In terms of the transmission-line theory, a general synthesis of a new class of optimum Chebyshev-type ultra-wideband bandpass (UWB) filter prototype composed of multistage stepped-impedance resonators (SIRs) and two short-circuited shunt stubs positioned at input- and output- ports is presented. By the comparison of the real and theoretical transfer functions, the design/characteristic equations are obtained for the design of the proposed filter prototype rather than the traditional design tables. The explicit expressions of one-stage and two-stage filters are then derived and reported. Accordingly, bandpass filters with an arbitrary FBW (Fractional Bandwidth) and passband ripple can be easily designed by solving the design equations. As an example, a 10-degree Chebyshev distributed filter (two-stage filter) with an FBW of 110% is synthesized to meet FCC's outdoor mask. The synthesized circuit model are confirmed by a commercial circuit simulator and then optimized by an EM simulator, fabricated in microstrip line and characterized by the network analyzer. The good agreements between the measured and predicted frequency responses validate the effectiveness of newly proposed filter prototype and the corresponding synthesis technique. In addition, the designed filter exhibits good characteristics of comparatively low insertion loss, quite sharp skirt, very flat group delay and good stopband (especially in lower one) as well. It should be also highlighted that, compared with the conventional filters composed merely of parallel-coupled SIRs or shunt short-circuit-stubs, the new prototype can reduce the overall length of the filter by more than 3/4λ_g. Moreover, in terms of the presented design technique, the proposed filter prototype can be also used to easily realize the UWB filters with an FBW even greater than 110%.