Design of multi-stage power divider based on the theory of small reflections

This paper presents a novel multi-way multi-stage power divider design method based on the theory of small reflections. Firstly, the application of the theory of small reflections is extended from transmission line to microwave network. Secondly, an explicit closed-form analytical formula of the input reflection coefficient, which consists of the scattering parameters of power divider elements and the lengths of interconnection lines between each element, is derived. Thirdly, the proposed formula is applied to determine the lengths of interconnection lines. A prototype of a 16-way 4-stage power divider working at 4GHz is designed and fabricated. Both the simulation and measurement results demonstrate the validity of the proposed method.