Reference-Invariant Permittivity Determination of Low-Loss Solid Dielectric Samples Using Spectral Free-Space Measurements Without Prior Thickness

An extraction method has been proposed for relative permittivity determination εrs of low-loss solid dielectric samples using free-space measurements. It relies on a reference-plane invariant expression with no thickness information a priori, making resistant to conventional free-space measurement errors which may arise from improper information of sample position and thickness. In addition, the method constructed by the state transition matrix (STM) uses closed-form expressions – a feature distinguishes our method from previous STM-based extraction methods requiring a numerical tool or optimization procedure. Furthermore, provided that the sample thickness L is evaluated, as a by-product, first using the derived closed-form objective function away from any thickness-resonance region, the proposed method then determines εrs and L free from thickness-resonance effect, which otherwise can introduce ripples around or at the thickness-resonance frequency. Numerical analysis is performed to validate and assess the performance of our method. Free-space measurements at X-band of two low-loss samples with substantial thickness are performed for validation and accuracy comparison of our method against other similar methods.