Theory and Experiment of Parasitic Element Effects on Spherical Probe-Fed Antenna

Transcription

1 Journl of Informton Systems nd Telecommuncton Vol. 1 No. 3 July - September Theory nd Experment of Prstc Element Effects on Sphercl Probe-Fed Antenn Jvd Solemn Megun* Fculty of Electrcl nd Computer Engneerng Assstnt Professor Semnn Unversty Semnn Irn jvd.megun@eee.org Mnouchehr Kmyb Fculty of Electrcl nd Computer Engneerng Professor K. N. Toos Unversty of Technology Tehrn Irn kmyb@eetd.kntu.c.r Ahmd Hossenbeg Fculty of Electrcl nd Computer Engneerng K. N. Toos Unversty of Technology Tehrn Irn hossenbeg@eee.org Receved: /Aug/013 Accepted: /Oct/013 Abstrct Theory nd experment of sphercl probe-fed conforml ntenn wth prstc element mounted on sphercl multlyer structure re presented n ths pper. Rgorous mthemtcl Method of Moments (MoMs) for nlyzng vrous rdtng sphercl structures s presented n ths pper by usng Dydc Green's Functons (DGFs) n conjuncton wth Mxed Potentl Integrl Equton (MPIE) formulton. Lner Ro-Wlton-Glsson (RWG) trngulr bss functons re ppled n MPIE formulton. Current dstrbutons on coxl probe nd conforml rdtng elements re computed by usng sptl domn Dydc Green's Functon (DGF) nd ts symptotc pproxmton. A prototype of such n ntenn s fbrcted nd tested. The effect of the prstc element on the nput mpednce nd rdton ptterns of the ntenn s nvestgted. It s shown tht the ntenn chrcterstcs re mproved sgnfcntly wth the presence of the conductng prstc element. Good greement s cheved between the results obtned from the proposed methods nd the mesurement results. Keywords: Asymptotc Approxmton; Dydc Green s Functon; Sphercl Probe-Fed Antenns. 1. Introducton Probe-fed mcrostrp ntenns embedded n lyered sphercl med hve been studed theoretclly nd expermentlly n recent yers. Lner or crculr polrztons cn be cheved by proper desgn of these ntenns mkng them pplcble n bse stton stellte communcton systems. There s n ncresng nterest of usng mcrostrp ntenns n erodynmc pplctons due to ther low profle ese of fbrcton nd conformblty. Full-wve nlyss of these ntenns cn be dvntgeous n desgn procedure. Full-wve numercl technques bsed on Green's functons of the structures re too effcent nd fst [1]-[3]. In [4]- [5] full-wve nlyss of n rbtrry shpe perture coupled ntenn plced on lyered sphere hs been nvestgted by usng sphercl DGFs n combnton wth electromgnetc felds ntegrl equton formultons. Rdton propertes of hemsphercl delectrc resontor ntenn consstng of monopole ntenn plced n delectrc hemsphere hve been theoretclly exmned n [6]. The effect of delectrc superstrte on the rdton pttern of rectngulr mcrostrp ptch ntenn hs been nvestgted bsed on the spectrl-domn MoMs n conjuncton wth the sttonry phse method [6]- [7]. In [8] numercl method hs been presented to nlyze stcked mcrostrp ntenns consderng the shpe of the rdtng elements the juncton of the probe nd the feed current. A strp model n the volume-surfce ntegrl equton (VSIE) formulton hs been used to smplfy the nlyss of the probe-fed conforml mcrostrp ntenns wth rbtrry shpes [9]. An pproch bsed on hybrd volume-surfce ntegrl equton formulton n combnton wth sphercl dydc Green's functon (DGF) s presented n [10] to nlyze perture-coupled multlyer hemsphercl delectrc resontor ntenns (DRA) wth conforml conductng ptches. In ths pper n order to model probe nd ptches wth rbtrry shpes RWG method [11] s used to nlyze sphercl probe-fed ntenns wth prstc elements. Sphercl DGF s ppled n the moment s method formulton. As conforml rdtng elements re consdered n ths pper symptotc pproxmton pproch s * Correspondng Author

