ISSN: 78 8875 Vl., Issu, March 0 Prrmanc Micrstrip Dirctinal uplr Using Synthsis Tchniqu Vijayan T Asst. Prssr, Dpt E&I, Bharath Univrsity, hnnai-60007, India ABSTRAT: Th intrducd dsign mthd rquirs nly th inrmatin th prt impdancs, th cupling lvl, and th pratinal rquncy. Th dsign charts that giv all th physical dimnsins, including th lngth th dirctinal cuplr vrsus rquncy and dirnt cupling lvls, ar givn r alumina, Tln, RO00, FR, and RF-60, which ar widly usd in micrwav applicatins. Furthr wrk includs validatin analytical rsults using a planar lctrmagntic simulatin tl (IED) and xprimntal vriicatin. KEYWORDS: upld lins, dirctinal cuplrs, micrstrip. I. INTRODUTION Micrstrip dirctinal cuplrs hav bn cmmnly usd in micrwav systms r masuring transmittd and rlctd pwr with accuracy. Thy hav svral advantags. Such as manuacturability, Fig. Tw-lin micrstrip dirctinal cuplr rpatability, and lw cst. Extnsiv rsarch has bn cnductd n th dsign micrstrip dirctinal cuplrs du t thir widsprad applicatin. Th xisting dsign prcdurs in th litratur dpnd n knwldg th physical gmtry th dirctinal cuplr. As a rsult, availabl dsign charts giv physical dimnsins th dirctin al cuplr vrsus vn-and dd-md impdancs th dirctinal cuplr. Hwvr, in practic, th physical lngth th dirctinal cuplr is initially unknwn t th dsignr. Dsignrs hav nly inrmatin abut th prt impdancs, th rquird cupling lvl, and th pratinal rquncy at th initial stag thir dsign. Bcaus this, it is quit cumbrsm t us xisting dsign chats with n prir knwldg th gmtry th dirctinal cuplr. This rquirs svral itratins t inali th dsign.th gmtry a symmtrical micr strip dirctinal cuplr is shwn in ig.. Th mthds givn by Bryant and Wiss [] and Kirschning and Jansn [] ar amng th irst rliabl and accurat mthds t btain inrmatin n cupld micrstrip transmissin lins. Many rsarchrs usd tchniqus similar t th ns prsntd in [] and [] and studid micr strip dirctinal cuplr dsign r mr than 0 yars. Hwvr, dsign charts in th litratur giv nly th physical paramtrs th dirctinal cuplr vrsus th vn-and ddmd impdancs and, as a rsult, ar nt practically applicabl n ral applicatins. On has t us ths charts and wrk backward t btain th rquird dsign paramtrs r b dirctinal cuplrs. This is a quit tdius and inicint way digning any RF/micrwav dvic. Akhtarad tal. [] giv a dsign mthd that sms t rlct th dsign prcdur that inds an applicatin in practic. In [], th synthsis tchniqu is usd, and it has an intrmdiat stp calculating th strip width th singl micr strip lin that crrspnds t vn-and dd-md impdancs th cupld lins. Hwvr, sm critical crrctins hav t b applid t th rmulatins givn in [] t hav accurat rsults. Thr ar tw sparat crrctins rprtd by Hintn [] and Gupta tal. [5] r th wrk in []. Althugh th rrr sms t b rducd in cmparisn t th n in th riginal wrk [] with th applicatin ach crrctin, th rrr can still b mr than 0% r th lw-prmittivity matrials such as Tln and r small valus shap and spacing ratis i th crrctin in [] and [5] ar nt mplyd tgthr. W rprt that whn th crrctins in [] and [5] ar mplyd tgthr, th accuracy th rsults incrass and th rrr rducs t within pyright t IJAREEIE www.ijari.cm 76
