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This paper extends the Z-source concept to matrix converters and explores a family of Z-source matrix converters. Their principles and characteristics are analyzed, and a simplified voltage-fed Z-source matrix converter is used as an example to demonstrate its operation, voltage gain versus modulation index, PWM method, boost control, and implementation of the control. Both simulation and experimental results verify operation of the proposed Z-source matrix converter, analytical results, and control method. The Z-source converters can achieve buck and boost operation with reduced number of switches needed, therefore achieving low cost, high efficiency, and reliability, compared to the traditional matrix converters.