Relevance. Active and passive elements of transformer power equipment have sufficiently reduced the potential for modernization and improvement that requires new innovative solutions. This largely relates to mobile and autonomous power supply systems, in particular for geoengineering tasks when changing the location of geo-surveying works. Aim. New design of transformer power equipment based on cryogenic technologies with improvement of their electrical, technical and economic characteristics involves the use of liquid nitrogen with a temperature of 77 K as a cryogenic dielectric medium. Methods. Mathematical modeling of the skin-effect by a finite-element method, determination of the amorphous alloy magnetic core characteristic by an empirical method, and physical simulation of an experimental model for a high temperature superconducting transformer prototype. Results and conclusions. The paper introduces the analysis and synthesis of characteristics of amorphous iron magnetic core and superconducting windings in a high temperature superconducting transformer. The authors have derived/obtained dependencies and charts illustrating the effect of increased current frequency on thermal losses associated with hysteresis and eddy currents, which determine the losses in the magnetic core. The papwer demonstrates the dependence of mass and dimensions reduction and winding material consumption on frequency and current density in high temperature superconducting tapes, which can reach 500 A/mm². In its turn, this affects the size of transformer windings and, therefore, the size of the magnetic core. The most significant result with the use of superconductivity in high temperature superconducting transformers is the fact that this transformer is an ideal diamagnetic, and the windings have high electrical conductivity. Therefore, the problem of current concentration near the conductor surface skin-effect and resistance increase is eliminated in transformers and electric machines. The absence of skin-effect in high temperature superconducting conductors due to zero resistance is proved with the theoretical analysis using Bessel functions. The importance of the results involves the increase of transformer efficiency at higher frequencies due to the synthesis of properties of transformer active elements, such as amorphous iron magnetic core, high temperature superconducting windings and liquid nitrogen as a dielectric medium. On this basis, a 25 kVA high temperature superconducting transformer industrial prototype was designed and assembled.