Measurements of the complex permittivity of low loss ferrites at millimeter wave frequencies

Significant progress has been achieved in millimeter-wave technologies, enabled by the development of dielectric and magnetic materials operating at such frequencies. Conventional resonance dielectric characterization techniques are not applicable due to small required sample sizes. Measurements of the complex permittivity of spherical samples available from ferrite manufacturers are proposed, performed in metal cavities by employing spherical dielectric resonances. Rigorous analysis of the resonance structure allowed the determination of the diameter of an equivalent spherical enclosure, which negligibly affects the result accuracy but allows to reduce the 2D electromagnetic problem to a 1D one. Measurements have been performed on yttrium-iron- and calcium-vanadium-garnet samples having diameters in the 1.2 - 2.8 mm range at frequencies 25 - 58 GHz. The permittivity of these samples was found to be in the range of 14 to 16 and the dielectric loss tangent in the range of $1.6\times {10}^{-4}$ to $9.6\times {10}^{-4}$.