Analysis of Components of Butler Matrix With Arbitrary Gains and Phase Shifts

Abstract

In this report, the components of 4 4 Butler matrix are analyzed. The standard Butler matrix consist of branch line coupler, crossover and delay lines. In order to obtain arbitrary phase shift and gain in the Butler matrix , the branch line coupler is modi ed in two ways. Firstly, the branch impedances and lengths are varied to achieve the desired gains and phase shifts. The mathematical analysis of the modi ed branch line coupler is performed and the simulations are carried out for di erent combinations of branch lengths and impedances. Further, the results are veri ed by CST simulations. Secondly, the feed line lengths and impedances of the branch line coupler are modi ed in CST to vary the gains and phase shifts but the variations are not much signi cant in this case. Finally, di erent crossovers are analyzed in CST and their simulations are compared. The desired and more directional radiation pattern is obtained when the array of antenna elements is integrated with the Butler matrix . The radiation patterns are analyzed for 2 2, 4 4 and 8 8 Butler matrices and the e ect of change in the parameters of antenna array like frequency of operation and distance between the antenna elements are also studied. vi