Design of Filtering Nolen Matrix With Uniform and Nonuniform Power Distribution

This article introduces an innovative design method for a$3\times 3$Nolen matrix with inherent filter function. The matrix, composed of a broadband 90° coupler and two 180° filtering couplers as well as the compensation resonators, provides output phase differences of −90°, 150°, and 30° and exhibits fourth-order bandpass filtering characteristics. Based on the$3\times 3$filtering Nolen matrix, a$3\times 5$matrix with nonuniform power distribution is realized by adding two power dividers at the output ports with a division ratio of$K$. The design procedures and synthesis methods for both filtering matrices are described in detail. To validate the approach, the prototypes of the$3\times 3$and$3\times 5$matrices, designed for a center frequency of 2.4 GHz with bandpass characteristics, were fabricated and experimentally tested. Measurement results show good agreement with simulations, demonstrating the feasibility and effectiveness of the proposed design.