tratioal Joural of Elctroics ad Commuicatio Egirig. SSN 974-266 Volum 4, Numbr (2), pp.3-38 tratioal Rsarch Publicatio Hous http://www.irphous.com Circular Array of Taprd Nylo Rod Atas: A Computatioal Study R.V. Satyaarayaa ad M.V.S. Prasad 2 Profssor of ECE, Sri Vkatswara Uivrsity Collg of Egirig, Tirupati-5752, A.P., dia 2 Asst. Profssor, Dpt. of ECE, R.V.R. & J.C. Collg of Egirig, Gutur-5229, A.P., dia E-mail: v.s.raviutala@gmail.com, mvs_prasad67@yahoo.co.i Abstract this papr th computatioal studis wr prformd o circular arrays usig taprd Nylo (ε r =3) dilctric rod atas, of lgth () qual to 6λ ad tapr agl (θ ) qual to 2.5, as lmts ar prstd. Th objctiv of th computatioal study is to fid th optimum choic of umbr of lmts i th array. Th atas ar uiformly spacd aroud th circumfrc of a circl. Th umbr of radiatig lmts i th array is varid from 8 to 28, with a icras of 4 lmts. Th pricipal pla pattrs ar computd, usig th pricipl of pattr multiplicatio. For ach st of lmts, Half Powr Bam Width (HPBW), Sid ob vl (S), ad Dirctivity (D ) ar dtrmid. Th pricipl pla pattrs ad 3D pattrs ar prstd for th optimum choic of lmts. Kywords: Nylo rod ata, Circular array, Array factor, Dirctivity, Sid ob vl, Half Powr Bam Width. troductio a circular array, th radiatig lmts ar placd alog th circumfrc of a circl with uiform spacig. Ths arrays fid wid applicatios i radio dirctio fidig, air ad spac avigatio, radar ad soar systms []. Svral ivstigatios has b carrid out usig circular arrays usig with diffrt typs of radiatig lmts ad ar rportd i litratur [2]-[5]. A importat fatur of th circular array that is s i most of th applicatios is th scaig of th mai bam through 36 i th azimuthal pla (pla of th array). Howvr, by propr choic of th lmts, thir oritatio ad phas xcitatio it is possibl to obtai a mai bam i th dirctio of zith ad sca it ovr a small agl co, aroud th zith dirctio,
32 R.V. Satyaarayaa ad M.V.S. Prasad with a littl chag of ithr bam width or sid lob lvl. Th choic of Nylo rod ata of lgth 6λ ad tapr agl 2.5, is mad o th basis of th rsults of computatioal studis, carrid out o th radiatio pattrs of taprd Nylo rod atas, rportd i [6]. this papr, th rsults of computatioal studis of th radiatio pattrs, of a circular array of taprd Nylo dilctric rod atas ar prstd. Radiatio from Taprd Nylo rod ata Th radiatio from a dilctric rod ata maily dpds o th dilctric matrial usd to fabricat th ata, physical shap of th ata, ad th mthod of xcitatio of th ata. Th dilctric rod ata is xcitd i th hybrid HE mod. Th advatag of asymmtric HE mod is that it givs maximum radiatio i th axial dirctio ad it dos ot shows ay cut off bhavior. Th amplitud of sid lobs ad back lobs may b rducd, by taprig th dilctric rod ata, util th diamtr is rachd for which th wav impdac bcoms qual to that of fr spac impdac. Taprig th dilctric rod miimizs th stadig wav distributio causd by rflctio at th fr d of th rod ad th lctric fild distributio riss to maximum ar th mid poit of th lgth of th rod ad th falls off towards th fr d [7]. Th