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Bandpass filters with an optimal rejection bandwidth are designed using parallel-coupled stepped impedance resonators (SIRs). The fundamental (fo) and higher order resonant harmonics of an SIR are analyzed against the length ratio of the high-Z and low-Z segments. It is found that an optimal length ratio can be obtained for each high-Z to low-Z impedance ratio to maximize the upper rejection bandwidth. A tapped-line input/output structure is exploited to create two extra transmission zeros in the stopband. The singly loaded Q(Qsi) of a tapped SIR is derived. With the aid of Qsi, the two zeros can be independently tuned over a wide frequency range. When the positions of the two zeros are purposely located at the two leading higher order harmonics, the upper rejection band can be greatly extended. Chebyshev bandpass filters with spurious resonances up to 4.4fo, 6.5fo, and 8.2fo are fabricated and measured to demonstrate the idea.