Complex Permittivity and Permeability Extraction of Ferromagnetic Materials For Magnetically Tuned Microwave Circuits

Ferromagnetic materials, such as ferrites, are employed for magnetically tuned radio frequency (RF) circuits. Ferrites exhibit both electric permittivity and magnetic permeability and independent RF characterization of these two properties is crucial for accurate design and modeling of RF circuits. A method that independently extracts each property over Wi-Fi frequencies is presented here, where complex permittivity and permeability of ferrite nano-particles are extracted using resonance frequency sensitivity of a 3D printed metallic cavity to various samples under test and their placement in the cavity. Air-filled 3D printed rectangular cavity using acrylonitrile butadiene styrene (ABS) are shielded using copper sheets; the structure of air-filled cavity is designed to excite TE
_101z
as the dominant resonance mode that resonates at 2.4 GHz. A cylindrical shape material under test (MUT) was added to the cavity at different positions for high electric and magnetic fields, while the resonant frequency change and degradation in quality factor of the resonant cavity are employed for accurate independent extraction of electric permittivity and magnetic permeability of MUT. The sample was prepared with volumetric distribution of 60:40 nanoparticles to glue ratio. In particular, a 3D printed composite sample of ABS with NiFe
₂
O
₄
magnetic nanoparticles is placed in positions of high electric or high magnetic energy densities of the metallic cavity, while any changes in resonant frequency and its frequency selectivity are observed from the cavity insertion loss characteristics. Both perturbation theory (as analytical) and finite element method (as numerical) techniques are employed for extraction of complex permittivity and permeability of NiFe
₂
O
₄
. The perturbation theory provides accurate extraction, which is also numerically confirmed using curve fitting of the full wave simulated scattering parameters to the measured results.