A Lumped-Element Unit Cell for Beam-Forming Networks and Its Application to a Miniaturized Butler Matrix

A lumped-element unit cell for designing compact beam-forming networks (BFNs) is proposed. It is a reciprocal four-port network, which is lossless, isolated, and matched at all ports. The unit cell is designed to behave as planar and compact directional couplers with both arbitrary output amplitude and phase distributions, as well as crossovers with arbitrary output phase distributions. For both cases, design equations are derived. The design procedure is validated numerically and experimentally through several examples. The versatility of the unit cell allows the design of BFNs using only the proposed network topology. As an example, a 4 × 4 Butler matrix is implemented. A strong size reduction is also achieved with respect to classical designs thanks to the lumped-element implementation. The prototype footprint is approximately 25 times smaller than typical transmission-line-based Butler matrices. The structure shows also a very small area compared to state-of-the-art miniaturized 4 × 4 Butler matrix designs. Measurement results confirm the behavior of the Butler matrix as a BFN. The achieved bandwidth is approximately 8%.