Electromagnetics 7

8/13/2019 Electromagnetics 7

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rlc HAf I r RPlane-tWavePropagation

7l RdsvoiwamdPhen7 2 line.Hamonic Fieldsi I Pl.n- avePropagationonssles Media7 4 WavPolarizrlion? 5 Pla.e'WrE Ptopagalonn hsYMedia7.6 Cu(.nt Flos ! a G@d Conducror7 7 Ele.tomagDeticowerDensirr_

sa


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UilBouNoEDMWAvEsW. .sbblidEd in Chaprr 6 rblr r rime urritre etes.:c fcld E() prldrcd a riac-varying @godi. 6cldrl!) md, @rvcEly. r .im.-v[yinE mssnetic6cjdaoducesm elecd. neld This cyclic parrd geicr.?s .l.crom8neric (EM) wavescapablcof ptupagar+ though iir 3t* tul in tuidial nEdi& wnan n.lp4ard n suid.d by a mscial shcruE. such$ I:ffrsid l'ft, rheEM srve n sid !o bebreling ii arrr.r' adirn Flnn\ suifaand idndphde6N.i!!c,$.ilel bdnd4t.s of . darunt 3uidinsshcoe tor drc.-tag.rion of shon-*N. ddio drsnissions ir rhe HF..d ll to 30 MH7):the onosphee r gmd refiedor. ln.se requ.n.i.s. th.r.by allo*,ns dr. *aves ro u !a!'iscnd.rsoboundri.slFig ?,ll.EM*av.salsocanrEl,n!rr.!r&dner'izrllBh.wav6.ni(.dbyln.sun-.r dd'ohtuhxsionsbymrennas 9ticolcxampLs.

l igmT't:14.imosphen.lay(bouddedbydcMo

Whencne'AyiscmnrcdbyasollR,suchaunanna.irexpmdsouNardlyodric:ourcrnth.fodot jr^..ndl,rr.r. d depic@dn Fis. ?-2(a) Even notreh heanrcnnanay ndiare n'o( encr$ alon! some irtcrioi s hanaton!orhc^, ln. spherical ravena!ls ar rhesme spad i'r ltldinos md dd.fort expandsd th. sm. Er.. To $obsdd very tu Nay fom rh. burcqtE,ar.Jtunt olrhesphcn.al vavc lppcrs app@inlrely p/@a^ as t I*ert pd .t a uniJon ?t'n2 ,.r( will) unilom propertics allpoinG inlne plre ene.nr b rhewavelrcnrlFig.7 2(b)j Plre.ware popagdi'latcdby cddsie cmrdinares. hlch e easierb so.k*irhnatnenDticalt)t nrhcsphencatcm'dirulesN.dcdrordes.ribing h. propagarion r a sphencal .!d Hsnce.d.n rhough ndry sparinsaDftfom pl.n. sa\r crnnorexrt,s.!illnon.rh.r.suseninrhis.hap..rroJoclop! physicalndcnhdms tor 3ve propagarionn o$tcsmdtosymed4edlhenrnchlprd9w.w rexaminehNwavese en..!d by andtusnitcdrhto3h hEndei.sbrwEn dnsimild media.The pc6es ofndiarion mdrc.plion ofwNs by mrn..t e @acd in chrter Io.

7-1 RviewlWavesndPhasoNAsrpElud.rooueunmahonorEMwlves.veshrlleo.noughqu,crreviessofnreedaredbpics.'lhe6drop'cderk rnh hor wendhemarcalty deelib. i sintrsoidrl*!verDrncg.ncmlcase.resrdlesofhelherornorirnmEM *ave The coid isasunndr of6. rul.roralg.bngov.nng codprex numbr. ud rhe li ftvi.r cov.6ph6or malysisshcn applied o soly


3/48

193 CHAPTERT PIINE WAVEPROPACATI

'nfin n 'd,rr!rta.. rlu .M fdrh. tjEing $!r fti.bond f@ o tc tnd!4 drftby rllwi

tarcring onrLL sude..,l rdd,lr 6 ett b b. ttttlz.4 r d,. \ 4 t nr.nldp th?anrtttdc ll th" \ t\. t l t.n

snd dcnotcs hedishe of w.v. t.v.l. lnc fundid.pndence fr on rime r rd ln. spalill cs.din,G r

\h.E A n'hcdr4rr!/.or'lr.trI e, Ii, trnriep,1 Bn\\pltint Ntlt.nst^, xnd 4 \ z nle4n, rTh.qu :nnr r1 t r r . r i r l .ob . . *p rcs .dth . fmr ( ' J r = a . o s o ( ! r ( 7

/ 2x t ) a \ \4 i . r =\ r - r + t u /Tn rsl.CLr 4 a !.ll.i rhepr'dr. l rher,!e,&d

. *ar.3.n.nr.d on n. wersurfecrotrvel in&frniwi.hno o$ in .n.qy lf) tLmcs rh. h.{hr of rlF w

of .,h.9rmChds.enp.ir'strequriro'heua\d.n

suife.relativ.rorh.mdhcigllr(undn[6.dcondjl:

sluld notbc.onfu$i virh rh. rLEnc. ph.* 6, *li

Ir FiB 7-.1Foreachplor.comsp.nd, Ds oa spciiicv

r.onsrr \i'h R\Frr robdnrimemd par. Phem.rd rcdb ' h . )ame !n i6aongk ' ' h rnddn6(

7-1.1 SinusoidalWavena osslessttiumR.gedl.s of ih. mehdnn r.sponsiblcror Bertratingrhcm. ll qav.s cm b. d.$nb.d mdhcnaricllly i. .om'mort.ms By $ay of an.rmpL. lerusconsidd save

or d.3r.s. wnh?r ndi6s - 160'I! ds r6r analyz rhcsmpl. cak when = 0:T)Thc r l oKmFC r .hnq he \Md ' .n . rL r , r r t r i d r| = 0 3 n d r h l r , = 0 T l l e l r e p e m R p . r b iat ! sp3.d pnod alons r dd ar a t.mponi p..od

llrrbre mesnapshdsofthewarcrsurfa., rh. hcinnhre1ri) ro!rd eihrbir he nu5oidrr nrems

(b) Plane ffv! irprori@doo

rlEh'blbdbfkmqi.t9hm.dyldrci6.6itr G), b, ditur ob-dd. hd.v.i rh. wv.rrcd Ems

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Tlx lpp6EntElriry of rharn d h.*l'tblhg dE j* d.'iYriiv. ofEq (t.?),nd.d in ho.or of the oclrfu physicist H.ifich(135?-1394),*ho piod...d rh. dcvclopftnr ol

C}IAPTER PLANEWAVEPROPAGATI

t?3) UsDs&.(zlo),Eq(74)ub.E*nfrm

*tudSres$rrr,(z xlr.i4 !p &s

*hcrc ., r thea,R,ldr x|,.fu ord. wave nd kphat. .onsua| tar *n|.ntnhe|).dentd6a=2al \ttdl\r. (7rr,)a='l t'*-t. t' rrb)

* : , t = iSotu wchrvceiminedrhcbh*iorof qaved!rcin rhe +rrlitcrion To d.etib. a Mve td.l,ng ttrriiution.s.E!!FotNknof I i.Eq (? l2):

r ( r , r = A c o d @ r + P r ) O lBiv.opEviouslyn Eq.1? ).Eq. 7.12)hould. wnncna=)n l

a-:" a.m - r ! : / r l n v s r ( 7 r )prcadingo.quario.s 'vesh. clalo.

or rd fd innn u r r d : pohed ,$L l l e h i f r dspacorume spdNer .E lau \ .L .aP lo rsnh f tA p lu ' r r i , . , ra ! rmcuonr r d r sP( '6d

r L , r ) = r r o . ( @ r - ! r + d j t 1 l

br r rmnufl 0i Tn6 h 'llusrdedb) rh. ploc s

* ( " '

E

+.)Th. pn* v.hny. als calcd rherroFsatiot vto.it!'sttt \dr.n\ ol tht rdr. p.r.rh 6*!rersurfac.nre dc tlf monlY{lrn rh. waveN\c tom o. Poindo.s normov.phy$cally alongsith {Th. diFction ol sa\e propasuior $by isFding rhe ignsolrhet'dJ t.ror h.phded (r. l I s'ven yEq (7 rrJl ak t th. nttrI N:nft .l tht ottut n n.taltin ?lnNi ltu rfl\!\ dn ctu,ndtullthtttr vn\d,.:nn( $ bnth E nqdti2, th.n hrh?,.!dL r \ dJr.tu Tb. conidr phlt rcteEncedrhdioinnu.n*[email protected].

Tit.e!.n.) ora situsodd w!ve. t. r 'h. EcQcd

Thesaveftqucf,y/,*hi.hisnesucdincyd.!Pecs-ond.h6b..na*i3n.dL\.unn(Hz)(lonounc.d"hetur'Jrn Fis.7-5.l! obsn. rha! hcn 6 ,r posnv.,r!.hes irs pert lalue. or mt other sFcilied vn

' - \


6/48

REI'IEWOFWA\'ESANDP}I,ASORS

Probofr(0., = rcos(r4?) +tbl rq $ drfi.am dEs orlh. ryEErccpnrc 6e,trBrn r tha' whcn b= 0.Thus.tre ave irh drD ,/,1, qid roL,/ rhe avewrth o= 0 r.y phar. uan lr ri and m'larl), lrew.vewnh6 = -il4is sad o.r rie Rav. *nh di = 0 by a r'r4r. r,s orrl4 A slve_4.ion'ith a ncs ve6r.k slon8.rrorcehasiv.nrue ol )(r) rh.n &. 40 ph& rcferemcunciimilFi irsvaluss posirlv.,6stsnifiesph6e ead n:tr, ed *h.n tr s nc8aiivc,r 3isnj66. lhe la811.2 Sinusoldatavon. Lossy edium'r *.k r rrEling in h. iiurjoni,a tas! nediun,s mprtode*ilt deftasc 6 . d,. Thn tetor is calt.dt ad.ndb, ld4 ,nd d i cs ed th. on.ndion,rtarr or rhumediun nd unn s nep. r n.r.r

) ( r . r ) = , { . - e (o r - / r +6 ) (717)-? $ave mphudes no{ ,4.-dr.dd 0or un n. FiluElshNsa t lo ro I r ( r . r )asa fu rc i ton . r ,a ,= o- r . ,. = r0n . , r= 2n ,a = 02Np/n .udco o Nore1tu enveropf$. waEpaden -ees 6. -.

Ther.d!nnorcis( l/m)rrhenepd(Npl|anisadrnenronre$,diriclaladj.ctverradirodltyus.d.sarenindertulh. unir (Np/m) rcfc^ ro dr {(.nm.ion consbnroriil'r*'' 't *''s'"e I"t" """ tDdmlnqeadrjun

Q7-r Hosmnyour if.*deistray.rin8inrheposiriv.r{mcnon or 6. n sabv.r.diEcnon?Q7.2 How ,les rheenvelopcof rnesirh disbrce m G)a toshs m.drn aid (b)a to$y neQ7.r why dcs a nesaNeqtm ofco sisirryaphN

diatl so dwr!rtr|lv.rtan acoun'cwale Favehngn rheJ-diEctio, i, I nuid('quidor Sas)s.hddenzed by r djfr.rcntiatrresur


7/48

PLANEWA\'EPROPACA

p(r,, Theunit o.presuEn i. *(N/nr). FiDdanexprtsion or p(r.r) rora sitrusoid.l$und w.vc lIrlins in rh. sxniv.siv.i th3t ln. %v. ftlqu.n.y h I kHz. rh. Y.lery orsndinw!...( I 5kr/s.di.*.ve.mphrudeisl0N/sr.md ,(r. r) ws oben.d b bc at is maximumv,in. ar, = 0 lnd r = 0.25 n. Td vd.r G a 1631.$ nEdiunsolurion:Aeodingrorhts.neralfomeiv.nbyEq.7.1)ro.a*av. hklin! inrh. positire.directiotr.

/ ) a 2 n \ - . .P ( ' . ) = A 6\ l7 l - - ( + 0 ! / rMn , .' n anp l , rdc = 10N/mr .T= l / / = l 0 i s .od

! . 1 5 . I n '[ = 7 = | 0 : l i m

ro*.(2", ,0' , {,*o) r", . ' r

L0= urcs( r 0 ?t+db. l/ - a \: r os ( 1 + f t /

{hich )icldr &e ftsulr (lib - n/1) = .os '(l).

r r ' . ' r=o- . ( , " o ' f '+1)^ lAcfbrLn ^r I'shrptupis.rin8 mugh heatsphne chrsr.turd byanelcdn. eld nrersirys'

rso?oo'cod3t lorl lorr) (v/m).

