Broadband quasi-chebyshev bandpass filters with multimode stepped-Impedance Resonators (SIRs)

Planar broadband bandpass filters of order up to 9 are synthesized based on the multimode property of stepped-impedance resonators (SIRs). Based on the transmission line theory, the modal frequencies of the SIRs are calculated based on the impedance and length ratios of its hi- and low-Z segments. In the synthesis, the SIR coupling schemes are determined by the split mode graphs. Using one, two, two, three, and three dual- or triple-mode SIRs, quasi-Chebyshev filters with four, six, six, eight, and nine transmission poles, respectively, are synthesized with a fractional bandwidth (BW) Δ = 50%. Emphasis is placed not only on designing the I/O coupling structures for matching the external Q (Q _ext) and the circuit BW, but also on matching the resonant peaks of the circuit with the nominal Chebyshev poles. Measured results of experimental circuits show good agreement with simulated responses.