Design and Analysis of Broadside Arrays of Uniformly Spaced Linear Elements

Transcription

1 Volum 156 No 6, Dcmbr 16 Dsign and Analysis of Broadsid Arrays of Uniformly Spacd Linar Elmnts Raji A. Abimbola Dpt. of Elctrical and Elctronics Enginring Fdral Univrsity of Agricultur, Abokuta, Nigria Amusa K. Akinwal Dpt. of Elctrical and Elctronics Enginring Fdral Univrsity of Agricultur, Abokuta, Nigria ABSTRACT In this papr, quation for computing th radiatd far fild of broadsid arrays of uniformly spacd lmnts, assuming sinusoidal currnt distribution is drivd. Computational data ar obtaind for th antnna paramtrs such as array factor pattrns, ovrall radiation pattrns and dirctivity of arrays consisting of 5, 9, 13, and 1 lmnts with valus of intrlmnt spacing ranging from.5 to. Computational rsults for array factor pattrns and ovrall radiation pattrns, rprsntd in graphical formats ar consistnt with thos rportd in litratur and clarly suggst that array structurs with intr-lmnt spacing blow would produc rmarkabl and dsirabl bam radiations which may find usful applications for long rang transmission. Numrical data for dirctivity as a function of numbr of lmnts for valus of spacing considrd display fatur that is consistnt with th xpctation, as bing charactristic of any antnna typ. Gnral Trms Antnna Dsign, Numrical Analysis. Kywords Broadsid array, array factor, radiatd far fild, distant communication, intr-lmnt spacing. 1. INTRODUCTION Jams Clrk Maxwll in 186 at Univrsity of London bgan humanity first stp towards unifying th thory of lctricity and magntism by rprsnting th rlations btwn ths two phnomna through a st of formidabl diffrntial quations, othrwis calld Maxwll s quations. This important milston pavd th way for various applications such radio, tlvision, radar and mobil phons. Critical to ths aformntiond applications is an antnna dsignd to transmit or rciv lctromagntic wavs. Communication btwn two rmot locations has bn mad possibl by th us of this structur. A singl dipol antnna is mostly not usd for far distant communication bcaus of limitation of smallr covrag occasiond du to smallr gain or dirctivity of th antnna. Dipols in array form ar th most dsird for far distant communication. Antnna arrays could b dployd for myriad numbr of applications such as radar, sonar, radios and mobil communication systms [1,,3]. Diffrnt forms of array radiations ar broadsid, nd fir and phasd arrays, Hansn-Woodyard array. Antnnas dsignd to radiat broadsid is usually charactrizd with dirction of radiation bing normal to th axis of th array. This is illustratd in Fig. 1, in which main lob radiation is normal to array orintation. x z 9 Broadsid radiation Fig. 1: Illustration of broadsid radiation and array orintation Fw of contributions on antnna array ar highlightd in this papr. Comprhnsiv tratmnt of th usag of antnna array for mobil communication applications was givn in [1]. Th papr also highlightd som of th advantags such usag could portnd. [] proposd a nw tchniqu for dsigning a concntric circular array antnna of isotropic lmnts with a viw to gnrating a pncil bam of rducd sid lob and grating lob lvls. Gntic Algorithm was adoptd in [5] to find th optimum wights of antnna array of linar lmnts that could b usd to gnrat radiation pattrns of rducd sid lob lvl. In this papr, numrical rsults ar obtaind for antnna paramtrs such as, radiation fild pattrns, and dirctivity of broadsid arrays whos lmnts ar uniformly spacd. Ths rsults ar rprsntd in graphical formats and dpict faturs which hav bn rportd in th litratur as bing charactristic of th antnna.. THEORETICAL FORMULATION Accurat dtrmination of radiation charactristics of an antnna dpnds on th natur of currnt on th structur. Bcaus of difficultis involvd in obtaining accuratly currnt distributions by xprimntal mans, frontirs in th fild of antnna workd with uniform currnt, travlling-wav currnt and standing-wav currnt distributions [6]. Drivation of radiatd fild of broadsid array assuming sinusoidal currnt sourc is xplaind in what follows..1 Radiatd Fild Th ovrall radiation pattrns of antnna lmnts in array form can b computd from quation drivd by multiplying th radiatd fild of a singl lmnt or a dipol from th rfrnc point by th array factor. This quation is writtn as, Etot E (at rfrnc point) arrayfactor (1) y 19

