This paper investigates the stability of LCL-filtered grid-connected inverters with capacitor current feedback (CCF) active damping. The impact of time delays in the digital controller on active damping and its equivalent virtual impedance is analyzed. The inherent relationship between these time delays and stability is illustrated. Specially, a critical value of the CCF active damping coefficient kdamp_c is proposed to define three distinct regions of stability evaluation. If kdamp_c >0, a sufficient but smaller damping coefficient (kdamp < kdamp_c) is recommended as optimum damping solution; if kdamp_c = 0, system will be unstable irrespective of active damping; and if kdamp_c <0, active damping is not necessary to design a stable system. Necessary conditions to ensure stability are identified; guidelines for controller design are then presented to optimize the performance of active damping and dynamic response. Simulation and experimental results confirm the presented analysis.