General Synthesis and Design for Unequal Filtering Rat-Race Coupler With Complex Impedances Using Dielectric Waveguide Resonator

In this article, the comprehensive general synthesis theory and design method for unequal filtering rat-race coupler (FRC) terminated complex impedances is presented, and the hardware is implemented using dielectric waveguide resonator (DWR). First, the response calculation and synthesis method of the multiport coupling matrix (CM) with complex impedances are presented. Based on the generalized Chebyshev filtering function polynomials, the $S$ -parameter polynomials of the FRC with arbitrary power division ratio are analyzed. Subsequently, the initial multiport CM of FRC can be synthesized and transformed to some physically realizable topologies. In addition, the transmission zeros (TZs) of the filtering response can be arbitrarily placed. Furthermore, the in-band power division nonflatness in FRC using DWR is revealed and addressed in this work. Some examples are given using DWR not only unit ports but complex impedance ports. Finally, a 12-cavity FRC using DWR terminated complex impedances in a sixth-order filtering response with two TZs operating in the U6G subband is designed, simulated, and manufactured. The good agreement validates the feasibility of the proposed method and design.