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

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


Falih M. Alnahwi

Yasir I. A. Al-Yasir

Abdulkareem S. Abdullah

Abdul Raed A. Abd-Alhameed


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 fo, 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% (0.55fo–1.45fo), (90°∓5°) phase difference bandwidth equal to 100% (0.5fo–1.5fo), 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.

Journal Article Type Article
Acceptance Date Sep 8, 2023
Online Publication Date Sep 9, 2023
Publication Date 2023
Deposit Date Sep 8, 2023
Publicly Available Date Sep 9, 2023
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 23
Issue 18
Article Number 7773
Keywords phase shifter; stub-loaded filter; reflection coefficient; transmission coefficient; differential phase


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