volume | PIER Journals

Abstract

In this paper, a new formula for calculating the self-inductance of a thin conical sheet inductor is given. The presented work is derived in a semi-analytical form based on the complete elliptic integrals of the first, second, and third kind plus a term to be solved numerically. The analytical formula is obtained in the special case when the thin conical sheet inductor is degenerated into a thin wall cylinder. The validation of the presented formulas is done by triple, double, single integration and by the semi-analytical formula. These self-inductance calculations of the thin conical sheet inductors can be especially useful in broadband RF applications and wireless power transfer systems where conical inductors have been used.

1. Maxwell, J. C., A Treatise on Electricity and Magnetism, 3rd Ed., Vol. 2, Dover Publications Inc., 1954.

2. Grover, F. W., Inductance Calculations, Chapters 2 and 13, Dover, 1964.

3. Snow, C., "Formulas for computing capacitance, and inductance," National Bureau of Standards Circular, Vol. 544, Washington, DC, USA, 1954. Google Scholar

4. Rosa, B. E. and F. W. Grover, "Formulas and tables for the calculation of mutual and self-inductance," NBS Scientific Paper, 3rd Edition, No. 169, December 1916. Google Scholar

5. Kalantarov, P. L. and L. A. Zeitlin, Raschet Induktivnostey (Calculation of Inductances), 3rd Ed., Energoatomizdat, 1986.

6. Wheeler, H. A., "Simple inductance formulas for radio coils," Proceedings of the Institute of Radio Engineers, Vol. 16, No. 10, October 1928. Google Scholar

7. Lorentz, L., "Uber die fortplanzung der elektrozatat," Annalen dwe Physik, Vol. VII, 161-193, 1879.
doi:10.1002/andp.18792430602 Google Scholar

8. Babic, S., C. Akyel, and N. Boudjada, "The simplest formulas for self-inductance, mutual inductance and magnetic force of coaxial cylindrical magnets and thin coils," Recent Research in Circuits and Systems, 2012, ISBN 978-1-61804108-1. Google Scholar

9. Conical Tesla Coil, , , coil32.net.

10. Wire Gauge Conversion, , , www.engineeringtoolbox.com.

11. Winslow, T. A., "Conical inductors for broadband applications," IEEE Microwave Magazine, Vol. 6, No. 1, 68-72, March 2005.
doi:10.1109/MMW.2005.1418000 Google Scholar

12. Lopez-Villegas, J. M., A. Salas, N. Vidal, and J. Sieiro, "3D-printed low-pass filter with conical inductors for broadband RF applications," 2018 48th European Microwave Conference (EuMC), 292-295, 2018.
doi:10.23919/EuMC.2018.8541713 Google Scholar

13. Hadadtehrani, P., P. Kamalinejad, R. Molavi, and Sh. Mirabbasi, "On the use of conical helix inductors in wireless power transfer systems," 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), 1-4, 2016. Google Scholar

14. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press Inc., 1965.

15. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics, Series 55, 595, December 1972.

Dr. Slobodan Babic