Vol. 52

Latest Volume
All Volumes
All Issues
2013-06-10

Travelling-Wave Modelling of Uniform Multi-Conductor Transmission Line Networks --- Part I: Analytical Derivation

By Ioannis C. Papaleonidopoulos, Nickolas J. Theodorou, and Christos N. Capsalis
Progress In Electromagnetics Research B, Vol. 52, 253-293, 2013
doi:10.2528/PIERB13012007

Abstract

In Part I of this work, analysis of uniform multi-conductor transmission line networks is performed on travelling-wave basis, via "quasi-TEM" approach. Narrowband interpretation of the modal theory in the time domain and quantification of the multiple reflections effect are both included. Theoretical demonstration and analytical formulation are provided, along with guidelines towards computational implementation. Any network formed of lossy, diagonalisable uniform multi-conductor transmission lines of either distinct or degenerate eigenvalues is covered. This work applies especially in the field of Power-Line Communications, as High-Frequency transmission over the power electric network is dominated by multipath propagation.

Citation


Ioannis C. Papaleonidopoulos, Nickolas J. Theodorou, and Christos N. Capsalis, "Travelling-Wave Modelling of Uniform Multi-Conductor Transmission Line Networks --- Part I: Analytical Derivation," Progress In Electromagnetics Research B, Vol. 52, 253-293, 2013.
doi:10.2528/PIERB13012007
http://test.jpier.org/PIERB/pier.php?paper=13012007

References


    1. Dostert, K., Powerline Communications, 251-263, Prentice Hall PTR, Inc., Upper Saddle River, 2001.

    2. Mori, A., Y. Watanabe, M. Tokuda, and K. Kawamoto, "The power line transmission characteristics for an OFDM signal," Progress In Electromagnetics Research, Vol. 61, 279-290, 2006.
    doi:10.2528/PIER06042207

    3. Amirshahi, P. and M. Kavehrad, "High-frequency characteristics of overhead multiconductor power lines for broadband communications," IEEE J. Selected Areas in Communications, Vol. 24, 1292-1303, 2006.
    doi:10.1109/JSAC.2006.874399

    4. Esmailian, T., F. R. Kschischang, and P. G. Gulak, "Inbuilding power lines as high-speed communication channels: Channel characterization and a test channel ensemble," Int. J. Communication Systems, Vol. 16, 381-400, 2003.
    doi:10.1002/dac.596

    5. Papaleonidopoulos, , I. C., , C. N. Capsalis, C. G. Karagiannopoulos, and N. J. Theodorou, "Statistical analysis and simulation of indoor single-phase low voltage power-line communication channels on the basis of multipath propagation," IEEE Trans. Consumer Electronics, Vol. 49, 89-99, 2003.
    doi:10.1109/TCE.2003.1205460

    6. Zimmermann, M. and K. Dostert, "A multipath model for the powerline channel," IEEE Trans. Communications, Vol. 50, 553-539, 2002.
    doi:10.1109/26.996069

    7. Canete, F. J., L. Diez, J. A. Corties, and J. T. Entrambasaguas, "Broadband modelling of indoor power-line channels," IEEE Trans. Consumer Electronics, Vol. 48, 175, 2002.
    doi:10.1109/TCE.2002.1010108

    8. Liu, , D., E. Flint, B. Gaucher, and Y. Kwark, "Wide band AC power line characterization," IEEE Trans. Consumer Electronics, Vol. 45, 1087-1097, 1999.
    doi:10.1109/30.809186

    9. Tanaka, , M., "Transmission characteristics of a power line used for data communications at high frequencies," IEEE Trans. Consumer Electronics, Vol. 35, 37-42, 1989.
    doi:10.1109/30.24652

    10. Andreou, , G. T. and D. P. Labridis, "Experimental evaluation of a low-voltage power distribution cable model basedon a finite-element approach," IEEE Trans. Power Delivery, Vol. 22, 1445-1460, 2007.

