Development of widebnd circulrl polrised squre- nd rectngulr-loop ntenns R.L. Li, S. Bst, A. Trille, J. Lskr nd M.M. Tenteris Abstrct: New tpes of widebnd circulrl polrised (CP) squre- nd rectngulr-loop ntenns re developed nd discussed. It is shown tht the bndwidth for circulr polristion of loop ntenn cn be significntl incresed b dding prsitic loop inside the originl loop. The ddition of the prsitic element cn crete one more minimum il rtio (AR) point, which cn ppropritel combine with the originl one, leding to significnt enhncement for the AR bndwidth. It is found tht the AR ( r db) bndwidth of squre-loop ntenn cn be incresed from.% to % b dding prsitic squre loop. B replcing the squre loop with rectngulr loop, the AR bndwidth cn be further enhnced. For rectngulr loop with n spect rtio of /, bndwidth of nerl % for AR r dbisobtinedwithginof.-. dbi. A brodbnd blun is introduced for impednce mtching. Introduction Squre- nd rectngulr-loop ntenns re usull used s linerl polrised ntenns [ ]. In recent ers, it hs been found tht squre- or rectngulr-loop ntenn cn lso rdite circulrl polrised (CP) wve if gp is introduced on the loop [, ]. The reson for the CP rdition is due to the trvelling-wve current distribution tht becomes ecited long the loop. An importnt feture of this tpe of CP ntenns is tht the sense oirculr polristion cn be esil switched from left-hnd to righthnd, nd vice vers, b ltering the gp positions [] using rdio-frequenc (RF) switches such s microelectromechnicl sstems (MEMS) [], optoelectronic switches [], or PIN diodes []. Although it is possible for rectngulrloop ntenn to chieve bndwidth close to % for n il rtio (AR) of less thn db [], the bndwidths of squre- nd rectngulr-loop ntenns re still much less thn those chieved b spirl ntenns []. In this pper, it will be shown tht the AR bndwidth of CP squre- or rectngulr-loop ntenn cn be incresed significntl b dding prsitic loop (lso with gp) inside the originl loop. The ddition of the prsitic element cn result in two minimum AR points tht (b n pproprite combintion) led to considerble enhncement for the AR bndwidth. As the dditionl prsitic element is plced inside the originl loop nd there is no direct electricl connection to its surroundings, there is no significnt increse in the sie nd compleit of the ntenn structure. r The Institution of Engineering nd Technolog IEE Proceedings online no. doi:./ip-mp: Pper first received th Februr nd in revised form th June The uthors re with the Georgi Electronic Design Center, School of Electricl nd Computer Engineering, Georgi Institute of Technolog, Atlnt, GA -, USA E-mil: rlli@ece.gtech.edu Widebnd squre-loop ntenns We begin the development of widebnd CP squre-loop ntenns with single squre loop. Figure shows squre wire loop plced bove ground plne t height h. The length of one side of the squre loop is ¼.l nd thewirerdiusisr ¼.l,wherel is the free-spce wvelength t reference frequenc f. The squre loop is driven in the middle of one side b voltge source V ( ¼ volt). To produce CP wves, smll gp (the gp width Ds ¼.l ) needs to be introduced on the loop []. The gp position nd the height h cn be djusted for n optiml on-is (i.e. in the direction) AR performnce. B numericl simultion, it ws found tht the optimised gp position should be t one of the two corners nerb the driving point. For emple, gp t the right corner corresponds to left-hnd circulr polristion (LHCP). The sense oirculr polristion cn be switched from the LHCP to right-hnd circulr polristion (RHCP) b chnging the gp position from the right corner to the left corner. Figure presents the simulted results of the on-is AR s the height h bove the ground plne vries. (Note tht lmost ll results shown in Sections nd were obtined b numericl simultion using NEC., method-ofmoment (MoM) bsed softwre.) The optimised height is found to be h ¼.l, which corresponds to minimum AR close to db t f. It is noted tht the bndwidth for AR r db of the single squre-loop ntenn is onl bout.%. The AR bndwidth of squre loop cn be enhnced b dding prsitic element ( concentric squre loop with gp) inside the driven element (see Fig. b). Although loop ntenn with prsitic element hs been investigted before [], the bndwidth for circulr polristion ws not significntl improved. Here, the purpose for the ddition of prsitic squre loop is to introduce new minimum AR point. B djusting the sie of the prsitic loop nd the position of its gp, it is possible to move the new minimum AR point (due to the prsitic loop) close to the originl IEE Proc.-Microw. Antenns Propg., Vol., No., June
