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Noncylindrical Helix Waveguide 1 LG. UNGER Smal uniform oformations of ern ein af hic wooed poe tie cova etic owes eighty, Brom Gere perorbtions the ited tivelar elie wae tea fa Soweto moray defame. blir wone- free, For a nunionenly formed eis seepaide Mase eqetions fre eos to pence telegraphs mpi, By a approimate fain for ema deformations, mde coer an ear clr se loon ore foe Tendon improve eh meu nveaton dt cause an aserape sean ete wae To et 8 arty itp of he tall Impede Teich the ice jute? pore tonbe bate inte. eee eaey the some ao in amar me Near BD Se the ree ele of ep Siamter donee shat ot 8 are than 4085 ok or hat an The ereenge nat move Qa 14 per ent of TP oe ew peat inc Enid Gianoser ogee pa et te By oo i Bete ace of fh ne ssi ante. Helis waveguide sumed 4F slosely wea’ insulated copper wie revo ith Jaret of dilvtvie materia! en surround by » mia tke eld ina goed transition edu for cieular lie wn Th long distance comenaratian wil Those weaves belic waves ie slums and iter, oe nex de ant pacieueay ea trae so ine opens be deren: wpoteaoas ot helis wep roe tiforent parwries wi jorket and sbild, Coreewevuling deigh Tulse ye Fs re ant “The lwo iver eerie wave in a matalic waveguide doves stouty with iezeasiay fears i HE the guide every nod ‘Tow seme i trap for che hls wivegide. a angitain tho Towtss Doprstive of tbe siren elptrie wae, the lic wasyguide mst he rinsed ta ig dere of uatdoese and us¥oray 251 ume uu svraon maniest soULNAty sasteaue NL As Tong the gid sein, i, any devigton from: roamaese ‘3 independent of distance elone the guide, increased cisculareloetne ‘nave les ths only elle of wich devatios irom roves. But if at the seme time this deviation changes with leah, the tranemission ches frcvistiss of th guide will be further degraded by mode vonverios- fecanveron forts Akay eangiof eesti sao the gle, power of the evalar elise nivel be peatenal int anand ‘nodes ud view wera Th noua! pe sainned depend a ly {on Ue nag neha a on ne ea amg Hk ff then desis eo rnd Tayo ves, dit of the walle: sameiratue Beds wage and Ua athe rani Tex wasegtidr, sl Fe aneleaed sopesasey. Ta the Girl vant erhaiesthe neral en of fhe von uve vl give spl siege, Lu i sotond 24s eraser, Maxell et ious will br corvereed nto generalized telegrapist’s equations,” en the resus appa: to be much more snvolre. Train poper ply sepresmnts nw exter on sala sylsdric metalic sasoge Tadic vige, end ply oe Te rest. of a aeons sls hid rae none rexel ‘The mathematical monk lls whi felis wal sursouming jhe strut i eprint nals ie an aeotpically eonduoting seach, Le sheath eocdets perrely sn creurferential dtetion ad hoe a miteee iopesance Z in imgiacine! dracon. eindreal eo crite syste (ype) wll ee, which r — 0 eines ith he fis of tho vide, AU prevut the suer nai ef tho gid fe Tein of only = aj + 6 a The onisatenpie elsath impos the fling tat onion aren oe "Th deviavon item the wotsinel eas ie reamed to bo small wd soe «1 wd & @ "Then the clstromngisti fle oom eoivanientiy bo represen as evr ow the i Uae wud guide of rans ey Baits 6) Wm hth Furshermore the fest.» = o ean be written i terms oth is at fag) = alone) | ante) Wet) 1 Bilas) = Bile ed | matey eles cr 6 the unperanbod ellis of seule eeesie form with By = Bae = hy = Ueto, upon ontettating m8 ito te boundary: eocision 2, a Pay pies cu Tor nse. Fhe peur in flr then hewitt in lose the urperisted bed othe etecar eerie wae Bafa + ce = cient m The benny’ coalition (8) imgwees ex adi prt fold rewvtenat on the si w Conditions 7) wie (8) soe Wo ealelate the eamplete pecurhation ft Bean” ” wt ao = vex Tite, ed eae mesial peceilviy of tho waveguide interns sie the ana equeney. 