Permittivity Measurement Method for Thin Sheets Using Split-Cylinder Resonator With Protrusions

Abstract

We propose a permittivity measurement method for a thin, low-loss sheet sample using a split-cylinder resonator (SCR) with protrusions. In the SCR, the TM₁₁₁ mode is separated from the TE₀₁₁ mode because the resonant frequency of the TM₁₁₁ mode is shifted toward a higher frequency band because of the protrusions. If an SCR does not have protrusions (or grooves), it is impossible to measure the permittivity of thin samples, which are commonly measured samples in the marketplace. When a sample is inserted between the flanges of the SCR with protrusions, the resonance curve of the TE₀₁₁ mode never overlaps with that of the TM₁₁₁ mode, and the permittivity of the sample is measurable until the resonance curve of the TE₀₁₁ mode overlaps with that of the TM₁₁₀ mode, where the resonant frequency of the TM₀₁₁ mode is much lower than that of the TE₀₁₁ mode. In addition, we newly derive an inequality that expresses a range for measurable permittivity based on the thickness of a sample and show that the range is much greater than that for an SCR with grooves. Moreover, we demonstrate the estimation accuracy for permittivity using a dimension correction method in which only the TE₀₁₁ mode is used, and we demonstrate that relative permittivity can be estimated within 0.3% over a permittivity range of less than 10 below 50 GHz if the real dimensions of the radius and length of an SCR have no deviation or deviate from the design dimension by the same ratio.