Capacitor current feedback active damping is extensively used in grid-connected converters with an LCL filter. However, systems tends to become unstable when the digital control delay is taken into account, especially in low switching frequencies. This paper discusses this issue by deriving a discrete model with a digital control delay and by presenting the stable region of an active damping loop from high to low switching frequencies. In order to overcome the disadvantage of capacitor current feedback active damping, this paper proposes a modified approach using grid current and converter current for feedback. This can expand the stable region and provide sufficient active damping whether in high or low switching frequencies. By applying the modified approach, the active damping loop can be simplified from fourth-order into second-order, and the design of the grid current loop can be simplified. The modified approach can work well when the grid impedance varies. Both the active damping performance and the dynamic performance of the current loop are verified by simulations and experimental results.