r il rtio, db h =.λ h =.λ h =.λ ~ V r..... r ~ V s prsitic loop driven loop b Fig. Ail rtio of squre-loop ntenn for different heights bove ground plne Geometric prmeters: ¼.l, r ¼.l,ndDs¼.l f / f r =.λ =.λ r =.λ prsitic loop D V D ~ A A c il rtio, db...... f / f driven loop h C C θ ground plne Fig. Development of widebnd circulrl polrised squre-loop ntenns Single loop b Single loop with prsitic element c Twin loops with prsitic elements minimum AR point (due to the driven loop). Note there is no need to chnge the sie, the gp position nd the height h of the driven loop, despite the ddition of the prsitic loop. A proper combintion of the two minimum AR points leds to AR bndwidth enhncement. Figure demonstrtes how the side length ( ) nd the gp position (s ) of the prsitic squre loop ffect the AR bndwidth performnce. Indeed, two minimum AR points re observed t lower (thn the centre frequenc ) frequenc nd t higher frequenc, respectivel. As the B B il rtio, db s =.λ s =.λ s =.λ..... f / f b Fig. Bndwidth enhncement for il rtio of squre-loop ntenn b dding prsitic squre loop Geometric prmeters: ¼.l, r ¼.l, r ¼.l, Ds ¼.l, Ds ¼.l,ndh¼.l With different side lengths of the prsitic loop (s ¼.l ) b For different gp positions on the prsitic loop ( ¼.l ) side length increses ( m) or the gp position moves towrd the corner nerb the driving point (s k), the two minimum AR points move closer to ech other. If the side length is too long (e.g..l ) or the gp position is too close to the corner (e.g. s o.l ), the two minimum AR s IEE Proc.-Microw. Antenns Propg., Vol., No., June
points become overlpped nd eventull retrogrde to one minimum AR point. The optimised side length nd gp position re found to be ¼.l nd s ¼.l, respectivel, which correspond to n optiml bndwidth of % for AR r db. It should be mentioned tht it is difficult to enhnce the AR bndwidth b plcing the prsitic element outside the driven loop. The bndwidth for circulr polristion cn be further improved b introducing in cscde one more identicl squre loop to form twin-squre-loop ntenn, s illustrted in Fig. c. One side of the introduced squre loop is overlpped with side of the originl squre loop nd driven b the sme voltge source. Also, gp is introduced on the new squre loop to chieve CP rdition nd prsitic element is dded for bndwidth enhncement. The positions of the new gps re opposite (with respect to the is) to those of the originl gps, leding to configurtion similr to figure-of-eight (or S-shped) loop [, ], or dul-spirl ntenn [, ]. It will be demonstrted tht the twin-squre-loop ntenn lso chieves wider AR bndwidth. Figure shows the dependence of AR performnce of the twin-squre-loop ntenn on the gp position of the prsitic loops. The optimised gp position is t s ¼, i.e. t the corner most nerb the driving point. Note tht the rest of geometric prmeters (such s,,ndh) re kept unchnged fter the introduction of one more squre loop. The optiml AR bndwidth for AR r db is found to be %. Figure shows the frequenc chrcteristics of the input impednce nd gin of the twin-squre-loop ntenn with prsitic elements. The input resistnce is bout O nd the gin is round. dbi. The current distributions on the driven loop nd on the prsitic loop of the twin-squre-loop ntenn re plotted in Fig. t the centre frequenc ¼.f. A trvelling-wve current distribution is observed on the driven loop. The current distribution on the prsitic loop mnifests some properties between trvelling wve nd stnding wve. The contribution to the CP rdition from the driven loop is dominnt due its lrger ntenn sie nd higher current mgnitude. There is no significnt chnge for the current distribution t other frequencies in the AR r db bndwidth. Hence, il rtio, db s =.