Galvanically isolated ac-dc converters are crucial for integrating distribution generation, energy storage, dc microgrids, and electric vehicles with ac distribution system. The typical industrial approach involves a two-stage setup (ac-dc/dc-dc) with a bulky dc link capacitor, and dual-active bridge converter (dc-dc) for isolation. However, this leads to increased power losses due to multiple power processing stages. To overcome this issue, this paper proposes a three-phase bidirectional isolated ac-dc matrix-converter, as a candidate solution. This topology employs a high-frequency link, eliminating the need for a traditional intermediate dc link found in a standard two-stage solution. As a main contribution, a quasi-resonant modulation strategy is introduced to allow all semiconductors to operate under softswitching for a wide operating range. A 3.5 kW prototype was built to compare proposed one with the twostage ac-dc converter. The experimental results show that the proposed converter achieved 96.5% efficiency at nominal power, outperforming the conventional converter, which reached 95.4% efficiency, mainly due to the extra power processing stage in the two-stage solution.INDEX TERMS Direct matrix type, isolated rectifier, matrix-converter, three-phase power factor correction (PFC) converter.