Simplified Complex Permittivity Measurement of Dielectric Materials Using a Compact Waveguide and a Machine Learning Technique

The Nicolson–Ross–Weir (NRW) algorithm is widely used to extract the complex permittivity of dielectric materials. Conventional NRW-based setups typically require machining dielectrics to fit waveguide apertures and to achieve precise adjustment across frequency bands, implying the need for multiple dielectrics comparable to waveguide aperture sizes. To address these limitations, this paper introduces a simplified non-destructive measurement setup that enables the direct placement of the dielectric material between two commercial waveguides, thereby eliminating the need to insert a precisely machined dielectric into a waveguide. The methodology is further streamlined by employing a fixed-size dielectric that facilitates complex permittivity extraction across multiple frequency bands without requiring multiple specimen preparations. Specifically, we use high-permittivity alumina to design a compact waveguide operating within the low-frequency range (0.95–1.23 GHz) that achieves an aperture size approximately three times smaller than conventional commercial waveguides. Using a dielectric of consistent dimensions, we successfully extracted the complex permittivity across both the 0.95–1.23 GHz and 26.5–40 GHz frequency bands. More importantly, a machine-learning approach is integrated into the complex permittivity extraction process to mitigate potential electromagnetic artifacts arising from the dielectric’s exposure to air.