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This paper proposes a design of single phase z-source buck boost matrix converter. The proposed converter can buck and boost the input voltage to the desired output level. And also the converter can step up or step down the frequency at the output. This proposed converter employs a safe commutation to establish a continuous current path, which reduces the voltage spikes on the switches without a snubber circuit. Compared to the traditional ac-ac converter which is a two stage converter with a large energy storage dc link capacitor, the proposed converter is a single stage converter which provides a wide range of ac output voltage with buck and boost function and it offers inherent bidirectional power flow. The proposed converter is simulated using MATLAB package and found to provide the source current THD less than 30% and improve the input power factor to more than 0.95.