λ s =.λ s = +.λ....... f / f Fig. Ail rtio of the twin-squre-loop ntenn for different gp positions on the prsitic loops Geometric prmeters: ¼.l, ¼.l, r ¼.l, r ¼.l, Ds ¼.l, Ds ¼.l, h ¼.l ; s ¼.l mens tht the gp position moves.l w (+) or towrd ( ) the driving point from the corner prt of the role pled b the prsitic element is probbl to mintin good trvelling-wve current distribution on the driven loop over wide rnge of frequencies, which, in input impednce Z in, ohms Z in = R in + jx in gin R in X in....... f / f Fig. Input impednce nd gin of the twin-squre-loop ntenn with prsitic elements current, ma current, ma driving point D' A on driven loop B position on prsitic loop A' B' position b C rel imginr mgnitude C' rel imginr mgnitude phse phse D D' Fig. Current distributions on the twin-squre-loop ntenn with prsitic elements On driven loop b On prsitic loop gin, dbi phse, deg phse, deg IEE Proc.-Microw. Antenns Propg., Vol., No., June
turn, helps the loop ntenn to chieve widebnd CP performnce. Widebnd rectngulr-loop ntenns The AR bndwidth of squre-loop ntenn cn be incresed b replcing the squre loop with rectngulr loop. In this Section, it will be demonstrted tht the AR bndwidth cn be incresed to % b chnging the spect rtio (the width divided b the length) of rectngulr loop. Figure illustrtes the geometr of twin-rectngulr-loop ntenn tht consists of two driven rectngulr loops, ech with width nd length b. A prsitic rectngulr loop with width nd length b is introduced inside ech of the driven loops. To keep the coupling between the driven loop nd the prsitic loop s tight s possible, the distnce between two djcent sides of the loops is set to be constnt d, therefore the spect rtio /b is not ectl equl to /b in generl. The gp positions on both the driven loops nd the prsitic loops need to be djusted for n optiml AR performnce. B simultion, it is found tht s the spect rtio of the rectngulr loop decreses (i.e. the driven side becomes shorter), the gp positions need to move w from the corner ner the driving point. b b V ~ r s d r s driven loop This is resonble becuse the rdition field (i.e. E in the direction) from the shorter sides of the rectngulr loop decreses with the decrese in the spect rtio. Correspondingl the rdition field (i.e. E ) from the longer sides hs to be reduced for good CP rdition. This cn be chieved b moving the positions of the gps w from the corner. Another prmeter tht needs to be djusted is the height h bove the ground plne. It is found tht, s the spect rtio decreses, the height needs to be incresed. The dependence of AR performnce on the ntenn height bove ground plne hs lso been observed for other plnr CP ntenns, such s spirl ntenns bcked b conducting plne reflector []. Our investigtion revels tht decrese in the ntenn height chnges the trvelling-wve current distribution on driven loops, thus deteriorting the AR performnce. To demonstrte the AR bndwidth enhncement b the replcement of rectngulr loops, two different spect rtios re investigted: /b ¼ / nd /b ¼ /. The perimeters of the driven rectngulr loops nd the prsitic rectngulr loops keep the sme s those of the squre loops, i.e. (+b) ¼.l nd ( +b ) ¼.l. Figure displs the AR vritions s function of frequenc for the rectngulr-loop ntenns with spect rtio /b ¼ /. The AR bndwidth of the single-rectngulr-loop ntenn without prsitic element is onl % (AR r db). B introducing the prsitic element, the AR bndwidth is incresed to %. The AR bndwidth for the twinrectngulr-loop ntenn with prsitic elements is found to be % (much wider thn the % AR bndwidth chieved b the twin-squre-loop ntenn). This phenomenon is similr to tht observed for rhombic-loop ntenn, where the AR bndwidth increses s the rhombus verte