Jonathan Herring, Mario Righi, Wolfgang J. R. Hoefer
Modal absorbing boundary conditions have been applied to a graded mesh using the hybrid node, and to homogeneous waveguides of arbitrary cross-section. The best performance is obtained with rectangular waveguides but examples show that the method can also be used for other geometries. A T-junction circular-to-sidecoupled rectangular waveguide example is given. For rectangular waveguides, the modal field distribution is well known. In the application of modal boundary conditions to TLM, it is convenient to work directly with the voltage pulses, rather than with the total tangential field components. This is possible because the link-line voltages are a linear combination of the electric and magnetic fields. For a graded mesh using the hybrid node, three different impedances are assigned to the three sets of link-lines contributing to each component of the magnetic field. The modal Green's function is determined by the timestep and the node dimension perpendicular to the boundary; it is independent of the mesh grading in the cross-section. Typical Green's functions for the dominant mode in a WR28 waveguide are shown, for the cases of (i) cubic nodes with the maximum timestep, (ii) cubic nodes with half the maximum timestep, and (iii) cuboid nodes of twice the length in the perpendicular direction and with the maximum timestep.
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Further details can be found in: J. L. Herring, M. Righi, W.J.R. Hoefer, "Modal Boundary Conditions For Waveguides of Arbitrary Cross-section With SCN TLM" in 1997 Intl. Microwave Symposium Dig., pp. 325-328, Denver, Colorado, June 9-13, 1997.