    11. Andreou, G. T. and D. P. Labridis, "Electrical parameters of low-voltage power distribution cables used for power-line communications," IEEE Trans. Power Delivery, Vol. 22, 879-886, 2007.
    doi:10.1109/TPWRD.2006.881577

    12. Papaleonidopoulos, , I. C., , C. G. Karagiannopoulos, and N. J. Theodorou, "Evaluation of the two-conductor HF transmission-line model for symmetrical indoor triple-pole cables," Measurement, Vol. 39, 719-728, 2006.
    doi:10.1016/j.measurement.2006.03.007

    13. Faria, and J. B., "Evaluation of indoor cable capacitances taking into account conductor proximity and dielectric heterogeneity effects," IEEE Trans. Power Delivery, Vol. 21, 1919-1926, 2006.
    doi:10.1109/TPWRD.2006.877096

    14. Faria, , J. B. and M. G. das Neves, "Accurate evaluation of indoor triplex cable capacitances taking conductor proximity effects into account," IEEE Trans. Power Delivery, Vol. 21, 1238-1244, 2006.
    doi:10.1109/TPWRD.2005.860233

    15. Papaleonidopoulos, I. C., C. G. Karagiannopoulos, N. J. Theodorou, and C. N. Capsalis, "Theoretical transmission-line study of symmetrical indoor triple-pole cables for single-phase HF signalling," IEEE Trans. Power Delivery, Vol. 20, 646-654, 2005.
    doi:10.1109/TPWRD.2005.844329

    16. Meng, H., S. Chen, Y. L. Guan, C. L. Law, P. L. So, E. Gunawan, and T. T. Lie, "Modeling of transfer characteristics for the broadband power line communication channel," IEEE Trans. Power Delivery, Vol. 19, 1057-1064, 2004.
    doi:10.1109/TPWRD.2004.824430

    17. Lazaropoulos, A. G., "Towards broadband over power lines systems integration: Transmission characteristics of underground low-voltage distribution power lines," Progress In Electromagnetics Research B, Vol. 39, 89-114, 2012.
    doi:10.2528/PIERB12012409

    18. Levin, , B. M., "Calculation of electrical parameters of two-wire lines in multiconductor cables," IEEE Trans. Electromagnetic Compatibility, Vol. 50, 697-703, 2008.
    doi:10.1109/TEMC.2008.927924

    19. Pignari, S. A. and A. Orlandi, "Long-cable effects on conducted emissions levels," IEEE Trans. Electromagnetic Compatibility, Vol. 45, 43-54, 2003.
    doi:10.1109/TEMC.2002.808023

    20. Cannas, , B., A. Fanni, and F. Mardei, "Neural characterization of wire bundles multiconductor transmission lines," IEEE Trans. Magnetics, Vol. 38, 785-788, 2002.
    doi:10.1109/20.996203

    21. Brand~ao Faria, , J. A. and J. Hildemaro Briceno, "On the modal analysis of asymmetrical three-phase transmission lines using standard transformation matrices," IEEE Trans. Power Delivery, Vol. 12, 1760-1765, 1997.
    doi:10.1109/61.634202

    22. Machado, , M. V. M., J. A. Brandao Faria, and J. F. Borges da Silva, "Ground return effect on wave prop-agation parameters of overhead power cables," IEEE Trans. Power Delivery,, Vol. 5, 825-832, 1990.
    doi:10.1109/61.53089

    23. Gurbaxani, , S. H. and A. K. Agrawal, "Further experimental verification of frequency-domain multiconductor-transmission-line characterization," IEEE Trans. Electromagnetic Compatibility, Vol. 25, 374-376, 1983.
    doi:10.1109/TEMC.1983.304105

    24. Paul, C. R., "Solution of the transmission-line equations for three-conductor lines in homogeneous media," IEEE Trans. Electromagnetic Compatibility, Vol. 45, 216-222, 1978.
    doi:10.1109/TEMC.1978.303651

    25. Paul, C. R., "Reference potential terms in static capacitance calculations via the method of moments," IEEE Trans. Electromagnetic Compatibility, Vol. 20, 267-269, 1978.
    doi:10.1109/TEMC.1978.303657

    26. Paul, , C. R., "Computation of the transmission line inductance and capacitance matrices from the generalized capacitance matrix," IEEE Trans. Electromagnetic Compatibility, Vol. 18, 175-183, 1975.

    27. Paul, , C. R., "Computation of the capacitance matrix for systems of dielectric-coated cylindrical conductors," IEEE Trans. Electromagnetic Compatibility, Vol. 17, 238-248, 1976.

