Broadband equivalent circuit modelling of spiral resonators for printed circuit board applications

Broadband equivalent circuit modelling of spiral resonators for printed circuit board applications

For access to this article, please select a purchase option:

Buy article PDF
(plus tax if applicable)
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Your details
Why are you recommending this title?
Select reason:
IET Circuits, Devices & Systems — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

This study presents a new equivalent circuit modelling methodology for various-type spiral resonators in printed circuit board environment. The N-turn spiral resonator can be decomposed into an N Π-equivalent circuit model, and each Π-model is comprised of a series inductance, parallel capacitance, two shunt capacitors and the resistances of the conductor and dielectric. Both the inductance and capacitance of the equivalent circuit are calculated by the proposed formulas, which are based on the electromagnetic theory. It has been demonstrated that the proposed equivalent circuit model of the spiral resonator is well matched in S-parameters, Q-factor and inductance values as well as in self-resonance frequency values within 8% tolerance with measurement and full-wave electromagnetic field solver.


    1. 1)
      • 1. Long, J.R., Copeland, M.A.: ‘The modeling, characterization, and design of monolithic inductors for silicon RF ICs’, IEEE J. Solid-State Circuits, 1997, 32, pp. 357369 (doi: 10.1109/4.557634).
    2. 2)
      • 2. Koutsoyannopoulos, Y.K., Papananos, Y.: ‘Systematic analysis and modeling of integrated inductors and transformers in RFIC design’, IEEE Trans. Circuits Syst. II, 2000, 47, (8), pp. 699713 (doi: 10.1109/82.861403).
    3. 3)
      • 3. Bae, H.C., Oh, S.H.: ‘Parallel-branch spiral inductors with enhanced quality factor and resonance frequency’, J. Korea Electromagn. Eng. Soc., 2008, 8, (2), pp. 4751.
    4. 4)
      • 4. Jiang, Z., Excell, P.S., Hejazi, Z.M.: ‘Calculation of distributed capacitances of spiral resonators’, IEEE Trans. Microw. Theory Tech., 1997, 45, pp. 139142 (doi: 10.1109/22.552045).
    5. 5)
      • 5. Mohan, S.S., Hershenson, M., Boyd, S.P., Lee, T.H.: ‘Simple accurate expressions for planar spiral inductances’, IEEE J. Solid-State Circuits, 1999, 34, (10), pp. 14191424 (doi: 10.1109/4.792620).
    6. 6)
      • 6. Cao, Y., Groves, R.A., Huang, X., et al: ‘Frequency-independent equivalent circuit model for on-chip spiral inductors’, IEEE J. Solid-State Circuits, 2003, 38, (3), pp. 419426 (doi: 10.1109/JSSC.2002.808285).
    7. 7)
      • 7. Gil, J., Shin, H.: ‘A simple wide-band on-chip inductor model for silicon-based RF ICs’, IEEE Trans. Microw. Theory Tech., 2003, 51, (9), pp. 20232028 (doi: 10.1109/TMTT.2003.815870).
    8. 8)
      • 8. Huang, F., Lu, J., Jiang, N., Zhang, X., Wu, W., Wang, Y.: ‘Frequency-independent asymmetric double-π equivalent circuit for on-chip spiral inductors: physics-based modeling and parameter extraction’, IEEE J. Solid-State Circuits, 2006, 41, (10), pp. 22722283 (doi: 10.1109/JSSC.2006.881574).
    9. 9)
      • 9. Kang, H.D., Kim, H., Kim, S.G., Yook, J.G.: ‘A localized enhanced power plane topology for wideband suppression of simultaneous switching noise’, IEEE Trans. Electromagn. Compat., 2010, 52, (2), pp. 373380 (doi: 10.1109/TEMC.2010.2044415).
    10. 10)
      • 10. Chung, T.H., Kang, H.D., Yook, J.G.: ‘Power noise suppression techniques using spiral resonator in high-speed PCB’. IEEE Electrical Design of Advanced Packaging and Systems, December 2010, pp. 14.
    11. 11)
      • 11. Kim, D.Y., Joo, S.H., Lee, H.Y.: ‘A power plane using the hybrid-cell EBG structure for the suppression of GBN/SSN’, J. Korea Electromagn. Eng. Soc., 2007, 18, (2), pp. 206212 (doi: 10.5515/KJKIEES.2007.18.2.206).
    12. 12)
      • 12. Bahl, I.: ‘Lumped element for RF and microwaves circuit’ (Artech House, 2003).
    13. 13)
      • 13. Greenhouse, H.M.: ‘Design of planar rectangular microelectronic inductors’, IEEE Trans. Parts Hybrids Packag., 1974, 10, (2), pp. 101109 (doi: 10.1109/TPHP.1974.1134841).
    14. 14)
      • 14. Chung, T.H., Kang, H.D., Yook, J.G.: ‘Equivalent model of circular-type spiral inductor in printed circuit board’, Microw. Opt. Technol. Lett., 2013, 55, (2), pp. 337340 (doi: 10.1002/mop.27287).
    15. 15)
      • 15. Johnson, H., Graham, M.: ‘High-speed digital design’ (Prentice-Hall, 1993).
    16. 16)
      • 16. Chung, T.H., Kang, H.D., Yook, J.G.: ‘A noise suppression technique using dual layer spirals with various ground structure for high-speed PCBs’, Prog. Electromagn. Res. B, 2013, 46, pp. 337356.
    17. 17)
      • 17. Horng, T.S., Wu, J.M., Yang, L.Q., Fang, S.T.: ‘A novel modified-T equivalent circuit for modeling LTCC embedded inductors with a large bandwidth’, IEEE Trans. Microw. Theory Tech., 2003, 51, (12), pp. 23272333 (doi: 10.1109/TMTT.2003.819772).
    18. 18)
      • 18. Kolding, T.E.: ‘On-wafer calibration techniques for giga-hertz CMOS measurements’. IEEE Int. Conf. Microelectronic Test Structures (ICMTS), March 1999, pp. 105110.
    19. 19)
      • 19. Hsu, H.M.: ‘Analytical formula for inductance of metal of various widths in spiral inductors’, IEEE Trans. Electron Devices, 2004, 51, (8), pp. 13431346 (doi: 10.1109/TED.2004.832094).
    20. 20)
      • 20. Yue, C.P., Wong, S.S.: ‘On-chip spiral inductors with patterned ground shields for Si-based RF IC's’, IEEE J. Solid-State Circuits, 1998, 33, pp. 743752 (doi: 10.1109/4.668989).
    21. 21)
      • 21. Shi, J., Yin, W.-Y., Liao, H., Mao, J.-F.: ‘The enhancement of Q factor for patterned ground shield inductors at high temperatures’, IEEE Trans. Magn., 2006, 42, (7), pp. 18731875 (doi: 10.1109/TMAG.2006.874186).

Related content

This is a required field
Please enter a valid email address