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Phase Locked Loops using phase detector based on a multiplier and a moving average low pass filter are computationally simple, and provide adequate attenuation for the multiplier generated harmonics, which are responsible for distortion at the output signal. They are a good choice for synchronizing power electronics converters connected to the grid. Previously published papers based on proportional-integral control and moving average filter present long settling times. This paper uses the exact model of the moving average filter by its discrete high order transfer function, and applies the discrete root locus method to impose the dominant closed loop poles in a region defined by desired performance specification. It leads to a significantly shorter settling time, when experimentally compared with other recent proposals in the literature.