Analysis of arrays of printed strip dipole antennas and broadband antennas of six series fed strip dipoles

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1 Iteratioal Joural of Wireless Commuicatios ad Mobile Computig 213; 1(3): Published olie August 3, 213 ( doi: /j.wcmc Aalysis of arrays of prited strip dipole ateas ad broadbad ateas of six series fed strip dipoles Ariait Maraj 1, Ruzhdi Sefa 2 1 Faculty of Computer Sciece, Public Uiversity of Prizre, Prizre, Republic of Kosova 2 Faculty of Electrical ad Computer Egieerig, Uiversity of Prishtia, Prishtia, Republic of Kosova address: ariait.maraj@ui-prizre.com (A. Maraj), ruzhdi.sefa@ui-pr.edu (R. Sefa) To cite this article: Ariait Maraj, Ruzhdi Sefa. Aalysis of Arrays of Prited Strip Dipole Ateas ad Broadbad Ateas of Six Series Fed Strip Dipoles. Iteratioal Joural of Wireless Commuicatios ad Mobile Computig. Vol. 1, No. 3, 213, pp doi: /j.wcmc Abstract: Dipole ateas are suitable i wireless multi-bad techology, because they are simple to desig ad have excellet radiatio properties. Also, it is well kow that aalysis of series-fed strip dipoles ateas are very hard to do because of the presece of dielectric ihomogeeity. I additio, the strip dipoles are closely spaced ad coected through trasmissio lies that are itegral part of the atea. Therefore, a aalysis method that takes ito accout the presece of dielectric substrate ad the effect of coectig lies is preseted to accurately desig these ateas. I this paper, arrays of prited strip dipoles ateas are aalyzed based o momet method i the spectral domai. The double-sided cofiguratio has bee selected because it offers several practical advatages. I this paper, further we will complicate the aalysis by takig ito accout broadbad ateas comprised of six series fed strip dipoles. Keywords: Dipole Ateas, Momet Method, Striplie, Double-Sided Cofiguratio 1. Itroductio Prited dipole ateas are commoly used as radiatig elemets i wireless commuicatios as they are easy to fabricate, have low cost, ad high performace. The ateas are comprised of a umber of closely spaced arrow coductive strips prited o electrically thi dielectric substrates. Although the ateas are easy to make ad iexpesive, they posses tremedous performace capabilities icludig high gai, dual polarizatio, broadbad or multi-bad operatio [1-4]. I additio whe these ateas are fed i series they geerally produce edfire radiatio makig them suitable for use with plae or shaped reflectors, a cofiguratio commoly employed i base statios of wireless commuicatios systems [5]. Prited dipole radiators have bee popular cadidates for phased array ateas that cotai may elemets because of their suitability for itegratio with microwave itegrated circuit modules [6-8]. These ateas have also bee cosidered for applicatio i far-ifrared ad millimeter-wave imagig systems [9, 1]. Although prited strip ateas are itrisically simple, the presece of the dielectric ihomogeeity presets a sigificat challege i fidig computatioally reasoable CAD tool for desigig these ateas. Sigle strip dipoles prited o electrically thi, low permittivity substrates behave similarly to ordiary dipoles, ad they have ofte bee desiged based o experimetal trial ad error [11, 12]. However, whe dipoles of differet legths are closely spaced ad/or coected with each other with trasmissio lies, the radiatio characteristics deped o a large umber of desig parameters. A aalysis method that ca hadle three-dimesioal structures cotaiig both dielectric ad coductig materials should be used to correctly aalyze these ateas. However such a aalysis is computatioally itesive ad it provides o easy way to select optimal desig parameters. A more efficiet full wave aalysis would be to cosider dipoles prited o a ifiite substrate, ad apply a momet method i the spectral domai. Such a approach is used here to aalyze strip dipoles prited o a thi ugrouded dielectric substrate. Similar techiques have bee employed for the aalysis of strip dipoles prited o a grouded dielectric substrate [13] ad o a dielectric halfspace [1]. The procedure for aalyzig arrays of prited strip dipoles ateas based a momet method i the spectral