2 Volum 156 No 6, Dcmbr 16 whr, E tot is th total lctric fild of an array, E is th radiatd lctric fild of a dipol in th ˆ - dirction. Th array factor dscribs th ffct of aggrgating svral radiating lmnts in an array without taking into cognizanc th spcific radiation pattrn of an lmnt. For th purpos of invstigation, an array of dipol lmnts is considrd hr. Th radiatd fild of a half-wav dipol l, lying along z-axis, propagating in fr spac, is xprssibl in a form givn as l l jk R E j sin I z ' dz ' () R whr, j is an imaginary numbr, is th fr-spac prmability, k rprsnts fr spac propagation constant, Iz ' is th filamntary sourc currnt, and R is th distanc btwn th sourc point, rprsntd by r ' and th fild jk point r, and R / R is th fr spac Grn function. Th dipol is assumd to b fd with sinusoidal currnt distribution of th form ' cos I z I k z (3) Substitution of qn. (3) in () yilds, jkr j E I kz dz R sin cos ' ' () whr I is th maximum currnt, using k in qn. (), w hav jkr jk I E k z dz R sin cos ' ' (5) is th fr-spac intrinsic impdanc. Introducing amplitud and phas approximations associatd with far zon lctric fild as commonly mployd in antnna work in qn. (5), such that R r r' r (amplitud approximation) (6a) R r r' r z'cos (phas approximation) (6b) Eqn. (5) bcoms jk r jk I E k z dz r jk cos z ' sin cos ' ' (7) Th intgral xprssd by qn. (7) is asily intgratd using th procdur highlightd in qns. (8) (9b): mz mz cos nz dz m n mcos n z n sin mz (8) whr m jk cos (9a) n k (9b) Employing qns. (8) (9b) in (7) rsults in E jk r jk I r sin j k jk cos z ' cos k jk cos cos k z' k sin kz' Solving qn. (1) yilds (1) ji cos cos jk E. (11) sin r Th normalizd array factor of uniformly spacd array of linar lmnts lying along z-axis is xprssd in a form givn as sinn AFn N sin (1) whr AFn is th normalizd array factor, N is th numbr of lmnts in th array, and is th rlativ phas btwn th lmnts. Th maximum of th normalizd array factor as spcifid in qn. (1) occurs at. That is, kd cos (13) whr, is th phas angl by which th currnt in ach lmnt lads th currnt of th prcding lmnt, d is th spacing btwn th lmnts, k has bn dfind arlir. For broadsid arrays, th maximum radiation is dirctd towards 9, it thrfor follows that k dcos 9 (1) With, th normalizd array factor of qn. (1) bcoms k dcos sinn AFn k dcos N sin (15) Employing qns. (1), (11) and (15), th total radiatd fild of th array taks th form xprssibl as, Et k dcos ji cos cos jk sin N.. sin r k dcos N sin (16) It is important to stat hr that th normalizd valu of E would b invokd whil utilizing qn. (16) for th computation of th total radiatd fild of th broadsid array.. Dirctivity This is th ratio of maximum radiation intnsity in a givn dirction to radiation intnsity avragd all ovr th dirction [7]. Dirctivity D of an antnna is xprssibl in a form givn as