ISSN: 78 8875 Vl., Issu, March 0 % with th xprimntal rsults, vn whn using lw-prmittivity matrials such as Tln and FR. This is rprtd by Erglu [6]. Hwvr, in [6], th mthd has nly bn applid n Tln and FR, and dsign charts and paramtrs hav nt bn givn r discussd. Dsign charts ar critical in th dsign prcss and mak it pssibl t dsign dirctinal cuplrs withut using any quatins. In additin, th mthd accuracy has nt bn vriid using dirnt dilctric matrials br. Furthrmr, th applicatin th crrctins n th rmulatins has nt bn prsntd. In this papr, a thr-stp dign prcdur with accurat clsd rmulas that giv a cmplt dsign symmtrical tw-lin micrstrip dirctinal cuplrs that includ th physical lngth at th dsird pratinal rquncy is intrducd. Our dsign prcdur rquirs knwldg th prt trminatin impdancs, th cupling lvl, and th pratinal rquncy. W als giv th dsign charts that ar mst ndd by th dsignr. Our dsign charts btaind r th iv mst ppular matrials usd in micrwav applicatins: alumina, Tln, RO00, FR, RF-60. In th dsign charts, th cupling lvl is givn vrsus th physical dimnsins th dirctinal cuplr. W als prvid dsign charts that shw th physical lngth th dirctinal cuplr l vrsus th rquncy r th givn cupling lvl. W validatd ur analytical rsults with th planar lctrmagntic (EM) simulatin tl [7] and thn xprimntally vriid thm. W shw that th rrr btwn th analytical and th simulatin rsults is rducd t b within 0.% r high-prmittivity matrials lik alumina. Th cmplt dsign a tw-lin micrstrip dirctinal cuplr can b btaind r th irst tim using ur rsults in this papr. A dsignr can us ithr th clsd-rm slutins r th dsign charts prsntd hr t hav a cmplt dsign. II. FORMULATION AND SOLUTIONS In ral wrld nginring applicatins, th physical paramtrs th dirctinal cuplrs ar unknwn t th dsignr at th bginning th dsign. Th nly inrmatin availabl t th dsignr at th bginning dsign is th prt trminatin impdancs, th cupling lvl, and th pratinal rquncy. In practic, th trminatin impdanc r ach prt th dirctinal cuplr is dsird t b 50Ω r mst applicatins. Th matchd systm is accmplishd whn th charactristic impdanc = is qual t th prt impdanc. Th xisting dsign prcdur bgins with inding th vn-and dd-md impdancs and by using th charts givn r w/ h and s / h.thn, th dsignr nds t calculat th cupling lvl and th charactristic impdanc. I it ds nt givn th dsird cupling lvl, prcdur nds t b rpatd until th spciicatins ar mt. This prcdur is quit cumbrsm. Furthrmr, thr sms t b n dsign chart availabl r th physical lngth th dirctinal cuplr. Th physical lngth th dirctinal cuplr l r cupld lins dpnds n th ctiv prmittivity cnstant ε th structur ar knwn. Th analytical mthd that is givn by Bahl [8] sms t b accurat and is adaptd in this papr t ind th physical lngth th dirctinal cuplr. In this papr, w us th mthd prpsd by Akhtarad tal. [] t btain th spacing rati s / h and th shap rati w/ h th dirctinal cuplr illustratd in Fig.. W cncurrntly apply th crrctins givn in [] and [5]. Th physical lngth th dirctinal cuplr is btaind using th mthd givn in [8]. As utlind in sctin. W assum that th prt impdancs, which ar qual and rrrd t as th rward cupling lvl, and th pratinal rquncy, ar knwn paramtrs at th bginning th dsign. Basd n th knwn paramtrs, th prpsd dsign prcdur has th llwing thr stps. Stp -Find Evn- and Odd-Md Impdancs Th vn and dd impdancs and th micrstrip cuplr givn in Fig. can b und rm = 0 0 0 0 () 0 0 0 = 0 () Whr rward cupling rquirmnt and is givn in dcibls. Stp -Find Physical Dimnsins w/ h and s / h Th physical dimnsins th dirctinal cuplr ar und using th synthsis mthd prpsd in [] and applying th crrctins givn in [] and [5]. Whn th crrctins ar mplyd, w gt th llwing quatin r th spacing rati s / h th cuplr in Fig.: pyright t IJAREEIE www.ijari.cm 76
