# Design of 4 × 4 and 8 × 8 filtering butler matrices utilizing combined 90° and 180° couplers

Qiang Shao, Fu Chang Chen, Yi Wang, Qing Xin Chu

Research output: Contribution to journalArticlepeer-review

## Abstract

In this article, a novel design approach for designing $4\times 4$ and $8\times 8$ filtering Butler matrices is proposed. The matrices, composed of combined 90° couplers and 180° filtering couplers as well as phase shifters, provide incremental phase shifts and a bandpass filter performance. The detailed design process and synthesis method for the Butler matrices are presented. A three-layer symmetrical stripline structure is used to realize the Butler matrix, allowing a fully planar structure without interlayer connections. For experimental verification, two prototype $4\times 4$ and $8\times 8$ filtering Butler matrices, operating at the center frequency of 2.4 GHz with a bandpass response, are devised, manufactured, and tested. The test results match well with the simulation ones. Based on the measurements, array factors have been calculated, which further indicate the acceptance of the measured results.

Original language English 3842-3852 11 IEEE Transactions on Microwave Theory and Techniques 69 8 14 Jun 2021 https://doi.org/10.1109/TMTT.2021.3085879 Published - Aug 2021

### Bibliographical note

Funding Information:
Manuscript received January 26, 2021; revised April 9, 2021; accepted May 11, 2021. Date of publication June 14, 2021; date of current version August 5, 2021. This work was supported in part by the National Natural Science Foundation of China under Grant 62022035, in part by the Guangdong Provincial Key Research and Development Programme under Grant 2020B010179002, and in part by the Guangdong Basic and Applied Basic Research Foundation under Grant 2019B151502032. (Corresponding author: Fu-Chang Chen.) Qiang Shao was with the School of Electronics, Electrical and Systems Engineering, University of Birmingham, Birmingham B15 2TT, U.K. He is now with the School of Electronic and Information Engineering, South China University of Technology, Guangzhou 510640, China.

## Keywords

• 180° couplers
• 90° couplers
• Bandpass filter
• Butler matrix
• stripline