PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 149 > pp. 45-54

FULL-WAVE SEMI-ANALYTICAL MODELING OF PLANAR SPIRAL INDUCTORS IN LAYERED MEDIA

By Y. L. Li and S. Sun

Full Article PDF (675 KB)

Abstract:
In this paper, we present a full-wave semi-analytical solution to calculate the self and mutual impedances of two coupled spiral inductors with rectangular cross sections. In low-frequency electromagnetism, the self and mutual impedance of planar spiral inductors can be obtained based on the eddy current approximation, where the displacement current is disregarded. As the frequency increases, the size of the system can be designed to be smaller. However, the displacement current becomes more important in inductively-coupled systems. By directly deriving the Maxwell's equations without the eddy current assumption, the obtained full-wave model could be applied to both homogeneous and planarly layered media for wireless power transfer systems. Compared to the traditional methods, the newly derived impedances show a considerable discrepancy at GHz frequencies for millimeter-sized inductors, indicating the significance of the displacement current if the operating frequency of wireless power transmission reaches the GHz-range.

Citation:
Y. L. Li and S. Sun, "Full-Wave Semi-Analytical Modeling of Planar Spiral Inductors in Layered Media," Progress In Electromagnetics Research, Vol. 149, 45-54, 2014.
doi:10.2528/PIER14072404
http://www.jpier.org/PIER/pier.php?paper=14072404

References:
1. Maxwell, J. C., Trearise on Electricity and Magnetism, Oxford Clarendon Press, 1873.

2. Grover, F. W., Inductance Calculations, Dover Publications, New York, 1946.

3. Hurley, W. G. and M. C. Duffy, "Calculation of self and mutual impedances in planar magnetic structures," IEEE Trans. Magn., Vol. 31, No. 4, 2416-2422, 1995.
doi:10.1109/20.390151

4. Zhong, G. and C. K. Koh, "Exact closed-form formula for partial mutual inductances of rectangular conductors," IEEE Trans. Circ. Syst. Fund. Theor. Appl., Vol. 50, No. 10, 1349-1352, 2003.
doi:10.1109/TCSI.2003.817778

5. Babic, S. I. and C. Akyel, "New analytic-numerical solutions for the mutual inductance of two coaxial circular coils with rectangular cross section in air," IEEE Trans. Magn., Vol. 42, No. 6, 1661-1669, 2006.
doi:10.1109/TMAG.2006.872626

6. Snow, C., Formulas for Computing Capacitance and Inductance, 544, National Bureau of Standards Circular, Washington, DC , 1954.

7. Mohan, S. S., M. Hershenson, S. P. Boyd, and T. H. Lee, "Simple accurate expressions for planar spiral inductances," IEEE J. Solid-State Circuits, Vol. 34, No. 10, 1419-1424, 1999.
doi:10.1109/4.792620

8. Nguyen, M. Q., Z. Hughes, P. Woods, Y.-S. Seo, S. Rao, and J.-C. Chiao, "Field distribution models of spiral coil for misalignment analysis in wireless power transfer systems," IEEE Trans. Microw. Theory Tech., Vol. 62, No. 4, 920-930, 2014.
doi:10.1109/TMTT.2014.2302738

9. Savio, A., M. Carmina, A. Richelli, L. Colalongo, and Z. M. Kovacs-Vajna, "A new lumped model for on-chip inductors including substrate currents," Proceedings of the 15th International Conference on Microelectronics, 2003. ICM 2003, 9-11, 2003.

10. Richelli, A., L. Colalongo, M. Quarantelli, M. Carmina, and Z. M. Kovacs-Vajna, "A fully integrated inductor-based 1.8-6-V step-up converter," IEEE Journal of Solid-State Circuits, Vol. 39, No. 1, 242-245, 2004.
doi:10.1109/JSSC.2003.820859

11. Poon, A. S. Y., S. O’Driscoll, and T. H. Meng, "Optimal frequency for wireless power transmission into dispersive tissue," IEEE Trans. Antennas Propag., Vol. 58, No. 5, 1739-1750, 2010.
doi:10.1109/TAP.2010.2044310

12. Kim, S., J. S. Ho, and A. S. Y. Poon, "Wireless power transfer to miniature implants: Transmitter optimization," IEEE Trans. Antennas Propag., Vol. 60, No. 10, 4838-4845, 2012.
doi:10.1109/TAP.2012.2207341

13. Kim, S., J. S. Ho, and A. S. Y. Poon, "Midfield wireless powering of subwavelength autonomous devices," Phys. Rev. Lett., Vol. 110, 203905, 2013.
doi:10.1103/PhysRevLett.110.203905

14. Park, S. I., "Enhancement of wireless power transmission into biological tissues using a high surface impedance ground plane," Progress In Electromagnetics Research, Vol. 135, 123-136, 2013.
doi:10.2528/PIER12110902

15. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, 1995.

16. Chew, W. C. and B. Anderson, "Propagation of electromagnetic waves through geological beds in a geophysical probing environment," Radio Science, Vol. 20, No. 3, 611-621, 1985.
doi:10.1029/RS020i003p00611

17. Chew, W. C., S. Barone, B. Anderson, and C. Hennessy, "Diffraction of axisymmetric waves in a borehole by bed boundary discontinuities," Geophysics, Vol. 49, No. 10, 1586-1595, 1984.
doi:10.1190/1.1441567

18. Paulus, M., P. Gay-Balmaz, and O. J. F. Martin, "Accurate and efficient computation of the Green’s tensor for stratified media," Physical Review E, Vol. 62, 5797-5807, 2000.
doi:10.1103/PhysRevE.62.5797

19. Tsang, L., C. Huang, and C. Chan, "Surface electric fields and impedance matrix elements of stratified media," IEEE Trans. Antennas Propag., Vol. 48, No. 10, 1533-1543, 2000.
doi:10.1109/8.899670

20. Dural, G. and M. I. Aksun, "Closed-form Green’s functions for general sources and stratified media," IEEE Trans. Microw. Theory Tech., Vol. 43, No. 7, 1545-1552, 1995.
doi:10.1109/22.392913

21. Zhao, J. S., W. C. Chew, C. C. Lu, E. Michielssen, and J. M. Song, "Thin-stratified medium fast-multipole algorithm for solving microstrip structures," IEEE Trans. Microw. Theory Tech., Vol. 46, No. 4, 395-403, 1998.
doi:10.1109/22.664140

22. Gabriel, S., R. W. Lau, and C. Gabriel, "The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues," Phys. Med. Biol., Vol. 41, No. 11, 2271-2293, 1996.
doi:10.1088/0031-9155/41/11/003


© Copyright 2014 EMW Publishing. All Rights Reserved