Abstract: This paper introduces a novel approach for estimating the complex permittivity of liquids using a rectangular waveguide. The approach uses the finite difference time domain (FDTD) method, enhanced by perfectly matched layer (PML) boundary conditions to minimize reflections and ensure accurate calculation of the S-parameters. To address the challenge of sealing the waveguide ends, the waveguide is sealed at both ends with a resin sample of known complex permittivity, incorporating a small hole in the waveguide for liquid insertion. A Nelder-Mead optimization algorithm is then used in conjunction with the FDTD-PML method to estimate the complex permittivity of the liquid by iteratively comparing the calculated and measured S-parameters. Validated in the X-band frequency range, this technique demonstrates accurate estimation of the complex permittivity of liquid dielectric materials and offers a reliable means for liquid characterization.

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