Positions and magnitudes of fixed phase shifters in Butler matrices incorporating 90 degrees hybrids

The author deals with the positions and magnitudes of fixed phase shifters used in Butler matrices with 90 degrees hybrids. These matrices are symmetrical networks which produce phase shifts that are odd multiples of pi across the output ports. Simplified design procedures are detailed for positioning the fixed phase shifters, and their magnitudes are given for a 32*32 matrix. A 16*16 matrix is also shown and procedures for a matrix of any order are indicated.