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This paper proposes the generalized direct modulation for Conventional Matrix Converters (CMC) using the concept of analytical signals and barycentric coordinates. The paper proposes a novel approach to the Pulse Width Modulation (PWM) duty cycle computing, which allows faster prototyping of direct control algorithms. The explanation of the new idea using analytical considerations demonstrating the principles of direct voltage synthesis has been presented in the article. The study concerns mainly the CMC3 × 3 but solutions for 3 × n, 5 × 5, and 5 × 3 topologies have also been discussed. The transformation of instantaneous input voltages to analytic signals great permits for simple presenting of real input voltage conditions such as waveform type, asymmetry or other deformation like higher-order harmonics. The proposed interpolation methods allow for determining the values of PWM duty cycles using simple formulas based on the determinants of the 2nd-degree matrices. Therefore, the proposed method, which based on the barycentric coordinates, frees an algorithm from trigonometry and angles.

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