Vol. 23
Latest Volume
All Volumes
PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2012-02-01
Improved Numerical Method for Computing Internal Impedance of a Rectangular Conductor and Discussions of Its High Frequency Behavior
By
Progress In Electromagnetics Research M, Vol. 23, 139-152, 2012
Abstract
An efficient numerical solution is been developed to compute the impedances of rectangular transmission lines. Method of moments is applied to integral equations for the current density, where the cross section is discretized, to improve the convergence, by a nonuniform grid that obeys the skin effect. Powerfulness of this approach up to rather high frequencies is verified by comparing with asymptotic formulas and other references. Detailed discussion is given for the current density distribution and its effect to the impedance, especially for a high frequency range.
Citation
Makoto Matsuki, and Akira Matsushima, "Improved Numerical Method for Computing Internal Impedance of a Rectangular Conductor and Discussions of Its High Frequency Behavior," Progress In Electromagnetics Research M, Vol. 23, 139-152, 2012.
doi:10.2528/PIERM11122105
References

1. Edwards, T. C. and M. B. Steer, Foundations of Interconnect and Microstrip Design, 3rd edition, John Wiley & Sons, 2000.

2. Paul, C. R., Analysis of Multiconductor Transmission Lines, 2nd Edition, John Wiley & Sons, 2008.

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

4. Gunston, M. A. R., Microwave Transmission Line Impedance Data, Noble, Atlanta, 1996.

5. Cockcroft, J. D., "Skin effect in rectangular conductors at high frequencies," Proc. Roy. Soc. London, Vol. A122, 533-542, 1929.

6. Bickley, W. G., "Two-dimensional potential problems for the space outside a rectangle," Proc. London Math. Soc., Ser. 2, Vol. 37, 82-105, 1932.

7. Flax, L. and J. H. Simmons, "Magnetic field outside perfect rectangular conductors," NASA Technical Note, Vol. NASA-TN-D-3572, 1-19, 1966.

8. Pettenpaul, E., H. Kapusta, A. Weisgerber, H. Mampe, J. Luginsland, and I. Wolff, "CAD models of lumped elements on GaAs up to 18 GHz," IEEE Trans. Microwave Theory Tech., Vol. 36, No. 2, 294-304, 1988.
doi:10.1109/22.3518

9. Rong, A. and A. C. Cangellaris, "Note on the definition and calculation of the per-unit-length internal impedance of a uniform conducting wire," IEEE Trans. Electromag. Compat., Vol. 49, No. 3, 677-681, 2007.
doi:10.1109/TEMC.2007.903043

10. Haefner, S. J., "Alternating current resistance of rectangular conductors'," Proc. IRE, Vol. 25, 434-447, 1937.
doi:10.1109/JRPROC.1937.229047

11. Weeks, W., L. Wu, M. McAllister, and A. Singh, "Resistive and inductive skin effect in rectangular conductors," IBM J. Res. Dev., Vol. 23, No. 6, 652-660, 1979.
doi:10.1147/rd.236.0652

12. Faraji-Dana, R. and Y. Chow, "Edge condition of the field and AC resistance of a rectangular strip conductor'," IEE Proc. H, Vol. 137, No. 2, 133-140, 1990.

13. Barr, A. W., "Calculation of frequency-dependent impedance for conductors of rectangular cross section," AMP J. Technol., Vol. 1, 91-100, 1991.

14. Sarkar, T. K. and A. R. Djordjevic, "Wideband electromagnetic analysis of finite-conductivity cylinders," Progress In Electromagnetics Research, Vol. 16, 153-173, 1997.
doi:10.2528/PIER96060200

15. Antonini, G., A. Orlandi, and C. R. Paul, "Internal impedance of conductors of rectangular cross section," IEEE Trans. Microwave Theory Tech., Vol. 47, No. 7, 979-985, 1999.
doi:10.1109/22.775429

16. Heinrich, W., "Comments on 'Internal impedance of conductors of rectangular cross section'," IEEE Trans. Microwave Theory Tech., Vol. 49, No. 3, 580-581, 2001.
doi:10.1109/22.910570

17. Berleze, S. L. M. and R. Robert, "Skin and proximity effects in nonmagnetic conductors," IEEE Trans. Education, Vol. 46, No. 3, 368-372, 2003.
doi:10.1109/TE.2003.814591

18. Matsushima, A. and H. Sakamoto, "Application of wire model to calculation of impedance of transmission lines with arbitrary cross sections," Electronics and Communication in Japan (Part II: Electronics), Vol. 85, No. 7, 1-10, 2002.
doi:10.1002/ecjb.10036

19. Harrington, R. F., Field Computation by Moment Methods, Macmillan, New York, 1968.

20. Higgins, T. J. and Appl. Phys., "Formulas for the geometrical mean distance of rectangular areas and line segments,", Vol. 14, No. 2, 188-195, 1943.