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.
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.
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.
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.
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.
10. Bueno, M. A. and A. K. T. Assis, "A new method for inductance calculations," J. Phys. D: Appl., No. 28, 1802-1806, 1995.
11. Ruehli, A. E., "Inductance calculations in a complex integrated circuit environment," IBM J. Res. Develop., 470-481, 1972.
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.
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.
17. Piatek, Z., "Impedances of Tubular High Current Busducts," Polish Academy of Sciences, 2008.