High-frequency (HF) transformers have gained great interest in recent years due to the advent of powerful soft magnetic materials with low core loss in semiconductor power switches. Also, the optimal design of the HF transformer is a significant issue for high-performance energy conversion systems. In this paper, a 40W 50/12.5/25 V universal input and two output discontinuous-conduction mode (DCM) flyback transformer is designed by using mathematical calculations and analyzed via 3D ANSYS/Maxwell simulation including electromagnetic and loss analysis. It is shown that the simulation results accounting for hysteresis losses, eddy current losses, copper losses, and magnetic flux density determine the accuracy of the mathematical model calculation. Analyzes are performed at 100 kHz frequency levels. Results obtained will include core magnetic flux density, core/copper losses, leakage/magnetizing inductances, windings parasitic capacitances, input/output voltage, current values, and all design parameters. Finally, the proposed HF transformer's overall efficiency is calculated and presented. Significantly, the HF transformer achieves 97.8% efficiency thanks to the transformer's core and coil selection, B-H and B-P characteristics, one-to-one dimension design, and mesh operation. The dynamic and mathematical results of the designed transformer demonstrate the design and efficiency success