The Transmission Line Matrix Method

The transmission line matrix (TLM) method [1–3], developed and first published in 1971 by Johns and Beurle has emerged as a powerful method for computer modeling of electromagnetic fields. In TLM the space is subdivided into cells. The electromagnetic field dynamics is modeled by wave pulses propagating between adjacent cells and scattered within the cells. The main advantage of the TLM simulation resides in the capability to model circuits of arbitrary geometry, and to compute and to display the time evolution of the fields. The TLM method exhibits an excellent numerical stability and is also suitable for modelling of lossy, dispersive and nonlinear media.

[1]  Peter Russer,et al.  Field-theoretic foundation of two-dimensional TLM based on a rectangular mesh , 1994, 1994 IEEE MTT-S International Microwave Symposium Digest (Cat. No.94CH3389-4).

[2]  P. Johns A Symmetrical Condensed Node for the TLM Method , 1987 .

[3]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[4]  T. Mangold,et al.  A multichip module integration technology on silicon substrate for high frequency applications , 1998, 1998 Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems. Digest of Papers (Cat. No.98EX271).

[5]  Jan M Smith Mathematical Modeling and digital Simulation for Engineers and Scientists , 1988 .

[6]  T. Itoh Numerical techniques for microwave and millimeter-wave passive structures , 1989 .

[7]  Peter Russer,et al.  On the dispersion in TLM and FDTD , 1994 .

[8]  P. Russer,et al.  Full-wave analysis and model-based parameter estimation approaches for Y-matrix computation of microwave distributed RF circuits , 2001, 2001 IEEE MTT-S International Microwave Sympsoium Digest (Cat. No.01CH37157).

[9]  P. B. Johns,et al.  Application of transmission-line modelling (TLM) to thermal diffusion in bodies of complex geometry , 1986 .

[10]  Peter Russer,et al.  The hilbert space formulation of the TLM method , 1993 .

[11]  Peter Russer,et al.  Application of TLM to Microwave Circuits , 2000 .

[12]  P. Russer,et al.  The alternating transmission line matrix (ATLM) scheme , 1995, Proceedings of 1995 IEEE MTT-S International Microwave Symposium.

[13]  Karl F. Warnick,et al.  Teaching Electromagnetic Field Theory Using Differential Forms , 1997, Teaching Electromagnetics.

[14]  On the theory of discrete TLM Green's functions in three-dimensional TLM , 1995 .

[15]  Wolfgang J. R. Hoefer,et al.  The Transmission-Line Matrix Method--Theory and Applications , 1985 .

[16]  Peter Russer,et al.  Lumped element equivalent circuit parameter extraction of distributed microwave circuits via TLM simulation , 1994, 1994 IEEE MTT-S International Microwave Symposium Digest (Cat. No.94CH3389-4).

[17]  Peter Russer,et al.  Applications of TLM to EMC Problems , 2000 .

[18]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[19]  J. W. Thomas Numerical Partial Differential Equations , 1999 .

[20]  Chu-Sun Yen,et al.  Time-domain skin-effect model for transient analysis of lossy transmission lines , 1982, Proceedings of the IEEE.

[21]  Wolfgang J. R. Hoefer,et al.  A complete dispersion analysis of the condensed node TLM mesh , 1991 .

[22]  H. Jin,et al.  Direct derivations of TLM symmetrical condensed node and hybrid symmetrical condensed node from Maxwell's equations using centered differencing and averaging , 1994 .

[23]  Wolfgang J. R. Hoefer,et al.  FAST S‐PARAMETER COMPUTATION OF A MICROSTRIP INTERDIGITAL FILTER USING TLM, PRONY'S AND DIGITAL FILTERING TECHNIQUES , 1996 .

[24]  W. Ross Stone An Introduction to the use of ModelBased Parameter Estimation in Electromagnetics , 1999 .

[26]  L.-T. Hwang,et al.  A review of the skin effect as applied to thin film interconnections , 1992 .

[27]  Chrysostomos L. Nikias,et al.  Parameter estimation of exponentially damped sinusoids using higher order statistics , 1990, IEEE Trans. Acoust. Speech Signal Process..

[28]  K. Yee Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[29]  P. Russer,et al.  Modeling of nonlinear active regions in TLM (distributed circuits) , 1991, IEEE Microwave and Guided Wave Letters.

[30]  Jorgen Staal. Nielsen TLM analysis of microwave and millimeter wave structures with embedded nonlinear devices. , 1992 .

[31]  Peter Russer,et al.  A field theoretical derivation of TLM , 1994 .

[32]  A. Messiah Quantum Mechanics , 1961 .

[33]  C. Christopoulos,et al.  The Transmission-line Modeling Method: TLM , 1995, IEEE Antennas and Propagation Magazine.

[34]  W.J.R. Hoefer,et al.  An alternative way of computing S-parameters via impulsive TLM analysis without using absorbing boundary conditions , 1995, Proceedings of 1995 IEEE MTT-S International Microwave Symposium.

[35]  P. B. Johns,et al.  Use of the transmission-line modelling (t.l.m.) method to solve non-linear lumped networks , 1980 .

[36]  Wolfgang J. R. Hoefer,et al.  The discrete time-domain green's function or Johns matrix - A new powerful concept in transmission line modelling(TLM). , 1989 .

[37]  C. K. Yuen,et al.  Digital spectral analysis , 1979 .

[38]  P. B. Johns,et al.  A simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation , 1977 .

[39]  Peter Russer,et al.  Two‐dimensional FDTD and TLM , 1994 .

[40]  Peter Russer,et al.  Full-wave modeling and automatic equivalent-circuit generation of millimeter-wave planar and multila , 1999 .

[41]  R. J. Lomax,et al.  A finite-difference transmission line matrix method incorporating a nonlinear device model , 1990 .

[42]  Keith D. Paulsen,et al.  Origin of vector parasites in numerical Maxwell solutions , 1991 .

[43]  Peter B. Johns,et al.  Numerical solution of 2-dimensional scattering problems using a transmission-line matrix , 1971 .

[44]  Peter Russer,et al.  Modelling of nonlinear active devices in TLM , 1991 .

[45]  G. Kron,et al.  Equivalent Circuit of the Field Equations of Maxwell-I , 1944, Proceedings of the IRE.

[46]  Chi-Chung Wong,et al.  Transient response of lossy transmission lines with arbitrary loads , 1992 .

[47]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[48]  J. E. Sitch,et al.  Transmission-line matrix method with irregularly graded space , 1981 .

[49]  Steffen Hein Consistent finite difference modelling of Maxwell's equations with lossy symmetrical condensed TLM node , 1993 .

[50]  W. Siebert Circuits, Signals and Systems , 1985 .

[51]  Luca Zaccarian,et al.  Mathematical Methods for System Theory , 1998 .

[52]  P. Russer,et al.  Modeling of Multichip Module Interconnections by the TLM Method and System Identification , 1997, 1997 27th European Microwave Conference.