2 Iteratioal Joural of Wireless Commuicatios ad Mobile Computig 213; 1(3): domai is preseted. The dipoles ca be coected to each other. 2. Atea Cofiguratio Fig. 1 is a schematic drawig of a array of series-fed prited strip dipoles. The atea cosists of several prited strip dipoles of differet legths, with the arms prited o opposite sides of a electrically thi dielectric substrate that are coected through parallel striplies. Figure1. Drawig of a series-fed prited strip dipole atea The parallel striplie cosists of two broadside-coupled strips; each sectio may have differet widths, ad is characterized its characteristic impedace Z ad effective relative permittivity ε eff. The atea is fed from ad the other ed is ope circuited. I geeral, some strip dipoles may be parasitically placed ad several dipoles ca be fed simultaeously. Usually a microstrip-to-parallel striplie trasitio is used to feed the atea from a covetioal coaxial coector [14]. The double-sided cofiguratio has bee selected because it offers several practical advatages such as: whe required the lie polarity betwee the strip dipoles ca be easily reversed as show i Fig. 1, parallel striplies offer low as well as large values of lie impedaces with practically reasoable coductor widths, ad parallel striplies do ot radiate sice they are closely spaced. 3. Aalysis Model Aalyses of series-fed prited strip dipole ateas are complicated by the presece of the dielectric ihomogeeity. I additio, the strip dipoles are closely spaced ad coected through trasmissio lies that are itegral part of the atea. Sice they are prited o fiite dielectric substrates, they represet three-dimesioal composite structures cosistig of coductig ad dielectric parts. A space-domai momet method aalysis would require solvig for the coductig currets o the strips ad the polarizatio currets i the dielectric volume, resultig i a large umber of ukows [15]. To simplify the aalysis, it is assumed that the coductive strips are prited o a ifiite dielectric substrate ad the effect of the coectig lie is accouted for separately by usig a stadard trasmissio lie theory. The approach used to aalyze the ateas is described i the followig. Figure2. Geometry of a group of l parallel prited strip dipoles. Fig. 2 shows the geometry of l strip dipoles prited o a dielectric substrate of height h ad relative permittivity ε r. The strips have dimesios L 1, w 1, L 2, w 2,..., L l, w l ad are separated by distaces d 1, d 2,, d l. They are assumed to be thi ( w i << Li, i = 1,2,, l ) so oly the x directed currets are cosidered. All the strip dipoles that are coected with trasmissio lies are assumed to be fed by delta gap geerators. The procedure is similar to that used for aalysis of microstrip dipoles [13]. The x compoet of the electric field o the strip side of the dielectric substrate due to strip currets ca be expressed as: Ex( x, y,) 1 G 2 xx 4 j( kx x+ y) ( kx, ) Jx( kx, ) e dkxd = π (1) where J k, k ) is the Fourier trasform of the surface x ( x y curret desity o the strips, j x ( x, y), ad G k, k ) is the spectral domai Gree s fuctio give as: xx ( x y Z k k k k k Gxx ( kx, ) = ε 1h k a x 1 2 y ( k k h + jk k h) + ( k k h + jk k ) r 2 cos 1 1 si 1 1 cos 1 2 si 2 β Tm Te (2) Tm = 2( ε rk2 cosk1h / 2 + jk1 sik1h / 2)( k1 cosk1h / 2 + jεrk2 sik1h / 2) (3) T e = 2( k2 cosk1h / 2 + jk1 sik1h / 2)( k1 cosk1h /2 + jk2 sik1h /2) (4) Where = ε k k 1 r β, Im( k 1 ) <, k 2 =k β, Im( k 2 ) <, β =k x + k y, k = ω εµ, adz a = µ /ε. A electric field itegral equatio is formed by requirig that the total electric field, the scattered electric field of Eq. (1) plus the icidet field be zero o the strip surfaces. I order to solve this equatio, first the ukow curret desity o the strips is expaded i a set of N = N1 + N2 + + N l basic fuctios with ukow coefficiets I as: f( x, y) = π N jx( x, y) = If( x, y) (5) = 1 ( w / 2) i ( y y) ( l x x ) sike sikeh,

