volume | PIER Journals

Abstract

Mutual external inductance (MEI) associated with fringing magnetic fields in planar transmission lines is a cause of socalled "ground plane noise", which leads to radiation from printed circuit boards in high-speed electronic equipment. Herein, a Method of Edge Currents (MEC) is proposed for calculating the MEI associated with fringing magnetic fields that wrap the ground plane of a microstrip line. This method employs a quasi-magnetostatic approach and direct magnetic field integration, so the resultant MEI is frequencyindependent. It is shown that when infinitely wide ground planes are cut to form ground planes of finite width, the residual surface currents on the tails that are cut off may be redistributed on the edges of the ground planes of finite thickness, forming edge currents. These edge currents shrink to filament currents when the thickness of the ground plane becomes negligible. It is shown that the mutual external inductance is determined by the magnetic flux produced by these edge currents, while the contributions to the magnetic flux by the currents from the signal trace and the finite-size ground plane completely compensate each other. This approach has been applied to estimating the mutual inductance for symmetrical and asymmetrical microstrip lines.

1. Wadell, B. C., Transmission Line Design Handbook, Artech House, 1991.

2. Mongia, R., I. Bahl, and P. Bhartia, RF and Microwave Coupled- Line Circuits, Artech House, 1999.

3. Edwards, T. C. and M. B. Steer, Foundations of Interconnect and Microstrip Design, 3rd edition, 2000.

4. Maloratsky, L. G., Passive RF and Microwave Integrated Circuit Design, Elsevier, 2004.

5. Bahl, I. and P. Bhartia, Microwave Solid State Circuit Design, Wiley, 2003.

6. Kiang, J. F., S. M. Ali, and J. A. Kong, "Modeling of lossy microstrip lines with finite thickness," Progress In Electromagnetics Research, Vol. 04, 85-117, 1991.

7. Takuma, T., Y. Tajima, T. Ichida, A. Z. Elsherbeni, V. Rodriguez- Pereyra, and C. E. Smith, "The effect of an air gap on the coupling between two planar microstrip lines," Journal of The Franklin Institute, Vol. 333, No. 2, 201-223, 1996.
doi:10.1016/0016-0032(96)00009-9

8. Watanabe, K. and K. Yasumoto, "Coupled-mode analysis of coupled microstrip transmission lines using a singular perturbation technique," Progress In Electromagnetics Research, Vol. 25, 95-110, 2000.
doi:10.2528/PIER99042602

9. Chai, C. C., B. K. Chung, and H. T. Chuah, "Simple time-domain expressions for prediction of cross-talk on coupled microstrip lines," Progress In Electromagnetics Research, Vol. 39, 147-175, 2003.
doi:10.2528/PIER02060902

10. Khalaj-Amirhosseini, M. and A. Cheldavi, "A new twodimensional analysis of microstrip lines using rigorously coupled multi-conductor strips model," J. of Electromagn. Waves and Appl., Vol. 18, No. 6, 809-825, 2004.
doi:10.1163/156939304323105880

11. Khalaj-Amirhosseini, M., "Determination of capacitance and conductance matrices of lossy shielded coupled microstrip transmission lines," Progress In Electromagnetics Research, Vol. 50, 267-278, 2005.
doi:10.2528/PIER04061601

12. Arshadi, A. and A. Cheldavi, "Simple and novel model for edged microstrip line (EMTL)," Progress In Electromagnetics Research, Vol. 65, 247-259, 2006.
doi:10.2528/PIER06100401

13. Nashemi-Nasab and A. Cheldavi "Coupling model of the two orthogonal microstrip lines in two-layer PCB board (Quasi-TEM approach)," Progress In Electromagnetics Research, Vol. 60, 153-163, 2006.
doi:10.2528/PIER05040601

14. Khalaj-Amirhosseini, M. and A. Cheldavi, "Wideband and efficient microstrip interconnects using multi-segmented ground and open traces," Progress In Electromagnetics Research, Vol. 55, 33-46, 2005.
doi:10.2528/PIER05013102

15. Ymeri, H., B. Nauwelaers, K. Maex, and D. D. Roest, "New modeling approach of on-chip interconnects for RF integrated circuits in CMOS technology," Microelectronics International, Vol. 20, No. 3, 41-44, 2003.
doi:10.1108/13565360310487945

16. Van Horck, F. B. M., Electromagnetic Compatibility and Printed Circuit Boards, CIP-Data Library, 1998.

17. Leferink, F., "Inductance calculations: methods and equations," Proc. 1995 IEEE Int. Symp. Electromagnetic Compatibility, 14-18, 1995.

