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This paper presents an efficient analysis of a substrate integrated waveguide (SIW) single-layer hybrid ring coupler (rat-race) for millimeter-wave and microwave applications. The scattered field from each circular cylinder is expanded by cylindrical eigenfunctions with unknown coefficients that have been solved by electric and magnetic tangential boundary on each metallic via. The coupler S-matrix is calculated by using mode matching that uses the cylindrical vector expansion analysis to minimize the computational time and provides more physical insight. To achieve higher bandwidth, the radiuses of the coupler under analysis have been optimized in Matlab code by invasive weed optimization (IWO) method, and the results have been verified by CST package. The return loss and the isolation are less than −15 dB, and −18 dB, respectively. The insertion loss is divided equally -3±0.2 dB, with 0±5 and 180±10 degrees in output ports over the operating frequency bandwidth and the agreement of phase differences in output ports has been examined objectively by feature selective validation (FSV) technique

Analysis of a Substrate Integrated Waveguide Hybrid Ring (Rat-Race) Coupler