About the Mutual Induction Coefficients and Interaction Forces in Circular Coaxial Loops
Keywords:
mutual induction coefficients, coaxial loops, interaction forces, alternative expressions
Abstract
An analysis of the literature suggesting expressions for mutual inductances and interaction forces in circular coaxial loops with current in parallel planes may lead to conclusions lacking strict uniqueness. These literary sources [1—10] are quite diverse in nature, and expressions with full elliptical integrals, including their numerical realization, occupy a significant place in them. The article considers alternative expressions for the mutual induction coefficients and interaction forces between circular coaxial loops. The advantage of using these expressions with the associated second-kind Legendre functions with a semi-integer index for numerical realization is shown.
References
William R. Smithe. Static and Dynamic Electricity. Third edition. Revised printing. Taylor and Francis, 1989, 623 p.
Milan Wayne Garret. Calculation of Field, Forces, and Mutual Inductances of Current systems by Elliptic integrals. — Journal of Applied Physics, 1963, vol. 34, No. 9, pp. 2567—2573.
Simon Ramo, John R. Whinnery, Teodore Van Duzer. Field and waves in communication electronics, 1993, 844 p.
Gerard Hurley W. and Maeve C. Duffy. Calculation of self- and mutual impedances in planar sandwich inductors. — IEEE Trans. on Magnetics, 1997, vol. 33, No. 3, pp. 2282-2290.
Clayton Paul R., Inductance: Loop and Partial. New-York: Wiley, 2011. 379 p.
Демирчян К.С., Нейман Л.Р. Коровкин Н.В., Чечурин В.Л. Теоретические основы электротехники: Учебник для вузов, СПб.: Питер, 2003, т. 3, 377 с.
Калантаров П.Л, Цейтлин Л.А. Расчёт индуктивностей: Справочная книга. Л.: Энергоатомиздат, 1986, 488 с.
Уэйт Д.Р. Электромагнитное излучение из цилиндрических систем/Пер. с англ. М.: Советское радио, 1963, 238 с.
Цицикян Г.Н. Взаимные индуктивности и силы взаимодействий соосных контуров, соленоидов и катушек. — Изв. АН СССР. Энергетика и транспорт, 1985, № 6, с. 90-100.
Ганичев Г.А., Цицикян Г.Н. Электромагнитное поле цилиндрической катушки, экранированной плоским проводящим слоем. — Электричество, 1972, № 8, с. 6-10.
Marc T. Thompson. Inductance calculation Techniques. Part 2. Approximation and handbook methods. Power control and intelligent motion. December 1999, pp. 1—11 [Электрон. ресурс] website http:www.pcim.com. (Дата обращения 11.02.2019).
Справочник по специальным функциям с формулами, графиками и математическими таблицами/Под ред. М. Абра- мовица и И. Стиган. М.: Наука, 1979.
Таблицы присоединённых функций Лежандра. М.: ВЦ АН СССР, 1965, вып. 26.
Цицикян Г.Н. Векторный потенциал поля медленно движущихся тел в приложении к задачам электродинамической левитации. — Изв. РАН. Энергетика, 1994, № 4, с. 130—144.
Ki-Bong Kim, Enrico Levi, Zivan Zabar, Leo Birenbaun. Restoring Force between two noncoaxial circular coils. — IEEE Trans. on Magnetics, 1996, vol. 32, No. 2, pp. 478—484.
Simpsons J., Lane J., Iiiiiiier C., Youngquist R. Simple analytic expressions for the magnetic field of a circular current loop. NASA technical documents, 2001.
William R. Smithe. Static and Dynamic Electricity. Third edition. Revised printing. Taylor and Francis, 1989, 623 p.
#
Milan Wayne Garret. Calculation of Field, Forces, and Mutual Inductances of Current systems by Elliptic integrals. — Journal of Applied Physics, 1963, vol. 34, No. 9, pp. 2567—2573.
Simon Ramo, John R. Whinnery, Teodore Van Duzer. Field and waves in communication electronics, 1993, 844 p.
Gerard Hurley W. and Maeve C. Duffy. Calculation of self- and mutual impedances in planar sandwich inductors. — IEEE Trans. on Magnetics, 1997, vol. 33, No. 3, pp. 2282—2290.
