Complex electric permittivity and magnetic permeability of ferrites calculated from scattering parameters

The problem of scattering parameters (S₁₁, S₂₁) for a rectangular waveguide (width a and height b) loaded with a dielectric and gyro tropic material of length d is considered, targeting the estimation of the electric permittivity and the parameters of the permeability tensor. The measurements are collected with a vector network analyzer equipped with a calibrated rectangular wave guide loaded with a parallelepiped Y₃Fe₅O₁₂, with dimensions a_s ≈ 3/4", b_s ≈ 3/8" and length d ≈ 15.1 mm. The electric permittivity as a function of frequency is estimated by comparing the experimental measurements with the theoretically calculated, using a Debye type of relaxation for ϵ = ϵ\´ - j ϵ" with ϵ_dc = 16.5 and relaxation time τ = 1 × 10^-15 s. The parameters of the magnetic permeability tensors are estimated by comparing the experimental data (|S₁₁| and |S₂₁|) measured under a dc-magnetic field with results of computer simulations.