Abstract—

A modified resonator method for determining the complex permittivity of materials based on the theory of small perturbations where a resonator of a reflective type is used as a resonator has been considered. It has been shown that the resonator’s openness to the surrounding space in the form of holes for placing the sample and exciting vibrations leads to the fact that the minimum measurement errors of permittivity ε are achieved at optimal (but not minimum) sample sizes. The numerical modeling for the materials with a real part of ε from 4 to 30 and the dielectric tangent being from 5 × 10^–4 to 2 × 10^–2 has been performed and the dependences of the optimal transverse dimensions of square-section samples have been obtained when measuring the permittivity. There is a good coincidence of the results obtained theoretically and experimentally.

中文翻译：

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基于反射型谐振器的小扰动理论的改进谐振器法测定材料的复介电常数

摘要-

已经考虑了一种基于小扰动理论的用于确定材料复介电常数的改进的谐振器方法，其中反射型谐振器用作谐振器。已经表明，谐振器以孔的形式对周围空间开放，用于放置样品和激发振动，这导致在最佳（但不是最小）样品尺寸下实现介电常数 ε 的最小测量误差这一事实。ε 实部为 4 到 30 且介电正切为 5 × 10 ^–4到 2 × 10 ^{–2的材料的数值建模}已经执行并且在测量介电常数时已经获得了方形截面样品的最佳横向尺寸的依赖性。理论和实验得到的结果有很好的一致性。