2 184 Megun Kmyb & Hossenbeg Theory nd Experment of Prstc Element Effects on Sphercl lso expressed. To vldte the proposed method prototype of ths ntenn s mplemented nd tested. Comprson of the mesured nd clculted nput mpednce nd rdton ptterns shows good greement between the results.. T h e o r y Fgure 1 shows conforml mcrostrp ntenn nd conductng prstc stck embedded n four-lyer sphere. A PEC sphere s locted n the core of the structure nd cn be ssumed s the ntenn ground plne. The prstc ptch mproves mpednce chrcterstc nd drectvty of the ntenn. In order to compute current dstrbutons on the ptches MoM n conjuncton wth DGF of four-lyer sphere s used [1]..1 Mxed Potentl Integrl Equton Formulton One of the effcent numercl methods wth hgh pre-processng gn for nlyzng electromgnetc structures s the method of moment where the source regon must be dvded nto smll cells. In ths method the unknown source currents re obtned v n ntegrl equton formulton wth pproprte Green s functon. Such ntegrl equtons cn be n spce domn spectrl domn or both of these two domns. In generl due to meshng the fnte re source methods bsed on ntegrl equton formultons re more ccurte nd requre less memory nd tme. For ny clss of ntegrl equtons nmely Electrc Feld Integrl Equton (EFIE) Mgnetc Feld Integrl Equton (MFIE) or Mxed Potentl Integrl Equton (MPIE) pproprte type of Green s functon should be used [11-1]. A set of formulton whch uses uxlry potentls nd leds to MPIE formulton s wekly sngulr nd cn be esly ppled n MoM. Fg. 1 Conforml ptch nd prstc element wth probe-fed modelng on lyered sphere. To pply MoM conductng surfces re meshed wth lner trngles nd Ro-Wlton- Glsson (RWG) trngulr bss functons re used to compute current dstrbutons on common edges between two djcent cells [11]. Hence the surfce current nd electrc flux denstes re expnded n terms of ther correspondng bss functons s follow: N M S s In n n1 J ( r) f ( r) (1) In order to derve MPIE formulton n dydc spce mgnetc potentl DGF ( ) nd electrc sclr Green's functon ( ) re requred. cn be formulted by equtng EFIE () wth MPIE (b) nd usng ntegrl nd vector equvlence theorems: ( fs ) Ej GE. J ( r ) ds f s ( fs) A E j A j G. J( r) ds f s () ( fs) G. Jr ( ) ds s (b) ( fs ) ( fs ) 1 ( fs) GA GE G j f (3) where s the electrc feld dydc Green's functon of multlyer sphere presented n [1]. The prmed nd unprmed coordntes nd subscrpts s nd f refer to source nd feld qunttes respectvely. If the source regon s segmented by lner trngles unknown current coeffcents n the ntenn cn be determned by pplyng RWG bss functons nd stsfyng the boundry condtons. Snce tngentl component of electrc feld vnshes on perfect conductng metl mpednce mtrx s formulted s follows:

3 Journl of Informton Systems nd Telecommuncton Vol. 1 No. 3 July - September j f p( r). G A. fq( r) Z pq dsds s s. f p( r) G. fq( r) (4) Where nd re mgnetc potentl DGF nd electrc sclr Green's functon respectvely. Glerkn s method s ppled for test functons nd the ntegrton over the testng trngles cn be voded by usng the centers of feld trngles nd pproxmte Glerkn s method [11]. Typclly n solvng ntegrl equtons by MoM ntegrtng over segmented cells tkes bout 90% of computton volume. The Gussn qudrture method cn be used for ntegrton over source trngles n RWG method. Applyng 3-pont Guss qudrture s suffcent for ths ntegrton. Regrdng Fg. 1 n order to obtn the mpednce mtrx of MoM ll nterctons between source trngles (s=1) nd feld trngles (f=1) should be consdered.. Asymptotc Method for Sphercl DGFs By usng wve trnsformtons some solutons of the wve equton n vrous coordntes cn be pproxmted by specfc functons. Assocted Legendre nd Hnkel trnsforms re used wdely n sphercl coordntes s mentoned n detls n [15]. In multlyer sphere symptotc pproxmtons of the electrc DGFs between lyers cn be used nsted of usng conventonl forms of DGFs. As ll nterctons between current elements should be consdered n computton of the MoM mpednce mtrx symptotc