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The unapodized and apodized step-chirped gratings (SCGs) for broadband frequency converters based on quasi-phase-matched second-harmonic generation with pump depletion in lithium niobate waveguides have been theoretically modeled and simulated as a function of the number of sections, and compared with the linearly chirped gratings (LCGs) for the first time to our knowledge. It is shown that for the same length, using fewer sections with more segments and larger amounts of chirp, the efficiency and bandwidth of an SCG approach over that of an LCG and can be extensively improved with apodization. Moreover, the increasing chirp period and duty cycle for the SCG structure may provide a more convenient method for fabrication and poling. In addition, we present useful relations for the band-widths that help to find the appropriate number of segments in the proposed SCGs of a given length.