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

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, 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-1.45f), (90°∓5°) phase difference bandwidth equal to 100% (0.5f-1.5f), 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.