18. Hubing, T. H.T. P. Van Doren, and J. L. Drewniak, "Identifying and quantifying printed circuit board inductance," Proc. 1994 IEEE Int. Symp. Electromagnetic Compatibility, No. 8, 205-208, 1994.

19. Hockanson, D. M., J. L. Drewniak, T. H. Hubing, T. P. Van Doren, F. Sha, and C. W. Lam, "Quantifying EMI resulting from finiteimpedance reference planes," IEEE Trans. Electromagn. Compat., Vol. 39, No. 4, 286-297, 1997.
doi:10.1109/15.649814

20. Ooi, T. H., S. Y. Tan, and H. Li, "Study of radiated emissions from PCB with narrow ground plane," Int. Symp. Electromagnetic Compatibility, No. Paper 20A101, 17-21, 1999.

21. Hockanson, D. M., J. L. Drewniak, T. H. Hubing, T. P. Van Doren, F. Sha, and M. Wilhelm, "Investigation of fundamental EMI source mechanisms driving common-mode radiation from printed circuit boards with attached cables," IEEE Trans. Electromagn. Compat., Vol. 38, No. 4, 557-565, 1996.
doi:10.1109/15.544310

22. Holloway, C. L. and G. A. Hufford, "Internal inductance and conductor loss associated with the ground plane of a microstrip line," IEEE Trans. Electromagn. Compat., Vol. 39, No. 2, 73-77, 1997.
doi:10.1109/15.584929

23. Celozzi, S.G. Panariello, F.Schettino, and L. Verolino, "A general approach for the analysis of finite size PCB ground planes," Proc. 2000 IEEE Int. Symp. Electromagnetic Compatibility, Vol. 1, No. 8, 357-362, 2000.

24. Leone, M., "Design expressions for the trace-to-edge commonmode inductance of a printed circuit board," IEEE Trans. Electromagn. Compat., Vol. 43, No. 4, 667-670, 2001.
doi:10.1109/15.974648

25. Akdagli, A., "An empirical expression for the edge extension in calculating resonant frequency of rectangular microstrip antennas with thin and thick substrates," J. of Electromagn. Waves and Appl., Vol. 21, No. 9, 1247-1255, 2007.

26. Yang, F., V. Demir, D. A. Elsherbeni, and A. Z. Elsherbeni, "Enhancement of printed dipole antennas characteristics using semi-EBG ground plane," J. of Electromagn. Waves and Appl., Vol. 20, No. 8, 993-1006, 2006.
doi:10.1163/156939306776930330

27. Ataeiseresht, R., C. Ghobadi, and J. Nourinia, "A novel analysis of Minkovski fractal microstrip patch antenna," J. of Electromagn. Waves and Appl., Vol. 20, No. 8, 1115-1127, 2006.
doi:10.1163/156939306776930268

28. Shams, K. M. Z., M. Ali, and H.-S. Hwang, "A planar inductively coupled bow-tie slot antenna for WLAN applications," J. of Electromagn. Waves and Appl., Vol. 20, No. 7, 861-871, 2006.
doi:10.1163/156939306776149879

29. Kuo, L.-C., H.-R. Chuang, Y.-C. Kan, T.-C. Huang, and C.- H. Ko, "A study of planar printed dipole antennas for wireless communication applications," J. of Electromagn. Waves and Appl., Vol. 21, No. 5, 637-652, 2007.
doi:10.1163/156939307780667355

