A Microstrip 4X4 Butler Matrix for Beamforming and Steering: Design Analysis for Sub-6 GHz Applications

This work details the development of a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{4} \times \mathbf{4}$</tex> Butler matrix by designing and simulating its elements tailored for wireless communication applications. The proposed design incorporates a 3dB hybrid coupler, crossover, and phase shifter, optimized to operate at a frequency of 3.5 GHz. The design is implemented on FR-4 substrate having relative permittivity of 4.3 and thickness of 0.8 mm. The Butler matrix exhibits an amplitude imbalance of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1. 5 5 5 ~ d B}$</tex> and phase deviation of 0.785 degrees across its operational bandwidth of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3-4 \text{GHz}$</tex>. The design and simulations were performed in CST Suite.