Z Patch Antenna Embedded in Superstrates Anisotropic Media

Transcription

1 IOSR Journal of Electronc and Communcaton Engneerng (IOSR-JECE e-issn: ,p- ISSN: Volume 11, Iue 6, Ver. III (Nov.-Dec.016, PP Adnan Affand 1, Mamdoh Gharb 1,Abdullah Dobae 1 1 (Department of Electrcal and Computer, Engneerng/ Kng Abdul Azz Unverty, Saud Araban Abtract:Z hape of Mcrotrp patch antenna embedded n upertrate unaxal Anotropc layer preented. The Anotropc effect ha been enhanced the patch charactertc le drectvty and gan. The formulaton of the canoncal problem of determnng the feld produced by mpreed pont electrc (or magnetc current ource n the preence of a multlayered unaxally anotropc medum, where the ource and obervaton pont are aumed to be n any layer nvetgated va plane wave pectral ntegral repreentaton of the dyadc Green' functon of the layered medum. The radaton feld ha been analyzed analytcally va matlab Code than compared wth CNT Studo Smulaton, and the reult good agreement. Keyword: Anotropc Supertrate, Patch Antenna, Gan, Drectvty, Return lo. I. Introducton Prnted crcut antenna have receved much attenton nce 1953[1]. Thee antenna are popular due to ther attractve feature and many advantage, ncludng low profle, lght weght, conformty to a gven urface, low cot, eay ntegraton wth mcrotrp crcutry, and hgh relablty. Snce then, th technology ha been under contnuou growth. A mple method for analy to approxmate a rectangular patch a to two parallel narrow radatng lot eparated by ome dtance[]. Although the tranmon lne model gve a mple formula for the nput mpedance and reonant frequency, t uffer from ome erou drawbac. It can only be appled to the rectangular hape patche, o other patch confguraton cannot be analyzed by th model. A frngng factor mut be emprcally determned n th model. It gnore the feld varaton along the radatng edge, and alo gnore the urface wave effect. To overcome mot of thee dffculte of approxmate approache decrbed above, the moment method (MM oluton of th cla of mcrotrp tructure ha been propoed by everal author [3,4]. Many materal ued a ubtrate for prnted crcut antenna or ntegrated mcrowave crcut exhbt delectrc anotropy whch ether ntroduced durng the manufacturng proce or occur naturally n the materal. Degnng patch antenna requred a prece nowledge of materal delectrc contant. Becaue of varaton n for many materal batche, an error n prntng patche degn ntroduced and reduced t repeatablty. Anotropy erve to mprove crcut performance n ome applcaton [5]. To protect patch antenna from envronmental hazard, we ue Supertrate (cover delectrc layer. Whether a cover layer naturally formed or mpoed by degn, t may affect adverely the antenna bac performance charactertc, uch a gan and radaton retance. For th reaon, t mportant to analyze upertrate effect o that the prnted-crcut antenna performance can be predcted wth hgher accuracy.[6] Alo, better undertandng of the cover parameter may be mplemented to advantage n the enhancement of the prntedcrcut antenna performance. In th tudy, the formulaton of the canoncal problem of determnng the feld produced by mpreed pont electrc (or magnetc current ource n the preence of a multlayered unaxally anotropc medum, where the ource and obervaton pont are aumed to be n any layer preented. The formal oluton of the problem obtaned va plane wave pectral ntegral repreentaton of the dyadc Green' functon of the layered medum. The formulaton decompoe the dyadc Green' functon nto TE and TM wave and expree t n term of Weyl-type ntegral. Recuron relaton for approprately defned reflecton and tranmon coeffcent are preented. Alo, the plane wave pectral form of the dyadc Green' functon expreed n term of the uual Sommerfeld form ntegral. II. Dyadc Green' Functonfor Unaxally Anotropc Layered Meda Conder the layered medum hown n Fg. 1 wth mpreed ource located n an arbtrary layer (. The layer are aumed to be unaxal n both Anotropc and. That = z (1 DOI: / Page

