Geodesic
Conformal transformation method as applied to finding the current density distribution and induced magnetic field in a strip conductor with a rectangular cut
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1678-1685 
V. V. Amelichev; T. N. Gerasimenko; P. A. Polyakov; S. I. Kasatkin. Conformal transformation method as applied to finding the current density distribution and induced magnetic field in a strip conductor with a rectangular cut. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1678-1685. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a11/
@article{ZVMMF_2014_54_10_a11,
     author = {V. V. Amelichev and T. N. Gerasimenko and P. A. Polyakov and S. I. Kasatkin},
     title = {Conformal transformation method as applied to finding the current density distribution and induced magnetic field in a strip conductor with~a~rectangular cut},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1678--1685},
     year = {2014},
     volume = {54},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a11/}
}
TY  - JOUR
AU  - V. V. Amelichev
AU  - T. N. Gerasimenko
AU  - P. A. Polyakov
AU  - S. I. Kasatkin
TI  - Conformal transformation method as applied to finding the current density distribution and induced magnetic field in a strip conductor with a rectangular cut
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2014
SP  - 1678
EP  - 1685
VL  - 54
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a11/
LA  - ru
ID  - ZVMMF_2014_54_10_a11
ER  - 
%0 Journal Article
%A V. V. Amelichev
%A T. N. Gerasimenko
%A P. A. Polyakov
%A S. I. Kasatkin
%T Conformal transformation method as applied to finding the current density distribution and induced magnetic field in a strip conductor with a rectangular cut
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2014
%P 1678-1685
%V 54
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a11/
%G ru
%F ZVMMF_2014_54_10_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

Given a conductor with a rectangular cut, the problem of determining the direct current distribution and the induced magnetic field in the conductor is solved with applications to the testing of chip conductors. An analytical expression for the current distribution is found assuming that the corners are rounded. The magnetic field induced by the given current is calculated.

[1] Shokhin A. V., Tipovoi tekhnologicheskii protsess montazha pechatnykh plat s primeneniem SMD-komponentov, RAP, SPb., 2000

[2] Tupik V. A., Tekhnologiya i organizatsiya proizvodstva radioelektronnoi apparatury, SPbGETU LETI, SPb., 2005

[3] Kasatkin S. I., Vasileva N. P., Muravev A. M., Plotnikova N. V., “Kontrol i diagnostika pechatnykh plat i mikroskhem posredstvom analiza ikh magnitnykh polei”, Datchiki i sistemy, IKA, 2008, no. 1, 49–53

[4] Kozlov A. S., Scherbakov S. A., “Opticheskie metody kontrolya soedinenii na pechatnykh platakh i bezopasnost ekspluatatsii elektronnykh ustroistv”, Voprosy teorii bezopasnosti i ustoichivosti sistem, 2006, no. 8, 186–196

[5] Spence H. F., “Printed circuit board diagnosis using artificial neural networks and circuit magnetic fields”, IEEE AES System Magazine, 9:2 (1994), 20–24 | DOI

[6] Petersen T. H., Carpenter K. H., May C. M., “Comparison of experimental measurements of current distribution in a flat conductor with simulated results from the partial inductance method”, IEEE Trans. Electromagnetic Compatibility, 51 (2009), 345–350 | DOI

[7] Lai Y.-S., Kao C.-L., “Characteristics of current crowding in flip-chip solder bumps”, Microelectronics Reliability, 46 (2006), 915–922 | DOI

[8] Choi W. J., Yeh E. C. C., Tuc K. N., “Mean-time-to-failure study of flip chip solder joints on Cu/Ni(V)/Al thin-film under-bump-metallization”, J. Appl. Phys., 94 (2003), 5665 | DOI

[9] Zhang K., Gong L., Unbehauen R., “Field analysis of a circular thin-film/foil resistor”, Archiv fuer Elektrotechnik, 76 (1993), 423–426 | DOI

[10] Smait V., Elektrostatika i elektrodinamika, Izd-vo inostr. lit., M., 1954

[11] Sveshnikov A. G., Bogolyubov A. N., Kravtsov V. V., Lektsii po matematicheskoi fizike, Izd-vo MGU, M., 1993

[12] Gerasimenko T. N., Ivanov V. I., Polyakov P. A., Popov V. Yu., “Primenenie konformnykh preobrazovanii k kraevym zadacham rascheta tokov v poloskovykh provodnikakh”, Fundamentalnaya i prikl. matem., 15:6 (2009), 3–14

[13] Gerasimenko T. N., Polyakov P. A., Application of conformal mapping technique to problems of direct current distribution in thin film wires bent at arbitrary angle, arXiv: 1112.0506v2 [math-ph]

[14] Polyakov P. A., “O gidrodinamicheskom opisanii voln v plazme s uchetom spinov elektronov”, Izvestiya vuzov SSSR. Fizika, 1979, no. 3, 101–103

[15] Polyakov P. A., “Teoriya diffuznoi domennoi granitsy”, Pisma v ZhETF, 60:5 (1994), 336–339

[16] Berezin I. S., Zhidkov N. P., Metody vychislenii, Fizmatgiz, M., 1962