A theoretical limitation on the formation of lossless multiple beams in linear arrays

It is well known that through the use of lenses, several independent beams can be formed from a single antenna, with each beam having essentially the gain corresponding to the aperture of the lens. Recently, feed systems have been developed for linear arrays which achieve similar performance through the use of directional couplers. In this paper it is shown that the shape of the beams which can be formed from an equispaced array by such a feed matrix is not arbitrary, unless one is willing to accept losses in addition to normal plumbing losses. It is shown that the array space factors associated with the individual beams must be such that they are mutually orthogonal over a period of the space-factor pattern.