3 Volum 156 No 6, Dcmbr 16 D U U max (17) av whr U max is maximum radiation intnsity in a givn dirction, and U av is th radiation intnsity avragd all ovr th dirctions. Radiation intnsity, blow is xprssd as [8] U U of broadsid array of spacing N k d sin cos N k d cos Avrag radiation intnsity, U av is of th form (18) 1 Uav U sin d d (19) From qns. (18) and (19), on obtains N k d sin cos sin d d N k d () 1 Uav cos Equation (1) nsus aftr solving quation () N k d sin cos sind N k d (1) 1 Uav cos Assuming a larg array, th solution of qn. (1) assums this form U av () Nkod At 9, th maximum valu of th radiation intnsity U max and using qn. () in qn. (17), dirctivity of N- lmnt linar broadsid array can b xprssd as N k d D (3) Substituting for k in qn. (3), th dirctivity xprssd in trms of th oprating wavlngth taks this form Nd D () In dcibl unit, th dirctivity is writtn as Nd D1log1 (5) 3. NUMERICAL RESULTS For th purpos of analysis, computational rsults ar obtaind for antnna paramtrs for broadsid arrays of linar lmnts, whos spacing (d) btwn th lmnts rangs from.5 to. Ths ar discussd in what follows, starting with th array factor pattrns. 3.1 Array factor pattrns Graphical rprsntations of array factor pattrns of broadsid arrays consisting of 5, 9, 13, and 1 lmnts, computd by th us of qn. (15) for d varying from.5 to ar shown in Figs. (a) through (). In ach of thos illustrations, solid rd lin, dashd blu lin, solid yllow lin, and solid black lin, rspctivly, indicat computd rsults for 5- lmnt, 9-lmnt, 13-lmnt, and 1-lmnt broadsid arrays. It is vidnt from th graphical illustrations dpictd in Figs. (a) to (), that, thr ar main lob radiations in th forward and backward dirctions, this is consistnt with th xpctation, as array factor taks lss cognizanc of spcific radiation pattrns of individual lmnt. This obsrvation is consistnt with rsults rportd lswhr [9]. Th rsults also rval that th main lob bamwidth dcrass with incrasing numbr of lmnts and spacing btwn th lmnts. This dcras in bamwidth is associatd with incras in th numbr and lvls of sidlobs; this appars to b th tradoff. As vidnt in Fig. (d), thr appars to b an occurrnc of grating lobs at d, howvr, at d, numrous grating lobs ar producd as dpictd in Fig. (). 3. Total far fild pattrns of th array Th far zon filds radiatd by th broadsid arrays consisting of 5, 9, 13, and 1 lmnts computd from qn. (16) for all valus of spacing considrd ar displayd in Figs. 3 (a) to 3(). It is of intrst to not that, thos graphs rprsnt th summation of contribution of far fild from ach lmnt of th diffrnt forms of array considrd for analysis. As notd arlir, solid rd lin, dashd blu lin, solid yllow lin, and solid black lin indicat rsults for 5-lmnt, 9-lmnt, 13- lmnt, and 1-lmnt arrays. Th numrical rsults graphically dpictd in Figs. 3(a) through 3(), indicat that radiation for all valus of d considrd is concntratd in th forward dirction only, in contrast to rsults displayd in Figs. (a) through (). Th rsults also show that, main lobs of th fild pattrns bcom dirctiv with incras in th numbr of lmnts and spacing btwn th lmnts. This rduction in th main lob bam width is accompanid with incras in th numbr and lvls of sid lobs. Thr appars to b th occurrnc of grating lobs whn th spacing btwn th lmnts bcoms. Bcaus of rcurring apparanc of grating lobs whn d, it is not out of plac if th nsuing sction of this papr focuss on th discussion of th radiation lob calld grating lob. 3.3 Grating lobs A grating lob is an unwantd sid lob which is a rplica of main lob that bams its radiation in a dirction othr than th dsird dirction. In transmitting antnna, sid lob radiation is a wast of lctromagntic nrgy, and usually constituts lctromagntic intrfrnc, thus causing unintndd rcivrs to pick up stalthy and classifid information. In rciving antnnas, sid lob allows lctromagntic nrgy from unwantd dirctions to ntr th systm, thus incrasing th lvl of undsirabl nois in th rcivr. Howvr, thr ar instancs in which grating lob can b usful, such as in radio intrfromtry usd in radio astronomy [1]. 1

4 Volum 156 No 6, Dcmbr 16 Fig. : Array factor pattrns of 5, 9, 13, and 1-lmnt broadsid arrays at th spacings of: (a) d.5 (b) d.5 (c) d.75 (d) d () d

