Determination of complex permittivity of a thin low-loss dielectric sample using state-space approach from waveguide measurements

Abstract An extraction procedure is proposed for relative complex permittivity (ₑₒ) determination of thin low-loss samples positioned/deposited on a supporting substrate material using waveguide non-resonant microwave measurements. Its substrate thickness and sample thickness independence makes it unique extraction method in comparison with the available retrieval methods which are free from either substrate thickness information only or sample thickness information only. Its theoretical model is constructed on the state-transition matrix and state vector through which the link between ₑₒ and measured scattering (S-) parameters is established. Compared with previous works in the literature, a closed form (explicit) expression of ₑₒ is derived for a two-layer (sample on a substrate material) composite structure, thereby eliminating any numerical analysis or tool. Numerical analyses are implemented for validation of the proposed method as well as assessing the effect of noise and any possible air gap between the sample and its substrate. X-band (8. 2-12. 4 GHz) waveguide measurements of a thinner (around 1. 00 mm) polyvinyl chloride (PVC) for different measurement scenarios and measurements of a thin zinc oxide film (1. 0 m) were performed to evaluate the performance of the proposed extraction method against other similar methods in the literature. Our method can find applications for ₑₒ characterization of thin-film, radar-absorbent material coatings, anti-corrosive paints, or thermal barrier coatings where sample thickness (and substrate thickness) can vary from one sample to another from the same batch.