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This paper proposes a unified PWM method for matrix converters so as to establish a common platform which can generate various types of PWM methods in real time by adjusting the free parameters in the modulation algorithm. As a foundation for unification, the general form of the modulation functions for matrix converters is derived using geometric transformation approach. All eligible direct modulation matrices are shown to be of indirect form and are expressed in terms of instantaneous phase quantities. This paper also presents a new viewpoint to consider a matrix converter as a generalized three-level inverter and to apply the double-carrier-based dipolar modulation technique of the three-level inverter to the matrix converter. Several concepts of the two-level PWM inverters are then generalized to the matrix converters for better visualization and understanding of the modulation process.