= rr25m f(u 2l or= LoN/d'lB

E


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REVIEWOFWA\,?SA\TDP}IASORS 203ab@ r r .lE dtube iion lhe soug in n.cN. n. NrEnu{ionLdrctolbsmp.idbyatusphe.c3s.s. D.br6iE(d rf,.di@io of Mw hEl o)rhc u.v. v.bity,,trd(c)t}l. ruvc mpllodc ar a djsbc. of 2m m.$lution: (.) sin@ he cficidc 6f, md j in rhe r8u-r ofth.cosin tunctionhavcolfosic stns. rh. raveaus b. hkline in rhc+'-diEtid

7-1.3BeviewlCompler{uobcrs4.,,,9r.r n!"?rz issrirb in r rom

(7 . t3 )vh.rrmdIerheE /(x.J md u dsir.a On) psnsot., rcsperively.nd = J-t ftarn.

@ l - 1 0 .! r = = _ = r . l 0 . n t l' h'.h .gu!l ro.. theElmiq ofliChrn fG space.,Arr = 200m.thee,nplirud.ofEtr.) n

150? 0 r ' ) 6= 037 (v /m) r

rt8crsEr.l rlr..lerrictierdofrhvclins.le.rnmac,

: . r = r 0 l u j ' , r 0 ' + t r 2 l t 5 + r / 6 r ( v / t o r .

Alrernailell : mrr-hcqnknrnp,r,r/.ru *. = . 1 . ) " : l z 4 \7.2!J)

lhcd :l n d. naSnirudef .. ir s nsphre anSle,dd!h.fom/!trausciulshonhmdrpro$nbrioncommonl\,ueniDnumetualcalculations!'pt.!inEur?t it/,ntitJ,

w.crn.onlrd i lod potr fdn'. as n !q (7lo. inroe.hnsurr fo,n.6 in&. (7 t3).? = l z t . r d = . o s d + r . t s i n d \ j t 2 )

:{.minc (.) rhc didion or waE pmpasaron, (b) rhe$. fi.qu.n.y /.(c) i's *av.tensrh,., nd d) rsph6c{tr!. (.) -? didrion, (b)/ = s MH4 (c) . = 30n.jrlr = l5 x l0! nys. (se a):nfl crsET Anetec@D!3nericwrverprepaga(inEinr:diErioninalo$ymediumlirhanenmrioiconsdrr = 0.5Np/n Ir rhe av.\ clccric fieldarnptirudes! v/n d . = o, how fd cm rh. warc revet &foE irs-pl'tude*rrrhavebeenfducedro(a)0v/m.(b) v/n.

" r + 'r-\1.2!)

The *o fomsm ilrusraenEnphicdtyn Fis ? 7.WlEnusi4E! (721)..d.shouldeb*.n o.nsm &ar s nIh.properqurdi.nr.tsonorerhar.incezt r, Fsirir.quasu]' d,"rhep. iv.@rin Eq.(?.24)is,mticable.This sdemred r- he+ sisnsbov. hes{uft [email protected]. .o,,pl& .,,j!sar. of:. d.nor.i wiln 3 {r superscnF(oran.dsk).isobrainolbyftplaciisilrhercv*rft. (r),16m. b)9 2n,lc)l7nr

( 7 t )


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, =1r/i7

fkunaTi Rddbo kr$er rcdhAulir md Fre crasunms ot codpLx numbr =: +ir = 121'

CIIAP1ERT PLANEWAWPROPACATIOi

= t.r Llrlcon4 0:)+ i si'(d'+q)1. 0.

J

Themsnirude : xdlualbUEPospmducr f: and scompl.rconlugare

L: = i { . l r rh)w. noshishl,shrome frhe mp.dieslcomplexlsebra h.rwesill likcly ensuner,tr tutuEchlpt6

rrL+r),J E:lll( r ' r r+) ' ' t+ i ( r r lL r ,J , )

- r t .osLdr 4 ) + l s ld -d : r l .Pry.^: Fo. nyp6niv. nreE{,.

= . , a r , , = . t " ( s . d + . / $ , r ) .

= +.t,/,t6(r/2) + j sin(d/2)l

(7.r1

t9!ar4: Ir rwocompLxnunbds ' mda m Sivd by: , = \ + i ! = t :1 . ,4 . t1 .21 )r = D + , : = r . ' 4 . ( 7 . 2 3 )

rhcn : r= a i fand Y i r iL.9uival.mly,' = .r sdrr = dl

, / i =Q' ' " t ' , 1 1. + r = ( r r + r r + r o , + r : l

: 6rt


10/48

REVIEWOFWA\,'ES ND PITASORS

ldllqlii v/o rD! rncml|d runt6Civ.n No conplei nurb.rsv =.) , j4 ,r =


11/48

CTTAPIERT PUNE-WAVEPROPAGATION

lnonsiiu\oidrl) sdodc ime unchoi. rh ar a square*av. or e sequ.n.. or pules Bv . rpanding$. lo0 ngtumrion inro a Foud.r si.s of sinusoidalmdpon..rs.*.c!' solve orth. dcsEd veiable trsin!ph6or3rulvsnror ..ch Foft.r conp.ncnr or &e foone fmcrcn spaEr.ly. A.cordinEro rh. p.inciple of suDcipoerion.hesumor fte rotunonsdue@all of lnc Fouirercompon.nBeives he $m resul.,s on. volld oboin hld rh. lrobl.m bc.n sohen cndaly in rhcrime donlin rithout rhead of Founerrepesnbbon The obvious dwnhs. drrhepha\or Foudc' aPpr&ch s sinplicq Mo@q 'nrhccas or nonpcriodiceu.. runctions.suchasa siqleruhe. rhe uDction! d beexlass.d 6 Fouds inksals.a.d d \imilr aeplicaionof rhepdncipl. of strpcrposioon

'nr. sidple RCciruir shownn Fig 7 9 condts ! ssoid.llytim.-varyingsl63.$urce8rv.nbvu.(r)= Yisin(d! +4h). 0.33)

shert vi isth. a'npiud.. @ s $. angultrfrcqGnct ,nd6narefcEncephe ApplnrionofKirhnotr\volbselawgiver he ollN'ng [email protected]:

our objetiv. is b obbin s dFr$ion tu in dnEi (r).w. cd do dis by solvingE9 (?39) n ln. ri@dGdin,[email protected] uJt) is. dnMid Alcmdv.lv embL4'rno8e oldE phM @hnique lollesSEtl1: Atltt a.a:in( aJ..klThh mos rhar . should.xPts $e lorcins llmks s conne. il nor arrcadJ_n lnar ldm, and h.nc. ari'ne rq-ing funclons. sucha\ the cuft in dr. crqasnd rhemlfugcs eo$ R and a will a1$ ha\t 3 cosi-

*hereseutd$eprop.nlessinr =.os(n/l r)

\rt) 2: t ! 'rtn nn.d.rad.d \trurt! ^ rirrq\AnycorinusoidauyriB.aryingfundion?(r)crb.

, = ' n ' 1 7 . " 1 .

(1'- )(,,-" )

qhs. Zr d',m.,ndernd.n' iuid,on\,rr.dth.pr.ofdrc rarrrr.ols funclo! (r' Todisungud trano6 qmtiti.s fFm m.tr pb6or councadr 3d.noti4 . phasdrn Siven3 nldc (-) ovd IE l.er!olra-!e. ( ) gren byEq (7a0).rb.c6tintn.Imtvit@'6 41

[\", ' l


12/48

1 REVIEWOFWA}'ESAI{DPHASORS 2n

t(^ - ta)= o, (pha'dom'n)o.as)rd ifrhe equarionw. m Eymg o sotveconraios e,iva.rs d 'naeEl!, v. trs.rhc ouowing Mo pmpfrics:

_jrE{l.q v,, cmspondila b th. ri@ fuknon !,(r),$dis.nplirude ud phe infoma.ion but r ind.penErof t . tim wt bl.,. N.i *. d.tft ilE unlNn,rirbl. i (t) in rems of! phaor t-.

SiDaborhx sd Ce Ealqudrjrcs Md rhe$d )oDcFarion sdnriburive.F4 (7.47) nptjfi.s b

t,

B.fore s. lpply &. rc( n.p, wc ned b conven hc4h.h8nd sirt of Eq. ?49) inro h. fom ,0.r, sirn /o

ia fi:ft-.4t + t - R c )

Tne rime trdor .,,' h.r dhrppcred because r wb.onrdn-d . , rhE r.m. rquf"n I a3 .. d,.pttsr donain e{ruiv?re otEq (7.39).

\7.45) st(p1: sr'R ttE h&trdonain .!ut."Fnm& (7,$)(hcphaorcuft. /i\stvcnby

I ta, l*ria*ta,:n ([ i* '*)/ i \- * \ ; , - ) t116)

lu5.diaarcnriarionofhetncflncrion(4ncluivar.nr, mulriplicatiodfnsph6d / by./d.andnresraron

l. & art th. .iifeiidt / ittlatt qr,.ti nr3illinsEqs (7 42). 7..r4), nd ?46) n& (7.re).

r I r( / . - ' )+:s, rh *e Mvetrs.n he denfiy i = .rr. D'e phcdsreo' = kn' (@Ic) bd hesnrhe imquad.rnrot

r;dc "r 4 ,i,4 +;i-F _

(i*)


13/48

CHAPTERT PLANEWA\,I PROPACATISkp5 Fnl th. neonbnhuxvlutTonDdi(r),s.iiDplyrpplyEq.(? 4) IlqrE r.Dul!-ptydicphdd i giEn bt Eq (7 J0)bv .rd ud rhcnu*.

ir,rt.l- - - lcond + db 0,) (7.51)ia +;n:d

InsunnDjy.*.co.v.n dalltme varyi4-quaotit.sfrode ph.sor domain.solv.d for rhephasd 1 of ln. desnedidanraicou\curcnri(rj,ddrb.0convencdblcktotheift domlin ro ot*ain M *pr$sion for i(r) Table7 IFov'dcsr sumnaq of soft tim.-doroin

fundionsrdfi cnphbordomrnequrvardb

Tlt voxas. ourc. tmecncuit bNn in Fi8 7 l0istrnt = tsi.(4 r ldt 30") (v) 1152)

ob6in r arpNis fd rhc clhs. tss rhe ndcrorSolurionrTh. volbge [email protected]. L ciEd n

r , + r a = " . u r

Trb|.'i:TtftloniisilBid,lluEliffie.i.diEjt'd.elbq-ealii.quiYJa!

AeroreconvenngEq (? 5l) inlo thephaor domrn,ne .d 'o . rpE*EqO 5 : "n rc i i o r i . s i n . a reEu5(r) 5sin(4 ldr 30')

= s.c(a r loa' 120") (vl (7ThcrcntrLenrr, \pe\'h$ rh.Jngulrriequen.t d1x l0r (nd/s)The olragcha\orcotustoM'ns

i = 5 . , 1 ) r 1 v ) .andrheFr\orequanorcotrcspondinetoLq75l)ir

z,i,,-):.4;;FRt- ' j

!z '

Ii


14/48

TIME.HARMOMCFIELDS.tvi4 r( uF culmtphas i *. h.ve

- i .Ans. (r) / = 150/(i + i@r) = o.3zlqtlA), (b)(O=0.36(d -36 .9 ) iA ) . (s f r t )&nO$ 7.6 A ph.o htbg. isSiE. by i = 15v.AN, u(t)=5cos(ar+'/2) = -5sinor (v)

7-2 Time-HarmonicFietdsrr rhcrimerrlitrgcas..tneetsticandmr$e c ticlds.E, D, B, od H. dd lnet blrei lh. chrgc dGil} Add cuEnr de.siry . e each,n qenemt. funclion fue spand odiiares (r,).2) aid rhciimcvtuiabte.If rl'c;rimeuridio' [email protected]'!!icscanb.rpEknredb! 3 rLm. ideFnd.nl fisr lhJ don l ) t s $e \e ro rphNr [ r , \ . . r qu t rG l l ond , f , ! ! ,he r(hrrneoN 6etdE(J. ), zrr) n de6ned c.ordrn!

