Design Formulas for Broadband Concentric Circular-Loops Antennas

Transcription

1 ADVACED ELECTROMAGETICS, VOL 4, O, JUE 25 Dsg Fomulas Boadad Coctc Ccula-Loops Atas Sam M Al Hamd * ad Ashaf A Osma 2 l Vall Uvst, Suda 2 Folsom CA, USA * cospodg autho: alhamd66@hotmalcom Astact Ths pap psts a smpl mulas dsgg oadad coctc ccula-loops atas (CCLAs) Th loop dmsos wdst adwdth a dvd ad xpssd tms of dv loop soac fquc Th aalss addsss CCLAs wth ad wthout goud plas saosth dvd mulas a usd to dsg multpl CCLAs Fo xampl, a 3-lmts CCLA of a maxmum adus of 634 cm ca dsgd to opat wth a voltag stadg wav ato (VSWR) < 2 ov th fquc ad wth factoal adwdth of 69% wth a mmum dctvt of 39 db Addoatoall, a 4-lmts CCLA of maxmum adus of 5 cm ca dsg to opat th fquc ad xtdg m 825 MHz to 99 MHz (factoal adwdth of 83%) wth a VSWR < 2 ad dctvt hgh tha 52 db ov th t ad Futhmo, th aalss shows that a 3-lmts CCLA ackd wth a coductg goud pla mpovs th factoal adwdth to 96% ad dctvt to 95 db ov th ad of tst Th aaltcal sults o dsgd atas a valdatd wth smulato sults otad usg th A-SOF ata smulato softwa A xcllt agmt s osvd tw aaltcal ad A-SOF smulatos sults Idx Tms: Aas, oadad atas, goud pla, loop atas Itoducto Th ccula loop ata has attactd xtsv sach du to ts staghtwad aalss xpaso of th cut as a Fou ss, as wll as ts smpl gomt [- 5] It s kow that th maxmum dctvt of a sgl solatd ccula loop ata s aout 45 db ad has a aow mpdac adwdth wth a flcto coffct gat tha -6dB wh th loop s fd a 5 Ω l Th dctvt ad/o voltag stadg wav ato chaactstcs of a loop ata ca mpovd usg a mult-tu loop sstm o ackg th loop wth a flctotp coductg ods Yag-Uda aa of ccula loops ca dsgd hgh dctvt tha that of a sgl loop dpdg o aa lmts um ad lmts spacg [] Such a aa of two lmts ca optmzd to gv a dctvt of 8 db [2] Rsach has show that wh ccula loop ata s ackd wth plaa flctos, th dctvt ca ach db [6,7] B S Hoo t al [8] hav show that wh stg coctc g(s) wth loop lmt, th th loop ata mpdac adwdth ca mpovd R L L t al [9] hav aalzd a dsct squa mult-loop ata sstm of lmts wh t was show that a VSWR < 2 adwdth of 6% s otad wh = 7 O th oth had, H akao t al [] dmostatd that th adwdth of ccula polazato ca sgfcatl casd wh a paastc loop s std sd a loop ata S Hamd t al [, 2] hav show that th psc of a coductg od of voluto tp flctos a a loop ata ca mpov oth ata dctvt ad VSWR Ev though xtsv sach s coductd o loop ata aas ad sstms as Yag-Uda ad log podc aas, sldom pulshd wok o coctc loop aa cofguato ca ud O 958, Schll t al [3] potd o a coctc aa of th-w loops wth th ccumfcs g multpl tgs of th wavlgth Each loop s gzd popl though fd pas appld o ach loop wh th ata was usd adato patt sthss pupos Th ado fquc dtfcato (RFID) sstms th UHF ads (84 MHz 96 MHz) hav ud a cosdal attto ctl ma sachs th vaous applcatos [4-2] Th RFID sstm cossts of a tag, ad ata, ad a pocssg ut Th dsd chaactstc of th ad ata whch plas a