DGFs between lyers s well s those on lyers f=s= re requred. In ths pper cn be 1 or regrdng mcrostrp ptch nd prstc element postons shown n Fg. 1. Asymptotc formulton relted to four-lyer sphere s presented s follows: ( f ) ( fs) g I ; f s G A 0 ; f s (5) j k 1 R j (11) e G g1 g g3 4 k 1 R (5b) j k R j (1) e G t1 g g3 4 k1k R (5c) j k 1R j (1) 1 e G 1 w1 g g3 4 k1k t1 R (5d) j k R j () e G g1 g g3 4 k R (5e) g ( f ) e j k f R R (5f) e j k R g w r R 1 w 1 t 1 1 R r r R r d rd ; cos (5g) (5h) (5) (5j) cos cos cos ' sn sn 'cos( ') (5k) Where nd s the unt dyd. Therefore the nput mpednce of n ntenn locted on multlyer sphere cn be obtned usng DGF or symptotc pproxmton methods. Although symptotc pproxmton method yelds hgher convergence speed n ntenn nput mpednce clculton t cnnot be utlzed for rdton pttern determnton snce feld nd source ponts re not t the sme dstnce from the sphere center. It should be mentoned tht the proposed ntenn cn lso be smulted wth commercl softwres. However smultor pckges re hghly dependent on meshng the structure modelng the probe nd sze of rdton box. Therefore more tme nd memory s requred to obtn precse nd stble results from smultor pckges. Due to fst computton speed of the presented method t s very effcent for the nlyss of vrous sphercl ntenns..3 Sphercl to Crtesn Trnsformton of DGF In order to obtn electromgnetc feld components we requre multplyng DGFs nd current element vector components for the cse of nterest. In order to perform multplcton both DGFs nd current vectors should be n the sme coordntes. For the cse tht conforml ntenn re s dvded nto curvlner trngles s shown n Fg. () current components to be consdered re nd whch re n hrmony wth sphercl components of DGFs [1]. However curvlner meshng s complcted s compred wth lner trngulr meshng consdered n ths pper. Fg.. () Curvlner trngle (b) Lner trngle.

4 186 Megun Kmyb & Hossenbeg Theory nd Experment of Prstc Element Effects on Sphercl As current elements on common edges of lner meshes hve Crtesn components new pproch for dyd nd vector multplcton s presented n ths subsecton. In order to multply current vectors nd DGFs ether Crtesn current vectors should be converted to sphercl vectors or sphercl DGFs should be converted to Crtesn ones. Convertng current vector V ; whch connects two vertces of trngle; from Crtesn to sphercl coordntes results n J non-unque vector becuse J nd re dfferent n ech pont on the edge such s V shown n Fg. (b). Snce there re unque trnsformtons of vectors from sphercl to Crtesn coordntes converson of sphercl dyd to Crtesn dyd cn be exctly mplemented. Therefore by employng the centers of the feld nd source trngles n the clculton of DGFs n Crtesn coordntes the electrc feld vector cn be expressed s: ( ) ( ) ( ) E Crtesn j Crtesn. Crtesn f G J ( r) ds s (6) Thus by usng trngulr lner meshes n Crtesn coordntes only G needs to be converted from sphercl to Crtesn coordntes. For ths purpose ech unt vector should be trnsformed from sphercl to Crtesn coordntes. As DGFs represent nterctons between feld nd source ponts the frst nd second vectors of ech dyd correspond to feld nd source ponts respectvely. All sphercl dyd components cn be converted to Crtesn dyds. As n exmple the converson ˆ equton of ˆr component of dyd s extrcted s follows: rˆ ˆ (sn cos xˆ sn sn yˆ cos zˆ ) f f f f f (cos cos ˆ cos sn ˆ s s x s s y sn s zˆ ) (7) whch subscrpts f nd s refer to feld nd source ponts respectvely. Therefore the Crtesn DGFs comptble wth vector currents components cn be obtned by usng the forementoned converson method. Usng ths pproch s effcent when vector s requested s the output of n ntenn problem soluton. For exmple to determne the ner nd fr feld Ex Ey Ez rdton ptterns of n ntenn ll components of electrc feld cn be clculted. It should be noted tht the proposed ntenn cn be smulted wth commercl softwres. However smultor pckges re hghly dependent on meshng the structure probe modelng nd the sze of rdton box. Therefore more tme nd memory s requred n order to obtn precse nd stble results from smultor pckges. 