F , , , : / r : e t .[ - u . . : , . I

- r&,t \.hagephaeracros h. nducior elared tby

: j 4 ! 1 0 " 2 t , 0 t x 0 . 5 ? ' r r_4 . r ' q .n r , 4? r r . N) ,: oecotrespono'4 'nsMl.Mnsvot6Se ur(, )nrh:r,

n"Iylr- lm,[4" ,$ , !a ' , , ]

r wh) r ']]. phrqqhn'que uqrutr whn a n: HN6rheph6odehrjqueu*drhetrrheforc,nglii \rnon stru$'dalperiodicavefom.such a

C/St?.5 a.enerRarrcrrhronneded'uJ\otilgc.:.giv.nbyuJ, = l50cosorlv).Find(a)iheph6o.:or 1ard(b) fte nsonraneou\uftnr i (r) for R =:r / = r mJl,and@= llt rrdl5

&d rm'lI dennirionsQply ro .h. olherndds md ro andJ Fora ind. ,srrcpic, ud homog.nds ndiunchall@iad b) elffiicatp.mtu\r) r. m,Cruc prme:briJ /. in'r(undudtrny,, dd dilhtrs rh!rdrfr.r.emaioninrherihedon'in.oft spoidstonutriplicarionby/@rn.hephasordomrin.Mlrlelquauonsdv.n6vEqs. 6 l )b (6.a)astrm{h. fo o*;g r.,n i" l|l pr,,"or

e i= i,h. ti.slr)v f r=0. l7s7o

o 5rdl\hee re have ed rhe ctarionsD,EandB = /HThis ct f.quarionsefneshe adins o{. or he ub,[email protected] hded in rhnchrFer


15/48

7{-1 ComplerPsmitivilyInIEdilnrirh.4dudiyiry',rh.cw dosityJislr&db f, byJ = dE. Cms.q6dy, Eq. ?.57d)myb.

7.2.2 Wavcquallonsloraiary._reeA n.diln k eid to b. chr4. fd ifn conbinsnoch!rE.s, d is. lA = 0. Upon .pleing E.0.57d)

v ! f r = I + r , . E

By ituoduc,ig !'te."pLJ P.rDrt'ir.v 3" d.tin.d as

Eq 1?53)caibelfr." 'nGnas ve:k byutii8 rhe urlotb.rhsi&sof Eq (76v " (v a)= -i,a(e " fr) o

&. (?60)ad sire A = 0 in E4. 7.5tu).rlar.quarionsd r chae.-frcc mdiiumb.on.

In descnb . prcpasatonolM ENI$!ve ir !:h.le m.di!m. se ned todtriv.wav.drudionsfo.E.andrhensolverhcn!oonkltreiPI'.it.xprs'oNldfrarafurcuorolLhe\pdn.l\mbles(r. :r Torhi

L | .nn .ub j t r umeEqr h ld r 'n lo q 7 64r$ehNv, (v " i) = -r.&(t.c.E)=.'!."E o

FromEq.(r 5),rhccurlofthecnrlor6ns iv.nbyv, (v i) = v(! .E) v ' i .

rh.re 9ri is n. Llphcim ol E rd isgivenn c

t - 'I i v ieworEq76r r ) .Nhrhnaresrhs tvi=0 .or& (7.66)inE ?65) s,ves

s: i+ . . ! r .E =0.

'Inec.mpldpmirrivity! SntnbyEq (759)wri(.n itrt.m! of, rci p.n . ind an rosin?ry

For lo$les mdluh e nh o

! i.)''r=/l: *

v . E = 0 .v i i=0.


16/48

PLANEWAVEPROPACANON LOSSLESS EDIA 2 ! ttlch is call.d rhe raoa.z.rawa |. "qdi.a !* E,u inLarduciq he furrsar':ou .oatad y d.nned

v ' ! . 'p , " .

r. d..rins& O 70), . s@dbyr*jry rh.culor, ']j nd.sof er. 17.6Jb)nd hen e us.d Eq. 763d) o-tri cquatoninEonly.lf$eEv.6.rheprmes.rhar, r*cnrnbyhl,ngdiccu orborhid* ofEq 7.61d)nlfi ciu$Eq (76rb),w.obh'n.hewrv.cquarionforfr

.= rhea,r.,t,,tios dE-dfr * orrh. "-cfo-.Yr soluhons ill hr* $. sme fom.lso'3 Plane-WavePropagationin Losslessedia-? Fopag.don po!.ni.s of d ct*roftisneric sa!e,d a ns ph6. lcleiry !! and wrv.lcngd L m gov--rd br- neaiAulafrcqn.ncy aand rhe h@ $nstirutiv.ffd.^ of ttr trEdiun: r. 4. md o. lt $e mediun nr , ,rrdr'8 (r = 0), rhewaved-Tuanor as r ravels tluluShrhem.dium.rnd hene lherjumtrsridrobr,s/e$ From& (7.59)..!=. ina..rsnted'um,'nwhichcas.lq (7.69)brcmes

Wnen E m.diumn h$hs, n iscuionury b inr./uerh. ,u,.,!''.r t &tinedbyr = @!/ii \71\t

In , , s n fEq 772 r .y r= l l andEq ?70rbdnm6v' i + : i =o

7-3.1 lJnilom laneWavesFord.rdic 6.ld ph.d livcn in cd6js cmrdinie!

f r=iE,+i; ,+i ;_:.subjirunonolEq767)inroEqr 7J) ives/ a : a : , , \ , - -l a , ,+ , , : + a i J r + j . , + iE

+ t:(i; , +ii, +r;.) =oTo $nfy E9. {7.76),eachvoror coalon.nrlefr-hddsideol rh. eqoarjonas o.guale6 H

/ , 1 : a , a ) - \ -{ d r + a l + r - + i . J A . naidsinilr.\pEsionsapptyo , n,j ilA unihn plznee.y. is.neevdkrt'r .t{mag.eric .id! rharhave nifom pmpni.sar l@oso'nnnicplmetFig.? 2(b)1tlnisispl.re, h$ E bd H donorvry unh r md I,tr,/ar = 0 mdaE,/a],= 0, nshichms&

- -

,t E, (? 73),f,.H


17/48

2t2i = 4 = 0 ro shrydd 4 = 0, lcr usconsid.r$. ?


18/48

PLANI,WAIts PROPAGATIONN LOSSLESS EDIA 2 l l

!isdR 7 ll: A hisk^e .le.hmasndi!OEM) o.]4 rg r l nu i i l h .dn . . ' j o i l = ' f u . r1TEM{a !6 .

th. uv.Ln3lhr. Fftn rh. hardial on avcmorion iv.ninSeriotr? L I, *. deduc.&ar rheprrre lr&rr}, ofrhc

4 : i -,4n Jt,

II then?dian k nclun,. = |.ar rhePhaseeleny r! lnd rhc

* = , = - ! = : " r o '. i ;

rheE.(!h.vdeit)_ollighrand

=1d=ro, .

:: rtansved? ztedtomsn?ti. (rEM) *Ne oth.t .\--fLc! ofTEM wav.s nclu& cylindd. *rv.s hv.l:: ]longcoA[l h6mi*ion llnes-Jpr.r 3) and phencar 5ves ndrcd by ocm6ln he cm6lc6e,Eionay beacospl.x u.ndtconrrdot!nagnnud. r; .nd phise nlled'.Irar n.

E:"= EI"b- 0 BB)'. ri{rniflmus.ldnc !n'i magndic elds E$.nE,: .=q. [Ek).r ' ]

=i,t'o conar- l: +{-) (v/m). (7Bea)tl ,. ):fi. lfr(.)./-]=ir:.s]c6(d, r:+dr) (A/m) (?39b)

!..-Jtr*E(!. ) andH(:,r) eihrbnhe .N fuNrional. bd /,!] ! ; lhcn:.r,nphrMe.f on.of d.m issmaii,num.rh.rnprirude' rfu orher s a nExisum also. Tlis in-phlsc prupnl. .hracrniic of wrve\ pmpasdins in l$sles media-ktrrimevriarion6d.6!e'iby$.oscrll.!onfrequen.y

= o/2r. lnd $.n sparialtuidionscbd.denad by

'tlilnlit-3: ErPr.irw.v! ri arrThir.rantreisanatogoulorh._Sou

Fobremdes.ribedbyrampte IThe.led.lieldofa1.MHzlmc+.dierioi inairpoin( alon8 he diuion Itthe p.ak!.lucol, i\ l.2r (mv/m) ndE irnd: = 50m.obhinexpre$'oisforE(:.) mdH(:. r).andthei ld.hescvaridioni6rfundionofar = 0.$hnirn: Ar/ = 1MHz. hc rrv


19/48

l l 4

.-=-r@ad rhe clresp.ndins wav.numb.( * = (22ll0o)(md/m).ni.E ne6l.rprGsioi fo. ofi.ld rNelin! in $. +r dielion n SivenbyEq (7 39r)f,(: ,)=i Elo con@,-tz+0r)

=r r r 'ms l r r ' r i i l -=+c+ l ( 'n ! / 'n )$.6.1d E(.,!) isnaximumhencsinefunctionaNrhzroornuhiple!or2nrr = 0and = 50n,rhiscondnioi

- - - tF +d- =0

E ( . , ) = i r r ' c N h , ! 1 0 6 ,

md ton E4.C 39b). havc

= r r u r c 5 l r r r 0 1 - = +*hcB {. haveusd theapproximinon

",.=*'o-,(ff i)" ( . . 0 ,= t ' o - ' ( . n ' 4 : )

PloholEi? 0) rnd H(2.0) ftrhNn

.j. i ' = i

i) ''"'''


20/48

PI.ANE-WAVEPROP^GATION N LOSSLESSMEDIA_1.2 Gene.aleldionelwenand! jr b.3hNn rh{, fdty unifom plane av. hv.line! , ,r6ihry didid dddd 6y th. $ir Eb t, ln.r$..jc 6.ld pn.s H is irhlrt?d to tlE.ldi. f.ld

H = : t r x F r 7 q 4 s )

a: m$ produdtu b. phr.r.d in rcm ofrhe ollNiog.rt hndnle: $en *e ntat'h. laufaF{s of the richl.t ltun th? dnttd aJ L toMrd th. diftdi.t .J tt. rhu,lt) \i Nnr ih th. dd, i.n rt w,r, tu,rL k\ rcrdiom 3ircnby Eqs.17err andb) ac varidnoronly.- 6des m.dia. ur or 1o$ymedia *c[. Asw silld l.r.r in Sdion 7-5. h..xpr.sion fd I of r lssy-z.iumisdin re tmmr]larsrrenbyEq7n6) Asrong. 6. erprcsio usedor 4 ir aptaprua rc $e m.dium: rhl.hlhewoEhhvelin8.rh.el..ionsBiv.nby&s.L.' usapply&. (7.94a)rorhwrv. sivm bJEc (737a)-! d,Erion of propasation = t lnd E =; E:C)

ir;,*1.r Elil rr.ss)!i,.h tr th. smc $ th. Esurtgiven by Eq (7 37b) For.r.tmv.loginrhe :.'lirec.onwih!n.lecticficld

f rn o r i rEq i ?q , ,8 i vs=-15. , "

and ie s*iLd ru8ftn.6.ld E

App l i fa ' i uno fE 1794a rs i ! s

In g.neral,a unitm pllne+unnatiol wy havebotn r

f r : i t - , z r +

By.q!aLinsEq.l?.o3biroE!? 9,lr rehav.

t19J lDoinbn theEga.ve)rlic.ton

Thcsc sulis E lhnraredn Fi-s7 rl The !v. mathemnsiderd rhe umof r*o *aves.me *irh (r:. r4r )comronenltlndanorhqui'hEl. d._)comp.ne.bi

Ftuc 7-lr: Ti. uv. (E.H, n 4ufare b rhesn oi'so{!xr.or N,d icu\ (Ei s,1) or&oddtr"h(.i.4). *"i b.dihrrtic Ii6. +zl]'drm

.-s:-E

r i xE= r ( r

a


21/48

2t6s.ffil. a TEM raE my hlvc D.l4tic fr.ld in anvdiEdid in rh. Dlf. ordrsonal to th. didion or wa*lreI. dd$. ei.r.d ds&tic 6.Htrlsin dE sgftplm $d i6 didioD is dicotd by 84.(7 94a)

Q7.6 wh{ is a un,rorm l.new.ve?D.{'ibe is popeni.s.bolnphysisrly !n'1,trmarhemticalcm\ Und{vhd condnids s n !ppoD.i!r. to d.r a sph.ncal lvc

a7.7 s-* i mdit * !o".-.d bywave qudioNordEsn romtEqs 7?0)and(7l)1,dcsnrollosrhrtQ7,3 lf!TEM*rvcndv.li4rln.innerioqcani[.lecticfeldhav.conponenrrlo4i.i.rdt?Explain

ElERClSCT.Tl0'MHzunifomplr. *!ve t r hv.hgin r nonnagndicd*diuD vitn a - /r. atd.. = 9. F nd(a)rh. phae nlmitn (b) lnc wrtnumb.r, (c) rheMv.Lngth n $e medium.nd 'r) he ntrinncmFnmc. .t

l t r . L , ) ! r : I l o r d r . i h ' r = 0 2 ' m ' i / m ( r, = rom i)4= 125 7a rsc t)ExFAClSET.lh.el*ric6eldph6orofaunilomplaiesav.tnElins,nalo$l.s mediumith m intinrc imra-- orrgi s a i. ei"* ty E = t l0?r'"r(mv/m)ft kmiela)$.rssiat.dnas*ti.lieldphsddd (brrhen{rtaneouserPftsionror(}. r) if hem.druit r

Ans. (r) fr = i5k rrir (rA/m). (b)E( r , r )= t locon6 ' r lo t r a r l ) (mv/m) (se !

