Instability issues of the grid-connected doubly fed induction generator (DFIG) based wind turbines (WTs) during low-voltage ride-through (LVRT) have got little attention yet. In this paper, the small-signal behavior of DFIG WTs attached to weak ac grid with high impedances during the period of LVRT is investigated, with special attention paid to the rotor-side converter. First, based on the studied LVRT strategy, the influence of the high-impedance grid is summarized as the interaction between phase-looked loop (PLL) and rotor current controller (RCC). As modal analysis result indicates that the underdamped poles are dominated by PLL, complex torque coefficient method, which is conventionally applied in power system to study the interaction between mechanical and electrical subsystems of synchronous generator, is generalized to analyze how the PLL-RCC interaction influence the phase motion of PLL. Then, the concerned small-signal stability of the PLL-synchronized DFIG system can be discerned by the developed complex phase coefficients. Impacts of PLL's and RCC's parameters are highlighted, as well as the system's operating conditions during LVRT. Finally, the analytical result is validated by experiments.