Reflective Butler matrices

A conventional Butler matrix can be modified to achieve a network which is symmetric about an axis midway between the input and output lines. Such a Butler matrix network can be further modified so that the input and output ports are identical. In this manner the half-matrix appropriately terminated in the plane of symmetry corresponds to a reflection-type system in which the feed positions are in the aperture region. This paper describes the modifications which make the Butler matrix symmetric and the method for terminating the network on the symmetry plane so as to achieve a reflective matrix. A computer program has been written to generate and plot these network configurations.