sgfcat ol th RFID sstm pmaca [2]: compact sz, dctoal wth hgh ga, ccula polazato, good mpdac match, as to tgat, ad low cost Futhmo, t s qud that ths chaactstcs to stal wth a wd ag of fqucs Th loop ata cofguato dmostats all of th amtod chaactstcs ad hc t ca pojctd as good caddat of a RFID ad ata Ma sachs hav potd o usg loop atas RFID sstm dsg as ad ata a-fld ad fa-fld applcatos [5-8] Th aov ltatu dcat that a pop loop ata dsg wth mult-loops sstm wth o wthout a coductg ods ca gatl hac ata adwdth ad dctvt Th ojctv of ths pap s to pst smpl mulas that ca usd to dsg a oadad CCLA Two scaos a cosdd th dscusso: ) A CCLA wthout a goud pla ad 2) A CCLA ackd wth a goud pla Gal dsg paamts oth cass a xpssd tms of a ata soac fquc Th ata chaactstcs a aalzd thotcall usg th wllkow ccula loop atas tho ad coaxal aa of ccula loop atas aalss pstd [2] Th poposd mthodolog s mplod to dsg vaous multlmt ata ad dv th chaactstcs Aaltcal sults show attactv dsgs that a sutal oadad fquc ag ad adquat uvsal UHF RFID applcatos To futh valdat th poposd tchqu, th A-SOF ata smulato s mplod to

2 poduc ata dsg chaactstcs umcall A xcllt agmt tw aaltcal ad umcal smulatos s osvd Th ata gomt ad thotcal dvlopmt a dscussd scto 2 Th dsg tchqu s pstd scto 3, ad umcal sults a dscussd scto 4 A f cocluso s povdd scto 5 2 Thotcal Dvlopmt Th gomt of th polm s show Fg Th adus of loop ( =, 2,, ) s ad ach loop s mad of a pfctl coductg th w of adus a Loop s xctd a dlta voltag souc at φ = A xp(jωt) tm covto s assumd thoughout ths pap ad s suppssd covc 2 Th Cut Dstuto ad Iput Impdac Th cut o ach loop ca xpadd Fou ss as [ - 4] = = jφ ( φ ) = I = I I cos I φ Ecg th ouda codtos o th sufac of ach loop, a sstm of la quatos a otad as Z I = V (2) Loop # # # I(φ ) I(φ ) I(φ ) V δ(φ ) x Fgu : Gomt of th polm Wh V s th xctato matx wth lmts V I s th cut coffct matx to dtmd ad ts lmts a I Z s th galzd mpdac matx Sc th loops a ccula ad coaxal, th lmts of Z ca otad usg th sam aalss as [2] ad [7] wth th lmts hghts aov x- pla a d =, ad j, wh (j =, 2,, ) Solvg (2) cut coffcts th I = z j = j V j R = (, θ, φ) =, 2, 3,, () (3) j a th lmts of th matx Y, wh ( Z ) Y (4) = Th mpdac at th put tmals of ach loop ca otad m () ad (3) as Z = I V ( φ = ) = j V j j= = 22 Th Fa-Flds ad Dctvt Th Fa-fld xpssos CCLA ca otad m that of a aa of ccula loops documtd [2] susttutg axal lmts spacg d =, th E + η cosθ θ j I s 2 β φ = = E φ η 2 + η 2 V [ J ( u ) + J ( u )] β I = + = = ( u ) + [ J ( u ) J ( u )] + J j j β I cos φ Wh β s th wav um ad u = β sθ Assum P s th put pow ad o losss, th th dctvt s 2 2 ( Eθ + Eφ ) ηp (5) (7) 2 D = (8) 3 Th Dsg Fomulas Ou goal s to pst smpl mulas that ca usd to dsg CCLA atas wth a wdst possl fquc ad VSWR< 2 Th ata s assumd to dv though o of th loops whl oths a paastc lmts, sc w a skg a smpl stuctu If th dv lmt s loop, th V = V ad V j = all j Th loops a of th ws of thckss paamts Ω = l( / a ) Ud ths codtos, (3) ad (5) spctvl, duc to ad I = V (9) j 2 = + j j Z () = Th VSWR asd o a 5 Ω l ca otad m + VSWR = ( Z 5) ( Z + 5) ( 5) ( + 5) Z Z () (6) 46

