Modeling of Miniaturized 4×4 and 8×8 Butler Matrix Based on Complementary Rose Curves Resonators

This work focused on the design of miniaturized 4×4 and 8×8 Butler matrices (BMs) using a metamaterial approach. The proposed structure is based on complementary Rose curve resonators (CRCRs). The frequency of the design was 2 to 4 GHz. Because of the negative permittivity structure of the metamaterial and the coupling of this resonator with the stripline, the RF component can be reduced in size. Using this reduction strategy to replace crossover places, the suggested Butler matrix produces results that are favorable with respect to those found in the literature.