Advertisement

Some Remarks on the Transmission Line Matrix (TLM) Method and Its Application to Transient EM Fields and to EMC Problems

  • Peter RusserEmail author
  • Johannes A. Russer
Chapter

Abstract

Wolfgang J.R. Hoefer has pioneered the Transmission Line Matrix (TLM) method and made it a powerful tool for time-domain modeling of electromagnetic fields. In his scientific work, Wolfgang Hoefer always is placing a strong focus on imagery thinking and geometric and physical understanding of the electromagnetic phenomena. In this contribution, we invite the apt reader to stroll with us through the garden of TLM and would like to share with him some thoughts on the origin of the TLM method and also present some specific applications. We discuss the relation of the TLM method to Christian Huygens’ model of light propagation and show how the TLM method can be deduced on the basis Huygens’ model by application of network theory. We show how the TLM scheme can be embedded in a general discrete time circuit concept. The application of the TLM method to electromagnetic compatibility (EMC) problems is discussed. As a time-domain method, the TLM method is optimally suited to model broadband and transient electromagnetic phenomena and therefore, combining the TLM method with the Integral Equation method yields a powerful tool for the modeling of complex electromagnetic structures separated by large distances in free space. Introducing network models allows the application of correlation matrix methods for the modeling of stochastic fields.

Keywords

Transmission line matrix Electromagnetic compatibility (EMC) Huygens’ principle Stochastic electromagnetic fields Hybrid methods 

Notes

Acknowledgements

This article is based on research projects funded by the Deutsche Forschungsgemeinschaft.

