Studying the characteristics impedance of coaxial transmission line using X-band.

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1 Intentionl Jounl of Engineeing nd Tehnil Reseh (IJETR) ISSN: , Volume-2, Issue-4, Apil 2014 Studying the hteistis impedne of oxil tnsmission line using X-bnd. Mhdi Hsn Suhil nd Fud mlik mut Abstt Mt Lb pogm (Vesion 7) is used fo design nd simultion of the miowve iuit using oxil Tnsmission line in X- bnd fequeny. An implementtion hs been done on oxil tnsmission line of (53.5Ω) hteisti impedne fo dieleti mteil Polyethylene with pemittivity The esults shows tht impedne of the line depend on the oxil line deeses s the inne diuses () nd oute diuses (b) ineses. The TEM tnsmission lines e hteized by some bsi pmetes suh s hteisti impedne ( Z 0 ),efletion oeffiient ( ),wve dmittne (Y),voltge stnding wve tio (VSWR) nd totl ttenution (α),in tem of physil pmetes like popeties of the dieleti onstnt. The optiml vlue of the line pmetes ou when the line teminted to esistne equl to hteisti impedne of the line. But when the line temintes to lod esistne less thn hteisti impedne we obtin mximum nd minimum vlue long the line, while the vlue hnged in phse shift when teminted the line to lod esistne gete thn hteisti impedne of the line. This phse shift depends on the pmetes nd the effet of ( R L ) on them, the phse shift exists on the inident wve beuse of the dditionl losses (pitne & indutne losses). Index Tems hteisti impedne, losses, oxil Tnsmission line, Resonnt fequeny, Bndwidth. I. INTRODUCTION The eletomgneti wves e used to tnspot enegy fom ple to nothe. Suh s TV o bod sting sttion.ntully, lge potion of the enegy of suh wves is lost. Anothe nd n impotnt pplition is in the tnsmission of eletomgneti enegy fom soue to single eeive. In suh ses, it is desible to minimize the tnsmission losses to the ptil eeive. Sine the eletomgneti wves popgting though fee spe e not the most suitble type fo this pupose, it is neessy to design nd dives some system guides of the eletomgneti wves. Tnsmission line is devie designed to guide eletomgneti enegy fom one point to nothe [1].The tnsmission line hs single pupose fo both the tnsmitte nd the ntenn. This pupose is to tnsfe the enegy output of the tnsmitte to the ntenn with the lest possible powe loss. How well this is done depends on the speil physil nd eletil hteistis (impedne nd esistne) of the tnsmission line [2] The min gol of tnsmission line mesuement is to detemine the pmetes tht hteize the line ove fequeny nge of inteest, s well s lote disontinuities tht use unusul loss o stnding wve. Although these pmetes desibe the intinsi popeties of the line, in some ses, ptiully with unshielded lines (e.g.miostip) [3]. The hoie of the tnsmission line is typilly bsed on the following itei [4]: Fequeny opetion, Attenution, Powe hndling, Chteisti impedne nd Towe loding (size & weight). The oxil tnsmission line onfigution is simple beuse thee is n ext solution fo its impedne nd popgtion veloity in tems of the physil pmetes (onduto sizes). Equtions fo mny tnsmission line types hve been deived by mpping thei physil shpe into oxil shpe whee the solution is known extly [5]. Thee e two types of Coxil lines, igid (i) oxil line nd flexible (solid) oxil line. The physil onstution of both types is bsilly the sme; tht is, eh ontins two onenti ondutos. Tble (1) Tnsmission line Pmetes fo Some Common lines. Tble (1 ) Tnsmission line Pmetes fo Some Common lines [7] Mnusipt eeived Mh 28, Mhdi Hsn Suhil, Dept.of Physis, ollege of siene, Univesity of Bghdd Fud mlik mut, Expet ministe of Edution, G.of uiul. 19

