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2013-08-25
Analytical Calculation of the Inductance of Planar Zig-Zag Spiral Inductors
By
Progress In Electromagnetics Research, Vol. 142, 207-220, 2013
Abstract
An analytical procedure for the calculation of the inductance of planar zig-zag spiral inductors is proposed. The procedure is based on the partial inductance concept and models the inductor as a series of a number of parts. The self-inductance of each individual part, which has the shape of a parallelogram, and the mutual inductance between any two parts of the inductor are determined. The inductance of a planar zig-zag spiral inductor can thus be obtained for any width, length and angle of the saw-tooth configuration. The procedure is validated with experimental measurements; the agreement between estimated and measured inductances is very good.
Citation
Leonardo Sandrolini, Ugo Reggiani, and Giovanni Puccetti, "Analytical Calculation of the Inductance of Planar Zig-Zag Spiral Inductors," Progress In Electromagnetics Research, Vol. 142, 207-220, 2013.
doi:10.2528/PIER13071105
References

1. Sandrolini, L., U. Reggiani, G. Puccetti, and Y. Neau, "Equivalent circuit characterization of resonant magnetic coupling for wireless transmission of electrical energy," Int. J. Circ. Theor. Appl., Vol. 41, No. 7, 753-771, 2013.
doi:10.1002/cta.1873

2. Schmukle, F. J., "The method of lines for the analysis of rectangular spiral inductors," IEEE Trans. on Microwave Theory and Techn., Vol. 41, 1183-1186, Jun./Jul. 1993.

3. Greenhouse, H. M., "Design of planar rectangular microelectronic inductors," IEEE Trans. on Parts, Hybrids, and Packaging, Vol. 10, No. 2, 101-109, 1974.
doi:10.1109/TPHP.1974.1134841

4. Kuo, J.-T., K.-Y. Su, T.-Y. Liu, H.-H. Chen, and S.-J. Chung, "Analytical calculation for dc inductances of rectangular spiral inductors with finite metal thickness in the peec formulation," IEEE Microwave and Wireless Components Letters, Vol. 16, No. 2, 69-71, 2006.
doi:10.1109/LMWC.2005.863256

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

6. Patterson, W. F. and E. T. Roland, "Spiral antenna with zigzag arms to reduce size,", US Patent 3,454,951, 1969.

7. Grover, F. W., Inductance Calculations Working Formulas and Tables, 2nd Edition, D. van Nostrand Comp., Inc., New York, USA, 1947.

8. Ruehli, A. E., "Inductance calculations in a complex integrated circuit environment," IBM Journal of Research and Development, Vol. 16, No. 5, 470-481, 1972.
doi:10.1147/rd.165.0470

9. Rosa, E. B., "The self and mutual inductances of linear conductors," Bullettin of the Bureau of Standards, Vol. 4, No. 2, 301-344, 1908.
doi:10.6028/bulletin.088

10. Stojanovic, G., M. Damnjanovic, V. Desnica, L. Zivanov, R. Raghavendra, P. Bellew, and N. McLoughlin, "High-performance zig-zag and meander inductors embedded in ferrite material," Journal of Magnetism and Magnetic Materials, Vol. 297, No. 2, 76-83, 2006.
doi:10.1016/j.jmmm.2005.02.058

11. Hoer, C. and C. Love, "Exact inductance equations for rectangular conductors with applications to more complicated geometries," J. Res. Nat. Bur. Stand. Sec. C: Eng. Inst., Vol. 69C, 127-137, Apr.-Jun. 1965.
doi:10.6028/jres.069C.016

12. Paul, C. R., Inductance - Loop and Partial, 246-306, John Wiley & Sons, Hoboken, NJ, USA, 2010.

13. Piatek, Z. and B. Baron, "Exact closed form formula for self inductance of conductor of rectangular cross section," Progress In Electromagnetics Research M, Vol. 26, 225-236, 2012.

14. Campbell, G. A., "Mutual inductances of circuits composed of straight wires," Phys. Rev., Vol. 5, 452-458, Jun. 1915.
doi:10.1103/PhysRev.5.452

15. Kamon, M., M. J. Tsuk, and J. K. White, "FASTHENRY: A multipole-accelerated 3-D inductance extraction program," IEEE Trans. on Microwave Theory and Techn., Vol. 42, No. 9, 1750-1758, Sep. 1994.
doi:10.1109/22.310584