    28. Musolino, A., M. Raugi, and M. Tucci, "Cyclic short-time varying channel estimation in OFDM power-line communication," IEEE Trans. Power Delivery , Vol. 23, 157-163, 2008.
    doi:10.1109/TPWRD.2007.910995

    29. Ma, Y. H., P. L. So, and E. Gunawan, "Comparison of CDMA and OFDM systems for broadband power line communications," IEEE Trans. Power Delivery , Vol. 23, 1876-1885, 2008.
    doi:10.1109/TPWRD.2008.919043

    30. Crussiµere, , M., J.-Y. Baudais, and J.-F. Hielard, "Adaptive spread- pectrum multicarrier multiple-access over wirelines," IEEE J. Selected Areas in Communications, Vol. 24, 1377-1388, 2006.
    doi:10.1109/JSAC.2006.874425

    31. Ma, , Y. H., P. L. So, and E. Gunawan, "Performance analysis of OFDM systems for broadband power line communications under impulsive noise and multipath effects," IEEE Trans. Power Delivery, Vol. 20, 674-682, 2005.
    doi:10.1109/TPWRD.2005.844320

    32. Shanmugam Surendran, K. and H. Leung, "An analog spread-spectrum interface for power-line data communication in home networking," IEEE Trans. Power Delivery, Vol. 20, 80-89, 2005.
    doi:10.1109/TPWRD.2004.838468

    33. Zhang, Y. and S. Cheng, "A novel multicarrier signal transmission system over multipath channel of low-voltage power line," IEEE Trans. Power Delivery, Vol. 19, 1668-1672, 2004.
    doi:10.1109/TPWRD.2004.835424

    34. Del Re, E., R. Fantacci, S. Morosi, and R. Seravalle, "Comparison of CDMA and OFDM techniques for downstream power-line communications on low voltage grid," IEEE Trans. Power Delivery, Vol. 18, 1104-1109, 2003.
    doi:10.1109/TPWRD.2003.817517

    35. Nishiyama, T., T. Shirai, M. Itami, K. Itoh, and H. Aghvami, "A study on controlling transmission power of carriers of OFDM signal combined with data symbol spreading in frequency domain," IEICE Trans. Fundamentals, Vol. E86-A, 2117-2124, 2003.

    36. Fantacci, R. and S. Morosi, "Multicarrier spread spectrum techniques for downstream power-line communications on low voltage grid," Int. J. Communication Systems, Vol. 16, 401-416, 2003.
    doi:10.1002/dac.599

    37. Biglieri, E., "Coding and modulation for a horrible channel," IEEE Communications Mag., Vol. 41, 92-98, 2003.
    doi:10.1109/MCOM.2003.1200107

    38. Katayama, M., "Introduction to robust, reliable, and high-speed power-line communications systems," IEICE Trans. Fundamentals, Vol. E84, 2958-2965, 2001.

    39. Thrimawithana, D. J. and U. K. Madawala, "Generalised mathematical model for high-voltage pulse propagation along electric fence structures," IET Science, Measurement & Technology, Vol. 5, 109-116, 2011.
    doi:10.1049/iet-smt.2010.0053

    40. Barmada, S., A. Musolino, and M. Raugi, "Wavelet-based time-domain solution of multiconductor transmission lines with skin and proximity effect," IEEE Trans. Electromagnetic Compatibility, Vol. 47, 774-780, 2005.
    doi:10.1109/TEMC.2005.857868

    41. Bandurski, W., "Simulation of single and coupled transmission lines using time-domain scattering parameters," IEEE Trans. Circuits and Systems --- I: Fundamental Theory and Applications, Vol. 47, 1224-1234, 2000.
    doi:10.1109/81.873876

    42. Raugi, M., "Wavelet transform solution of multiconductor transmission line transients," IEEE Trans. Magnetics, Vol. 35, 1554-1557, 1999.
    doi:10.1109/20.767266

    43. Mao, J.-F. and Z.-F. Li, "Analysis of the time response of multiconductor transmission lines with frequency-dependent losses by the method of convolution-characteristics," IEEE Trans. Microwave Theory and Techniques, Vol. 40, 637-644, 1992.
    doi:10.1109/22.137402

    44. Djordjevic, A. R. and T. K. Sarkar, "Analysis of time response of lossy multiconductor transmission line networks," IEEE Trans. Microwave Theory and Techniques, Vol. 35, 898-908, 1987.
    doi:10.1109/TMTT.1987.1133776

    45. Hatziadoniu, C. J., N. B. Harp, and A. J. Sugg, "Finite-element models for open-air power lines in broadband PLC," IEEE Trans. Power Delivery, Vol. 21, 1898-1904, 2006.
    doi:10.1109/TPWRD.2006.874625