3. R e s u l t s In order to vldte the proposed method prototype of sphercl probe-fed mcrostrp ptch ntenn s mplemented nd tested. The ntenn dmensons re gven n Tble I. The PEC sphercl shell conssts of two hemspheres constructed by CNC nstrument. Two holes re cut on two sdes of the sphere to pss the coxl cble through the sphere nd connect the nner conductor of the cble to the mcrostrp ptch. The structure cn lso be tested wth only one hemsphere bove plnr perfect ground structure. The ntenn s excted by 0cm RG- 58U coxl cble of 50Ω chrcterstc mpednce. The cble s connected to the mcrostrp ptch t 1cm dstnce from the center of the ptch. The crculr ptch ntenn hs been mde from RT/durod 5870 substrte of 0.8mm thckness nd delectrc constnt of.33. A crculr prstc element s locted bove the ptch by usng spcer mterl of unt reltve permttvty. Fgure 3 llustrtes the fbrcted ntenn. Tble 1: Dmensons of the Probe-Fed Sphercl Antenn PEC sphere rdus Lyer (εr=1) thckness Lyer 3 (εr=.33) thckness Conforml Ptch Antenn Prstc Element 5 cm 0 mm 0.8 mm Ptch 0 7 Prstc The prstc element hs been dvded to 36 trngles yeldng 48 common edges between plus nd mnus trngles nd the conforml ptch hs been segmented nto 104 trngles ledng to 145 common edges. The probe s meshed nto 4 trngles. Hence there re 198 bss functons used n the MoM. In the computton of nput mpednce s source trngles re ner feld trngles t lest 70 terms of sphercl hrmoncs seres should be consdered n electrc sclr Green s functon to obtn good soluton. On the other hnd consderng the frst 0 terms of sphercl hrmoncs s suffcent to obtn rdton ptterns of bout % error. Fgure 3 llustrtes the return loss of the ntenn wth nd wthout the prstc stck. The nput mpednce/dmttnce of ntenn depends on current dstrbuton of source elements n the ntenn nd ths fct comes from the ntegrton method n conjuncton wth MPIE formulton.

5 S 11 (db) Journl of Informton Systems nd Telecommuncton Vol. 1 No. 3 July - September As t cn be notced usng the prstc element yelds better return loss nd ncreses the return loss bndwdth. As llustrted n Fg. 4 there s good greement between the results obtned from mesurement symptotc pproch nd DGF method dB Mesurement Present Computton wth DGF Method Fg. 3 Prototype of the sphercl probe-fed mcrostrp ntenn 0 30 () 0 0dB Antenn wthout Prstc Element (Mes.) Antenn wth Prstc Element (Mes.) Antenn wth Prstc Element (Asymptotc Method) Antenn wth Prstc Element (DGF Method) Frequency (GHz) Fg. 4. Computed nd mesured return loss of the sphercl multlyer probe-fed ntenn. 10 Mesurement Present Computton wth DGF Method -10 Fg. 5 demonstrtes the rdton ptterns of the sphercl probe-fed ntenn t 3.15 GHz wth prstc element obtned from nlytcl soluton nd the mesurement of the ntenn. As t cn be notced good greement between the results s cheved. The dfference s due to the probe nductve rectnce prtl delectrc over the PEC sphere nd fbrcton tolernce. Typclly mtchng crcut should be desgned for sphercl perture-coupled ntenn to mtch the nput mpednce of the ntenn to 50Ω lod. In the presented method t tkes bout 8 mnutes to compute E- or H-plnes rdton ptterns (wth 60 dvsons of ) wth Core GHz processor. The fst computton tme of ths method s consderble n comprson wth CAD smultor pckges nd s very effcent for nlyss of sphercl ntenns. Fgure 6 llustrtes the mesured rdton ptterns wth nd wthout the prstc element. It s observed tht the stck ncreses the ntenn drectvty nd decreses sde lobes levels n the rdton