By derivation, we find that when the group velocity difference between the pump wave and the generated idler wave is small, the pump acceptance bandwidth is broad. In a PPLN crystal, when the pump wavelength is 1050 nm and the generated idler wavelength is about 3.4 μm, the group velocity difference between the pump wave and the idler wave is small, and thus the corresponding pump acceptance bandwidth is wide. In addition, we report an ultra-short-pulse-pumped DFG, by using a 1-mm-long PPLN crystal with a poling period of 29.5 μm, and we obtain mid-infrared sources with bandwidths covering 2.724.15 μm and an average power of 7.5 mW. Meanwhile, as indicated in the simulation, when the central wavelengths of the pump wave and the signal wave are 1050 nm and 1525 nm, respectively, increasing the bandwidth of the pump wave can increase the bandwidth of the generated idler wave.