2 = z where and are the permttvty and permeablty tenor, repectvely. For an mpreed electrc ource located n the layer (, the wave equaton for n the layer ( gven by E (r E ( r = J ( r (3 where = 1, and the Kronecer delta. The dyadc Green' functon G equaton ( r, r G ( r, r G The electrc feld E gven by, ( for the unaxally anotropc layered medum atfy the followng 0, ( r r = I ( r r, = (5 E ( r = G ( r, r J ( r dv and V the volume ncluded by the ource n layer (. The dyadc Green' functon G atfy the followng boundary condton V zˆ G = z ˆ G( 1 (6 zˆ G = z ˆ G ( 1 ( 1 (4 (7 at the nterface z d ( 0,..., n. In the layer ( (ource, the dyadc Green' functon G can be expreed a a uperpoton of the unbounded dyadc Green' functon G ( p due to the prmary exctaton and ( a cattered dyadc Green' functon G. Hence for any layer ( G = G ( p + G (8 where G atfe the homogeneou equaton ( G ( r, r G ( r, r = 0 (9 When the mpreed ource are magnetc, we have Hˆ ( r = ( r, r M ( r dv (10 V where a magnetc type dyadc Green' functon dual to and M the magnetc current dtrbuton. atfy dual boundary condton to Eq. 6 and Eq. 7. We can expre the cattered dyadc Green functon G ( r, r n term of the followng two-dmenonal Fourer tranform: Subttutng n Eq. 8, we get 1 ~ G ( r, r d G (, z, z e ( ( ( r r (11 L ( ~ G (, z, z 0 (1 e( z where L e( ( ~ z a dyadc operator gven by DOI: / Page

3 and L e( ( ~ z = ( ~ ~ I ~ z z d zˆ From Eq. 13, the tranformed operator can be wrtten explctly a L e( ( ~ z (13 (14 1 d y 1 x y d x z z 1 1 d x x y d y z z d x d y z (15 Ung Eq. 1 and Eq. 15, t can be hown that all the component of G dfferental equaton gven by [7] where G ( = [ G ] { det ( ~ L } G and { det L (~ } e ( z e( z ( 0,, =1,,3 atfy the ame determnant of the operator L e( ( ~ z. Than, { det ( ~ } where L e ( z d e d h z = ( ( z ( ( z [ ][ ] ( h ( z z (16 (17 and. ( e ( z Hence, we may defne two poble oluton to G d d [ ( ( h ] G 0 z [ ( ( e ] ( h ( G 0 z ( e ( z ( governed by DOI: / Page (18,, =1,,3 (19,, =1,,3 (0 Ung Eq. 19, Eq 0 Eq. 1, and Eq. 15 t can ealy be hown that ( h G (1 Hence G G ( e ( ( h ( G 3 ( 0 ( h ( h x G1 ( y G ( 0, = 1,,3 ( atfyng Eq. 19 repreent the electrc feld of a TE feld. Smlarly, t found that ( e ( h y G1 ( x G ( 0, = 1,,3 (3 d G d ( e G ( e ( e x y ( ( (, = 1,,3 (4 ( ( e 3 ( 1 z z repreent the electrc feld of a TM wave. And G( repreent the uperpoton of TE Wave that ( h ( e G G G (5 ( ( (