lctric filds radiatd by a taprd dilctric rod ata ar aalyzd by Aad Kumar ad Rajswari Chattrj usig th Schlkuoff s quivalc pricipl [8]. Th pricipl stats that th lctromagtic fild isid a surfac S, du to sourcs outsid th surfac ca b producd by sht lctric currts J ad sht magtic currts M ovr th surfac S giv by th followig quatios, J = H () M = E (2) whr is a uit ormal vctor dirctd outwards from S, E ad H ar th valus of E ad H o th surfac S. Th gomtry of taprd dilctric rod is show i Fig.. Followig th aalysis i [8], th lctric fild compots radiatd by a taprd dilctric rod ar giv by: 2 λ r A ad jxp(jβr) Eθ = j(/fε ) si + j(/2fε ) cos si2 2 j(λ/2)cosθ cos si2 3 jλcosθ si 4 + j2πη si θ si 6 π ((+ δlη ) + [(βl /β) + ηδl]cosθ) xp( jβll) si 7 π ((- δlη ) + [(βl /β) - ηδl]cosθ) xp(jβ ll) si 8 (3)
Circular Array of Taprd Nylo Rod Atas 33 2 λ r jxp(jβr) E A = j(/fε ) cosθ cos j(/2fε ) cosθ si si2 2 + j(λ/2)si si2 3 jλ cos 4 + j2π si θ cos + π ((+ δlη ) cosθ + [(βl /β) + ηδl]) xp(jβll) cos 7 + π ((- δlη ) cosθ + [(βl/β ) - ηδl]) xp(jβll) cos 8 5 (4) Z FREE END a l P (r, θ, ) θ R a ρ r z ' Mdium- θ P' (ρ, ', z) Mdium- Є 2 = Є o, a o O Y X FEED END Figur : Gomtry of taprd dilctric rod ata. whr A is th xcitatio costat for H mods ad 2 = xp (jβ z) δ rj (r) { si J ( ξ) + cos2[j ( ξ)/ ] }dz (5) o ξ J( ξ ) 2 = xp (jβ z) δ krj(r) 2 J ( ξ ) ξ dz (6) J( ξ) 3 = xp (jβ z) krj(r) 2 J ( ξ) dz (7) ξ
34 R.V. Satyaarayaa ad M.V.S. Prasad 2 J( ξ) 4 = xp (jβ z) krj(r) cos J ( ξ) cos2 ) dz (8) ξ rj (r) ( δη )J(r) J ( ) dz 5 = xp (jβ z) ξ (9) = xp (jβ z) δrj (r) + δ J(r) J ( ) dz m η () 6 ξ a 7 = R J (R) J ( ξ ) dρ () a 8 J ( ) [ 2J (R) RJ (R)] 2 ξ = J( ξ ) dρ (2) ξ with ξ = β o a si θ ad ξ = β o ρ si θ (3) - (), δ is th ratio of xcitatio costats for E ad H mods. Th valus of δ ad k may b computd, by rprstig thir variatio giv i Fig.2 of [8], by picwis liar modls as: δ =.7 for a/λ. (3) δ = (2.9 a/λ ) / 4 for a/λ. (4) ad k =.5 (5 a/λ ) for a/λ.2 (5) k =.2 (5 7 a/λ ) for a/λ.2 (6) δ is th valu of δ at z = i Fig.. Th H-pla pattr may b obtaid by sttig =, ad th E-pla pattr by sttig =9 i (3) ad (4). Array Factor of Circular Array Th circular array of isotropic radiators is show i Fig.2. Radius of th circl, ρ is ρ = Nλ / 2π (7) whr N is th umbr of lmts i th array ad λ is th wavlgth. Elmts ar placd at azimuthal agular itrvals of 2π / N. Th azimuthal agl of th th lmt is
Circular Array of Taprd Nylo Rod Atas 35 2π = (8) N Array factor, AF, of a circular array of N qually spacd lmts may b writt [] as N AF= = xp { j[ β ρ si θcos( - ) + α ]} (9) whr = amplitud xcitatio of th th lmt, ad α = phas xcitatio of th th lmt, β = 2π / λ is th phas costat. For uiform amplitud xcitatio of ach lmt = o, a costat. To dirct th maximum of th mai bam i th (θ o, o ) dirctio, α may b chos to b α = βρ si θcos( - ) (2) Fig.2, R = r ρcos( ψ ) (2) whr r is th distac from origi to poit P, ρ is radius of circl, ad ψ is th progrssiv phas btw th lmts i th array. Z P(r, θ, ) θ r a r R ρ ψ Y a ρ N- N 2 X Figur 2: Gomtry of circular array of N lmts.
