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E - Bibliothèque et Archives Canada

E - Bibliothèque et Archives Canada

segmentation applieâ to

segmentation applieâ to al1 geomatries and pulw basis fundons and point mtching. lt covers TEz and TMz polarization scattering of stri-ps and cylinders. The second de, TECYL (2-0 TE radiation and scattering from conduding CYLinders) b based on [l6]F a1 81. lt uses the integral equation and m n t rrmthod. It deals only +th the TG case but covers open end ci& condudng surfaces. It uses p idse sinusoidel basis fundion and Galerkin's mthod. In the early stages of this investigation TDRS and TECYL were usd intensively to be able to determine the radiation patterns of electrically small scatteren, but of different shapes. In the case of a mgnetic line source illuminating a strip of width = 5 L (source heightss0.2 L) the nurnber of segments required by TDRS was at 1-st 50 times higher than the number of segments nquired by TECYL to achieve oie sam accuracy. This finding was interesting because TDRS uses pulse basis and point mtching and TECYL uses pieceWise sinuaoid bads and Galerkin method. Sinœ a that point no decision was yet taken on the independent rnethod to be used to compare UTD derivecl results. an investigation was due and what follouw is the result. For a 2-D thin plate (stnp). illuminatexi by an infinite magnetic line source (TE2 case), TDRS based on [2] has suggested the following impedanœ tem Zm (between segmnt rn and segment n):

form # n&Im-al s 2 & and x, king the rniddle points of segmants m and n mspedvely. A&, = width of segment n. It should be noted here that equation (2.26) is an exact formula. Equation (2.25) is derived from equation (2.26) using the approximation [2] of the Hankel function for small arguments: mkP) = Ji(kP) - jfi(kP) j for k~ + 0 king the distance f m a point on segment n to xm) This approximation converges for small segments (kp + O), but sinœ it is used kp can Vary frorn 0.1% to 5. At kp = ~ YC, it is obvious that the Hankel function approximation is poor. As for equation (2.24) it was derived diredly from a mixed potential equaüon (refer to section 2.4.1 b) leading to an exact fomwla consisting of an integral of Hankel H',*)d functions. Accurate approximations m#c used for aie Hankel functions at that point: instead of using the crudo approximation as was done in the case of equation 2.25, additional ternis 151181 were used in represenüng the Hankel fundion for small arguments.

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