Effect of Ground Conductivity on Radiation Pattern of a Dipole Antenna

Transcription

1 Intnationa Jouna of Coput and ctica ngining, Vo., No. 3, August ffct of Gound Conductivity on Radiation Pattn of a Dipo Antnna Md. Shahidu Isa, Md. Shohidu Isa, S. Mb, I, Md. Shah Aa Abst This pap ais fisty to dvop a thotica fouation of ctoagntic fids abov th ath sufac taking into account th finit and infinit conductivity of th gound- which has th advantags of bing asonaby fast to coput, scondy to invstigat th ffct of gound poptis on th ctic fid intnsity. Fo this pupos w hav anayzd adiation pattn fo finit and infinit gound conductivity, fquncis and diffnt antnna ngths. Th onopo is fd to its bas. Th cunt distibution aong th potion bow gound is th iag of th cunt distibution aong th oigina onopo.th iag souc fo cacuating ctic fid, abov th infinity conducting gound sufac is just opposit to that of th oigina souc. Th iag souc fo cacuating ctic fid abov th finity conducting gound sufac is not just opposit to that of th oigina souc. It is affctd by th gound poptis. Fo sa fquncy and idntica antnna ngth but at diffnt gound conductivity, th xists vaiation in adiation fid. It is obsvd that at sa vau of gound conductivity th adiation fid is sa aso th diction of adiation fid changs. Futho it is obtaind that is of fquncy incass th adiation fid shapy in a paticua diction. Finay w can say that at a fixd antnna ngth, th xists a iniu fquncy fo asuab adiation fid. Indx Ts Antnna, Radiation, Iag Cunt, Dipo Mthod, Gound Conductivity I. INTRODUCTION Antnnas hav bco incagy ipotant to ou socity. Thy a vywh: at ou hos, wok pacs, on ou cas and aicaft whi ou ships, satits and spaccaft bist with th. Mtaic as w as dictic stuctus can b dsignd to aunch o adiat wavs fficinty into spac and to focus o concntat ths wavs in a paticua diction; ths stuctus a fd to as antnnas. Thy a opat accoding to th basic pincips of ctoagntic. Bandwidth, ba width, poaization a th pincipa paats of antnna. An antnna ust incud ipdanc atching. Whn th souc atchs th oad, axiu pow is obtaind. Th antnna ust hav th abiity to atch th tansission in. Th antnna ust sowhat as a sonant cicuit.th adiation pattns shown so fa hav bn obtaind on th assuption that th antnna o antnna aay was situatd in Manuscipt civd on Mach, 9. This wok was suppotd in pat by th Dpatnt of Coput Scinc & ngining, RUT and DUT, Rajshahi-64 and Gazipu-7, Bangadsh spctivy. Md. Shahidu Isa and Md. Shah Aa a B.Sc ng. in ctica and ctonics ngining, zona xcutiv of Gan Phon Liitd in Bangadsh. Md. Shohidu Isa is with th Dpatnt of Coput Scinc & ngining in Dhaka Univsity of ngining & Tchnoogy, Gazipu-7, Bangadsh. f spac fa ovd fo any oth conducting bodis o fcting sufacs. II. TRMINOLOGIS A. ctic Fid Th aa aound an ctic chag ov which th infunc of that chag xists is known as ctic fid. B. Magntic Fid Th aa aound a agntic po ov which th infunc of that po xists is known as agntic fid. C. ctoagntic Fid Th agntic fid poducd by th fow of cticity is known as ctoagntic fid. D. Radiation Pattn A pictoia psntation of th dictiv poptis of an antnna s adiation is fd to as its adiation pattn. This pattn is obtaind by potting th agnitud of th fa fid ctic fid at a fixd distanc fo th antnna as a function of and φ. Ony th vaiation of ctic fid nd b pottd as th agntic fid is atd to th ctic fid by η in th fa fid. W ay dtin th fo of th wavs adiatd fo an antnna if w know th cunt distibution ov th sufac of th antnna. W assu f spac and wit Maxw s cu quations fo usoida fid quation as Εˆ µ Ηˆ ( Ηˆ Εˆ Jˆ s ( Th t Ĵ s in quation ( is a phaso cunt dnsity in th gion, and w wi tat it as bing th souc (know of th fid. W y on two basic vcto idntitis.. A ˆ...(3 Wh Αˆ stands fo vcto agntic potntia.fo any scaa fid V, w ay wit that Β ˆ Αˆ...(4 Appying Lontz condition w hav, Α ˆ µ ˆ...(5. V Ug quation (4 agntic fid can b wittn as Η ˆ Αˆ...(6 µ

