A direct synthesis method of multi‐port filtering power divider with arbitrary phase shift, power division and reference impedances

Abstract In this study, a direct synthesis approach is proposed to extract the coupling matrix of multi‐port filtering power divider (FPD) with arbitrary phase shift, power division as well as reference impedances, for the first time. This method provides an attractive technique to synthesise a multi‐functional device that combines the characteristics of bandpass filter, multi‐port power divider and ideal phase shifters as well as the impedance matching network, which can effectively diminish the overall size and improve the performance of the microwave front‐end network. A newly defined coupling matrix corresponding to arbitrary multi‐port topologies that introduces ideal phase shift by virtue of constant frequency‐independent reactance at the source and load is developed in FPD synthesis process. The coupling matrix is obtained directly by optimising the presented cost‐function in this paper, avoiding complex similar transformation process of coupling matrix. Finally, several numerical examples of multi‐port FPD with equal/unequal power division ratio, arbitrary phase shift and reference impedances are synthesised to well verify the proposed synthesis method, and a practical example is given to verify the validity of arbitrary phase shift and arbitrary reference impedance.