Analysis and Synthesis of Singly-Curved Microstrip Structures Utilizing Modified Schwarz-Christoffel Transformation

A new conformal mapping-based method to analyze and synthesize singly-curved microstrip structures is presented. The cross-section of such structures is usually an elongated region with curved boundaries. Under a conventional Schwarz-Christoffel Transformation (SCT), elongation causes the undesirable crowding phenomenon. Also, the curvature is not taken into account. To circumvent crowding, SCT is modified so that it maps an elongated straight strip into a polygon with both ends at infinity. Curvature is accounted for by fitting each segment of the curved boundaries with a second degree polynomial function of SCT prevertices. This mapping is called Modified Schwarz-Christoffel Transformation (MSCT) which proves to be a fast and accurate method to deal with electromagnetic structures. As a test case, a composite right/left-handed (CRLH) conformal leaky-wave antenna (LWA) located on an elliptic cylinder is investigated. The antenna is designed to have broadside radiation at 7.75 GHz and Bloch impedance 50 Ω around its radiation regime. Its scattering parameters and E-plane radiation patterns are calculated by MSCT and are compared with full-wave simulation and fabrication results which show good agreement.