Multiple beams from linear arrays

The problem of devising a passive RF transmission line feed system to provide independent multiple outputs from a linear array is considered. It is shown that a lossless, matched feed network is possible only for uniform aperture distribution. The general feed system for connecting
2^{n}
inputs to
2^{n}
elements is shown to consist of conventional hybrid junctions with associated phase shifters. In order to increase the possible number of elements in the array, the problem of finding applicable junctions more complex than the hybrid is considered. Junctions with three inputs and three outputs and with four inputs and four outputs are derived for use in multiple feed networks, expanding the number of elements in the array to
2^{l}3^{m}4^{n}
.