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Multiphase (more than three phases) power electronic converters are required mainly for feeding variable-speed multiphase drive systems. This paper presents one such solution by using a direct ac-ac converter that can be used to supply a nine-phase drive system. The input is a fixed-voltage and fixed-frequency three-phase input, and the output is a variable-voltage and variable-frequency nine-phase output. A simple pulsewidth-modulation technique is developed for the proposed ac-ac converter named as a nonsquare three-to-nine-phase matrix-converter configuration. The developed modulation technique is based on the comparison of a high-frequency carrier signal with the duty ratios. Although the carrier-based scheme is widely employed for the control of back-to-back converters, it has recently been used for controlling a three-to-three-phase matrix converter. This concept is extended in this paper for controlling a three-to-nine-phase matrix converter. With the two techniques that are proposed, one outputs 0.75 of the input magnitude and the other outputs reach 0.762 of the input. This is the maximum value of the output voltage in the linear modulation range that can be achieved in this configuration of the matrix converter. The viability of the proposed control techniques is proved analytically through simulation and an experimental approach.