Design of a Wideband Antenna with Stable Omnidirectional Radiation Pattern Using the Theory of Characteristic Modes

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1 Desg of a Wdebad tea wth Stable Omdrectoal Radato Patter Usg the Theory of haracterstc Modes We, D; Hao, Y; Wag, H; Zhou, H 217 IEEE. Persoal use of ths materal s permtted. Permsso from IEEE must be obtaed for all other uses, ay curret or future meda, cludg reprtg/republshg ths materal for advertsg or promotoal purposes, creatg ew collectve works, for resale or redstrbuto to servers or lsts, or reuse of ay copyrghted compoet of ths work other works. For addtoal formato about ths publcato clck ths lk. Iformato about ths research object was correct at the tme of dowload; we occasoally make correctos to records, please therefore check the publshed record whe ctg. For more formato cotact scholarlycommucatos@qmul.ac.uk

2 > REPLE THIS LINE WITH YOUR PPER IDENTIFITION NUMER (DOULE-LIK HERE TO EDIT) < 1 Desg of a Wdebad tea wth Stable Omdrectoal Radato Patter Usg the Theory of haracterstc Modes Dglag We, Yag Hao, Hayag Wag ad Ha Zhou bstract I ths commucato, the desg procedure of a wdebad atea wth omdrectoal radato patter s demostrated based o the theory of characterstc modes. osstg of a dpole ad a loop atea, the atea has a very smple structure. wde mpedace badwdth s obtaed because of the smultaeous exctato of the atea s frst two modes. Meawhle, due to the fact that these two modes share a smlar omdrectoal radato patter, a stable radato patter s also acheved across the operatg frequecy bad. I order to detfy the atea s dfferet modes, a characterstc mode aalyss of the atea s carred out frst. The, a feed cofgurato s specfcally desged to excte the desred modes. To valdate the atea desg, a prototype was fabrcated ad tested. Measured results agree well wth the smulated oes. Measuremet shows that a wde mpedace badwdth of 44.2% wth S11 <-1 d ( GHz) ad stable radato patters at both E-plae ad H-plae were acheved over the operatg frequecy bad. Idex Terms haracterstc modes, multmode atea, wdebad atea, omdrectoal atea, stable radato patter. I. INTRODUTION Recet commucato servces, such as 2G, 3G, LTE, 4G, W-F, ad WMax, boost the hgh demad of wdebad ateas wth wde mpedace badwdth ad stable radato patters over ther operatg frequecy bads. Oe approach to obta a wde mpedace badwdth s by adoptg frequecy depedet atea cocept [1], such as log-perodc ateas [2], spral ateas [3], ad cocal ateas [4]. Ufortuately, these ateas [2-4] are always too complex ad bulky ther geometrcal structures, whch makes them dffcult to be fabrcated. O the other had, patch ateas have bee wdely studed for ther smple structure ad large umbers of feedg techques were proposed to broade ther mpedace badwdths, such as slot couplg feedg [5], U-shaped slot feedg [6], L-shaped probe feedg [7], etc. Slot atea s aother good caddate for moder wreless commucatos for ts smple ad plaar structure. great umber of papers about wdebad slot ateas have bee publshed recetly [8-1]. terestg paper about slot atea was publshed 215 [11], whch a slot stub s added to shft the hgher mode dow to the lower mode ad as a Mauscrpt receved February ##, 216. Ths work was supported by Huawe Techologes (UK) O., LTD. D. L. We ad Y. Hao are wth the School of Electroc Egeerg ad omputer Scece, Quee Mary ollege, Uversty of Lodo, Lodo E1 4NS, U.K. (e-mal: dglag.we@qmul.ac.uk, y.hao@qmul.ac.uk). H. Y. Wag ad H. Zhou are wth Huawe Techologes (UK) O., LTD, Readg, erkshre, U.K. (emal: hayag.wag@huawe.com, ha.zhou1@huawe.com). result, a wde mpedace matchg s acheved. However, all of these ateas [5-11] have a weakess of ustable radato patters across ther operatg frequecy badwdths. other approach to desg wdebad atea s by usg the theory of characterstc modes (TM) [12-16]. The bggest advatage of t over other approaches s that the TM gves us a drect sght to the radatg pheomea occurrg o the atea. Therefore, desred radato patters ca be obtaed by exctg the correspodg modes. Ufortuately, oe of these authors [12-16] have cosdered obtag stable radato patters whle broadeg the ateas mpedace badwdth by utlzg the TM. To obta a stable radato patter, the cocept of mageto-electrc dpole atea was frst proposed [17] 26. y combg a electrc plaar dpole ad a shorted patch, whch s treated as a magetc dpole, a stable radato patter s acheved over ts operatg frequeces. other way to acheve a stable radato patter s by usg mult-dpole atea, the prcple of whch s explaed detal [18]. y usg two pars of dpoles [18], a wde mpedace badwdth of 6% wth SWR<1.5 ad a stable radato patter across the operatg