Transmission-line matrix method: Difference between revisions

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The '''transmission -line matrix (TLM) method''' is a space and time discretising method for computation of [[electromagnetic fields]]. It is based on the analogy between the electromagnetic field and a mesh of [[transmission line]]s. The TLM method allows the computation of complex three-dimensional electromagnetic structures and has proven to be one of the most powerful time-___domain methods along with the finite difference time ___domain ([[FDTD]]) method.

== Basic principle ==

[[Image:SingleNode2DTLM.png|thumb|500px|right|2D TLM example: an incident voltage pulse in two consecutive scattering events.]] The TLM method is based on [[Huygens Principle|Huygens' model of wave propagation]] and scattering and the analogy between field propagation and transmission lines. Therefore it considers the computational ___domain as a mesh of transmission lines, interconnected at nodes. In the figure on the right is considered a simple example of a 2D TLM mesh with a voltage pulse of amplitude 1 V incident on the central node. This pulse will be partially reflected and transmitted according to the transmission -line theory. If we assume that each line has a characteristic impedance <math>Z</math>, then the incident pulse sees effectively three transmission lines in parallel with a total impedance of <math>Z/3</math>. The reflection coefficient and the transmission coefficient are given by

: <math>R = \frac{Z/3-Z}{Z/3+Z} = -0.5</math>