volume | PIER Journals

2011-03-02

Mutual Inductance for an Explicitly Finite Number of Turns

John Thomas Conway

Professor John Thomas Conway

University of Agder

Norway

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Progress In Electromagnetics Research B, Vol. 28, 273-287, 2011

doi:10.2528/PIERB10110103

Abstract

Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly finite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared out over the solenoid windings is explored.

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John Thomas Conway, "Mutual Inductance for an Explicitly Finite Number of Turns," Progress In Electromagnetics Research B, Vol. 28, 273-287, 2011.
doi:10.2528/PIERB10110103

References

1. Havelock, T. H., "On certain Bessel integrals and the coefficients of mutual induction of coaxial coils," Phil. Mag., Vol. 15, 332-345, 1908.

2. Wolfram, S., The Mathematica Book, 5th Ed., Wolfram Media, Champaign, IL, 2003.

3. Conway, J. T., "Inductance calculations for noncoaxial coils using Bessel functions," IEEE Trans. Mag., Vol. 43, No. 3, 1023-1034, 2007.
doi:10.1109/TMAG.2006.888565

4. Watson, G. N., Treatise on the Theory of Bessel Functions, 2nd Ed., Cambridge, 1944.

5. Graf, J. H., "Ueber die addition und subtraction der argumente bei Bessel'schen functionen nebst einer anwendung ," Math. Ann., Vol. 43, 136-144, 1893.
doi:10.1007/BF01446617

6. Gervois, A. and H. Navelet, "Integrals of three Bessel functions and Legendre functions I and II," J. Math. Phys., Vol. 26, 633-644, 1985.
doi:10.1063/1.526600

7. Gradshteyn, I. S. and I. M. Rhyzik, "Table of Integrals, Series and Products," Academic, New York, 2007.

8. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, Dover, New York, 1972.

9. Conway, J. T., "Inductance calculations for circular coils of rectangular cross section and parallel axes using Bessel and Struve functions," IEEE Trans. Mag., Vol. 46, No. 1, 75-81, 2010.
doi:10.1109/TMAG.2009.2026574

10. Akyel, C., S. I. Babic, and M. M. Mahmoudi, "Mutual inductance calculations for non-coaxial circular air coils with parallel axes," Progress In Electromagnetics Research, Vol. 91, 287-301, 2009.
doi:10.2528/PIER09021907