil repres(nlstion 5inic cach onJr'clorhasL cerlrin engthmJJin"tlr,-ii*ill n*"^.sistarcc

andan ,ductanocsinc hcrearc wo wires loseto'eachother. hercwill be capacitalcc etwccnhcm' The wires areseprated ye'."afrt "if"a tlle diettictt'ic'\'hich cannotbc perlect n its

insulation;he cuftnti.lrf."r" t'tt us l i,."n t' . reFrc'ented) J JrunL !'ndu'lxnccThc csrhing qLri\almlcircuij s a' "hor n ln Figure '2 Norc hdt ll lhequanliLieshcwn areProportronalm.irl" ii,l*i'"iil"-ii"", '" nrtuntesseasurer)ni quatettet unit ensth'heJtet"""ttYii"ul,n u"ou"n.ies,he nducliveeactancesn''uchargerhanhent.."p".iii'" *"-.ip,""ce salsomuchargerhanhe.'hunt,condlcrrnceothC-n*i u" ignn'.a.''."rhinsn a liDehat s con'ideredossle:,f^li"'Y ii^ptr."ii*it"ii i"t fr *lcu;dons) Theequivalentjrcuits simplifid

ssho{n''"u'" 'nui ,, ,u nurru hat hequuntities, R, c ' (ndG' shownn Filllres.77-3,arc al.lmeasut.dParunil ength' 8 ' permetu, becautehq' occur'hi tni in". fnaf ire nu: rlisiihuted hrouShouthe angthof.theLinecir"ir"ton"u" "nu'thq' be $sumed o be lufiped t an) one

poinl'

7-1.2Characteristicmpedancennfclt.uir rnor on.ist'o 'cricsanJshu t nroedaDctsusthave nmpui;J;:'iliffiil:iii;:,"'iil'ili;;.il;;irr-o"iJ ,r'..,jp.'tii"ngifrnnJ ft" ".ntinur;"n t hc ar end.To simpljly escdpijonnd

FIGURtr 7'3 Transnrission"lincF equiv'lentciruuit'


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r l ' - -1."1 r.-L, N I l r . I-rS{19' i I

1

2'

_riC !_ri{I

poqri iiansinrue0$lror cxxlnplt. ngltln hxs P':aliPowc'of ll l ln', rnd to idianeter nlrst be

o{ ,tll inePl)lertiesa certrin cnglha dar.ewo vircschset{r

re soPAraiedl rirccunnte csiulliD!.quilderlw anjPrcPortionaloulit l(ni:th' theJat !

han he esislancsodlRandAsa {crYgooosimPliiicdasslrown r

j| i !rp:.i.rir.e Lrirdcr:crlriD nmd.rif sn)rplc d orisil! rrinrilu.ii)]. roirdiiions !i .r i icn rs h. !ctetr)ce ff l 's cal lodl)e trdra,1., i !r inipr./dt, t( ,r i hr i l i i re.nr,i.lilititri tlt. thttttl!tisti( inD.tltrlLt tl Lthdtinnit.\x)i itt -.,. i! 1tu'il ldtltttin!tsttftd dl thr i)ryut l thi\ itr'r'|t.i it! ltj!1!lt ! irt4"ir.. tirrdcr hosc oirlitions hely|,eof lcf|niratil)nat the af cndhasno cffcct,andcor$rxlucnll)! noi nreolioed r)the dcfiniti0n.MielhDds { c?lautr.rtkrni crlr nowbe slrwn thal thectriacrerlstic NpcdrDcc f rli e will irr nrcasurcd t it\ inputwhen he linc is tuminnod :rt thi. far eod n ar lirnpedaflcequfll o Z0 (Zir - Zodmirxpowef rnslbr). no natler whal enlth lr lrnchas.This s rmporirnL.,ecase$uola siturtions frr easicro rrilrodtr(c or nlorsure-nronrpurposcr hn a line of irlinitc length.tf a inc hashfinitc longlh, ll hepowcf 0rl nlo l will br:-tr$(n$ccl.r shouldbe hirly obvious hat or ono moves wry liom thc input. voltllgo nd culnrnlwill(lecro"rscbnS the ine. its a resultol thc volLagerofis rcrosslre fidu0lanfc rrdcu,.|entr l(l|gc hrcugh hecapaciluncc.rom hemeaning f infi it],, hepojntsL'-2'of Figurc -4 ro iustas lar f ronrihefarendof th is l ineaslhepoints l-2: fhustheimlcdAncc ccrr t l'-2' (looliing c therigh0 is also20, although he culYent dvoltrjgo rc k)worLhrn t l-2. Wcca0 irussay hxl thc rpui tcnnioals ee piece ll incuf to l ' -2' , l i t l {)wcd y a cirouit hich ns ho npul n1!danceq al o 20. tqui tcobviou$h,.k)csol mattsr hat he circui t o thc r ightol l ' -2'consrsts l ,pfolidodLhat t hlis n input npcdance qLrnlo rhc ch rdcrofis(icmpedancef thelr1c.Zr \fillh( ukn\urul I the tlput )ld tfnt,.]|ai$ionin! il th( atnt) it llrminuted;n 20. Undcr hc$cconditions 0 s considcreduxily rgsidivcIt filllows from filier theory hal thc characreristicmlcdanccof a ilerativeorfcnrloon$istingf sc cs .lnd $hrnlelenrenlss givenbyiz2,,= \7 {7'l)

n Ft\tn s 7'2 )ndlh,\' ,a.t 'tvtindrcrtt)'l tfu litL UnLlotopoi

''i"'"' whcrcZ = $critrsrDpednncecr snlion= /l +Jd,l ((Iiflr herc)and $ the| .= shunl dnri anccpcr scdi0nC ."a' \n. 7.t\- l!l!yL\ (; + io(._

lerie$ lnpedrnce fOfshunl dr)itrancc ef unrl


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i9{} ELra'fROllIC aol'tltliLr:'iia,I. la)ll 51-STEI1S+: 'al(:liitE 7S i ur*nissior]lin. {conr(t,-l.

sror ine nrxt b. .o lr rpl .x. Nr iLlDdccd t ! . r \ ot i , " I rs esl{c i l l l r - r lnrccomrn0nici-rions. j.c . t.lctLro|J rt \oic. frcqncnci$. ^t tudlo |equencics thL: csisiivecornpGncl l tsof the oqul ! . t lent i fc j t be()menrsi : r r r i l jcrnr .nf thee). |ncssr( i ) rZ0rcduccL

1- s ensur.dn honrysol nreler rd a in f.udr l)!r rretef; t lbllowslriiEquati(rr (7-3) sirows hc chllrtulcristjc mp.dal)ceof Lrie n olrnls,nd ls .li cnsiolr-"rlly cor]ect. lr als,, shows thal tiris (,drrkk:ri.\tit it)rt1r'hnL( t(siniv'.tt tftlio ltN- :

..1,.

Physic,rlll, h ftLcteristicr)\xrdances detefrnincdy theAeoDrelry,ircandsplcing ol dreconducLors,nLl hy llle dielcclric onstmtol lho nsulatorcparatithefir. r |nlJ be cllcuh(cd lRnr thc li)llowing brrnllas, hc vrrious crns ravingnL\. i . l I r !s,\ \ l ' '1$r n Fi"r e - 5lin thc p.r'lrllel-wircire, wc hrvczt,- 216 'g+ t1

f-or hecoaxir l ine,Lhissl :18 t)Zt= vTt ' tE- \ l

(:1-4)

whele = diclcclr ic onsL l of lhc nsuhi i0n.No|c hathe igurc138scqurl o l20rrr. $lrerc 20?r 37? is hc mped-rrre oI lrcc st :e, md ? is thebrsc ol the nrtural og{rithnr yslem: 76 s2 x 138gqurl ion 7:l) rpperrs take o accoLrrll lLrc ic lectr iconst.rnr1$cnrsula{in8 rLc rl. Ihis is becausehe Nrrefi l is vcfy olicndir bf frm llcl-wircines;rnd its licleclfic onsrrnrs rnity The bilirlr tbr iheZo oi Lr ,tllLlcedinc vith ollddiclecttic s rlnnsr iclcnLic.rl.j(ccpt hit tlc 1irct efm bccomos 76/Vt.

(7.s)

---,e!

Tlrc rLsnatngc o1chrt , rcrsf ist icnr l ) !daDcoibr balrnccd incs s 150 o 6000, rnLl {01o 150O lof corx l l incs.bolb bcing i lD i l fd by rhci f gcorrelry ' ' fh is,?swell rs lhc mo(h(Jd l Lrsln! becharlrclcfisticurpodanccinnrulns.will besho$n n r!next thrlc cxrmples. r ii i


7/37

0l .r lmrsurs.in line conlmunin

llrc rc!'rtrvs cornpo.lor 70 red ccr

[RnNSI\ , l iSS10NiNES n91

Fr !M. l t r - l \ { h ' ' i , , '. . l . . , r . l "" , o, . ' r rihc diiN.tcr oi thc ,nn.r i,nduckn i\ 1)JS'1 nn rnd rhediclcdri. .on(ldl of tnrsulallo.n I 23, rvhrt s rhc uler en d.L{tr irnr.rer?SOI,UTloN

zt: ' laI o .. | , l . l133 1)21, ti roe ,

- . 1) 1-= l l : Lr rl l \ \ I i8 \ 2.21DrD: lrL i log0.8l - l ) .51t4 i ( i .157 3.17 Nr

ilXAMPLIl T"2 Whrl js lhe Di.iiium ulue lhal Lle.hrrrctcfisiic inrPodrtrcc ir raifrlielcctric t.rallcl-{i' 'e lifle drld have?sor,uTl{lNMirrimu i p(lr]cr: silloccorwhcn 2si./ s alsonrnrnnu,n.nd Ihis s rcrchc(lwhei6c LBo$jfcs ol Figrnj 7'5d 0s1urh [t ii lher seeo hrt r - /. so thaLw0 htrlczi . i i i = t76 loa: r I * 216x 0.3010' 83 r l

EXAN{I'LD7'3 A corxialcublc, rvingan L!rer iaLrercr f0 025 n]D rd usiug '1iisula(tr with a diclcctric onstunLi 2.56, s to hrve ! clmmctcrisLicmPdnroc of2000 ). Wh0t nrsrbc the oulercondLrdor ianreLcsoLUtloN

D Zt j , ( : 'n ^ t . (' t - t l1h\ t t - ,8v:50 - l ]^= 23.1884/) = r /x rnr i tog23.t8t j4=0.025 l0:r rx I 543=t.86 x l0: nnn= 3.86x 10, i km

Ln6 . t0 ' _^-9.44 l f t '

A lighl-yc|r, rs Lhc fle !u8!esls, s thc disLmcc olcrcd by lighl irr I ycu dl alclocil] o1300,01)0d pcrsccordTllc igurcoi 409 ighrlcurs s AlnoslexrcilyL0t)liDrcshc distDcc 1)f lr nc^rcsl l! (PfoxinaCcntNri) frcn Llre olar.qysrcnr,nl llh is xrDf lc r cs o show onclrs i lc lyhr l dr ^highvf lueoldAaotcr ist jcinpcdrncc s irn not ossilrlel

Lla highvr luc ol ch. l | crer ist icrntedalce s nccdc( l ,t is ieen l r r l thc onduc'tors uslbeverys|nal lL( 'g iv.al , l rgeidrclanceperuni t lcrgth.Thedjslnrrcchclwccihem rrrsl be vefy lafgc Lo yickl as stnall a dNnt catrtrihnce Per unrl lcngLh s

(7.3)l lbllows hd

nd s dnnension.ti.istir? dt tadio fte.thereometry, izensula(or epamtiDge v fi(ms ern$ havjrg

= 377O is thc mped-76 s 2 x 138constant i tlrcbf parallcl-wircines,b.rlancodinc wilh solid76l\4ines s 150 o 600thcngeo etry .Thrs,4swill beslrowr n he,


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iro$sihlc Onc .v.rnurll) ruirs oLIt 'fdislllnce. lLti hc orir.f crd ol ilre sc.r.. theenacroppoliLc rpplics Thr( is. dillxn.es b. reeD.ondlrciors beconrc con\eirtcntlysn{llior .orxial imes f | . i bccomc ntos\ ib lc oi t r rx l lef $ire ines, incc f . r laDingofconducl . rs \r r ldoccur i1 aZr lcssl l ian!3 l ) $ere al le iLple{ i .

