INVESTIGATIONS ON A NOVEL MICROWAVE TRANSMISSION LINE USING MATLAB

Transcription

1 INVSTIGATIONS ON A NOVL MICROWAV TRANSMISSION LIN USING MATLAB Q.. Pham and S. Adta School of lctrcal & lctronc ngnrng Naang Tchnologcal Unvrst Nanang Avnu Sngapor mal: SAdta@ntu.du.sg Kwords: Prntd wavgud; planar hl; prntd slowwav structur; surfac wavs; crcularl polarsd flds. Astract In ths papr a nw tp of wavgud structur has n nvstgatd. Th structur can farcatd usng prntdcrcut tchnqus. Th charactrstc quatons for th dffrnt mods of th structur hav n drvd and th dsprson charactrstcs hav n od usng MATLAB. Th slow-wav natur of th structur th cut-off havour of dffrnt mods and th ffcts of varaton n th phscal paramtrs hav n amnd. Ths wor focuss on a planar structur mplong a par of ansotropc scrns; ach scrn s prfctl conductng n on drcton and prfctl nsulatng n th prpndcular drcton. Such a scrn s calld a undrctonall conductng UC scrn. As shown n g. th structur studd hr comprss a par of paralll UC scrns. Th rgons nsd and outsd th scrns consst of dffrnt dlctrc matrals n gnral. Introducton Thr s a trnd towards us of hgh mcrowav frquncs for wrlss communcatons radar and automotv applcatons. At such hgh frquncs on can achv hgh data rats and small componnt-sz. owvr at such frquncs convntonal wavguds ar pnsv to farcat and prntd transmsson lns such as mcrostrp and coplanar wavgud suffr from radaton and surfacwav phnomna. Th man octv of ths wor s to nvstgat a nw tp of structur whch can farcatd usng prntd-crcut tchnqus and s fr from th prolm of laag through surfac-wav phnomna. gur : Smplfd modl of th structur Th structur wth ts constructonal paramtrs s shown n gur. Th dsc twn th par of scrns s. Th mda nsd and outsd th scrns hav rlatv prmttvt of ε r and ε r rspctvl. Th scrns ar confnd n th transvrs drcton. Ths confnmnt can n th form of a mtal wavgud paralll conductng plans or lctronc photonc andgap. or th cas studd hr th sparaton twn th confnng conductng plans s a. As shown n g. 3 th drctons of conducton of th two scrns ma qual and oppost angls wth th drcton of wav propagaton. In g. 3 z s th drcton of propagaton; and ar th drctons of conducton for th top and ottom scrns. gur : Structur of planar hl

2 gur 3: A par of undrctonall conductng UC scrns; z s th drcton of wav propagaton. and ar th drctons of conducton for th top and ottom scrns. A par of UC scrns s found to hav lctromagntc gudng proprts that hav consdral smlarts wth thos of a crcular hl. Thrfor ths structur s also rfrrd to as a planar hl []. Som proprts of a par of UC scrns wthout transvrs confnmnt th structur s nfnt n th transvrs drcton.. drcton n gur 3 hav n amnd n dtal. Th dsprson charactrstcs hav n word out whn th mda nsd and outsd th scrns ar dffrnt. In [] t was found that th structur wthout confnmnt has som propagatng mods that ar vr smlar to thos of a crcular hl so ths mods ar calld hl mods. Othr mods supportd th structur ar ssntall smlar to thos of a dlctrc sla gud. It was also found that th hl mods ar strongl affctd th drctons of conducton of th scrns angl whl th othr mods ar almost unaffctd. urthr th flds supportd ths structur wr found to crcularl polarsd. Th applcatons of ths structur n frrt phas shftrs [] and travllng-wav tus [3] hav n studd n som dtal. Proprts of non-radatng dlctrc sla NRD dlctrc sla wth confnmnt hav also n nvstgatd n dtal [4]. In an NRD a dlctrc sla s confnd transvrsl twn a par of conductng plans. Th spacng twn th conductng plans s pt small nough to p th domnant mod low cut-off outsd th sla. urthr th opratng mod s so slctd as to hav a low conductor loss. Th NRD has n shown to hav applcatons n a numr of wavgud componnts as wll as la-wav antnnas [5]. Th structur studd hr s pctd to hav som proprts smlar to thos of th nfnt planar hl and som proprts smlar to thos of NRD. In addton a strong advantag of th planar hl s ts potntal for farcaton on a dlctrc sustrat wth prntd-crcut tchnqus. So t has th potntal of volvng nto a nw nd of low-cost wavgudng/radatng structur for hgh mcrowav frqunc applcatons. Scton Charactrstc quatons dscrs rfl th mthod of analss and gvs th charactrstc quatons for smmtrc and ant-smmtrc solutons. Scton 3 Mthod of soluton usng MATLAB plans th mthod adoptd to solv th charactrstc quatons. Th asc da and th flow chart of th program ar gvn n ths part. Scton 4 Dsprson charactrstcs shows som of th mport rsults od n ths wor. Th dsprson charactrstcs vs. dagram ar shown. Th rsults ar compard wth th dsprson charactrstc of non-radatng dlctrc sla gud NRD. Th cut-offs of dffrnt mods ar dscussd. Th ffcts of varatons n angl of conducton and th dmnsons of th structur rato /a ar also amnd. Scton 5 mntons th conclusons of th proct. Charactrstc quatons gur 4a: Sd vw of th structur gur 4: Top vw of th structur gurs 4a and 4 dpct th sd vw and top vw of th structur rspctvl. rom Mawll s quatons all fld

