A Novel Analytical Framework of Apparent Power in Resonant Magnetic Coupling Using Square Coil Configuration

This paper presents a novel analytical framework for evaluating the volt ampere (VA) rating of near field magnetically resonant coupled coils. To overcome the limitations of time intensive electromagnetic simulations, the proposed method derives closed form expressions for essential electromagnetic and circuit level parameters, including magnetic flux density, magnetic field intensity, magnetic flux linkage, self inductance, mutual inductance, open circuit voltage, and short circuit current. The framework is applied to three representative coil geometries: Helmholtz, distributed turn, and helical turn configurations. These geometries are widely adopted in practical magnetic coupling applications due to their structural simplicity, implementation flexibility, and compatibility with diverse system requirements. Square shaped coils are used as a reference geometry to generalize and streamline the mathematical formulation. The analytical predictions are validated through full wave CST simulations and experimental measurements, showing excellent agreement across all configurations. This framework provides a fast, reliable, and scalable approach for evaluating the power handling capabilities of magnetic coupling structures, with broad applicability in wireless energy transfer, magnetic resonance imaging, power electronic systems, and electromagnetic actuator design.