Research On Non-2~n Butler Matrix Based On FFT

Butler matrix is a well-known beam-forming network(BFN)that can be used to achieve multi-orthogonal beams.As an important beam-forming network for multibeam antenna,Butler matrix has the advantages of being simple,balanced and inexpensive.It has been widely used in wireless communication and modern radar systems.However,the port number of the classical Butler matrix is limited to 2~n,which caused the limited applications.In this thesis,according to the non-2~n FFT signal flow graph,the non-2~n Butler matrix network structure is studied and derived.The main contributions are as follows.(1)An optimized design of Butler matrix with non-2~n beams based on FFT is proposed.Compared with other methods,the number of components used in the proposed non-2~n Butler matrix is minimum.The design guideline includes:according to the signal flow graph of FFT,to determine the Butler matrix network structure;to write the transmission matrix of the Butler matrix;to derive the target matrix based on antenna array pattern theory;by making the transmission matrix of the Butler matrix equal to the target matrix,to determine the parameters of each device in the network structure.Finally,we should design all the components and connect them according to the network structure,and the parameters should be adjusted carefully to achieve a good performance.(2)A 5×5 Butler matrix with center frequency of 5GHz is designed based on the proposed design guideline.The existing 5-point-FFT flow graph is simplified to a structure which only consists of the butterfly structures.The designed 5×5 Butler matrix consists of orthogonal branch couplers,microstrip crossovers and microstrip lines.It is simulated and optimized by using full wave analysis software HFSS.The output signals of the output ports have equal amplitude,and the phase differences are-144°,-72°,0°,+72°,+144°.This matrix is used to feed a 1×5 microwave antenna array and the antenna array patterns are measured.The five different beams point at-44.5°,-23°,0°,22°,45.5°,respectively.(3)A 6×6 Butler matrix with center frequency of 5.1GHz is designed based on the proposed design guideline.Because the number N=6 can be decomposed into N=2×3,based on mixed-radix FFT the flow graph of a 6-point FFT can be made up of three 2-point FFT flow graphs and two 3-point FFT flow graphs.The 6-point FFT signal flow graph is used to obtain the structure of the 6×6 Butler matrix.The designed 6×6 Butler matrix cosists of orthogonal branch couplers,microstrip crossovers and microstrip lines.It is simulated and optimized by using the full wave analysis software HFSS.The signals of the 6×6 Butler matrix output ports have equal amplitude,and the phase differences are-150°,-90°,-30°,+30°,+90°,+150°.This Butler matrix is used to feed a 1×6 microwave antenna array,and the measured six different beams point at-47°,-26°,-9°,10°,28°and 47°,respectively.