frequecy bad are obtaed. Other atea desgs wth stable radato patters have also bee vestgated recetly for base stato systems [19-21]. Sometmes, a omdrectoal radato patter s more preferable wreless commucatos whle all of the ateas radato patters [17-21] are udrectoal. I ths commucato, a wdebad atea wth stable omdrectoal radato patter s proposed accordg to the theory of characterstc modes. The TM gves us a drect sght to the radatg pheomeo takg place o the proposed atea ad explas how stable radato patters are obtaed over the whole operatg frequecy bad. The proposed atea ca acheve a wde mpedace badwdth of 44.2% (SWR<2) from 1.85 to 2.9 GHz ad a stable omdrectoal radato patter at H-plae over ts operatg frequecy bad. The atea also has a smple structure ad s easy to be bult by usg P fabrcato techque. II. HRTERISTI MODES NLYSIS. Theory of haracterstc Modes The theory of characterstc modes was frst proposed by Garbacz ad Turp 1971 [22], ad the t was refed by Harrgto ad Mautz 197s [23, 24]. The TM s a powerful tool to desg ateas because t ca provde a drect sght to the radatg pheomea occurrg o the atea. I recet years, t has bee wdely used to desg all types of ateas, such as moble hadset atea, electrcally small atea, platform atea, plaar moopole atea, etc [25]. I ths secto, oly basc cocept of the TM wll be preseted. The full defto ad explaato of the TM ca be foud [22-24]. For a gve coductg object, ay electrc curret ( J ) o ts surface ca be expressed as a sum of characterstc modes or egecurrets ( J ) wth dfferet product coeffcets ( ):

3 > REPLE THIS LINE WITH YOUR PPER IDENTIFITION NUMER (DOULE-LIK HERE TO EDIT) < 2 VJ J J (2-1) 1 j where J are the egecurrets, are the modal weghtg coeffcets, are the egevalues, ad V are the modal exctato coeffcets, whch s defed by: V,E E J J ds (2-2) S where E s the mpressed source. Modal weghtg coeffcet ca be expressed as follows: V 1 j (2-3) Modal sgfcace ( MS ) s always used to determe how effcetly a mode ca radate. The expresso of MS ca be preseted as: 1 MS (2-4) 1 j other mportat parameter that wll be utlzed the atea desg procedure s characterstc agle, whch s defed as: 1 18 o ta ( ) (2) Whe a mode J s resoat amely, MS 1 ad o 18 ca be obtaed accordg to (2-4) ad (2), respectvely. Therefore, the mode radates all of the eergy whe 18 o ad the closer s to 18 or s to, the more effcetly the mode radates whe excted. ccordg to equato (2-1), how well a mode J s excted depeds o the modal weghtg coeffcet. Meawhle, s depedet o two parameters,.e., egevalue ad modal exctato coeffcets V. For a resoat mode at ts resoace frequecy, s equal to so formula (2-3) ca be chaged to: V (2-6) However, for some o-resoat modes, ther egevalues are very huge over the observed frequecy bad. Ths meas that o matter how you excte the coductg object, whch s atea our case, the modal weghtg coeffcet s always very small. We address these modes as sgfcat modes. I our followg study, oly sgfcat modes are take to cosderato, whose characterstc agles are close to 18. ased o formula (2-3), whe egevalue s fxed, the modal weghtg coeffcet s totally determed by how we excte the atea. The accordg to (2-2), order to obta a large value of modal weghtg coeffcet, the exctato should be placed where the egecurret s very strog.. haracterstc Modes alyss I ths secto, a detaled aalyss of characterstc modes of the proposed atea wll be gve. Note that all of the smulatos performed ths secto was carred out by usg DFEKO Sute 7. [26]. To smplfy the process, the Fg. 1. Geometry of the proposed atea. haracterstc gle(degree) GHz 3.5 GHz 3.25 GHz 4.1 GHz Mode 3 Mode Frequecy(GHz) Fg. 2. haracterstc agles of the frst four modes of the proposed atea. (c) (d) Fg. 3. urret dstrbutos of mode 1 at 2. GHz, mode 2 at 3.5 GHz, (c) mode 3 at 3.25 GHz, ad (d) mode 4 at 4.1 GHz of the proposed atea. atea to be aalyzed ths secto s set to be perfect coductor wth zero thckess ad wthout ay substrates. The dea of the proposed atea was spred by the fact that the dpole s half-wave mode ad the folded dpole s oe-wave mode share the smlar omdrectoal radato patter. ascally, the atea s a combato of a dpole ad a loop atea, as llustrated Fg. 1. The proposed atea s frst four resoat modes characterstc agles are preseted Fg. 2. Fg. 3 ad Fg. 4 llustrate these four modes curret dstrbutos ad radato patters at ther resoat frequeces, respectvely. The proposed atea s frst two modes are the modes we eed because they share a smlar omdrectoal radato patter, whch ca be observed Fg. 4. ctually, t ca be see from Fg. 3 that these two modes are smlar to dpole s half-wave mode ad the folded dpole s oe-wave mode, respectvely.

