Magnetic susceptibility of MnZn and NiZn soft ferrites using Laplace transform and the Routh–Hurwitz criterion

This paper is devoted to study the Routh–Hurwitz stability criterion from the MnZn and NiZn soft ferrites using a phenomenological model with the gyromagnetic spin contribution and domain wall contribution. The magnetodynamic equation and the harmonic oscillator equation have been used to obtain the domain walls and the spin contribution of the magnetic susceptibility. The ferrite materials have been considered as linear, time invariant, isotropic and homogeneous, and the magnetization vector is proportional to the magnetic field vector. The resulting expression of the magnetization in time domain of both ferrites under study has been obtained by mean of the inverse Laplace transformation applying the residue method. The poles of the magnetic susceptibility have negative real parts, which ensures that the response decays exponentially to zero as the time increase. The degree of the numerator's polynomial of the magnetic susceptibility is less than the degree of denominator's polynomial in the magnetic susceptibility function: and the poles are located in the half left s-plane. Then the system is bounded-input, bounded-output (BIBO), and the results agree with the Routh–Hurwitz stability criterion for the MnZn and NiZn soft ferrites.

Research Highlights
► Laplace transform of the magnetic susceptibility of the MnZn and NiZn soft ferrites.
► Routh–Hurwitz stability criterion of magnetic materials.
► Bode plot of magnetic susceptibility.
► Inverse Laplace transform using residue theorem.