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A tri-band dual-mode chip filter, which is fabricated with a commercial monolithic microwave integrated circuit technology and suitable for millimeter-wave applications, is presented in this paper. This filter is constructed by using stacked ring resonators with individual perturbation and feeding capacitors, thus fractional bandwidths and center frequencies of three passbands can be flexibly controlled. An equivalent model of the tri-band filter that considers coupling effects between the stacked ring resonators is adopted, and then a new set of design equations that can determine element values of dual-mode ring filters realized with different length ratios of upper parts over lower parts of the ring resonators are derived and proposed to design the filters with desired characteristics. Theoretical and experimental results reveal that dual-mode ring filters realized with different length ratios can change the positions of transmission zeros while keeping their widths of passbands equal, provide different characteristics of roll-off rates, and stopband suppressions. By following proposed design guidelines, the layout pattern of the tri-band dual-mode filter can be determined quickly. To verify the proposed design concept, an experimental prototype, locating three passbands at 60, 77, and 100 GHz, respectively, was fabricated on GaAs substrate. The size of the filter is about 0.46 × 0.91 mm2 and the measured insertion losses in the three passbands are less than 2.4, 2.7, and 3.5 dB over the frequency bands of interest, and their associated return losses are greater than 18, 17, and 8 dB, respectively.