7- i . f Lolses io ' f ransExissioDI- , ; esTrpesoflols.s Thefe] lc hree r ls in Nhch ncrgI. pt l icclo a r l ]nsrnissionine,rlry bocorne issipated eiiJre erching he oad:nttidtn,t, (onrlkl.it h{alin! ont

Rrdi.ilion osscs ('cur 'c(ausc lransNissrm nenn) actas n {nteruufthescparrrior )l llre conducl{)rss rir rfprcciablc ilcrion of a NrleleDgth. hrs ptliesnn)rc o tamllcl u'ire irrs thiro c co^xi l ines l{ ilti(lr k)sses redjiTiculLoesti-nrate.bejngnornrally rci$ured thcrthrn calculatcd. hcy llcrcase!itlr treqLrcncyfor lny riven tl1nsririssionine. everturll) endurghrl Inrc's'rse{ulnesst some ighaon.luctorhcalins.or /rR loss. s propor'lionalo cuncnt lnd lrcrcforeu-veNell tfopoltiollll 1ocharlrctcris{icrnped.tnce.t also ncrcases ith iqLLcncy,hislinre bcorusc f the !/.tn7r( r. Dic cclrichcaLnrgs proportionalo the ollrgeacrcssthc dielectfic nd hencenver$ely r1)por'lional{) hc charrctcisticmpedancebfany

porler r|nsnittcd.11 gai|] ncreaseNith feq0ercyforsdid diclcctdcines) ocauseol graclually oscning )folerlieswith increasingfequercyot m] givDn iclecticmodiuln.For r . howrvrx. diclcclrichertiDg cmainsDegligible. jlcc thchst twolossesfe f,roporti r0 l l) crglh. thoyarl.usurlly umpcd ogcther ndgivenby manu-iirctureNn chnrts, xllrc$sedu decjbels el 100metcrs. orpraclicnl o,rxialines tI CH/-, hese sscs ofy lom s nll|chns20C)B/]00 m for a solid-dicleclric,lcjiible6-mm line, rc l]s little ns 0.94 clB/100m lbr a rigid, air-dicledric127-mmine.Veloaity ilcior Thevclocitl of ligbtandall oLher lcclrunngneticaves epen& nthcLrediumhrough hich hcy rrvcl . 1 svefyncarlyi x lOsntsinov0cuumandslowerr l l othermcdia. hcvck)ci ly f l igf i1 n a modiurrs given y

llf Er-E(- RL,i\llc aali4l"iLiNlllr\lirili sYsTEi\is

'= \awhcl l , '= vcloci tyn lhe Drediumv,.- veloc y ol light in a lrcuuln11"6J

,t - dielectric ()Dstanll thcnlidiunr 1 lr a vaclllrln ndveryncsrly fornir)Tl \e : lo(i i lAdu ol.t ,J iolect| iclbslancc.nd bus fa crblc, s he eloci tyrcdlrcli(trrntio and s lheretine ive by

(.7"1),1= .li' . . . '

The diele(ldc .o st rLs l nr.uori.rlsoDrmorly sed m l|ansmission rncs angel ior i l rborL l .2 Io 2.8. givrrgcorrcspondingohci ty lar tors lorn0.9 o 0.6. Noledlsothal sincc v ' /I rnd/is constant.hc wrvllLrDglh i'i :rlso cducedby a mtio cqull t9


9/37

Er!:"t'-'sf..ii

l i i r . . r r i l rer i id o1'r l r i .; { ' , r le.1lncf0n. rii.lJn'enre .pxfLJi.l \rir liitr. j;rr.t o','erLqil l ! ) s. i . Lr t [ r t t .d. I

i ; ! r l l : i . i r t l r I ! i . . . j13 t ! l : ,

L i r . r . l (J i i i r . r r , : ! : , ' i r . ! : i [ r ! ] i ,1. , , . , : - . ' . , , i , . , ! . ' i ( ,n1)L'i i i , i ] " ' 1, ,' . , , , . r " .L1i- i I l r r , tn rjl i r l iLr . f . . ( r i t l r r r 'L ' r f , r rs l ' i i '1 i r l f

r , .Lr .n{ l f r j r

i l t I sr r l , r t ing, l l t t "e ' t i , , : r r . t : r l i r , | . i i : : i tL,) , r r i* i r r ,L. . , : . : r i r i : , i r . . , . r , , . i .

- . r , l r ' i , l " L i r i ! ' r | r ' ' i lhr ! ' r ' r l ) t i r1.1 l l r o l. irun nr l r ra.Lrsir l run1c(' , : uf ' "

, i r r r , i | i , ' rL i . , . : r r , r t , r r ' r . i , r r r r : n lL l rL]r r r ior L, l \ r . ,o i rn! lh. Thi i t1, i t ( t t t ll'.!dirlior l(,rs.s rri diilicLrLr;

i r t r "r , r u l 'u iousn. l f je io lcJ . l ls ls. lhegr i iNref ihc, . l l l l i rcn. . l \ \ , .$r h. | ) i ! l inrpcd|foirortbrll to cu enl rnd thcfd

rpcr l0nc; [oU1itsIength]L1hcI i | ! i : i | ( ) !s l0 ls.0rxr1cduc.cL|1P0nent i l | i | \

c l2?.nrdthePowe| i ! l r.us|a: |10dbac|{0I l1b| lhbeiwoo| | l ]ei to l , jguru '3) l l r i re ord i r i i )cdnncc rs r vt lue b. i$, |eD0 u|( l iz, iof I 'c lv ' . ( : l r 0 Ur( lqd' 'osci | | | t ]onsst i | l t t l l iop|lCe.Thist i lnethe. ln, i lUdgd(:c|c l l | t ] l

lca y 3 x l( i r nts in a vacL( j shtrQl ] s lho irhr t o l L l rc ord i r r l )odnn(c pprorrch$l jr 'n ledir rn s gi \ ,en t i

i i:'illff,1ffi,.il;il"ll];l,J:;fi:i'1,];"ri.'iliiil::lllli:ll$';I, thc rp|lled powcf. lLrc olllLlrc d currcirLwtv(s trrvel rothe bril t n spec(l lighttI less han , dencrLCin!)n LhcvckJoily:t1ctot.l Z! .'Zr. thc lond bsotusnll rlreI powor.,rr


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- l - I * i - i

, t - r i , .ut r"\ i , r l ll r' ! i isTr-t i

0- J

i.ii{illl{E 7-i' l,osslcssii,.lcrnrilatt{i in r sho.(.n(nit

Corsideronly thennrvr (i Lralcling oltagc dnd cLrrert wtrcs lbr Lhc$omenrAl 1he oad. lhe lolt.ige rvill bc zoro rnd the cuNnt I n.rxi unr bccauscLhc {)adiaslnrl cinaril. Note hrt {lre nrelt hrt r llnitc vrlLre jnc.: hc ine hls an nr|cdanceArLhxt nsilnl o1 irnc. rhe sanre onditn)|s dso applv rl I loinl exrcUy onc w vclengthon the gcncnl sdc of lhe lord, and so on. The crrront at the lo it tdwaysnraxirnLtnl,lthough Llrc ize of ihit m|rirnurrr variespcriodioallywilh limc. sirrcehe:, l ip l r l ur \c r ' i r . . r - '1. '1.

The rcflcctioo lhll trkcs phcc rl thc sln)rl cirtuit rtfccls hoth vollagea0dcurrent. "fhrrcur'rcnlnow shrts lrLt\cling bflck ro thc gcner0br. uDchangedn phNc(scrie$circuil thcory), b 1 t/r( roltttt( i! r(llqttrl r'r, o lu0" lfta.r. r{,'(,'vl. At i ,poinr exaotly a quatcf-\ralelength f|.()n thc load lhe curcnL is /rlrolrdt4 zero assho\\,n D lrigurt ? 6). This is becdlsc tho linward rurd rclloctedcuLrentwaves{eex ctly 180' out ol phdsc,as hc reflectcd$avc hlN hLrd o truvel a distance f,\/4 +,\/4 = i/2 fafihcr thrn rlrc brwrl(| wavc.'Lhc lwo oirncel.anda cunenl nodc s estab_Iished.Thc volt^gc $'avc hn$alv) hncl o travel {n cxtra distanccol ,\/2, but sinceit: Iondcrwcnl r lljo! pha$c ovcri"rl (n rclleclion. ils ntal Phase hrngc is 360" Rein'Io icenrcnt i l l t rkc Llce. fesul l ingn a vol ! ge art inodc t Prcciscly l ro ame ointrs '

A hrll-wavclcngtlr {|rnn hc loal is I Point0t u hich thcrcwill bc a voltaSe clo lrnd d currcnL nxinrunr. fhis lrriscsbcctlusc hc Ioflirllld rnd revefse uncn(woves rsnow ir phrso (currcntbrs had o rrlvcl t(nal distrrrceof onc wrvelengih to relurn 0this poinr) . SimolhrcolLsl) ho vol t rge wrrveswi l l cdncel ,bcc' tuscbe 1110"hasertvofsri on rclloction nrusrbe a.lded 1() hc oxtl1tdisrance hc rcllectedwavehas o(r'ltvcl.Ail lhcsc condiliolrswill rcl)citlat hrlf-wavclcngth dislllnccs.as shownh Fjg-ufc l 6 tjvery Lir e l poinl is.(ltsklered t}rf is )/2 lnrLher rom the lord Lhan onre'pfevkruslyconsidcrcdpoinl. lhc rcflL,cLcdnvc \ltshrd io lravcl one wholc wavelengtnfnrlhef. Thgrclbre il h.is the strnre eluti(nr o Lhc bl'w d wave:!s it hfd rt the iNl

l1 frus( bc e rphrsized hr{ lhis silurtlion s |)orrrnent for rny given bad and sdorcrnrir)ed y iLi suchwr!cs nt truly \/r,z/irs wave\. r''ll the noilcsarep.nn,rnenLlyi i \ , , . . , . lc t"" I r , , . 1 . ,1r " ' r , ' le ,re (un:u i \4. ,1\ . ,1 1 ir ,c onJ ioo'' . t t ly ' l lc lo: .1r . , r l ' i r r : r , \ "pr r | |Jr r r r , u r r r' n ' 'n anJ u l"gr


11/37

-1t8fffl- Tlr-r,-l'.]sl1ll3sl3r.Iil',1tss9sr i l r . i i rL! f ! ) is I lL, lr ' ! i l l1 . l { : . \ r i i ' t r r i i o f r t Lrr : r- ' | le i :1rI ' ierr : I i r $r l ' l ' l r i t _ i / ' i i ' / / r '1 , , : ' ,11, , , " . i ' , , , t t i , , t . , ' ' ; t ; t ' ) . i t ! t . i i ts! . r ; , .11 t ! , ' , t t t i l t i . ' t ' . r l i . ! ! : rn ' ht : tkt t l l t t t i

. l i t ) : ) t t i l t l t . \ \ l . t i ! t t l i i l i i ! i \ t i i t t ' l

srrir.li.!.i:tle i:li{} (.ql1t'iil llk itliiti )i )Nl.,rnux tt:tt"t ir !)tiiirN' tut'nt, r i ' i t i r / rdnt , i i . rx i , , i r in !r i r i l l . r r t r ' r / l "L1" , .qrrrr i ( t ' i t t ' . t15t \ t tk noot t t i l i \ t tJt tnt; , , r , t r ;u* ,n, , , : t , , 'y. th i .h i . t t t l t l r '1 l t . t ) t t t . r / ' , r tD ihc: l [ /Risr n.rsu ' of(hcnri:rnr.n.L bc{*i: ill!: l,r.!.1 |i,l ihc lin.. !td is II}e llist xrrd ll*( ilrlll)ii'tnt qilrnlit}. i r icrL i. r l { i o i r prf i lcu lrr o.r ' l ihoSv, l l t iscqnrl l tu0irv(rdesimblecordlr ion)$hcn1'x lo l( l is pef f .d ly m.r ich.d Uhenthcl inf isrcnlr ir r l le l iDtpuf ' r lyresisl i \e lort l thcstr drt ! \ t r ! t i t t 'o r ! grt .D tr)

br thenromertbec use he oarlsarone veLengLhal thc load k alwalsawith ime, since hc

oth vollagca dLr)changcdr plussr.r,r,rr.r/.Ai ilt r f(m1nnc t1l zeto Ncurrslt wavesarca dislllnco l'i/4 +cuflrnt nodc s estab'of i/2, but $iDcets:160". lein-e sa$ePoir laswill bea \,oltagc etollrrenlwilvcs Lewirvelengtllo lclurn 0ho ltl0" ph$crcilccrcd',ravehas orsshow in Fig'k,ad hansonleonewholewavclcngthas t hada1 hc lintrn] gilen lord rd snodc$ rcperm.tnerllY

y f thc sanEconditiollsmini um (andvoltagc

:i\itil . zl)i1.1/. c\rrii - /i r /!i, lwhiclrilcr i\ luryc t? ll )wlrcn t. is iho Lord es;s(xrrccIaiscuikn ary opot l)e argcrquanliLrn theDumcrrlor l tlre iaction $o halrhe i ioui l l aiwrrsb. grer tofhan Rcgard l l ol whclhcrte oad si t t ' rnceshulfa! lrlge or twic,i as arg(, rs h* lire chrrirc(efistlcnpe(LNncc,hc rntrool I \'ollagcn,axin,r,r,,o a "tnrager.ininrurrrs 2: I . {nd thc dc8r:(r f nrisrrratchs le s'L e

