Compact 4 × 4 Multilayer Butler Matrix With Four-Slot Array

Novel multilayer Butler matrix (BM) miniaturizing layouts applicable to any $N \times N$ are proposed, reducing the conventional size by more than twofold. The layouts eliminate crossover couplers, considerably enhancing compactness and isolation. A $4 \times 4$ multilayer BM is designed based on the layouts, and the components used to build the overall structure are designed and analyzed to fit with any $N \times N$ BM. The BM is based on air microstrip lines (MSLs) packaged by an artificial magnetic conductor (AMC) to suppress wave leakage and radiation loss. It operates from 27 to 31 GHz with a 0.6 ± 1.4-dB insertion loss and a phase imbalance of ±8°. An isolation better than 14 dB with a good matching level is achieved. A four-slot linear antenna array is connected to the BM. The measured and simulated radiation characteristics are compared and found to be in good agreement.