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As the conventional matrix converter has the drawback of low voltage ratio (max. 0.866), a novel matrix converter called z-source matrix converter is proposed, According to the topology of the different main circuits, they are called z-source indirect matrix converter (ZSIMC) and z-source direct matrix converter (ZSDMC). The basic configuration of the new topology and their fundamental principle are firstly introduced. The control scheme is clarified respectively. The analytic expression concerning functional relation of voltage transfer ratio to duty cycle is analyzed, Finally the validity and feasibility of the new topology are tested by simulation, the results indicate that the voltage transfer ratio and output frequency can be realized optimally by proposed ZSIMC, the voltage transfer ratio of proposed ZSDMC can be achieved 1. Furthermore the voltage transfer ratio can be controlled by controlling shoot-through duty cycle D, the harmonic distortion of waveform is low, so the inherent drawback of low voltage transfer ratio of traditional matrix converter is effectively settled. This study may provide inspiration for further engineering application.