5 Volum 156 No 6, Dcmbr 16 Fig. 3: Radiatd far Fild pattrns of 5, 9, 13, and 1-lmnt broadsid arrays at th spacings of: (a) d.5 (b) d.5 (c) 3. Dirctivity Numrical data ar computd for dirctivity using qn. (5) and ths ar rprsntd in graphical format as shown in Fig. (), in which dirctivity is plottd against numbr of lmnts in th arrays. Th rsults show that dirctivity incrass with th numbr of lmnts ovr wid rang of valus of spacing considrd. This cannot b an abrration as prvious rsults dpictd in Figs. (a) through () and Figs. 3(a) through 3() hav shown that main lob bam width of array pattrns rducs as th numbr of lmnt incrass d.75 (d) d () d rsults displayd for th array factor and radiatd far filds for all valus of spacing considrd that, main lob bam width rducs as numbr of lmnts and spacing btwn th lmnts incras. This is consistnt with numrical data obtaind for dirctivity which rvals that arrays dirctivity incrass with numbr of lmnt. For th sak of comparison, array factor pattrns xhibit bidirctional bam radiation (backward and forward radiation), whras, ovrall far fild pattrns dpicts radiation in th forward dirction. It is of intrst to not that whn th spacing btwn th lmnts is blow, both th array factor pattrns and ovrall far fild pattrns show rmarkabl and dsirabl bam radiations, whras whn th spacing is byond, numrous grating lobs ar producd. Ths rsults suggst that array structurs with spacing blow could find usful application for far distant communication whil array structurs with spacing byond could b dsirabl in radio intrfromtry usd in radio astronomy. It should b rmarkd hr that, to avoid th occurrnc of grating lobs, th spacing btwn th lmnts should b lss than. Applications of analysis outlind in th papr as wll as th us of othr mthods in tackling such problms will b xplord in th futur. 5. REFERENCES [1] Godara L.C Applications of antnna arrays to mobil communications Part I: Prformanc improvmnt, fasibility, and systm considrations. Procding of th IEEE, Vol. 85, No 7, [] Tsoulos G.V. 1. Adaptiv antnnas for wirlss communications, IEEE Prss, Piscataway, NJ. [3] Chandran S.. Adaptiv Antnna Arrays: Trnds and Applications, Springr. Fig. : Variation of th dirctivity with th numbr of array lmnt at diffrnt intr-lmnt spacing. CONCLUSION AND SUGGESTION FOR FUTURE WORK Th drivation of th radiatd far fild of broadsid array assuming sinusoidal currnt sourc has bn prsntd in this papr. Numrical rsults ar compild in graphical formats for th array factor pattrn, ovrall far zon radiation pattrns and dirctivity of diffrnt forms of array. W find from numrical [] Krishna P.R., Lakshmi S.S., Srdvi I., Khan H., Aditya M.P.K., Krishna V.V., Lavanya J. 1. Sidlob supprssion of concntric circular arrays using nonconvntional bamforming tchniqu. Intrnational Journal of Modrn Enginring Rsarch (IJMER), Vol., No 3, [5] Lastha T.S.J., Sukansh R. 11. Synthsis of linar array using Gntic Algorithm to maximiz sidlob 3

6 Volum 156 No 6, Dcmbr 16 rduction. Intrnational Journal of Computr Applications, Vol., No. 7, [6] Adkola S.A., Mowt I. A.., Ayorind A. A. 7. A rigorous analysis of th radiation charactristics of hlical bam antnna. Europan Journal of Scintific Rsarch, Vol. 16, No, [7] Kraus J.D. 1988, Antnnas. McGraw-Hill, Inc., USA, nd Edition, 6. [8] Balanis C.A Antnna Thory: Analysis and Dsign. John Wily and Sons, Nw York, nd Edition, [9] Amanprt K. and Amandp S. 1. Analyz th ffct of Numbr of lmnts on Radiation pattrn of Broadsid array and End fir array. Intrnational Journal of Computr Applications, Vol. 5, No. 18, 31-3 [1] Orfanidis S.J.. Elctromagntic wavs and Antnnas IJCA TM :