The advent of the SiC Bidirectional FET (BiDFET), a monolithic 1.2 kV bidirectional switch, has rendered the single-stage three-phase AC/DC converter topology a promising approach for implementing AC/DC converters. This topology, which integrates a full-bridge converter with a single-phase to three-phase matrix converter via a high-frequency transformer, is particularly suitable for applications requiring galvanic isolation, buck-boost functionality, and bidirectional power flow. The single-stage design eliminates the need for bulky and unreliable electrolytic capacitors, and utilizes a single magnetic component for power transfer. In the matrix converter, bidirectional switches, which were traditionally implemented using combinations of multiple semiconductor devices such as MOSFETs, IGBTs, and diodes, can now be realized using the single-chip solution, BiDFET. This advancement leads to a lower switch count, compact converter implementation, with lower inductance commutation cells, thereby enhancing the overall efficiency and compactness of the system. The paper presents a unified model of the converter, considering all control parameters, including the duty cycles and phase shift of transformer voltages. Detailed expressions for power transfer, transformer currents, and currents at AC and DC ports are provided. Additionally, the paper outlines the conditions necessary for soft-switching of all switches and the commutation schemes required for the practical implementation of the matrix converter modulation scheme. A hardware prototype of a 10 kW, 480 VRMS, LL/ 800 V AC/DC system has been developed, and experimental results are presented to demonstrate its performance.