Theory of low loss minor loops in soft magnetic composites

Abstract

A theory of low loss, unbiased minor loops in an isothermal macroscopic composite of soft magnetic particles is developed. The theory predicts an effective macroscopic shape factor for the composite, from the average of the inverse shape factors of the particles. The low loss and composite nature of the material implies the hysteresis loops are self-similar and conjugate. Self-similarity assumes that B scales with Bm, the maximum value of B on a minor loop; while H scales as Hm, the maximum value of H on the minor loop. Conjugacy assumes that unbiased minor loops obey Bm±(−H)=−Bm∓(H), where Bm± are minor loops for the composite. The resulting theory depends on two non-dimensional numbers, α and β, with α being a small number (0<α<1) determining magnetic energy loss for a minor loop, while β is approximately unity, and determines the skewness of the minor loops. This theory is tested against different volume fractions of magnetic ferrite powder composite, which support the concept of self-similarity in the low loss regime, holding when H<1000 A/m. Estimates for α are available, if the composite permeability μΔ is known. Estimates for μΔ depend on the volume fraction C of the magnetic material, together with the macroscopic shape factor N.