Mathematical Models of Microwave Ferrites

Abstract
Computer-aided design (CAD) of ferrite microwave devices requires an accurate, yet simple mathematical model of the permeability of polycrystalline ferrites. Contrary to earlier mathematical models, the model described in the present paper takes account of the variation of dc moment with bias field, and incorporates the "low-field loss" observed in ferrites, when magnetized incompletely. Typical input parameters are : frequency, external magnetic bias field, demagnetizing factor, saturation magnetization, remanence ratio, anisotropy field (or equivalent), and two phenomenological damping constants. The calculations are based on the assumption that the polycrystalline ferrite consists of grains having different orientations. In the simplest version of the theory, the easy axes of all grains are all inclined at the same angle to the bias field direction (but are otherwise randomly oriented), and the grains have uniaxial anisotropy. In more sophisticated versions of the theory, the angle between the easy axes and the field direction is characterized by a suitable distribution function. Two self-contained FORTRAN subroutines based on these mathematical models and suitable for CAD of ferrite microwave devices are described.