Clayton Paul R., Inductance: Loop and Partial. New-York: Wiley, 2011. 379 p.
Demirchyan K.S., Neyman L.R., Korovkin N.V., Chechurin V.L. Teoreticheskiye osnovy elektrotekhniki (Theoretical principles of electrical engineering). St. Petersburg, Piter, 2003, vol. 3, 377 p.
Kalantarov P.L., Tseytlin L.A. Raschet inguktivnostey (Calculation of inductances). Leningrad, Energoatomizdat, 1986, 488 p.
Ueyt D.R. Elektromagnitnoe izlucheniye iz tsilindricheskikh sistem/Per. s angl. (Electromagnetic radiation from cylindrical systems/Trans. from English). Moscow, Sovetskoe radio, 1963, 238 p.
Tsitsikyan G.N. Izv. AN SSSR. Energetika i transport — in Russ. (News of the USSR Academy of Sciences. Power Engineering and Transport), 1985, No. 6, pp. 90—100.
Ganichev G.A., Tsitsikyan G.N. Elektrichestvo — in Russ. (Electricity), 1972, No. 8, pp. 6—10.
Marc T. Thompson. Inductance calculation Techniques. Part 2. Approximation and handbook methods. Power control and intelligent motion. December 1999, pp. 1 — 11 [Electron. Resurs] website http:www.pcim.com. (Data obrashsheniya 11.02.2019).
Spravochnik po spetsial’nym funktsiyam s formulami, grafikami i matematicheskimi tablitsami/Pod red. M. Abramovitsa i I. Stigan (Handbook of special functions with formulas, graphs and mathematical tables/Edit. by M. Abramovits and I. Stigan). Moscow, Nauka, 1979.
Tablitsy prisoedinennykh funktsiy Lezhandra (Tables of associated Legendre functions). Moscow, Computing Center of the USSR Academy of Sciences, 1965, iss. 26.
Tsitsikyan G.N. Izv. RAN. Energetika — in Russ. (News of Russian Academy of Sciences), 1994, No. 4, pp.130—144.
Ki-Bong Kim, Enrico Levi, Zivan Zabar, Leo Birenbaun. Restoring Force between two noncoaxial circular coils. — IEEE Trans. on Magnetics, 1996, vol. 32, No. 2, pp. 478—484.
Simpsons J., Lane J., Immer C., Youngquist R. Simple analytic expressions for the magnetic field of a circular current loop. NASA technical documents, 2001.
Milan Wayne Garret. Calculation of Field, Forces, and Mutual Inductances of Current systems by Elliptic integrals. — Journal of Applied Physics, 1963, vol. 34, No. 9, pp. 2567—2573.
Simon Ramo, John R. Whinnery, Teodore Van Duzer. Field and waves in communication electronics, 1993, 844 p.
Gerard Hurley W. and Maeve C. Duffy. Calculation of self- and mutual impedances in planar sandwich inductors. — IEEE Trans. on Magnetics, 1997, vol. 33, No. 3, pp. 2282-2290.
Clayton Paul R., Inductance: Loop and Partial. New-York: Wiley, 2011. 379 p.
Демирчян К.С., Нейман Л.Р. Коровкин Н.В., Чечурин В.Л. Теоретические основы электротехники: Учебник для вузов, СПб.: Питер, 2003, т. 3, 377 с.
Калантаров П.Л, Цейтлин Л.А. Расчёт индуктивностей: Справочная книга. Л.: Энергоатомиздат, 1986, 488 с.
Уэйт Д.Р. Электромагнитное излучение из цилиндрических систем/Пер. с англ. М.: Советское радио, 1963, 238 с.
Цицикян Г.Н. Взаимные индуктивности и силы взаимодействий соосных контуров, соленоидов и катушек. — Изв. АН СССР. Энергетика и транспорт, 1985, № 6, с. 90-100.
Ганичев Г.А., Цицикян Г.Н. Электромагнитное поле цилиндрической катушки, экранированной плоским проводящим слоем. — Электричество, 1972, № 8, с. 6-10.