4 In an unbounded regon wth parameter and gven by Eq. 1 and Eq., repectvely, the dyadc Green functon atfy the followng wave equaton ( p G p ( r, r G ( ( r, r = I ( r r (6 a an ntegral repreentaton by mean of t three- p Startng from Eq. 6 and expreng G dmenonal Fourer tranform, we arrve at where and G ( p 1 r, r ( ( r, r zz ˆ ˆ ( r r 8 ( d e 1 hhe ˆ ˆ ( h z 1 hhe ˆ ˆ ( h z ( h z ( h z z ( zz ( zz 1 ( e z 1 ( e z vˆ vˆ ( e ( e v ˆ z e ( e ( e v ˆ z z z ( e z ( zz e ( r r ( e z ( zz, z > z, z < z (7 ˆ ( h ( h 1 h hˆ( hˆ( z z ( zˆ (8 v( 1 ˆ h( ( e ( e ˆ z zˆ z z ĥ a unt vector n the drecton of the electrc feld for TE wave and vˆ a vector n the drecton of the electrc feld for TM wave. In the above the reoluton of the feld nto TE and TM wave follow ealy by ( h ( e collectng together term contanng z and z,repectvely. The G 00 ( r, r wll be drven. Thu, f we conder the ource to be located n the upper half-pace of the layered medum, G 00 can be repreented a a uperpoton of G ( p gven by Eq. 7 and a cattered dyadc Green functon G whch the contrbuton from the layered medum. Thu, we have G00 ( r, r = where for z z : g00(, z; z ( r r zz ˆˆ + (9 0 r r d e ( g z z 00 (, ; 8 (30 ( h = ˆ ( h ( ( ( ( ˆ h 0 z z0 z0 TE + ˆ h ˆ h h h e R h h 1 ( h 0 z ( z0 z 0 ( h 0 e 1 ( e ( e z + e e z z TM ( e ( + ( 0 and for z z : g00(, z; z ( ( e e z0 z0 v v e R v v e ( ( ( h = ˆ ( h ˆ ( h 0 z ( z0 z0 TE ( ( + ˆ h ˆ h h h e R h h 1 ( h 0 z ( z0 z 0 ( h 0 e 1 ( e ( e z + e e z z TM ( e ( + ( 0 ( ( e e z0 z0 v v e R v v e ( ( (31 (3 DOI: / Page

5 Fgure 1. Geometry of the Problem III. Reult And Dcuon Z patch numercal reult embedded n anotropc upertrate tructure hown n Fgure. The effect of anotropy of Supertrate layer n S-parameter, Axal Rato, Drectvty and gan are nvetgated. To mulate the Far Feld Radaton of Z Patch Antenna, a Matlab program wrtten. For Valdaton propoe mulaton oftware CST STUDIO SUITE ued. The compered reult between the Two program wa good mlarty. A mcrotrp Z patch of length Lp = 7 mm and wdth W = 5.5mm on the top of Roger an otropc ubtrate of permttvty ɛr = 3.38, and thcne h = 1.5mm. The Ground plate of rectangular hape wth length L= 1mm and W=8mm.. The Z patch fed wth coaxal probe. The followng anotropc upertrate are ued: prolytc boron ntrde, or pbn ε xx = 5.1; ε zz = 3.4, apphre (ε xx = 9.4; ε zz = 11.6, Eplam-10 (ε xx = 13; ε zz = For ε r = 1(vacuum or Ar ue Foam flae ε r =1.1, whch good approxmaton. Fgure. Z Patch Antenna 3.1 E-Plane Radaton of Z Patch wth one Supertrate Anotropc layer The Anotropc Supertrate effect for Z Patch Antenna conducted.the Supertrate Layer aumed to be anotropc meda wth permttvty Eplam-10 (ε xx = 13; ε zz = The E- Plane Radaton of Z Patch antenna fed by Coaxal Cable wa hown n Fgure 3. Fgure3. E Plane radaton of Z Patch Antenna The CST Smulatng reult almot dentcal to the theoretcal model. DOI: / Page

6 3. Farfeld Drectvte and ganof Z patch wthout any upertrate A Z patch wthout any upertrate wa condered. Fg. 1,how, the crcut of Z patch. Fgure. Drectvty of Z Patch at Fr=9.5 GHz F GHz Drectvty db Gan db Table 1, Drectvte and gan of Z PatchAntenna wthout Supertrate Fgure 3. Gan of Z Patch at Fr=9.5 GFgure 4, S11 of Z Patch Antenna Hz Fgure 5. Gan over Frequency of Z Patch Antenna Fgure 6. Axal Rato of B Patch Antenna CST Studo Sute degn the Z patch (Fg. 1. Fg.4. Show S11 for th confguraton.it clear from Fg., Z patch drectvty 9.1dB.The gan of that patch 9.14 db a hown n Fg. 3. Gan over Frequency hown n Fg. 5, where Axal Rato hown n Fg. 6. DOI: / Page

