A planar sensor designed using the fourth Hilbert fractal curve iteration for solid material characterization at multiple frequencies is reported in this paper. The fractal curve is self-similar with space-filling properties. The Hilbert fractal geometry is used to form a compact resonator, with a multiband frequency response where miniaturization is achieved since a large transmission line length is effectively confined in a limited area. The sensor provides five resonances in the frequency range from 0 to 5 GHz. The resonant frequencies are 0.56, 1.68, 2.72, 3.69 and 4.72 GHz, all used to measure the real permittivity of known samples with a sensitivity of 7, 20, 27, 43 and 50 MHz/permittivity, respectively. The sensor is used to measure dielectric samples with 20 × 20 mm² areas with several thicknesses. Simulations and measurements demonstrate that the Hilbert fractal geometry can be used to design a multiband planar sensor for solid dielectric material characterization.

本文报道了使用第四次希尔伯特分形曲线迭代设计的用于在多个频率下表征固体材料的平面传感器。分形曲线是自相似的，具有空间填充特性。希尔伯特分形几何结构用于形成紧凑的谐振器，具有多频带频率响应，其中由于将大传输线长度有效地限制在有限的区域内，因此可以实现小型化。传感器在0到5 GHz的频率范围内提供五个共振。谐振频率分别为0.56、1.68、2.72、3.69和4.72 GHz，全部用于测量已知样品的真实介电常数，其灵敏度分别为7、20、27、43和50 MHz /介电常数。该传感器用于测量20×20 mm ^2的电介质样品厚度不同的区域。仿真和测量表明，希尔伯特分形几何可用于设计用于固体介电材料表征的多频带平面传感器。