2 nie mets eveREM nuMRGERt sOLANAL, JAMA 19ED “Tho percuroation @ of tae notninalsneus fs 9 yi Fanetion af A For expansion i shtefce in ade: th Doeaspe. cy ‘Terns ith én pe have ben amie fro (10) Thay lay ad ieotialpeetartationa wih ewe laanion. Sst Fae (8) td (10) Into Ba yu, pe ay ‘Tho exprveson suggests aa expansion of che pertrtotion fells nto cms which individually setidy Maxwells equations and have the y find» depenenes of th toms n (11) Sh qld i tine ram wee Functions Py = Erma) sn 0 a (12) Tq = Lmyahe ert eo pee oe sth owing formas: hits A “ (43) jt BOT nae To oe jp = -ies a = Tm gui [191 wis Ge) fr (11) ad comparing in bis nution she efits ef woe a tin eee dy a By 32 ‘brained ay ovemusonieat noise WaPHENNDE wt Anichor relation between a sd a) ebtained by sokstituting for ea by Bn {18 ino 28 22 saline = 4 Lelithdae — 8 Ptttoans] pagsations (14) an (15) cx be soled for eg, an ar» For exuuple: ee FIT sa: Jaws Tylts) ~ SC) PT Se {With oi woe nye pnturbaion fede iculeeelciuie waves are Snows as finetione of the fy Thus the cet eral slectie waver ian ight detormed rue weaeguide can be writen in cere uf the emt weve std pertasisow Enid he propagation constr rine uneanged sad elt chin fvstner toproxitcasion Now ff [ast che effet ofa deZormainn on ‘he propugation constant aad expovinly ot a reel per, the atenine ‘ioe aoustent, which ie rset important. Orsini igher ender of Apvdmation would be reeeseey” ta devermine this atzzuatin. But hove. as a esvinssaguctie prsblems when: thr diespated egy Ie Sl cup to tho stn peopled uate, the Toss ay be Foiralaed trom a Doser order of sppinsteation? ‘the eetenuason on ant ihe ratio of power Pe disipatd per sol gs tn lhe pow aint by the wane Ps Ba Power is disinmted bythe perturbation Geld trough the anistropic shld co he wal Simple 2 neal alone the as ior rade of the ie eto fast onder cal tothe tog lg the nominal alive ay RelZ BOE ecctt ¢ ne 1H the poner Pow of the citar weetre wer woe assumed 0 be rarity Sbstienting fore rome (3) 0 117, wel meng (6), is Foun 298 me eta avare merestost JERR, FINUAEY 10ST that each Borie sonponent of te wsharisel deformation eomibutes so etal fee a- Lay, where ° MOO ee rare “This exprsshon for the adda iteular electric wave oltenvation in 9 forted lis waveguide agrees woth sore obits Any deforma toon of pce reaeive all dager rae any clreuineelecaie wave attenuation, 2) sad 6 rere hanes in diner and feanaveese di Dplacenent, respectively, af an olBerwine round. guide, The einer ‘oes ware eligi i nt hay! We her. Conceqsently a =O. Ezjuation (18) va fo bt oe apis ene. "The abelute vate in the denote ier wheneser Var shacketerie equation (GL) (0 ‘Aopenli A Fo li seco moe of pastel ender atie= fial by 8)- Whenever a mode of pth taithal onler Ia te sare topagarion conerant as she eer ovis ware, ome al 5 moy be, cauiee 9 substantial change of the normal eioaler lecse tmode teat rat ao Leger be deseo! ly The portation expreon of 8). "The propegation comstaat uf any of the arymmetric modes, to be equal tog, requreea purcly eurtive wall npedance, Beeson of fine Lom, pti sl inane value will alway be a: ast sll restive; (0s) wil therefore be valid oe al practical eas, “Worse typinal enor sstonal deviations, (18) ean be empl: ropesenss an elipsieal deformation: ea ~ Teta 9) Bg ropreent el dlr: hs omy = ae (z) ? a TE gyre (1 = 7_ypican re Waal SUNENLINOMICAL MuLLK WAVACLEDE 230 represents 9 quadufail deformetion: Retz) # en “ te. for any uli defarnetion Hore the rlativeceformaton 8 of sho vie rl: wil wo omy Be ‘asetion fp be will ho chyna wish =. Ty Appendix A Mlanws ‘naons are eeaverted ita qoverlised egeaphis' fortis structure "The deformation # is Gs seed Is hviependnt 2. The fle jn she deformed elie’ srg ane repeated in tere af norma: moder of the petfeely Tone helix Waveguie. The coke repmeseatation (or the field soroninte i ther ssinuved inte Max wets ceatatoas, With The Inlay veralitne 2) ant 8) ana en Grihoganatiy reaion between mnie? ses of the elie miveguide, 3 Ss ol sialon st ter iferecial esti: is abt, wish sores the edeprndsce ob eh sete of his ers esi Tebe cocci ease oH ey eee aeltuces cd St of forse acu Ir hal Ieeling ve of Tae tomes guide odes, then the yee of evan or Une Ae and B's ca be