2 Studying the hteistis impedne of oxil tnsmission line using X-bnd. The igid oxil line onsists of entl, insulted wie (inne onduto) mounted inside tubul oute onduto. Howeve, in oxil line no eleti o mgneti fields extend outside the oute onduto. The fields e onfined to the spe between the two ondutos, esulting in pefetly shielded oxil line. Anothe dvntge is tht intefeene fom othe lines is edued. Flexible oxil lines e mde with n inne onduto tht onsists of flexible wie insulted fom the oute onduto by solid, ontinuous insulting mteil. The oute onduto is mde of metl bid, whih gives the line flexibility. Ely ttempts t gining flexibility involved using ubbe insultos between the two ondutos. Howeve, the ubbe insultos used exessive losses t high fequenies. Ptilly the use of the oxil line is t highe fequenies,this is lgely beuse of the onvenient onstution nd ptilly pefet shielding between fields inside nd outside of the line, typil oxil line n hve hteisti impedne nging fom 30 Ω to 100 Ω but most ommon impedne vlue fo oxil ble e 50 & 75 Ω Physil onstints on ptil wie dimetes nd sping limit Z 0 vlue to these nges.the 50 Ω RG-58 ble ws developed duing wold w II to onnet ntenns whih hd n impedne of 50 Ω.[6] Beuse of the high-fequeny losses ssoited with ubbe insultos, polyethylene plsti ws developed to eple ubbe nd eliminte these losses. Polyethylene plsti is solid substne tht emins flexible ove wide nge of tempetues. It is unffeted by sewte, gsoline, oil, nd most othe liquids tht my be found bod ship. The use of polyethylene s n insulto esults in gete high-fequeny losses thn the use of i s n insulto. Howeve, these losses e still lowe thn the losses ssoited with most othe solid dieleti mteils [2]. The pupose of this study involves the study of the hteisti impedne [53.3 Ω] fo polyethylene dieleti mteils [t fequeny 10 GHz], nd the othe hteisti of the oxil tnsmission line like (Wve impedne, Refletion oeffiient, Mximum vlue of eleti field inside the line, Powe, Cuent in the onduto, Cpitne nd Indutne pe unit length, eleti nd mgneti field). II. COAXIAL TRANSMISSION LINES EQUATIONS Fo pue TEM mode popgtion on oxil tnsmission line, the eleti field hs only edil omponent nd the mgneti field hs only n zimuthl omponent.the oxil ble, depited in figue (2-6) is the most widely used TEM tnsmission line. It onsists of two onenti of inne nd oute dii of () nd (b), with the spe between them filled with dieleti, suh s polyethylene o Teflon. [8],[9] Figue (2-6) Coxil Tnsmission line [9]. The equivlent eletostti poblem n be solved onveniently in ylindil oodintes,.the potentil (,) stisfies lple's eqution: T Beuse of the ylindil symmety, the potentil does not depend on the zimuthl ngle, thee fo, 1 0 B ( ) A BIn Whee A, B e onstnts of integtion. Assuming the oute onduto is gounded: ( ) 0 t b, nd the ( ) V inne onduto is held t voltge V,, the onstnts A,B e detemined to be B V ln( b/ ) nd A Blnb, esulting in the potentil: V ( ) Ln ( b / ) Ln( b / ) (3) It follows tht the eleti field will hve only dil omponent, E It follows tht the eleti field will hve only dil omponent,, nd the mgneti field only n E zimuthl omponent H / : V 1 E Ln( b / ) V 1 H Ln( b / ) Integting uent: 2 E (1) (2) (4) (5) H ound the inne onduto we obtin the 2 V 1 2 V I H d d In( b / ) In ( b / ) 0 0 It follows tht the hteisti impedne of the line Z V / I, nd hene the indutne nd pitne pe unit length will be: (6) 20

