Model for Nonlinear Flux Reversals of Square-Loop Polycrystalline Magnetic Cores

The theory of the reversal wave forms of polycrystalline magnetic cores proposed by Goodenough is based on the growth of ellipsoidal domains of reverse magnetization which originate from nucleating centers at grain boundaries. The present model extends this theory with the assumption that the nucleating centers are randomly distributed throughout the core volume. Radial field variations are neglected. The rate of change of reversed magnetization area of the irreversibly moving and colliding walls is calculated as a function of their position, starting from a Poisson distribution of nucleating centers, and then converted to a function of flux. The equation derived for rate of flux change is $$\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{\text{4.82}}{S_w}{\mathrm{(H-H}}_0\text{)(1−x)}{\left(-\ln \frac{\text{1−x}}{2}\right)}^{\frac{2}{3}}$$ , where S_w is the switching coefficient, H₀ is the threshold field, H is the applied field, and x is the ratio of flux density to retentivity. This nonlinear differential equation is solved for the simple case of constant current drive. For more complicated circuit conditions, solutions of the core equations require numerical methods. Programs have been written for the IBM Type 704 DPM to calculate the behavior of circuits containing many such cores interacting and switching together. Results obtained check reasonably well with experimental evidence.