Numerical response and causality study of the magnetic permeability-frequency function of NiZn ferrites using Genetic Algorithm

The magnetic permeability of a ferrite is an important factor in device design such as inductors, transformers and microwave absorbent materials. In this paper, the magnetic permeability of NiZn ferrites doped with yttrium was simulated as a function of frequency using a magnetic permeability model, which contains six parameters that depend on the material. The model's parameters were adjusted using the Genetic Algorithm. Genetic Algorithms are probabilistic search procedures that generate solutions to optimization problems using techniques inspired in biological evolution. The convenience of the Genetic Algorithms method is it that does not require estimated initial values for the parameters, which allows to find a stable global minimum. The magnetic loss of a NiZn ferrite was numerically investigated by using the Kramers-Kronig relationships. Due to the principle of causality and time independence in the relation between magnetization vector M and magnetic field H, the real and the imaginary part of the complex magnetic permeability are mutually dependent, and the correlation is given by Kramer-Kronig equations. In this paper, the imaginary part of the magnetic permeability was obtained numerically by applying the Hilbert transform to the simulated real part. Causality was suitably verified through the KK relationships.