MUTUAL INDUCTANCE OF FINITE LENGTH TWISTED-WIRE PAIR
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1 PONAN UNIVE RSIT OF TE CHNOLOG ACADE MIC JOURNALS No 69 Electcl Engneeng 0 Kstof BUDNIK* Wojcec MACHCŃSKI* MUTUAL INDUCTANCE OF FINITE LENGTH TWISTED-WIRE PAIR Twstng of bfl le s commonl use n vous fels of electcl nstuments n mesuement sstems n oe to euce te electomgnetc ntefeence EMI. Knowlege of nuctnces fo elcl conuctos s neee fo funmentl electomgnetc clcultons e.g. n electomgnetc comptblt stues. In te ppe clculton meto bse on te Neumnn s fomul s pple fo te mutul nuctnce clculton of twste-we p of fnte lengt. Te eempl clculton s lso pesente.. INTRODUCTION Twstng of conuctos ps s well known meto use n telepone communctons to mnme cosstlk mong lnes n bune cbles. Genell te effect of twstng cn be utle wen te mgnetc fel s poblem. Ale pctce s twstng of nsulte g-voltge tee pse powe cbles n snglepse stbuton cbles s well 7. Fg.. Twste-we p Twstng of bfl le s n Fg. s commonl use n vous fels of electcl nstuments n mesuement sstems n oe to euce te electomgnetc ntefeence EMI. In te twste-we p two nvul nsulte conuctos e twste togete n ec conucto cn be epesente b elcl lne. A elstc moel fo te twste-p cble s bfl el ouble el tt conssts of two elces vng te sme us n ptc; te elces e locte 80 sptl egee fom ec ote. Inuctnce clcultons fo elcl conuctos e neee fo funmentl electomgnetc clcultons. * Ponn Unvest of Tecnolog.
2 44 Kstof Bunk Wojcec Mccńsk In te ppe clculton meto bse on te Neumnn s fomul s pple fo te mutul nuctnce clculton of twste-we p of fnte lengt. Te eempl clculton s lso pesente.. MUTUAL INDUCTANCE OF COAIAL HELICAL THIN CONDUCTORS WITH FINITE LENGTH Conse genel cse wen two ffeent elcl conuctos e locte coll n te Ctesn co-onte sstem Fg.. Te mutul nuctnce between te elcl cuent lnes cn be compute usng te ouble ntegl Neumnn s fomul 7: 0 M 4 c c Hee s sown n Fg. c n c e te contous of te flment stuctues espectvel n e nfntesmll smll ntegton elements s te stnce between lne elements n ; te smbol µ 0 enotes te mgnetc pemeblt of te vcuum 4π 0 7 H/m. c I L L c I 0 φ 0 φ 0 φ Fg.. Two col elcl cuent lnes Denotng te wnng us of te -t = el b te ptc stnce of te el b n te φ co-onte of te pont wee te el ntesects te
3 Mutul nuctnce of fnte lengt twste-we p 45 plne =0 b φ 0 te pmetc equtons of te -t elcl lne wt espect to te pmete φ n wt φ 0 0 e: sn 0 In oe to ppl te fomul we ve to fn sutble epessons n φ. B lookng t Fg. n tkng nto ccount te eqn.: sn 3 wee e ectngul unt vectos. Te scl pouct wen we e gven te Ctesn components of te two vectos n tkes te fom: 4 wee sn 5 Remembeng tt / 6 t follows fom tt: / 0 0 sn sn 7 Fnll te mutul nuctnce between two col elcl conuctos wt ffeent fnte lengts L n L ffeent ptc stnces n n ffeent wnng n tkes te fom: / l l M 8
4 46 Kstof Bunk Wojcec Mccńsk Te ntegl fomul 8 s to be solve numecll. It soul be note tt te fomul eve llows clcultons of te etenl nuctnce of sngle elcl conucto wt te fnte us s well. 3. EAMPLE OF CALCULATIONS Mutul nuctnce of twste-p cble Te clcultons ve been cue out fo 3 m long twste-p cble wt ¼ nc mete n 3-nc ptc lengt fome b no.8 coppe wes locte 80 sptl egees fom ec ote s n 8. Te mutul nuctnce s been clculte numecll ccong to te fomul 8 fo followng pmetes: = = 0.3 cm = = 7.6 cm L = L = 300 cm φ 0 = 0 φ 0 = 80 gvng: M = 3.5 μh. Te mutul nuctnce s numecll obtne bsng on te ptve Smpson qutue pove b Mtlb. 4. FINAL REMARKS In te ppe clculton meto bse on te Neumnn s fomul s pple fo te mutul nuctnce clculton of twste-we p of fnte lengt. Te fomul eve llows clcultons of te mutul nuctnce of two-we el s well s te etenl nuctnce of sngle elcl conucto wt fnte us n cn be use b softwe tool wen te mgnetc fel s poblem e.g. n electomgnetc comptblt stues. REFERENCES T. Tomnk Inuctnce clculton fo elcl conuctos Supeconucto Scence n Tecnolog pp. 4. T. Tomnk Vecto potentl fo sngle elcl cuent conucto Nucle Instuments n Metos n Pscs Resec A pp T. Tomnk. Cb Low fequenc nuctnce fo twste bfl le Jounl of Pscs D: Appl. Ps pp T. Tomnk Self- n mutul nuctnces of long col elcl conuctos Supeconucto Scence n Tecnolog 008 pp.. 5 T. Tomnk Vecto potentl fo sngle elcl cuent conucto Nucle Instuments n Metos n Pscs Resec A pp J. Fnek M. Koll Detemnton of self n mutul nuctnces of ouble-el col Jounl of Electcl Engneeng vol. 60 no pp D.J. Gffts: Intoucton to Electonmcs. Pentce Hll Englewoo Clffs N.J. 989.
5 Mutul nuctnce of fnte lengt twste-we p 47 8 J.R. Mose R.F. Spence Pectng te mgnetc fels fom twste-p cble IEEE Tns. on Electomgnetc Comptblt vol. EMC-0 no. 3 Septembe 968 pp IMPEDANCJA WAJEMNA SKRĘTKI JEDNOPAROWEJ O SKOŃCONEJ DŁUGOŚCI Skętk jenopow jest wkle wkostwn w óżnego oju uąenc elektcnc elektoncnc sstemc pomowc w celu eukcj nekostnc spężeń elektomgnetcnc. Impencj wjemn skętk jenopowej ukłu wóc wjemne skęconc pewoów o kstłce els jest postwową welkoścą wkostwną w oblcenc np. kesu komptblnośc elektomgnetcnej. W pc o wncen mpencj wjemnej skętk jenopowej o skońconej ługośc wkostno wó Neumnn. peentowno pkł oblcenow.
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