3 Th ata adwdth VSWR< 2 ca computd usg (4), () ad () 3 Th CCLA Th dsg stps th oadad CCLA ca summazd as llows: ) Th dsg stats wth a sgl soat ccula loop ata (A#) of adus Ths ata s dv 5 Ω l at th soac fquc f o Th thckss paamt th loop s Ω = ad at th soac fquc, s otad as 4) A 4-lmts CCLA (A#4) s otad addg a thd paastc loop wth adus > + to A#3 Smlal as aov, th adwdth VSWR< 2 s computd usg (9) - () A#4 as a fucto of 2 th ag > + kpg +, ad at th pvous valus wth Ω = all lmts I ths cas, th valu that gvs st adwdth A#4 s = 2 83 as cla m Fg 4 ad ca wtt as = 283c (5) + = (2) c Wh c s th spd of lght f spac 2) A paastc loop wth adus < s addd to A# to ota a 2-lmts CCLA (A#2) To dtm th valu of maxmum possl adwdth, th adwdth VSWR < 2 s computd A#2 usg (9) - () as a fucto of th ag < takg Ω = oth lmts Th vaato of adwdth agast s dsplad Fg 2 Th adus maxmum adwdth ca ud m Fg 2 as = 774 I tms of f o = 774c (3) Fgu 3: Vaato of th adwdth of a 3-lmt CCLA wth + Fgu 4: Vaato of th adwdth of a 4-lmt CCLA wth +2 Fgu 2: Vaato of th adwdth of a 2-lmt CCLA wth - 3) A scod paastc loop wth adus + > s addd to th A#2 to ota a 3-lmts CCLA (A#3) Th adwdth VSWR< 2 s -computd usg (9) - () A#3 as a fucto of + th ag + > wth Ω = all th lmts ad kpg ad at th pvous valus Th vaato of adwdth agast + s dsplad Fg 3 I ths cas, th valu + that gvs st adwdth A#3 s + = 96 as ca s m Fg 3, th + = 96c (4) 5) Mo lmts ca addd wth ad lss tha o gat tha a smla ma as 2) to 4) Howv, th st adwdth usg ths tchqu s dtmd mal th fst u lmts of ad,, +, Addtoal lmts ma usd to mpov th VSWR aoud ct fquc o cas th dctvt Th out lmt gvs adwdth > 6% th ag 9 < < 4 as show Fg4 Lag cass th sz ad dctvt of th ata So, ca adjustd accodg to th sz, dctvt, ad adwdth qumts Addg mo lmts ma mpov th dctvt wth th qud adwdth Howv, ths wll cas th sz of th ata 6) Th ct fquc of th ata ca skwd to th ght o lft scalg th dmsos of th ata to th qud fquc Th pocdu dscd th aov stps ) to 6) dcats that wh a lmt s addd ach stp, (9) () a usd to -calculat th cut dstuto, put mpdac, 47

4 VSWR ad adwdth Ths s cssa caus ths paamts dpds o th um of lmts ad th dmsos Vaous CCLAs a dsgd st adwdths usg th dsg pocdu lstd ) to 6) stps Th optmal adwdth atas wth dmsos latv to th dv lmt a summazd Tal Th adwdth = 4, 5, ad 6 lmts a al th sam as show Tal, whch dcats that th s o sgfcat mpovmt th VSWR wh xcds 4 lmts Th computd VSWR th fst fv atas Tal a plottd Fg 5 as a fucto of latv fquc f/f o Th VSWR a sgl loop s also supmposd to compa wth mult-lmt ata havo Th VSWR = 2 l s addd to Fg 5 to dcat dsd opatg ads Tal : Szs of dfft CCLA st adwdths Rad of th lmts latv to that of th BW dv lmt (/ ) wh = c /f o ad (%) Ω = -2 / - / / + / +2 / +3 / dlctc costat of ths dlctc s ε at mcowav fqucs Wh th sd of th goud pla W satsfs oth of th codtos: W > 5 ad W > 5d, wh s th adus of th out loop, t ca cosdd appoxmatl ft wth spct to th loops [7] I ths cas th mag tho ca appld ad th sstm of la quatos gov th cut coffcts (2) a Z Z ss ms Z Z sm mm I I s m + V = V (6) wh s th loops ad m mags of th loops Sc ss mm ms ms m s Z = Z, Z = Z ad I = I, th (6) ducs to ss sm s ( Z Z ) I = V (7) ss sm Th lmts of Z ad Z ca otad usg th sam pocdu llowd Z (2) wth d = d th loops ad d = d th mags Oc I s s dtmd m (7), th chaactstcs of th CCLA ackd wth a goud pla ca otad Th fa-flds compots ths cas ca otad supmposg flds m th loops ad th mags Fgu 5: Compaso of VSWR st adwdth of dfft CCLAs wth that of a sgl loop Th thckss paamt ach loop s Ω = 32 Th CCLA Backd wth a Goud Pla Wh th CCLA s ackd wth a pfctl coductg goud pla as show Fg 6, th goud pla wll affct th cut dstuto ad th ata chaactstcs W assum that th goud pla s a squa shap of sd W ad th spacg tw t ad th CCLA s d A spac of a hocom dlctc ca std tw th goud pla ad CCLA to suppot th stuctu of th ata Th Fgu 6: Gomt of th CCLA ackd wth a coductg goud pla Th fa-flds compots m th loops ad th mags 48

5 ca otad a smla ma as (6)ad (7), th CCLA aov th goud pla th fa-flds compots a H θ j s j s ( β d cosθ ) β I J ( u ) ( β d cosθ ) H φ j β I [ J ( u ) J ( u )] cos φ + jcosθ s = + = = ( β d cosθ ) [ J ( u ) + J ( u )] sφ (8) j β I (9) = = + + wh u = β sθ Th dctvt ad VSWR of th CCLA ackd wth a goud pla ca otad m (8) ad () usg (6) (9) spctvl Th aalss shows that a 3-lmts CCLA ackd wth a goud pla as show Fg 6 ca gv a oadad chaactstcs wth hgh dctvt I ths cas, th ad a 2, ad ad d s th ata hght aov th goud pla Takg as a dv lmt, th ad th st adwdth a: CCLAs a dscussd 4 CCLA Boadad UHF Applcatos Th CCLA ca dsgd fa-fld RFID applcatos as a ad ata Rfg to Fg 5, th 4-lmts CCLA gvs a factoal adwdth of 83% wth th ag 96 < f/f o <, whl 3-lmt CCLA gvs a factoal adwdth of 69% Ths atas ca dsgd to cov all th fquc ads UHF RFID applcatos, whch a xtdd m 84 MHz to 96 MHz B choosg f o = 9 MHz, th fquc ad satsfs VSWR < 2 4-lmts ata s 825 MHz < f < 99 MHz Th adus of th dv lmt at 9 MHz m (2) s = 53 cm ad th oth lmts ca computd usg (3) - (5) Th ad th dfft CCLAs th st adwdth (BW) a summazd Tal 2 wth th mmum dctvt D m ach ad Tal 2: Dfft CCLAs th UHF RFID ads D m (db) BW (MHz) Rad of th lmts cm(thckss paamt all lmts sω = ) = c, = 832, 2 = 678 d = 38 (2) Th VSWR th CCLA of dmsos gv (2) s show Fg 7 as a fucto of omalzd fquc f/f o dfft thckss paamts Th thckss paamts of th loops hav a sgfcat ffct o th VSWR ad adwdth of th CCLA as ca s m Fg 7 Small chags th thckss paamt ma sults a sgfcat adwdth vaato Fgu 8: VSWR ad dctvt of oadad CCLAs Fgu 7: VSWR 3-lmt CCLAs ackd wth a goud pla Th hght aov th pla s d = umcal Rsults Ths scto psts sults wth dscusso CCLAs th UHF ad mcowav fquc ads usg th mulato otad th pvous sctos Both th adwdth ad th adato chaactstcs dfft Th VSWR ad dctvt 2-, 3- ad 4-lmts CCLA a computd ad dsplad Fg 8 as a fucto of fquc Th sults th 3-lmts cas usg A-SOF softwa s also otad ad dsplad Fg 8 to chck th aaltcal sults Both th aaltcal sults ad that m A-SOF a xcllt agmt Futhmo, Fg 8 shows that th adwdth of th 3- ad 4-lmts atas covs th whol UHF RFID fquc ad (84-96) MHz 49

