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E - Bibliothèque et Archives Canada

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l T G case - non

l T G case - non diaaonal ternis; Equation 2.1 8 gives an expression with Hankel functions of O and 2- orâers. Sinœ maat subroutines limit their output to Hankel fundions of O and 1" order only and since [2] the tm from equations 2.18 and 2.19 can be written as: -For m and n on ~arallel but not the same surfaces - For m and n on the samo surface kos~2c~")=l~ - For m and n on mmendicular surfaces The terms in equations 2.34.2.35 and 2.36 can al1 be cornputeci by numerical integratîon. c)TEz case Diaaonal terni (self inmedance): When mn. the integral in equation 2.18 a. experiences a singularity. To be able to evaluate this terni, we need to follow its derivation since the beginning. The vector potential equation can be written as Ë=-jd-vv

In two dimensional cases and at a certain match point m [2] (v2 + k2)&L) = -fi+) and where C is thc petrimeter of the scatterer and p is the linear distanœ from the origin. Similarly [11][12] the rame can be stated for the scalar voltage potential Where p. is the surface charge density. If the surface of the scatterer is divided into segments of width A and the current is representeâ by pulse basis funcüons and point matching is used, the contribution of the vector potential 1 to the electric field and henœ to the impedanœ from a segment n to a point m located at the middle of aie segment is Equation 2.37 is equivalent to equation 2.30. Since p diructeâ surface current is relateâ to the charge by &=-jmp, then dp Sinœ the current is represented by a pulse. its derivative with respect to p is a positive impulse (delta fundon) at p and a negative one at prr . Now if m=n,

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