2 Intnationa Jouna of Coput and ctica ngining, Vo., No. 3, August III. MATHMATICAL FORMULATION A. xpssion of ctic Fid fo Infinit Gound conductivity ctic fid is obtaind dicty fo quation (6 Εˆ Ε ffid Ηˆ j Id ˆ..(7 j a φ (8 Pacing th cnt of dipo at th oigin of th sphica coodinat syst as shown in Fig. Z d ˆ t I ( z t j jµ t ( W a considing ony fa fid, th adiation distanc fo th cnt of th dipo at point p, w b appoxiaty qua ( and angs and wi b appoxiaty qua to (, as shown in Fig. I ˆ ( z Z/ P z z cos / Y Fig. Fa fid appoxiation Th dipo dictd aong th Z axis, w ay thfo wit an xpssion fo th cunt distibution aong th wi as, considing infinit conductivity, th ua cunt Z Z Iˆ X / ( Z I ˆ( z ( 9 Th iag cunt ˆ Z i I ( Z......( Z Consid th infinitsia sgnt shown in Fig.. If th fid point of intst P is ocatd a distanc away fo th cnt of th dipo and ang, and a distanc and ang fo th cunt nt. Th fa fid ctic fid in quation (8 du to this nt has ony a i Z-/ Fig. Th ong ina dipo antnna W ay substitut into th dnoinato of j quation (, but w shoud not substitut this th t fo th foowing ason: this t ay b wittn as j π.( and its vau dpnds not on th physica distanc but on th ctica distanc ; Thus, it is not a asonab appoxiation to substitut fo in quation (.Thus, w assu that th fid point is sufficint fa, physicay, fo th antnna.fo Fig.. W ay obtain...(3 z cos Substituting quation (4 into th phas t in quation ( and into th dnoinato, w obtain dˆ..(4 z j ( z cos Th tota ctic fid is th su of ths contibutions- coponnt and a dpndnc. Thus w hav

3 Intnationa Jouna of Coput and ctica ngining, Vo., No. 3, August z z.(5 z Intgating quation (5, w obtain η j j jz cos cos[..cos ] cos.. ˆ j I.(6 Th thta vaiation t fo infinit gound conductivity in quation (6 wi b dnotd by cos[. Putting,..cos ] cos π π π cos[( cos ] cos(.....(7 (8 B. xpssion of ctica Fid fo Actua cunt Fo th quation (5, w hav th fa fid fo ua cunt I ˆ ( z is z.(9 z z j ( z cos I ( z...( Fo quation (9 & ( w hav, I j { z. ( z }...( Intgating quation (, w obtain j zcos I 4π j cos j.( cos j cos....( Th vaiation t fo ua cunt of ( dnotd by F ( j cos cos j cos....(3 π Sinc, Thfo π π [{cos(.cos cos( } π π j{(.cos cos. }]...( 4 π π Lt, a cos(.cos cos( π π And b (.cos cos. Fo quation (4 w obtain ( a jb...(5 C. xpssion of ctic Fid fo Iag Cunt Fo th quation (5, w hav th fa fid fo iag cunt I ˆ ( z I ( z Sin j ( zcos is ( dz z.(4. Sinc, z i ( ( I Sin ( z (5. z Putting z-z Fo quation (4. & (5., w hav - 8 -

4 Intnationa Jouna of Coput and ctica ngining, Vo., No. 3, August ( (. z {. I j z cos j ( ( z} (6 ( K, ω ( π π a cos(.cos cos( and π π b (.cos cos. Intgating quation (6 w hav, I j (.( ( j cos cos ( j cos....(7 Ra pat of quation (5 is a R(...(8 Sin Th vaiation t fo iag cunt is dnotd by (.. ( j H, cos cos j cos D. xpssion of Tota ctic Fid fo Finit Gound Conductivity Th tota ctic fid fo finit gound conductivity: ( (...(3 ( ( j η I 4 π cos I j j j.( cos.( j. ( cos. j cos ( cos j cos... (33 Th vaiation t fo tota ctic fid in (33 dnotd by: [{ a( K Lb} j{ b( K La}]...(34..(9 H, π Putting π π a cos(.cos cos( and π π F ( [ K {cos(.cos cso ( } π π π π b (.cos cos. L{(.cos cos.( }] j π π [ K {cos.( (.cos } IV. ANALYSIS In this pap ctoagntic fids hav bn anayzd π π L{cos(.cos cso ( }] ( 3 nuicay ug th thoy dvopd in th pvious [( Ka Lb j( La Kb]...(3 chapt. Th typica od of usoida cunt is usd in anayzing ctoagntic fids. Nuica suts ug nwy dvopd dipo thod a shown fo th foowing paats such as: conductivity of th gound.ho/,.ho/,.ho/,.ho/, and ho/; ativ pittivity of th gound 7 is usd whn ath is dy. Th ffct of gound conductivity on th fid pattn of ina cnt fd onopo antnna

