Alternative Formulations of the Fields’ Constitutive Relations for the Efficiency of the Time Domain Analysis of Magnetized Ferrites

In this paper, the constitutive relation of longitudinally magnetized ferrites (LMF) is simplified and transformed to an equivalent relation involving tensors with first-order dispersive components more suitable for use in the time domain analysis. Further treatment leads to a diagonal permeability tensor that yields approximating formulas to relate the magnetic field to the magnetic flux density, which allows eliminating this later and reducing the number of field variables involved. Later, a similar result is achieved using a variable transformation. This reveals that magnetized ferrites actually have a permeability tensor simpler than the Polder tensor, in addition to a permittivity tensor with first-order dispersive components, which contradicts the known theory about ferrites. Finally, it is shown that the results obtained for the LMF case could be extended to the transversely magnetized ferrite case and to the general case of arbitrary state of magnetization. Some examples are presented with numerical results to validate the proposed formulations.