Compact Tri-Band Bandpass Filter Based on $\lambda/4$ Resonators With U-Folded Coupled-Line

This letter presents a novel compact microstrip tri-band bandpass filter (BPF) based on <formula formulatype="inline"><tex Notation="TeX">$\lambda/4$</tex> </formula> resonators. The first and third passbands are realized by coupling the two dual-band <formula formulatype="inline"><tex Notation="TeX">$\lambda/4$</tex> </formula> stepped impedance resonators (SIRs) with synthesized frequency response. Meanwhile, the second passband in the middle is achieved by introducing the two coupled <formula formulatype="inline"><tex Notation="TeX">$\lambda/4$</tex> </formula> uniform impedance resonators (UIRs). A non-uniform coupled-line with the U-folded shape on one line is then proposed to independently achieve the dissimilar external couplings as desired in the tri-passbands. In parallel, the quadruplet topology for each band is formulated by introducing an additional weak I/O cross coupling, thereby bringing one pair of transmission zeros at each side of all the triple passbands, In final, a tri-band BPF with the central frequencies of 1.8, 3.5, and 5.8 GHz, and respective fractional bandwidths of 7.0%, 5.0%, and 3.5% is designed and fabricated. The measured results show good consistence with the simulated ones.