Transmission-line matrix method: Difference between revisions

Revision as of 01:49, 14 February 2017

Revision as of 23:42, 16 February 2017

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Therefore, the [[energy conservation law]] is fulfilled by the model.

The next [[scattering event]] excites the neighbouring nodes according to the principle described above. It can be seen that every node turns into a secondary source of spherical wave. These waves combine to form the overall waveform. This is in accordance with Huygens principle of light propagation.

In order to show the TLM schema we will use time and space discretisation. The time-step will be denoted with <math>\Delta t</math> and the space discretisation intervals with <math>\Delta x</math>, <math>\Delta y</math> and <math>\Delta z</math>. The absolute time and space will therefore be <math>t = k\,\Delta t</math>, <math>x = l\,\Delta x</math>, <math>y = m\,\Delta y</math>, <math>z = n\,\Delta z</math>, where <math>k=0,1,2,\ldots</math> is the time instant and <math>m,n,l</math> are the cell coordinates. In case <math>\Delta x = \Delta y = \Delta z</math> the value <math>\Delta l</math> will be used, which is the [[lattice constant]]. In this case the following holds: