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E - Bibliothèque et Archives Canada

E - Bibliothèque et Archives Canada

2.4.4 Evaluation of T b

2.4.4 Evaluation of T b & TEz Z,,,,, Tema As shm in d o n 2.4.3, the evaluaüon of 2, temg is very important and couM Iead easily to misleading resub if not done properly. Approximations and closeâ bmis of typical 2, terms can be found in the open literature (21 [12], but sinœ the accuracy of results will be ednmely sensitive to the adequacy of Zm evaluation, the derivation of al1 Z, irnpedance t em in dosmi or integral and approximate lomg will be done hem. Only scatterers made of surfaces parallel to the x or y axis are dealt with in this work. a)TMz case Ftom equation 2.17 and 2.21d with pulse basis functions and point rnatching, the impedanœ tem of a strip segment n of Mdth Ax (aligned with the x axis) is: where, The integral in equation 2.27 experiences a singularity when mn and it Now rince axis small. kp is a small argument. The approximation of the Hankel funcüon when k m is [2] (2.28)

If we insert 2.29 in 2.28 w have: Now sin- xln(x)zO Men x+O, then the same analysis applies to stnp segments aligned wîth the y axis but with Ay replacing Ax Henœ the &,, evaluations suggemted are: Equation 2.32 is to be evaluated by numarical integration on a srnall segment n of a strip on the scattefer with p bain$ the linear distance on the surface of tb strip (usually its fixed origin is one edge of the strip). In equaüon 2.32, R=&&-J~)%(~-~Y and the expression is a crude approximation but yields in general good rcwults. It should be noted that the p is a linear distanœ that mn k in the x or y direction.

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