Using z-variable Functions for the Analysis of Wave-based Model of Microstrip Stub-line Structure

Transcription

1 irtaaa rvia Dcmbar 9. Uig -variab Fucti fr th Aayi f av-bad d f icrtrip Stub-i Structur Biaa P. Stšić Abtract A fficit mthd bad trafr paramtr apprach i prpd t btai th cattrig paramtr i - dmai f paar micrtrip tub-i tructur. A wav digita twr DN rprt a digita md f th tructur. DN i cmpd f cacadd uifrm gmt ad thr-prt adaptr with p tub cctd t thir dpdt prt. Uifrm gmt tramii i ad tub ar rprtd by vra cacadd uit mt. A a imp mdig apprach f th -ucti dictiuity which ivv chagig i gth i giv hr. A imuati vaidati f th prpd mdig ad aayi apprach i prvidd by ma f a p -ratr circuit raid i micrtrip tchiqu. Kywrd av digita apprach wav digita twr micrtrip circuit tub-i tructur -ratr circuit - dmai fucti cattrig paramtr I. INODUCION av digita fitr DF rprt a ca f digita fitr with a particuar itrt. DF wr dvpd iitiay by Afrd Fttwi [-] i th at 96 fr digitiig umpd ctrica circuit cmpd f iductr capacitr ritr ad thr mt f caica twr thry. h DF apprach i bad th travig-wav frmuati f umpd ctrica mt. A dtaid rviw f DF thry i giv i rfrc [-5]. w thry f DF i ud fr mdig f th paar tructur. cty paar micrtrip tppd-impdac tructur ar mdd ad aayd by u f th -dimia D wav digita apprach [5-8]. h wav digita twr DN ar th md f th micrtrip tructur mdd by wav digita mt day addr mutipir ad adaptr. Aftr a xtiv arch i th itratur it wa fud a appicati f Advacd Dig Sytm ADS [9] t imuati f diffrt micrtrip tructur bad thir wav digita twr rprtati []. h quivat circuit md ca b vd thrugh a circuit imuatr. I th ca f th tub-i tructur th Ky-Lchbaum impmtati f adaptr with may mutipy mt i ud. h mai mphai f thi papr i t giv a rigia ad gra mthd t charactri th bhaviur f micrtrip tub-i tructur by u f th wav digita twr i ALAB virmt []. av digita apprach it ALAB prvid ay imuati f micrwav ayut uch a micrtrip tructur f diffrt gmtri. A aw th ur t gt th fatt rtur ut f 3D Authr i with th Uivrity f Niš Facuty f Ectric Egirig Aadra dvdva 4 8 Niš Srbia E-mai: biaa.tic@fa.i.ac.r ctmagtic t ivtmt. w-mutipy md f th thr-prt adaptr ar gig t b ud hr. h quivat rprtati f thi tructur i ALAB i much imp t prat tha th hw i []. i w th wav-bad md f tub-i tructur ar aayd dircty by u f bc-bad Simui md []. A hrt ummary f th D wav digita apprach i giv i Scti II. A wav trafr matrix apprach fr rp cacuati i dpictd i Scti III. p ca b cacuatd ithr i th frqucy r i th tim dmai dircty frm w twr fucti i -dmai [3]. h cattrig paramtr f DN S ad S ar drivd a ratia fucti f - variab. h micrtrip dictiuiti aciatd with th -pattr ratr uch a p-d ad -ucti ar cidrd i Scti IV. I Scti V a imuati vaidati f th prpd mdig ad aayi apprach i prvidd by ma f tw xamp f p -ratr circuit. II. A SHO SUAY OF D AVE DIGIAL APPOACH hi cti i itdd t rviw th mt imprtat dfiiti f th wav digita apprach i aayi f th micrtrip tub-i tructur []. ay f th imprtat rut i mdig ad aayi f micrtrip tppd-impdac tructur ar ummarid i th papr [8] i rdr t mphai thir igificac. If th cmpx tructur cmpri vra uifrm gmt ach f thm ha t b rprtd a a cacad ccti f a crtai umbr f uit mt. hi i bcau f thir day which vary frm athr. A way f dtrmiati a miima umbr f i DN f cmpx tructur i bad th giv rativ rrr a dcribd i th papr [6-8]. A prbm f apprpriat chic f a miima cti umbr i th md d t b carfuy addrd bcau f it dirct ifuc th ampig frqucy f that digita md ad accuracy f th dird rp. h am ccui ad prcdur hrty dcribd abv ca bviuy a b appid t th mdig f th tub-i tructur. h baic ida i t trat th tub-i tructur a a ccti f paratd uifrm tramii i UL gmt. h imuati f ccti btw th thr UL gmt i achivd by thr-prt para adaptr with prt big dpdt. A p tub i cctd t it dpdt prt. h DN drivd frm tub-i tructur hav firt b dfid i th papr []. 6