trboth

l f thek)ads purcly o cl j le, SWR f l l bc nl l r i tv Tht strtrc ondit ion i l l1p1. r . . , ' l ' . ' . ' r ' rr .r r ' , r ' r rn: ' r i "r ' i . r ' . n . ' l rhf ' \ ' * no.v. r . " f ' . . ' . . r ! : . r '1 , . i s : ' \ .1 , . , r l r " r ' ' . ( l ' r ' {$r 'ifl)ere lonf lhc inccortrflcle lrr)tcll:rtiorlill oc(:ur'.iring volta!c dro,and re ccSWRm st bc irfiDirc.Whm the otrtl s corrylcx.SWRc n slill bocoln|utcd'huthL nrLch :*rcr " t i .r .r .rr i r ' . f rorr ' trrn n r' " ' rr l ; r r r" l :u: ' r ' ' r ' o n Irrc ' r iLrrJ'ihc higbcr he S$/lt, thsgrcltlcr ireDrismatchclwccnine aDd )adof ' lofthatnlltlcr. betwocn cncrukn nd linc ln pro0licr] iDcs.Powcfk)ss ncrlrase$llnSq/R.an( l o a low v0luc f si ndiDg-waveul io $ l lwaltso!rgh(,xccpl l len hcfioosmissiolrine is beifl-e scd$ lr pufc rcac(anocr us L uncd ircuit l'his will bcdrou'n r) (xi l ion -l : i

l,lorm$iirdtionol imFerlafiat I( scns{orturyt) rt)r'l.rl];rr n mPcdanccrtlr c$fcctlo the iIlo to whioh t ir icourxjcLed..c , lo dividc l)is rn|odan'e y tllc charactcnstrcir fcdanccof lhc lit)e. rs4.-. zr

rhur oblrinin! lhr rtornraliT-Lxlnrl)edrnoc.(Note that Lhenol'ln'llizcd lnpod'iucc s tdimsnrionlossrtl| Dlit-v' nol n) bc ner$uftd or givdr ir ohnrs') Thii i! vcry Lrsclrlbccausc lf l)rjhr,\,iofol thc linc dcperrdr x, l on rlc rhsolut0 mrgnitu'le oi lhe loldnnDe( l ce. r r i o ' r i lsvrlur i r . l r r i lc loZr) Ihis l : rc l an b{:secn ionr Eqrrr (Jr (7- t i ) :r l ; swR on r l i r r . wi l l l )s I reg f t l lcssof ' \ 'hcrh' rZo - 75 l) a d / i7-- 150 ) orZ. - :100 } ll](l n/ = 600 0 Thc nornrxlizingof inrl)c'lrnccopensu) Irossitrilniesi) llfansllission lllrc clrafts. ll is similar 10 thc ptucess uscd to oblain thc rrnrvefsrl esu,rse curycs for l ued cifcLrilsa d Ra'.ouplcd rnrflilient

(7-9J

I


12/37

1 .. ... 1.. "."i '': . '\ ' "' r. ' -','.

. ., !

lrltr:rl,lt' l r-:r l,$it:rr lia. icruin:ri.C ir : ,r. t r.:r:'1, :r. irririr.r r : i , Z{ i&rc thll' : ! ; ! r t : i 1 i1, I i . r{ i . r l ! : : i l r i i !11 11i,

- ' - , , i l i l | . i r i r r l1 ! . i i inrnrf Lo }.ct .a r( i ,1frns | : r i , , rL l : i rc, i r . t i r , , \ tRt . lZ\ lSin.p the ol t rse rd cUr lur t | r ) r lors ihc l inc. s sl rowLrn r igurc '7 , sowitLheresrstancr)f unpcdxu Flowe\er . ,k l i i io ls do r . l ) |ar . r y hr j r' r r l t lcnglh. r \r i turdv, t r l l rnc( l i ' i t idt ,e r i rL. r { l ' l l j l l i , r ' fq l r l l | ! lNr ( ' i l t , , i . , :Ld.t p rs nlr i r l l \arci IgLI x\yr t , 'on) t Ie i ( i rc lxn( t Lir t i : ( i r i r *1. ! r .

7- r : ' . ' t . : - r : : C I l : . j f - - :1 . i jnf i . . . !r i f r t r ( r r i { , ' l l1rni I r i l , i i ,Dr le! lh i r t r i f r i ] fL i r ! ! i r i ln.r - ' r ' , , ( , t f | r r i lL. r t l r l t ,wr !e-lcnAlh lo0! |r\r inrtrrJt; iu rlat|ce-rr{nslin.nr g Prl)Pcrlios.nd 0,f riren used orthis furtxjse lt dir IicqucLroles.juch lires w11l )1,,,,\,c JisrLrssedlfirpe{lllrllac nv$r$h,-r i)}, (nuortora{rivellengtthinxt$ (brsiCur FilrLr|lj?-ti. wlrrchirowri rLoad of i!nfedlir0eZ/ co|neclcd10 licce oi rlltnsnrisr!iln inLoi leug(h undhf rir{ l0 as ls cI fNclcri ic in{Lxbuce. Whcir hc lengdr jr cj{aclh, (t!afier,wa!c-lcn! lh Jinc of 0| ]orklnr l rnbo.ol ua| . ter-wa!ctgt l rs) Lndhc inc e .ssicss,hcn h0inrpcL|uruo l,. sccn ,'/her)lo')kirg to\,{rrd rhc Jo d. is !ivcn by.- 7i

11.

I [G[kE 7-8 l-o. ,dcd inf-

(7-r0)lhi$ |chtil)nrlriJ' is vn ctjnrus ct\llcti ,ll"dfi( lr,/ra.ta,r(.4 .| rhr qLrutcr-wnvelorsrh cl lc($ lhc oppf,r i i l r f i t lL loadrr t r (hroe E. lrmion 7 i( ) ) rcpfescntsvef) inrl)()l1anfn(l llLrrdonr(Nnalclrtion. whidr i! sfilowh t to(i ooJrpt,rx o derivelrerr 1)Ur lroscrflrrh lny 1,. rdiclrred$ ,i,llo\',,s. tnh$sa lord is fclis(i!e nni.t qulll1() hc (hr f tc lefr r ic idrprxl^Dccft i re inc ro $ 'hich t js 11)nrcc1cd.l : r rd ing Nlcs fvol l rg i i f ( l f011dnl rr i r ( L ' f r lo lg thc ine.$nh r r lc ($r l nr jnod( j t! ,J l1, l i lnn e


13/37

'i l l,"I.i.!klss !l-1i{L,llits l!i7

tltaft zo (notelh.ri{a;UtillTr} !;{$rtlirtstlei !1osg I mitdlat'lied i':rmsilissk'n ii'r' i iflPcdlnc'

i' ' iersi{' i'

n,,;li:i"i;iiltiirririi,'.-:'.ili;r;;"::: i'i* i':'"'"'"'"';;l;i;,;'1,:i',,i:,i,l,ll,. '1",1ii"i"-,.',n.,-',",-"0*+-iri-Uil",ii:i:il'#i:;,

: ;r" r:r:;;i:r'r';",,,'rit,,'..lt il**',i\[*,lir+l#l-**i*f*li+ru*tt*ffii*li" *i*il;it:l ':lnlru:'H,ffi'il; : l,'"'l;":il;llf:;:l"l'''n:::,',,,,'m*ils::l:il;"1;'l,j;'ntli):';ll*;r^j;l'"'iti)":

. -; - l

irutz"Zo

-t"""".1i.?ii,'Ji.- resurtsntoEqu'rrion8-1r) ivcs

suchhat i / *2 in l ; igure -7, lo i l l$oh 1:\t.!clength,0f Lhc ud, i f P hr

r r balf-we,/sire oltcn sed or

Figure7-8, whiclrine ol length andis cxucllyoLllrartor-uavciT ossjcss.henhe

(r.r0)i.c., the quulel-(7-10) rePrcsenLsl

t(x) conlPloxk) 4civcload is resistiveand equd

slandingwav$ ofantin)cle) cl t non rrlc

Z, -ZO7-o Zt(?-11)

ZI

' , t r


14/37

i l f l j .a: l l i . i ' l \Jt i . l ( i l r ' ; ' / rLr i l l ' 'L l l i l i i i " ' i i r : r i l i ;

ir. -.2,, ur "rnr',"r',a,4! joo;:ro'.) l-l5l)

" '" '' ' ' ' "rj'll',:','il:,1':iiil-:l,i':l;, ,r ,,!. ,i, i : ,r,,r '.c'i . ' . , t t i r i , , r r . , r r , , r ' r ' l i r l , . . l ' ' r i l r " ! i : l ] r r t i ln irr i i ' ! r i . r l l i r ' i r rn ' : t {

!11l l l i i i r r ' i ! l l l iL tlnj:;;::r,1,;,1,f:;:li:tit;li;:t:,,",,'iillrt,i'.,ii;lii, i , , , , . , ,1, ' , ' r ' , . , , i l ( i t . r i \ r L;rrr l r i r fL,r l i t i ! ' l ! i r ' i r rJ! l) ' rd^- r l n l t l r : r i r r i i !L ir is l ' t; , , . , " , i , , , , , " , 11.r ir . 1r ' , : : r . , i ! thr l i ! re!1 Lrrr ' i r r i . lJ! t ! Lr( \ l

{)uaIt._r.r.r!r iri;i,1lti riiier t:n'j iiLrp{{nnLrrjriu irliiig in fLrrly xl i rnLri!i' irrir (r -l : : : : , : : . ,1; . ; l i ; :l ; ' t r , , ; , . ' ;i , i ' j l i : : : :1. ." ' ' , ' ,' , , ,

r" ' r ' . l " l r ' 'e r ' l i r ' " ' ' r ' I i r ' ',iiiu,ii"",r,i,",'i,n,",'";t':lflili::::ll,l;j;ili:i;;l:i:ill$iii,llli:j];",llilll,"'ii,,,'lll;,iii,li;;;'"'i',lllfii,fi;irrrp,rr,r,ccL;r,r,i,rr''a'tn"'ro,1, . , , , . . ,1 ' , . , . ,I . l ' l , , l : ' r j ; : , l i t : lt . ' j ; : l : ; , ,* . ..',,..,,l' ",,q,'"", i,l : :::,1,,;,".:l;i,];il, ;.| ll;, ,,;il:; ' i l ,: i l:; ' i l ' . ' ,, i,.. i ' l ;,: i i"l l, '- .,. ', ( :nru n. 'I ' , 'i",,,",:.,,i1,""^,i",",.o,diAry'dther('rd,lrl,il,l:",ifi,,lllli'"iJ'ii,,il,,li:'lliillii'i"lll;'Iilii,v((,,Lncei,i:n'|,]k,ad

lii,lill:!,l;i"il,l!'lil:i';1ill"$illili,ilili'liiLl'lllllixill;llllJllli,,'t"i' i"l"" *i",r,"1;' "'e( liJI his 'rr'r)o!c'l il iscrnrrlocrc(riL\axlt(i hc ortrl50L[n [0Nii''(chNdio,:,w'i.'-.1:lrli,ili:"llr:illlT;1,:ij,llrJjrlliiil]" ,.'lhill,iI:1:l l$ ll:'l',ill:,llll;ff?ii,ri..',,, i i*", '; r':r

1 l l l

{7. l . l l

. i

nt, l l lnn, (7- l l ) ! r \ (L ' ) iQd l i ) r lh is exdl i i . ' r l r l i \ u ir i !cf ! r t i I r | ln i 'xrnn'u


15/37

.rqBr.rLL,o.rr'(.q, s* ,xrs,lrnr.)r *rn rs.,)u.nbau,::iiil:illJill lii:.q slnr..J|rrnsui i iluo roN pasfutsno.ixni"npr u.'\ s' s'qJ siiurr.rrs.r rl'r'rdt..(r r^rtr'rpul unqs ) s.r.rissu prsrl rq ^!Iu srlorrl]nrnrloo.u'l'irorssrtttstm.Ir.soq..riqloo1rrettljLrsuDrt "rrpssr eq,{NlU uII uorssrursuP.rro .r.r'd .lqrrrns ! su snrgiti!'l rlollJ!!$rrnllr.rf o so$Jodo.i.ie?uBlr{rou 9 l.li l-l uortiis ur |.ssnisrp$p onitllsrrl qt Jo ltnnsmr ir.'l-..lcrf.qr.rolnr3qr pll? ror.ril ,{rlroli^ iqr.u!!u.rrr.p'(nLu.,'\lpsNln.pi aq ulri)ur l.qt B|loir l,a .rlt -ro {tr.olor qt 'qtBurl:r,tur uu cuinbirJ jo oif.l,{ou)i rql (u)lC',(lctunoorri^ pornsuauq trrrruJUII lqt tuoN qliuelr^!.{a'.1ll?qput ,{ruor\ba!srql o otu,rl)uc,3rlt oJpalr.uuoJaq uft .srr or9sJuru x] !lrncllrJn)qs I u'\\ou)i lFuiis r.p trruonbru.r Jr {tlrrur.{ ratir do}s'p0eq .tL|().!qsnqr jl)q rl i^r.l -.rltrr.tt rrqs atm riJn)qf iqj '{Jtrcnbe'lllr,rlrur rl l ro{ ftA\v -r {l.rtlprrr rrqr.njt.nr r!lJr {lprc.dsr'llr,$$.l:)r) rnq N|filrrql $sl,!lroull^\ trru.nbnrlNrl.L t0Fuotr^ta-JlIlLlv sr ou'I firlls eq] qilq,r rr {rLrcnbo.! qrrt {1uo nq lu()Ll rxU u pr'rrn.rr. .()Lls

