Sensitivity of effective relative permeability for gapped magnetic cores with fringing effect

Magnetic component tolerances are caused by variations in air‐gap and core relative permeability. This study presents the derivation for sensitivity of effective relative permeability to variations in the relative core permeability and relative gap length for magnetic cores with and without fringing effect. The expressions for the fringing factor and effective relative permeability for the magnetic cores have been derived. The effect of air‐gap on the core properties, which includes core power loss density, magnetic flux density, and magnetic field intensity is addressed for cores used in low‐frequency and high‐frequency applications. An example core is selected to support the theoretical predictions. The expressions to determine the inductor tolerances are presented.