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.
"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
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
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.