Phase sensitivity study of 4×4 Butler Matrix architectures for enhanced 5G sub-6 GHz network performance

In a 5G antenna system, the Butler Matrix (BM) plays a crucial role in antenna array beamforming, enabling efficient and accurate signal distribution to multiple antenna elements. However, the effectiveness of the conventional BM is limited by its frequency-dependent design, which restricts operation to a narrow bandwidth. While several techniques can extend the bandwidth, they often result in increased size, particularly at lower 5G frequency bands such as sub-6 GHz (3.5 GHz). This paper analyzes the frequency-dependent behaviour of a 4×4 BM, from the initial stage to the complete configuration. The study employs Stage 1 and Stage 2 structures with varying geometries to characterize phase–frequency behaviour and sensitivity. This analysis applies the phase-to-frequency gradient to establish a mathematical correlation between BM parameters, specifically electrical length and phase components. This correlation provides a foundation for the design of more complex BMs with higher numbers of elements and applicability to higher frequency bands.