3 componnts can rprsntd n trm of scalar potntals and as followng: z z ωµ ωε ϖε whr ϖµ r z z z z z 4 5 z ϖ µ ε ε ε In th aov and susqunt quatons ϖ µ ε : phas-shft const : wav-numr for fr spac : dca const n mdum : dca const n mdum : transvrs wav-numr n -drcton r 3 6 W amn two dffrnt cass: Smmtrc solutons and ant-smmtrc solutons. Smmtrc solutons: s vn wth rspct to and : In ths cas w loo for solutons that satsf: Mdum : Mdum : A sn B cos A sn cosh B cos whr snh / / nπ n3 a / / Susttuton of th aov potntals n quatons 6 lds all th fld componnts. Th fld componnts ar furthr suctd to th followng oundar condtons: z z ' ' or cos z sn cos z sn at / v ' ' or cos z sn at / Ths lads to th followng charactrstc quaton: ± a ± a / To satsf th aov condtons th scalar potntals ar chosn as followng:

4 h h s odd wth rspct to and : Smlar to th prvous cas th scalar potntals ar chosn as follow: Mdum : cosh sn snh cos B A / Mdum : / / sn cos B A / whr a n π n3 Thn from quatons -6 all th fld componnts can found. Suct to th oundar condtons mntond arlr th charactrstc quaton s found to : coth coth Ant-Smmtrc solutons: In ths cas w hav two solutons: s vn wth rspct to and odd wth rspct to s odd wth rspct to and vn wth rspct to Th procdur to fnd th charactrstc quatons s vr smlar to th mthod adoptd to fnd th charactrstc quatons for th smmtrc cas. Ths solutons can od from smmtrc quatons wth a mnor modfcaton. 3 Mthod of soluton usng MATLAB Th man MATLAB functon mplod n ths proct s fsolv of th Optmsaton Toolo. In th charactrstc quatons all th varals can normalzd multplng thm wth a factor of /. Thn for ach valu of normalzd frqunc / w fnd out th possl solutons for normalzd dca const for mdum /; ths lads to th dffrnt valus of th normalzd phas const /. Thrfor dffrnt mods can found. To fnd out dffrnt solutons for ach valu of / th fsolv functon s usd wth dffrnt ntal gusss. Th graphc capalt n MATLAB s hlpful n fndng out dffrnt ntal gusss for fsolv functon. Durng th procss of root fndng somtms w nd to fnd th compl roots of th charactrstc quaton. Snc fsolv functon dos not hav th capalt to rturn compl root w hav to sparat ral and magnar parts of th quaton. B solvng ths two quatons smulousl compl roots can dtrmnd. Lt γ th quaton w hav to solv. W nd to fnd th compl soluton n th form: γ. Thn w hav: γ whr ] Im[ ] R[ rom w hav: B solvng and smulousl usng fsolv functon th compl root γ can found. 4 Dsprson charactrstcs 4. or 3 /a.5 ε r ε r.55 th dsprson charactrstcs of th confnd planar hl for th smmtrc solutons ar shown n gur 5.