References

  1. 1.
    P.B. Johns, R. Beurle, Numerical solution of 2-dimensional scattering problems using a transmission-line matrix. Proc. IEEE 118(9), 1203–1208 (1971)Google Scholar
  2. 2.
    W.J.R. Hoefer, A history of time domain electromagnetics—a voyage back in time, in 2012 Asia-Pacific Symposium on Electromagnetic Compatibility (APEMC), pp. 137–140 (2012)Google Scholar
  3. 3.
    W.J. Hoefer, The transmission line matrix method-theory and applications. IEEE Trans. Microw. Theory Tech. 33, 882–893 (1985)CrossRefGoogle Scholar
  4. 4.
    W.J. Hoefer, in Numerical Techniques for Microwave and Millimeter Wave Passive Structures, ed. by T. Itoh. The Transmission Line Matrix (TLM) Method (John Wiley, New York, 1989), pp. 496–591Google Scholar
  5. 5.
    W.J.R. Hoefer, Huygens and the computer-a powerful alliance in numerical electromagnetics. Proc. IEEE 79(10), 1459–1471 (1991)CrossRefGoogle Scholar
  6. 6.
    C. Christopoulos, The Transmission-Line Modeling Method TLM. (IEEE Press, New York, 1995)Google Scholar
  7. 7.
    P. Russer, The transmission line matrix method, in Applied Computational Electromagnetics, ser. NATO ASI Series (Springer, Berlin, 2000), pp. 243–269Google Scholar
  8. 8.
    D.G. Swanson, W.J. Hoefer, Microwave Circuit Modeling Using Electromagnetic Field Simulation (Artech House, London, 2003)Google Scholar
  9. 9.
    S.A. Kosmopoulos, W.J.R. Hoefer, A. Gagnon, Non-linear TLM modelling of high-frequency varactor multipliers and HalversTM. in 13 International Conference on Infrared and Millimeter Waves, 1988, pp. 239–240http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1256162=Opt
  10. 10.
    P. Russer, P.P.M. So, W.J.R. Hoefer, Modeling of nonlinear active regions in TLM [distributed circuits]. IEEE Microwave Guided Wave Lett. 1(1), 10–13 (1991)CrossRefGoogle Scholar
  11. 11.
    J.S. Nielsen, W.J. Hoefer, Generalized dispersion analysis and spurious modes of 2-D and 3-D TLM formulations. IEEE Trans. Microw. Theory Tech. 41(8), 1375–1384 (1993)CrossRefGoogle Scholar
  12. 12.
    C. Eswarappa, W.J. Hoefer, One-way equation absorbing boundary conditions for 3-D TLM analysis of planar and quasi-planar structures. IEEE Trans. Microw. Theory Technol. 42(9), 1669–1677 (1994)CrossRefGoogle Scholar
  13. 13.
    C. Eswarappa, W.J.R. Hoefer, Diakoptics and wideband dispersive absorbing boundaries in the 3-D TLM method with symmetrical condensed node. IECE Trans. 74(5), 1242–1250 (1991)Google Scholar
  14. 14.
    M. Righi, W.J. Hoefer, M. Mongiardo, R. Sorrentino, Efficient TLM diakoptics for separable structures. IEEE Trans. Microw. Theory Technol. 43(4), 854–859 (1995)CrossRefGoogle Scholar
  15. 15.
    M. Righi, C. Eswarappa, W.J. Hoefer, P. Russer, An alternative way of computings–parameters via impulsive TLM analysis without using absorbing boundary conditions, in 1995 International Microwave Symposium Digest, Orlando, FL, USA (1995), pp. 1203–1206Google Scholar
  16. 16.
    C. Eswarappa, W.J. Hoefer, Fast s-parameter computation of a microstrip interdigital filter using TLM, Prony’s and digital filtering techniques. Int. J. Numer. Model. Electron. Netw. Devices Fields 9, 237–248 (1996)CrossRefGoogle Scholar
  17. 17.
    P. Russer, U. Siart, (eds.) Time-Domain Methods in Modern Engineering Electromagnetics, A Tribute to Wolfgang J.R. Hoefer, 1st edn. Springer Proceedings in Physics, vol. 121 (Springer, 2008)Google Scholar
  18. 18.
    P. Russer, M. Righi, C. Eswarappa, W.J. Hoefer, Lumped element equivalent circuit parameter extraction of distributed microwave circuits via TLM simulation, in 1994 International Microwave Symposium Digest. San Diego, CA, USA, 1994, pp. 887–890Google Scholar
  19. 19.
    T. Mangold, P. Russer, Full-wave modeling and automatic equivalent-circuit generation of millimeter-wave planar and multilayer structures. IEEE Trans. Microw. Theory Tech. 47(6), 851–858 (1999)CrossRefGoogle Scholar
  20. 20.
    P. Poman, H. Du, W.J. Hoefer, Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks. IEEE Trans. Microw. Theory Tech. 53(4), 1496–1505 (2005)CrossRefGoogle Scholar
  21. 21.
    C. Christopoulos, P. Russer, Application of TLM to EMC problems. in Applied Computational Electromagnetics, NATO ASI Series. (Springer, Berlin, 2000), pp. 324–350Google Scholar
  22. 22.