0q lrr'A 0r luft?(laql rurl urxtlr?rlt ssolrr pitisuuoi sl o(l]l uorsgrusunrl r^\-.llr?tlpitln l. oqlig ir 'unr"aritr pr?otrqt !L().rr{ ,rr (.lr) qtfu$tiûrA-JltqD p.irrtdst ttn ti trortsoqtJl poumtrlo(l ltr^\srlnsrr 'rur?sru, itqlss.i ? ,{llclrrs{tidui $!Fqt rrod ,' c qll uorssrusurxtlnrrrLi-tJorlst ,{fi9soaauilu t.ulos tl'rllurQVpl]oliqr tt().'t s{'lu.t.^r^\-Jl'rqo riqttnnr loq^\ u.Io) 0.'0cl.û,rJItLI? q)r\^\ ..unJsIpu ru Frol oqt or pl)riiuuo. lrJrt 0orssrurruril) tuoF l,.rrsr,3[roq {tm ..wFdtul.qt 'isu. oqr8ur.q srru ilt.o.lf pl,ot r io i.rurrp.Llrur l nsre(ool lrtqt.riprdrlnru.r o ,{.rrrsr r 'i.urlsLl|n'C furur Jlx At.|lrdo.diqt to si;ult|r^pr: rq,l'nr3predap-,{.uinl))4I rr uur,'il rLr() q rurlsnlt o !.uplll)dllll )nslr.trr ]qr eqr o roijro.ii.t)0r$ ,(i.ridrjrdltl.t i{r] .^')^{-Jtrjqlql Jo pu. rEt irlt tx p.intd tLr)t .ql Jo .rutp.dur .{ ot tcnbr iq ts|nu ]urpid'ur nrduJ.r| rxt l' ( ! .donl ql :r jq iur()tsrrr.r l s . i | r t V i tr.) i r p:.u|ptdrru '1)ls)r )r i0rr.rr l r | ] i iual ;r^r,{- l trrq.qrtsr i {).rd'uulrr i rLr!,rqro rrrs!.rJr.rr)q.rrr)r. 'odtulur sr.ruljp.dur p.t..tJs.r ql Ilsnorîrd F ouuflr' s'j.lr V n.!ll ttliiuota,tE.{1"JlBFn'!.trLl.) tras I s1l0-nrsnLrtr. tr ' .urt i )rs\trusuf! to tnr : , ( { r!rN ,Jirot(r ( ! uorr|r{)drs,,q' t 'x) lirLlr r rL (,d rrtsrsi.r s.!rir ir | lr Fr..!uo. ,t lr.rrurils rt '!irr)t Ltr uiorl i)Ilrrsrptirrlnrtftr..d )!ol)srt !ir:r.uu.r .q i(ou rsn(r rr rirll p.sn rq ltrt:^ rr r.!rrolnulrrr. \r{ r . trrnh.q.L)r i ,pr l ro.ru o, rxr^r)srs.rt . ' fd urr l r .r t i ' rJ :1.. '1t, .)t Lro lrqrtrpr^t. \ ! ! f ,()u nrqr\}u(is-ruo)rq$Lr. i )"1i t tJ tr l t . ' ! )rrurl l r xrptrr(tr \ lr l tpr, \1fu.q!rsLr.rrrr, iqrr iqr Lrrr. , !1ol l rrr\ .) .urtsr.r qi l rq o f.rrnrrs-u. . :q rs|n!rrtr!)r\urrr Lr] r.r j l lbr! i iLrt lJr" l rr.) lL) i i )Ll ' rrrur:qJIr). i !] 'arrIU' lur r r ruo pfLJt:rt ;uqri . i t rn)r. l; rrrr: i ) i r i , r j : l$rrxJfuLrr: , \ i rd r r- .1 i : i r l f . r .erl r s.)rru, :Li ' rorsuLIr. \1r ri r .rDrbqr r(, rr i ! | ) .rdL,l j l r , .1Ltrprr rr l r i rq:11e:p:trrd

. r . . , . t - . , ,I I ] lNrs ' .-rCs.isrt tr J i}-rrr ' rLl :rp| I rC:f- i rurni). ! , !1 q;rf| r l l ' r t i t ru.m).r. i lr r ( )' \LrrctN iy jc srir. . l r r : i i : ! ,1: i ,rs lr i r t. ,r \ r .rrnb. r iat i r1)., !r ! ! i rLrxt srrL i 1i16{ ,!i:lill'l i.:Ci:-lirll{l:-.lv:.l

ll n'u, ou.'",r0'l''t ".'"nln' r rr'i'

( t l"r l

{ll!j*ifirthlir'*;in'xr

t t'::l'iii J":'l,l'*t**:**:l**,'"'li:lil' l;ii:'[]lJ:: '"-"::lill'[i"i:'i'i::li:1"i.":ill'1""rr":$ri,;i'

)rLrJrrilr r \ , r rr r ,q' : r l l I r r r r |u) ') , , \ i i r r l r i i ' l ' r r l ! iF i r l l rl:, 'l ,': l ::,'ll:'-r \ . , , r ' , . Lrh I r ' i I \J|

l i r-1,1

_l


16/37

loc nL -aTRoNii aL:l'i it i]iic^ alcli sYiiTlll',lsOp$r: l$C ahcrt" . i r .u i lcd i f l i is :$ ul l .ed i rer i fs ' th. i r fu iLrr in.dx.eol Iqudl tcr-s r. piec. oi karsmissror lilre. Jro.l circui{ed l th. t1. cnd is inilni(r, and he inehxs rrnstbiJn.d short i r .u i t nto m oter c i r .u iL. h is r l l l i is ot i ) x i thc requenc]!1 wlr lch hc i .c. oI l ;nc \ . r r ic l lv ) .1r n leJrglh. t sorre equerrcy er ' l l ls . the ires ill be ust .r liliie lorger or sll(,lcr thrn ,\/'!, so thrl rt this iiequ.D.J the tinpedancc$j l l l lo l be nl imr) The nnhel $e frolc, in l icqrercv ,wr! f rum thc or lg iot l , helow.,r siil b. rhc mp.drncc ol this piccc i lirc. .i/. dreidfofcs!'.rD o halc r pafallelrLrre.l i'nrxit. or al leastsomclhirr.shal trehrrves s(ne Sllcb a hrre s oflcn llsed orlhrs pu.posc l Ui{F. rs ln o\iiJl!(r r.lnii circLrit secFigure LL -r)o. in cther .Pplica-

if thc qrafier wave lrre is opcncircuilcd al tlre far cnd, thcn, b! a slmilarprocrss 1]1 ersoning. a \cri$ lunfd.iicuil is obhnrcd Sinrlllrlv. I sho|l-cl.cuitedhalf wa\c Ii e will behave rs N scrics ulrcd circuir. in the manncrdescfilredn the/ecednlg section.Such shof of opcn circrited lines may he enrployedat high fie"quercics in placc ol lal circLrils In Faclice. shi,ft tilcLlircct ines .irt prelered, sinceopen-cjrcuiLedincs lcnd to radiate.

Proprticsofli esoflariolls lengths JtestatinghcNsitior, wc krx)w hatapieceoitr:usmissiorrinc i/l lorg dndsho 'rrfcuited t the frr cnd (or I/2 long andopcn-circuitod l *re fur cnd) ooks ij{e anolxrncircuitandbhrlcs ra./b'likc a Ir mlleftu cdcicrLi t .I the icquccl ofoperut ions ow(1cd,he hun|rducl i l 'ccactanceofthjs uned ircuit s lowcr' |nd beshunL apacitjrecrcLnce s highct. ndLrctircul_rcntprcdorinatos, nd hcrefotchc Npodancefthecircuit spurely ndlrctiveNow,this pieceat thc ncw fleqlrencys lcss han i/4 lo g. sincc he wrvclength sno\lgreflter rrd he engthol line is aturallyunchngcd We thushave hc iDportrntpropeftyhata shorl-circuitedine esshan 14 knrg ehares t apore DductanceAnOpcn-oircuilodine lcss han I/4 long appea$as purec0pircitance.lle lariouspssihilitjes aro$lrownn Figurc7-10,which s rcrlly a tableoi various ire lengthsltnd cfininati(rrs nd hcir cqriv lont ,C clrcuits.

Sl bs Ifa load s conDcctcdo a transmissionire andma(chin8srcquired, quadct"'wave f:rnsfornd may bc uiicd l 4. is purelyrcsislivc lf the load imPcdancesconr cx, oneof thcwaysofnratchingt!) thc ine s to ttrrrc ut bc rcaclancertn nio.lucr(Jr r a catacilor,xnd hcD o lnalchwi(h I qualtcr_w e tfanslbrrner'hod_circuiLodransnissionines IIemoreoltonuscd hdn umped onrPonents^1vcryhighiiequencicsi tflrnsmissionine souscd s callod trr/, (seeFiSurL -l I ). Tlrcprccs-durcdopted is as follows:l. Calculdteoad rdnriltance.2. alalculrte tub sL'sccptmce.3. Connecl lub to lond. thc rcsulting dmilrance cing he lor.l conduchnoe'4. TrarNform onductrlcc {) csisLrtrce,nd calculatc L ol theq der wavcnrs;lfoffrer a$bclbre.


17/37

ota qrllll.r-_ s'nnnny.ard lelreat Lherequenr!earthrs,rhein;reqLren.y he nledaiQLr(nn nc o'rginal,$ie s.crnro ravea panllet.jrne rs olier usedor3l or m oiheraptlici.thcn,by I sinihr sho(-dcuiledmnncr describedn lsbe empLoyedt highft.

I

l. ft . =

I t | - ttr I. f

i , lq . l i - l l i l - l ; ! r ! l - l l l iS f ,L l l

I li ,-

{

hrcsrrc preftlred, na...

wo (now hatapieceld of .tr/z ongand pe|l.c;r,r.-/b'ke aparallsl.,rductiveeactanoele s highcr. nducliveur'l s puiely nductive.o\,/ihe wavelengths no{thus havc the nPonurl9 tpurc nduclanceloApacilanoc.hevaiousof variousine cngll$

- ll ls ,= +t.64x l0 rS X,, , r ,=--= -610l llL=c; / .=4.38xl0jS. - -L-=228r)4. l lJ t0

r __ r-.__ 200-175zt 20r t'j'15 40,000's62s1.38 rc-r 11.64 l0 "

II{;I-IRE ?-iti ?&!nnxitsi$F!im. i,\'int .dri rLh.ir ( tqrivaien(9.

Itxl,Ml,ll,ft 7'5 A 1200_Fi75)-() lodd s to be rtrdlchcdo.i l(Xlll lirc 10grvcSIVR 1 {lalcul re hc rcncl noco th!:stub nd tlE chflnclcrislic ledancc ol rh')(lurreFwrle Lrmsll) ILr, Lrolh onnccldLdneclly o hc londsOl.u 1(]N

2.3.

zi)= \/i'7; = '"50i", ntj = 2(,2rlmpodanco arifltloDalonga trdsmatrhod inc When c()lnflcr loild s conLrcctedto a tmnsDrissi( ilro, standjng 'a!cs esLLltvcn , the nrrAnirudc1 he o d inrwdunces cqual o thochruaclcri(icmpodance f thc linc ll,1 is lhc noanrlizcdordinueclarcc.hcn^, rBrtedanccs inlcriiga{(xl long hc irre, . wjll l)cn)errtrrcd.{i2Ltwnyiorn 1be oad, .trd then I !.rcrcssive{/2 tntcfvk }heo thc ino is losslessA normalizeCnpedalrce q rl ro -vrwill be mersursdi4 rway lionr(he ord(andal succ"-ssive/2 intorvrls iom thcn r) . Il :f , I Lr , thc nomrali/.\l rped'ancemcrsLrred,tr/4{hl'x on lvill be gircn b}

i:,,i1*ll!,1,:#,'r,lk 11-r4)


18/37

. l : i l : a. ! r _ l f l t l . . ia i : 'Lr i , : l t i l l , . - i f i - i : \ ' r ; - ! i i r l-i-:.

I

v-7

flculiE7'llI Slub (,irit* la l rdll fd iiiloli uridg o[ l rartsilltN !ints (l ' nrd (l ) Slrbhu :g ibr i,ox:;iil itd. Z0 s lhc th{ftri.iisiil itilled{ntt 4lihc line;Zn rcf'reicot 1l tiDtcdrrt rri$il d,ir..:rr!c..

