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1. INTRODUCTION Matrix converter is an ac/ac converter that can directly convert an ac power supply voltage into an ac voltage of variable amplitude and frequency without a large energy storage element. The research in focused on step-up/step down frequency operation with a safe-commutation strategy. Applications of single-phase matrix converters have been described for induction motor drives, radio-frequency induction heating, audio power amplification, and compensation voltage sags and swells. It has been reported that the use of safe-commutation switches with pulse width modulation (PWM) control can significantly improve the performance of ac/ac converters. In the conventional single-phase matrix converter topology, the ac output voltage cannot exceed the ac input voltage. Furthermore, it is not possible to turn both bidirectional switches of a single phase leg on at the same time; otherwise, the current spikes generated by this action will destroy the switches. These limitations can be overcome by using Z-source topology. Research on Z-source converters has focused mainly on dc/ac inverters and ac/ac converters. Recently, the work on Z-source dc/ac inverters has focused on modeling and control, the PWM strategy, applications, and other Z-network topologies. The Z-source ac/ac converters focus on single-phase topologies and three-phase topologies. In applications where only voltage regulation is needed, the family of single-phase Z-source ac/ac converters proposed in has a number of merits, such as providing a larger range of output voltages with the buck–boost mode, reducing inrush, and harmonic current. However, no one has designed a converter based on a Z-source structure and a matrix converter topology that can provide ac/ac power conversion with both a variable output voltage and a step-changed frequency. In this paper, we apply the Z-source concept to a single-phase matrix converter to create a new type of converter called a single-phase Z-source buck–boost matrix converter. In contrast to the existing single-phase PWM ac/ac converters, this proposed single-phase Z-source buck–boost matrix converter can provide a wide range of output ac voltages in buck–boost mode with step-up/step-down frequencies. We show from operating principles, analyses, simulation, and experimental results that the proposed single-phase Z-source buck–boost matrix converter can buck and boost voltages in step-up/step-down frequency operation. We use a safe-commutation technique that is very simple to implement as a free-wheeling path to provide the required free-wheeling operation similar to what is available in other converter topologies. The safe-commutation scheme establishes a continuous current path in dead time to eliminate voltage spikes on switches without a snubber circuit. To verify the operation of the proposed converter, we constructed a laboratory prototype with the passive R load based on PIC16F877A; we also performed a participative simulation integral manufacturing (PSIM) simulation. Both the simulation and experimental results show that the output voltage can be obtained at three different frequencies 120, 60 & 30 Hz and in the buck–boost amplitude mode. Thus, the proposed single-phase Z-source buck–boost matrix converter can be used for voltage applications that require step-changed frequency or amplitude.