6 ad th mmum dctvts ths ad th 3-lmts ad 4-lmts atas a aout 39 db ad 52 db spctvl Th dctvt 4-lmts CCLA ca casd ov 6 db adjustg th sz of th out lmt I fact, th adus of th out lmt has a wd ag of chocs asd o th qud dctvt, ata sz, ad adwdth as show Fg 9 Moov, Fg 9 shows that, th dctvt s al stal th ad (84-96) MHz valus of xtdg m 7 cm to 22 cm Fo th ag 26 cm < < 3 cm, th dctvt at 96 MHz dcass to lss tha 3 db whl t s aov 38 db at 84 MHz Fgu 9: Th ffct of +2 o th dctvt ad adwdth of 4-lmts CCLA Fgs ad spctvl Th gal shap of th patt oth atas s smla to that of th soat sgl loop ata Howv, th am-wdth of th 3- lmts ata s wd tha that of 4-lmts Th halfpow am-wdth (HPBW) ad th maxmum dctvt (D) th wad dcto oth atas ad th dmsos a show Tal 3 Tal 3: Radato patts of 3- ad 4-lmts CCLA at 9 MHz HPBW Rad of th lmts D (db) plas (cm) φ = φ = CCLA Backd wth Goud Pla at Mcowav Fqucs Th paamts ad dmsos dsgg a 3-lmts CCLA ackd wth a ft coductg goud pla a dtmd scto 32 Rfg to Fg 7, ths ata gvs a factoal adwdth of 96% wth th ag 926 < f/f o < 22 B choosg f o = 245 GHz, th fquc ag MHz VSWR < 2 ca otad as 227 GHz < f <275 GHz Fom (2), th adus of th dv lmt at 245 GHz s =95 mm ad th oth lmts a: - =6 mm, -2 =32 mm ad d = 22 mm Th dctvt, VSWR ad th adato patt of th ata a dsplad Fgs 2 ad 3 spctvl Th sults th VSWR usg A-SOF softwa a also otad ad dsplad Fg 2 to chck th aaltcal sults Th aaltcal sults ad that m A-SOF a xcllt agmt Fgu : Radato patts of th 3-lmts CCLA at 9 MHz Fgu 2: Dctvt ad VSWR th 3-lmts CCLA ackd wth goud pla wth -2 = 32 mm, - = 6 mm, = 95 mm, d = 22 mm, ad Ω = 98 Fgu : Radato patts of th 4-lmts CCLA at 9 MHz Th adato patts at 9 MHz 3-lmts ad 4- lmts CCLA of dmso gv Tal 2 a dsplad Th CCLA ackd wth goud pla gvs a stal dctvt of aout 95 db ov th t adwdth of tst Usg th codtos dscussd scto 32, th goud pla of sd W = 265cm ca cosdd as a ft goud pla to th loops It s ovous that th adato patt of th CCLA ackd wth a goud pla to udctoal as show Fg 3 Th HPBW th pla of φ = s 779 ad th pla φ = 9 s 673 Th adwdth VSWR < 2 ad dmsos of th CCLA ackd wth a goud pla at 245 GHz ad 58 GHz a show Tal 4 5