36 R.V. Satyaarayaa ad M.V.S. Prasad Circular Array of Nylo Rod Atas Th taprd Nylo rod atas, with fd d diamtr qual to.25m ar usd as radiatig lmts i th array. Th lmts ar uiformly spacd with a ctr to ctr spacig of λ m btw th lmts. Th radius of th array to plac N umbr of lmts without ovrlappig is th giv by ρ =N λ /2π (22) with this radius th array factor ca b computd usig(9). Total fild, E, of th array ca b computd usig th pricipl of pattr multiplicatio as: E = E (Fild of Sigl lmt) Array Factor (23) Th compots of E radiatd by a sigl Nylo rod ata ar giv by (3) ad (4) ad th array factor is giv by (9). Th pricipl pla pattrs ar computd usig (23). Softwar has b implmtd i matlab to plot th radiatio pattrs. Rsults ad Discussio Circular array of taprd Nylo rod atas of lgth () qual to 6λ, ad tapr agl (θ ) qual to 2.5 is cosidrd, to comput th pricipal pla pattrs of th array at a frqucy of GHz or λ =.3m. Th lmts ar uiformly placd aroud th circumfrc of th circl. Th umbr of lmts is varid from 8 to 28 with a icras of 4. Th pricipal pla pattrs ar computd for ach st of lmts ad HPBW, S, ad D ar computd for ach st of lmts ad rsults ar prstd i Tabl-.Th Dirctivity may b computd usig Kraus s formula []: Dirctivity (D ) = 4253/ (θ E θ H ) (23) Whr θ E = HPBW i E-Pla (dgrs) θ H = HPBW i H-Pla (dgrs) From th rsults prstd i Tabl-, it may b obsrvd that, with icrasig umbr of lmts i th array th dirctivity as wll as sid lob lvl icras, ad it may also b obsrvd that N=6, may b cosidrd as a optimum choic, bcaus i this cas dirctivity is 3.52 db ad sid lob lvl is -9.9 db. all othr cass, v though dirctivity is high, th S is slightly highr compard with N=6 cas. Th 3D radiatio pattr for optimum choic is show i Fig. 3. Th pricipl pla pattrs for optimum choic of lmts ar show i Fig.4.
Circular Array of Taprd Nylo Rod Atas 37 Tabl : Variatio of HPBW, S, ad D w with umbr of lmts. S.No. Numbr of Elmts(N) 2 3 4 5 6 8 2 6 2 24 28 Radius of th array i cm.27λ.9λ 2.54λ 3.8λ 3.8λ 4.45λ λ λ λ λ λ λ HPBW (Dg.) S (db) = =9 = =9.2 8.2 8.2-2.4-3.98 -.46 -.6 6 4.8 4 3.4 6. 4.6 4 3.4-9.37-8.64-8.4-8.4-9.9-9.2-8.64-8.64 D (db) 25.255 27.888 3.52 32.722 34. 35.52 E = =9.3. 3 Rad Figur 3: Fig 3D diatio pattr circular array of Nylo rod atas 3D Radiatio patt of array of Nylo rod atas. (a) (b) Figur 4: Pricipal Pla pattrs of circular array (N= =6). With a dirctivity of 3.52 db ad sid lob lvl of -9.9 db, this array may b a attractiv choic for radar applicatios.
38 R.V. Satyaarayaa ad M.V.S. Prasad ist Symbols Symbol Maig Uits f Frqucy Hrtz λ o Fr spac wav lgth Mtrs ε Prmittivity of mdium Farads pr mtr μ Prmability of mdium Hris pr mtr β o Phas shift costat of fr spac Radias β Phas costat of guidd wavs isid th dilctric rod ata Radias β Valu of β at z = i Fig. Radias η o Fr spac wav impdac Ohms η Wav impdac of lctric fild compot Ohms m η Wav impdac of magtic fild compot Ohms ρ Radius of circl i th array cm N Total umbr of lmts i th array ψ Progrssiv phas shift btw th lmts Dgrs a r Uit vctor i th dirctio of r cm a ρ Radial uit vctor i th dirctio of ρ cm x, y, z Rctagular coordiats ρ,, z Cylidrical coordiats r, θ, Sphrical coordiats Rfrcs [] Costati A. Balais, 22, Ata Thory Aalysis ad Dsig, 2 d ditio, Joh wily & Sos c., pp 324-328. [2] Rody G. Vaugha, J. Bach Adrso ad M.H. aghor, 988, Circular array of outward slopig moopols for Vhicular Divrsity Atas, EEE Tras. Atas propagatio, Vol.36, No., pp 365-374. [3] Roaold W.P. Kig, 989, Suprgai atas ad th Yagi ad circular arrays, EEE Tras. Atas propagatio, Vol.37, No.2, pp78-86. [4] Sog izhog, Maig, i Chogsh ad Wuqum, 28 simulatio ad aalysis of a microstrip circular array ata at 5 GHz, EEE Xplor, [5] Nav Kumar Saxa ad Dr. P.K.S. Pourush, 29, Circular array of Triagular patchs as filtr, EEE Xplor. [6] Dr. J. Subramayam ad M.V.S. Prasad, 29, Radiatio from taprd Nylo Rod Atas A Computatioal study. CFA Joural of Elctrical ad Elctroics Egirig, vol., issu o.3, pp. 4-24. [7] D.G. Kily, Dilctric Arials, st ditio, 953, Mathu & Co imitd, odo, pag 4. [8] Aad Kumar, R. Chattrj, 968, Radiatio from taprd Dilctric Rod Arials, SC Joural, vol.5, issu o.4, pp. 374-392.