Retrieval of Permittivity and Permeability of Homogeneous Materials from Scattering Parameters

Abstract

On the basis of measured scattering parameters, we present a general assessment of the main problems with the Nicholson-Ross-Weir retrieval procedure: First, the inherent instability of the method for low-loss materials at frequencies corresponding to integer multiples of the transmitted wavelength in the sample; second, the multivalued solutions for the complex wavenumber when the electrical length of the sample exceeds a wavelenghth. It is shown that the presence of small perturbation or noise on the transmission coefficient T at around |T| ≈ 1 suffices to trigger the instability when retrieving the impedance of the sample. Unlike the ill-conditioned expression of the impedance, the product με (refractive index squared) is stable to perturbation in T. For nonmagnetic materials (relative permeability μ_r = 1), therefore, the product με reduces to the complex permittivity, which is then correctly retrieved without divergent ripples as shown by the extracted permittivity spectra in the X-band (8.2–12.4 GHz) for a slab sample of Teflon of arbitrary thickness.