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The matrix converters are a good alternative to back-to-back converter in variable speed AC generation to supply energy to a stand-alone load or grid. In case of the unbalanced load, the four-leg matrix converter is required because this topology can effectively provide a path of neutral current. In this paper, a carrier-based PWM modulation is proposed to control the four-leg very sparse matrix converter. The proposed method has less computation complexity for digital signal processor. The algorithm uses only one carrier signal to generate PWMs for both rectifier stage and inverter stage control. The simulation and experimental results are provided to validate the feasibility of the proposed method.