2 Dcmbr 9 icrwav viw UL UL A U S A B B 3 B A A B UL UL Fig.. av digita twr f a paar micrtrip tub-i tructur UL Bm U L A m hi ad t a uivra ad ffctiv prcdur capab f vig a wid rag f practica prbm. III. AVE-BASED ODEL AND IS ANSFE AVE AIX hi cti prvid cmpt thry f th trafr wav matrix apprach. h cacuatig f th cattrig paramtr f th w DN i dicud hr [3]. A paar micrtrip tub-i tructur ca b rprtd a uifrm gmt cctd i a typica way. h wav-bad md i.. wav digita twr f th paar tub-i tructur i cmpd f thr typ f buidig bc: uifrm gmt ctai vra cacadd tw-prt adaptr ad thr-prt adaptr with prt big dpdt. A DN that ctai t ad thr-prt adaptr picturd i Fig. i aayd hr. hi DN i a tw-prt circuit havig at ach prt a iput ad a utput wav variab. Each i aciatd with it day ad prt ritac at ithr prt whr.... h imuati f ccti btw th thr UL gmt f thm i a p tub cctd at dpdt prt i achivd by thr-prt para adaptr. Each thr-prt adaptr i aciatd with it cfficit ad 4... ad thr icidt A A ad A ad thr rfctd B B ad B wav whr h icidt wav A i qua t vtag U S f th urc ad th rfctd wav B m i qua t vtag U L th ad. h firt ad th at twprt ri adaptr ar ud fr matchig urc ad ad ritac t th rt f th DN. h prt impdac f i bc ar qua which ma that thy ca b dircty cacad cctd cfficit f tw-prt adaptr ar r. h trafr wav matrix fr uifrm gmt which i mdd by cacadd i whr th trafr wav matrix fr a ig i. h th thr-prt para adaptr with prt ch a dpdt prt Fig. i dcribd by t f quati B B A A B B A A B A A A A A whr th mutipir cfficit ar G G ad 3 G G G G G G ad G G ad G ar th prt cductac. A p tub i cctd t th prt big dpdt ad fr thi prt th wav variab ca b writt A B. 4 h wav trafr matrix fr th th thr-prt adaptr with a p tub cctd th dpdt prt i btaid by u f rati -4 ad it i 5a whr th matrix mt ar 5b 5c 5d ad. 5 h cmpt trafr wav matrix crrpdig t th aayd DN i a prduct f th wav matrix f twr buidig bc a 7

3 irtaaa rvia Dcmbar Cidr w th matric f tw-prt ri adaptr a fw 7 ad 8 whr adaptr cfficit ar ad 9 with th prt ritac ad aigd a hw i Fig.. h rati dictat that th matrix f uifrm gmt mdd with ca b writt i th frm whr... N. h umbr N dpd th umbr f gmt i tructur a big dd. fr big v fr N Accrdig t rati 5 th matrix f thr-prt para adaptr with a tub dpdt prt which i mdd by i giv i th frm a whr th mt f matrix ar b c d ad... N. Accrdig t th rati 6- ad du t th tta umbr f uifrm gmt th pymia ca b writt i th frm N fr v 3 r fr dd. 4 h cmpt matrix ca b rprtd i th frm N fr v 5 r N fr dd 6 whr th matrix crrpd t th at uifrm gmt i th ri brach. Fiay th cmpt wav trafr matrix du t th umbr f gmt i th tructur ca b writt i f tw frm fr v 7 r fr dd. 8 I thr wrd th mt f cmpt wav trafr matrix ca b writt i th frm f pymia 9 whr idx crrpd t v r dd umbr. h wav matrix mt ar th ratia pymia fucti f ad thy ar m m. 3 h pymia cfficit f th wav matrix mt dpd y adaptr cfficit. Accrdig t rati -3 y tw mt ad hav t b cacuatd. If cary tw thr mt ad ca b drivd frm rati ad.

