Improved approximation for effective permeability in microwave ferrites

The nonlinear eigenvalue problem of microwave ferrite phase shift and control components is in general a function of three frequency-dependent variables. Below ferrimagnetic resonance a reasonably accurate approximation has been used to reduce the number of frequency-dependent variables to two, thereby simplifying the eigenvalue problem. Above resonance, accurate solutions are only achievable via a computationally expensive iterative solution of the nonlinear eigenvalue problem. To avoid this, a new approximation is proposed, and supporting modal frequency calculations presented for two axisymmetric configurations suggest that the effective permeability can be computed to within 6% accuracy.