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

The problem of scattering parameters (S 11 , S 21 ) 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 Y 3 Fe 5 O 12 , 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 (|S 11 | and |S 21 |) measured under a dc-magnetic field with results of computer simulations.