Electromagnetic Characterization of Electrically Thin Low-Loss Materials Through Uncalibrated Frequency-Domain Free-Space Measurements

An extraction procedure is proposed for electrically thin (W < λ/4 where W is the sample thickness and λ is the wavelength) low-loss samples taking into account of an antenna error model. Different from previous models, the examined error model considers the more general case of networks for transmitting and receiving antennas with non-zero and non-identical reflection terms, arising due to impedance mismatches and ringing effects, which are hard to be eliminated for wideband frequency-domain measurements. An objective function free from all error network terms and reference plane transformation factors is first derived and then specialized for unique relative permittivity (εr) determination of electrically thin low-loss samples only. Our method produces multiple-solutions for thicker samples (W > λ/4). Minimum W and minimum and maximum εr values that our method is applicable are also analyzed. Sensitivity and uncertainty analyses were followed to examine the performance of our method. Free-space measurements of standard electrically thin low-loss Rogers 4350B and FR-4 samples were then performed over X-band (8.2 − 12.4 GHz) for validation of our method.