IIEBCI$7.q If$e mag*i.field phddofa plm.

7-4 Waveolarizalion

hv.hns r nEdLum"n mhtu( 'mp.dTc. a = l0tr sm by E = d ro + trr. /' io-A'/dr'6dssid.d clatic 6.ld pi''sAni i=( t+ i2) . r ' ' (v /n) . s ! t )EXERC|SIT.i0.par r.rci* 7.9loia magD.tcFi,.nbyfr=illo. rt - 20rr) n^/h): r"" . =-tk, '+2"n')ry/-) (seq

Ine r-rdnrdD, .r r unilonn planewrvc l.n,btr\ h a F M , t t r , ! , " l t h . r y a t t h t F \ ? b t t t a h zo hDcavt b ttt.1n&tio al Paurdion)tt o e'p"tnt rr,). !\n lnnd|a'l tir' lnthenostzra\., lne c6 of Ii is anellipse, nd0'. *ave Bc?/lir,idtryprhn:.d Undff .en.incondnions.rheelmayd*.n oc'nroacnd.sr$8n.nrorastarghlin*hicbcase$.poh.&ria,'hen$eicalled.i

As *as shosn n secrion?, rhe: component tcl.ddc andn.3mic 6eldsofa -poPasaring phm.r bod,zco. Hcnce,L\e.lcctic fi.ld phsor Ek)consisr.r n {om|nmnr, ,:,(z). nd ) como ro r

wheF a,i and i lre the odpleramphtudesf 6,xnd ,(r. cspecnlely orrhesrr.orvnpli.itv.rh.Irris;pR\np'hrkensuppas.drJuuuAhour$.rtivesiBn'n. r^rissufiicienitorcnindusrhar!h.( hveline ii rhcposniv. -d1ftd'on

6(, = ;,r ' )+i t , (.).


22/48

.] WAVEPOT-A-REATION

.herc., :140 fd,r = E,i are h.na3rirud6 l: and rro, esptuvelyhtrs.ydcnnidon,,, d,,,\ rora$uncic3ari levalue\si.-eEqs71034lidrolb) n Eqs.7.r02a)nd 7 02h),he orallerri(

Ett=t ; i ' ,+ i""""v t '"d .hemspondi4 inshhndus 6eld s

F./ : ,=,n. tE, . ,d1

Tn.tmmpl,o&sEbmdEtse,in8.ned,comDlcxsdtl.s. vnn 4h ch|mc.iz.d by a rognirud. md ane 63L. Th. pbe of ! eow ir &6r.d rcliiE b a:ircd'di!q.such6z :oand, =0ormtorh....mbidationol z rd r. rylv. rdl/nulioh d.plhdt or1 phaszol En Etoliv to that oI E,x b't Mt dt th?:ltlute ph6d al Ea ana Ea llene. fo. anvcnlen@,r.r'i1lchesrhephaseof E oasourfrcna(rh.r.bys'snmsfiaph6eegleofaro),dd$. rld.'or.rfiar.r E.o. cla.iv. o rhar l 4,0, as Tnu! t nr ,rd. lrtr zn.e b.rween rhe .ompon.n! of E and: r {omp.nent A@'d4ty. sc dcfrncai md trro .\

'I}l.letic 6eldE(:. , h6 conpoi.nls along h. r- dd)itEc.ids A. ! spaific po$ion :. uh. dierion otE{.. Ohd.6n di,th.J ) pbn. (drhr vrlu. ord ry |h.imliMriona8le V, d.,in d lirh Espr.r bL5. zcpheaterenc.conponeD.ofG. o.trhichis$.r{mponcnr

, i(..,)"*,(;#)

D(0.,)= (*a, +i.,)cosar (ii,phas). (7103a)f,10. ) = (i., ia,)cosd. lour,orph!s.).(7l03b)L.r Ds crmn.0'. ouhf phas.cE(0.0) =ia id,, whichneans h.rE exr.nds omrheong in i nF ,3 .7 .14b$cp . i nr t , , , , , ) $de roonhqu!'lEntrrher _r lMe.Ar r ,n.Ea*s. dF modulusl

r'i rhegenemrcase..rh rr'e ircn\iryolE(..r) andn\d'Roro'mtuldnnsof rmJ,.Ne

7-4-1 Llnear olariution'Ite polrianion s6te ofa wa\. Frv.linSin &ezdrrec.ionisdereminedbyr..lns hefi .tE(2. 4asalun.rionoflncii aDlan onno-qonalo rh.dnslion ot {rlt hn lForconve.ienceand*nhouro$otsenerahrreusualttchmse he = 0 plane r{,/ i\ sd t' ht ttr.. \Ntati:..j 1l E,l. a aD.]E,l.ti ) ot oat .t r"6? tr = n) rn1\ish.c!ui.. at a spe.iliedvallcofu.sryu= 0.fieriporE(o. )rtuesashrshrnF,n rhe r p rane .A r : 0 l nd fo r , = 0o . r ,Eq . (7105)

:ie. chectnzin8 Illc bhrvior of a EM ruvq rworip.ni.s ofpdiculaincan arcde i .nrly anddire.: ri ol nsel{ric fi.ld Tlrc deNnr ofE(.. rissnenby. modulusltk. 4 , n,n r,E r z , = t E j L z , + F t : l I l

r i o , , = t 4 l , i , - , @ , .sd'h.i'nli'urionr!l!Llrl'ne,lhJ E9 L? 0rlr!^.nhy

+, lmsr(d r?+r)1Lrr7.106) '=* +)


23/48

I ',/--

213 CIIAP'IER7 PLANE.WA\PROPAO

!.h'hrid Cid|n ILHCIolrd.llor

shdly, rh. wav. Fleiation is crlLd tzf'brd.i*lEn 3 = | /7,nd tiscttt dnA,fthtnd .wuat

rsd, =,r = dudt = r/2,Eqs.(? 104) nd 7.1

i@=\r .+ io . t 'n ) . r '=d( i+r i ) . r r : . (7 .11Ek.O='r , [a(?).P ' ]

= idcond! t, +id.odor a. + t= ; .o \ (@r I J j , s i n ( l r r : ) ( 7 .11

The cor.sponding modulus nd incl'nabon dsk

E ( : ) l =l E i r r . , ) E ' r : , ) l=tcr.o;@ r.) +drsin1,",

rngkde.Rn(qrh'n!reringrime A. llusufledi07-l5k).rherlpof(r)hccs!cirleindEr ltlu..mr erinrc|(|(}i\edndionasafundionoftin.(

'n thir ce th. mc{ulur of( ind.pndem or borh : and ,, whecrs Ipcnd\ or b!'h $d:hle\ Tn.{ ruironrldenciesm rhe convcrs of rho* rypli.able roAt a hxedpoiion z. say. = 0,8! {'7.lllb)t = -or:lhr.eldive siSdm&nsrhar hc nclin

which r ii&JEndent or bdh z a'd ,. I}jus, r]lc lcn3$of rhe d Eprsnhg E(0, r) &.ra*s to zero ard = r/2, rhdnv.6$dne!im ondrtrdebtal+a;lrrriirhessidquldmrorft r )pramd@r=r SimcV h independentrboth and , E(:. t)m,inrans.dircrion long thc in. m*iig an,rs|e ,r'lf or = 0, V = 0' o. 130',andrh.'a\rb.omeir srlaized. lnd ir d, = 0, ,y' = 90' or -90', rod the

Vr.. ,r=,-l- l

7-4.2CircuhrPolariralionw.id.onsiderrhespc,alcase*hen(heasnitude\olrh.r rnd {ompon.nh of E(, m.qnal, nd ihephaRdifis.nce,= +n/2 Foftasonnhlrwillh.om..vd.nr viNllg the wav. appmach'ng)snch a $ak '!


24/48

.J WAVEFOLARTZATION 2 1 9

.h.haad ircular\ prlrned b&Ne, whcn h. dumbr de eirh dpointsalol8$ednetid ofpmFganon f]qave(in..-diriodinrhisca*).&eorhcrfourling.rsrtr r lhcdirccrion f dnon of E1!il-Hard irc!larnHCl oklizalion1,, = ar: drnd6= -'l2. rr have

Thehceo t r j a \afu i d i ono t r r sho$ i i i F i g 7 ts rb )rorz = 0 ForRHCpolrrjzrton.hc in!.^ ol$e rilhrhandpoinrinrhediEaonorrohrionofwhenrherhmhr arong heprupagarion tredjon Fisure 7 16depi.h anghlhdd dculrly p.bnTcd !a!e radiared y a hehcalkle1n.* trJ4u,t htun' oJ h. nnni.r.lEA ttrurr.n llhtu r,' ttr

s0lulion:s'Dc.llrsalcisrrvelinSltrrhe+r-dircsrion.n\6.ldconponcn6mu{bealongrh.rmdz diFcrions'Ihercrarionofll(). r) nd.picredinFl! 7 lT,rhereit\ou(oltn. pageay compeison id tn. RHc pol.dzd

q r rh. +?riiGrion (0r or d.


25/48

!!0 CH-APTERTPIIAE WAVEPROPACmd rh. inrituic inp.n"(. 4 ( gi\.o by

FiEuEt-r7r Rishr lHtd orulul, p.l&ikd $Ie of Fr

raveshownn Fi8 7.15(b).e asisn tbc.conponeirori(t!Farmek oreomdther{omponcntr phscshfr, = r/2 Borhcompon6hav.amrsnirudea:l

itl) = t, + tE_.= t ' . F |2 r ! + i . J t '=(-ii +t)3.,t (6v/m).

lidlpplicd,orof (7.94a)3iv.s

=. l i ' I i ; +ar" ,, '= 11;7 r" r, r..v.,

Wiho = l'l = 2x x l0r(rad/o,he rrenumbrn. . / r ? , . l rF "6 4 . .

