This paper presents the Single Phase Matrix Converter topology which offers many advantages with unrestricted switch control or with minimal reactive device use, as an all silicon solution. It elucidates the implementation of Single Phase Matrix Converter as an inverter and as a Controlled Rectifier. Also, with proper switching control algorithm, a type of converter that can buck and boost with step-changed frequency called a Single-Phase Z-Source Buck-Boost Matrix Converter is proposed. It employs a safe-commutation strategy which results in the elimination of voltage spikes on switches without the need of a snubber circuit. The operating principles of this converter for all these configurations are described and the circuit behaviour is confirmed by MATLAB / Simulink simulation results.