The nri nalizeil Lord rirl'tdxlco sas in'luctivli. rr!(l !cl ftom lxl a(ion ? 14).lhc noinr.rlizodrnl).(idnccscon /4 aN!! liDrr lhc i!'r ii crrli'cirjvc it is ('hvious haL'sorllowhcrcbrl$ciif Llrese o Poirrts. l .rrlrsihl|lc lre t pufely rctinn'e '11i5point sno1 col l rsar i l l .n/8 onr (tre oa({ . l )ot ' .1 i ( r lbat l cr is lsat al l s oi l r t t r i r rxfor lncc'fhc posifloDol'tlic |rrfol! rusistj\c point is vcry diilicrrlt 10c'tlculrte witho t ch trirch as Lhr", nitl clrrrr prcdorll) t c i'rrred Mlr)] ira snis$id lir)ccaloulationste1 .rdc ea$icrby tlre sq ()1'cl'ra|1s. d rrorro i]orc so thtn t|osc iDvolvirrg incs wilh

AND T5 APPt,iCAIIONISi'lE sMl'l'l'l cl'lARl''lh. vtrfiorLsropc, ict ol tiurrlrrrlissionirrcsnrnyhc nirfcsonledmthir:nl)v n.any l,r la,genr.rrlli,eiol h rLs ]he m(x! Lr$cM cProlonhri(Dsto iho$c h t givo heirrrpci lanccrefui iorrsa)orgribs$lc$sl i rrcfof( l i l l ' ' rorr lt i ld oLrdi t ionthotnstwidelvusccl rlcuhlo. ol thir llpe is thc inith charl'

? 2.1 f'$ndafln0Dtal$oi tLr( lli$jtrh fltNiirtfh$eriFlhlN] thc |nn LllrlJ,idrn.olirgr nr, or Srriih ehl''r rLs lis nn)l'( 'o'nmoDuLnu'n, l , i t tu.r rul" , t in ' ig i r l .e l2 l lcr : r rs ist l , ( r txrotrLsoloi t ! lc$or:rLi 'ofc i |c lcs '\ ih ic} l .ue si , : r r r t ' r rge( ll r r l' - r f joLrsrr \xr f t . l lL(u.rnl i l iorrorrnecto( li ih rr r isnr tchedtransrnist ioninesnr iy hc t lu lLe{ l tndc\rhr tcd l l i r l } c is i lv ' l lc complct ' i i rc les'rvhosc . lefs ic (rnLhe uly si r ! isht inr orr he' l i ' t11,nnlr3pold 1o nr iou! d es()1ro|nlal izcd $ir l rn.o 1/ = / i /Z( i ) lon! rh. I ioe Th! i r r r ' rsl c i r les' toei thofsidcoLlhe struighl inli. snnilrrly corrrspon.l o varioLlsvrlres 01 ornrxliTed nt rertcLancelr - i.X;o A tllr1'ful look 0l thc wry in which ihc circlcs rrte$ccl shi)ss heln o he


19/37

lMp[D;\f.,]cE'i A)[,1lrlAl!ca losiiDil]ATEs

Equation7-14),t is obvioushat,Thii point{8rcl|1mponance,witliouta chaltcalculationsnineswith

nanY fhal give heThenrosltidely

morecomnrollyol atcsofcircles,d with flismatcbede completercles'alues1cilherside f .ine

FIC{J]RE7-12 Smi{hah t.

20?


20/37

:i,:! llI ,:i'irioi'ria a{ rlillvr l'lialr^.li,1i{ SYSTil'\1. r r j r r :ur!1. Ti iL! l : r . i rns ir : !1 ntrgel l lsdtr ! 'n lo i i r . . i r r l . \ . t ih ' |n in l o l i r lb lsir io ,\!oLrldh. rt|nunll tdl.rir(!;drhi . TLe |rtf oLls n clr\ $J 'o|ftli'l:l:!1 M"" s. * ,trl! . i r so lr l t i , .nr i i l r r t lsnr r l i rL. ' i t i r r r : i ter lnxd 1i . fonst ln l : l$ ' I { l corespon(r lr t i r f ic r l i ru n r . ihe hr. i \ r i th l ! ccr l r r a l i re .r r ie i o l thr 'hxf i lhr \ .Lppl iesoi i ,1\1. \s l ln.s tr the Lrr fc x i ! ' lsc 01 , ' i$ Rf I n. i . xn in\ ' ! r r l : rU ' . , """ , * iJ, , l iin: i rcrdol i l i . . r l f i . .s j r i r rhc[dof lh. \cr ;cslhtrnnFi! r : ' i | ]h. l l r \L lhe0hanli r jorf i! ir!rulr ifsisri\. llzf ror oDIl fettu'iitt il s no'nr:rlizedesirhlr , r l { ) r1,r ' f . \ ro,rds( i ihr n lnding w!!e f rLi t ) rs i fnrr r " , 11"" i , , , ' 1161 i i ' irhef I t , r r t rLr i r . i rc lc h.rs ei l (h! ! , 'noi . r Snnthchrr i l . hc SWll conesponduLpL0iL )xt bc rcrr ol l thochrrL l the .rnl 11wir ic ' i hc . l r rNn cncLc l t r j rsectslre ysi r ighi incol l 1r . j r t rL. !L Lf f igh(ol thecha .cnLc'r ' lh isSi \Rislhuscqrr l r0 lrc!rhLcoL r: i ( inr lh.r lpoinlr hc nlersccl i ( l ro he cl i 011h! 'cha ccrr t r cor |est) ln i t r

. :1*

ro lr . i t \ \ , (nr l le i l useot l i l i ( hrd )ccf locidcdls ' rys Io t rsc alucsof SWRc\i'i hc gfeillcn |dvxnlrgc of thc Snrith ch:ut rs lhat tf.rlel rkng a losslcss jne

rorcstonds 1o )x)rcrr lenlkng a co ccl ly dnrvn corshnt : iWR circlc Close xR .| l l ion oI LiLc | r in lu.es hows Lhe.hrr t ha bcen dirun lor usow'th lromal izedimfcclru(es rllf N(|nillances Tltis avo(ls lhc rted li) hrvr SnrLlhchrt(s lo l eveLyir r r ig inablel lue of l j e chrr ctcf is i ic nrpedrncc l f I p l r t icul f vr luc ol Z0 s m-ploycd wklcly or cxclusilely. il bccornesworthwhile to (mstmol I ohtrt for halt,,r irulxr vrlLrcol Z0 Fof c)ianlFlc. hc Ccneral Rrdio O)rrlPiLn) rd(es I 50-1) h{1l in nsr wirh i ls Lr r jnr isr i iorrquipnrr t l l 1mr r ls( ' bo uscd or : rn) ot l lcr50-0si luxt ior)s)d rvoi . ls hc nccd oi no ]r r l l iat i (nr ' )Als( \ r r (ne hr lLhc har lcov0rsdistrnce of ('oly rt hrllwrl\]clcnglh, liince crnnliti( s repcrt cxlclly cvcry half"w c'lengthon k)sslcs!i re. th0 inpedanoe t 17.716 \ 0wr l ] l ior [ t l l0 d on I l in0 soircily tbc silnrcas thc inrpechrcc0:1f,,\ iro.r thrl loid rrrd oan be fcnd ioro the

Bca inS tlrete two poinl$ n mir)d, $'e sec hLr( rrpeaarr(jcs ocountcrcd l suc'ue$sivcpoinrs rlong A k)srless iic nrry olLsilybe li)und loln t[c chrrt -fhc] lic atcofieslxrrdi A *ro{essivc Points long Lho orerl l,'fl]f, (this $ut i$ rcPcrtcd oorr r ;$ izo l re lret hAlsrrch ci fc lc mustbcdrnwnh). Lrc r r ierl Lhechr foreichprcblcnr. ts oFlloscdk) tLrc ruLrret)usirclcs nludf Prcscnl0n lho Snrithoharl)con'srnut S\\/R cifckr on thc ch$1. Dislnnoc l(ntg a llno is rtprtscntod by 0mgula0dis-rirncerrornd lhc chrn ar)d rray bc fcad fnnn thc cifcunlc$ncc ol lhc cha$ as aJiactior ol $avclongrh Cl)nsider poinl somc dislrrcc lrway rurn s(nr)e 0' lIhdorcnuinc hc iine impedllrceaL0.(171)\ 0wry lion lhis nclv l('rnl, il quicldy bccoflescl i l lcr t thr t thcru fc two Points t h isdistrnce, ncclosef oLhc oad d one adhet, iwtyhiJt \ t i t . fh?i t t t t t \ t tt r&utth( t \ t t r r rPaint ! t f i l / to7r(71.!arr . ' lhis isevident i iooe ol thesl:Nnrrs just hrlf'eos to bc volrrge nodc The olhor foin!. beirg 2x0.07S 0.15! l xw y lR'r i the { i |s l , . rnn{n possibly c .mothcfohrge nodc Thcsrrre Jeri\(nrilg pplies in dl olher silrLlli( s. The dircclion ol nr(^'orDenl rotrrdaconsL.rnt WR circlc is rlso ol iLrporLtrncelhe Snlith ch n hr\ been shrrdrldizcd 0rhurnrole'nonl r$rry lrunr the l,)lil. i c . towrd lhc gorerakn, correspor'lsn) clolkwise or)tion of ihc ch.]|l. Movcmelt l(Nv.Lfdhc lord cotrcspondso co ntcrclock$rsenrolionrthis is alw:rysnr,lrkcdon lbc rinr of corrrrtercialSrni(hcna s NItd sslrorvnf i , -( ' ' .


21/37

ri i rr(ir .(n rrtr[etlj0lNee|rhr:l!,;1) .orerFft LLIi hi\ rpllies oflr l": rustbedr ir \ it ,l bcio! tirt chLrLriolririized nsillfi&

5,t ! rnon (l l ) f l r ls.:'ri'{ .onestrl]nililrrtoi r t . s.( ls he nlri r l i r rh|s qurt torr i l l l rL .nrcf corresDrdrris: \r!!:r\ 0l SWlt tJ l

I'l(nrg losriessiDci i r . lc. Close irui "

i l ! " f r t , , , t : i t rL l i : l i i ts ?{5

Jrq i t . lor ' rLi i i j : r i . r' I i r i t r i r r ; r :i , r ,n, . r r r : . i .Lr i t i i i r d i l i : r r r : r .u: t : r :1:r r i rgtLhi !r ; r r l . .c i r t,- , r . r , i r l : r i r ! r r i ' r l r r i : i r . , r- r \ : i . , i r r , r i r i : r r i :L : j . r i . l l -izedrr :pr l" , . , ' . . =1: i . . !J i i . ] , r i r i i : t , r i t , r ! : r . i r r l . f . lh i r l ; r f i re. : j i t r !I . . , , js i I t , ; r r r , i , . . r ' r | r , i : . t f l l t \Jr - : 4. : . . i i , i i . l i r i r . i l r . r : . , . : isr i . - r r r i . ! , r , . r . ri : i i i.o.1! .L l l f l ,1r ' : I i r . i . i r r ' : ,1 ] l j . r r ; . i i , ra, l ,c: . i l1 i r . t i r r : :1r i t l | . i r t f i , ! i : r i ! t : r fI 6 Tlr . r | r t t r1- i r , i . r , i ! ! , ,1 l rert i r r i ] , , i r i , . ! 13 r l t [ f i i , ! ]n i i : d, : r r ! i ! , t r i th.: , ' , . i . : ' . ' r ' . i l, . i 1. . . , , i " . . :

A.pptr i . : l1 i r f t$- i r . r , i l ( , r \ in! i tJor i l r .t ) r r1tr .Jxi I f inr t rLir t rtuar t t i .11roi l rL) ii ; , i jnr t ih

1. Adnr ir i rnce r l ( ! l l i i (ns. Tl | is rnr t i { r ; . r is b,r .d rn lhe icr rhr t t rc r r t . r tx. . r :r rdasu: i r i l t r f . { ju i l l r ( } hr rxlmir l | l f . r ( l , j i I xf -dg r. ! . i1- t . rpr l lxrd ; f o irhc slnre: jWR.i ic le Thi ! ix;hovr l j l f , i ! ( r fc 7 t : lhc r r r t r . an. . - rr ! isj - j l , rnr l I i r . ' ! s i rDplc ,r tctrht tonlo\ i l ' l t r r t t l t rc Nf lx jnnccis 0 5 +J0 5.:rs t wls r P. 1t'dr tire roucsoordir!r rdmift$rc. is jn.teid I /1. r| reril {,1{ar ?. i r .e rhf 1(r i i r i \ rr . c i r f t . , t t | , . j j ] l r i t \ .Lr i r j r i ) r_sf | I l 'n hr t f h i , , . i . jn! , r labng tt( i"rc. r qlaricr !q!c errg{|, orcrDtxrds kr a $cmjoirclO 1 s j,.t necf$slry to lnc $rru ,1/4 lrcurd tllo cide fro|r ,.', hul norcll, i0 p(3iixrt i[e ljn.thrc gh ,! d tire 0 rief 01r|c chLrrtntil it irrterscdr be drrwr cjrelc ,i {? on tl)eother side (,/\iihoLrirl:urh an;rtpticxrkn) r nor vcry ir fo{ant i ir$otf, t d r f,eenfoundol-gre vLriuc Jr ilirrizijrg srullrrtNwilh thech rt lllld wjth rhe il|)lhod j.convc(inlr il lt)r,rslr lr an r{lnrirrl1nt |c)r.rit. hlri trej g cr;$e i l fo, 0tul rllculr-ClJcul,rlioIol Lho rihdlrnxj or trnillrnoe ( anl poinl, oD |n) Lrarirnrisriioirc,wi th Jny kr i rd rn( l sr t r l | l l r eo$s rk' t r la l ior j i t l )oSWk on ( lrc i0e. l .h isf i ) bcdone i) r lorslcs!or lossy ines, )ut is In! .h orsi l ) r i ) I io j rs lc$ inor .C,rlcuLrtio,i ,l lh r l,)|Ath oi n dxnlj irc ii,:j(l ie.. r)f lralsmissioIr irc io iri\,c-J. , r r i .J r . rn. , f i r iv. i i ' i . t , ' . r ' rc e{ ! . , r , . ( . I r , l . , . re ) n: | l i r f , .r d,c t . r1 l0. /0onr lc lc l l - ] l ,xrLls i (h; i l l io i thechrf t , r t l r . i r r , rvoJjngrow!f t t i l rcgorerr11)u[ t i ]thc conlrd yalueor rorciiutco s relr(hcd. |le.nAit!elv. it I s scupti,,"",,t tuun"nv.r lues Rxtujrcd.xn ,r r hc r ighl ' t land In ol i j r ( . fh d 1 hepoin( . l , $rd wcfttorvitldttre tIL:rcirt(i rL!air. 'lhis crlcn]rtim is riw,r]s ped.finrc(l n N(,i,Ir.c1i(Jnwith sh( ' ,1{ i ! r i r i r ,a llutrs.

