An Approximate Approach to Determining the Permittivity and Permeability Near Lambda/2 Resonances in Transmission/Reflection Measurements

Abstract

Abstract-We present a simple and straightforward approximate approach to removing resonant artifacts that arise in the material parameters extracted near half-wavelength resonances that arise from transmission/reflection (T/R) measurements on low-loss materials. In order to determine material parameters near one such λ/2 resonance, by means of the 1st-order regressions for the input impedance of the sample-loaded transmission line, we approximate the characteristic impedance of the samplefilled section that is, in turn, dependent either on the relative wave impedance in a coaxial transmission line or on the relative permeability in a rectangular waveguide case. The other material parameters are then found, supplemented with the refractive index obtained from the conventional T/R method. This method applies to both coaxial transmission line and rectangular waveguide measurements. Our approach is validated by use of S-parameters simulated for a low-loss magnetic material, and is also applied to determine the relative permittivity and permeability from S-parameters measured for nylon and lithium-ferrite samples. The results are discussed as compared to those from the well-known Nicolson-Ross-Weir (NRW) method and are experimentally compared to those from the Baker-Jarvis (BJ) method as well.

Low-Loss Complex Permittivity and Permeability Determination in Transmission/Reflection Measurements With Time-Domain Smoothing

“…Using the wave impedance or the permeability calculated from the characteristic impedance, the permittivity was computed, supplemented with the refractive index found by the conventional T/R method. In this way, the approximate approach in [11] was able to provide reasonable estimates of the material parameters near the frequencies associated with geometric resonances in T/R measurements made on low-loss materials.…”

“…This present work, which is an alternative to the technique introduced in [11], proposes a more accurate approach to determining the complex permittivity and permeability of low-loss materials for frequencies near geometric resonances or (FPRs). Similar to [11], this new approach starts with an assumption that the T/R method ensures a smooth refractive index at all frequencies, but in contrast employs the inverse discrete Fourier transform (DFT) of a frequency response for the wave impedance that is obtained from the conventional T/R method, with an appropriately truncated frequency range.…”

“…In our previous study [11], we circumstantially investigated one of those issues that arise in the T/R method -artifacts that arise in the material parameters extracted near half-wavelength (λ/2) resonances when measuring a low-loss material with the conventional T/R method. These artifacts stem from geometric resonances called Fabry-Pérot resonances (FPRs) that appear when a test sample has a low-loss material property and its dimension is an integer multiple of λ/2 [12][13][14].…”

“…Similar to [11], this new approach starts with an assumption that the T/R method ensures a smooth refractive index at all frequencies, but in contrast employs the inverse discrete Fourier transform (DFT) of a frequency response for the wave impedance that is obtained from the conventional T/R method, with an appropriately truncated frequency range. Subsequently, in this time-domain regime, we use windowing to permit zero-time components of the wave impedance.…”

“…In [11], we approximated the input impedance of the sample-loaded transmission line by means of 1st-order regressions to remove resonant artifacts. From this approximate input impedance, we calculated the characteristic impedance of the sample-filled section that is, in turn, either a function of the wave impedance of the material filling a coaxial line or a function of the permeability filling a rectangular waveguide.…”