The Point Ground Electrode in Vicinity of the SemiSpherical Inhomogenity


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1 SEBIAN JOUNAL OF ELECICAL ENGINEEING Vo., No., Novembe 005, 637 he Point Goun Eectoe in Vicinity of the SemiSpheic Inhomogenity Nen N. Cvetković, Peg. nčić Abstct: Chcteistion of the point goun eectoe pce in the suounings o insie of the semispheic eth inhomogenity n fe by ow fequency (LF) cuent using isote ething conucto, is pesente in this ppe. he goun impence (esistnce n ectnce) n potenti istibution on the goun sufce e etemine. Imge theoy fo twoye semiconucting mei, s we s fo the one point eectoe pce neby o insie of the spheic boy is use uing the nysis. Keywos: Gouning system, Impence, Potenti, Geen s function. Intouction he spheic n semispheic inhomogenity in the suounings of the gouning cn be pesente in nysis n soving of iffeent pobems. Fo exmpe, concete fountion of the pi cn be ppoximtey tete s inhomogenity of this kin. Aso, the obtine esuts cn be use fo chcteistion (etemining impence, step votge, touch votge n potenti istibution) of the ine gouning eectoe pce t the bity iection in the suounings o insie of nye inhomogenity, teting eth s semiconucting meium. Combintion of the qusisttiony imge theoy fo twoye semiconucting mei n fo semiconucting spheic inhomogenity, ws ppie. he esut of the peviousy escibe nysis is the Geen s function of the point eectoe pce neby o insie of the semispheic eth inhomogenity [, ]. heoetic Bckgoun he point goun eectoe hving ius 0 fe by LF cuent I n pce insie n outsie of the semispheic semiconucting inhomogenity of ius is obseve (Fig. b). he eectoe is pce t the epth h. he eth is so tete s semiconucting meium. he nom istnce between the Fcuty of Eectonic Eng. of Nis, A. Meveev 4, 8000 Nis, S&M, Emi: Fcuty of Eectonic Eng. of Nis, A. Meveev 4, 8000 Nis, S&M, Emi: 63
2 N.N. Cvetković, P.. nčić eectoe n the cente of the semispheic inhomogenity is L. he cente of the spheic coointe system coincies with the cente of semispheic inhomogenity. he position of the point eectoe is efine by the vues of the spheic coointes = ( h L ) n α = ctn( L h). he conuctivities, pemitivitties n pemebiities of the system shown in Fig. b e bee with i, ε,, i = ε0 εi μi =μ0 i = 0,,, whee inexes 0, n coespon to the fee spce, semiconucting goun n semispheic inhomogenity, espectivey. he compex conuctivities e: 0 = jωε0 fo fee spce ( 0 = 0 ), = jωε fo semiconucting goun n = jωε fo semispheic inhomogenity, whee ω is the ngu fequency. ) b) Fig. Point goun eectoe outsie () n insie (b) of the semispheic inhomogenity.. etemintion of the potenti n gouning impence Poceue of potenti etemintion of the system shown in Fig. b is bse on combine using of the qusisttiony imge theoy fo twoye semiconucting mei [] n imge epesenttion of the point eectoe pce ne the semiconucting spheic boy []. In gene cse, the equivent system cn be fome combining ppiction of imge theoem in pne semiconuctive mio n semiconuctive semispheic inhomogenity. In obtine cse, the conition, >> 0 is stisfie. Afte ppying the imge theoy, the equivent system is fome of point eectoe, n its imge pce t the istnce h bove the bouny sufce, t nom istnce L fom the 64
3 he Point Goun Eectoe in Vicinity of the SemiSpheic Inhomogenity 65 cente of the spheic coointe system. he equivent imge cuent is I 0 (when gouning eectoe is insie of the inhomogenity) o I 0 (when souce is outsie of the inhomogenity), whee ) ( ) ( = n ) ( ) ( = e the efection coefficients. By tht, since it is 0, >>, it cn be ssume tht, 0 0. Aso, in this cse, fte ppying the imge theoy, the semispheic inhomogenity cn be tete s spheic semiconucting boy. he potenti of the fie point in the goun is obtine s esut of the potenti supeposition of the souce n its imges. his potenti pesents the Geen s function fo the point eectoe pce neby o insie of the semispheic eth inhomogenity (Fig. b), when 0, >>. It is ssume tht souce n point in which potenti is etemine e pce in the sme te = c ψ pne of thespheic coointe system. Now, potenti cn be expesse s θ α θ α π θ α θ α π ϕ = I I, n n 4, n n 4 () when eectoe is pce outsie, n θ α θ α π θ α θ α π ϕ = I I, n n 4, n n 4 (b) when eectoe is pce insie of the semispheic inhomogenity. By tht e:
