Compact BMs using cascaded section elements

In this paper, two new compact Butler matrices (BMs) operating at 2.4 GHz for Wi-Fi applications are proposed. The two circuits' layouts are based on a simple transmission line theory which allows replacing each quarter-wavelength line in a conventional Butler matrix by an equivalent three cascaded circuit element composite line. In the first design, three short length-segment lines having certain characteristic impedances are used. Their total physical length is less than the conventional line's physical length. In the second design, a composite line of relatively one high characteristic impedance short length-segment line confined by two series-connected shunt capacitors is replacing each quarter wavelength line in the BM. The resultant two BMs have super compact sizes (>40%) with very good responses.