    L. Pierantoni, S. Lindenmeier, P. Russer, A combination of integral equation method and FD/TLM method for efficient solution of emc problems. in Microwave Conference and Exhibition, 1997 27th European (1997), pp. 937–942Google Scholar
  23. 23.
    L. Pierantoni, G. Cerri, S. Lindenmeier, P. Russer, Theoretical and numerical aspects of the hybrid MoM-FDTD, TLM-IE and ARB methods for the efficient modelling of EMC problems. in Proceedings of the 29th European Microwave Conference (Munich, 1999), pp. 313–316Google Scholar
  24. 24.
    S. Lindenmeier, L. Pierantoni, P. Russer, Hybrid space discretizing-integral equation methods for numerical modeling of transient interference. IEEE Trans. Electromagn. Compat. 41(4), 425–430 (1999)CrossRefGoogle Scholar
  25. 25.
    R. Khlifi, P. Russer, Hybrid space-discretizing method–method of moments for the analysis of transient interference. IEEE Trans. Microw. Theory Tech. 54(12), 4440–4447 (2006)CrossRefGoogle Scholar
  26. 26.
    R. Khlifi, P. Russer, A hybrid method combining TLM and mom method for efficient analysis of scattering problems. in 2006 International Microwave Symposium Digest. San Francisco, CA, USA, 2006, pp. 161–164Google Scholar
  27. 27.
    N. Fichtner P. Russer, A total-field/scattered-field technique applied for the TLM-integral equation method, in IEEE MTT-S International Microwave Symposium digest, 2009. MTT ‘09. IEEE (2009) pp. 325–328Google Scholar
  28. 28.
    N. Fichtner, P. Russer, A hybrid TLM-integral equation method using time-domain plane-waves for shielding effectiveness computations. in 26th Annual Review of Progress in Applied Computational Electromagnetics (ACES) (Tampere, Finland, 2010)Google Scholar
  29. 29.
    N. Fichtner, P. Russer, An accelerated hybrid TLM-IE method for the investigation of shielding effectiveness. Adv. Radio Sci. 8, 13–18 (2010)CrossRefGoogle Scholar
  30. 30.
    J.A. Russer P. Russer, An efficient method for computer aided analysis of noisy electromagnetic fields. in Microwave Symposium Digest (MTT), 2011 IEEE MTT-S International. IEEE, 2011, pp. 1–4Google Scholar
  31. 31.
    J. Russer, P. Russer, Network methods applied to the computation of stochastic electromagnetic fields. in 2011 International Conference on Electromagnetics in Advanced Applications (ICEAA). (IEEE, 2011), pp. 1152–1155Google Scholar
  32. 32.
    E.P.Wigner, The unreasonable effectiveness of mathematics in the natural sciences. Richard courant lecture in mathematical sciences delivered at New York University, May 11, 1959. Commun. Pure Appl. Math. 13(1), 1–14 (1960)Google Scholar
  33. 33.
    R.S. Elliott, Electromagnetics—History, Theory, and Applications (IEEE Press, New York, 1991Google Scholar
  34. 34.
    H. Hertz, Gesammelte Werke, Untersuchungen über die Ausbreitung der elektrischen Kraft, vol. 2 (Johann Ambrosius Barth, Leipzig, 1894)Google Scholar
  35. 35.
    F. Wilczek, in A Piece of Magic—the Dirac Equation, ed. by G. Farmelo. It must be beautiful—Great Equations of Modern Science. (Granta Books, New York, London, 2002), pp. 102–130Google Scholar
  36. 36.
    A. Sommerfeld, Über die Ausbreitung der Wellen in der Drahtlosen Telegraphie. Ann. Physik 28, 665–737 (1909)CrossRefzbMATHGoogle Scholar
  37. 37.
    A. Sommerfeld, Partielle Differentialgleichungen der Physik (Akademische Verlagsgesellschaft Geest & Portig, Leipzig, 1947)Google Scholar
  38. 38.
    L.B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice Hall, Englewood Cliffs, 1972Google Scholar
  39. 39.
    R. Collin, Field Theory of Guided Waves, 2nd edn. (IEEE Press, Inc., New York, 1991)Google Scholar
  40. 40.
    R.E. Collin, The role of analysis in an age of computers: view from the analytical side. IEEE Antennas Propag. Mag. 32(4), 27–31 (1988)CrossRefGoogle Scholar
  41. 41.
    M.B. Steer, J.W. Bandler, C.M. Snowden, Computer-aided design of RF and microwave circuits and systems. IEEE Trans. Microw. Theory Tech. 50(3), 996–1005 (2002)CrossRefGoogle Scholar
  42. 42.
    R.F. Harrington, Field Computation by Moment Methods (IEEE Press, San Francisco 1968)Google Scholar
  43. 43.
    K. Yee, Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14, 302–307 (1966)CrossRefzbMATHGoogle Scholar
  44. 44.
    T. Weiland, A discretization method for the solution of Maxwell’s equations for six-component fields. Electron. Commun. (AEU) 31, 116–120 (1977)Google Scholar