Th. fthMus rmti6 Et,. t) .nd H() l) e

IE(/).r-l[ ( - i r+t) ] . r . r- l[E(r)" ' ' ],tii+it, "'.'^ ]

=ra l | t l - " t . , l . r l i , ln t . , , r l t tMih ,= t ' , r r ' tnd / rmJ l =4r / r t ! . r 'n r .7-'1,3ElliplicalPolarizallonIn ftc n6, g.i$J.:n lhere, - 0 u, + 0,, I 0. rhe it orE hc* r.llips in rhe -)and heeavessad obelliptcallypoldad Theof oE .llip* md ia hod.drc$ (l.ft hfld n li3hlokrion)kderdin.dbyrhcvaiFsolrher io(a,/5idrheNhnarunpha(ditr (n.eiThepo lm- t ru ie l l i p { rhdn nF iS l3hasaris,r aion! th. q dnali.n md a m'Dornis ., a|mtrnna.on. The ,rdfun ,rrr. / s dehn.d5 rheb.scn Lrnmajoruir otdr..llits Md aEreEncediuon.chornher h b. 'he ( sn,rilhi b'ng\rhinftctuf,!! a 2 : / r a/2 Tne)hJF.of'prdJtr!h rJcdnesr.thr:cIenaJbJ'h../ 'rd

$(h 'heplu ngn.otrspondin! u [f'.h.nded3ndrhem'n!5!3nc.ft pondinstonEhra'dcdrc


26/48

- \\A!'E POLARIZATION 221Sinc. rhe munitldes ,, and r m. by deirnlnon,nonesdv. nunb.B. th. rario ,/a, my vry b.rw*nd ar e r-Fldai UM poleidjfi .!d @ rqa ' poldzen [n6 polaridior. Co.s.q*Dtly. rh. ogleVoslinjledtoL6.dnS.o V0 90' ApplisrionofEq. 7.I l4a) .!ds roMlEssibl. blutiosfqtl*yrlue

ol),,bothofhichfall*irhinrh.&fi.dmn3.fDD'/2!o r/2. Thc coGr choie issov.m.dby rhe ouowing

lnsummary.. signol rhe chrion gl. y is rh. samersrhesiSnofosra.d$cs3'orrheelliFicityrglers

1)r = lta2't'|)cos3 | ,/2ar- : r = Gin2Vo)s in l t /a : I

.lLmi( ror x ae ,/1 ! r ! '/4 Thequanriry, = d. /dr ir calkd rhe rul db of tnepolrianionrr, and r vdics betwen I fd circuls toldanion- i r ror liner p.ldzario. Th. poldiatior ugles yr.6 o,. or, and bY '

Detedine hepola.zanoinat.i a plane r!. *nhEG, : i3conor l . +30 ' )

i 1 ! ' \ , d l : +45 ' ) i n !h ' .

rra \r0 s ana0riliaJyangl. d.lin.d by( 0 . ^ = l )

'F(n M b {d E {.r. P"rprr 4op'{. No Yqr

:.r.hesol$.polaiarionellipsrcshown inFig.7-19. \a.iouscombimtionsolrh..ngl.s(y.) Thecll,pser .Lcs roac la l e ro r , +45 'mdroa l i n . to r x=0x,. ntu"t.tl )t tn.^pottins to sinr > o. nr". tidt?t nh t.ft hatut 1ntun'',, ..,.!r,n/tf n, snit < 4,ort.$o.iatdnnh

Soludon:we bgin y onvdin! fi. 34nd h oro aE =i3codd, - tr + l0')

i4c6do , tz+45" 9 {1= i3co(o ! r .+30J i . l cod@r t : 45 ' )Thccoft poldingetdphnori(z)s

a(z) ir. rn,' i4" r'. r"_i3. r r . r t + i4" r : . / l t . , rm=ir. r,.,r. + i4. r':./ n .

shere !e brve rcplaced hen*ahver.m vith e/ tr in oid to hav. p6niv. anplnudes orborh remi .nerby arb*ins us ro ur. L\. dcfinnionssntn in Serion7-4I Aao'n'ng Io the xpEssoo or


27/48

TECI{NOI.OCY PJEFUQUIDCRYSTA!DISPLAYPhysicalPdncipleuquid cry$ds e Biihd . 9u6 .did 6 .llquld, bul alhor a ftbdd ol boih. Om pa6rl6ty ol Inreest s the wistednemariciouidta| {n6e mled65 haE a nalual tendnct

l-iquidryslalisplayLC0)lcos @ @d in dlrt i do.*., el|dd phdE,dahop .nd l.plop @mpu!.6, and &m loldlsi6 rnd omd |6lDnic aysloE. They otle. a&d


28/48

HNOIJOCY RIEF:UQUID CRYSTAL TSPLAYLCD)nr6 wiih ns Fhrialion adiEclion l .lclrr;) pqElll lo the g@w s dicton.

0 Slructurcrngldptel Lco slruclures3hMn n(ar)and) tor lh6 OFF and ON stet*, rnh OFF @re-dingloa bnqhl-l@kingi4land ONloa daft-lng pirel Th smdwichd iquid-crys lalyer.'r@lly on th6 orderot 5 micons n rhE*ness, r20 0l rh ldh ol a humanhairl s slBddlodbvdtr ot opti@l r1i66wiihorthogonalola zations.ren no oIas is applied cross he crystal aler

90' as il lc'llows he molellar spi@l and I nalyeEs rDm the ext polarizer,Aivinghe xirdlaea brghrappearance.uslulLat!@ lne.

: in@mingnpo. zed Ehr9i6polanzeds l4 rhough heent6n@polar er, he. rotars

6hage ditlbn ac6$ rhe laye.),The degre6u.lwiElingdpendso. lhe slrcnglh oi lhe 6l&tic. Wth nosDilio rolaie heMw @la zationaslighr rawb rholgh tho cry8ial, he ightpotar

;iic liqu'dcrysrassrharh6 6pnal tw sls 82)ef rhe nl lu6nc6 l 6n lecrricild mduced v

rione,lllb odhogonal o rhatol the erit poa.2er,rr&ing no ighr opss lh.oughl He@ lhep'rel.dibn daAapp6Ence.

tio-DimonsioiaArayai enndinohe.on.epl a n'o-dioe^sona ra. ol pirelsand dwisinAa *hene lo conrollhe'nage aco$ eaohp xel ndiudually usuallyby us..l alhlnjilm r@nsistod,@mplelemage n beayed s illusrBledn (C).Forcoror splays,pitel is made up ol *l subpirels wilh@m.

E.naryelor lihsG (@d,[email protected],and bluo).


29/48

o0

o C C o0

6 o t , f r ( U r a b P o j M q

2? 5' L.fr ?lriFjc.r Frsizrim

,,t -*r*r*'**^* 0" "''.**''*-nds mmbiMiois or rk 9olriarioi fsrr 1/. x ) fd , ryaE fedrs od of L

224

f u I .md } tonp .nenGf tgivi4 apte difi.Enc. , =r05'.rneaunriarymsk% is

rhich civ.s r*. sortrti.ns or r,. naruly y = 20 3! ody : 692 ' S i i eco ! , < 0 . rhecona tvdueo f i \

ar

= * ( j ) = " ' " :0 93 or r = 14.0'Thcmagnnud.ofindiqc.rhdrhe rEis.llipoldizn and rspoin. poldty \p.ilies trr rob

Q7-9 Anellipricauy.lanz.danpltuder , and., id by hc


30/48

PLAIIE.WAVE ROPACATIONN I]OSS MED!\ 225dd,y e b.tlj tnzm. whd should6 b. in od.r for rhelldiarion sbt. ro e'luc. ro ined p.la;ationlq7.10 wl'ich of.h. follNing r,o descdprions efn.sr RHCpoleian *iE: A *a!. iftid.ntulon b Dben.r:RHCpol'i&[email protected] brh.oten.r

'on(r)! a unction{ rinc in s lircd plmc p.rp.ndiculd to L5e ledion ofr3yehv.l ft (b).sa uncrion thv.l dirl@ !r a ix.d

wh*.' = . rd.' = r/d. Si@ ), s.oh!l.x, w.y - s + j P , ( 7 1 1 3 )

*hec is'Jl.Mudinn aLtlLnr of rh. mditrn.ndt is i6pr6. .onstant.By rcpttin8 ), wirh10+ Jp) jn

ta+ jpJ l= td ' -F1)+ jzs f= b1 ! t + j . ) r t t11 ts )

TlErul6of complexrkebmrcqdElheftledima8D&ypatud onesideofanequaoono b. rEpdtiv.iy eqElrothe ealandm$ndy pmson heorhe! ide.Hcncc,AERClSE7.11hc.leticI'ddolaplecwaveisgiv.trt : . , ) : i rco(or r r+ iacodor ra (v/6)>rmne ir)$.BrrrianionnaE. b)lheDodutustE,\u. (a)Linu,lb) tr = 5cos(or tJ (V/m),G)ItR6lSETl? Ir6. ele.ri. cldphasd ta ItM save. giveibyE (t tj)? r^',det.miDcrhepolaiarion{6 RHC oleialioi. (Se. a).::'E7.5 Plane-Waveropa0ationnLossyItedia

savepropeeariotrn a onducrinscdium.rhe av. equ'lior Brveny Eq. ?70).

d1 u. = .D . ! i ,2d f =o tu r "

Solvingrheser"nguahoisforo nd,sne\

! i l l , ' F , , , ,=o'nE solurionotihx *av. equalion.!d! ro

_ For a unirbm plane rav. qirl d elecric tieldE = i r.(:)ttrv.lineirrh.+.liEion,In.wmequa.rio.g'veibyF4 (7.116)Educesro

i r . r : iE,r . r : ; i r , r - = iE,t . d. . . .(? .123)

"=-l+llq'J-!ll-*-,.{+[,n6.,]f


31/48

CHAPTERT PTJNE WAVEPROPAGAIITlc sni0rd tl@cric h.ld H cd b. d.cmiEn.nhtrrr)b) apprrd3jq (757b)v ' E = t@qll,\ttbySlyirgEq.l? Ctr): || = (t ! E)/4i, wb.rt ft is h. ,.,,irsnn^p.arn .ottt Ls!n lliur, ((3)by ealog/wirhdEl6d6c6. Adyorc ofdEs,ppo.h.s Biv.s

- t 4 ( , : ) rrpF 7-?0:andudd or E rg'nnd. or;, (:) *irdnaE z.rn. sk drerh n $. !atu.orr { wni.hrE,c)l/ ,0 = "-'. o,. = 6.= r/o.Wand.d.eliedh3tinnonconducrin3edium,G. ) rinphas.u&H(:. ),bur eau* 4. racomtlerqu{nrirrrn s@nduclingmedium, e frelds o onger r\ e equaiphtuetus'lr b. rru{ra.edi Exampt, 3)FmmEq? l?l).rh.nagnnudeol trj(:)'\ ivcnb!

E , \ : ) E " e ' . ' ' = t E , , . .whnh dars.s.rponrnrirUy widrr ara na sp..iti.d bydEemajoi cotuhr d. SiE l'r = E,/a".rh.nalrtu.Lor 4 ako a{cnuar.sar?-d Tne enuarion pllE$.onv.ns panol theenersycdi.d by rheekcromgnericw!v. inrohear sa ftsuk.f conduclionn rhemediun.Thogh r dinance.= 65 u.h har

b. *ave n,eiiud. d-rcases y r tr.rd of. = 0t7compared ih ri laluear: = 0,asshowi n iis 7 2{)'Ilis disrdce 4. callcd rhe *t d.rrr' or d. n.dium,chmdcie\ ho{ $r an .tsrotrrsncric {rvecar pcn.rnt. 'nto a condu.ring .dium ln r prrerd,.r4rnc.d = o:h.nc..d = oandrhcrcfoe{ = !

"=:,@Thui. n ie spa.e pthe*?v.cmpmpag.r*irhno'n magnitudcridcdnnelyn heo.herexrsne.f L\cdiumtrJpcrftd.ondurntr,f i ' : LFeor. = o/i n& ( ' r . l 2 l a ) l e rdsbd= d lndhence l , = 0 .r colrial cabG, ii. ou&r condudor n dsrgn.n bs.v.ial rkln deprhshick. i. s.: ro prcv. (n.rnsd. th. cable iom ls*i4 ourwrd, rs s.ll ar ro.hi.gdni rhep.n.rarion otsbidr cldhoa3dic.

rh .An f ts t .n !sne 'bJ qs t2 ta l . ( r : tb ) ,(7 rr5lroru /e. nJ ! * !d'd rtr,ny tinearmmd homogene.u\.rlium f $e med,umsaFndelecbc d = 0). rhesexpresDns duc. ro h. 6sce Isaton? rl.wheErd = 0. r:t = drla-rs.? = i FrJ io$y nedrum. h. o"o / I = d/app.&s n an d.sd .rpresion! 'id ptlys .n iranr ore n derefrinin!how dsy a 'nediuh !."/t 1. h. dediumsch.turcdzd.z Eoodeohducto. n Vxnce. rheh.dium mayb. Fe l rdcd r l o l l osdLe lech. i f f ' / : ' < rO : .! s .conducrorl. /. > l0r. anda\ a qk{i..or&.ir


32/48

PL-AIVE.WA\ROPAOANONNLOSS MEDLA DIr'5.1 lou-LossDistsctrlc:nn & (?.1 7), u1i.S.i.Et.xFrssiod fd,,i, grvo by,=. ,ar( :i ) ':ranyq@rirylrl < t,rhefuErion0 r)!rcanbcaFrDrlnorsr byrhei6(*0adsofibbi'mjaj si*: $ar'l r)r/:: l r/2 ByDplyingsuchanexpansi.iEq (7 r23)forrto*,tosdiet.crri. rhJ = it,,/.,

,=* .r ; ( , - ti mrod ihaginary ds of Eq i7.t29)sive

.: .or. dlr &. exprc$i.n rbr/l is rhesaG 6 rhai 0 de. Lenumb.r I ot a losles o.djuh. Apptying nebinoDrq'poximrn (t-r-r, : (l+r/2)toF,s1 125)

( ' - ' * ): snc..heseappmrirur.xpassionsford,r,ddr.- r


33/48

223 CHAPTER] PI,ANEWAVEPROPACAI1

TrbkT,r: Elprc$nNrqo., 4. !r l(0,

f, (t'I'trr ;: ,7 ,cJ4

To iercf ineo, r. rd rc rd sea$areuatins hc ario /. . Fom rh. aBlmen! or rhecositrefumnonolH(o. ,, *e rt dE rh:td : 2n x l0r (r.dt.$ d d . r c f o f t / = l k n z H c n e .2, x lor x 30 x (10 ,/16,)

= 9 ' l 0 !Sirce. /' > l. sw!(.i is ! Eoodconduclorar I kHzrolexprts'onsgNen

"=J,.rp= \ / ; lo ix1; , lo r ' 4

/ r=d =0 126 (nd lm) .