7 3.3.Farfeld Drectvte and ganof Z patch wth one upertrate layer Table Drectvte and gan of Z Patch Antenna wth one Anotropc Supertrate layer, ε xx = 5.1; ε zz = 3.4 F GHz Drectvty db Gan db Fgure 7. Drectvty of Z Patch at F=39 GHz wth one Anotropc Supertrate layer, ε xx = 5.1; ε zz = 3.4 Fgure 8.Gan of Z Patch at F=39 GHz wth one Anotropc Supertrate layer, ε xx = 5.1; ε zz = 3.4 Fgure 9. S11 of Z Patch Antenna wth one Anotropc Supertrate layer, ε xx = 5.1; ε zz = 3.4 Fgure 10. Gan over Frequency of Z Patch Antenna Fgure 11. Axal Rato of B Patch Antenna wth one Anotropc Supertrate layer, ε xx = 5.1; ε zz = 3.4 DOI: / Page

8 Fg. 7. Show the drectvty for Z patch wth prolytc boron ntrde, or pbn ε xx = 5.1; ε zz = 3.4 upertrate le than Z patch wthout Supertrate. In addton, the gan alo decreaed f addng a upertrate. Fg, 9, how S11.Gan over Frequency hown n Fg. 10, where Axal Rato hown n Fg Farfeld Drectvte and ganof Z patch wth two upertrate layer F GHz Drectvty db Gan db Table 3 Drectvte and gan of Z Patch Antenna wth two Anotropc Supertrate layer, and ε1 xx = 9.4; ε1 zz = 11.6( layer, ε xx = 13; ε zz = 10.6 (layer. Fgure 14. S11 of Z Patch at F=47 GHz wth two AnotropcSupertrate layer, and ε1 xx = 9.4; ε1 zz = 11.6( layer, ε xx = 13; ε zz = 10.6 (layer. Fgure 15. Gan over Frequency of B Patch Antenna wth two Anotropc Supertrate layer, and ε1 xx = 9.4; ε1 zz = 11.6( layer, ε xx = 13; ε zz = 10.6 (layer. DOI: / Page

9 Fgure 16. Axal Rato of B Patch Antenna wth two Anotropc Supertrate layer, and ε1 xx = 9.4; ε1 zz = 11.6( layer, ε xx = 13; ε zz = 10.6 (layer. In th confguraton, apphre (ε xx = 9.4; ε zz = 11.6 for Supertrate 1 ued. Whle, Eplam-10 (ε xx = 13; ε zz = 10.6 ued for Supertrate. From Fg. 1 Drectvty wa ncreaed to 11.7 db, and the gan wa 11.3 at frequency fr = 47 GHz at Fg. 13. Fg. 14, how S11. Gan over Frequency hown n Fg. 15, where Axal Rato hown n Fg Farfeld Drectvte and ganof Z patch wth three upertrate layer F GHz Drectvty db Gan db Table 4. Drectvte and gan of Z Patch Antenna wth three Anotropc Supertrate Layer, ε1 xx = 9.4; ε1 zz = 11.6( layer 1 and ε xx = 13; ε zz = 10.6 ( layer,ε3 xx = 1; ε3 zz = 1( layer 3 Fgure 17. Drectvty of Z Patch at F=47 GHz wth three Anotropc Supertrate Layer, ε1 xx = 9.4; ε1 zz = 11.6( layer 1 and ε xx = 13; ε zz = 10.6 ( layer,ε3 xx = 1; ε3 zz = 1( layer 3 Fgure 18. Gan of Z Patch at F=47 GHz wth three Anotropc Supertrate Layer, ε1 xx = 9.4; ε1 zz = 11.6( layer 1 and ε xx = 13; ε zz = 10.6 ( layer,ε3 xx = 1; ε3 zz = 1( layer 3 DOI: / Page

