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A method to design microstrip bandpass filters with ultra-wideband (UWB) performance, wide stopband, and practical dimensions is presented. According to the proposed method, three subsections of different lengths and coupling factors are connected to form a stepped-impedance parallel-coupled microstrip structure. A theoretical model is derived and used to find the optimum length and coupling factor for each of those subsections for an UWB passband and suppressed second and third harmonic responses in the stopband. The required performance is realized by generating and proper positioning of three transmission zeros in the upper stopband and three transmission poles in the passband. The derived model shows that the total length of the three-subsection coupled structure is one-third of the effective wavelength at the center of the passband. The theoretical model is used to find the required design values for the whole structure. The presented method is validated by building a bandpass filter that has a passband from 3.1 to 10.6 GHz with less than 1-dB insertion loss and a wide upper stopband that extends up to 28 GHz.