For synchronization with the grid and controlling the injected active and reactive currents of the LCL-filter based grid-tied inverters, capacitor voltages can be sampled. An LCL filter attenuates the switching harmonics effectively but needs an extra sensor for the LCL filter resonance damping. Popular methods use capacitor currents for the LCL filter resonance damping. Theoretically, the derivative of capacitor voltage, which is proportional to the capacitor current, damps the resonance, and the extra sensor is avoided. However, traditional discretization methods for digital implementation of the derivative operator are not valid when the resonance frequency is high. Indeed, they don't preserve the phase and magnitude of the ’s’ function in the resonance frequency region. This paper introduces an effective method for discretizing the ’s’ function in the desired frequency range. The capacitor voltages of the LCL filter are sampled and the proposed function makes their derivative. The output of the derivative function with a tuned gain is added to the controller’s output for damping the LCL filter resonance. The simulation results show the effectiveness of the proposed method.