3×3 Microstrip beam forming network for multibeam triangular array

The design of a beam forming network (BFN) for a triangular cell of three elements is considered. A useful relation between phase excitation of the elements of the cell, beam direction, wavelength and distance is given. The BFN is studied based on a Butler matrix, using balanced and unbalanced hybrid couplers to obtain a three inputs and three outputs network which is used to develop a multibeam structure. A system of three equations is also presented to calculate the lengths of the transmission lines which connect the couplers of the network. These equations allow a flexible design of the network depending on the needed specifications. Finally, a microstrip BFN circuit that demonstrates the utility of the design has been developed.