ngle decreses []. Figure shows the AR bndwidth enhncement for the rectngulr-loop ntenns with spect rtio / b ¼ /. It is observed tht the AR bndwidth for the singlerectngulr-loop ntenn without prsitic element is bout %. The introduction of prsitic element increses the AR bndwidth to %. For the twin-rectngulr-loop ntenn with prsitic elements, n AR ( r db) bndwidth of nerl % is chieved. To double check the chievement, we simulted the sme ntenn structure using Microstripes., TLM (trnsmission-line mtri) d d single rectngulr loop single rectngulr loop with prsitic element twin rectngulr loops with prsitic elements d prsitic loop il rtio, db (spect rtio /b = /) h θ....... f / f ground plne Fig. Geometr of widebnd circulrl polrised twinrectngulr-loop ntenn with prsitic elements Fig. Frequenc chrcteristics of il rtio for rectngulr-loop ntenns with spect rtio /b ¼ / Geometric prmeters: ¼.l, ¼.l, b ¼.l, b ¼.l, r ¼.l, r ¼.l, Ds ¼.l, Ds ¼.l, s ¼.l, s ¼.l, d ¼.l,ndh¼.l IEE Proc.-Microw. Antenns Propg., Vol., No., June
bsed full-wve simultion tool. In the TLM-bsed simultion, the wire model used for the MoM-bsed simultion ws replced b stripline with width equl to four times the wire rdius. Also.l.l conducting copper plte ws used s the ground plne in the TLM-bsed simultion. (Note tht the sie of ground plne ws ssumed to be infinite for the MoMbsed simultion.) The TLM-bsed simulted AR is compred with the MoM-bsed simulted result in Fig. nd good greement is observed. Note tht the height of the twin-rectngulr-loop ntenn needs to be incresed from h ¼.l (of the single-rectngulrloop ntenns) to h ¼.l. It is lso interesting to notice tht the optiml distnce d between two djcent sides of the loops is lws round.l, no mtter how much the spect rtio is. B simultion, it is found tht the AR il rtio, db input impednce Z in, ohms Z in = R in + jx in X in single rectngulr loop single rectngulr loop with prsitic element twin rectngulr loops with prsitic elements (MoM) twin rectngulr loops with prsitic elements (TLM) (spect rtio /b = /)....... f / f Fig. Frequenc chrcteristics of il rtio for rectngulr-loop ntenns with spect rtio /b ¼ / Geometric prmeters: ¼.l, ¼.l, b ¼.l, b ¼.l, r ¼.l, r ¼.l, Ds ¼.l, Ds ¼.l, s ¼.l, s ¼.l, d ¼.l, h ¼.l for the single-rectngulr-loop ntenns, nd h ¼.l for the twin-rectngulr-loop ntenn spect rtio / b = / spect rtio / b = / R in gin spect rtio /b = / spect rtio /b = /....... f / f Fig. Input impednce nd gin of the twin-rectngulr-loop ntenns with prsitic elements gin, dbi performnce of the loop ntenns is not ver sensitive to the wire rdii (i.e. r nd r ) of the loops nd the gp widths (Ds nd Ds ). As rule of thumb, it is suggested tht we choose r ¼..l, r ¼..r nd the gp widths equl to times the wire rdii []. As the gp widths re much smller thn the loop sie, it is possible to replce the gps with RF switches, such s MEMS or PIN diodes to chieve polristion configurtion. The frequenc chrcteristics of the input impednce nd gin of the twin-rectngulr-loop ntenns re displed in Fig.. The input resistnce decreses s the spect rtio decreses. This tendenc is similr to the vrition of resonnt resistnce for linerl polrised rectngulr-loop ntenn []. The gin slightl decreses s the spect rtio decreses (BdBi for /b ¼ / ginst.. dbi for /b ¼ /) due to the incresed height h bove the ground plne (h ¼.l for /b ¼ / ginst h ¼.l for /b ¼ /) []. If the spect rtio further decreses, the AR ( r db) bndwidth m be more thn %, but the gin will decrese considerbl s the height needs to be further incresed. As n emple, we emined the cse for spect rtio /b ¼ /. The AR ( r db) bndwidth ws found to be pproimtel % with n optimised ntenn height h ¼.l, but the on-is gin becme BdBi t the centre frequenc D.f nd B dbi t the higher frequenc D.f, becuse the mimum rdition no longer occurs in the direction. An eperimentl emple To demonstrte the bndwidth enhncement eperimentll, twin-rectngulr-loop ntenn with n spect rtio close to / ws fbricted nd mesured. The reson for selecting this spect