Complex constitutive characterizations of materials in the X-band using a non-destructive technique

Abstract

In this article, a measurement technique based on the Nicholson–Ross–Weir formulation to retrieve the complex permittivity, εr = ε0r+iεr, of materials from the measured S-parameters, S11 and S12, at the X-band, 8 GHz up to 12 GHz, is discussed. Finite element method simulation based on Comsol software package formulations is invoked to evaluate the S-parameters based on the retrieved complex permittivity and to compare them to their measurements. Then, a parametric study is conducted for the simulation to match the numerical results to their identical measurements by considering the retrieved permittivity as an initial guess. Nevertheless, the complex permittivity is measured using network/impedance material analyzer in the frequency range from 1 MHz to 1.2 GHz to be compared against the evaluated values at the X-band. A PTFE sample is considered as an example to validate the precision of the proposed method. The obtained εr is found to be about 2.04−i0.0001, which is very close to the manufacturer range. Finally, excellent agreement between the measured and simulated S-parameters is observed.