Steinmetz Equation for Gapped Magnetic Cores

This letter presents a derivation of the modified Steinmetz empirical equation for power loss density and power loss in magnetic cores with air gaps. The modified Steinmetz equation relates the core power loss density with the air gap length, magnitude and frequency of the sinusoidal excitation current, and the permeability of the core material. The reluctance model of a representative core structure is used. The expression for the magnetic field density in gapped cores is derived. In addition, the minimum air gap length required to avoid core saturation is determined. The modified Steinmetz equation for power loss is analyzed using the specifications of a practical magnetic core used in high-frequency applications. The effect of the air gap length and the excitation frequency on the core power loss density is discussed.