30. Ren, W., J. Y. Deng, and K. S. Chen, "Compact PCB monopole antenna for UWB applications," J. of Electromagn. Waves and Appl., Vol. 21, No. 10, 1411-1420, 2007.
doi:10.1163/156939307783239401

31. Eldek, A. A., "Numerical analysis of a small ultrawideband microstrip-fed tab monopole antenna," Progress In Electromagnetics Research, Vol. 65, 59-69, 2006.
doi:10.2528/PIER06082305

32. Ali, M. and S. Sanyal, "A numerical investigation of finite ground planes and reflector effects on monopole antenna factor using FDTD technique," J. of Electromagn. Waves and Appl., Vol. 21, No. 10, 1379-1392, 2007.
doi:10.1163/156939307783239410

33. Grover, H. W., Inductance Calculations: Working Formulas and Tables, Dover Publications, 1962.

34. Hoer, C. and C. Love, "Exact inductance calculations for rectangular conductors with applications to more complicated geometries," Journal of Research of the National Bureau of Standards, Vol. 69 C, No. 2, 127-137, 1965.

35. Maxwell, J. C., A Treatise on Electricity and Magnetism, 3rd edition, 1892.

36. Kaden, H., Wirbelstroeme und Schirmung in der Nachrichtentechnik. Technische Physik in Einzeldarstellungen Herausgegeben, and von W. Meissner (ed.), 2nd edition, 262-282, 262-282, 1959.

37. Ruehli, A. E., "Inductance calculations in a complex integrated circuit environment," IBM Journal on Research and Development, Vol. 16, No. 5, 470-481, 1972.

38. Carson, J. R., "Wave propagation in overhead wires with ground return," Bell Syst. Techn. Journal, Vol. 5, 539-554, 1926.

39. Kobayashi, M., "Longitudinal and transverse current distributions on microstriplines and their closed-form expression," IEEE Trans. Microwave Theory and Techn., Vol. 33, No. 9, 784-788, 1985.
doi:10.1109/TMTT.1985.1133127

40. Holloway, C. L. and E. F. Kuester, "Closed-form expressions for the current density on the ground plane of a microstrip line, with application to ground plane loss," IEEE Trans. Microwave Theory and Techn., Vol. 43, No. 5, 1204-1207, 1995.
doi:10.1109/22.382088

41. Van Horck, F. B. M., A. P. J. van Deursen, and P. C. T. van der Laan, "Common-mode currents generated by circuits on a PCB — Measurements and transmission-line calculations," IEEE Trans. Electromag. Compat., Vol. 43, No. 4, 608-617, 2001.
doi:10.1109/15.974641

42. Holloway, C. L. and E. F. Kuester, "Closed-form expressions for the current densities on the ground planes of symmetric stripline structures," IEEE Trans. on Electromagn. Compat., Vol. 49, No. 1, 49-57, 2007.
doi:10.1109/TEMC.2006.890219

43. Vaidyanath, A., B. Thoroddsen, J. L. Prince, and A. C. Cangellaris, "Simultaneous switching noise: influence of plane-plane and plane-signal trace coupling," IEEE Trans. on Advanced Packaging, Vol. 18, No. 3, 496-502, 1995.

44. Berg, D.M. Tanaka, Y. Ji, X. Ye, J. L. Drewniak, T. H. Hubing, R. E. DuBroff, and T. P. Van Doren, "FDTD and FEM/MOM modeling of EMI resulting from a trace near a PCB edge," Proc. IEEE Int. Symp. Electromagnetic Compatibility, No. 8, 135-140, 2000.

45. Watanabe, T.O. Wada, Y. Toyota, and R. Koga, "Estimation of common-mode EMI caused by a signal line in the vicinity of ground edge on a PCB," Proc. of IEEE Int. Symp. Electromagnetic Compatibility, Vol. 1, No. 8, 113-118, 2002.

Professor Marina Koledintseva

Professor James Drewniak

Dr. Thomas Van Doren

Dr. David Pommerenke

Dr. Matteo Cocchini

Dr. David Hockanson