4 Dcmbr 9 Prvidig A m th utput rp frward vtag tramii cfficit i B S m 4 A A m ad th iput rp iput rfcti cfficit i B S. 5 A A m IV. ODELING OF HE -JUNCION DISCONINUIY I thi cti y dictiuiti aciatd with th - pattr ratr uch a p-d ad -ucti ar cidrd. Sic dictiuity dimi ar uuay much mar tha th wavgth i a micrtrip thy ca b mdd by umpd-mt quivat ciruit. A p-d dictiuity ccur frquty i a umbr f circuit uch a ratr matchig tub fitr ad micrtrip ata. A cd frm xpri fr cacuatig th xc gth f tramii i [4] ar ud hr. O f th mt imprtat ad frquty utiid dictiuiti i micrtrip tructur i th thr-prt - ucti. It i a vry fft ud i th micrtrip circuit uch a micrtrip tub ad pwr dividr [4]. hi dictiuity i mt bviu i th rat frqucy f th tructur a a hift dwward i frqucy. Iput w UL d w UL d UL3 Fig.. Layut f a tub-i micrtrip tructur d 3 w 3 Output Cidr w a -pattr ratr dpictd i Fig.. - ucti dictiuity mut b cidrd ad cmpatd. A w mdig prcdur f th -ucti dictiuity i bad dcraig i gth. h crrcti fr - ucti ffct ar d a fw: th phyica gth f th ri i which gth i d ad width w i dcrad by th vau w i.. it i dcrad by th vau f haf f width f th tub i. h phyica gth f th tub i with gth d ad width w i dcrad by th vau w i.. it i dcrad by th vau f haf f width f th ri i. hi apprach f th mdig ffct f thi dictiuity which ivv chagig i gth i a vry imp. A it i vry accptab bcau thr ar t w bc hr. h prpd mthd rduc draticay th cmputati tim whi givig accptab accuracy. V. ESULS AND DISCUSSION icrwav viw I thi cti a imp xamp f tub-i micrtrip tructur i aayd by u f uggtd D apprach. A. Frqucy p f -ratr Circuit - Examp I A micrtrip tub-i tructur with tub -cad - ratr circuit dpictd i Fig. i ud fr vrificati f th prpd mthd. h ubtrat dictric ctat i r.3 ad th bard thic h.58 mm. -ratr circuit i apprximatd by ccti f thr uifrm gmt with paramtr giv i th ab I ad II. I rdr t abrb dictiuity ffct w i gth ar cutd. A -ucti dictiuity i mdd by dcraig gth f th i i th ucti. h ffct f th p tub i cmpatd by icraig gth f th gmt UL. Accrdig t th paramtr giv i th ab it ca b ccudd that th umbr f tramii i i th am i bth ca but thir phyica gth diffr athr ad bacu f that thir day diffr ithr. ABLE I ANSISSION LINE PAAEES IHOU ODELED DISCONINUIIES v d [mm] w [mm] Zc [Ohm] v [p] ABLE II ANSISSION LINE PAAEES IH ODELED DISCONINUIIES v d [mm] w [mm] Zc [Ohm] v [p] A miima umbr f cti fr th giv rrr ca b fud a dcribd i th papr [3]-[4]. I th ca wh th dictiuiti wr mdd fr th giv rrr _ r.% a tta miima umbr f cti i th 3 brvd DN i t 447. Fr gmt UL ad UL3 a umbr f cti i 34 ad fr gmt UL i 79. A tta day fr th digita md f th tructur i t t mi q p whr q 34 i a mutip factr ad mi mi p i a miimum day. A tta ra day f th tructur i 3 p A ampig frqucy f th digita md f th paar tructur fr th ch miima umbr f cti i F t t GH. I thi ca a rativ rrr f day i r.8457 %. Adaptr cfficit ar.5 ad

