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This paper presents a novel topology for a direct ac-ac power converter, called as the “three-to- k” phase matrix converter. The input to the proposed matrix converter configuration is a three-phase fixed voltage and a fixed frequency supply from the grid. The output is a variable voltage and variable frequency ac supply of any number of phases (k phase). However, the discussion is limited here for a k that is equal to odd number of phases. As an example, a “three-to-five” phase matrix converter is utilized for discussion and analysis. This paper also proposes two pulsewidth modulation (PWM) control techniques for the general topology of the “three-to- k” phase matrix converter. This is based on the so-called direct duty ratio PWM (DPWM). In one presented technique, the output voltage is limited to one half of the input voltage. For the other proposed scheme, the output voltage is enhanced to 78.86% of the input voltage. The proposed control algorithm is validated using simulation and an experimental approach.