Tri-Anode GaN Schottky Barrier Diodes (SBDs) have recently shown excellent DC performance with low turn-on voltage and large breakdown thanks to their 3D contact structure around the two-dimensional electron gas (2DEG) channel. However, the 3D nature of the Tri-Anode structure is also often believed to hinder the device switching performance. In this work, we demonstrate that, on the contrary, the Tri-Anode architecture significantly enhances the device switching performance with respect to conventional planar SBDs, as shown by a substantial decrease in the recovery charge and an improvement in frequency response. The Tri-Anode SBDs excellent static and dynamic performance is then applied to a real circuit to demonstrate a monolithically integrated high-frequency Full Bridge Rectifier. These results show the potential of Tri-Anode SBDs for high-efficiency and fast-switching power integrated circuits.