5 irtaaa rvia Dcmbar S [db] - -3 S [db] DN withut dic. DN with dic. ADS E f [GH] Fig. 3. Frqucy rp Fig. 3 hw rp f -ratr bth imuatd i ALAB by a w prpd apprach ad btaid i ADS imuatr []. h S [ db] rut ar imiar i gra. h DN rut hw y a ma diffrc f th rac frqucy i cmpari with th rut f ctrmagtic imuati i ADS. I thi tructur a umbr f uifrm gmt i dd 3 ad accrdig t that th frward vtag tramii cfficit i -dmai i S ad th utput rfcti cfficit S. h cfficit ar th ratia fucti whr th pymia i umratr ar ad th pymia i dmiatr i A prviuy tatd i th Scti III it i quit ugh t cacuat th cattrig paramtr th twr utput S ad S. Fr th magitud f th paramtr ca b writt S S ad S S. h pha charactritic diffr frm athr. B. Frqucy p f -ratr Circuit - Examp II h -ratr circuit dpictd i Fig. i ud fr vrificati f th prpd mthd. h tructur i fabricatd CuF ubtrat with dictric ctat r.7 ad width h.58 mm. h S paramtr f th tructur at th frquci frm 3 H t 6 GH ar hw i Fig. 4. h tramii -4 DN imuati withut dic. DN imuati with dic. aurd data f [GH] Fig. 4. h maurd ad imuatd tramii paramtr f th p -ratr circuit paramtr wa maurd by a twr aayr. It i imprtat t tic that th maurd data hw a ma diffrc f th rac frqucy i cmpari with th DN imuati rut DN imuati with dic. curv. hi diffrc i caud by th micrtrip -ucti ad th p-d which ar t dcribd accuraty ugh by th md. Accrdig t th prviu dicui a imp wav digita apprach ca prduc rut that ar imiar t th much mr phiticatd mthd. h imuati hwd that th dictiuiti f th -ratr tructur had a grat ffct th rac frquci. C. Cmpari f Aayi thd h brvd tub-i tructur ha b aayd i thi papr dircty i bth frqucy ad tim dmai. h prpd apprach bad wav trafr paramtr i impmtd uig ALAB a Ptium V pra cmputr pratd.4 GH. h purp f thi part i t cmpar th durati f tw rp cacuati way bad th rut f thir imuati ru. I th papr [] a vry imp bc-diagram mthd f aayi f DN i ud. Bc-bad DN i frmd dircty i th Simui tbx f th ALAB virmt. Frqucy rp i btaid by dirct aayi f frmd bc-bad twr. I that ca rut ar btaid i.65. If th twr i aayd hr dircty i th tim dmai much mr imuati tim i rquird ad a mmry prbm i vry frqut. A tim fr drawig DN i th Simui tbx dpd y ur i ad it i t giv hr. Frqucy rp frm th w twr fucti i - dmai ca b fud i tw diffrt way. h firt ca tart with th rp cacuati dircty i th tim dmai uig diffrtia quati. O th fia tag Furir trafrmati i ud fr frqucy rp cacuati. A tim f i dd fr rp cacuati. I th cd ca a tim fr a rp cacuati i th frqucy dmai dircty i.6. h rut ar hwig

6 Dcmbr 9 igificat diffrc btw th tw tim. A grat advatag f th cd rp cacuati way i it cmputatia fficicy bcau a cary cacuati ta pac dircty i th frqucy dmai. hi tudy fcu a cmpari f imuati tim. A hr th impt way fr rp cacuati i dirct aayi f DN i th frqucy dmai ad u f twr trafr fucti i -dmai. hi fucti ca aiy b btaid frm th wav trafr matrix. I that ca thr i high mmry rqut ad a vry hrt tim fr rp cacuati i rquird. VI. CONCLUSION hi papr prt m f th currt dvpmt a w a chag i appyig -variab fucti fr aayi f th wav-bad md f micrtrip tub-i tructur. hr ar vra mai ccui that ca b draw hr:. h purp f thi papr ha b t appy th thry f th wav digita fitr fr th trafr charactritic f paar micrtrip tub-i tructur. h wav digita pricip cmbid with trafr paramtr apprach ca b ud advataguy t dtrmi rp f DN. hi cmbiati i a vry fficit way fr vauatig th cattrig paramtr f DN. A imp agrithm fr cfficit cacuati