4 > REPLE THIS LINE WITH YOUR PPER IDENTIFITION NUMER (DOULE-LIK HERE TO EDIT) < 3 T1 L5 W1 W5 (c) (d) Fg. 4. Radato patters of mode 1 at 2. GHz, mode 2 at 3.5 GHz, (c) mode 3 at 3.25 GHz, ad (d) mode 4 at 4.1 GHz of the proposed atea. W3 W5 W4 G2 W2 W6 1. Modal Sgfcace Mode 3 Mode Frequecy(GHz) Fg. 5. Modal sgfcace for the frst four modes of the proposed atea. Modal Weghtg oeffcet Pot : Pot : Pot : Frequecy(GHz) Fg. 6. Modal weghtg coeffcets for the frst two modes of the proposed atea wth dfferet feedg locatos. The ext stage of the atea desg s to create a feedg structure to excte the proposed atea s frst two modes smultaeously. ccordg to formula (2-2), to excte a certa mode, a drect feed should be located where the egecurret s very strog. Fg. 3 shows that the best feedg locato for mode 1 s the mddle of the dpole, amely pot, where the curret s the maxmum whle pot or may be a secod opto. For mode 2, the best feedg place s pot or whle pot s also possble. I order to obta the best feedg locato, three cases wll be dscussed,.e., pot, pot ad pot. Modal sgfcace for the frst four modes are preseted Fg. 5. It ca be see that all of the modes have a Fg. 7. Geometry of the proposed atea: 3-D vew; top vew; L1=61.8, L2=5, L3=3, L4=32.2, L5=6, L6=8, W1=2, W2=L2, W3=2, W4=.8, W5=1, W6=4, R=.5, R1=1, R2=1.58, G1=1, G2=.8, T1=.8 (Uts: mm). large modal sgfcace aroud 1 at ther resoat frequeces, whch meas the correspodg modes ca radate very effcetly aroud ther resoat frequeces. However, ether mode 3 or mode 4 ca be excted those prevously descrbed cases because ther currets at pots, ad are ulls, as show Fgs. 3(c) ad (d). I other words, ther modal weghtg coeffcets are very small though a large modal sgfcace s observed at ther resoat frequeces. Therefore, the followg study these two modes wll ot be cosdered. Fg. 6 shows the modal weghtg coeffcets for the frst two modes of the proposed atea wth dfferet feedg locatos,.e., pot, pot ad pot. s ca be see, whe a voltage source s added at pot, both mode 1 ad mode 2 are strogly excted, especally aroud ther resoat frequeces; the other two cases, mode 2 s well excted but mode 1 s ot excted equvaletly eve at ts resoat frequecy. Therefore, we ca draw a cocluso that pot s the best feedg locato. III. NTENN DESIGN ND PRMETRI STUDY The geometry of the proposed atea wth detaled dmesos s show Fg. 7. It s desged usg a 8 mm 4 mm.8 mm FR4 substrate wth a permttvty of 4.4 ad a loss taget of.2. s llustrated Fg. 7, the atea cossts of a dpole, a loop atea, a feedg le ad a coaxal feed. oth the dpole ad the loop atea are prted o the lower sde of the substrate whle the feedg le s o the upper sde. coaxal feed s selected to excte the proposed atea. It has already bee kow from Secto II that the optmum feedg locato s the mddle of the dpole. To mplemet ths feed method, the dpole has bee altered, as show Fg.