4 N.N. Cvetković, P.. nčić n = [ ( α θ, )] = [ ( α θ, )] = [ α θ ] = [ ( α θ. )] he efection n tnsmission coefficients n in expessions (b) e s foows: = ( ) ( ). = he istnce of the imges fom the cente of the semiconucting sphee, obtine using the imge theoy fo the spheic semiconucting boy, is bee with =. In the fme of the pesente nysis, it is ssume tht LF omin is consiee ( f = 50H, ω = 00π/s ). Afte etemining the potenti on the eectoe sufce ϕ = U, it is possibe to obtin the goun eectoe impence tht hs cpcitive chcte, Z = U I = j X. g g g 3 Numeic esuts he esistnce n ectnce of the point gouning goun eectoe hving ius 0 n fe by LF cuent I shown in Fig. (when point gouning is pce outsie of inhomogenity), vesus the istnce L, fo iffeent tio s pmete, e shown in Fig.. he vues of the pmetes e h = 0.5 m, = m, 0 =.5 cm, ε = 0, ε = 3 n = 0.0 S/m. he potenti istibution on the goun sufce fo point gouning shown in Fig., fo iffeent tio s pmete, is shown in Fig. 3. he pmetes vues e L = m, h = m, = m, 0 =.5 cm, ε = 0, ε = 3 n = 0.0S/m. he esistnce n ectnce of the point gouning fom Fig. b (when point gouning is pce insie of the inhomogenity), vesus the istnce L, fo iffeent tio s pmete, e shown in Fig. 4. he vues of the pmetes e h = 0.5 m, =m, 0 =.5 cm, ε = 0, ε = 3 n = 0.0S/m. 66
5 he Point Goun Eectoe in Vicinity of the SemiSpheic Inhomogenity Fig. esistnce n ectnce of the point goun eectoe (Fig. ). Fig. 3 Nomie potenti istibution on the goun sufce (Fig. ). 67
6 N.N. Cvetković, P.. nčić he potenti istibution on the goun sufce fo point gouning shown in Fig. b, fo iffeent tio s pmete, is shown in Fig. 5. he pmetes vues e L = 0.5 m, h = 0.3 m, =m, 0 =.5 cm, ε = 0, ε = 3 n = 0.0S/m. he esistnce n ectnce of the point gouning pce t the sufce ( h = 0 ) vesus the istnce L, fo iffeent tio s pmete, e pesente in Fig. 6 (when point gouning is pce on the inhomogenity sufce), n Fig. 7b (when gouning is on the eth sufce). he vues of the pmetes e =m, 0 =.5 cm, ε = 0, ε = 3 n = 0.0 S/m. When the point gouning is pce in the cente of the inhomogenity, it is possibe to obtin its compex impence in the e fom s 0 Z = j X =. () g g g π0 Fig. 4 esistnce n ectnce of the point goun eectoe (Fig. b). 68
7 he Point Goun Eectoe in Vicinity of the SemiSpheic Inhomogenity Aso in this cse of h = 0, when the point gouning is pce t ge istnce fom inhomogenity ( L >>> ), with incesing L, the compex impence ppoches the imit vue Z g = g j X g =. (3) π0 he compison of esistnce obtine using expessions (b) n (), when point eectoe is in the cente of the inhomogenity, is pesente in be. he vues of the pmetes e =m, 0 =.5 cm, ε = 0, ε = 3 n = 0.0S/m. Goo geement between compe esuts is notbe. he compe esuts fo esistnce obtine using expessions () n (3), (the point eectoe is t ge istnce fom inhomogenity) e given in be. he vues of the pmetes e = m, 0 =.5 cm, ε = 0, ε = 3 n = 0.0S/m. Vey goo geement cn be notice yet fo L =. 5. ) b) Fig. 5 Nomie potenti istibution on the inhomogenity sufce (), n on the eth sufce (b) fo the gouning eectoe shown in Fig. b. 69
8 N.N. Cvetković, P.. nčić Fig. 6 esistnce n ectnce of the point goun eectoe when eectoe is pce on the inhomogenity sufce (Fig. b). Fig. 7 esistnce of the point goun eectoe when eectoe is pce on the eth sufce (Fig. ). 70
9 he Point Goun Eectoe in Vicinity of the SemiSpheic Inhomogenity pp. vue Fig. 7b ectnce of the point goun eectoe when eectoe is pce on the eth sufce (Fig. ). be esistnce of the point eectoe g (Ω) pce in the inhomogenity cente n vue obtine using exp. () exp. () be esistnce of the point eectoe (Ω) pce t L =. 5 fom the inhomogenity cente, n vue obtine using exp. (3). he potenti istibution on the goun sufce in the vicinity of the point goun eectoe pce insie n outsie of spheic inhomogenity n fe by LF cuent using the isote ething conucto, s we s point eectoe 7 g pp. vue exp. (3) Concusion
10 N.N. Cvetković, P.. nčić compex impence, e etemine in this ppe. he content of this ppe pesents intouctoy nysis fo soving moe compex pobems such s chcteistion of the ine goun eectoe pce in bity iection in the vicinity of the semiconucting inhomogenity o insie of the inhomogenity teting goun s semiconucting meium. 5 Acknowegement Authos eicte the ppe to the te pofesso gutin M. Veičkovic (94004). Fist utho thnks the AA fountion n the echnic Univesity of Imenu, Gemny fo the significnt suppot of iffeent kin in the fmewok of the Joint Poject. 6 efeences [] P.. ncic: A new concept fo ine gouning systems nysis (invite ppe), Fouth Intention Symposium of Appie Eectosttics, PES 96, Nis, Yugosvi, 4. My, 996, Poceeings of Ppes, pp []. M. Veickovic: Geen's function of spheic boy, Euo Eectomgnetics, EUOEM'94, 30. My 4. Juni, 994, Boeux, Fnce, Confeence Poceeings, Hp [3] P.. ncic, L. V. Stefnovic, j.. jojevic: A New Moe of the Vetic Goun o in wolye Eth, IEEE ns. on Mgnetics, Vo. 8, No., pp , Mch [4] P.. ncic, L. V. Stefnovic, j.. jojevic: An Impove Line Gouning System Anysis in wolye Eth, IEEE ns. on Mgnetics, Vo. 3, No. 5, pp , Septembe [5] P.. ncic, Z. P. Stjic, j.. jojevic, B. S. osic: Anysis of Line Goun Eectoes Pce in Vetic hee  Lye Eth, IEEE ns. on Mgnetics, Vo. 3, No. 3, pp , My
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