Marc T. Thompson. Inductance calculation Techniques. Part 2. Approximation and handbook methods. Power control and intelligent motion. December 1999, pp. 1—11 [Электрон. ресурс] website http:www.pcim.com. (Дата обращения 11.02.2019).
Справочник по специальным функциям с формулами, графиками и математическими таблицами/Под ред. М. Абра- мовица и И. Стиган. М.: Наука, 1979.
Таблицы присоединённых функций Лежандра. М.: ВЦ АН СССР, 1965, вып. 26.
Цицикян Г.Н. Векторный потенциал поля медленно движущихся тел в приложении к задачам электродинамической левитации. — Изв. РАН. Энергетика, 1994, № 4, с. 130—144.
Ki-Bong Kim, Enrico Levi, Zivan Zabar, Leo Birenbaun. Restoring Force between two noncoaxial circular coils. — IEEE Trans. on Magnetics, 1996, vol. 32, No. 2, pp. 478—484.
Simpsons J., Lane J., Iiiiiiier C., Youngquist R. Simple analytic expressions for the magnetic field of a circular current loop. NASA technical documents, 2001.
William R. Smithe. Static and Dynamic Electricity. Third edition. Revised printing. Taylor and Francis, 1989, 623 p.
#
Milan Wayne Garret. Calculation of Field, Forces, and Mutual Inductances of Current systems by Elliptic integrals. — Journal of Applied Physics, 1963, vol. 34, No. 9, pp. 2567—2573.
Simon Ramo, John R. Whinnery, Teodore Van Duzer. Field and waves in communication electronics, 1993, 844 p.
Gerard Hurley W. and Maeve C. Duffy. Calculation of self- and mutual impedances in planar sandwich inductors. — IEEE Trans. on Magnetics, 1997, vol. 33, No. 3, pp. 2282—2290.
Clayton Paul R., Inductance: Loop and Partial. New-York: Wiley, 2011. 379 p.
Demirchyan K.S., Neyman L.R., Korovkin N.V., Chechurin V.L. Teoreticheskiye osnovy elektrotekhniki (Theoretical principles of electrical engineering). St. Petersburg, Piter, 2003, vol. 3, 377 p.
Kalantarov P.L., Tseytlin L.A. Raschet inguktivnostey (Calculation of inductances). Leningrad, Energoatomizdat, 1986, 488 p.
Ueyt D.R. Elektromagnitnoe izlucheniye iz tsilindricheskikh sistem/Per. s angl. (Electromagnetic radiation from cylindrical systems/Trans. from English). Moscow, Sovetskoe radio, 1963, 238 p.
Tsitsikyan G.N. Izv. AN SSSR. Energetika i transport — in Russ. (News of the USSR Academy of Sciences. Power Engineering and Transport), 1985, No. 6, pp. 90—100.
Ganichev G.A., Tsitsikyan G.N. Elektrichestvo — in Russ. (Electricity), 1972, No. 8, pp. 6—10.
Marc T. Thompson. Inductance calculation Techniques. Part 2. Approximation and handbook methods. Power control and intelligent motion. December 1999, pp. 1 — 11 [Electron. Resurs] website http:www.pcim.com. (Data obrashsheniya 11.02.2019).
Spravochnik po spetsial’nym funktsiyam s formulami, grafikami i matematicheskimi tablitsami/Pod red. M. Abramovitsa i I. Stigan (Handbook of special functions with formulas, graphs and mathematical tables/Edit. by M. Abramovits and I. Stigan). Moscow, Nauka, 1979.
Tablitsy prisoedinennykh funktsiy Lezhandra (Tables of associated Legendre functions). Moscow, Computing Center of the USSR Academy of Sciences, 1965, iss. 26.
Tsitsikyan G.N. Izv. RAN. Energetika — in Russ. (News of Russian Academy of Sciences), 1994, No. 4, pp.130—144.
Ki-Bong Kim, Enrico Levi, Zivan Zabar, Leo Birenbaun. Restoring Force between two noncoaxial circular coils. — IEEE Trans. on Magnetics, 1996, vol. 32, No. 2, pp. 478—484.
Simpsons J., Lane J., Immer C., Youngquist R. Simple analytic expressions for the magnetic field of a circular current loop. NASA technical documents, 2001.