ptterns (b) Fg. 5 Rdton ptterns of the sphercl probe-fed ntenn t 3.15 GHz wth prstc element; () E-Plne (b) H-Plne. As shown n Fg. 6 prstc element mkes ntenn rdton ptterns more drectve but t ncreses cross polrzton rdtons. The ltter s becuse of electromgnetc felds perturbton due to the exstence of prstc element. The ntenn effcency s mesured by Bluetest reverberton chmber setup nd s bout 86% nd 83% t 3.1GHz nd 3.GHz respectvely. A stndrd ntenn s used to mesure the gn of the ntenn wth nd wthout the prstc element. Tble II shows the ntenn gn t dfferent frequences. It s notced tht the gn of the ntenn s ncresed wth the presence of the prstc element. -150

6 188 Megun Kmyb & Hossenbeg Theory nd Experment of Prstc Element Effects on Sphercl Fg. 6 H-Plne rdton ptterns of the sphercl probe-fed ntenn wth nd wthout prstc elements t f=3.ghz. Tble : Mesured Gn of the Sphercl Probe-Fed Antenn Frequency (GHz) Gn Wthout Prstc Element (db) Gn Wth Prstc Element (db) dB -30 Hplne wthout Prstc Hplne wth Prstc Concluson Full-wve nlyss of probe-fed mcrostrp ntenn wth conforml prstc element mounted on three-lyer sphercl structure hs been presented n ths pper. Green s functons requred n MPIE formulton hve been extrcted. The ntenn hs been nlyzed by usng lner trngulr cells nd by modelng the coxl probe. Ner nd fr felds of the ntenn hve been clculted resultng n computton of the nput mpednce nd rdton ptterns of the ntenn respectvely. To vldte the present computton sphercl probe-fed mcrostrp ntenn hs been mplemented nd tested. Robustness nd ccurcy of the proposed method hve been verfed by comprng the results of our method wth those of the mesurement. The prstc element mproves the ntenn chrcterstcs such s nput mpednce gn nd rdton ptterns. Acknowledgements The uthors would lke to thnk the K. N. Toos Unversty Wreless Test Lb. for the mesurement of the ntenn effcency. References [1] C. T. T Dydc Green s Functons n Electromgnetcs Theory New York: IEEE Press [] W. C. Chew Wves nd Felds n Inhomogeneous Med New York: IEEE Press [3] A. Fllh nd B. Oswld On the computton of electromgnetc dydc Green's functon n spherclly multlyered med IEEE Trns. Mcrowve Theory Tech. vol. MTT-59 no. 6 pp Jun [4] Jvd. S. Megun M. Kmyb nd A. Hossenbeg Theory nd experment of sphercl perture-coupled ntenns IEEE Trns. Antenns Propgt. vol. 61 no. 05 pp My 013. [5] Jvd. S. Megun M. Kmyb nd A. Hossenbeg Sphercl Aperture-Coupled Antenns wth Prstc Element Appled Computtonl Electromgnetcs Socety (ACES) Journl vol. 7 no. 1 pp Dec. 01. [6] Z. Spus N. Burum nd J. Brtolc1 Anlyss of rectngulr mcrostrp ptch ntenns on sphercl structures Mcrow. Opt. Technol. Lett. vol. 36 ssue 4 pp Feb [7] T. Fortk L. Djouneb F. Chebrb & A. Benghl "Rdton of rectngulr mcrostrp ptch ntenn covered wth delectrc lyer" Interntonl Journl of Electroncs vol.95 ssue 9 pp [8] J.P. Dmno nd A. Ppernk Survey of nlytcl nd numercl models for probe-fed mcrostrp ntenns IEE Proc.-Mcrow. Antenns Propg. Vol. 141 no. I pp Februry [9] M. He Q. Chen Q. Yun K. Swy X. Xu A Smple Strp Model n the Volume-Surfce Integrl Equton for Anlyss of Arbtrry Probe-Fed Conforml Mcrostrp Antenns IEEE Antenns nd wreless propg Letter vol. 8 pp Feb [10] A. Hossenbeg M. Kmyb nd Jvd. S. Megun Theory of perture-coupled hemsphercl delectrc resontor ntenns wth rdtng elements Interntonl Journl of Electroncs nd Communctons (AEU) Avlble onlne 31 My 013. [11] S. M. Ro D. R. Wlton nd A. W. Glsson Electromgnetc sctterng by surfces of rbtrry shpe IEEE Trns. Antenns Propg. vol. 30 pp My 198. [1] L.W. L P. S. Koo M. S. Leong nd T. S. Yeo Electromgnetc dydc Green s functon n spherclly multlyered med IEEE Trns. Mcrowve Theory Tech. vol. 4 pp Dec [13] R. F.Hrrngton Feld Computton by Moment Methods IEEE press seres n Electromgnetc Wves 1991.