3 Intentionl Jounl of Engineeing nd Tehnil Reseh (IJETR) ISSN: , Volume-2, Issue-4, Apil 2014 Z Ln ( b / ) 2 L Ln( b / ) 2 2 C Ln ( b / ) (7) (8) (9) The tnsmitted powe Pt n be expessed eithe in tems of the voltge V o in the tems of the mximum vlue of the eleti field inside the line, whih ou t, tht is, E V /( In( b / )) (10) V PT V E ( ) Ln ( b / ) (11) 2Z Ln( b / ) The smlle the dimensions & b the lge the ttenution [10]. III. RESULTS & DISCUSSIONS FOR COAXIAL TRANSMISSION LINE: A. Chteisti Impedne: Idel tnsmission lines with TEM field distibuted e hteized by thei type (ble o pln) nd hteisti impedne [11].To study the hteisti impedne of oxil line in tnsmission line, eqution (7), whih epesents the eltion between the hteisti impedne ( Z 0 ) nd the inne () nd oute dius of onduto (b) ws used. Dieleti mteils of Polyethylene with eltive pemittivity ( =2.25, ws used, It is notie tht the vlue of the hteisti impedne deeses s the vlue of ( & b) inesing, s shown in the figues (1) nd (2) fo polyethylene. Figue ( 2) Chteisti impedne s funtion of oute dius vition fo Polyethylene B. Tnsmitted powe: Eqution (11) estimte the tnsmitted powe thought the line ( P ) due to the inne & oute diuses fo the t polyethylene mteil s in figues (3) & (4).It is notied tht the vlue of the tnsmitted powe inese due to inne & oute diuses inese. Tht is men the smlle the dimension & b the lge the ttenution. We n see tht the vition in tnsmitted powe vlue duing the ineses of the inne dius () t the smll vlue of (b) is so obvious while t lge vlue of (b) the vition is so smll & lose. Figue ( 1) Chteisti impedne s funtion of inne dius vition fo Polyethylene Figue (3) Tnsmitted powe s funtion of inne dius vition fo Polyethylene 21

4 Studying the hteistis impedne of oxil tnsmission line using X-bnd. Figue (4) Tnsmitted powe s funtion of oute dius vition fo Polyethylene Figue (6) Mximum vlue of the eleti field s funtion of oute dius vition fo polyethylene. C. Mximum vlue of the eleti field: The vlue of the mximum eleti field inside the line E ) is lulted by eqution (10).we obseved tht the ( vlue of ( E ) deese when () nd (b) vlue inesing s in figues (5) & (6) fo polyethylene, similly fo Teflon & Nylon. We lso notied tht the vition in the mximum vlue of the eleti field duing the ineses of the inne dius () t the smll vlue of (b) is so obvious & lge omped with the vition in the mximum vlue of eleti field when (b) is lge. D. Cuent in the onduto: Fom eqution (6),uent inside the onduto ( I ) due to inne & oute dius of the oxil line e lulted.it is notied tht the uent ineses with the inesing of inne () &oute (b) diuses s in figues(7) & (8) fo polyethylene. Fom ll tht it is obvious tht the ineses in the dieleti onstnt ( ) of the insulted mteil mens the inesing of the uent in the ondutos. We n lso notie tht the vition in vlue of uent inside the line duing the ineses of the inne dius () t lge vlue of dius (b) is so smll & lose,while t smll vlue of (b) the vition in uent inside the line is so lge & obvious. Figue (5) Mximum vlue of the eleti field s funtion of inne dius vition fo polyethylene. Figue (7) Cuent in the onduto s funtion of inne dius vition fo Polyethylene 22

5 Intentionl Jounl of Engineeing nd Tehnil Reseh (IJETR) ISSN: , Volume-2, Issue-4, Apil 2014 Figue (8) Cuent in the onduto s funtion of oute dius vition fo Polyethylene E. Cpitne & Indutne pe unit length: The pitne pe unit length (C) due to inne dius () & oute dius (b) ws lulted using eqution (9). It is noted tht the pitne vlue ineses s the inne & oute diuses inesing s shown in figues (9) & (10) fo polyethylene. As in the pevious ses it is notied tht t lge vlue of (b) duing the ineses of the inne dius () the vition in pitne vlue is so smll while t smll vlue of (b) the vition is lge nd obseve. Figue (10) Cpitne pe unit length s funtion of oute dius vition fo Polyethylene The indutne pe unit length (I) due to inne & oute dius of the onduto ws lso lulted using eqution (8). We n notie tht the indutne deese due to inne () & oute (b) dius inesing, s in figue (11)& (12) fo Polyethylene, Teflon & Nylon, It is notied tht the vlue of indutne pe unit length didn't depend on the insulted mteil inside the line. Figue (9) Cpitne pe unit length s funtion of inne dius vition fo Polyethylene Figue (11) Indutne pe unit length s funtion of inne dius vition fo Polyethylene 23

