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Numerical Analysis in Electromagnetics: The TLM Method by Pierre Saguet

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Chapter 1

Basis of the TLM Method: the 2D TLM Method

1.1. Historical introduction

Historically, this method is based on the Huygens–Fresnel principle, which states that each point of a wave front can be considered to be an isotropic, spherical, a secondary source, and the energy is isotropically distributed in all directions, as illustrated in Figure 1.1.

Figure 1.1. Huygens’ principle

ch1-image01-01.gif

The 2D TLM method was formulated by Johns in 1971, based on the principles outlined below.

Space is modeled using a Cartesian matrix of points or nodes separated by a gap Δl, where Δt represents the time taken for a pulse to travel from one node to another.

Figure 1.2. Transmission line network in the XY plane

ch1-image02-01.gif

Johns [JOH 71] applied this principle in order to solve electromagnetic problems and create secondary sources by connecting transmission lines, regularly spaced in a series or in parallel.

If a Vo=1V Dirac pulse is applied to any branch of this parallel node, propagating to node A, we obtain:

ch1-image02-02.gif

If every branch of the node has the same characteristic impedance Zc, then the impedance “seen” by the incident pulse will be equal to Zc/3 and will be reflected with a coefficient:

[1.1]

The voltages ...

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