Inductance Formula for Square Spiral Inductors with Rectangular Conductor Cross Section

Main Article Content

H. A. Aebischer

Abstract

Planar spiral coils are used as inductors in radio frequency (RF) microelectronic integrated circuits (IC’s) and as antennas in both  radio frequency identification (RFID) and telemetry systems. They must be designed to a specified inductance. From the literature, approximate analytical formulae for the inductance of such coils with rectangular conductor cross section are known. They yield the direct current (DC) inductance, which is considered as a good approximation for inductors in RF IC’s up to the GHz range. In principle, these formulae can simplify coil design considerably. But a recent comparative study of the most cited formulae revealed that their maximum relative error is often much larger than claimed by the author, and too large to be useful in circuit design.


This paper presents a more accurate formula for the DC inductance of square planar spiral coils than was known so far. It is applicable to any design of such coils with up to  windings. Owing to its scalability, this holds irrespectively of the coil size and the inductance range. It lowers the maximum error over the whole domain of definition from so far  down to . This has been tested by the same method used in the comparative study mentioned above, where the precise reference inductances were computed with the help of the free standard software FastHenry2. A comparison to measurements is included. Moreover, the source code of a MATLAB® function to implement the formula is given in the appendix.

Downloads

Download data is not yet available.

Article Details

How to Cite
Aebischer, H. (2019). Inductance Formula for Square Spiral Inductors with Rectangular Conductor Cross Section. Advanced Electromagnetics, 8(4), 80-88. https://doi.org/10.7716/aem.v8i4.1074
Section
Research Articles

References


  1. H. A. Aebischer, Comparative Study of Analytical In-ductance Formulae for Square Planar Spiral Inductors, Advanced Electromagnetics, vol. 7, no. 5, 37-48, 2018.
    View Article

  2. J. Chen and J. J. Liou, On-Chip Spiral Inductors for RF Applications: An Overview, Journal of Semiconductor Technology and Science, vol. 4, no. 3, 149-167, 2004.

  3. D. Paret, RFID and Contactless Smart Card Applica-tions, John Wiley & Sons, Ltd, West Sussex, 2005.
    View Article

  4. R. A. Potyrailo, C. Surman, S. Go, Y. Lee, T. Sivavec, and W. G. Morris, Development of radio-frequency identification sensors based on organic electronic sens-ing materials for selective detection of toxic vapors, Journal of Applied Physics, 106, 124902-1 - 124902-6, 2009.
    View Article

  5. H. M. Greenhouse, Design of Planar Rectangular Mi-croelectronic Inductors, IEEE Trans. on Parts, Hybrids, and Packaging, vol. 10, no. 2, 101-109, 1974.
    View Article

  6. J. Crols, P. Kinget, J. Craninckx, and M. Steyaert, An Analytical Model of Planar Inductors on Lowly Doped Silicon Substrates for High Frequency Analog Design up to 3 GHz, IEEE Symposium on VLSI Circuits, Honolulu, Digest of Technical Papers, 28-29, 1996.

  7. H. Ronkainen, H. Kattelus, E. Tarvainen, T. Riihisaari, M. Andersson, and P. Kuivalainen, IC compatible planar inductors on silicon, IEE Proc. Circuits Devices Syst., vol. 144, no. 1, 29-35, 1997.
    View Article

  8. S. S. Mohan, M. del Mar Hershenson, S. P. Boyd, and T. H. Lee, Simple Accurate Expressions for Planar Spi-ral Inductances, IEEE Journal of Solid-State Circuits, vol. 34, no. 10, 1419-1424, 1999.
    View Article

  9. S. Jenei, B. K. J. C. Nauwelaers, and S. Decoutere, Physics-Based Closed-Form Inductance Expression for Compact Modeling of Integrated Spiral Inductors, IEEE Journal of Solid-State Circuits, vol. 37, no. 1, 77-80, 2002.
    View Article

  10. H. A. Aebischer and B. Aebischer, Improved Formulae for the Inductance of Straight Wires, Advanced Electro-magnetics, vol. 3, no. 1, 31-43, 2014.
    View Article

  11. J. C. Maxwell, A Treatise on Electricity and Magnetism, vol. 2., Dover Publications, New York, 1954, una-bridged 3rd ed. of 1891.

  12. E. B. Rosa, The self and mutual inductances of linear conductors, Bulletin of the Bureau of Standards, vol. 4, no. 2, Washington, 1907.
    View Article

  13. F. W. Grover, Inductance Calculations: Working For-mulas and Tables, Dover Publications, New York, 2004, first published by D. Van Nostrand Co., New York, 1946.

  14. M. Kamon, M. J. Tsuk, and J. K. White, FASTHENRY: A Multipole-Accelerated 3-D Inductance Extraction Program, IEEE Trans. on Microwave Theory and Tech-niques, vol. 42, no. 9, 1750-1758, 1994.
    View Article

  15. W. M. Haynes, Th. J. Bruno, and D. R. Lide, CRC Handbook of Chemistry and Physics, 95th ed., Internet Version 2015, p. 12-41, 2015.

  16. H. A. Aebischer and H. Friedli, Analytical Approxima-tion for the Inductance of Circularly Cylindrical Two-Wire Transmission Lines with Proximity Effect, Ad-vanced Electromagnetics, vol. 7, no. 1, 25-34, 2018.
    View Article

  17. H. A. Aebischer and B. Aebischer, The GMD Method for Inductance Calculation Applied to Conductors with Skin Effect, Advanced Electromagnetics, vol. 6, no. 2, 77-92, 2017.
    View Article

  18. https://en.wikipedia.org/wiki/Square_pyramidal_num-ber.