Influence of the directional coupler’s parameters on the characteristics of Butler matrix 4×4
Keywords:Butler matrix, directional coupler, phased array
AbstractIntroduction. A brief description of the Butler matrix operating principle and structure is given. The purpose of the study is defined and justified.
Mathematical model of Butler matrix. The overall scattering matrix of 4×4 Butler matrix without crossovers is obtained. A well-known method of multipoles cascade connection is used to derive the scattering matrix. 3 dB 90° symmetric and lossless directional couplers are used as building blocks for Butler matrix. The phase shift of phase shifters assumed as frequency-independent.
Modeling of the directional coupler’s real characteristics. Four characteristics of directional coupler are considered as affecting the overall performance of Butler matrix: amplitude and phase imbalance at the output ports, reflection and isolation of input ports.
Analysis of the results. The plots of amplitude distribution at the output ports and phase difference between adjacent output ports versus the characteristics of directional coupler are shown. The analysis of results is given. Maximum permissible parameters of directional coupler are determined to obtain a qualitative Butler matrix.
Conclusions. General conclusions of the paper are given. Possible directions of further research are identified
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