5 > REPLE THIS LINE WITH YOUR PPER IDENTIFITION NUMER (DOULE-LIK HERE TO EDIT) < L1=58mm L1=6mm L1=61.8mm L1=64mm L1=66mm Frequecy(GHz) Fg. 8. Effects of L1 o the atea s reflecto coeffcet L4=28mm L4=3mm L4=32.2mm L4=34mm L4=36mm Frequecy(GHz) Fg. 9. Effects of L4 o the atea s reflecto coeffcet. 7: a slt s made the mddle of t; the wdth of the dpole aroud the feedg structure s creased; a etched part s also made the dpole s rght arm. Fg. 7 shows that the outer coductor of the coaxal cable s soldered to the rght arm of the dpole whle the er part s coected wth the feedg le through the substrate. The other ed of the feedg le s boded to the left arm of the dpole usg a metal va. Two holes wth a dameter of 1 mm are drlled the FR4 substrate to realze the feed. To demostrate the aalyses preseted Secto II, the effects of some key parameters of the proposed atea o ts reflecto coeffcet wll be dscussed the followg part, such as the legth of the dpole L1, the loop atea s sde legth L4 ad L5, ad the gap wdth betwee the dpole ad the loop G2. Note that whe oe parameter s studed, the others are kept as a costat. ll of the smulatos ths secto were carred out by usg soft HFSS v. 15 [27]. The frst parameter studed was the legth of the dpole L1. s see Fg. 8, the proposed atea has two resoaces from 1.5 to 3.5 GHz. Whe L1 equals 61.8 mm, they occur at about 2. GHz ad 2.75 GHz, respectvely. These two resoaces correspod wth the frst two characterstc modes of the atea, as dscussed Secto II. Fg. 8 also shows that whe L1 creases the frst mode s resoat frequecy shfts to a lower frequecy; however, the secod mode s sestve to the chage of L1. The reaso for ths pheomeo s that the frst mode s caused by the dpole ad the secod mode s troduced by the loop atea. Therefore, whe the dpole s L5=2mm L5=4mm L5=6mm L5=8mm L5=1mm Frequecy(GHz) Fg. 1. Effects of L5 o the atea s reflecto coeffcet. Modal Weghtg oeffcet mm 6mm 22mm 66mm Frequecy(GHz) Fg. 11. Effects of G2 o the atea s modal weghtg coeffcet mm G2 G2=.4mm G2=.8mm G2=1.8mm G2=5mm G2=1mm Frequecy(GHz) Fg. 12. Effects of G2 o the atea s reflecto coeffcet. G2=.4mm G2=.8mm G2=1.8mm G2=5mm G2=1mm legth creases ts resoace should occur at a lower frequecy. I order to make the frst mode resoates at a proper frequecy, L1 was chose to be 61.8 mm. The secod ad thrd parameters studed were the loop ateas two sdes legth, L4 ad L5. Ther effects o the proposed atea s reflecto coeffcet are show Fg. 9 ad 1, respectvely. It ca be see that the frst mode s resoat frequecy keeps uchaged whe L4 or L5 creases whle the secod mode s resoace occurs at a lower frequecy both of the cases. These pheomea demostrate that the frst mode of the atea s determed by the dpole whle the secod mode s caused by the loop atea. Hece, for a wde mpedace badwdth, L4 ad L5 were set to be 32.2 mm ad 6 mm, respectvely.