rtio is tht the bndwidth of our ntenn-rdition-pttern mesurement sstem is less thn %. The ntenn mesurement sstem emploed is the NSI ner-field sstem which is cpble of mesuring mplitude nd phse ptterns. The used probe (s TX source ntenn) is WR open-ended wveguide probe tht covers the frequenc rnge.. GH, therefore we chose GH s the centre frequenc. The configurtion nd dimensions of the printed twin-rectngulr-loop ntenn re illustrted in Fig.. The twin rectngulr loops with prsitic elements re printed on thin dielectric substrte (substrte thickness ¼. mm) with low dielectric constnt (RT/duroid, e r ¼.). The printed twin-rectngulr-loop ntenn is mounted mm bove mm mm copper plte. The ntenn is fed b brodbnd blun which ws fbricted on the sme tpe of RT/duroid substrte s used for the printed loop (nmel, e r ¼. nd thickness ¼. mm). This tpe of brodbnd blun hs been widel used for brodbnd printed dipole ntenns [ ] nd, to our knowledge, however, this is the first time for it to be used for CP loop ntenn. The brodbnd blun cn ecite the blnced mode b mking use of the coupling between the microstripline printed on one side of the substrte to the slot which is etched on the other side (which lso serves s the ground plne for the microstripline) of the substrte. A good impednce mtching cn be chieved b djusting the length l s of the slot, the height h m nd the length l m of the microstripline. Figure presents the simulted nd mesured results for voltge stnding-wve rtio (VSWR) of the brodbnd blun fed twin-rectngulr-loop ntenn, which shows brodbnd impednce bndwidth of B% (VSWR r ). IEE Proc.-Microw. Antenns Propg., Vol., No., June
... driven loop il rtio, db simulted il rtio mesured il rtio simulted gin mesured gin gin, dbi........ frequenc, GH prsitic loop Fig. Ail rtio nd gin of printed twin-rectngulr-loop ntenn with prsitic elements θ l s SMA w b w f w s w p w m ground plne h f l m brodbnd blun h m Figure presents the simulted nd mesured results for the il rtio nd gin, showing good greement. The AR bndwidth for AR r db is found to be bout %. The mesured gin is round dbi over the AR r db bndwidth. The rdition ptterns simulted nd mesured t. GH,. GH nd. GH re compred in Fig.. Good greement is obtined in the min bem of the copolristion (i.e. LHCP). As epected, the bemwidth (B) inf ¼ cut (the - plne) is wider thn tht (B) inf ¼ cut (the - plne), becuse the ntenn structure is two times longer in the direction thn tht in the direction. The bcklobe level nd the cross-polrised rdition (i.e. RHCP) re less thn db. VSWR -Ω microstrip line RT/duroid mesured simulted ground plne unit: mm Fig. Printed twin-rectngulr-loop ntenn with prsitic elements The strip widths of the driven loops nd of the prsitic loops re. mm nd. mm, respectivel; the gp widths on the driven loops nd on the prsitic loops re. mm nd. mm, respectivel; w b ¼. mm, w f ¼. mm, w s ¼. mm, w m ¼. mm, w p ¼. mm, h f ¼. mm, h m ¼ mm, l s ¼ mm, l m ¼. mm........ frequenc, GH Fig. VSWR of printed twin-rectngulr-loop ntenn with prsitic elements Conclusion A new tpe of widebnd CP squre- nd rectngulr-loop ntenns hs been developed nd etensivel discussed. It hs been demonstrted tht the bndwidth for circulr polristion of loop ntenn cn be significntl incresed b incorporting prsitic loop inside the originl loop. The incorported loop serves s prsitic element nd introduces n dditionl minimum AR point. A proper combintion of the originl nd dditionl minimum AR points leds to n AR bndwidth enhncement. It hs been found tht the AR ( r db) bndwidth of squre-loop ntenn with prsitic squre loop cn be incresed from.% to %. The AR bndwidth of single-loop ntenn cn be improved b combining two loops into twin-loop ntenn. The gin nd AR bndwidth of twin-squre-loop ntenn is found to be. dbi nd % for AR r db, respectivel. The AR bndwidth of the twin-squre-loop ntenn is further enhnced b replcing the squre loop with rectngulr loop. A bndwidth of pproimtel % for AR r db is obtined with gin of.. dbi for the twinrectngulr-loop ntenn with n spect rtio of /. The impednce mtching hs been chieved b introducing brodbnd blun. As the sense oirculr polristion of the widebnd CP loop ntenns is controlled b the positions of severl smll gps on the loops, it is possible to relise polristion configurtion (e.g. to chnge LHCP to RHCP, nd vice vers) using RF switches such s MEMS or PIN diodes. IEE Proc.-Microw. Antenns Propg., Vol., No., June