3 76 Ariait Maraj et al.: Aalysis of Arrays of Prited Strip Dipole Ateas ad Broadbad Ateas of Six Series Fed Strip Dipoles x x < l, y y < w i / 2 (6) Where l is the half-legth of the expasio mode, x ad y are the coordiates of the ceter of mode, w i is the width of the strip to which the mode belogs, ad k e is chose as ke = k ( ε r + 1) / 2. Eq. (1) is the solved usig a Galerki momet method solutio, leadig to the followig equatio: [ Z ][ I ] = [ V ] (7) where [ Z ] is the impedace matrix of the atea with elemets give by: 1 * Z m = Gxx, 4π 2 ( kx, ) Fm ( kx, ) F ( kx ) dkxd, (8) F ( kx, ) is the Fourier trasform of the expasio mode F x + l jk jy ( k k ) f x y e xx = (, ) e dxdy x l y + w/ 2 x, y, (9) y w / 2 ad * deotes the complex cojugate. The elemets of the excitatio voltage matrix [V ] are all zero except the elemets correspodig to the geerator locatios. The impedace matrix elemets are obtaied through umerical itegratio. The residues at the Gree s fuctio poles are computed with pole sigularities extracted before the itegratio. These poles correspod to the zeros of Eqs. (2) ad (3), that correspod to the characteristic equatios for the TM ad TE surface-wave modes of the ugrouded dielectric substrate [16]. There is always a amout of power coupled ito these surface-waves because both the first TM ad TE modes have zero cutoff frequecies. As the substrate thickess icreases, the power coupled to the first TE surface-wave mode icreases rapidly [9], so strip dipole ateas are efficiet oly if prited o electrically thi dielectric substrates. Nevertheless, the amout of power coupled to surface-waves ca be determied usig the described method. For plaar ateas aalyzed usig the spectral domai approach, a statioary phase method is usually used to obtai the radiatio patters [1,13]. This method gives coveiet ad useful results except for poits close to the dielectric substrate. I fact, patters calculated i this way appear to have ulls at the air-dielectric iterface sice the substrate is assumed to be ifiite. I practice, the H-plae patters of strips prited o electrically thi ugrouded dielectric substrates of fiite size show o ulls there. If strips are ot prited close to the dielectric edge, the strip currets obtaied via Eq. (7) would be accurate eve though the dielectric is of ifiite size, ad accurate radiatio patters are obtaied by assumig the strips radiate ito free space. I this way the cotributio of the polarizatio currets is ot take ito accout, but they are egligible for electrically thi dielectric substrates [17]. Figure3. Geometry of a group of ( l 1) coectig prited striplie. To iclude the effect of the coectig lie, the complete atea system is cosidered as a parallel coectio of two l -termial etworks, which ca be represeted by their admittace matrixes. Oe l -termial etwork, [ Y A], represets radiatig elemets with self ad mutual admittaces of Fig. 2, which are obtaied by usig the preseted approach. The other l -termial etwork, [ Y L ], represets the coectig lies with termials at places where strip dipoles are coected as show i Fig. 3. The elemets of the [ Y L ] matrix are determied usig stadard trasmissio lie equatios (see ext equatio): Y1cot β1d1 ± jy cscβ1d1 [ Y L ] = ± jy1cscβ1d1 jy1cot β1d1 jy2 cot β2d2 jy2 cscβ2d2 jy( l 2) β ( l 2) l 2) jy( β( ± jy ( csc β( Z i = 1/ Yi, i β, ad d i, ± jy2 cscβ2d2 jy2 cot β2d2 jy3 cot β3d3 ± jy ( csc β( l 1_ jy ( cot β( i = 1,2, l are the characteristic impedace, the propagatio costat, ad the legth, respectively, of the coectig lie sectios betwee strip dipoles. If the lie polarity betwee the strip dipoles is otreversed (reversed), the plus (mius) sig must be used for off-diagoal elemets. The l -port etworks, [ Y A] ad [ L ] are coected i parallel as show i Fig. 4. The overall l - Y, port etwork as show i Fig. 1 has ( l 1) ports ope circuited, so that the iput impedace at the first port ca be readily obtaied, ad hece the performace of the atea. The equivalet admittace matrix is also used to fid the complex voltage of delta gap geerators that are used to derive radiatio characteristic of the atea. I geeral ot all prited dipoles have to be coected with trasmissio lies. Some of them ca be made parasitic to form for example Yagi-Uda arrays of prited dipoles.

