Design Equations of Dual-Band Dual-State π-Type Couplers and Their Computer-Aided Solutions

This work establishes design equations of generalized branch-line coupler (BLC) and rat-race coupler (RRC) with distributed π-topology using the y-matrix method. Here the term generalized indicates unequal power division and arbitrary phase difference or transmission phase at the output ports. The design equations are extended for dual-band operation with different output phase differences or transmission phase and power-division ratios at two design frequencies. To obtain additional dual-band 180° phase shift for rat-race coupler dual-band C-section, π-network, T-network, and extended π are used. The dual-band design equations are non-linear trigonometric equations with no analytical solutions. A semi-analytical method has been proposed to solve these dual-band design equations. It has been shown here that the solutions of dual-band design equations only sometimes exist. As the dual-band design equations involve a multi-variable input-output relationship, it is not easy to show the variation of design variables with the input parameters. A Windows application is developed to design and analyze single-band and dual-band couplers.