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1.6 Transmission Line Matrix

by Jose Alves

The Transmission-Line Matrix (TLM) method is a method for computing electromagnetic fields that discretises both space and time. It draws on the analogy between electromagnetic fields and a network of transmission lines, allowing for the simulation of complex three-dimensional electromagnetic structures. Alongside the Finite Difference Time Domain (FDTD) method, TLM is recognized as one of the most effective time-domain methods available.

The TLM method is grounded in Huygens' model of wave propagation and scattering, viewing the computational domain as a mesh of interconnected transmission lines at nodes. Like FDTD, TLM discretises the electromagnetic wave propagation in both time and space using an iterative approach, focusing on two main processes: scattering and connecting. The scattering process calculates the reflected impulse voltage at the nn-th node at time (k+1)Δt(k+1)Δt, based on the known incident voltage at time kΔtkΔt. The connecting process then determines the incident pulse at a node using the reflected impulses from adjacent nodes.

TLM shares similar advantages and challenges with FDTD and is applied to comparable problem types. It is indeed possible to mathematically derive one method from the other.

An illustrative example of TLM's application is in computing the wideband cellular performance on a large vehicle platform. The method's ability to handle wideband responses and its non-complex mesh structure offer significant benefits, such as reduced memory requirements and faster runtimes, compared to other methods.

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