A modified Schwarz-Christoffel transformation (SCT) is used to obtain guided- and radiated-wave characteristics of a singly-curved rectangular patch antenna. The method is to map a straight channel into an arbitrarily-curved channel. This simplifies the problem to that of a planar rectangular patch antenna. Applying conventional SCT to the problem confronts two difficulties: The region under investigation is elongated, and it has curved boundaries. Therefore, SCT is modified to handle the problem. Input impedance, VSWR and radiation patterns of a conformal patch antenna on a parabolic surface are obtained utilizing the proposed SCT and either numerical or analytical treatment of a planar patch antenna, and the results are verified. Effect of parabolic curvature on the above-mentioned characteristics is investigated.
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