Bandpass Impedance Transformers With Extremely High Transforming Ratios Using  $\Pi$ -Tapped Feeds
Bandpass impedance transformers (BPIMTs) with extremely high transforming ratios by adopting the proposed <inline-formula> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula>-tapped feeds are realized in this paper. <inline-formula> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula>-tapped feeds composed of two shunt stubs and one-section line performing the impedance transforming function are introduced. To validate the generality of the proposed approach, two different types of bandpass transformers, i.e., type-A and type-B adopting a short-ended parallel coupled-line and a via-inductive coupling as their interstage couplings, respectively, originating from two coupled-resonator filter topologies are designed. The synthesis procedures and design formulas of the two transformer types are provided, and the auxiliary graphs for different impedance transforming ratios are thoroughly investigated. The circuit-level simulated results of the proposed BPIMTs agree well with the theoretical results calculated from the coupling matrix, thus validating the design approach. Specifically, two type-A prototypes with the transforming ratios of 20 (200 <inline-formula> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula>/10 <inline-formula> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula>) and 95 (475 <inline-formula> <tex-math notation="LaTeX">$\Omega /5~\Omega $ </tex-math></inline-formula>), respectively, and one type-B prototype with a transforming ratio of 104 (520 <inline-formula> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula>/5 <inline-formula> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula>) were demonstrated. The proposed transformer is capable of satisfactorily matching the low and high impedances, and it also possesses the highest impedance transforming ratio ever reported in the literature.