PIER Letters
 
Progress In Electromagnetics Research Letters
ISSN: 1937-6480
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 46 > pp. 59-66

THE EQUIVALENT SELF-INDUCTANCE OF N COUPLED PARALLEL COILS

By G.-Q. Zhou

Full Article PDF (176 KB)

Abstract:
Based on Faraday's law of electromagnetic induction and the existence condition of non-trivial solution to a homogeneous and linear differential system of equations, the equivalent self-inductance of N coupled parallel coils has been derived by uing some algebraic techniques. It can be expressed as the ratio of the determinants of two matrices, with ranks of N and N-1, respectively, and constructed with the self and mutual inductance of those coils. In addition, special conclusions are deduced and/or discussed in detail for three particular cases: 1, the completely uncoupled case, 2, the identical and symmetrical case, and 3, the completely coupled case, which are coincident with the existing results in the references.

Citation:
G.-Q. Zhou, "The Equivalent Self-Inductance of n Coupled Parallel Coils," Progress In Electromagnetics Research Letters, Vol. 46, 59-66, 2014.
doi:10.2528/PIERL14031105

References:
1. Koledintseva, M. Y., J. L. Drewniak, T. P. Van Doren, D. J. Pommerenke, and M. Cocchini, "Mutual external inductance in stripline structures," Progress In Electromagnetics Research, Vol. 80, 349-368, 2008.
doi:10.2528/PIER07111503

2. Babic, S. I., C. Akyel, and , "New mutual inductance calculation of the magnetically coupled coils: Thin disk coil-thin wall solenoid," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 10, 1281-1290, 2006.
doi:10.1163/156939306779276794

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

4. Ravaud, R., G. Lemarquand, and V. Lemarquand, "Mutual inductance and force exerted between thick coils," Progress In Electromagnetics Research, Vol. 102, 367-380, 2010.
doi:10.2528/PIER10012806

5. Babic, S. I., C. Akyel, F. Sirois, G. Lemarquand, R. Ravaud, and V. Lemarquand, "Calculation of the mutual inductance and the magnetic force between a thick circular coil of the rectangular cross section and a thin wall solenoid (Integro-diĀ®erential approach)," Progress In Electromagnetics Research B, Vol. 33, 221-237, 2011.
doi:10.2528/PIERB11062111

6. Lorrain, P. and D. R. Corson, Electromagnetism: Principles and Applications, 292-293, W. H. Freeman and Company, San Francisco, 1979.

7. Alexander, C. K. and M. N. O. Sadiku, Fundamentals of Electric Circuits, 1st Ed., 528-530, 535-537; 569-571, McGraw-Hill Companies Inc., 2000.

8. Nilsson, J. W. and S. A. Riedel, Electric Circuits, 5th Ed., 521-524; 534-535, 537, Addison-Wesley Publishing company Inc. , 1996.

9. Guo, Y. Y. and G. Q. Zhou, Electrodynamics, 1st Edition, 29-31, Wuhan University Press, Wuhan, 2008.

10. Hu, Y. Q. and F. Z. Cheng, Electromagnetics, 319-324, Higher Education Press, Beijing, 1994.


© Copyright 2010 EMW Publishing. All Rights Reserved