6 > REPLE THIS LINE WITH YOUR PPER IDENTIFITION NUMER (DOULE-LIK HERE TO EDIT) < XOZ Plae YOZ Plae Fg. 13. Effects of L4 o the atea s radato patters at 2.8 GHz d Smulated Measured Prototype Frequecy(GHz) Fg. 14. Smulated ad measured reflecto coeffcet ad ga of the proposed atea. Fg. 15. urret dstrbutos of the proposed atea at 2. GHz (frst resoace), 2.75 GHz (secod resoace). The fourth parameter studed was the gap wdth betwee the dpole ad the loop G2. For the secod resoace, the dpole works as a couple feedg structure of the loop atea, so the gap wdth G2 determes how well the secod mode ca be excted. Fg. 11 shows that a greater value of G2 yelds a smaller modal weghtg coeffcet of the secod mode, amely a weaker exctato of ths mode. It ca be see from Fg. 12 that whe G2 creases from.4 mm to 1 mm, the frst resoace shfts slghtly to a lower frequecy whle the secod oe moves gradually to a hgher frequecy. ddtoally, as G2 s greater tha 5 mm oly the frst mode ca be excted. To acheve a good mpedace matchg over a wde frequecy bad, G2 =.8 mm was selected. These four parameters (L1, L4, L5 ad G2) mpact o the Ga(d) 1 33 XOZ Plae XOZ Plae YOZ Plae YOZ Plae Fg. 16. Smulated ad measured radato patters of the proposed atea. proposed atea s radato patters at frequeces of 2. GHz, 2.4 GHz ad 2.8 GHz have also bee vestgated. mog these twelve cases, oly the effect of L4 at 2.8 GHz s sgfcat, the curves of whch are plotted Fg. 13. It ca be see that the atea s radato patters deflate whe L4 s too large or too small. Ths s because the secod resoat frequecy shfts away from 2.8 GHz, as ca be see Fg. 9. s a result, the atea s mpedace matchg ad atea ga deterorate. The optmzed value for L4 s 32.2 mm. IV. EXPERIMENTL RESULTS ND VLIDTION To verfy the desg approach, a prototype of the proposed atea was fabrcated ad measured. Fg. 7 gves the detaled dmesos of the maufactured atea. The reflecto coeffcet of the atea was measured by usg a R&S ZNT 8 24-port vector etwork aalyser whle radato patters were obtaed by employg a far-feld atea measuremet system a EM screeed aechoc chamber. Fg. 14 shows the smulated ad measured reflecto coeffcet ad ga of the proposed atea. It ca be see that a good agreemet s acheved for smulated ad measured results. The measured mpedace badwdth shfts slghtly to hgher frequeces due to the fabrcato tolerace. Overall, both the smulated ad measured reflecto coeffcet curves show that the proposed atea ca operate betwee 1.85 GHz ad 2.9 GHz wth <-1 d. O the other had, t ca also be observed from Fg. 14 that the atea ga s greater tha 2 d across the whole badwdth. The electrc curret dstrbutos of the proposed atea at ts two resoat frequeces, amely 2. GHz ad 2.75 GHz, are depcted Fg. 15. It ca be see that for the frst resoace the curret s maly dstrbuted o the dpole. Though the

7 > REPLE THIS LINE WITH YOUR PPER IDENTIFITION NUMER (DOULE-LIK HERE TO EDIT) < 6 curret o the loger sde of the loop closer to the dpole s also strog, t barely cotrbutes to the total radato. t the secod resoat frequecy, the dpole ca be regarded as the couple feedg le of the loop atea ad a folded-dpole-lke mode s excted. Therefore, these curret dstrbutos further demostrate our cocluso that the frst resoace s caused by the dpole (λ/2 mode) whle the secod resoace s troduced by the loop (λ mode). The pheomeo observed here agrees well wth our aalyss Secto II. Fg. 16 shows a great agreemet betwee the smulated ad measured radato patters. It ca be see that the atea has a 8-shaped radato patter the XOZ-plae ad a omdrectoal patter the YOZ-plae over the whole operatg frequecy bad. The measured cross-polarzato levels are slghtly hgher tha the smulated results whch s maly caused by the mpact of the feed cable. It ca also be see from Fg. 16 that stable radato patters are acheved at both E-plae (XOZ-plae) ad H-plae (YOZ-plae) across the etre operatg frequecy bad. V. ONLUSION ew wdebad atea wth stable omdrectoal radato patter has bee vestgated ths commucato. The desg of the atea s based o the theory of characterstc modes. fter a detaled parametrc study, a prototype of the atea was fabrcated ad measured. oth the smulated ad measured results reveal that the atea features a wde mpedace badwdth of 44.2% ( <-1) from 1.85 to 2.9 GHz ad stable radato patters are also obtaed at both E-plae ad H-plae over the operatg frequecy bad. Moreover, the atea has a smple ad plaar structure, ad t ca be bult easly by usg P fabrcato techque. REFERENES [1].. alas, tea Theory: alyss ad Desg, 3rd ed. New York, NY, US: Wley-Iterscece, 25. [2] R. DuHamel ad F. Ore, Logarthmcally perodc atea desgs, IRE It. ov. Rec., vol. 6, pp. 1391, [3] J. 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