Wide-band measurements for frequency dependence of complex permittivity of a dielectric rod using multi-mode TM0m0 cavities

To measure the frequency dependence of complex permittivity of a dielectric rod inserted in the center of a cylindrical cavity, a new method using the multi-mode TM_0m0 of the cavity is developed on the basis of the rigorous analysis, where the effect of sample insertion holes is taken into account. Three cavities using the TM₀₁₀ and TM₀₂₀ modes and two cavities using the TM₀₁₀, TM₀₂₀, TM₀₃₀ and TM₀₄₀ modes are designed and manufactured with different sizes. These five cavities enable frequency dependence measurements of complex permittivity of a fused silica rod sample over eight octave bands from 3 to 26 GHz. The amount of scatter in the measured values of the relative permittivity and loss tangent are within 0.5% and 10%, respectively.