Perfectly-Matched Bandstop Filters using Lossy Resonators

Transcription

1 Prfctly-Matchd Bandstp Filtrs sing ssy snatrs Andrw. ytt, Ian. Hntr, gr D. Pllard and Dglas. Jachwski Institt f Micrwavs and Phtnics, chl f Elctrnic and Elctrical Enginring, Univrsity f ds, ds, 9JT, U Micrwav Tchnlgy Branch, Elctrnics cinc and Tchnlgy Divisin, Naval sarch abratry, Washingtn, D 0375 Abstract Nrmal ralizatins f bandstp rsnatrs with finit nladd Q sffr frm dgradatin f prfrmanc d dissipatin lss. In this papr it is shwn thrtically that thr xists a class f scnd-rdr ntwrks which simltansly xhibit an idal bandstp rsnanc, with infinit stpband attnatin, and a prfct match at all frqncis. Thrtical analysis is backd p with xprimntal rslts fr thr diffrnt physical ralizatins. Indx Trms Passiv filtrs, lssy circits, ntch filtrs. I. INTODUTION Highly-slctiv filtrs ar a ncssity fr many applicatins sch as cmmnicatins transcivrs and radar systms. As filtr slctivity is limitd by th lsss assciatd with th tchnlgy sd t raliz th filtr, it is dsirabl t s dsign tchniqs which tak th ffcts f lsss int accnt. ch tchniqs incld passiv mthds sch as prdistrtin [], and activ apprachs []. Activ apprachs sffr frm isss sch as thir inhrnt nnlinarity which mak thir s fr many applicatins limitd [3]. Th prsnt wrk tilizs a passiv apprach t implmnt a narrwband bandstp filtr with thrtically infinit stpband attnatin, whil bing prfctly matchd in bth th passband and stpband. This wrk bilds pn th prfct-ntch cncpt prsntd in [] by shwing that an idntical transfr fnctin can b ralizd with lssy allpass ntwrks, which by natr ar prfctly matchd. ch ntwrks cld thrtically b placd in cascad t raliz mr advancd transfr fnctins. In this papr thry is prsntd which shws hw a lssy allpass ntwrk can b sd t raliz a prfct ntch, fllwd by a prfrmanc cmparisn t a cnvntinal rsnatr. Prttyp dsigns ar prsntd, inclding nvl dal-md vrsins. ( + )( + ) Nw if () ( + )( + ), thn 0 fr all, th ntwrk is prfctly matchd, and. (3) + If th ntwrk is lsslss thn is a ractanc fnctin: giving and N( ω) ( jω) j D ( ω) () ( ) D jn jω D + jn fr all (an allpass ntwrk). (5) () II. THEO Fig.. Evn-md admittanc f a lssy rsnant circit. A. ssy allpass ntwrks nsidr a symmtrical tw-prt ntwrk dfind by vnand dd-md admittancs and. Th -paramtrs ar thn givn by: Nw cnsidr th cas whr is a lssy rsnant circit. Fr xampl, lt p+ + (6) p /05/$0.00 () 005 IEEE