4 Iteratioal Joural of Wireless Commuicatios ad Mobile Computig 213; 1(3): the secod dipole maily cotributes to radiatio (see Fig 6-b). Figure4. Represetatio of the array of prited strip dipoles ad the coectig lies with admittace matrices. 4. Aalysis Results of Arrays of Prited Strip Dipole Ateas I this sectio, aalysis results for a series-fed array of two prited strip dipoles that operates as a dual-frequecy atea are preseted. First, the effect of dielectric substrate o the iput impedace of this atea is show i Fig.5 It ca be see that the calculated results agree well with experimets whe the dielectric substrate is take ito accout. Atea dimesios are like below: Strip width: w1 = w2 = 6mm Dipole legths: L1 = 134mm, L2 = 78mm Distace betwee dipoles: d = 5mm Dielectric substrate thickess: h = 1. 6mm Dielectric substrate permittivity: ε = 3. 2 r a) Distributio of each strip dipole at.9 GHz b) Distributio of each strip dipole at 1.55 GHz Figure6. Calculated curret amplitudes o the two strips of dualfrequecy atea. We also aalyzed the effect of the dielectric substrate o the radiatio characteristics of series-fed strip dipoles ad preset a series fed array atea of six-prited dipoles featurig broadbad operatio. This simple, easily maufactured atea is well suited for the base statio ateas of public mobile commuicatio systems. Figure 7 shows a schematic diagram of the array atea ad iput retur loss of this atea. Figure5. Calculated ad measured iput impedace of the series-fed array of two prited strip dipoles The dual-frequecy operatio characteristics of this atea ca be explaied by observig the curret distributio o each strip dipole at the two operatig frequecies. At the first frequecy of operatio, (.9GHz), the first dipole maily cotributes to radiatio (see Fig 6-a), whereas i the secod frequecy of operatio (1.55 GHz), Figure7. Retur loss of the series-fed array of six prited strip dipoles

5 78 Ariait Maraj et al.: Aalysis of Arrays of Prited Strip Dipole Ateas ad Broadbad Ateas of Six Series Fed Strip Dipoles The ed-fire characteristics of this atea are show i Fig. 8, where the relative frot ad back lobe levels ad atea gai agaist frequecy are plotted. broadbad ateas for fulfillig these requiremets with low cost. These wireless techologies are operatig i multiple frequecy bads. So, the idea is to use oly oe atea that radiates i multiple frequecies. The beefits of usig oly oe atea are multifold, but here we will metio the cost reductio ad the space. I this sectio, first, we have aalyzed a case of seriesfed arrays of six prited strip dipoles i frot of plae reflector. The dimesios are: Distace betwee dipoles D=16 mm ad dielectric substrate thickess h=3mm. Figure8. Relative frot ad back lobe levels ad gai of the series-fed array of six prited dipoles. a) Calculated retur loss Figure9. E- ad H-plae radiatio patter of the series-fed array of six prited strip dipoles. The calculated radiatio patters at two pricipal plaes at frequecies 1885 MHz, 24 MHz ad 22 MHz are plotted i Fig. 9. Small variatios o beamwidth of both E- ad H-plas ca be observed, showig broadbad radiatio characteristics of these ateas. 5. Aalysis ad Results of Broadbad Atea of Six Series Fed Strip Dipoles Wireless techology i geeral is developig more ad more. Icreasig demad for high data rate trasmissio through wireless techology has urged implemetatio of b) Calculated radiatio characteristics Figure1. a) Calculated retur loss ad b) Calculated radiatio characteristics I this case we have calculated oly six frequecies. I this case it is used reflector calculatio which is very itesive calculatio. I the figure 1, we have preseted calculated results of retur loss (S11 parameters), for differet frequecies. We also aalyzed the effect of the dielectric substrate o the radiatio characteristics of series-fed arrays of six