7 Fgu 3: Radato patts th 3-lmt CCLA ackd wth goud pla wth β = ad d = 384 Tal 4: 3-Elmts CCLAs ackd wth goud plas BW f Dmsos (mm) o RAGE (GHz) (GHZ) -2 - d W Coclusos Thotcal mulatos that ca usd to dsg oadad coctc ccula-loop atas a pstd ths pap Th mulatos a mplod to dsg vaous CCLAs wth ad wthout goud plas at UHF ad mcowav fquc ads Fo th CCLAs wthout goud pla, a factoal adwdth of 83% ca otad VSWR < 2 wth dctvt hgh tha 52 db th t adwdth Th CCLA ackd wth a ft coductg goud pla ca dsgd to opat a wd ad of factoal adwdth of 96% ad dctvt of 95 db wth th t ad of tst Th A-SOF ata smulato softwa s usd to valdat aaltcal sults wh a xcllt agmt tw aaltcal ad smulatd sults s osvd Th ma fatus of th CCLAs, that th a smpl, low cost, ad ca dsgd to cov th uvsal fquc ad UHF RFID applcatos Rfcs [] G S Smth, loop atas, Ata Egg Hadook, R C Johso ad H Jask, Eds w Yok: McGaw-Hll, ch 5, 27 [2] S Ito, Iagak, ad T Skguch, Ivstgato of th aa of ccula-loop atas, IEEE Tas Atas Popagat 4: , 97 [3] R W P Kg, Th loop ata tasmsso ad cpto, I Ata Tho, Pat I, Coll, R E ad Zuck, F J w Yok: McGaw-Hll, 969 [4] R W P Kg ad G S Smth, Ata Matt: Fudamtals, Tho ad Applcatos, Camdg, MA: MIT pss, pp , 98 [5] C A Balas, Ata Tho, Aalss, ad Dsg, w Yok: Hap ad Row, ch 5, 982 [6] A Shoamash, ad L Shaf, Chaactstcs of ccula loop ata aov a losslss goud pla, IEEE Tas Atas Popagat AP-29: , 98 [7] H A Hjas, S D Gd, ad K W Wht, Effct of a ft goud pla o adatd msso of a ccula loop ata, IEEE Tas Elctomag Compat EMC-36: , 994 [8] B S Hoo, L Bugj, ad J H Facs, Mult-ad tal loop ata wth std coctc gs mol tmals, Poc, IEEE Atas ad Popagat It Smposum, pp , 27 [9] R L L, G DJa, J Laska, ad M M Ttzs Ivstgato of cculal polazd loop atas wth paastc lmt adwdth hacmt, IEEE Tas Atas Popagat AP-53: , 25 [] H akao, M Fukasawa, ad J Yamauch, Dsct multloop, modfd multloop, ad plat-loop atasmultfquc ad wd-ad VSWR chaactstcs, IEEE Tas Atas Popagat AP-5: , 22 [] S M A Hamd ad M A H Aas, Radato m a ccula loop ata placd coaxall latv to a coductg od of voluto, IEEE Tas Atas Popagat AP-6: , 22 [2] S M A Hamd ad S O Bash, Chaactstcs of a ccula loop th psc of a coaxal coductg BOR attachd to a plaa Rflcto, IEEE Atas ad Wlss Popagat Ltts 2: , 23 [3] A C Schll ad E L Bouch, A coctc loop aa, Poc WESCO, pp 22-28, 958 [4] Z Ch, X Qg ad H L Chug, A uvsal UHF RFID ad ata, IEEE Tas Mcowav Tho ad Tchqus 57: , 29 [5] X Qg, C K Goh ad Z Ch, A oadad UHF a-fld RFID ata, IEEE Tas Atas Popagat AP-58: , 2 [6] X L ad J Lao, E-shapd sgmtd ad ata a-fld UHF RFID applcatos, Pogss I Elctomagtcs Rsach 4: , 2 [7] S Fa, S Zhg, Y Ca, Y Y, Y Hu, ad J Yag, Dsg of a ovl wdad loop ata wth paastc soatos, Pogss I Elctomagtcs Rsach Ltts 37: 47-54, 23 [8] Y L, Z X ad X C, Compact loop ata a-fld ad fa-fld UHF RFID applcatos, Pogss I Elctomagtcs Rsach C 37: 7-82, 23 [9] P Wag, G W, J L, Y Huag, L Yag ad Q Zhag, Wdad cculal polazd UHF RFID ad ata wth hgh ga ad wd axal ato amwdths, Pogss I Elctomagtcs Rsach 29: , 22 [2] X La, J Ouag ad P Yag, A cculal polazd compact ata UHF ad RFID ad, Pogss I Elctomagtcs Rsach Ltts 42: 9-27, 23 [2] J Udd, M B I Raz, M A Hasa, A od, M I Iahm ad M A M Al, UHF RFID ata achtctus ad applcatos, Sctfc Rsach ad Essas 5(): 33-5, 2 5