FDTD simulations of TEM horns and the implications for staircased representations

Two-dimensional (2-D) TEM horns are modeled using the finite-difference time-domain (FDTD) method. The boundary walls are perfect electric conductors and one wall, which does not align with the Cartesian grid, is approximated using a staircased representation. By carefully comparing the FDTD results to those of the analytic solution, one can make conclusions about the coarseness with which a boundary can be represented. It is found that staircasing errors are small when the staircase diagonal (the hypotenuse of the right triangle created by the stairstep) is smaller than half a wavelength at the highest significant frequency in the excitation. This rule-of-thumb is put forward as a necessary condition for the discretization of general problems. Results are also provided for some simple FDTD schemes that are designed to reduce staircasing errors. By using large aspect-ratio cells, a grid can be constructed that satisfies the rule-of-thumb given above. While this approach eliminates general staircasing errors, some errors persist owing to the presence of step discontinuities immediately adjacent to the horn feed. These errors can be further reduced by using a cell-splitting approach. It is shown that the contour path FDTD technique can be used to eliminate nearly all staircasing errors, while some additional improvement is shown to be provided by using a stabilized contour path FDTD approach. Finally, a recently proposed conformal technique that permits simple implementation is shown to provide results comparable with those of the stabilized contour path approach.