FDTD SIMULATIONS OF TEM HORNS AND THE IMPLICATIONS FOR STAIRCASED REPRESENTATIONS

Two dimensional (2-D) TEN horns are modeled using the finite differenc e time-domain (FDTD) method, The boundary walls are perfect electric c onductors and one wall, which does not align with the Cartesian grid, is approximated using a staircased representation By carefully compari ng the FDTD results to those of the analytic solution, one can make co nclusions about the coarseness with which a boundary can be represente d, It is found that staircasing errors are small when the staircase di agonal (the hypotenuse of the right triangle created by the stairstep) is smaller than half a wavelength at the highest significant frequenc y 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 sta ircasing errors, By using large aspect-ratio cells, a grid can be cons tructed that satisfies the rule-of-thumb given above, While this appro ach eliminates general staircasing errors, some errors persist owing t o the presence of step discontinuities immediately adjacent to the hor n 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 imp rovement is shown to be provided by using a stabilized contour path FD TD approach, Finally, a recently proposed conformal technique that per mits simple implementation is shown to provide results comparable with those of the stabilized contour path approach.