Dual-chirped difference frequency generation (DFG) is an advantageous technique for generating the broadband mid-infrared (IR) idler wave, which is inaccessible by a population-inversion-based laser system. In principle, the generated idler wave may even suffer a spectrum broadening compared with the driving pulsed lasers if the pump and signal waves are oppositely chirped. However, broadband phase-matching is always the determining factor for the resulting efficiency and the bandwidth of the generated idler wave. In this study, specific to an oppositely dual-chirped DFG scheme, we derive the precondition to realize broadband frequency conversion, wherein a negative