DC side dynamics are ignored in most of the research on grid-connected converter,which is dealt as a constant voltage source. In this case,the analysis result of small-signal stability is affected to some extent. In this paper,the impedance model of grid-following converter is reconstructed,then followed by stability analysis of the system considering DC side dynamics. Firstly,the applicable conditions are analyzed,that is to say,DC side is equivalent whether to voltage source or controlled current source. It is demonstrated that the DC side dynamics must be considered in case of small-signal stability analysis. Then,the impedance model of the grid-following converter is established based on harmonic state-space (HSS). Secondly,the stability of the system with different DC side structures is analyzed by Bode criterion under different grid strengths. Subsequently,it is revealed that the influence mechanism of grid strength on the stability of grid-following converter. In addition,the influence of different links on impedance characteristics of the system is analyzed,including phase-locked loop,current loop and filter. Finally,the theoretical analysis and electromagnetic transient simulation results show that under the condition of weak grid,the interaction between phase-locked loop and grid is strengthened,which reduces the small-signal stability of the system. Moreover,the critical short-circuit ratio of the system considering the DC side dynamics is larger.