Integrated research of the phase-shifting properties of a step structure of class II on connected transmission lines with mismatched loads

Background and Objectives: Fixed phase shifters on the transmission line are passive devices that provide a constant phase shift between the signals to the outputs of the reference and phase-shifting channels. They are the basic elements of electronic equipment for various functional purposes. One of the main tasks of frequency technology is to expand the working range of fixed phase shifters. The aim of this work is the synthesis, mathematical modeling and experimental study of broadband and ultra-wideband fixed phase shifters with a phase-shifting channel based on coupled class II stepped transmission lines loaded with a short-circuited stub. Materials and Methods: Parametric synthesis of fixed phase shifters was carried out in the approximation of TEM-waves. This made it possible to significantly reduce the required computing resources. Optimization was carried out using the simplex method (Nelder – Mead method). Schematic and electrodynamic modeling of the structure was carried out using the AWR Design Environment software package. The measurement of the frequency characteristics of the experimental sample of the phase shifter was carried out using a Rohde & Schwarz ZVA-40 vector network analyzer. Results: For the nominal values of the phase shift $\varphi_0 = 45^\circ$, $67.5^\circ$, $90^\circ$ and the frequency ranges $[f_1, f_2]$ with overlap coefficients $\chi = f_1/f_2 = 2, 2.5, 3$ (for $m = 3$) and $\chi = 3; 3.5; 4$ (for $m = 5$), the regularities of changes in the electrical lengths and wave impedances of even and odd types of excitation of connected transmission lines, electrical lengths and characteristic impedances of single transmission lines and a stub are established. On the basis of the solutions obtained in the TEM-wave approximation, a fixed phase shifter on a microstrip transmission line was developed for the case of $m = 3$, $\varphi_0 = 90^\circ$, $\chi= 3$. Its circuitry and electrodynamic modeling was carried out. A prototype phase shifter has been manufactured and tested. The experimentally obtained value of the phase shift is $91^\circ \pm 1.5^\circ$, the voltage standing wave ratio does not exceed $1.4$ in the frequency range $0.6$–$1.5$ GHz. The analysis of the reasons for the deviation of the calculated characteristics from the experimental ones is given. Conclusion: The results obtained open up new possibilities for using loops in the problems of synthesis of functional microwave devices. They can be effectively used as an initial approximation in solving the problems of synthesis of fixed phase shifters of the proposed structure on strip and microstrip transmission lines.