Epl equons fo elel petes of syel ouple osp lnes I.M. Bsee Eletons eseh Instute El-h steet, Dokk, o, Egypt Abstt: Epl equons e eve fo the self n utul nutne n ptne fo two syel ouple osp lnes. he obne ptne e use n lulng the nol oe petes (effeve ele onstnt n oe penes). he self n utul ptne fo sye ouple osp lnes e opute fo both flle n epty stutues fo sevel vlues of sp wth n. A set of esgn uves fo effeve oe penes e lulte fo ffeent geoe ensons he nuel esults e ope wth tht use oplete fel soluon. Intouon: Mosp ouple lnes hve onseble nteest ue to the potenl pplons n owve ut eleents suh s fltes, ouples, pene thng netwoks, et. In qus st nlyss of osp lnes the effeve ele onstnt n the oe penes n be obne by lulng the ptne pe unt length of the stutue une onseon. evel ethos e ntoue fo solvng ouple osp lnes, ong the e the lssl onfol ppng, usng ele Geen s funon, vonl tehnque, netwok nlogue, n the fnte ffeene etho. Dffeent oel eletogne sultos e vlble but they eque too uh oputonl e n eoy to be pple wth pl n oplex stutues. o eue the oputonl e, epl equons e eve fo fel solves by uve ftng to extt the nutne n ptne of osp ouple lnes wth equl wth []. In ths ppe, we ntoue epl equons fo nutne n ptne of syel onfguon then we use t n lulng the effeve ele onstnt n the oe penes n op the esults wth tht lulte usng fel nlyss soluons.
Epl Equons : Fg. Asyel osp ouple lnes he she g of syel osp ouple lnes s shown n fgue, whee, e the lne wths, s ele substte thkness, s the etll lne thkness n s the elve pevty of the ele substte. he equons fo the self n utul nutne n ptne ntoue by [] e ofe to be sutble wth syel osp ouple lnes n y be wtten s: 8.84 0.38 0.89 0.95 * 0.78.85 9.5 0.34 * 0.807.0.0 0.38.4 0.05 exp.86 * 0.563 0.07.96.3.0 0.6 0.337 0.365 µ 0 0.4.04 0.74 µ 0.0086.48.5 *.4 0.5 4 5 exp.9 * 6.9x0 0.3 * 0.4 0.3.9 0.0 0.455 e 0 n,, e the utul ptne n nutne espevely, e the self ptne n nutne of lne espevely the totl ptne n nutne, e efne s
Nol oe petes: In the se of two sye ouple lnes, thee e two funentl popgng oes nely - oe n - oe. he soluon of the oesponng egenvlue poble les to the followng expessons fo the phse onstnts n n the oe nubes, [ ] ( ) ( )( ) [ ] /, 4 l ( ) ( ) ( ) [ ] ( ) x, 4 he ol htes pene e lso etene n tes of the self n utul ptnes n nutnes usng known expessons gven by [] fo both the - n π- oes of popgon whee, e the - n π- oe phse popgon onstent, e the o of the voltges on the lnes on the two oes of popgon. e the - n π- oe htes pene fo lne. e the - n π- oe htes pene fo lne Une qus-em ssupon, the self nutne n be expesse n tes of the self ptne, lso the utul nutne n ptne e nteelte theefoe only the ptnes e neee fo the nlyss of ouple osp lnes [3].
he egenvlues of the syste of ouple osp lnes n be eve n tes of the self n utul ptne fo the epty eff, whee: [( ) ( ) ] ( ) eff ( ) / D ( ) / ( D ( ) D ) / D he oe pene e gven by: [ V ( )] [ V ( )] / / / n flle stutue s follows: Nuel esults: he self n utul ptne fo sye ouple osp lnes e opute fo both flle n epty stutues fo sevel vlues of sp wth n /, /, the esults e shown n tble / / / / / 0 0 0 / 0 0 / 0 0.5 5.79.69 -.44.35 3.096-0.497.0 0.56.7 -,53 3.0 3.0-0.54.5 5.8.7 -.58 3.65 3.04-0.56.0 34.0.7 -.59 4.38 3.05-0.5 A set of esgn uves fo effeve oe penes e lulte fo ffeent geoe ensons ( ffeent vlues of /, / n 0.) to be use n the esgn of vous pplons bse on sye ouple osp lnes, the esults e ope wth tht publshe n [4] n e shown n fg..
, 00 80 60 40 0 [4] [4] [4] [4] XY (tte) 9 0 0 0. 0.4 0.6 0.8 () Fg. he effeve oe penes fo sye ouple lnes wth ffeent sepons fo 9.7 0.6,., h 0.635 efeenes: [] Y. ohn, J. ee,. Pk n. ho; Epl equons fo elel petes of ouple osp lnes wth one se expose to Eletons ettes, vol. 35, No., y., 999. [] V. pth; Asye ouple tnssson lnes n n nhoogeneous eu IEEE ns. Move theoy n tehnque., vol. M-3,pp. 734-739, ept. 975 [3] N. Deeb, E. Abllh, M. leh; Desgn petes of nhoogeneous sye ouple tnssson lnes IEEE ns. Move theoy n tehnque., vol. M-3, No. 7, pp. 59-595July 983. [4] E. Knwy; Full wve nlyss of ouple peo osp lnes by usng the fnte eleent etho Ph.D. thess, 999.