Phase locked loops (PLLs) with frequency-adaptive prefilters could suppress input disturbances and thus are widely studied. However, their accurate models are absent in literature. In particular, the impact of frequency adaption is underestimated. This letter proposes an accurate and analytical modeling method with focus on the impact of frequency adaption, by taking the PLL based on dual second-order generalized integrator (DSOGI) as an example. The proposed model can precisely describe the transient behaviors of DSOGI-PLL, especially the couplings among amplitude, phase angle and frequency. Moreover, it reveals that the frequency adaption creates a positive feedback path, which is the essential reason for the instability phenomenon and the key factor limiting the PLL performance. Experimental results have verified the accuracy of the proposed model.