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2 BACKGROUND 2.1 UTD AS

2 BACKGROUND 2.1 UTD AS A HiGH FREQUENCY METHOD The fields generated by radiation and scattering of eldrornagnetic waves incident upon conducüng hno-dimensional wedges could be found using modal solutions. Most of these solutions however consist of infinite series, which are poorly convergent 121. To overcorne this limitation. the Unifom Theory of Diffraction (UTD) which is an extension of the Geometrjcal Theory of Diffraction (GTD) uses high frequency asymptotic techniques to make the modal solution rnathematkally manageable. Typically. GTD transfomg the modal solution infinite series into integrals and then obtains a high frequency (kp large) asymptotic expansion for them by means of residue cornplex calculus contour integration (geometrical optics tem) and the conventional method of steepest desœnt (diffraction te-) 121. Even though this rnethod separates and defines dearîy the total geometrical optics and total diffracteci fields, the formulation of the difhcted fields is valid only for observations made far frorn the incident and reflected shadow boundaries (kLa large). UTD is based on GTD but uses the so-called Pauli-Clemmow modified rnethod of steepest descent 131, which compensates for singularities along the corresponding shadow boundaries. This compensation is done by an additional discontinuous funaion (transition fundion) proportional to a Fmel integral. Away from shadow boundaries, this integnl is nearly unity and the UTD formulation reduœs to the GTD formulation. UTD provides the total field solution for the 2-0 scattering problem shm in fig 2.1 a as

ISB 1 Figure 2.1 : UTD 2-D wdge diffracaon geometry.(a) Canonical edge. (b) Combinaüon of two eâges (half planes. n=2) back to back to evaluate the local diffraction of each edge of a &fip.

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