= r ! / : . / ! . ) : : : : 0 0 ! ! . , , i .A\nou.pln inr.mrionhlh


34/48

.J CI'RRENTFLOW N ACOODCONDUCIOR 229

lr(0., = i

{(0,, =i225 t 0lco(2'xld,+ft-45) (rm).(7.116)9ymprin3& (7.135)virhE.rps3iod sivd in0rlmco(2r : 101+ s) ( t rwn) .

txEiClSET.il Ov.r ehat fr.qDercyrdsc nay dr),sil,wih rr = 3. 14 : l, dd r = l0 , is/n). b. Egd.d c. lwl6s di.lctic D.diM?As. / > 6oMH2. se a)gEno|st7.15 o. *av.bavelingn. ncdiun iinaskindaD$15,hd6ln.anpliru&of Earadtrcn.eof 6.compftd snh iB innial valueJAB. . ' : 0o5 . r5 ! t (S .e )

7-6 Cu.renllownaco0dConduclorwhenad crnlrrychconner.dacro$lheendsofcdndud1trC irc. h. cuRnt ilNing rhou8h hewir hrsaunitom cuftnr densny ovd $e *ire!cro$ srio'Thar h. J has hesame alue long rhearn or rh. s@ asllonsnsourer|eniEcr[Fi3 7 2t (a)] Ths sro tocin$ea ccar.Ass!villreshonly.rh

6-45" = 15 or 6 =60 .l.nce.'nefial*prc$ionsforEkLI)rdH(:. )ator . r )= ia { . , r l ! . cos(27r 101 0 .126 :60 . )

(mv/ml. (7 t37a)1 : . r= i looa !L r tco t i2 ' , to l o 126 :+15 . )

(hA/m). (7 37b)b, Iri d.prh r rhich $. dplitud. of Eh6 &cpsn, l16oritsinnidvaluertz0isobhinedfonr

In (o01)

ItRCjSE7.13TheconshDtiv.plmn.rdsot.oppe'ft. = !n = a r ! r 0 I (H /m) . . . o : ( r / r 6n ) : ro !: mr.rndo = 5.3x l0r(S/m) Asumingrhar!h.$pr!n.re^ @ tcqucnr) ind.pndenri ver whd tca&ncr--!e or rhe.r.dronasncric:p.chm heeFie I stnu\. t < | 0a i l0'. Hz. hich incrudfl hemd,oi.hm. rhe nfted dd vx,ble regions,an,lpd ol rhe-.nriolerresion (sa a)

ripFT 2l: crrtd deisirr i !condudrnc 'rrG)uiiromGosnscrc$s4rionindrd{cN.,bur(b) inb. &. c!s. J r h'ghes 3lo4 rhl riEf,Fii&i


35/48

2t0 CI{AP'IER? PI,ANE WA\'EPROPACAII

(o Lp.mfiially de!!'n! ri,

Iti

: t ,

nsrRT r: Erp.rtidarddy ordftni d.Niq i(.)'tuoushr) . s'ion ofvidd' 1 .rEndrnsb.'wq . = 0ud z = E is quidcrr b (b) a .osisr clE dco.

ducdng old is innntu ,r &plh ..d hd . pl.M soin.i{r.n. wirh rh. r-, ple. If .r z : 0 (Ju3irb. rufe). u r-Frrjild EM 6.ld *irh i = iriH - iEola dis6 ir rh. dFdiln abov. h. cdd@JmilalJ polcrizdEMii.l l * ill b. ioduc.din i.ing mcdiumard w;U(mnitoa ! pld. w.!. th.rilon3 rhe+ r didjon. A5 cunsgud.. ol ftecodnion nandatoe $4 rhehgcniial compon.ibco itru.useo$ rh. b.un'l!ry b.rlen any r*onsuousmedia. t = 0' (ius blow nc bounddy).lecricfi .ldorde ave r E(0)= iEo Thc '.ldsofEM *rr idj d.prh n$e.untludormLiengi!{

i i t r =i&. ' , . , , Q I

Fron' = dE,rhecuftnrflowsinrh.rdi@rion,adic)= i(.).

1\ . - .E" . -e r , - r r " ' , , i l .( ? r(7.1

Eq (? la:rne!undlen' Loa unii

n Eon rhen ,gn ' !deo fhe (u f t rd .de iInkm ofth.slind.prh , = l/ad.fi

hcvalying as. is maximum lons rheprimerer fteviernddec@$s.iponenri!llyasrtuicrioi f dhuncctowrdrh!dn olthe*ir lFi8.?-21(b)l i la.r.arverrhighfnlri.icsno!of rhccucnrno*s rhoughalhiiconddo( thecurenr frow\ .ntnely along h. surree of

BcroRw.dealwnhrh.snuanonforrwiEwirhcncu'ld.ss s.ion. lerusconsiderhe implng$n.ri] olr $ni.infiit solid. ! shownn Fig.7.2?k).T1r .on

J (.) Jo. r+,)t4 (A/ml.The.urenr .qrng ougb, Fcbn8utar\ripcxber*nzero d e in rhe dnecrionmdof drt

4nd in r i . su r& O r r )bJqh t rh5b16SLoJ ndu(tui Eq (7.ra!)onb\nr

rr


36/48

CURRENIFLOW N A C,oODCONDUCIOR 2llr ridrh u rd d.prh ,'. B@usc J,(!) d|tes .rpcErdlywirhd.prhz, icondddwirh!fi niErhick6dd b. drd inF&ri $ infiniLty dep a ldg d d k-.'al skind.prhs n .rEnr. rr' - 3rr [ind.d of 6 jn!,Dr.eElofEq (7.la2)1,\c.tr incDcd nusinsh.dk on he ighrhandide tEq.?.,42)s .s than %irn rrl = 56".h..mr isL$ ihu l9s.Ihe olhs.eos a engrh/tln.surfa..lFrg'?2(b)l

wh.E v. usd dE Eldid r, = I/u = | /J;7 ttz 6sbyEgO.l32a) ln rcrcof dEsu/@t zr!'e,c. r!. lhcd- Bi'&r.. of, slrb ofdddl u md asrh, isx = i , : = ' - ( o ) (7143)

ri = r o t = J : t

de. rhe rllpdaoce f a slabot *dh/ = r(oiinpnc.ice.d > 5r,),s

.rE 2,, rhdlch s cdled n. t !.rut d su4lu nrp-{.. ol rh. conducroisdchD.d $. impdmce lbr. ir lcngml= I m.ndaunir idn u - I m.Ihus.z.= -+ (o). (7146)

Th.cxpr$ion for rhea{ Mison* R n.quivalenrorhed-casistanc.oi ap1!ne onducror f lengrh aid cr.$'Ihecsulrsobrained.r rhe hid .ordudor rillno* be ei(e.ded tr rhe cdidl cable sho{n inFt. 7-21(a) f rh. Mduch e n!d. of copp..sithd = 5.8x r0rS/m. ]restin d.prh 3, - | U;1VA :0.066m ar I Ms4 sd iin d! vm6 6 llT. irbcomesn3lhrd hi8he' rqfsndudo( as ong rs its BdiDs tr g@tr lnan 5r5,or 0ll mm ar I MHz. rs deptb" ry b. rc8lrdedar semrnnn(e. d a smrlr cnreriotrfplles rhelni.rn*s oI rh! ouler otdudli The uRrr n.{inl

=l . tT ," , , t o^ ,

(a) co.ial cabk

G) tr EpE*i,n 'n lb) hy r prau.ondudor o.w d

T-taerh.fta!' \.pdofz. nFBintr. Z, {n bedeiincJ Sr

t Etln ikn' mm' oodrrcr

dS,-

"lt'


37/48

CHAPTR7 PLANLWAVEPROPAC.{TIrbmShrh.iDrercond(@rnconc.nhrsloniboudru.6.. dd is [email protected] d.ntd4 tlugh.|ni. Lydof d+.[ & EdcioDf.@2" Thh i. .quivd.nr b ! ploc anduh of *idrhu - 2nc,6 shornn FE.7-23(b).h.cmspon'n4cxha pq unn $h i. ohr,in bys.ftiryo = 2r .and vi'l'n8 y inE.0 ra0:

Q7.15 Comperh. fl& ofcuftn(hmqh i wire od cmdlc@s Compm Ll]. corcspondinsd< rld

7-7 EleclromagneticowerensityThis sec..i d.atr with lhe fior of powercdr.d b,

s'mr|[ry, ordr oureconducroine unetu conccn@r!l virlrina 6in lay.. oo rr rnde sudc of tnecondudoradjaccnr tne nsdabg mediunb.Neen hc *o.onducror,whi.h s wherc e EM ietd\exsr Th. Esnrmce].runir ensrhor rhe.urer oidu.lr wirh adius,

R;:= (c/n tandhe orar { rsisenc.prunr ters$n

Il s.xprcsidsillb.B.dinCfi arr.r3fdchmbitnsrherersbc.pcrunirldgrhof coaxidransnhrionline

erechnlagn.tcMve Forsywile\nhan.tecricEandmalncri.lieldI. rhe brnrins t!rr S sd.6

ItreunitofSn(v/m) x (A/m)- (w/nr).mdrtEdlof Sralongth.pmP3ganondidrionoirhersv..*.SrcpRynttheporelprunirkJtp.trerdcnsiry)cb \ d re d . x rd ' he \ re ' , mudcn rupon r :p .or are i trih oursad sudacc nr redor n.s sFi3 ? 24, lhen d. tol p.srr lnar rous .houth q'nrcNpred yrhe pcnurcs

P = \ 4 \ $ , \ h . r c s = s l

" t ^Q7,ll HwdesBof.lowidsdi.l.cdicmdiunr.onpaa b rharofa tostes nediun IQ7.t2 In aSo.d.onducror,es rhephrs.of H led orlrs rharot E andb),hownuchla7.lr alcrudrcn msn dd ! ravc to$seneBy s nprcpa3 .s in a lo$y n.dum. whar happnso rhe tojQ7.11 kacof dudi4m.diundispdveordnFBion

i \ ; * t )


38/48

1 ELECTROMACNETICO\IRDENSITY17.1 PlansWavena to$t6ss ediumi u1ctuid.r rh. riryL c ot I te *sE hElrnSr he+.ir(roo 'n.lsrt.s m.dum, 'tnE,lona E..nHtun. Th. .rpressionsor dE Dheorelaric andrsdetc fieldsof sxh a Mw @ grrcnby Eqs.0 e7s

Th.riGavdgcut@of Sisobbindbyidcgdinsov... tft pq'odI = l/f = 2rlo. rnu6.s., I / se.o r

@ / / r o . t E j . r i= , l J n 1 4 w ( h r t . d l=t? '* ' ' ' '

Th. frd of | /2 i a coN.]trene of rhe nretm.on ofes(o! - r, ov..or. p..iod

rniad!fr' aepoa.h oneurs s,. n roapplyheo.

s.,= In.rn, ii't (\vn,). rT.riri).h.-fr' nrh.co-pt.*cDij,gd.otfroae.nnrmr"rhd&. (7.t53)dfts inde.rpbvidilliisT o r') k tn*iEqs 7 5'1andb)in

s " , = l q , f - r . , . ,i 5 . . ' l: L a )='qdlrshouldbiorcd$ar.venL\oulhrhepr.cedin!demon$mio. *$ prro.mcdor6c sinlrecrf.f3 pt.newarcrav!iemalssl6!medium.tjq(? t$)ne4u lyappti_.a0r.r. atrywrk 1. any edium,ncrudinsosy medraliliri ?.9 so|aporliIf $lIilluninanon [email protected]*erdensnvor l kwmrarFdh,ssurface.ino uj,r,. oorp..

