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Multi-phase (more than three-phase) converters are required mainly for feeding variable speed multi-phase drive systems. This paper presents one such solution by using direct ac-ac converter that can be used to supply a seven-phase drive system. Simple Pulse width modulation (PWM) technique is developed for the proposed matrix converter configuration. The developed modulation technique is based on the comparison of high frequency carrier signal with the duty ratios. Although carrier-based scheme is widely employed for control of voltage source inverter, it is very recently being used for controlling a three-phase to three-phase matrix converter. The similar concept is extended in this paper for controlling a three-phase to seven-phase matrix converter. Two techniques are proposed, one outputs 0.75 of the input magnitude and the output reaches 0.7694 of the input with the other method. This is the maximum value of the output voltage in the linear range that can be achieved in this configuration of the matrix converter. The viability of the proposed control techniques is proved using analytical, simulation and experimental approach.