6 Iteratioal Joural of Wireless Commuicatios ad Mobile Computig 213; 1(3): prited strip dipoles i frot of plae reflector [18]. This simple, easily maufactured atea is well suited for the base statio ateas of public mobile commuicatio systems. Figure 7 shows a schematic diagram of the array atea ad iput retur loss of this atea. Whereas, H plae radiatios patter are show i the figure below: atea gai agaist frequecy are plotted. Figure12. Relative frot ad back lobe levels ad gai of the two parallel arrays of series-fed strip dipoles Figure 13 shows a schematic diagram of the two parallel of series fed prited strip dipoles as well as a iput retur loss of this atea s system. a) H-plae radiatio patter f= 1885Mhz, f=1955mhz, ad f=225mhz a) Calculated retur loss b) H plae radiatio patter for f= 21Mhz, f=2155mhz, ad f=22mhz Figure11. H plae radiatio patter for differet frequecies From figure 11, small variatios o beamwidth of H- plas ca be observed, showig broadbad radiatio characteristics of these ateas. Secod case sceario: Two parallel arrays of series-fed prited strip dipole i frot of a plae reflector. Oly six frequecies calculated with reflector. Lies are for the same case without reflector for compariso The ed-fire characteristics of this atea are show i Fig. 12, where the relative frot ad back lobe levels ad b) Calculated radiatio characteristics Figure13. a) Calculated retur loss ad b) Calculated radiatio characteristics

7 8 Ariait Maraj et al.: Aalysis of Arrays of Prited Strip Dipole Ateas ad Broadbad Ateas of Six Series Fed Strip Dipoles The calculated radiatio patters at frequecies 1885 MHz, f=1955 MHz, ad f=225 Mhz are plotted i Fig. 14.a. Whereas, the calculated radiatio patters at frequecies f= 21 MHz, f=2155 MHz, ad f=22 MHz are plotted i Fig. 14.b. a) H-plae radiatio patter f= 1885Mhz, f=1955mhz, ad f=225mhz b) H plae radiatio patter for f= 21Mhz, f=2155mhz, ad f=22mhz Figure14. H plae radiatios patter for a) f= 1885 MHz, f=1955mhz, ad f=225mhz ad b) f= 21Mhz, f=2155mhz, ad f=22mhz I figure 14, it ca be observed variatios o beamwidth of H-plas, showig broadbad radiatio characteristics of these ateas. As we ca see, i this figure x4.a, there is a very small differetiatio o beamwidth for differet frequecies, whereas i fig x.4b, it is hard to see ay differece for differet frequecies. 6. Summary I this paper have bee aalyzed differet scearios of prited strip dipole ateas. These aalyses are doe based o momet method i spectral domai. First, we have aalyzed a case of series-fed arrays of six prited strip dipoles i frot of plae reflector. I this case we have calculated oly six frequecies. I this case it is used reflector calculatio which is very itesive calculatio. Also we have aalyzed two parallel arrays of series-fed prited strip dipole i frot of a plae reflector. Oly six frequecies calculated with reflector. Lies are for the same case without reflector for compariso. For this case, we have preseted radiatio patters at frequecies 1885 MHz, f=1955 MHz, f=225 MHz, f= 21 MHz, f=2155 MHz, ad f=22 MHz. From this case, we ca see observed variatios o beamwidth of H-plas, showig broadbad radiatio characteristics of these ateas. I this paper have bee aalyzed arrays of prited strip dipole ateas. As i [18], here also it is used momet method i the spectral domai. The double-sided cofiguratio was selected because it offers several practical advatages such as: whe required the lie polarity betwee the strip dipoles ca be easily reversed. To simplify the aalysis, it was assumed that the coductive strips are prited o a ifiite dielectric substrate ad the effect of the