Coupling between electromagnetic waves and wires using transmission-line modelling
Three techniques are used to introduce wire models into Transmission Line Matrix (TLM) Electromagnetic field solvers. The first involves the setting up of a one dimensional time-domain transmission-line model of a pair of wires. Voltages and currents coupled into the wires can be obtained from the incident fields. The differentials of these fields are used as source terms of the one dimensional model. Results obtained by this model were compared with frequency domain results and good agreement was found. Non-linear loads can easily be modelled, and the response of a simple non-linear device is presented. Wires of realistic radii can only be modelled in 2- or 3-dimensional TLM by using a fine mesh. Using progressively finer meshes the modelled radius converges to an unexpected result. The problem lies with the two forms of the TLM mesh, each giving a different modelled radius. This can lead to velocity of propagation errors of up to 10%. A short-circuit node was developed but this has poor propagational characteristics and a radius equal to half the mesh spacing. Diakoptics was re-examined and some operating conditions suggested. Frequency Domain Diakoptics was also introduced and tested. Time Domain Diakoptics was used to create blocks of space containing wires which could be pre-solved for future use. Since a very fine mesh was used to describe the wire, but a coarse mesh was used for the remainder of the geometry there is a very crude approximation between the two meshes. This effect meant that long wires could not be constructed out of a multitude of pre-solved short-wires. A longer wire could be pre-solved as a single element and a reasonable modelled radius obtained. The technique became unstable after about 750 iterations. Comparisons between the wire models developed show reasonable agreement. The one-dimensional method was the easiest technique to use.