wa drivd. h dcribd apprach ca b impmtd vry ffctivy i ay matrix ritd mathmatica prgram. A th tudy f dictiuiti aciatd with th -pattr ratr i a vry imprtat. h impt mdig apprach fr -ucti dictiuity ivv chagig i gth.. Cmpt wav trafr matrix prcdur ma th dig aiy appicab t a bard varity f tub-i tructur diffrt umbr f uifrm gmt i wavbad md. 3. O f th mai mpha i th autmatic aayi f wav-bad md which i ivitab wh tructur with argr umbr f buidig bc ar t b dat with. 4. A ha b td prviuy rp ca b cacuatd ithr i th frqucy r i th tim dmai dircty frm w twr fucti i -dmai. Kw twr fucti ca b ud a iput data i m thr imuati. 5. I rdr t prv th bradbad accuracy f th prpd mdig ad aayig apprach tw xamp raid i th micrtrip i tchiqu uch a p -ratr circuit ar brvd. h rut f th aayi btaid by DN hav hw a vry gd agrmt with th btaid by thr prgram mtid abv. h rut f - ratr ar cmpard with maurmt prfrmd i th frqucy rag 3 H - 6 GH. A much bttr agrmt i achivd wh th dictiuiti i th brvd tructur ar mdd. 6. A ytmatic cmpari f th durati f tw rp cacuati way bad th rut f thir imuati ru i mad. By cmpari with th bc-diagram mthd th twr fucti mthd prvid fatr tructur imuati. icrwav viw Gray th mthd prvid th fat imuati vru cmpx ad tim cumig 3D md. A a grat advatag f th uggtd twr fucti mthd i it cmputatia fficicy. 7. Impmtati f DN i aayi f micrwav tructur ca b ud by micrwav gir bcau f th aciatd impicity ad accuracy. It ca b ud fr aayig th tramii i f variu uifrm hap prt i practic. EFEENCES [] A. Fttwi Digita Circuit ad Sytm IEEE raacti Circuit ad Sytm V. CAS-3 N. Jauary 984 pp [] A. Fttwi av Digita Fitr: hry ad Practic Prc. IEEE V pp [3].K. Ch h Circuit ad Fitr Hadb CC Pr 995 av Digita Fitr pp [4].V. Gmitrvić icrwav ad av Digita Fitr Facuty f Ectric Egirig Niš 7 i Srbia. [5] B.P. Stšić Aayi f Paar icrwav Structur dd by av Digita Emt Dctra thi Facuty f Ectric Egirig Uivrity f Niš Niš Sptmbr 8 i Srbia. [6] B.P. Stšić ad.v. Gmitrvić Impmtati f av Digita d i Aayi f Arbitrary Nuifrm ramii Li icrwav ad Optica chgy Lttr V. 49 N. 9 Sptmbr 7 pp [7] B.P. Stšić ad.v. Gmitrvić Dirct Aayi f av Digita Ntwr f icrtrip Structur with Stp Dictiuiti h 7 th SEAS Itratia Cfrc Sytm Scic ad Simuati i Egirig ICOSSSE 8 Itay Vic Nvmbr -3 8 pp [8] B.P. Stšić ad.v. Gmitrvić av Digita Apprach - Diffrt Prcdur fr dig f icrtrip Stp Dictiuiti Itratia Jura f Circuit Sytm ad Siga Prcig Iu 3 Vum 8 pp [9] Advacd Dig Sftwar Agit chgi Pag i ad Pa At CA 9434 USA. [] F. aggii im Dmai Ectrica Simuati uig Equivat Digita av Ntwr i ADS ADS Ur Grup tig m ay 3 9. [] ALAB - h Laguag f chica Cmputig Vri a Fbruary 8 h athr Ic [] B.P. Stšić ad.v. Gmitrvić Bc-bad Aayi f icrtrip Structur with Stub by u f D av Digita Apprach XLIV Itratia Scitific Cfrc Ifrmati Cmmuicati ad Ergy Sytm ad chgi - ICES 9 Bugaria Vi arv Ju pp [3] B.P. Stšić ad.v. Gmitrvić A av Digita Apprach i Obtaiig -dmai Fucti fr icrtrip Stub-i Structur h 9 th Itratia Cfrc cmmuicati i dr Cab Satit ad Bradcatig Srvic - ELSIKS 9 Srbia Niš Octbr V. pp [4] P.F. Cmb J. Graffui ad J.-F. Sautrau icrwav Cmpt Dvic ad Activ Circuit Jh iy & S Nw Yr 987.