Vol. 47
Latest Volume
All Volumes
PIERL 123 [2025] PIERL 122 [2024] PIERL 121 [2024] PIERL 120 [2024] PIERL 119 [2024] PIERL 118 [2024] PIERL 117 [2024] PIERL 116 [2024] PIERL 115 [2024] PIERL 114 [2023] PIERL 113 [2023] PIERL 112 [2023] PIERL 111 [2023] PIERL 110 [2023] PIERL 109 [2023] PIERL 108 [2023] PIERL 107 [2022] PIERL 106 [2022] PIERL 105 [2022] PIERL 104 [2022] PIERL 103 [2022] PIERL 102 [2022] PIERL 101 [2021] PIERL 100 [2021] PIERL 99 [2021] PIERL 98 [2021] PIERL 97 [2021] PIERL 96 [2021] PIERL 95 [2021] PIERL 94 [2020] PIERL 93 [2020] PIERL 92 [2020] PIERL 91 [2020] PIERL 90 [2020] PIERL 89 [2020] PIERL 88 [2020] PIERL 87 [2019] PIERL 86 [2019] PIERL 85 [2019] PIERL 84 [2019] PIERL 83 [2019] PIERL 82 [2019] PIERL 81 [2019] PIERL 80 [2018] PIERL 79 [2018] PIERL 78 [2018] PIERL 77 [2018] PIERL 76 [2018] PIERL 75 [2018] PIERL 74 [2018] PIERL 73 [2018] PIERL 72 [2018] PIERL 71 [2017] PIERL 70 [2017] PIERL 69 [2017] PIERL 68 [2017] PIERL 67 [2017] PIERL 66 [2017] PIERL 65 [2017] PIERL 64 [2016] PIERL 63 [2016] PIERL 62 [2016] PIERL 61 [2016] PIERL 60 [2016] PIERL 59 [2016] PIERL 58 [2016] PIERL 57 [2015] PIERL 56 [2015] PIERL 55 [2015] PIERL 54 [2015] PIERL 53 [2015] PIERL 52 [2015] PIERL 51 [2015] PIERL 50 [2014] PIERL 49 [2014] PIERL 48 [2014] PIERL 47 [2014] PIERL 46 [2014] PIERL 45 [2014] PIERL 44 [2014] PIERL 43 [2013] PIERL 42 [2013] PIERL 41 [2013] PIERL 40 [2013] PIERL 39 [2013] PIERL 38 [2013] PIERL 37 [2013] PIERL 36 [2013] PIERL 35 [2012] PIERL 34 [2012] PIERL 33 [2012] PIERL 32 [2012] PIERL 31 [2012] PIERL 30 [2012] PIERL 29 [2012] PIERL 28 [2012] PIERL 27 [2011] PIERL 26 [2011] PIERL 25 [2011] PIERL 24 [2011] PIERL 23 [2011] PIERL 22 [2011] PIERL 21 [2011] PIERL 20 [2011] PIERL 19 [2010] PIERL 18 [2010] PIERL 17 [2010] PIERL 16 [2010] PIERL 15 [2010] PIERL 14 [2010] PIERL 13 [2010] PIERL 12 [2009] PIERL 11 [2009] PIERL 10 [2009] PIERL 9 [2009] PIERL 8 [2009] PIERL 7 [2009] PIERL 6 [2009] PIERL 5 [2008] PIERL 4 [2008] PIERL 3 [2008] PIERL 2 [2008] PIERL 1 [2008]
2014-07-24
Elimination of Current Crowding Problem in Flat Conductors Bent at Arbitrary Angles
By
Progress In Electromagnetics Research Letters, Vol. 47, 41-46, 2014
Abstract
This work is devoted to a theoretical investigation of the current crowding problem in flat conductors bent at arbitrary angles. Using conformal mapping techniques, we succeed in obtaining an analytical expression for current density distributions in such conductors. It is shown that the current density increases in a small vicinity of the corner and approaches to infinity at its top. In order to eliminate the infinity, the vertex is replaced by an arc of a circle with a small radius. The method has been developed for an arbitrary angle; several specific examples are considered.
Citation
Tatiana Nikolaevna Gerasimenko, Peter Aleksandrovich Polyakov, and Igor Evgenyevich Frolov, "Elimination of Current Crowding Problem in Flat Conductors Bent at Arbitrary Angles," Progress In Electromagnetics Research Letters, Vol. 47, 41-46, 2014.
doi:10.2528/PIERL14062702
References

1. Choi, W. J., E. C. C. Yeh, and K. N. Tuc, "Mean-time-to-failure study of flip chip solder joints on Cu/Ni(V)/Al thin-film under-bump-metallization," J. Appl. Phys., Vol. 94, 5665, 2003.
doi:10.1063/1.1616993

2. Shao, T. L., Y. H. Chen, S. H. Chiu, and C. Chen, "Electromigration failure mechanisms for SnAg3.5 solder bumps on Ti/Cr-Cu/Cu and Ni(P)/Au metallization pads," J. Appl. Phys., Vol. 96, 4518, 2004.
doi:10.1063/1.1788837

3. Lai, Y.-S. and C.-L. Kao, "Characteristics of current crowding in flip-chip solder bumps," Microelectronics Reliability, Vol. 46, 915-922, 2006.
doi:10.1016/j.microrel.2005.02.007

4. Lai, Y.-S. and C.-L. Kao, "Electrothermal coupling analysis of current crowding and Joule heating in flip-chip packages," Microelectronics Reliability, Vol. 46, 1357-1368, 2006.
doi:10.1016/j.microrel.2005.08.009

5. Zhang, K., L. Gong, and R. Unbehauen, "Field analysis of a circular thin-film/foil resistor," Archiv fur Elektrotechnik, Vol. 76, 423-426, 1993.
doi:10.1007/BF01576021

6. Gerasimenko, T. N., V. I. Ivanov, P. A. Polyakov, and V. Y. Popov, "Application of a conformal-mapping technique to a boundary-value problem of current distribution in plain conductors," Journal of Mathematical Sciences, Vol. 172, No. 6, 761-769, 2011.
doi:10.1007/s10958-011-0219-8

7. Smythe, W. R., Static and Dynamic Electricity, McGraw-Hill Book Company Inc., New York, Toronto, London, 1950.

8. Trefethen, L. N., "Analysis and design of polygonal resistors by conformal mapping," Zeitschrift fur angewandte Mathematik und Physik, Vol. 35, 692-704, 1984.

9. Kober, H., Dictionary of Conformal Representations, Dover, 1957.

10. Hagedorn, F. B. and P. M. Hall, "Right-angle bends in thin strip conductors," J. Appl. Phys., Vol. 34, No. 1, 128-133, 1963.
doi:10.1063/1.1729052

11. Lavrentiev, M. A. and B. V. Shabat, Methods of Theory of Functions of Complex Variable, Nauka, Moscow, 1987 (in Russian).