l l l l t l , ' - : . . \ . ' . r , , . . r . . . . . . , . l .n, | .1. , , . . . , , , r1^,rr.( . ,. ,r . . , . t ,1. ,1, . ( . , . . r , . . i , . , . r I , i , r I n, , i . . I u.dn: . , .1 . . . - . .r ' |_ . I1. , t i { . t . i . , , . , , , , , , , ' , .1 . . . rr i . ran,n,: , rnru.1" . . . . r . , , r . . , t . . . ) ^U^i . \ . 1,r i tu .1, , . t t . . , ,Mjt .

l1h omulifdSrlri{h hrL|ts lr o\'e|!vrhrcol Zo som

I ohl loLdda 50-ll obrLri(n ruy o(her llriri lLlccha covellinr\erY boli{llvc.

fr('rn r k) d on { lift itd crr) bc rerrd tonr ht

c ((nlntorc(nL {0'LLrehrrt. Thc) lis o!,rrd is Le])Laledoof tll( cha( Lof rcll

on tho snrith oharl) oll'lccl rY (nnguld) itol ll c charlus'rl ]on s(nrroond lLopoinl. i( quicklYbocomcs

lhc lord ur)d rc fllfl]t'rl . l his sevidonl

flhcf Point, bcLng"oliage ode llllol rn.\'e lcfl arcum'

hr \ b!,enslNdddirodso(incsPnds t0 clocilo $urlcftlock{ sru,",4,.''**''"


22/37

III)\ir.l

s i i t , ! . i r l r r l I , ? . . , . i , l , : r t r isru\ i , r \ . r 'in l i ' ih ' i ( 'd

' ' ' 'r : , , . r11,1,' i : i ' t ' t r " ' "' . " t t " Lu ' lr 'J iL I ir

L ' rLL L

' _ /r lo( l I lo ' i ' i r !l ' , - in) . . l0 ',,,t"'' U tt't '\ _ ll l

ll / ')-00= h] 'l '" i

, : . i l : l " t: : l , , : , , ; ,1" ' , ' :' ; : ;' ; f , : : . r l' t i ' '

:,1' ' " 'ii : ' '' '" '1"""t ' " ' t t

l rL rr ! r " _

ifllr{tFiM: (rq iiigriri/rXiirr |'liti{!rinfr'i: !T11i"r'n r:i[('riitf:f

1;l'ill'lr$:i:l";,-':'' ": "]:::':"":::::' . , ; r ; l : ' : ' ' l l ' ) "1. , , i i r " j i i; ;" ' ;" ' , ' ' ' ' "" " ' ' ' " ' 'st ! l {J l l ( })r ' ' '- r l ' r i \ i l t l ' i l l ) r l t=, , , . , , , , , . : I ] ; . t . l , l . ; : l ll ; . ' : ;"1, ' ' ' l ' 'i ' . , ,1r ' :: i l " . ; ; " , , i r : ;11: ; l l , j , ' ' l t t ' t ' ' t l ' 'uu 'l :",,,rr:. .,: ' "

:;' . ,. ' ",.,;: , i ' :,, ' '1.l

, i r . : , : . , , i , . ' j , , , . "- . , ,


23/37

I

:mAl,{st{Islol.lLlNEs207

with tlc SmithcnarLscase\'aProceduBoth methods I

riscornectedoa

oYbe lr-,&r,Smith hirt solutionfExnmple '7' mntchirg ith aq srter'w{w rans'FICURE7"T3

lrl 39.8 ) is the csisrancehlch he i4li,Ansibnmrwill h:rvc o rnatcho le 75-Oiire. nid frcm this )oinLhc procedures a$ n ExunPl -4. Thereiorczi = \/Z,A = \f1'lx3t1 = sA.sr

-,i11',"Jf,'i:ixf;liffil;Tl"ll;'"'1.'il;H'ilf;ff'jilf l':",tilH:mswds rt drsiJ;cc= 0.080,1 nd Zi = 6s6 O.


24/37

,?$8 EIECTRCNIC COif l,ll]N icATiril"i SYSTEI\4s

I.ICURU ?'[.4 Slunr onuededto lt'{ited irassmi{llon Iirt i.r,Mfttchingoflond [c line with a sho -ciru:Niiferltub A "l ' is apieceofh"nsmis'l' ;sion ine wbich s nonnallyshorGcircuitedL he ar encl t mayvervoccasronauy . iopen'circuitcdt he distanl nd,bul eitherwny ls inrpcdaDces a ptlreLeactonceo i 'b;quitc plciso, ucha stubhr an rput adr rttance hjch s ap rcsusceptance,andit;r iis sedLo uncout thesuscePtanccomponent l the ire admitt0ncct some clmd Ipoint.Notc thal shon-circuitedtubs ]rc prcferrcd ecause pen-circuitcdieccsf Itraosmissionine lcnd to rrdiate ion tile opcnend.As shown n Figurc7_14,a slub s mrdeof tlc same ansnission ineas he 'i ione10which t is oonnected t thushas an udlantage vcr tbequarter_waver0ns' i: llbrmer,whichmustbc constructedo suit heoccrsionFurLhefirorc,hestubmaibe /i !made igidandadjustabc This s ofptidioularuse t thchigheriequencie$nd' ow! :ltbestub o be usod or a v$icty of loads. lnd/orovera flrngcof tiequcncics ]iir ' ' iM t!:king Proce urc ilill" Normalizc he load wilh resPect 0 the lire. and Pl(x the Pointon thecllJrt l2, Dmw I chcle hrough hispoint,ond ravelarourd t tluougha disttnce l l/4 |(i.e., strnighl hrough) o find lhc loadadnriltanceSince hc stub s placedn Ipotuif"t lif, tt '""in fi,te, t is dlwtyli ?cesslryo trork wilhadnittan(es hen'i"naking slub&lcttlati,h. , 'r l3. Stqftin| tatn thit |lc'.'pai t (ttowusi,,8he Smith hfft as dn tlmhtanclrhart,)'lind $; loint ncaresto the loadal which thc nonndizcdadmittancc I i: lr '' l 'h i t ipoi ti r t tu i , t tz ts tc tiono! thcdr, \1 'n&( l t \a ' i , l r ,c' '=I ' i f t l t ,w lchrsthe' I

only circlc thlough he cent;f of ihc irhafi 'fhit is the Poi t at which.a$ub ldesigncdo tLrne uL hc:l:J, colnporjl)ltwill bc placeclRc'idol l lhcdistancctravctcO rounOhe,-ircurricrcnce f the chrrti dris s the diskncc1() hcslub4. To fird Lheengthof the shorFcircuitedtub'stlrt f(nn drepoinldJ @on$eghGhand ln ol |he chari,sinoc la! is lhe adnrjllancc f a shol1 ircuiL5. Tiavclingcl.rckwisc rornd hecircumturcnce)1'thchart, i[d thepoinl't l vlrlcntbesusc+hDceuncsour he !, susccptm.e f thc ine at thepoint:rlwhichneslxtr s lo bc cornectcd.Fol e;rmde il thc liue admitianccs I +j0 43' the


25/37

l riANSrrililS tli.l LIl.ItrS2{}!

roquirccl usceptrncos -/0.43. l:nlurc thal lhe roaljet polltrity ol suscefl{ncch.tsbccll obtained: his ir alv!.ryrDllrkcd on thc ch r on thc lcll.hrnd rinr.

6- Read off the dishrce in wnvelcngths ion lhc slarling poinr .{,J o lo (he newpoini, (o.9.. b = 0.41 as abo!e). This is Lbe eqrired lengfi ol the stuh.

flXAMPn:ni7-{i (Refer o iigure7-15 A series a-conrbi"atio|r,av i g 'r i pcd-lncc ZL = (450 j600) O Nr 0 MHz. is .ornecbd to u 300-l) irc. CrluulateheposiiioDrnd e'rgth f a shorcclnuitcd tlb dcsigncdo nnich lhisJoado drc ine.

,1ibc

Pieces finc as iean$-

$e stubmaybeallows

the ch$ta dictancc f i/4s Pldcednudntlllancet hen

a cc chort),s I IJDwhich s ie,rt which ! stubof f the distance0 lrc stub6i F on txe

L*lj!"-;:#;---t---''\wl.lOt]RIt 7J5 Smithchluflolution ofEx*mplc ?-E.matchirl8 ith ! $tuort"ciraoitodtub,

thepoinlal whichpointat which he..1 +i0 43, he-


26/37

: : i l

!r i i r r 1! i i ! \ ( i l I ! ) iLLl l r rL. ncl ! r* |LD!q.. r\l . : r - : r . i j ! . /6 ' l l l r r l l r ( l l5 l lalrtl. Pn)Ll.d rrd hs S\irl = 'i li l-")lirl oLr!'1 1' 'i: , , , = ,1. : , I / { l l l , l lo in t i te i^rr' :h i . . r ! shotrn , , r i l r rc I i1 is , \ r ' : $r l i t ' l 's iLL.r ( r- i . I ! ! r : tsr | , , id i 01 ' - I 1.r i , is, l ' i l l1 i ,n ir nNnt l 1 i . . , (hcci l , r i r r l i ! r ! i t ( i /? lhc d islrrLr. l Lh Jrolf l od u lr l ( [d 0L. -{ . l r louNl xlot ! l l r . i i rn. f l |c rnrr l rnr l . l f r r ! i - ' ) l- r i \Lrn.e 1r, rub {r l l ! l i l ! f l = i ) I i { r , \

'fh.uii)re lnc {rb wili l{ llrr.d 0 L-1{ foi)i llr'1.{i rttl vili [x!' lo lute or l, : I I 7: thus i i . s lub DNsl htr ! . i $ tr .cP r.0.1 l ._/, { , 5, in i !a. Srf . r i rg no! '. / '' , xnd lcl i r l f lod 's ' i r . rrutrdthol iu io i thcchxr( 'on.,.crcl,es (hc lr.iot il . I ! ?: ii ls lr.rl'crl t .n LIF cl[rL ol Fitun:] 15 ii'tf' lhcchxrr. tlc dishn.e of 11$ foin( lionr lhc sho I cn.uil rddnLrrcc Ponit rs\ b.r .L .. . r . ' ( . 0r ' \

Efllrclr oX rcqua 1{'} l'or:$rli{'n A slub \\'ill rDltclr lond 10x rrrLn! isibn linconlvatthe freq!.:ncy at uhich 11w s dcsign!:d o do st) .irrd his aPlllicseqruliv ro r qnarler-\,\'nvc irnslo n(x lllhc lorrl in)podrnc(vnrics r'ilir ictlLrerrcv,ltis is r'ln'ious How-tr$r . i l r r ry l )e rorLdi lvlx)Nn lhr l iLnt( ' - r no lon!cr r N rct nr l lc l r r l l renc\rlftiqrfDfr e\,,rn i' lhtr lord irrrf rnrc rs urchlri.I0dConrti(icr hc ro$ulL i Iix.rn!J)lc-lj. in dhich it wrrs jrlcLrlIlod ilal rlrc oxdstui) eFr t ioushouklbc0. 3 , \ ' A l lhostr [d ] i (x l t rencyl l0 Mi lzt i lc i lnvelenl t l l is30 nr. so thrl thc RIb slrouldbc 3.9 nr n1i'N)'fonr llte lortl l alrequorcl ol ll j\4Hz snow (x)rsidcrod.lswavelengthi$25ln.ClearLy."r iqrrsl l rbrsnot013/rwayl iomllre loril 11 hi! ncw licqLrerlcy rror s itr )eLrFLlL.0115 l thc trcw wavclcn!fi Obvi-o0rly lhc stuh hns noitl$t lhe ixnrccl posilion0Ln hc )rrcct oDi:t)r t Lrny iequcncyorhof hdn ho onc Ior which Lwa$dc$i l l rcd A Dr is r l ichwi l l cxir iL tLroughl ustbe s,r id hxl i l thcf ruqucncy hn ge ls rot -qrci( .r rei lhcf ( lhe or isr i ratchIr o i len rr ic l r$ hal iotrd s nlxl rhcd t) a i iue r) tonc iequonry,Lruthc setLrPll]l|lri r so fu rula(ivcly los$lcsr und cllicinrl ()\'cr a ccfi in brrdwidll fhus' sonrcpr1)c,:dufe usl bo deviscd ior ualcrrlrliD! lhc S\rrR oD a Lmlrslnis$ionirrc ltLa fr_qucn(y /" il llrc i){d hts bccn nlrlchod corecil} L(i dre linc t I li0qrencv / Aproceriulc will iow bc givcn lor lirt |nd k'ad nrllchd iJ\ nro.Ln! f ! !lir(-circLrited!ull thc qur[cr-wr!c {r.rnslinrr)cr ilurlion is rrl lt)i]oLLs

