Tishreen University Journal for Research and Scientific Studies - Engineering Sciences Series Vol. ( ) No. ( ) Fractal Geometry.

Transcription

1 Tishrn Univrsity Journal for Rsarch and Scintific Studis - nginring Scincs Sris Vol. ( ) o. ( ) Fractal Gomtry Auto-similarity a.salh@fr.fr ١١٣

2 Tishrn Univrsity Journal for Rsarch and Scintific Studis - nginring Scincs Sris Vol. ( ) o. ( ) Analyzing and Dsigning Fractal Antnna Arrays and Comparing thm With Linar Antnna Arrays Dr. Alsamawal Salh Dr. Taj din Jarkas (Rcivd / /. Accptd / / ) ABSTRACT Th linar, fractal array has alrady bn accuratly studid and analyzd in ordr to find th optimal antnna and dfin its radiation pattrn. Fractal gomtry is an xtnsion of normal gomtry, spcially th auto-similarity objcts. Th location of fractal antnna lmnts adds svral dgrs of librty to th antnna dsign; that is du to th diffrnc btwn th txtur of fractal and normal objcts. This diffrnc augmnts th numbr of dsign paramtrs for fractal antnna bcaus th fractal array has diffrnt distancs btwn lmnts. This distanc changs whn th dimnsion of fractal objcts is modifid. Th analysis of th rlation btwn fractal objct paramtrs and antnna radiation pattrn and its comparison with linar array antnna shows that th fractal antnna has mor dsign paramtrs, so that it has a bttr capacity for idntifying th antnna rquird for a crtain application. Kywords: Fractal gomtry, Fractal dimnsion, stag of growth, linar array antnna, fractal array antnna, nw dsign paramtr. Assistant Profssor, Dpartmnt of Communications nginring, Faculty of Mchanical and lctrical nginring, Tishrn Univrsity, Lattakia, Syria. -mail: a.salh@fr.fr. Profssor, Dpartmnt of Communications nginring, Faculty of Mchanical and lctrical nginring, Tishrn Univrsity, Lattakia, Syria. ١١٤

3 Tishrn Univrsity Journal. ng. Scincs Sris Fractal Gomtry Auto-similarity km ١١٥

4 km (Fractal Gomtry) Fractus Fractal Zoom [ ] (D) Fractal Dimnsion log( ) D log(/ ) Itration (S) ( Stag of Growth S S S Lacunarity ١١٦

5 Tishrn Univrsity Journal. ng. Scincs Sris Cantor Bar distribution or Cantor fractal Multilayrs Initiator n n n L s ١١٧

6 S d P(r, ) ١١٨

7 Tishrn Univrsity Journal. ng. Scincs Sris I ji l _ jkr Sin r jil _ jkr Sin r ji l _ jkr Sin r jil r _ jkr Sin j j 3 I I. I I. j r r d. Cos kdcos jkdcos j r 3 r d. Cos r =r, I =I 3 jil r _ jkr Sin kdcos jkdcos j jil r _ jkr Sin kdcos j kdcos j Total 3 θ Total θ jkdcos j kdcos j kdcos j j ψ 0 j j j j kdcos j kdcos j kdcos sin sin ١١٩ j j n kd Cos kd kd ψ

8 sin sin sin Sin sin Total jil r _ jkr H sin Sin sin Total Total kd cos kd cos Fractal objct Cantor distribution ١٢٠

9 Tishrn Univrsity Journal. ng. Scincs Sris (a) (b) a r S r M= S r M r r rm rm d M.Cos r M r M d M.Cos r r r r d.cos r r d.cos d, d,... d M, d M ln( ) ln( ) D 0.63 ln( ) ln( 3 ) ١٢١

10 ١٢٢ L 7 L d S 3 L 9 L d S L 3 L d S F ) Cos kd j( ) Cos kd j( ) Cos kd j( Total... M F F.

11 Tishrn Univrsity Journal. ng. Scincs Sris (a) (b) θ 0 3 θ d λ 90 d λ 50 0 a a ψ ψ π ψ π ψ π d λ ١٢٣

12 ln( ) ln( ) D 0.63 ln( ) ln( 3 ) θ 0 θ 0 θ ψ ١٢٤

13 Tishrn Univrsity Journal. ng. Scincs Sris a λ b λ c ψ ln( ) ln( ) D ln( ) ln( 4 ) ln( ) ln( ) D 0.43 ln( ) ln( 5 ) λ λ q ١٢٥

14 ١٢٦

15 Tishrn Univrsity Journal. ng. Scincs Sris ψ ψ ψ ψ ψ ψ λ λ Matlab ١٢٧

16 [١] MADLBROT,B,B, Ls Objcts Fractals form Hasard t dimnsion, Paris: Flammarion, ١٩٧٥, ١٩٨٤, ١٩٨٩. [٢] JAGGARD; D.L. X. SU, Rflction from fractal Multilayrs, Optics Lttrs. Vol ١٥, n ٢٤, ١٩٩٠, ١٤٢٨-١٤٣٠. [٣] A.D JAGGARD; D.L. JAGGARD, Scattring from fractal suprlattics with variabl lacunariy, J. Opt. Soc. Amr. A١٥, ١٩٩٨, ١٦٢٦-١٦٣٥. [٤] A.-S. SALH; H.AUBRT, Us of variabl Lacunarity Multi-gap Cantor Slabs in Wavguids for th Dsign of Microwav filtrs, Microwav and optical tchnology lttrs, vol.٢٨, n ٢, January ٢٠٠١, ١٢٧-١٣٠. [٥] F.SURR, A.-S. SALH; H.AUBRT, Frquncy Rspons of Slf-Similar Planar Wavguids, Microwav and optical tchnology lttrs, vol.٣٧, n ٣, may ٢٠٠٣. [٦] Constant A. BALAIS, Antnna Thory, Analyss and Dsign, Scond dition, w York. ١٩٩٧. [٧] X.YAG, J. CHIOCHTTI, D. PAPADOPOULOS; L. SUSMA, Fractal Antnna lmnts and Arrays, Applid Microwav and Wirlss tchnical Fatur, vol.١١, may ٢٠٠٠, ٣٤-٤٦. ١٢٨