ISSN: 78 8875 Vl., Issu, March 0 w w csh csh - - csh h s h s s h w w csh - csh h s h s w h s w h and s gmtry, rspctivly. () ar th shap ratis r th quivalnt singl cas that crrspnds t vn and dd-md w h s is mdiid trm r th shap rati and is dirnt rm th n that is givn in [] and [5] and ar dtaild blw. w h is th crrctd shap rati r th singl micrstrip lin, and it is xprssd as [] w h 8 whr 7 R r r xp r -. 0.8 R xp r -. R r R (5) s and s w h s, rspctivly. Thy givn as s (6) ar th charactristic impdancs that crrspnd t singl micrstrip shap ratis w h s s (7) w w w w s (8) s h s h h s h Th crrctd trm w h in () is givn as [5] s w w w 0.78 0. (0) h s h s h s Th updatd rmula in () givs accurat rsults r th spacing rati s h th symmtrical tw-lin micrstrip dirctinal cuplr whn usd with (). Atr th spacing rati s h r th cupld lins is und, w can prcd t ind w h r th cupld lins, as dscribd in []. Th shap rati r th cupld lins is - s w h csh d - () h whr w csh g g - d h s () s g csh () h Stp -Find th Physical Lngth th Dirctinal uplr: Th physical lngth th dirctinal cuplr is btaind using c l () 8 whr c *0 m s, and is pratinal rquncy in hrt. Hnc, th lngth th dirctinal cuplr can b und i th ctiv prmittivity cnstant can b und using th mthd dscribd in [8] as llws: (5) and ar th ctiv prmittivity cnstants th cupld structur r dd and vn mds, rspctivly. and dpnds n vn- and dd-md capacitanc and as (9) () and pyright t IJAREEIE www.ijari.cm 76
ISSN: 78 8875 Vl., Issu, March 0 (6a) (6b), is th capacitanc with air as dilctric. All th capacitancs ar givn as capacitanc pr unit lngth. ) Evn-Md apacitanc alculatin: Th vn-md capacitanc is (7) p p is th paralll plat capacitanc and is dind as w p r (8) h whr w h is und in Sctin.B. is th ringing capacitanc du t th micrstrips bing takn aln as i thy wr a singl strip, which is qual t s p - (9) c Hr, s is th ctiv prmittivity cnstant a singl strip micrstrip, which can b xprssd as r r - s - Fw h (0) whr w is givn by th llwing h w 0.0- w h Fw h h w quatin:,, r h w r h () r w A xp h 0h A tanh -0.xp.-.5 () s h s s ) Odd-Md apacitanc calculatin: Th dd-md capacitanc is p ga gd () ga is th capacitanc trm in dd md r th ringing ild acrss th gap in th air rgin. It can b writtn as K k ga (5) Kk whr K k K k ln, 0 k - k k ln - k s h k s w h h 0.5 k, 0.5 k (6) (7) k - k (8) gd rprsnts th capacitanc in dd md r th ringing ild acrss th gap in th dilctric rgin. It can b und using pyright t IJAREEIE www.ijari.cm 76
r s 0.0 gd ln cth 0.65 h s h Sinc ISSN: 78 8875 Vl., Issu, March 0 (9) r - r c (0) () c thn w can writ () c c () Substituting (7), (), (), and () in t (6) givs th vn and dd-md ctiv prmittivitis and. Whn (6) is substitutd int (5), w can ind th ctiv prmittivity cnstant th cupld structur. Nw, () can b usd t calculatd th physical lngth th dirctinal cuplr at th pratinal rquncy..6.. vs [s/h] Alumina Tln RO00 FR RF- 60 [s/h] 0.8 0.6 0. 0. Fig.. 0-0 -8-6 - - -0 upling in (db) s h vrsus cupling lvl r alumina, Tln, RO00, FR, and RF-60. TABLE DESIGN PARAMETERS OF A TWO-LINE MIROSTRIP DIRETIONAL OUPLER AT 00 MHZ FOR 50 Z O III. DESIGN HARTS In this sctin, w giv th dsign charts t btain a cmplt dsign r a tw-lin symmtrical micrstrip dirctinal cuplr r th llwing iv dirnt matrials: ) alumina; ) Tln; ) RO00; ) FR; 5) RF-60. Fig. givs th spacing rati s h th dirctinal cuplr vrsus dirnt cupling lvls. Fig. givs th shap rati th pyright t IJAREEIE www.ijari.cm 765
