| Summary: | 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 <i>f<sub>o</sub></i>, 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 mm<sup>3</sup>. The comparison reveals the accuracy of the proposed computerized modeling with −10 dB impedance bandwidth equal to 90% (0.55<i>f<sub>o</sub></i>–1.45<i>f<sub>o</sub></i>), (90°∓5°) phase difference bandwidth equal to 100% (0.5<i>f<sub>o</sub></i>–1.5<i>f<sub>o</sub></i>), 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.
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