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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 x 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.

This paper presents a planar and compact microwave resonator sensor to characterize materials. The geometry of the resonator is based on the Sierpinski fractal curve and has four poles in the frequency range from 0.5 GHz to 5.5 GHz. Any of the four poles can be used to measure samples with low permittivity values, where the first pole is suitable for samples with high permittivity values. The sensitivity of the poles and return losses of the sensor are presented and obtained using a full-wave 3D simulator software. The device is manufactured and validated through a comparison between simulated and measured results. © 2020 P. H. B. Cavalcanti Filho et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.