5 od analtcall snc th charactrstc quaton s complcatd. gur 5: Dsprson charactrstc of confnd planar hl wth 3 /a.5 ε r ε r.55 As can sn from gur 5 a numr of mods can propagat n th structur. Thr ar ssntall two tps of mods: hl mods and wavgud mods. As can sn all th wavgud mods ar constrand low th straght ln ε r whl th hl mods ar not. l mods ar strongl affctd th angl of conducton of th UC scrns as shown latr. 4. Comparson wth NRD non-radatng dlctrc sla gud dsprson charactrstc gur 7a: Normalzd vs. gur 7: Normalzd vs. gur 6: Dsprson charactrstc of NRD wth /a.5 ε r ε r.55 gur 6 shows th dsprson charactrstcs of NRD gud wth /a.5 ε r ε r.55 whch ar th sam as for th confnd planar hl shown n gur 5. As can sn from gurs 5 and 6 th wavgud mods of th confnd planar hl ar almost th sam as th propagaton mods of NRD. Th onl dffrnc s that n confnd planar hl thr do st som spcal mods whch ar calld hl mods whch th NRD dos not hav. 4.3 Cut-off frquncs of dffrnt mods: As can sn from dsprson charactrstcs of th confnd planar hl gur 5 ach mod has a cr cut-off frqunc. Ths cut-off frquncs ma not asl gurs 7a and 7 show vs and vs for th confnd planar hl wth 3 /a.5 ε r ε r.55 rspctvl. rom ths plots w can prdct th cutoff condtons for dffrnt mods. or th hl mods th cut-off occurs whn and approach zro. Both and ar ral for ths mods. or wavgud mods cut-off occurs whn coms. In ths cas s magnar and rmans almost const ovr th whol rang of frqunc ffcts of varatons n /a gur 8 shows th dsprson charactrstcs of th confnd planar hl wth all th paramtrs th sam as th prvous cas cpt that th angl of conducton s changd to. As can sn all th hl mods chang trmndousl whl th wavgud mods rman almost th sam. Thrfor w can conclud that th angl of conducton of th UC scrns has a strong ffct on th hl mods of

6 as that of. In ths two cass th rato /a s rlatvl small. So th wavgud mods ar almost th sam for dffrnt valus of n. And for th hl mods VN and ODD solutons ar almost dntcal spcall at hgh frqunc. 5 Concluson gur 8: Dsprson charactrstc of confnd planar hl wth /a.5 ε r ε r.55 propagaton ut has vr lttl ffct on th wavgud mods. So n ths rspct th structur studd hr a confnd par of UC scrns s smlar to a hl. That s th rason wh t s calld confnd planar hl. In ths papr a nw nd of wavgud structur has n nvstgatd. Its dsprson charactrstcs ar amnd to fnd out th possl mods of propagaton and thr cut-off havour. A consdral smlart wth a hl and NRD has n rought out clarl. Ths proprts togthr wth ts strong advantag n farcaton ar pctd to ma th structur popular. Th structur has th potntal to volv nto a nw nd of prntd wav-gud structur for hgh mcrowav frquncs. urthr nvstgatons wll carrd out n futur wth rspct to th natur of th flds loss charactrstcs frqunc rang for sngl-mod propagaton ctaton tc. Rfrncs gur 9: Dsprson charactrstc of confnd planar hl wth 3 /a. ε r ε r.55 [] R. K. Arora B. Bhat and Shl Adta Gudd wavs on a flattnd shath-hl I Trans. vol. MTT-5 pp. 7-7 Jan [] Shl Adta and R. K. Arora Non-rcprocal dsprson charactrstcs of a planar hl on magntsd frrt slas I Trans. vol. MTT-7 pp Oct [3] D. Chadha Shl Adta and R. K. Arora ld thor of planar hl TWT I Trans. vol. MTT-3 pp Jan [4] T. Yonama Nonradatng Dlctrc Wavgud Ch. n K. J. Button d. Infrard and mllmtr wavs Acadmc Prss Nw Yor volum 979. [5] A. A. Olnr La-wav antnnas Ch. n R. C. Johnson d. Antnna ngnrng andoo 3 rd d. N.Y.: McGraw-ll 993. gur : Dsprson charactrstc of confnd planar hl wth /a. ε r ε r.55 gurs 9 and show th rsults for th frst fw mods for th cas /a. for dffrnt valus of th angl. As can sn th varaton of /a changs th dsprson charactrstcs to som tnt ut th chang s not as strong