5 Intnationa Jouna of Coput and ctica ngining, Vo., No. 3, August hav bn shown in th foowing figus.th diffnt antnna ngth hav bn considd (,, 3.Sinc th apitud fo is indpndnt of antnna ngth, ony th ativ fid pattns as givn by th pattn fo hav bn copad.in figu 3(a to 3(h A. Radiation pattn fo antnna ngth Fig. 3 and Fig. 4 a th adiation pattn fo ua cunt and Iag cunt spctivy fo infinit gound conductivity Fig. 5 Radiation pattn du to ua cunt Fig. 3 Radiation pattn du to ua cunt Fig. 6 Radiation pattn du to iag cunt C. Radiation pattn fo antnna ngth 3 Fig. 7 and Fig. 8 a th adiation pattn fo ua cunt and Iag cunt spctivy fo infinit gound conductivity Fig. 4 Radiation pattn du to iag cunt 5 8 Fig. 7 Radiation pattn du to ua cunt B. Radiation pattn fo antnna ngth Fig. 5 and Fig. 6 a th adiation pattn fo ua cunt and Iag cunt spctivy fo infinit gound conductivity

6 Intnationa Jouna of Coput and ctica ngining, Vo., No. 3, August Fig. 8 Radiation pattn du to iag cunt Fig. 9 and Fig. a adiation pattn fo tota cunt and fo iag infinit cunt, considing ho/ Fo this sach w can co to th nd that th adiation of antnna can b incasd by iniizing th gound ffct. Phi (φ coponnt of agntic fid intnsity can b dtind. Ug th ctic fid intnsity and agntic fid intnsity th avag pow dnsity vcto can b vauatd. RFRNCS [] Cayton R. Pau, Syd A. Nasa Intoduction to Magntic Fid Scond dition. [] David K. Chng Fid and Wavs ctoagntis Scond dition. [3] Sion Rao, John R. Whinny,Thodo Van Duz Fids and Wavs in Counication ngining. [4] Raakant John D. Kaus, Antnnas. Pubishd by McGRAW-HILL BOOK COMPANY, INC. [5] Raakant GORG KNNDY, BRNARD DAVIS, ctonics Counication Syst. Pubishd by TATA McGRAW-HILL BOOK COMPANY, LTD. [6] Raakant DWARD C. JORDAN & KITH G. BALMAIN ctoagntic Wavs and Radiating Syst, Pubishd by Pntic Ha INC. [7] Magdy F. Iskand, ctoagntic Fids and Wavs by Pntic Ha INC [8] R. Ludwig, A. Konad, A. D. Josph, R. H. Katz, Optiizing th nd-to-nd Pfoanc of Riab Fows ov Wiss Links,ACM/I MOBICOM 99, Satt, WA, Aug [9] Li, S. Q. and C. Hwang, Link Capacity Aocation and Ntwok Conto by Fitd Input Rat in High spd Ntwoks, I/ACM Tansctions on Ntwoking, vo. 3, no., Fb.995, pp Fig. 9 Radiation pattn du to tota cunt Fig. Radiation pattn du to iag infinit cunt V. CONCLUSION Th ffct of gound conductivity on adiation pattn of a dipo antnna has bn anayzd. A goundd onopo antnna is xcitd by usoida souc has bn considd fo this pupos. Fo th ffct of gound conductivity, th adiation fid dcass with th dcas of gound conductivity. Th iag cunt dpnds on th gound conductivity and th adiation fid is affctd by th iag cunt. Th iag cunt is aso dpndnt on fquncy. Fo th sa wavngth, adiation fid incass with th incas of fquncy