2 prt Dcmntatin Pag Frm Apprvd OMB N Pblic rprting brdn fr th cllctin f infrmatin is stimatd t avrag hr pr rspns, inclding th tim fr rviwing instrctins, sarching xisting data srcs, gathring and maintaining th data ndd, and cmplting and rviwing th cllctin f infrmatin. nd cmmnts rgarding this brdn stimat r any thr aspct f this cllctin f infrmatin, inclding sggstins fr rdcing this brdn, t Washingtn Hadqartrs rvics, Dirctrat fr Infrmatin Opratins and prts, 5 Jffrsn Davis Highway, it 0, Arlingtn VA spndnts shld b awar that ntwithstanding any thr prvisin f law, n prsn shall b sbjct t a pnalty fr failing t cmply with a cllctin f infrmatin if it ds nt display a crrntly valid OMB cntrl nmbr.. EPOT DATE JUN 005. EPOT TPE 3. DATE OVEED t TITE AND UBTITE Prfctly-Matchd Bandstp Filtrs sing ssy snatrs 5a. ONTAT NUMBE 5b. ANT NUMBE 5c. POAM EEMENT NUMBE 6. AUTHO() 5d. POJET NUMBE 5. TA NUMBE 5f. WO UNIT NUMBE 7. PEFOMIN OANIZATION NAME() AND ADDE(E) Naval sarch abratry,micrwav Tchnlgy Branch,Elctrnics cinc and Tchnlgy Divisin,Washingtn,D, PEFOMIN OANIZATION EPOT NUMBE 9. PONOIN/MONITOIN AEN NAME() AND ADDE(E) 0. PONO/MONITO AONM(). DITIBUTION/AVAIABIIT TATEMENT Apprvd fr pblic rlas; distribtin nlimitd 3. UPPEMENTA NOTE 005 IEEE MTT- Intrnatinal Micrwav ympsim Digst, -7 Jn. PONO/MONITO EPOT NUMBE(). ABTAT Nrmal ralizatins f bandstp rsnatrs with finit nladd Q sffr frm dgradatin f prfrmanc d dissipatin lss. In this papr it is shwn thrtically that thr xists a class f scnd-rdr ntwrks which simltansly xhibit an idal bandstp rsnanc, with infinit stpband attnatin, and a prfct match at all frqncis. Thrtical analysis is backd p with xprimntal rslts fr thr diffrnt physical ralizatins. 5. UBJET TEM 6. EUIT AIFIATION OF: 7. IMITATION OF ABTAT a. EPOT nclassifid b. ABTAT nclassifid c. THI PAE nclassifid am as prt (A) 8. NUMBE OF PAE 9a. NAME OF EPONIBE PEON tandard Frm 98 (v. 8-98) Prscribd by ANI td Z39-8

3 This admittanc is givn by th circit shwn in Fig.. Assming as bfr, thn and if : ( ) + ( ω ) ( + ) + ( ω ) ω ( jω) ω + Q ω ω ω ω which is th transfr fnctin f an idal lsslss bandstp rsnatr. Q is th nladd Q which is qal t Q and it may b shwn that hnc ω (7) (8) (9) 3dB ω Q ω ω (0) ω Q 3dB () Th ladd Q f th rslting band-rjct rsnatr is thrfr half f th nladd Q f th rsnatr. hwn in Fig. is a practical matchd ntch circit []. + I 0g + db ω ω + Q ω ω Th 3-dB bandwidth is: Nw lt () qal t (3): Thrfr at () + 3dB ω (3) Q ω : + Q Q () + I 0g + 7.8dB (5) That is, fr th sam nladd Q and 3-dB bandwidth as a bandstp filtr implmntd sing a lssy allpass ntwrk, th cnvntinal ntch rsnatr nly givs 7.8 db rjctin. ssy rsnatr sslss rsnatr OUT 90 Hybrid Fig. 3. nvntinal bandstp rsnatr. Effct f finit Q. III. POTOTPE DEIN IN Fig.. filtr. Hybrid circit implmntatin f a prfctly-matchd ntch B. mparisn with cnvntinal rsnatr nsidr a cnvntinal bandstp rsnatr (Fig. 3a). Th insrtin lss is givn by: Fig.. filtr. ± nralizd cpld-rsnatr mdl f a matchd ntch hwn in Fig. is a gnralizd cpld-rsnatr mdl f a prfctly-matchd ntch btaind by scaling nds f th