ISSN: 78 8875 Vl., Issu, March 0 w h vrsus dirnt cupling lvls. Fig. -8 giv th physical lngth l th dirctinal cuplr dirctinal cuplr vrsus rquncy at dirnt cupling lvls r -0dB..5 vs [w/h] Alumina Tln RO00 FR RF- 60 [w/h].5 0.5 Fig.. 0-0 -8-6 - - -0 upling (db) w h vrsus cupling lvl r alumina, Tln, RO00, FR, and RF-60. 6 x 06 5.5 Alumina Dirctinal uplr Lngth (in) 5.5.5.5 00 00 500 600 700 800 900 000 Frquncy (MH) Fig.. Dirctinal cuplr lngth l vrsus rquncy r alumina at -0(dB), cupling. 6 x 06 5.5 Tln Dirctinal uplr Lngth (in) 5.5.5.5 00 00 500 600 700 800 900 000 Frquncy (MH) Fig. 5. Dirctinal cuplr lngth l vrsus rquncy r Tln at -0(dB), cupling. 5.5 x 06 5 RO00 Dirctinal uplr Lngth (in).5.5.5 00 00 500 600 700 800 900 000 Frquncy (MH) Fig. 6. Dirctinal cuplr lngth l vrsus rquncy r RO00 at -0(dB), cupling. 5 x 06.5 FR Dirctinal uplr Lngth (in).5.5 00 00 500 600 700 800 900 000 Frquncy (MH) Fig. 7. Dirctinal cuplr lngth l vrsus rquncy r FR at -0(dB), cupling. pyright t IJAREEIE www.ijari.cm 766
ISSN: 78 8875 Vl., Issu, March 0.5 x 06 RF - 60 Dirctinal uplr Lngth (in).5.5 00 00 500 600 700 800 900 000 Frquncy (MH) Fig. 8. Dirctinal cuplr lngth l vrsus rquncy r RF-60 at -0(dB), cupling. IV.ONLUSION In this papr, a practical and cmplt mthd t hav a symmtrical tw-lin micrstrip dirctinal cuplr has bn prsntd by analytically intrducing a thr-stp dsign prcdur. Our dsign prcdur rquirs knwldg th prt trminatin impdancs, th cupling lvl, and th pratinal rquncy, which ar th thr paramtrs that ar knwn at th bginning th dsign in practic. Th dsign charts that giv th shap and spacing ratis vrsus dirnt cupling lvls r iv dirnt matrials that hav rlativ prmittivitis btwn.08 r 9.8 ar prsntd. W als giv dsign charts that shw th physical lngth th dirctinal cuplr vrsus rquncy at dirnt cupling lvls r th iv matrials. REFERENES [] Abdullah Erglu, and Jay Kyn L, Th mplt Dsign Micrstrip Dirctinal uplrs Using th Synthsis Tchniqu IEEE Transactin n instrumntatin and masurmnt, vl.57, n., Dcmbr. 008. [] T.G.Bryant and J.A.Wiss, Paramtrs micrstrip transmissin lins and cupld pairs micrstrip lins, IEEE Trans. Micrw. Thry Tch., vl. MTT-6, n., pp.0-07, Dc. 968. [] M.Kirschning and R.H.Jansn, Accurat wid-rang dsign quatins r th rquncy-dpndnt charactristic paralll cupld micrstrip lins, IEEE Trans. Mirw. Thry Tch., vl. MTT-, n., pp. 8-90. Jan. 98. [] S.Akhtarad, T.R.Rwwbtham, and P.B.Jns, Th dsign cupld micrstrip lins, IEEE Trans. Micrw. Thry Tch., vl. MTT-, n.6, pp. 86-9, Jun. 975. [5] J.J.Hintn, On dsign cupld micrstrip lins, IEEE Trans. Micrw. Thry Tch., vl. MTT-8, n., p. 7, mar. 980. [6] K..Gupta, R.Garg, and R.hadha, mputr-aidd Dsign Micrwav circuits. Nrwd, MA: Artch Hus, 98, ch.. [7] A. Erglu, Practical dsign micrstrip dirctinal cuplrs, in prc. IEEE AP-S, Jul. 9-, 006, pp. 89-85. [8] I.Bhal, Lumpd Elmnts r RF and Micrwav circuits. Nrwd, MA: Artch Hus, 00. [9] Dilctric nstant Rrnc Guid. [nlin].availabl:htpp://clipprcntrls.cm/in/dilctric_cnstants.html [0] Mat lab vrsin 7.. [] Transimmisin lins prprtis a strip n a dilctric sht n a plan, IEEE Trans. Micrwav Thry Tch., vl. MTT-5, pp. 6-67, Aug. 977. [] H.A.Whlr, Transmissin-lin prprtis paralll strips sparatd by dilctric sht, IEEE Trans. Micrwav Thry Tch., vl. MTT-, pp. 7-85, mar. 965. [] G.Plicky and H.L. Stvr, paralll-cupld lins n micrstrip, Txas instrumnts, inc, Rpt. 0-67-6. [], haractristics cupld micrstrip lins, RA Rv., vl., pp. 79-98, spt. 970. pyright t IJAREEIE www.ijari.cm 767