Generalized Concept and MATLAB Code for Modeling and Analyzing Wideband 90° Stub-Loaded Phase Shifters with Simulation and Experimental Verifications

Falih M Alnahwi; Yasir I A Al-Yasir; Chan Hwang See; Abdulkareem S Abdullah; Raed A Abd-Alhameed

doi:10.3390/s23187773

Generalized Concept and MATLAB Code for Modeling and Analyzing Wideband 90° Stub-Loaded Phase Shifters with Simulation and Experimental Verifications

Sensors (Basel). 2023 Sep 9;23(18):7773. doi: 10.3390/s23187773.

Authors

Falih M Alnahwi¹, Yasir I A Al-Yasir², Chan Hwang See³, Abdulkareem S Abdullah¹, Raed A Abd-Alhameed^{2

4}

Affiliations

¹ Department of Electrical Engineering, College of Engineering, University of Basrah, Basrah 61001, Iraq.
² Faculty of Engineering and Informatics, University of Bradford, Bradford BD7 1DP, UK.
³ School of Computing, Engineering and the Built Environment, Edinburgh Napier University, Edinburgh EH10 5DT, UK.
⁴ Department of Information and Communication Engineering, Basrah University College of Science and Technology, Basra 61004, Iraq.

Abstract

In the design of phase shifters, the modeling equations are too complicated and require some approximations to be derived correctly by hand. In response to this problem, this paper presents a generalized concept, algorithm, and MATLAB code that provide the exact modeling equations of the transmission parameters and the scattering parameters of any 90° wideband stub-loaded phase shifter. The proposed code gives the modeling equations in term of variables for any number of stubs and characteristic impedance value by utilizing the symbol-based analysis of the MATLAB code. It also illustrates the results as a function of normalized frequency relative to the center frequency f_o, and can be and can be tailored to any user-defined frequency range. As a matter of comparison, a three-stub wideband 90° stub-loaded phase shifter is simulated using CST Microwave Studio and experimentally fabricated on Rogers RT5880 dielectric substrate with dimensions of 30 × 40 × 0.8 mm³. The comparison reveals the accuracy of the proposed computerized modeling with -10 dB impedance bandwidth equal to 90% (0.55f_o-1.45f_o), (90°∓5°) phase difference bandwidth equal to 100% (0.5f_o-1.5f_o), and negligible insertion loss. The novelty of this work is that the proposed code provides the exact modeling equations of the stub-loaded phase shifter for any number of stubs regardless the complexity of the mathematical derivations.

Keywords: differential phase; phase shifter; reflection coefficient; stub-loaded filter; transmission coefficient.

Grants and funding

This work is partially supported by the innovation programme under grant agreement H2020-MSCA-ITN-2016 SECRET-722424 and the financial support from the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/E022936/1.