Permittivity evaluation of electrically thin low-loss materials by using a generalized free-space model without any formal calibration

A general free-space model based on reflection and transmission measurements is proposed for accurate permittivity determination of low-loss and electrically thin (where W is the sample thickness and is the wavelength) samples. Unlike previous free-space methods studied in the literature, the proposed new model generalizes previous free-space models by considering the case that transmitting and receiving antenna regions have different reflection and transmission properties. Such a model, valid at any frequency or over the entire frequency band, considers different antenna characteristics or different cable connections in addition to unequal and non-zero reflection properties due to impedance mismatches and ringing effects between antennas and the sample. An objective function constructed on this model is derived. This function is shown to be free-from error network terms of transmitting and receiving antenna regions and not dependent on reference-plane transformation factors. The effect of sample misalignment is considered to evaluate its effect on permittivity determination by the proposed extraction method. Free-space measurements at X-band (8.2–12.4 GHz) of low-loss Rogers 4350B sample (mm) and FR-4 sample (mm) were then carried out to validate our method.