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# E - Bibliothèque et Archives Canada

E - Bibliothèque et Archives Canada

## The interest here.

The interest here. however is to use the output of e subroutihe for this coefficient and to transfomi it into a. 3~ Sinœ tha dope difhction coefndent is \$\$, whefe Ds is given by equation 2.5, the main goal is to derive each terni between the brackets in equation 2.5 with respect to 9'. If we define fi- = g, - p' and p' = p + p' , oie term to be evaluated is, once evaluabd, the terms derived with respect to p- need to be multiplied by -1 to obtain the derivative with respect to @ . Since the difhction coefficient has thegeneralformof: h = KX(A + w - (0 + D)) wherethefinrthnro D temm only indude 6.

Usually subroutines will give the result of aie dope diffraction as an array of d,. It is msy to mltiply the relevant tem with a minus sign to get equation 4.6 frorn equation 4.5 to evaalate finally equation 4.4. The incident, reflected and dimacted tangential magnetic fields have bemn fomulated, the surface cumnt on the weâge can be obtaincd, frorn j,= nx B = IJZI = IH Pl 4.1.3 Code and Rnults Cornputer Code EEDGEFOR was created based on the preœding formulation using the rnodified slope diffraction coefficient. Figures 4.1 and 4.2 show the surface current density distribution on the '0' fece and 'n' face of a half plane and a 90°wedge respedively, iIlumiMted by a TMz plane wave (with a unit magnitude electric field at the edge) at 90' incidenœ. Note that in Figure 4.2, physical optics predicts ( J, 1 = 2/rl s 0.0053 Ah. Figure 4.3 shows both current curves superirnposed because the illumination (incidence 1359 is symmetical on the eâge (n=l .S). Figure 4.4 show the case of the haIf plane with almost grazing incidenœ (O.O5O), as expedeâ the cunant magnitude is low. In al1 Figures (4.1 to 4.4). the cunent at the edge seerrm to go singular and unbounded. This is a knm [6] singularity for the TMz case. Sina the UTD code using the slow diffraction coefficient subroutine is used for the first time in this wrk, an independent check was cansidered prckrable. Figure 4.5 shows the cumnt distribution for the same case as in Figure 4.1 but the mahd used to produœ it is ba88d on the modal solution computed by a fractional order

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