= simulted LHCP mesured LHCP simulted RHCP mesured RHCP = simulted LHCP mesured LHCP simulted RHCP mesured RHCP reltive power, db reltive power, db θ, deg θ, deg = simulted LHCP mesured LHCP simulted RHCP mesured RHCP = simulted LHCP mesured LHCP simulted RHCP mesured RHCP reltive power, db reltive power, db θ, deg θ, deg b = simulted LHCP mesured LHCP simulted RHCP mesured RHCP = simulted LHCP mesured LHCP simulted RHCP mesured RHCP reltive power, db reltive power, db θ, deg θ, deg Fig. Rdition ptterns of printed twin-rectngulr-loop ntenn with prsitic elements f¼. GH bf¼. GH cf¼. GH c Acknowledgments The uthors wish to cknowledge the support of the Georgi Electronic Design Centre (GEDC), the NSF CAREER Awrd ECS-, the NSF Grnt ECS- nd the NSF Pckging Reserch Centre. References Stutmn, W.L., nd Thiele, G.A.: Antenn theor nd design ( John Wile & Sons, Inc., ), pp. King, R.: The rectngulr loop ntenn s dipole, IRE Trns. Antenns Propg.,,, (), pp. Tsukiji, T.: Anlsis of two coupled coplnr loops, IEEE Trns. Antenns Propg.,,, (), pp. IEE Proc.-Microw. Antenns Propg., Vol., No., June
Jensen, M.A., nd Rhmt-Smii, Y.: Electromgnetic chrcteristics of superqudric wire loop ntenns, IEEE Trns. Antenns Propg.,,, (), pp. Levi, B.: Field of rectngulr loop, IEEE Trns. Antenns Propg.,,, (), pp. Shi, S., Hirsw, K., nd Chen, Z.N.: Circulrl polried rectngulrl bent slot ntenns bcked b rectngulr cvit, IEEE Trns. Antenns Propg.,,, (), pp. Sumi, M., Hirsw, K., nd Shi, S.: Two rectngulr loops fed in series for brodbnd circulr polrition nd impednce mtching, IEEE Trns. Antenns Propg.,,, (), pp. Morishit, H., Hirsw, K., nd Ngo, T.: Circulrl polrised wire ntenn with dul rhombic loop, IEE Proc., Microw. Antenns Propg.,,, (), pp. Weedon, W.H., Pne, W.J., nd Rebei, G.M.: MEMS-switched reconfigurble ntenns. Proc. IEEE AP-S Int. Smp.,, Vol., pp. Droush, A.S., nd Choe, B.: Opticll reconfigured ctive phsed rr ntenns. Proc. IEEE AP-S Int. Smp.,, Vol., pp. Chng, B.C.C., Qin, Y., nd Itoh, T.: A reconfigurble lek mode/ ptch ntenn controlled b PIN diode switches. Proc. IEEE AP-S Int. Smp.,, Vol., pp. Afsr, M.N., Wng, Y., nd Cheung, R.: Anlsis nd mesurement of brodbnd spirl ntenn, IEEE Antenns Propg. Mg.,,, (), pp. Morishit, H., nd Hirsw, K.: Widebnd circulrl-polrised loop ntenn. Proc. IEEE AP-S Int. Smp.,, pp. Nkno, H., Mimki, H., Wu, Y., Nkm, K., nd Ymuchi, J.: Loop ntenn with prsitic element. Proc. Smp. Antenn Technol. Appl. Electromgn. (ANTEM),, pp. Li, R.L., nd Fusco, V.: Printed figure-of-eight wire ntenn for circulr polrition, IEEE Trns. Antenns Propg.,,, (), pp. Morishit, H., Hmd, H., Nishid, K., nd Ngo, T.: A widebnd circulrl polried dipole ntenn. Proc. IEEE AP-S Int. Smp.,, pp. Hirose, K., nd Nkno, H.: Dul-spirl slot ntenns, IEE Proc. H, Microw. Antenns Propg.,,, (), pp. Nkno, H., nd Hirose, K.: Numericl nlsis of dul-spirl printed ntenn. Proc. IEE th Int. Conf. Antenns Propg., ICAP,, pp. Nkno,H.,Nogmi,K.,Ari,S.,Mimki,H.,ndYmuchi,J.: A spirl ntenn bcked b conducting plne reflector, IEEE Trns. Antenns Propg.,,, (), pp. Li, R.L., Ni, G., nd Nkno, H.: Numericl nlsis of printed superqudric wire loop ntenns, IEEE Trns. Mgn.,,, (), pp. Blnis, C.A.: Antenn theor: nlsis nd design ( John Wile & Sons, Inc., ), pp. Edwrd, B., nd Rees, D.: A brodbnd printed dipole with integrted blun, Microwve J.,, pp. Leong, K.M.K.H., Qing, Y., nd Itoh, T.: Surfce wve enhnced brodbnd plnr ntenn for wireless pplictions, IEEE Microw. Wirel. Components Lett.,,, (), pp. Sbtier, C.: T-dipole rrs for mobile pplictions, IEEE Antenns Propg. Mg.,,, (), pp. IEE Proc.-Microw. Antenns Propg., Vol., No., June