10 Fgure 19. S11 of Z Patch at F=47 GHz wth three Anotropc Supertrate Layer, ε1 xx = 9.4; ε1 zz = 11.6( layer 1 and ε xx = 13; ε zz = 10.6 ( layer,ε3 xx = 1; ε3 zz = 1( layer 3 Fgure 0. Gan over Frequency of B Patch Antenna wththree Anotropc Supertrate Layer, ε1 xx = 9.4; ε1 zz = 11.6( layer 1 and ε xx = 13; ε zz = 10.6 ( layer,ε3 xx = 1; ε3 zz = 1( layer 3 Fgure 1. Axal Rato of B Patch Antenna wththree Anotropc Supertrate Layer, ε1 xx = 9.4; ε1 zz = 11.6( layer 1 and ε xx = 13; ε zz = 10.6 ( layer,ε3 xx = 1; ε3 zz = 1( layer 3 In th cae, apphre (ε xx = 9.4; ε zz = 11.6, wa ued for the upertrate one. The Second one, Eplam-10 (ε xx = 13; ε zz = 10.6.The thrd one Foam ε r =1.1. ( The Drectvty equal 14.6dB from Fg. 17. The Gan 13.5 db from Fg. 18. S11 wa hown n Fg. 19. III. Concluon Z hape of Mcrotrp patch antenna embedded n Supertrate unaxal Anotropc layer ha been nvetgated. The Anotropc effect ha been proved to enhance the patch charactertc le drectvty and gan. The feld produced by mpreed pont electrc (or magnetc current ource n the preence of a multlayered unaxally anotropc medum ha been calculated va plane wave pectral ntegral repreentaton of the dyadc Green' functon of the layered medum.the radaton feld ha been analyzed analytcally va matlab Code than compared wth CNT Studo Smulaton, and the reult good agreement. Th wor how a hgh gan and drectvty for Z patch antenna embedded n multlayer anotropc meda. Alo, t how, how the anotropc phenomena can mprove the performance of the patch antenna. Reference [1] Nguyen, D.L, Paulon, K.S, Rley, N.G. : 'Reduced-ze crcularly polared quare mcrotrp antenna for.45 GHz RFID applcaton', IET Mcrowave, Antenna & Propagaton, 01, Volume 6, Iue 1, p. 94. [] Pexero, Cutodo. : Mcrotrp patch antenna: An htorcal perpectve of the development,mcrowave & Optoelectronc Conference (IMOC, 011 SBMO/IEEE MTT-S Internatonal, pp [3] R. Katner, E. Heyman, A. Sabban. : 'Spectral doman teratve analy of ngle- and double-layered mcrotrp antenna ung the conugate gradent algorthm', IEEE Tranacton on Antenna and Propagaton, 11. [4] E. H. Newman. : Strp Antenna n a Delectrc Slab, IEEE Tran. on Antenna and propagaton, September 8, 1978, Vol. AP- 6, No. 5, pp [5] K. C. Gupta, R. Gary, I. J. Bahl. : Mcrotrp Lne & Slot Lne, Dedham, MA Artech Houe, 1979, 3 rd edn [6] N. G. Alexopoulo and D. R. Jacon. : Fundamental Supertrate ( Cover Effect on Prnted Crcut Antenna, IEEE Tran. on Antenna and Propagaton, Augut 1984,Vol. AP-3, No. 8, pp [7] S M. Al, and S F. Mahmoud. : Electromagnetc Feld of Bured Source n Stratfed Anotropc Meda, IEEE Tran. on Antenna and Propagaton, September, 1979, Vol. AP-7, No. 5, [8] M. Gharb, A. Affand, S. Al, S. Applcaton of The Moment Method n The Spectral Doman,Lfe Scence Journal, 5,015,1 3. [9] G. Pett, Hertzan Dpole and Mcrotrp Crcut on Arbtrarly Orented Baxally Anotropc Meda,PhD Dertaton, Syracue Unverty, Syracue, NY, December, 008. DOI: / Page

11 [10] J. Graham, Arbtrarly Orented Baxally Anotropc Meda:Wave Behavor and Mcrotrp Antenna,PhD Dertaton, Syracue Unverty, Syracue, NY, 01. [11] A. K. Verma, Input Impedance of Rectangular Mcrotrp Patch Antenna Wth Io/Anotropc Subtrate-Supertrate,IEEE Mc. and Wr. Lt., 11, 001, [1] A. Affand, M. Gharb, S. Al, Plane Wave Spectral Integral Repreentaton of the Dyadc Green Functon of Layered Meda, Lfe Sc. Journal, 4, 015, DOI: / Page