coectig lie is accouted for separately by usig a stadard trasmissio lie theory. I this paper we also aalyzed the effect of the dielectric substrate o the radiatio characteristics of series-fed strip dipoles ad preset a series fed array atea of six-prited dipoles featurig broadbad operatio. We have also aalyzed differet scearios of prited strip dipole ateas. First, we have aalyzed a case of series-fed arrays of six prited strip dipoles i frot of plae reflector. I this case we have calculated oly six frequecies. I this case it is used reflector calculatio which is very itesive calculatio. Also we have aalyzed two parallel arrays of series-fed prited strip dipole i frot of a plae reflector. Oly six frequecies calculated with reflector. Lies are for the same case without reflector for compariso. For this case, we have preseted radiatio patters at frequecies 1885 MHz, f=1955 MHz, f=225 MHz, f= 21 MHz, f=2155 MHz, ad f=22 MHz. From this case, we ca see observed variatios o beamwidth of H-plas, showig broadbad radiatio characteristics of these ateas. Refereces [1] K. Fujimoto ad J. R. James, Mobile Atea System Hadbook, Artech House, Bosto, 1994, ch. 3. [2] F. Tefiku ad C. A. Grimes, Desig of broadbad ad dualbad ateas comprised of series-fed prited-strip dipole pairs, IEEE Tras. Ateas Propagat., vol. 48, pp , Ju. 2. [3] F. Tefiku ad E. Yamashita, Double-sided prited strip atea for dual-frequecy operatio, IEEE AP-S It. Symp. Dig., pp. 5-53, July [4] F. Tefiku, A broadbad atea of double-sided prited strip dipoles, It. Symp. o Ateas ad Propagat., Japa (ISAP 96), pp , Sep

8 Iteratioal Joural of Wireless Commuicatios ad Mobile Computig 213; 1(3): [5] F. Tefiku, Broadbad sector zoe base statio ateas, IEEE AP-S Cof. o Ateas ad Propagat. for Wireless Commuicatios, pp , Nov [6] A. J. Parfitt, D. W. Griffi, ad P. H. Cole, Aalysis of ifiite arrays of substrate-supported metal strip ateas, IEEE Tras. Ateas Propagat., vol. 41, pp , Feb [7] J. R. Bayard, M. E. Cooley, ad D.H. Schaubert, Aalysis of ifiite arrays of prited dipoles o dielectric sheet perpedicular to a groud plae, IEEE Tras. Ateas Propagat., vol. 39, pp , Dec [8] B. Edward ad D. Rees, A broadbad prited dipole with itegrated balu, Microwave J., pp , May [9] D. B. Rutledge, D. P. Neikirk, ad D. P. Kasiligam, Itegrated circuit ateas, i Ifrared ad Millimeter Waves, vol.1, pp. 1-91, K. J. Butto, Ed., New York: Academic, [1] M. Komiami, D. M. Pozar, ad D. H. Schaubert, Dipole ad slot elemets ad arrays o semi-ifiite substrates, IEEE Tras. Ateas Propagat., vol. 33, pp. 6-67, Jue [11] A. K. Agrawal ad W. E. Powell, A prited circuit cylidrical array atea, IEEE Tras. Ateas Propagat., vol. 34, pp , Nov [12] E. Levie, S. Shtrikma, ad D. Treves, Double-sided prited arrays with large badwidth, IEE Proc. H, Microwave, Opt. & Ateas, vol. 135, pp , Feb [13] D. M. Pozar, Aalysis of fiite phased arrays of prited dipoles, IEEE Tras. Ateas Propagat., vol. 33, pp , Oct [14] R. Sefa, A. Maraj, Desig of microstrip to balaced striplies trasitios The 1th WSEAS Iteratioal Coferece o TELECOMMUNICATIONS ad INFORMATICS (TELE-INFO '11), Icluded i ISI/SCI Web of Sciece ad Web of Kowledge. [15] I. Teki ad E. H. Newma, Space-domai method of momets solutio for a strip o a dielectric slab, IEEE Tras. Ateas Propagat., vol. 46, pp , Sep [16] R. F. Harrigto, Time Harmoic Electromagetic Fields, McGraw-Hill, New York, 1961, chap. 4. [17] R. Jaaswamy, A accurate momet method model for the tapered slot atea, IEEE Tras. Ateas Propagat., vol. 37, pp , Dec [18] R. Sefa, F. Tefiku, A. Maraj, Aalysis of arrays of prited strip dipole ateas Software, Telecommuicatios ad Computer Networks (SoftCOM), th Iteratioal Coferece, Date of Coferece: Sept, IEEE Coferece, 211