Vol. 26
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2012-10-22
Exact Closed Form Formula for Self Inductance of Conductor of Rectangular Cross Section
By
Progress In Electromagnetics Research M, Vol. 26, 225-236, 2012
Abstract
In this paper, self inductance for a conductor with rectangular cross section is investigated. Using the threedimensional Fredholm's integral equation of the second kind with weakly singular kernel we obtain an equation for the complex voltage drop in the conductor. Self impedance appearing in the equation is expressed in the form of integral relation for any current density distribution. The imaginary part of this impedance divided by angular frequency is the self inductance of a conductor of any shape and finite length. In the case of direct current (DC), low frequency (LF) or thin strip conductor of rectangular cross section the formulae for the self inductances are given for any length and for length much greater than the other dimensions.
Citation
Zygmunt Piatek, and Bernard Baron, "Exact Closed Form Formula for Self Inductance of Conductor of Rectangular Cross Section," Progress In Electromagnetics Research M, Vol. 26, 225-236, 2012.
doi:10.2528/PIERM12080314
References

1. Balzer, G., et al. Switcher Manual, 10th Ed., ABB Calor Emag. Mittelspannung GmbH, Ratingen, 2004.

2. Kazimierczuk, M. K., High-frequency Magnetic Components, J. Wiley & Sons, Chichester, 2009.

3. Paul, C. R., "Inductance: Loop and Partial," J. Wiley & Sons, 2010.

4. Antonini, G., A. Orlandi, and C. R. Paul, "Internal impedance of conductor of rectangular cross section," IEEE Trans. Microwave Theory Tech., Vol. 47, No. 7, 979-984, 1999.
doi:10.1109/22.775429

5. Broyde, F., E. Clavelier, and L. Broyde, "A direct current per-unit-length inductance matrix computation using modified partial inductance," Proc. of the CEM 2012 Int. Symp. on Electromagnetic Compatibility, Rouen, Apr. 25-27, 2012.

6. Hashemi-Nasad, M. and A. Cheldavi, "Coupling model for the two orthogonal microstrip lines in two layer PCB board (quasi-tem approach)," Progress In Electromagnetic Research, Vol. 60, 153-163, 2006.
doi:10.2528/PIER05040601

7. Koledintseva, M. Y., J. L. Drewniak, T. P. Van Doren, D. J. Pommerenke, M. Cocchini, and D. M. Hockanson, "Method of edge currents for calculating mutual external inductance in a microstrip structure," Progress In Electromagnetic Research, Vol. 80, 197-224, 2008.
doi:10.2528/PIER07101504

8. Arshadi, A. and A. Cheldavi, "Simple and novel model for edged microstrip line (EMTL)," Progress In Electromagnetic Research, Vol. 65, 247-259, 2006.

9. Matsuki, M. and A. Matsushima, "Improved numerical method for computing internal impedance of a rectangular conductor and discussions of its high frequency behavior," Progress In Electromagnetic Research M, Vol. 23, 139-152, 2012.
doi:10.2528/PIERM11122105

10. Bueno, M. A. and A. K. T. Assis, "A new method for inductance calculations," J. Phys. D: Appl., No. 28, 1802-1806, 1995.
doi:10.1088/0022-3727/28/9/007

11. Ruehli, A. E., "Inductance calculations in a complex integrated circuit environment," IBM J. Res. Develop., 470-481, 1972.
doi:10.1147/rd.165.0470

12. Grover, F. W., Inductance Calculations, Dover Publications, Inc., New York, 1973.

13. Kim, H. and C. C. P. Chen, "Be careful of self and mutual inductance formulae,", 2009, Online: http://ccf.ee.ntu.edu.tw/»cchen/research/CompInduct9.pdf..

14. Hoer, C. and C. Love, "Exact inductance equations for rectangular conductors with application to more complicated geometries," J. Res. NBS, Vol. 69C, No. 2, 127-137, 1965.

15. Konrad, A., "Interodifferential finite element formulation of two-dimensional steady-state skin effect problems," IEEE Trans. on Magn., Vol. 18, 284-292, 1982.
doi:10.1109/TMAG.1982.1061775

16. Piatek, Z., "Self and mutual impedances of a finite length gas insulated transmission line (GIL)," Elec. Pow. Syst. Res., No. 77, 191-203, 2007.
doi:10.1016/j.epsr.2006.02.017

17. Piatek, Z., "Impedances of Tubular High Current Busducts," Polish Academy of Sciences, 2008.