The design and implementation of a novel superconducting air-core power transformer for power conversion applications is described. The transformer is constructed using high temperature superconducting tape. The high temperature superconducting tape is made using Ag-clad (Bi,Pb)2Sr2Ca2Cu3O10+x using the oxide power-in-tube technique. Self-resonance techniques are used so that a lower switching frequency operation can be used. The loss calculation to demonstrate the improved efficiency that can be obtained with the proposed transformer is also presented. Experimental results are given to demonstrate the effectiveness of the proposed system for power conversion applications.