    46. Van der Merwe, J., J. H. Cloette, and H. C. Reader, "Transients on multiconductor transmission lines above dissipative earth," IEEE Trans. Electromagnetic Compatibility , Vol. 45, 404-415, 2003.
    doi:10.1109/TEMC.2003.811297

    47. Lu, T., X. Cui, and L. Li, "Transient analysis of aerial multi-conductor transmission lines with branch," IEEE Trans. Magnetics, Vol. 37, 3298-3302, 2001.
    doi:10.1109/20.952599

    48. Orlandi, A. and C. R. Paul, "An effcient characterization of interconnected multiconductor-transmission-line networks," IEEE Trans. Microwave Theory and Techniques, Vol. 48, 466-470, 2000.
    doi:10.1109/22.826849

    49. Rachidi, F., C. A. Nucci, and M. Ianoz, "Transient analysis of multiconductor lines above a lossy ground ," IEEE Trans. Power Delivery, Vol. 14, 294-302, 1999.
    doi:10.1109/61.736741

    55. Orlandi , A. and C. R. Paul, "FDTD analysis of lossy multiconductor transmission lines terminated in arbitrary loads," IEEE Trans. Electromagnetic Compatibility, Vol. 38, 388-399, 1996.
    doi:10.1109/15.536069

    56. Douvanis, A., L. Xin, M. S. Nakhla, and R. Achar, "Passive closed-form transmission-line model for general-purpose circuit simulators," IEEE Trans. Microwave Theory and Techniques, Vol. 47, 2450-2459, 1999.
    doi:10.1109/22.808992

    57. Wlodarczyk, A. J., V. Trenkic, R. A. Scaramuzza, and C. Christopoulos, "A fully integrated multiconductor model for TLM," IEEE Trans. Microwave Theory and Techniques, Vol. 46, 2431-2437, 1998.
    doi:10.1109/22.739231

    58. Nakhla, N., M. Nakhla, and R. Achar, "Simplified delay extraction-based passive transmission line macromodeling algorithm," IEEE Trans. Advanced Packaging, Vol. 33, 498-509, 2010.
    doi:10.1109/TADVP.2009.2032157

    59. Antonini, G., "A dyadic Green's function based method for the transient analysis of lossy and dispersive multiconductor trans mission lines," IEEE Trans. Microwave Theory and Techniques, Vol. 56, 880-895, 2008.
    doi:10.1109/TMTT.2008.919651

    60. Nakhla , N. M., A. Dounavis, R. Achar, and M. S. Nakhla, "DEPACT: Delay extraction-based passive compact transmission-line macromodeling algorithm," IEEE Trans. Advanced Packaging, Vol. 28, 13-23, 2005.
    doi:10.1109/TADVP.2004.841677

    61. Gunupudi, P. K., R. Khazaka, M. S. Nakhla, T. Smy, and D. Celo, "Passive parameterized time-domain macromodels for high-speed ansmission-line networks," IEEE Trans. Microwave Theory and Techniques , Vol. 51, 2347-2354, 2003.
    doi:10.1109/TMTT.2003.820169

    62. Gustavsen, B. and A. Semlyen, "Admittance-based modeling of transmission lines by a folded line equivalent," IEEE Trans. Power Delivery, Vol. 24, 231-239, 2009.
    doi:10.1109/TPWRD.2008.2002960

    63. Antonini, G., "A new methodology for the transient analysis of lossy and dispersive multiconductor transmission lines," IEEE Trans. Microwave Theory and Techniques, Vol. 52, 2227-2239, 2004.
    doi:10.1109/TMTT.2004.834581

    64. Douvanis, A., R. Achar, and M. Nakhla, "A general class of passive macromodels for lossy multiconductor transmission lines," IEEE Trans. Microwave Theory and Techniques , Vol. 49, 1686-1696, 2001.
    doi:10.1109/22.954772

    65. Oh, K. S., "Accurate transient simulation of transmission lines with the skin effect," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, Vol. 19, 389-396, 2000.
    doi:10.1109/43.833207

    66. Morhed, A., B. Gustavsen, and M. Tartibi, "A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables," IEEE Trans. Power Delivery, Vol. 14, 1032-1038, 1999.
    doi:10.1109/61.772350

    67. Maffucci, A. and G. Miano, "Irregular terms in the impulse response of a multiconductor lossy transmission line," IEEE Trans. Circuits and Systems --- I: Fundamental Theory and Applications, Vol. 46, 788-805, 1999.
    doi:10.1109/81.774223

    68. Celik, M. and L. T. Pileggi, "Simulation of lossy multiconductor transmission lines using backward euler integration," IEEE Trans. Circuits and Systems --- Fundamental Theory and Applications,, Vol. 45, 238-243, 1998.
    doi:10.1109/81.662697

    69. Bandi, V. G. and H. Asai, "Effent simulation of lossy coupled transmission lines by the application of window partitioning technique to the waveform relaxation approach," IEICE Trans. Fundamentals, Vol. E77-A, 1742-1752, 1994.