frr.r i &" r,ile.lorLhes![r ol\impti.irr qe suppresedi. phsir {p.r.npr ot Ero.OrB@th bobein anexrR$,onride aL?rd8.fn.r/.,!nof drc*a!c.s",.whichnih.:*{vec8e qlue or rhePoydr8 vrror s The arer.seiaraen{ry ft|'es.nb be po*cr tsr uqn etr.died- rhew^r. To..npure S!l.weco re r ii,nodomain-d!htrr! r'pdronJ/J nnpte' rn r . r .un r t k rn r$ !cu i .ob rL l . r b .Lh

-! iDsonr@us fia{rt cftsponrtin! ro Eqs.(7 ltr..1 b) ft givenby Eqs. 7.39aatul b)E(. , =i a,o co(o, tJ (v/,n). (7 t55a)H r ? = i a o i d - r : r i { r r . r ? r s 5 b

._.re. orsimplicn!dndwirhod o$dfsen.ntirr w.:..deteredrhephiseanCteC+ton.hcexDressionsTh.-.nrngYdof rrhenclvenby


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CHAPIERT PLANLWAVEPROPAGndiardbyd.strD,b)rbcror1lF*dinheprrdbyr,rrh..nd(c)dE.L.kicf ldolthcpo*.rd.n$yincid.ntuponElih rufENrdtr! rh{dlrh. sltiuuidio isatrsinllclftqefy.nEndiuof aln!dbneundttsun.R,, sappmxinaely 5 i l0r kn. md E?rrh\ trdSolr ionr(r) A$uningdu!h. sunGditr.s sotopically(.qDallynallddiont,rh.t@l Powtoq, ,4eh. 'herc ,(+trs th. da or a sph.ncal h.ll .rndiur ,lFis r.25(a)lrru!.

P-. = J-(4ri)= r x rd x 4' r (1s x loLr)l=23 i 10 . "

tb) wirh rer.ftm b Fk. 7-25(b), heP.*e. intrrcept.dby E!nh\ .o$ srion ,{. = n /r: $P" ,= . t , i 'R : )= I i l o r x ' i ( 633 106 ) l

= t 2s : lo r rw(c)Thrposerdensiry is elden o h. mgnitud. or.he

where. = l?7 O)torailHcncc.

s /

$d{< o.Edi$ R,. ind rb) kh5 id3a (ampk

i (z) ; , ra r ja,(,= 1 i . . ! + i t i ) ? ' r . / l

f r(J=1( ir. . +iE")." i . r , (z s

s

lE"='5t"s^ = "/t' t7 ' lo'= 37O (V/m). r

7-7.2 Plam lrvenaLossy ediumTheerF$ffi gn6byFqs (7 lzl)md(7 124)chraccriz. rhs r|{lnc .nd nagneti. fir'pols&d plam *av. prcpa8aringn a lo$y meniuh* i thapopas$m onsb t =d+ jp .3y *kndmE


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ELECTROMAGNET1COWER ENSITY

s'.,.,=1".rr h.E rc n UE ntiDsic tn!.d.M of$. )o$y nedium.\pplicaridofEq (7.I53) ives

. i ltimof th.p.wdBtio,pdicultlywh.nnw;calqtGsd P' /& @ pld.d asaimisoN ffiable ofinc6i. tr

G dBl3 l0 losC= lOto8TableTprcvid.scompd$nbers.en$hcvaluesof6-andh.cnsl.iding ratuesfo IdBl Erfl rhoushdc.'b.ls ar.denncdor po*cr .rrios. heJ-ansondimesbusldrocpftsc orh.rqurr.ic' Fdamptq tf I =vil R lhepo*erd(sipalcdinafts$or Rwirhvolbgevraco$ r atriner,, dndp, = vrrl r is rhe osq dnsipared'n he sancrilorar rimer. hen

6 r dB t =0 r o 3 ( 1 J= , n , " " t ! I \=20 tq (3 )e 3 ldB l .

*h.ft 3 = yrly,is$.rcl4.rario. N.r. th.t or vttoaet'ituadl nto\ h( lrtuJn- '\ 2o tdtttt rhuD0.*hichcsuhsin(;tdBl = stdBl

. - , ;

*(+)r\.rItrcs'ncrc r p.larfom

4. = l4.Et4 (7 6 t l

.krlf0 = I E,ilz+ f,!fli :rrhen'anrud.orirrd. = o wh.." . hc . l i 'E,zr-ar :r , r -" r *r t :!. "'. r powa d.nsity Sr ddl!&s 6 .--.. \r,1.nr q:v. pm9uaresrhegh a dhb& z = ,, = t/d, rhen3inud.s of ra elfic dd msnclc nehs &ct@ @! , : 3?% or rh.h inirial Etu.s, 'nd i6 NcE!. pow.rr : l416oriLrnniat alue17.3 DecibelScahlorPorernal iosrr unn orp.$a P n wak (w) In hxiyengineenigrnkns, rhe uMriry r nca$ h .hemrio r rwopow.r6d\,P rd P:,suchrs$eincidenrandrtnededpowe^da ansmissioroe. Dd ofr .n&e $tio PL pr ruy va9'ssrcral orde6ormagnirudehedecjbet dB)scak. roghthnic,th.rcbyprcvidinEa.dv.nierrep6.nh

("!)


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Tn ertdua re,rcVese tingrheBr. or{t@aaor$. m8niodc .'f S-(, as tuncrion t piopa8aoon

A= r obs l : = I= 3.63c: -0 tdB/nl: (dB)

we also ot thrt,sinc.S,,(r)isdrcctlyptupon'oMr!r

i = L Us l # l = : o L m 1 , L r B' ' ' t t o s 'E!it!"t-ll Pofrin4rMd irIs0hn. &ftdrirt

A submsne r deFhol 200 n trrodere signal nsmissionsarkHzDremineh.power&n'ry incid.ntupon he ubfrth. EM r.v. ofErmple 7 3.Sntnion:Fom Ermplc ?.3. ti = Ltr!. = 4.4(mvrn)., = 0.116(Ndn). nd,r.= 0014ll:lf,)Appl'carionrEq 7 I6r)siv*

s..r,r=;ff"'-,n,=, (1;4.,rt;ki),. i r,, m\15.: io . t6g orr r (mwm))

Atz = 2m m, h. incid.ntpo*.r d.nrty 6Sr =i(O 16x lO r.iE?'D)=2.' t r0 b (w,tn1 .

loft .I lnnd'ng'oL\. ul lop'igdedh.l \zlue of rh.n l i oG: (a )2 l dA . l h ) 4dB .k ) 3 6dBAns. (a) 1.11.(b)0.2,(.)0 6 (se O)

CHAPTENIOIILIGIITS

ralo (; I 'om ndudl numb6 ro dibcls G) 2 \,' \ n \ . G)36dR, (b )16dB. (c)5 2dB (See)

frERCrsr7 5 C.n!etrthefollNingv,iu.sorrhe

EltnC|st 1.17 Find h. rclug. Etio 3 'D dto.ai

A \nh.n!i lqre nd areJh), eun b{!mdproxim&ly ' un,fom plmc *!ve 'r l'JEe drt Tn. elerhc rd maSnc'tr rlds ol a r !.lmnasrcIc ( IEM) *arc ft onlqonal borhci md bo& m p.rp.ndiculd ro n. diE d

onheeleccic md muneft hclrelr'.db) rhe'nuinsic'mp.dn. wl\c polmLnon d.a riber h. !ha{r $d lcurhe p ot $. E lccior at a31verPoint n spicetuncrionoftmeThepoldzrdonn!c.Nhichmhner.Rulrr.!rcl i f l trl$emsnrudesol.nd(n.ditrerminphasb.(rh *o odhogoml omponcnbrlhe ddti.r M.dia ft cldsi6.d as losles. ld-qursiconducntre.r Emd conducringnbrsr.f ,hem,jo31. = o/or


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,ROBLEMS. Urti*. dE d< @, *h.Ein rhe cun nr iNiutlmush.wiE6disriblr.dunitdtr yrosirsc@s;srio, in dE 1{ @ m6r ot [E cuftnr isconhht d ilog.h. our.rprincrcrofdr. *irc. Pdd d.6ny cui.ti by r ple EM yrve ra!.tjn!n M Dboun.!.d nedium is atin lo rh. @.rcmi.dbyrhe ouage/cuftwveona b5misjon tine.

n0ELElts; *10n7 :W.e5rndP i rsoB- l A 4-k}]zsuid *rve hvcling ir rh.r.dneriof, in:: qasobraedrohavcadifi.rcntiatpRsuep(r ,) =\ m d J = 0 and = 25 s rl dre cferencehaeol. r.')s.12'.6ndacompldee\pAsionrorr(r., -,e:,xtr) orsoutulnann 330 rs-: Fodhepr$mewded.{nbdinExmpleT.ptorr , ( r . r t . ^6 ra r / =0! / ( r . t l " n ! r ra rJ = 0:,. {re ro ur appopnar. sales forr and $ rhat@h of!-' Pro!\ ov.n ar eanr*o cr,.l.s--r A h@onic *arc oavctinEaionga snn3 n een-:.d byanoscilhtorrharcomptcrs20 vibnrions cri.-ur. I|n n ob*rvcd nar Eivena.d.250cnin tos. harisrhe*av.t.nsrhl

h r { d .nn ( r td ,nh .!! and scittarer }t. sam. req!.ncy. ur)r(!) tcdds' h\ aphar an8le t60. Ifr ( r )= 4 .0


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233 CIIAP'IER77.ll_ Gld rso s?!6 chrrenz.d by h. fou.7' 1\ro q6 onr sting e SrEn by dE folloving

)(r., =-3cos(2or 30r)

dcs rna |.ad c las)' () $d by lhat pb& msl.?on a rrsmision line k siv.n by

r(:.r) = r. "sin(2n x lo' r .. 10I,

lheE zn lJ)e isuncen metca nm rhegeneBtorrr) Findn. trque'.r. warelen$. md phre v.llb) Arz = 2n.$.amplitudeolfteware*asm.{T.ll A dnaio.lrrum.srtic 'rv. E Eljo8 in*d.rs6ob$fl enrohrv.an6pli.!d.of 19.025(vad.trhot 0n. nd si 'mptlrM.ar 12 (v/m)dsof lm n What fte rtrenudiln cunsunruf s$ dz!

*h.rc t 6 in c.ntimr.G Tt. vlvd !e sd b intrrdcorsfrdiEly ph.n lhen suP.rportion 1):l = ll, + )!n a umum, md thcy in..rferc deshcuv.ly $hen lr.{.) wlrd c rhe dis.ions or popagarion ot *av.srbr Air = ('/s0)s.ar!hlrle!.onmrrldre mnrlucdrdy, and h a thecoft\pond-k) Ar' = ('/50)s.arsh3tlmauon'ntrrer. &inclveu ard *ha' n thecorespon'l'ns

7.3 c1ve.rpre$ionsor )(t. r) torhy.ling,lonsastrinsmrh.n.Eativc .dnerion.giEndatr"- = 20cn,I = 10cn.l = 5 Hz.and(h) ) ( r ,0 ) :0 . r t = 7 5cm7.9 Ai o$illator h s.nc{r.sasinNoidd*rv.onestins .ompler.s20 v'bra.otr in 30 s. Thc ravc plk nob*rcd rodv.l a disranc.ol2.3malons hcsting i7-l0 Itc v.tocli drsplr.ment ofa sring isEiv.nby he

) ( r , = 5 ! v ! 2 r l l n r , )

*h.r.rnrhehorTonraldnkncealonSuplos.rrinypd'cle*eEana.h.drothe tin*atr =tcn Obbinm erpresi.n fo hcvcdi.al rtlcny orrh.