SIXA{pr-ni 7-9 l]ictcr l! FiI,n: 7 l(.) CxlculaLcre iWR al I2 Mllz ftt lhc rcb_ldn ol Extrll. 7 ill;ox lTlLrNlriJ. bc purPo\.ol rhc ploe.(hrc. rl is rs{rricd lhrl l!e c^l(rLlrLiorr!('lving ih 'ndslrii rnd lc glbol a slLrb ash.cr.,rde rt r li.qrrcnur ', rnd ir is no$ riererfuryio cdorlarc hc S\VRot rhcn n,Int rl/" l,{.il.r elcning sPcjl-ici]lv o rliccrrntl . will bc slri,wn


27/37

poinrs

Mllz n LhcProb-

rtolvirg tlFd ir isnos'rrecessirv1o hcexrrt

oc only fl Iequxll) to i qultretis obvl{)us fto$'_

ralci it thc ncwhai lhe lolLC'

thovrrvdongtnrsl l2 MHz i$0 13 owoY roN

w w v.le !ih. obvit l|nY flcqLrencYllilir'lrgb ( musl

ut lho $ctLrPThu$. sorrrcinc al a,fre-

c ! , ftcquency./ Ac'1 r;ln)rl-circuLpo

t" . , : ."-:;".S-!c4J#--{-i:t:l_:=i:;

'il:rl,llL1i::.1!:ll rt i i-ri.'jji ?l l

-i'

ll drk! aregivei rs ro how i,c o.d hpe.drDcc die! with frequoDcy,alcul!ftlold inrFdlncc ibr lho rcw lrcqucrc). A scics ]?Ccombnulion tving& =45al_j600 nr l0 MlIz wi l l hrvc Zt . - 450 . i600x '%r=:150 _j500 utl2 t !4 l l / .1No nal izc his nnpcd.ocehcrezr-(450 1500)/300 1.5-ll.6? Nole imr l tlrc oad rnlcdrrcc k knowD o bc.(tr,srMt. his lcp n,rl! Lrconrirred, ir.. il wouklhavcbccDpcdbnlcd n thc inilirl sLut, alculali,r'.I'lol Lhis)oinlP' on thccbful,dmw hc usual ircle hnx,gh i, and1i l O', rhcnonn.rlizedoad ftlnrjtrlncc bcrc e' is 0.]0+10.331 ftonr the Smithchrtt.

FI(;UIqIJ7-!6 Sffith clulilsohr0iori fllxamplc 7-9,cliedr ol lncq clrrl fh{xrc "r!.r stuh

2.i,:N.

i


28/37

2!2 Er ariioNlal .

4.

5.

Anothcfcx plc s nowgivcn.cx)vcri this yl)eof ffoccdurerom he brybeginningbr r situiltionn whicb the k)xd nrpedrncoenMins onslanl

IJXAMI'LE 7-10 (Rctb 1o igurc 7-l?) tD Culc0lnlc he osiLionnd ongth i a$nxt-chluitedsllb dcsj$red c n)rLuh 20U0 toad(o a hrrsmj$rion ine wborcchaLnctclisLic$pcd{ce is 300O (r) Cdcul e rlrcSwll on thcnrin ljneNhen hefrcqucncys inuicrsed y l0 pcllctt. xssu ring rhardre o d And bc imped0nces

SOI-UTrcN. .4: - " r , - . l ' lut l j lgP.r lLcihnLgi\c rr ' iwq- l : i r r f lc 0 !hr_r in. . .or 1. , ' .1 ' f l " . r ! .1.I,oirt of irtcrricclil)n ith r - I circld,4- is fknls.l Dist cc iofl l, d adllnl'tdncc. . j r , s i i iurdcqual o 0 l l , l i lh is is dr . d is l t t r rcco i rcstubAI n, r\,," = I l0 4li hetr.c s,,b-.l0.4l PhtLiD!S andmtasuLinghedts_l- |c. orJ t r . { . . . . r t Bi \c. ruh c1-t1. . . . ' ) l l . .(1,)/ " = l l0 per lo;r l - l ' , io lh . \ ' = i / l l . Thus. hedistrncco stub 0 l l xt . t = 0.121 \ ' , .Dd rh lengLhf st t r lJs 0. : i l l x l . l = 0 342I ' , .Sld.tingiolr Ornd soirigdtound hcdftwn circlc hurSl a dis[ncc(f 0 l2l'\'yicllls hc ]rointn', rlre lislr;cc to lirc sub rttrchmerlLroinl t lhcncw liq'rcncy

t-ril\4r,iiilll,-lAllotJ sYs l iil.'1:;

Crlculxlc lh r dinrncc 10 lrt stub.t the nc$ iequcncy iIr tcms ofLhc ne\! wa!e-.r ' i . . l l , , . . rhr l 'or. ' i . r ,dr 11 r : 1 i . .11, ' ; . i ' rcJrr 'n. ! r l rhb. .0. 30x r. / , , -0.1:6' .1tinn thc load dniilLrn.epointq' . krvel doc\wise aouid ihe constant \lR. i rc lc lh,otrghthcdinanccjusrcr lculatddlh.rc0.56,{ ' ] rn(l rerdotTdreno.nired.( rni t r .nccr t th isPoinlR' lh.h ' r1"" '2. t+JL 7l Tl is s hc'dDi l la ice trhc c* fiequenct, cenby lhc inrh liic whcn dninrg ro$tun he loadat4' ,r|i.b is Lhe ointaLwhidr thc slrh wts plxccd l llr. onpnrLlcqucu.vCllcuuLe lrc lcngrhof Lhc sldb ii leldrs ol rhe ncw $rvelcDglh ]engtlr0.085 Lno- 0.102 lStxrtingNr_r./e N nsual, his tim. linl lhc $rscellrnccof tlro Lcccof sh)n-circuilcdinc wl,osc errgl| asctric(lilc.l D l( neccdirqsleP llcrc the cnglhis 0 L0: .\'. ar{l rliB rlrc srscctrr,)c! iorn d,c cbrrt 01 i8orc 7'16 k (atSJThe siLrxdo. t Lhcnew ilqdctrcl is thNtwe hnlc lwo adnrittrnceslacednr: . 1. . : r " l ' . . , . ' . , r r 'c \ ' 1, , { r r r l ' l r , , l , rc.) l l ' i \ .h._ ' i (J l i li r r . r "r . : r 'h.Jrv, l . . L, ' . ,1 ' . r r hL. .wn.qrc,Lj ' r ' l Jmr lc l , i 'nroL,.Ld l l " I ; l r rnac. ' ' , I ' : l ' r 'c ". r "^ or " d | |cr ' : JJrr r iLt .ur ic- lth i i to iDib] rddi tun.ul . rc rL, ,= \ L"b r , , , ' - . i 1 34+ 2 l I t 1 = 2 l +lloL rle tolx LdNiLtrnccr theclli[1(|oiDl T oir iglrc 7 16),draw hc constdlSWRc;clc thRrrglrt, rud rerd ofi thcswR'l his s thcstnn(l g-wrve utioonrhcmairr inear./i' br h line odd-slrrtrysle tlrt wrs natcbcd11l' lHere heSWli is 2.2. Ir DriBhL0 Dotedhat ltis s loworlhrn hcunnrrlcbedWRot3 9AllhoughlrnisnrLch ndolhtedly xists I l2 MHz. $olncmprovcNenLas cs'1c,tctcd thnLghnl{chhg rl 10 Mttz. Th s is I rulc, rulhs t[0n$ crccptjoi' frhf ru ' l ,c: . r . rcrc.. rc ' . , { , ' l ' l ) . lu.

- :. t' i


29/37

riarl o11Lhenomal-rs & adnnta& atthc load$ li ,=tl r liccc of shon_(oP [1le& he englhI 16 s (aL!' )

I 5 orruic i ( rdmL-ion loird dnnl-

1r t l rc tLoI J fd N truLlLChc orr

ce r0 sllb is ll lL xt i ' t ' rL r l ! r ' ! - r ^

n rl t kw lrRl ' t r r 'c)

n IlL JlLc\ dJBlurhal i, n h x rJt( l r isnLr i{ l r . o lx l rdmlun al idra{ thcNnrilanl

nJ ngr\r \urr l t r runl ' lHctc l tdr.ri(hcd\11(of 9i pnrlcrtcnl ar i cc'ldraLr0 cxcep'innr

PrccedureLomhcvstl

cnSlh' r Ilncwnuscthenuir Llilc l)c uend liLtcmpsdtrnccs

'fliAil illlsii l(li.l Lii:.Ijis 2l:!

. i . .===

: .- ' : i - . .li,r--#- {i-.

i[{;q]fif,1 7-17 Snritfi cfirrl {,luri{xr ot ilxdmlrlo 7-10, stul, mllchirig riith frcqut'cr

| i r r lhechrr t , hf rLlni l l r r fc r ro(nr f wrrd thc ord x( hrr ruinl r .c!d ol l r rr ' , " = 0.9! j0.19.sirni I y, ( r r l i igar- , lFoidrr i r of thcchlr . rnd uv,r l ingdnnd LLu,ugh di(ro.. ol 0.312 r' Sivcs hcpo ol !'. lJcrcLhc (ub dDilt^icc lrtLhcnelv fitqudr.y is iotrnd. iom lhc chra 01 iguLc 7 17, 10 bc I' r !: r/a),0:'thc loLxldtriiuh.c al drc stub tt^.hmcnlpoidl xr drc ncw licqucncys l:r"L,,L l',,. : +10.65+ 0 9,1 j(l.l{) - {l q4 I j0 26. Plotting his on thc snnLrrchan. . . . . LhcDiDt ol Figurt -17, r id s l i rg ing m xr 01 . i rc lc lhrn, l l i l i r r rSwlt l . :1. his s rhcdcsi 'cd str l l .


30/37

21,:nELE{ITRONICCOt'iMUNiCiTiON SYS'l'Et45

7-3 TRANSMISSToN-LTNECoMpoNENTS

7"3.1The

A r,, ,bJr ' l . . , . r .o, . . . rcre. l \ r rn r .u i- f . r ,rrr , l rn. . .1 i re. . , i to, .n. ,1,r . , .1. , e. , . . , ,u.un F,1, , , . , , .k , , . i " ,o in.omc.t. Onc rcrl obvioLrs tquirrlnent is loi somc sort oJ .rdjustrblesrub,qhichcouldcoP. vi th rcqu.nc!or lord mpedrnce.hrng.s. indsLl l l l !e rdequrc narching. Anothef s;ruatlon lien cncountered: firc ir which iL s (lsifedo sanryle nt! tbeu$Jr, Jr fer -t* r l ) t tu r . ' . . , .nIn: . Iv rr ' . , .1. . t ,-r ' . , 'e e\ i ' . A) . ,n. I o lr .n | l : , | . | , ( , . h: . ' . l . : lJr 'J r i 'e ,r r orc. , , r , r . . rnLrnbalancedne. Fnr,rlly. t would be lcry hrdy indeed o havea trallsrrissionine. ormeasureme purposes.on which thc vof!)us qLranrjriesrch as irodcs,antinodes.rSWlt could bc crsurcd at any point. Al i suc| ventuatjtics rc colcfcd by stecirlcorntoncr{s, or "hardwxre, which will no\l be discLrsscd

DoubleSt trIi r lransmissionine nrtchir|g cvice s to bc rLscluln { raDge f diftercnr raLobinSsilulrtions,Lnrurl hlvc as nrrny v.rfi ble paramcrofs.t (lqrec! L,J.liudon,$ h;\ tJnJ i! kL etDl lem inc. rh. fa l rern l ) . , . .$. ,J .J . (e,r f l iee,^rn ' t t rJS$.Rrr .t thcpositjon f the -irstmaximum). o must hestubnutcher.A siDglc rubof adiustablcpo"ir ion n.l lcnr ' r .r . l l .1. ' hL1,,. \ .-) $erl rr t(q.rcnrre.ci 'w r1, i ,r . , .o,. . . ! .rarg.. Ghis i|equcncy 0uge$ notrigjdly delincd,bur r irj conlmoniy ndcNloodooccupy hc$pectrunr|('n 1 o 100GHz. t is alsoci,\lledbrcadlyJ\eGttij ?tff n!e,srncche wo extremefequcnciesorrcslondc wavelengthsl 30and .3cm, respec-ti\,ely.)Al suchhigh requctcies o xiAl inosarc er !loyed nsrcrd'oipar0llel-wirlines,anddilliculticswith screencdlotsafesuch hntsrubs l rdjustubleosiiion !eTo prcvkle hesecond egrce f licodonr, second rub l,adjrsr.rblcositionis added o thc i rsrone.Thir rcsultsn r l ledoublc ub of l igLrre -18 nd s acomDl(nrlysed utchcf br 0oAXirlmicrowrvc ines.The wo stLtbsrc hccd0.375apart i conespondin{o thc cDnterieqlrcncyof the reqlriredangc), incc hatap,pcr||so be heoplimun sep ution.Twovariables reprovidcd, ndvcrygoodmatch- .ing is possible.Not all loadscoube lnltrched nder all conditions, inoehaving,lsccondvariable tub s nor quiren$ good s br,r'ing stubol ad.lusr,lbleosirio,r.Such0 nratchers no|lnally onnectedetwcenhc oad nd thenuin transnis-sion ine to en$urohosln)ftestossiblcengthol misrnarchcdiue. l nillurrll) hAshe

l{GtJltO 7.18 Dotrble{itrb Dalrhd-


31/37


32/37


33/37

lll.r: r;l:l i,ll:il|i i 'r l.i.:lE1 :1?