  45. 45.
    C. Huygens, Traité de la lumière: où sont expliquées les causes de ce qui luy arrive dans la reflexion, & dans la refraction, et particulièrement dans l’étrange refraction du Cristal d’Islande (Pierre Vander Aa, Leyden, 1690)Google Scholar
  46. 46.
    J.C. Maxwell, A Treatise on Electricity and Magnetism, vol. 1 (Oxford University Press, New York, 1998)Google Scholar
  47. 47.
    J.C. Maxwell, A Treatise on Electricity and Magnetism, vol. 2 (Oxford University Press, New York, 1998)Google Scholar
  48. 48.
    H. Hertz, Über Strahlen electrischer Kraft. Ann. Phys. Chem. Folge 36, 3(4), 769–783 (1889)Google Scholar
  49. 49.
    J.A. Russer, W.J. Hoefer, A TLM algorithm simulator for the visualization of time discrete electromagnetic processes, in Proceedings of the Second International Conference on Computation in Electromagnetics (London, 1994), pp. 120–122Google Scholar
  50. 50.
    S. Hein, Consistent finite difference modelling of Maxwell’s equations with lossy symmetrical condensed TLM node. Int. J. Numer. Model. Electron. Netw. Devices Fields 6, 207–220 (1993)CrossRefMathSciNetGoogle Scholar
  51. 51.
    M. Krumpholz, P. Russer, A field theoretical derivation TLM. IEEE Trans. Microw. Theory Tech. 42(9), 1660–1668 (1994)CrossRefGoogle Scholar
  52. 52.
    M. Aidam, P. Russer, Derivation of the transmission line matrix method by finite integration. AEÜ Int. J. Electron. Commun. 51, 35–39 (1997)Google Scholar
  53. 53.
    P. Russer, Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering, 2nd edn. (Artech House, Boston, 2006)Google Scholar
  54. 54.
    V. Belevitch, Summary of the history of circuit theory. Proc. IRE 50(5), 848–855 (1962)CrossRefGoogle Scholar
  55. 55.
    V. Belevitch, Classical Network Theory (Holden-Day, San Francisco, 1968)Google Scholar
  56. 56.
    A. Davis, On the axiomatic foundations of circuit theory. in International Symposium on Circuits and Systems, ISCAS 2001, vol. 2 (IEEE, 2001), pp. 783–786Google Scholar
  57. 57.
    M. Krumpholz, P. Russer, A field theoretical derivation of TLM. IEEE Trans. Microw. Theory Tech. 42(9), 1660–1668 (1994)CrossRefGoogle Scholar
  58. 58.
    P. Russer, M. Krumpholz, The Hilbert space formulation of the TLM method. Int. J. Numer. Model. Electron. Netw. Devices Fields 6(1), 29–45 (1993)CrossRefMathSciNetGoogle Scholar
  59. 59.
    J. Mlakar, Lumped circuit symmetrical TLM node. Electron. Lett. 28(5), 497–498 (1992)CrossRefGoogle Scholar
  60. 60.
    J. Mlakar, D. Kostevc, Direct calculation of scattering parameters of SCN node. Electron. Lett. 34(5), 468–469 (1998)CrossRefGoogle Scholar
  61. 61.
    S. Lindenmeier, P. Russer, The alternating rotated TLM scheme (ARTLM) for fast simulations in time domain. in Proceedings of the 26 h European Microwave Conference (Prague, 1996), pp. 493–496Google Scholar
  62. 62.
    P. Russer, The alternating rotated transmission line matrix (ARTLM) scheme. Electromagnetics 16(5), 537–551 (1996)CrossRefGoogle Scholar
  63. 63.
    L. Ljung, System Identification. Theory for the User. (Prentice Hall PTR, Upper Saddle River, 1999)Google Scholar
  64. 64.
    C. E. Baum, The singularity expansion method in transient electro-magnetic fields. in Transient Electromagnetic Fields, L. B. Felsen, Ed. Berlin: Springer, 1976Google Scholar
  65. 65.
    W. Cauer, Theorie der linearen Wechselstromschaltungen (Akademie-Verlag, Berlin, 1954)Google Scholar
  66. 66.
    P. Russer, M. Mongiardo, L.B. Felsen, Electromagnetic field representations and computations in complex structures III: network representations of the connection and subdomain circuits. Int. J. Numer. Model. Electron. Netw. Devices Fields 15, 127–145 (2002)CrossRefzbMATHGoogle Scholar
  67. 67.
    L.B. Felsen, M. Mongiardo, P. Russer, Electromagnetic Field Computation by Network Methods. (Springer, New York, 2009)Google Scholar
  68. 68.
    L. Chu, Physical limitations of omni-directional antennas. J. Appl. Phys. 19(12), 1163–1175 (1948)CrossRefGoogle Scholar
  69. 69.
    R.F. Harrington, Time Harmonic Electromagnetic Fields. (McGraw-Hill, New York, 1961)Google Scholar
  70. 70.
    O. Brune, Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency. J. Math. Phys. 10(3), 191–236 (1931)zbMATHMathSciNetGoogle Scholar
  71. 71.
    E.A. Guillemin, Synthesis of Passive Networks. (Wiley, New York, 1957)Google Scholar