4 admittanc matrix f th 90º hybrid circit in Fig.. vral micrstrip circits wr dsignd basd n this mdl, th mst practical and sccssfl f which ar discssd blw. All circits ar fabricatd n grs Drid 5880 with a r f., a sbstrat thicknss f.787 mm, and a mtal thicknss f µm. ircits wr tnd sing dilctric vrlays and/r slctivly rmving mtallizatin. A. Twin-snatr Th dsign in Fig. 5a cnsists f tw paralll-cpld halfwavlngth micrstrip rsnatrs cpld t a thr-lin. Th thr-lin is dsignd t giv a 90º phas shift btwn th rsnatr cplings. Witht tning th dsign gav 5 db f rjctin. Th cntr frqncy is 956. MHz and th 3-dB bandwidth is.0 MHz. calling that th nladd Q f th rsnatrs is simply twic th ladd Q f th filtr, Q is fnd t b 59. (c) (d) Fig. 5. Twin-rsnatr ntch filtr: micrstrip prttyp (0x99 mm ) masrd rslts. B. Dal-Md ircit siz can b rdcd significantly with th s f dal-md rsnatrs. hwn in Fig. 6(a,b) ar tw dal- Fig. 6. Dal-md ntch filtrs: micrstrip ring-rsnatr prttyp (56x56 mm ) micrstrip fldd-ring rsnatr prttyp (0x0 mm ) (c) ring-rsnatr masrd rslts (d) fldd-ring rsnatr masrd rslts. md ntch dsigns. Th dsign shwn in Fig. 6a cnsists f a ring rsnatr cpld t a thr-lin. Bth indctiv and capacitiv cpling is ralizd with paralll cpling lins with intrdigital capacitrs placd 90º apart. Th cpling 3

5 btwn th tw mds f th rsnatr is cntrlld by a small stb lcatd alng th lin f symmtry. Th tnd rspns is shwn in Fig 6c. Th cntr frqncy is.009 Hz, with a 3-dB bandwidth f 9.6 MHz. Th nladd Q f th rsnatr is 08. A dsign cnsisting f a fldd ring rsnatr cpld t a thr-lin with intrdigital capacitrs is shwn in Fig. 6b. As in Fig. 6a th cpling btwn mds is cntrlld by a tning stb. Th rspns f th tnd circit is shwn in Fig. 6d. Th cntr frqncy is MHz and 3-dB bandwidth is 0.9 MHz, giving an nladd rsnatr Q f 68. pint f viw, th capacitrs in th prttyp ar rqird t cmpnsat fr th finit dirctivity f th cpld lins, which dgrads th rtrn lss. Th circit is basically an xtnsin f th travling-wav ring rsnatr mntind in [5]. IV. ONUION/FUTUE WO ssy allpass ntwrks ar sd t implmnt prfctlymatchd bandstp filtrs. lvant thry is prsntd, alng with xampl dsigns basd n a simpl cpld-rsnatr mdl. Mlti-sctin matchd ntch filtrs ar crrntly bing cnsidrd, as wll as mthds t frthr incras slctivity sch as qalizatin. EFEENE Fig. 7. Travling-wav intrprtatin f th dal-md ring rsnatr ntch. Th tw mds f th rsnatr ar xcitd 90º t f phas, rslting in a singl circlating wav.. Discssin 0º 0º 90º -70º -90º Th twin-rsnatr dsign was fnd t b th asist t tn f all th dsigns d t th lack f intrdigital capacitrs. Th simpl ring rsnatr (Fig. 6a) gav th highst val f Q. In bth dal-md dsigns nrgy is cpld int th tw mds 90º t f phas, ffctivly stting p a singl wav circlating arnd th rsnatr. This is mst bvis in th ring-rsnatr ntch (Fig. 7). At rsnanc th pwr cpld ff frm th rsnatr at th tpt is qal in pwr and 80º t-f-phas with th signal xiting th thr-lin, and a prfct ntch is prdcd. Whn apprachd frm this thrtical [] J. D. hds and I.. Hntr, "ynthsis f rflctin-md prttyp ntwrks with dissipativ circit lmnts," IEE Prc.-Micrw. Antnnas Prpag., vl., n. 6, pp. 37-, 997. [].-. hang and T. Ith, "Micrwav activ filtrs basd n cpld ngativ rsistanc mthd," IEEE Transactins n Micrwav Thry and Tchniqs, vl. 38, n., pp , 990. [3] I.. Hntr and.. handlr, "Intrmdlatin distrtin in activ micrwav filtrs," IEE Prcdings - Micrwavs, Antnnas and Prpagatin, vl. 5, n., pp. 7-, 998. [] D.. Jachwski, "Passiv nhancmnt f rsnatr Q in micrwav ntch filtrs," prsntd at Micrwav ympsim Digst, 00 IEEE MTT- Intrnatinal, 00. [5]. Matthai,. ng, and E. M. T. Jns, Micrwav Filtrs, Impdanc-Matching Ntwrks, and pling trctrs. Nrwd: Artch Hs, 980.