ween 22 a ve Hoe be a oo 9 — ine = 15 Leads = td 1c te petunia ai i mpd int Fou series (U0), them the topling elite sue dbtermined BY the ‘sens of this nurer expansion Vhs Boain 5 Sih Wa hoe Fe Choo) po aon MEM y! hs WV i "Phe mele wasryie le fins eas a the balis waseuide with evo wall inp, ‘The normal yes of the bribe see de events in TE, aid TMyy «The separation canstont 260 ma ata nscan rutaunenh souat, aenvany 161 tho raat of Fb} = O for TE. medesand the root of Fly) = 0 for 7TMy. minke, The snpling eit (2) meder bn © & @ for inter seis Utes ‘PE al TMpy mde For interaction belo {nd TE,, modes the coupling cocci are Dade he fomton ~ 93a VI ep 1a maiforas belix waveguide the coupling coasts ein (22) ave innetions ofc, "Then (22) isa evstem of tirs-order linear differential fquations wilh varying metic For sell defnemstions ad sur Seouonty stall coupling seliints, lions (2) ea he lowe iy uceesive upproaimlivas Ln imply the evpneatation, the Bs of (22) are ld nthe A. Then ene thon aleaps pate of As esnatd vith propenation comet Jka ad — jh and epg evelfcents fe ad jee Te the Une ecoue of 23} eam be replaced iy tae lek Alone, The traraoemacion An OM 251 linet conn po Oy een os 7 5 8 26 “Tho ony il vena of pase are nn £40) = 1, BU) - 0 turn ATH) wave of wai mpi lamehed na nenunifenly deformed Ix wave, A Greturr sli of (2 wale Hoe itil roi BA) = b on Bid = “The fsene ston i tiated nto (2) for seeond-onder sla and 9 on ‘Asa types! example, n TR wie wl Le lune inta a waveguide Saad, ON) Nonevnannuioal Minn WavEOUIDE on tom & betwee © = es L nl i nna Te. he sande is thus saiform exeept far to dis fein ats Oxaié #4 The wav semis any gant 2 >t sv Fram 27) are, HFS lth — AMES ate, 291 ery ete me con p woven sae arplis i mcy be epee ae ng Irom the Tne ate tio discern # = and ¢ ~The the ners a ene wash ste on) rom (29) and {31), with & = fy, forma for mode eomersion be- ‘ren eieular cette waves at dlamseter changes cbc Ba Ba Bu Sidi (2) inoe Tikewise, a forma of otis waveguide vith 3 coe eran be wstten don. [a te aso ot Z ~ 0, te Formula Arseriboe made conversion wt see ofa metalic guide: a Boy 7 TW The an ad Ve rate oarrerion i fie 88) ‘Ve, mm El, sre sonvetsion a an abitraey dive in souvent omelet "Mie ronsemvs ata ebierary aomuifrm deletion of Ue eli wave, homerer found fens (2 “The wt impossant weston vay be wed now: What deformations cen less fv heli nase echo any exossive deerdtion Cr iss TH, Cansmibsion clastitee? Uhre ane te farts rhc grade Ins TE. tenemisson: (ay denna sal nate Te “sloerns Wels waveguie, a alelated ig Section T and destibed by 108), inerewes the wera Ty teauemision Ines. (6) Nee renserson fad recuuversion in monuiform sections of hele waveguil, as cal- 212 nue meu enema mucusteat suousan, sAMUAY LOOT ula in Seetion TIE gd deserbel by (27) and (28), casse mode con terion Insel rovonvetsion Mis-tion ofthe "PRy chapter 4 Norma Mote Lowe ‘The ansmal mode los of & uniformly deformed waveeuide will be femdom fra ely wave sn eure expesiental so al Uhe Tall Teton Taras a tual ise ive fay — 1 El A madian,froeeey of the planned operating nenge i 5.5 kate. To ‘tise verioue tsaasmiesion characterise, the sucoanding jacket Jus boon ma to presont a rel wall mgedance vo the interior thet Dulf of tre spies mmpedzmes Z — J fe Hor hee values, expres has (0). 20,6 i" IN the ade evar eleirie wave love hab cralased: ita = 488, uy — O58 88, co oye) = WSN 58 [iy faethe Tape Inssee ane cows yea lita dofaesintion. Ths Ionia Ins yf pstort exper wawegtide of nr ie linet 95.5 in TTX Ur | oder thatch acto of atonsation be not zone sat 10 per eet ofthis theoretical ls, tho eliptiee! deformation should be fy <8 x 10 The clipe digoterdfecontes x 2iceh helix avg shewle net exood J mil. This is que w elit reyuiremen Tis inverting v9 eompare Une Sues with loses in w deformed alle sven ad 5 82982, sp suai. Ths metallic waved i the tefl deformation hich eases most Is, Tender thot such strife Ueormstion not ease more sha 10