7.lJ [email protected] r the ollowing omplex umud.rpE$ L\. resulr n Ehgula roml


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'. 15- complexnmbeu : , ed z1 usiv.n by rhe olz t = 1 j 2z1 : -a+ j2

r) Exp$2,mdz: npolrfomb) F.dkL bynd l'plyin8Eq (7.:1) n,l h.nbJ' p.r Debotrc rhe ,qiucr oiopolIfood D.rcmiie rb. rno:r /,:: itr pol&foim.., Dd.mine:i inpotd om'16 If. : -2 + j3, d.knine rh.folowi4qmtit.t

- l i F i i d c o m p l e i=: - a. borh n polE rom. for.ach ot &. foltNrgr : , = 2 + i s a n d r r = t - j 2. t .=31a :6d r= ! / - \'i. :t = 311! adzl = \Z:J2rr complexnuDb.E.j and r rre siven ) rhc ol

.1 :22 ! :. Dereminche oduct. :r r polI fom.' Lxre.minerheprodu.r:r.:inp.lirlomDere'mrn. heniio n /- in p.I[ tom: Ddemr.rhen.iorT.;inporrfoirn. DcrcmineJa in polar106_lo lrr = I j4,6ndthevalueorl(J'ir

ll: =l j,l.lind rhe lluc ol.:

?-2l A volbgesom. Bivenbyurc)= l0s(2r x ldr _30) (v)

r conn-t.d @a sies f,C toa'l a shownn Fie ?,9. Ilx = I MOrdC : lmpF.ob6ina.xDr.;siorfor.!(rl rhcvolr{c acGs lne clpaci@r7-22 Findrh. ph?sA ofde fattNrg.im. fundions:ral !(r) = r c.(or - n/4) (v )r l , r l t ) = l 2s i n (@,, /a r (V)(c) ,(r,4 = 4. !sin(@r n/6) (Al! (d ) r ( , )= -2co (0 r +1 , /41 (A )(e) ( )=2sin(or+n/3)+sconar /6) (a)T.I Findhensbbneousime inusoidaluncrio.s..turpondin8ro.hefollo*ingth*or

7.24 A senesRaC .ircuir isconna.Ldb aseEaror*nh avoha8.,(r = y0.onor+r/3)(v)(a) wriG rhe oh!3cep.quarionn r.ms ofth. cuftdr t r ) . r? ..c ,ud r i ( , )(br On.airrhecorsponditr!pha\.rdonain.qudion

ld solve he.goariono obraii n.xpr$ion tor te

S..ri0r .3: rcpa!.lioni LosktsM.dhT.25 Them8neric iddofa $ a\r popagrrinehou8h. ceda'n.omaSnericarsid gnrnby

H = t50co(10 ' , 5 r ) (nJm)


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710 The lardc neu ol . pbn. *rv. plopagdin8(.) nE ditu.ion of *avc proplg4ionlc) Tne *rvelengrh in lhe rot id.(d) Tn. rhriv.9.miriiviiy ofrh. naarial.(e) Tn. dcdic fi.ld ph.s.

?.26 wn& gcneral.rpr$Dnr dd..ldic andmagnetic iclds of a I GHz sinusodll plan. *aE rdv.lins i nth. + | didion in a hnes nonm+n.b. '.d'nm snhrcl!.ivepeffii(ivny.,lzedslonCrher necion.i6p.ak! ueir3V/m.andi6rbnsnyr2v/nat = ord ) = 2sh.7.27 Th..lcddr i.ld phd$rnri un rnm pl,i. !rci\pn.nbr fi = t 10.'" lv/m) Irrh.nhr{ \dm'r} or.n.*av. is L5 x 103 s and he elativeelmab,lity t&cm.diuhisA, = 2.,1,6ndhc ollo*ing:rh) The Egu.ncy / ol thewavlc) Therelatrv.pmnrirr! l$emedum(d) The osneric idd H(:. ,7.r3 The eldtric h.ld ot aplrn. wnonrogncri. .t.ridl iJ ien by

8= l i r s i n (2n i r 0 r r 04 ' r )+ i4 !on2n r l0 l o4nr ) l ( v /n )

7.29- A*avmdinedbyasur.i.anisinodenrtrpona sorlsurfre. $heeupoi r td ofilrn an and 15cn ,n ln. $il meJium,what r rhesoil\alative Fmidvnr- l Assumeh. $il rd bc v.ry ls los

lo$lc$, nomagidic. d,eleric meid wirh , =

E: i20c6(3 r x 101- tu

Sldlon7.{:W.v! P0ldlz.tioic,7.11 tu RilC pur&Ll $re U|n a muJulusaLvh)isuareli'rt, fr(.prqe'nrhunc8! rz Jiuriwnr d,. expres,oi f.. rhe ravel erechc lierdsivcn harhe adensrh is6cm.7.3? Fora{av.chmrrizdbyrhecl(rnfield

Ek. r) = i,,.G(@' r:) + td).o(.4 r: +r )id.'.iry rhc ol!n?.rion sar.mslcs),,r ),and kerchhe(a ) . . = l v /m . , , = .1v /m ,and i 0(b) ,, = :l v/m. d) = .1 /n', ud , : 130'i c ) d , = l v /m . . . = l v /m ,mdd = 45"(d ) c , = 3v /n .c , = ,1v /m .and , I l 5 '

7.13' Thccl.dri(nc|dofaunifomplme{arepedi'rCrnfreefre a greibyi = ' + ; r r : t ' ' ' ' L v i ' r

Spedfy the modulusandd,rectionorrhe elednc 6.ldr cn i r yd$c ; = 0p laneEr , 0 .5 .and0ns


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',"r A h'wly polaiz.d phtr. vrv. of $. Ioda =ir.. 11'cmh..xF.ss.dasdpsumofmRHCpo-r*d *.8 witi D.griF& ,R. ,rd m LHc polaiz.dnr. sirh n gnitud. 4 . Pift .hk sbr.mdr by fndingrrsions fomR dd aL in lms of d,'-r5 The.ladicf.ldofan.lliptcatlypoldizdtlse

E( . . ' )= t i los iD(d , [z -60 ' )+ j20 (d t , ' J ' . r l i \h )

I Th. p.ldiDrion mgtes(),. , )i, Thednclion ofrhrion'-16 Compm&.poldarion!irc\orc!.hof ln.tol.i $hk I E' = i2cond - l:) +i2sin(a, - t:){?k 2, ' = i2cos(or + lr) +t2sin(a! + la. $!Lvr E':*2co(or r:) xz\in(@r k,wav .2 t : : i 2co (d r+ r : ) - i 2s i n (d '+kz )',17 Plor e tEU: ofE(0. r forapl.newavewldr

E(r .O = isn (@r r , + i2conar+ tu )l.rmin. rhep.ldianion s!r. fiomyourplo!.r.rtri7.5:PoprortrotrrirLosydium_-13 For h of (ne ollowirycor6imnonsofpthJ.. dcrermine,fhemacnal . b{io$ dicl.dn..nLconducrorr aBtud o ucrocrftthencalculr C l r$e i ln / , = l , + = 5 .ando l0 r :S rna l

r wdd* i rh ! . = l , . i = L

7J9 Dryo nchdeEiadby., = 2.5, , = l.dd = lo_a(vn). At eeh of tne ouowing ilgurdcics,d.coir if d'y eil ro), h. mnsid.Ed a good otrduc'tq ! quasi-cDnducroi,r a Nloss di.letic, dd rh.nca lcu la r .u . r , ) .aD.andrc :

7,40 In a n.diuncha@lenad y.r = 9. t = Land' = 0. S/m, .amin. thcphle sglc bywh'.hrhemagNlch.ldleadslneelecdcneldar00Mliz7.rl Cenenre pld ro. he k,ndepih! k6N fte'tuencylorsaw rfonheftnsefromIkllzbIoGHZ(us.lo! lo! *al.t Thc.ornnutv.pand.6s ol*rtrar.ran ! . = 1 . . , = 30 ,a ido= ,1S /d7.41 lgnooDgeffeclon ar th. an{mpftdeota2 CHzincidcmslye* ov/ndlnesu aeof ! lcr soil n.dium. er rhat depd will t b. dorn roI mv/m? w.t soil is chaetnzd b

in3mar.rialk2!nar5CBzDetrnrinerhephevelmiry

men.condrlcdar MHz.nq.sdc.cmincdrh3rrheiiriniclmp.drnceolacenai.medrumisz3.rlga(o) {trfu \ljrd.prlr^5 Deremineihehllosing(a) Thc.oidurivtryorihen'are.irl(b) Tl'eslclcrg$irrhemed'um


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7,rs' TlE.l6Eiclieldofaplane*!r.prqagadn3rnandmrgndic rEdiuh n Ava bYE=t?5. {,F(z' x 10,, aor)

Obhinrh..tftgndn8 .rp,sioo fd HsdionT 6:cutrrir ld Incoidocl!E7.46 lna.onnasneri..lo$l.dLeldti.h.di'rm,al0r)MHzplh.*xye is cha.trctdzedy !h. mgnedc ield

Obbintimiomain expEsionsfor lnc.letic andmE7.4? A @rangultr.oN.r blek k l0 cm in he'ghr(!lo.S:) I. rtrporse o, sav.ltrcidem pon h! bl(kfnm rboyc, cuftnr isnduc.d r th. blck in$e posiriver diacnd. Dekmin..h. ntioorrh.l. tshhce orlneblck b i$ dr Erisdc. ar I kHz The tleunr popcniesolcopp.r e EiEn in Append'rB.t.43 TlE,id rnd oud cond*r6 of a cMral crblehav. Edii oto.5cnanl I cn. rcsp.criv.ly.Th.conducror!anr!d.orcop0.r*L$.,= l.a, = l.sdd =5 3x loiS/[email protected] cnrhic* Ar 0MHz(r) Ad 6. .onducronhick.noueha b. considerdindnnely i.r as ars $. nN of cuftn(hrcugh(b) Dcrmic rh. sudac.ftsishcc &kr Detrmine h. a. R\nhicetr Mir knsrtiofrhr

S!.llor7.7: r'l Po*er .nrity7.49 nre magftri. ieldora plane rle rev.Lng,n!nngvc iby l l = i25s in (2n l0 r r r t ) (m tn )Decm,ft dE arerascpo*t d.nnry catri.d by h. *ave

?.50 a wrv. @v.lng in a ffir3dic medlqrr = 9 i! chaadizd by d.l@ic fi.ld g'En byt J5

t = L i7.51' Theclecrdc-neldphaerofaunfomplm.hvcli4 dwnq.rd insrrs is8iH by

E= Ii 3contr lorr+ rr)- i?6(r x to?! li)l (v/d)

Dad,D. dr. diErion.r *?ve tav.l rd avt!9.

i . to. or. Dr: (v/n)

shere is rhedownw:rd idrion and = 0 s the(a) Obbitrm expresion orrheaveEce ower e(b) D.reminehe ncnuaton..(.) Dermine lhe depthar which rh. por.' dcnsity

7Jl The rnrlrud6 or m dlipticaUy tolez.drr\. h\.lrg r a losl.$. Ntrn,8netr.mdium., = 4G rrj = 61mA/n)ad,c:o = 3(mA,/n)nirc rhc,v.;se po*.rno*ins $DUAhm ap.nua a.) up lme i f i rs@3isz0n)7.51 A $1\. rsehng 'n r l6ilcs. nomrgn.ricdium h6 an .lectnc 6eld mpliode ol24 56 V/naydagc0."rr densnyol4 wmr De(eminc dE7.s.1 A' mtrruqne Equ.nres.rhep&erd(nnrysidercdsalc or huNn .rpsuR is I (nwcnr) An d , r ' e \ $ $ L q n l ' : n d e . h . h ! l d a m p h ' d d ecaysi$ dnraNe sE(n) = (r.OI/i)(vh),Ri:$cdnhncermere^.wharsthecditrsolrhc


48/48

-r5 (jonsida the ima8b..y @d8rla bor shownn1 Dchircrh.dpo*..f,u P(,).nbd4dEboxdue o ade *ar in ansiY.nby

E=iEocadd - t_v) lv/m)\L Dcrcmin.d. n.r rin. avflage owd.nrenng he

7.56 ReparProbLn 7.55 or siv. raEliry in rlssyE=itm.-j'c(?z ! loer 40)) (v/n)H=- i064 : r l co (2 r ! 101-40) 3685 . )

(A/n)Theh.r h6 dih.Gions { = I cn,, = 2 cmjand

7.sr-7.6s AddnionalSolv.dPobl.ms-compleres

t - - - -

(t) The ime lveiagc cledric cnerBr- .nsft)-1 n . " . = . 1 , , , 1 , = : I , d d ,

rbr n.rim. avemg..Eieri.nergyensny' , " t" = t l" "^tu= tt 1,, u l ,

tc) shor thar u.)., = (ui,)!.

Electromagnetics 7

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Transcript of Electromagnetics 7