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Progress In Electromagnetics Research M | ISSN: 1937-8726 |

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## VALIDITY CHECK OF MUTUAL INDUCTANCE FORMULAS FOR CIRCULAR FILAMENTS WITH LATERAL AND ANGULAR MISALIGNMENTSBy S. I. Babic, F. Sirois, and C. Akyel
Abstract:
In this paper we derived the formula for calculating the mutual inductance between circular filaments with lateral and angular misalignment by using the approach of the magnetic vector potential. The results obtained correspond to those of F. W. Grover, although the latter used the general formula given by the Neumann integral instead of a vector potential approach. However, the major purpose of this paper is to clarify some confusion introduced in previous works regarding the mutual inductance calculation between thin filamentary circular coils with parallel axes in air. This problem has been solved by Kim et al. (1997) using the magnetic vector potential, but unfortunately it leads to erroneous results, even for slight misalignments of the coils' center axes. This is why we chose to use the approach of the magnetic vector potential to show that, when properly derived, the results must indeed reduce to the well known F.W. Grover's formulas.
2. Butterworth, S., "On the coe±cients of mutual induction of eccentric coils," 3. Snow, C., 4. Grover, F. W., "The calculation of the mutual inductance of circular lilaments in any desired positions," 5. Grover, F. W., 6. Kalantarov, P. L., 7. Dwight, H. B., 8. Kim, K. B., E. Levi, Z. Zabar, and L. Birenbaum, "Mutual inductance of noncoaxial circular coils with constant current density," 9. Abramowitz, M. and I. A. Stegun, 10. Gradshteyn, I. S. and I. M. Rhyzik, 11. Akyel, C., S. I. Babic, and M. M. Mahmoudi, "Mutual inductance calculation for non-coaxial circular air coils with parallel axes," 12. Conway, J. T., "Noncoaxial inductance calculations without the vector potential for axisymmetric coils and planar coils," |

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