t:lcl illl 7'llr

As !nrr l r , r . lurncf wrr !c l , r l rh slocrc ' l rhrcl r ,1\rn( lhc oLr( t ! on( l ' rc lor li recorxir l l i rcrr ( l i j . ( ! r r l rd.r l i i ) i t r l - ! At l l r |o i r r l r ' . lheret i r r ' i r ' l lwr l r 'orr r ' flhc rnt)cr l ce . . r j ' re ' l r . : i ( ! )hoLr&)1\r rr r l r ihr I rn ' i r i i " ior i l i l re brnuT'1 i l r r s i ( !cr ihe orL$ i) l . l t f r l i ol ( l |e ,ro i l l l inc is rnJir r l t ( i .h! cLr1f l i )nr luclof f lh!courul l inc r l , i i (ngcr l i rs 7( l , ' Lnr ldance1{, ioLrJ( i L \ . Oro ol nrc i ics ofrhcbr lancei l i0c r ,rybc | , ,nn, jcni ro i l $ i lhorL l ; r r o l bubg shoftr i rcui tcd r)g]1 'urd' jhc othcrbr l rxfc. l ' i i11 i : rconnculedJ lh. i fn ' I confrrc l cf thc(r)uj t i r l inc An!bal . rnccr{oar l . r r r :hs t |c sir rLpl l r l )o l f ar lennl thown in Figufc '720, l r r rJ nou bo

7-3,4 heSlottcdX,i,ieIt c n rc pprc{riatedh.r( piece l n-xnsnriirsionrrc, I coustfuftcdhLrlhc olt goorcul . rentt long l I n bc f l iasured ol l l i r i t rously, i , j I i ls lcr l$ i r .woLl l lbo {) f rcr l r rsc na lot oi nrci)srr|trrlrcrrtilulLiorrs.At r.latively lo\! liL{rL$roics, slr} uP lo al'orr( 100MHz, r t r i r o l ' r . r ra l ld-wircingi r r r r ] bc used.hrvir lg r r lvol ing det0clof' )orr ctcdhctwccn hcnr lhl f r i l . |cr (ns cLr t i i l ! n( , !1 'b lor id hrs l tc i l i l ics 1brdcl i11] in inl h!)distaLrcci ' thep )ho ionrcirhor lx l o l tho hnc. I l r r ' i (y ' rd / l r r l ' s thenn c give0 olhis piece fequi f r lkr , r . r l ! ,so high- l f l r {uono),l iu i r l lenl i t lho ' turr?// / / r ' . ls r lx)wr li r Lr ig!rc -21.

The$loirc( i nc jr :Lpiece,) lcorrxir l i r rc' ,v i th Lng rrr f t iu k)ngi ludi ' r r l lo lnr

$lll bc absorbedblns r0cnstrrehalrh thc uxi t iaryt ineo$ d d thedetcctor,ravcNedLhe atu

I '-fli

rr)be nc$uled. Thrcand enarlr rs cmoledherNLr)a lortionol ge

80'out l thlsc,ondalecoLiectlyf tils hr anymeasurcdna stAndarderhodilllc s me Powert.of forlvard0 cvolsos said )hllveacouplefs lsn lhemainineond 0dB 100:l)!

uscdoconneclildcmore (nnnon'nntennruoh so in Y lurcd flrov

rd secondtrli', l""o**ti'..,._o,a'tt" l" l+'r un, nLnor

Fi ! ' r r r 7 l0 f t i \knoqr ' -

thco ief colduclor .A l l r t th le rs nountod n ht orr lsr urduclor .wrlhd cofrcsl1()ndirg slol n i r ro rnr i tbc dclc. l ( / prcbe anirge. ( has l r rk i ( ' r l l rc i ( lc.wi lh I vef f io l1'o fricrowrv. iitqu.rcirs n) ir ioxl! lhc cnil(t pDsitiN ol thc pfobc. Thc probccxlcnds nio t l t ! i ) i , f , I rn! r i r i r . l lorc (o lr r i r t r ! ) 'cor( l r rL inol (hc i | . i ) hLr i o iLt)uchingt, Lrs h)sn i r FigLUe21, lnthis l i r : i r ion. .osc lnrpl in! a '$,eu l t r rc! 'x ipfubc s oblr iD(( lwhich r i rde. txar . :or nrei ls l l | t :nrr ts, ul snl | l lonrmglt$ rs noL onrlerfcfe lndulv 'j he slollcd line nurt hr\rc lhe rr.] rhaf!.niriit(i. inrpuJNnce r lhcD in lrnc , )whi.h i r is c(,Nrc. t , r ( ln kf ics. I l Dr sr r ls( ) hrvc r lenglh on'c ' r l r r t ncxccss l r hr i i 1!r ! . ldrglh nr thc owcsl f .qu.nc) ol oFrr l i (nr .Th. sloltcd li0c sirnfly perrrirs convcnicxrLnrl rccufrle nnstrfemcnt ol ilrel l I i , , . .c. I l ' l r ! . l l : . r r "r ' r . , r " r . , I l l . ' . , r . ' . . r ' r l . r r ' Lh qr 'crr"


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:iE aLaatTRllNiccarMh{LihI{,\Tlofl lYsrELl'ls

FI{;UIft 7-21 (dl Conlmtrlnrl tsifowtr}c sNottodine (r,rr,st d/ r/Ie $o i ManJd'tuttsd,/r'd"J)i (r ) {rosr sc{fionof rt lot{ctl lina

- t. . "ud&@". "':i

asDlrybedcsircd.wjlhout nLcrl'cringigniflcdnlly ith heq rntilies ,cingmersu.cdThe knowledgc f drcsequantitics cnnitsc0lculutionl'l. Lood rrpedancc2. Sronding'wavcltlio3. Requencyof thc geDcrntorcing sed

Thepractical rcasurerncnxndcalculiilio mcthodsLeno|n]llly rdicatednlhe iDstructionshrt conrewith a PArticuhr lotled inc Measurcmcnt cthodsorthcseprriLnlotershsl do nol involve he slottcdUne ls() cj(ist

. '-a

MULTIPLE.CI.iOICEOUESTIONSEath oJ t/.d ollowing ,tttLtiPtuLhaic?quenn'Ni tonlists tl trl iftottryl?lc ak e lJblk]\|td bt ft\lt (hoic?s la, h, t, onLl ) Cirdc th. l.cttt lltctttlittg tht linz that

t .u)rre(tll .otnPltt6 trlLh st'ttett(?

lDdicrte thc &h. statoDeni. Ihc S{rR on .ttr$sDrission line is inlinityr thc line is lolminatcd inh. a tionplex rmpedrnce

a. an opon fcrrlld. a purc crctance2. A (?5-i50) ) krxd s conDectedo co rirlt .rnsrnissiontrre fzo = 75I) , rr l0 GHz II


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t:li'r-i . ,lr ; r; i, :.iIrrii rl ,.r . ii r ,l ii,e ::ili li , I lrlr :: litr,: 'i i.i:ii:!ri! ii; i: 1.rrii:ltliiii !n xi :1: i1: ; l ! l r . r ,1- l r r , . i r . . i r i . l i ' . r i ' r f , , , i . ! ! : r . th;r o:r i : r1 l i r r i r i r tu:r ' i ' r_t ! r '1.r, !!.i1.i.t: r rl i,. !, r ll,:,,.. j 1,, )lii,rl, Ii r rr i,r,l :,r rl . i"h, lar .e:.iiil,Ii iir': tlli 'i Lhrl i . r l : . . , , ' .h i .h rhi . r ! isJ.r l r rc! r f l i i l . t r : : r , l lj . i r i . , r i r t i r r rer . rgr l ! ! i . . i r r . . rcfaf : t " t r . r ; : r .u11i1l i r ! . i i i : , ' i r l iLr i ( lnr rLr l . r t l .i i i , i l l i l r i r l i 11,- l \ . i l . l r r l I - ia,: i ' r ,e. . | i r l re"rr i i r r ie. i . . , i - i r r' / r i i l { }: , / ' r i i r . . . : r . l ' rg.r l i ' i r : l r hrr i . i r r i i rn i i i , L ln t r r r r , lot id lL i ; iLrxr ' r

l r . r I j r f , : ! i l i l | , ,nr l . j r lhr : l , r ld i r i l r r r l inr . r r : i l |cr 1r ! ,vt , "- . r ' r ! . ' ( ) i rnrr , l . , r 1he.; f r ,q . . ; i L i i Lr j r i i " t r l i rhre r l , . D ' i i i , l l i r t r l rn x) LirL:tx l . r1 ! .hr , r i r ' r : r rUr l : , i r , i i . t ! ,Lr , f : xt ! r r f : . I r i l ( , r r r1. !' , i ldr l r l r |1. . ' 1! i : -1 i ,i l l l r - - i r i r r i r i r r r r jJr ri i t l

, ; . l - : , i r )q r Jrr i l i r ' i r i fL .r l . ! r l t I . r lnr l r ; i ( i ! ! r r i r r . c i :L l r ol | !hr l r ier ! d i ' r r r t t r1 Il l )1,1, | r , i i { i l : i t ) - i l i i ic r l r ! - nr i r , i i i i in , i ( ) i f i r lLr i r l i l i i ( l i i ! rn l i r . i tu is ' r r ' . .c( i .elMI l r . ' /hxl \ r i l l b i l i r i ' l l or i drenrrLinort ; r0 lul j2I I ' l l t le hr i L l l ' : i ) rL l's ' r i i l r re! . r r ' i l l , r l r i i , i r lo l r i i r [ i t ] : . l l l r i ,c | l ( t ih i ! th, :y,r r i l i ' ,nuol ler l l lhof uhor f i rcLr i ru ls lubmLr l{r i ]1g , l l i0 i l l l . l l_ i t I , ) rJ 1,) . r i l l ) ) r1r ' r rn i i ish)rr i . ( i . "r i lntrnirgi lu i hc k' !dirrrpdrrce iinraurs |1 \taJ!1, inl the iihrii ,n rlr,i m{l! lijrc wlcn lile ri'r|l|rencJ s (tll;t(xc rxl by l{ ) lr(f(ii|ti 1l1)doub ed

llxvxEW uEls'x]()Ns1" V/brtdi l lerdrlyf$s lransurissioninc!are here?Invhutwavso irei l ppl icrrtrol !$diflef'/ What $ il tlr0l inril.r he n.rxirnrrmolvHr hey rn lrxndicll. Dfr\,/ the icne,trl xlriv|lcn1]rc'-riLl x ttrn$mis$i(nrir!i' ln(l i sifipliliedciraril lirra rrdio-l icqLorctinlr.Wlnt l )()rni lsl i5 s;J,r l l i f i l : rr l iorr lJ. Delinc lle chnnutclitlic rpedrtc0or iLuantrnissioni'rc Wlierr s tl)e DPrrtul0ed_flrcc oi lt !r'0o]i u$i(rnino o!Lral o itl chrlrLci\xi$liclnpfil ce?1. Ilisr!sr thiilyt$ oilosscs hat lay ocrrrt vithRf irollttr]issi(, inos. i wbatLrnilsretirljsr ossclrlornrllt, gi\,en?5. With r skclch,c,rplAir) 1edil'fcrcncc c 'vedll i,]nding Avcs nd uavclin8wnves[{p]ain how sin diDgw vo$occ r in rn inTcdocilyma(li1)(l rusmiss;onirc{i. Defldcarll e{Plrin ([r ntc]ningof the rrn rdtklinl rtr\: tatio \\l1,tt s hs orrnrrltrli)l i1 if lho krnd r p{rciy r)tislive'l hy i$ "t hrghvrlre ol SWR olL0n rtdsimL}lc!? li)r,l1Lill\rlly. w;rli su.I siien:hesr, r rr., rlit,licrbltr.tu rdnceploI irlrped,rtr'crrvril's({r 5t r ql-r lc. wr've rn,r.il , Frx whirlpurposlj; rn ihofl lonirthr l ol,'eri r drtl T r rilod {usnrissiLrrire ilcLrlcd? har is st|01Wlry f sl( '1-circir i tedlrbsptr lofred r oFer-circui tcdneri l9" 'r'illjrl nntclrin! i lord i(] { line Lry ralrs l Nslubuod Lqurder_lvlvc

tnrilnl)'li l rJr l ) : i ihlr icdt lhc ldodr. .c r i r proi jedurci t i ) jkN!.dV/htrt] i rhis r(clhrielWh]ar-c .lo)iltanccsrred r coDncoli(nwilh stub NrtchnrglWhrt doesn slub tctually ol10. \u,Jr i . r \ r , r lh l ' : ' r r ' l \\ r r . r i t i r '1 i l , l r . r ron l


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b7 Transmission lines 2 -comm theorem