    70. Bracken, J. E., V. Raghavan, and R. A. Rohrer, "Interconnect simulation with asymptotic waveform evaluation, (AWE)," IEEE Trans. Circuits and Systems --- I: Fundamental Theory and Applications, Vol. 39, 869-878, 1992.
    doi:10.1109/81.199886

    71. Tang , T. K., M. S. Nakhla, and R. Griffth, "Analysis of lossy multiconductor transmission lines using the asymptotic waveform evaluation technique," IEEE Trans. Microwave Theory and Techniques, Vol. 39, 2107-2116, 1991.
    doi:10.1109/22.106547

    72. Palusinski, O. A. and A. Lee, "Analysis of transients in nonuniform and uniform multiconductor transmission lines," IEEE Trans. Microwave Theory and Techniques, Vol. 37, 127-138, 1989.
    doi:10.1109/22.20031

    73. He, H., S. Cheng, Y. Zhang, and J. Nguimbis, "reflection of signal transmitted in low-voltage powerline with complex wavelet," IEEE Trans. Power Delivery, Vol. 19, 86-91, 2004.
    doi:10.1109/TPWRD.2003.820209

    74. Leva, S. and A. P. Morando, "Waves and complex power in transmission lines," IEEE Trans. Power Delivery, Vol. 18, 1320-1327, 2003.
    doi:10.1109/TPWRD.2003.817746

    75. Paul, C. R., "Solution of the transmission-line equations under the weak-coupling assumption," IEEE Trans. Electromagnetic Compatibility, Vol. 44, 413-423, 2002.
    doi:10.1109/TEMC.2002.801753

    76. Poudroux, C., M. Rifi, and B. Demoulin, "A simplified approach to determine the amplitude of the transient voltage induced on a cable bundle," IEEE Trans. Electromagnetic Compatibility37, Vol. 37, 497-504, 1995.
    doi:10.1109/15.477304

    77. Paul, C. R., "Literal solutions for the time-domain response of a two-conductor transmission line excited by an incident electromagnetic field," IEEE Trans. Electromagnetic Compatibility, Vol. 37, 241-251, 1995.
    doi:10.1109/15.385889

    78. Lindell, I. V. and Q. Gu, "Theory of time-domain quasi-TEM modes in inhomogeneous multiconductor lines," IEEE Trans. Microwave Theory and Techniques, Vol. 35, 893-897, 1987.
    doi:10.1109/TMTT.1987.1133775

    79. Djordjevic, A. R., T. K. Sarkar, and R. F. Harrington, "Time-domain response of multiconductor transmission lines," Proc. IEEE, Vol. 75, 743-764, 1987.
    doi:10.1109/PROC.1987.13797

    80. Gruodis, A. J. and C. S. Chang, "Coupled lossy transmission line characterization and simulation," IBM J. Research and Development, Vol. 25, 25-41, 1981.
    doi:10.1147/rd.251.0025

    81. Agrawal, A. K., H. M. Fowles, L. D. Scott, and S. H. Gurbaxani, "Application of modal analysis to the transient response of multiconductor transmission lines with branches ," IEEE Trans. Electromagnetic Compatibility, Vol. 21, 256-262, 1979.
    doi:10.1109/TEMC.1979.303736

    82. Paul, C. R., "Analysis of Multiconductor Transmission Lines," John Wiley & Sons, Inc., 46-76, 1994.

    83. Faria, J. B., "Multiconductor Transmission-Line Structures: Modal Analysis Techniques," John Wiley & Sons, Inc., 1993.

    84. Paul, C. R., "Decoupling the multiconductor transmission line equations," IEEE Trans. Microwave Theory and Techniques, Vol. 44, 1429-1440, 1996.
    doi:10.1109/22.536026

    85. Faria, J. B., "Overhead three-phase transmission lines: Non-diagonalizable situations," IEEE Trans. Power Delivery, Vol. 3, 1348-1355, 1988.
    doi:10.1109/61.193930