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

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.