6 Studying the hteistis impedne of oxil tnsmission line using X-bnd. Figue (12) Indutne pe unit length s funtion of oute dius vition fo Polyethylene The thee quntities [the eleti field ( E ) inside the guide, the powe tnsfe ( P ) & the onduto ttenution ( )], n be though s funtion of the tio tke the following foms: T x b nd V x ) E b ln x ln x b) PT E b x R s x 1 ) 2 b ln x By setting the deivtion of the thee funtion of (x) to zeo, we obtin the following thee onditions: ) ln x=1 1 b) ln x= 2 with solutions: ) ln x= 1 1 x b ) e b 2 b) e 1/ b ) The thee optimiztion poblem t fixed oute onduto dius (b), we n find the optimum vlue of () tht minimizes ( E ), mximizes of ( P ) & minimizes ( ). We hve thee diffeent nswes & it my possible to stisfy them simultneously t ny lgoithm geneti. The oesponding impedne (Z) fo the thee vlues of ( b ) e 60 Ω, 30Ω & 76.7Ω fo n i filled line nd 40 Ω,20Ω & 51Ω fo polyethylene filled line,so the vlue of 50Ω is onsideed to be ompomise between 30Ω & 76Ω oesponding to mximum powe & minimum ttenution. T The minimum of ( ) is vey bod & ny neighbo b vlue to will esult in ( ) vey ne its minimum. (TE) nd (TM) modes with highe utoff fequenies exist in oxil line [69], with the lowest being 11 mode with utoff fequeny f 0, whee ( ) n TE is the utoff wve length & ppoximted by ( + b).the opetion of the TEM mode is estited to fequeny tht e less thn ( f ). Fo exmple the RG-58 bles we my use (=0.406) mm & (b=1.548) mm esulting in mm & f =34.79GHz. Anothe exmple RG8/U&RG213/V bles we my use (=1.03) mm & (b=3.60) mm esulting in mm & f =14.68GHz. The bove utoff fequenies e f bove the useful opeting nge ove whih the ttenution of the line is eptble. IV. CONCLUSIONS: The vition in tnsmission line pmete (tnsmitted powe, mximum vlue of eleti field, uent in the onduto & pitne pe unit length) duing the inesing of the inne dius () t the smll vlue of (b) is obsevble while t lge vlue of (b) the vition is so smll & lose. The mximum vlue of eleti field nd the vlue of indutne pe unit length e independent on ( ), while the vlue of uent in the onduto nd the vlue of pitne pe unit length e inesed s the vlue of ( ) inesing. In the se of mthing line ( R L Z0 ) the totl powe bsobed by the lod is t the mximum, while t R L Z0, the best powe vlue is t (0& / 2 ), nd t R L Z0, the best powe vlue is t ( / 4 ). REFERENCES: [1] Sientifi Enylopedi (Vn Nostnd),1970 [2] [3] 3Mohmed A. Mohmed, M.S thesis "Design nd Implementtion of miowve feede nd powe divide using Co-plne wveguide tnsmission line "Univesity of tehnology, [4] G.W. Collins," fundmentl of digitl television tnsmission, John Wiley &Sons,In.,New Yok, [5] [6] Enst Webe nd Fedeik Nebeke, The Evolution of Eletil Engineeing, IEEE Pess, Pistwy, New Jesey USA, [7] Dvid M.Poz, "Miowve Engineeing", Seond Edition, John Wiley & Sons, [8] The ARRL Hndbook hpte 19: "Tnsmission lines".64 [9] Stut Wentwoth. Fundmentls of Eletomgneti", Hoboken, NJ: Wiley, 2005.pp [10] S ib Thib Alwn, Ph,D thesis A Simultion nd Mesuements of the Effet of Fille Type nd Multilye on Dieleti Popety of Some Composite Mteils t (X Bnd) Region [11] L.Lewin, D.C.Ching nd E.F.Kueste,"Eletomgneti wves nd uved Stutues, London: Pete Peeginus