  72. 72.
    F. Mukhtar, J. Russer, Y. Kuznetsov, P. Russer, Methodology for generation of Brune’s equivalent circuit models for linear passive reciprocal multi-ports. in 2012 International Conference on Electromagnetics in Advanced Applications (ICEAA) (2012), pp. 674–677Google Scholar
  73. 73.
    Y. Kuznetsov, A. Baev, T. Shevgunov, U. Siart, H. Yordanov, P. Russer, Generation of network models for planar microwave circuits by system identification methods. in International Conference on Electromagnetics in Advanced Applications, 2009. ICEAA’09 (2009), pp. 966–969Google Scholar
  74. 74.
    J.A. Russer, F. Mukhtar, A. Gorbunova, A. Baev, Y.V. Kuznetsov, P. Russer, Brune’s algorithm for circuit synthesis. in IEEE MTT-S International Microwave Symposium Digest (MTT), 2013 .Seattle, 2013, pp. 1–4Google Scholar
  75. 75.
    F. Mukhtar, P. Russer, A Brune’s two–port process applied to lumped element filter modeling. in IEEE MTT-S International Microwave Symposium Digest (MTT), 2013. Seattle, 2013, pp. 1–3Google Scholar
  76. 76.
    F. Mukhtar, P. Russer, Brune’s multiport lumped element equivalent circuits in admittance representation. in 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA) (2013), pp. 964–967Google Scholar
  77. 77.
    F. Mukhtar, P. Russer, Brune’s multiport lumped element equivalent circuits in admittance representation. in Paper Submitted for 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA) (Torino, Italy, 2013), pp. 1–4Google Scholar
  78. 78.
    J. M. Smith, Mathematical Modeling and Digital Simulation for Engineers and Scientists, 2nd edn. (John Wiley & Sons, New York, 1987)Google Scholar
  79. 79.
    A.V. Oppenheim, R.W. Schafer, Discrete-Time Signal Processing, 2nd edn. Signal Processing Series. (Prentice-Hall, 1989)Google Scholar
  80. 80.
    P. Russer, Network methods applied to computational electromagnetics, in Proceedings of the 9th International Conference on Telecommunication in Modern Satellite, Cable, and Broadcasting Services, 2009. TELSIKS ‘09 (2009), pp. 329–338Google Scholar
  81. 81.
    P. Russer, Overview over network methods applied to electromagnetic field computation. in ICEAA 2009, International Conference on on Electromagnetics in Advanced Applications (Torino, Italy, 2009), pp. 276–279Google Scholar
  82. 82.
    J.A. Russer, Y. Kuznetsov, P. Russer, Discrete-time network and state equation methods applied to computational electromagnetics Mikrotalasna Revija (Microwave Review), pp. 2–14 (2010)Google Scholar
  83. 83.
    P. Richards, Resistor-transmission-line circuits. Proc. IRE 36(2), 217–220 (1948)CrossRefGoogle Scholar
  84. 84.
    P. Lorenz, The Transmission Line Matrix Multipole Expansion (TLM-ME) Method. in 2006 IEEE MTT-S International Microwave Symposium, Workshop WFE, Advanced Methods for EM Computing, San Francisco, USA (2006)Google Scholar
  85. 85.
    J.J. Wang, Generalized Moment Methods in Electromagnetics (Wiley, New York, 1991)Google Scholar
  86. 86.
    J. Russer, P. Russer, Stochastic electromagnetic fields. in Microwave Conference (GeMIC), 2011 German (IEEE, 2011), pp. 1–4Google Scholar
  87. 87.
    J.V. Bladel, Electromagnetic Fields, 2nd edn. (Wiley, New York, 2007)Google Scholar
  88. 88.
    J.A. Russer, G. Scarpa, P. Lugli, P. Russer, On the modeling of radiated EMI on the basis of near-field correlation measurements. in European Microwave Conference (EuMC) (Manchester, 2011), pp. 9–12Google Scholar
  89. 89.
    P. Russer, J.A. Russer, Modeling and measurement of stochastic electromagnetic fields in EMI. in Proceedings of Asia-Pacific Symposium on Electromagnetic Compatibility APEMC (Singapore, 2012)Google Scholar
  90. 90.
    J. Russer, T. Asenov, P. Russer, Sampling of stochastic electromagnetic fields. in IEEE MTT-S International Microwave Symposium Digest (MTT) (2012), pp. 1–3Google Scholar
  91. 91.
    A. Baev, A. Gorbunova, M. Konovalyuk, J.A. Russer, Y. Kuznetsov, Planar stochastic sources localization algorithm in EMC problems. in 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA) (Torino, Italy, 2013), pp. 1–4Google Scholar

Copyright information

© Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Electrical Engineering and Information Technology DepartmentTechnische Universität MünchenMunichGermany

Personalised recommendations