In this paper, two wideband 10 dB backward directional couplers based on artificial perforated substrates over the frequency range of 25-35 GHz and 32-38 GHz are developed. An analytical method is proposed to design the coupler geometrical parameters. The theoretical modeling is established based on the coupled version of the transmission line (TL) theory using the extended version of the ABCD matrix for four ports microwave network. It is shown that using the proposed method, all required parameters of the directional coupler are determined using the per-unit-length of the applied lines. The geometrical parameters of primary designed couplers are optimized using the particle swarm optimization (PSO) procedure to improve the performance of couplers. The designed couplers are also simulated using High Frequency Structure Simulator (HFSS) software. Moreover, sensitivity analysis is carried out to investigate the effect of fabrication imperfections of the proposed couplers. The obtained results show that the simulated results agree well with the theoretical ones and a low insertion loss (IL) with high return loss is obtained over a wide frequency range bandwidth.

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