7 Journl of Informton Systems nd Telecommuncton Vol. 1 No. 3 July - September [14] W. C. Gbson The Method of Moments n Electromgnetcs Chpmn & Hll/CRC Tylor & Frncs Group 008. [15] R. F. Hrrngton Tme-Hrmonc Electromgnetc Felds IEEE press John Wley & Sons nc [16] S. K. Khms "Asymptotc extrcton pproch for ntenns n multlyered sphercl med" IEEE Trns. Antenns Propg. vol. 58 no. 3 pp Mr Jvd Solemn Megun ws born n 198 n Tehrn Irn. He receved hs B.S. from Semnn Unversty Semnn Irn nd M.S. from K. N. Toos Unversty of Technology Tehrn Irn n 005 nd 008 respectvely ll n Electrcl Engneerng. He receved hs Ph.D. n telecommunctons t K. N. Toos Unversty of Technology Tehrn Irn. Currently he s n ssstnt professor t the fculty of electrcl nd computer engneerng n Semnn Unversty. He hs prtcpted n mny projects nsde nd outsde the unversty. Hs reserch s mnly focused on the res of ntenns nd EM modelng numercl technques n electromgnetcs by usng dydc Green's functons ntenn desgn nd mesurement ctve nd pssve mcrowve nd mllmeter-wve crcut desgn. Durng hs PhD. studes he hs publshed 6 ISI ppers (ncludng IEEE Trnsctons on Antenn nd Propgton journl Appled Computtonl Electromgnetc Socety (ACES) journl Electromgnetcs journl Interntonl Journl of Electroncs nd Communctons (AEU) nd ELEX journl) 3 scentfc reserch ppers nd 3 ppers n conference proceedng. Mnouchehr Kmyb receved the B.S. nd M.S. from the Unversty of Tehrn Tehrn Irn nd the PhD degree from Mchgn Stte Unversty n 198 n electrcl engneerng. Hs reserch nterest ncludes the metmterls nd ther pplctons n ntenn engneerng electrclly smll ntenns mcrowve nd mllmeter-wve crcuts nd moble communcton systems. He ws professor n the Deprtment of Electrcl Engneerng K.N. Toos Unversty of Technology Tehrn Irn. Dr. Kmyb hs been ledng group of grdute students n the res of negtve-refrcton metmterls nd ther mcrowve pplctons ntegrted ntenns nd components for brod-bnd wreless telecommunctons novel ntenn bem-steerng technques mllmeter nd submllmeter-wve crcuts s well s sctterng nd nverse sctterng problems. Ahmd Hossenbeg ws born n 1983 n Tehrn Irn. He receved the B.S. n electrcl engneerng from Shhd Bhonr Unversty Kermn Irn nd M.S. n telecommunctons engneerng from K. N. Toos Unversty of Technology Tehrn Irn n 006 nd 008 respectvely. He receved hs Ph.D. n telecommunctons engneerng t K. N. Toos Unversty of Technology Tehrn Irn. Hs mn re of nterest s numercl technques n electromgnetc theory nlyss nd desgn of sphercl perturecoupled Delectrc Resontor Antenns (DRA) usng DGFs ntenn desgn nd mesurement mcrowve nd hgh frequency crcut desgn.

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