New Uncertainty Analysis for Permittivity Measurements Using the Transmission/Reflection Method

Abstract

We have developed a new algorithm for the uncertainty analysis of permittivity calculations of high-loss materials using the transmission/reflection (T/R) method. In the T/R method, several calculation procedures are performed to derive the permittivity. In our method, the permittivity is derived from measured S-parameters by solving an equation in which S-parameters are included in the form (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> + S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> )+β(S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> + S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sub> ), where β is a weighted factor to be optimized to minimize the uncertainty. We confirmed its efficacy by doing numerical calculations, as well as using actual measurement data for several materials obtained with a waveguide fixture. We also considered the effect of the type of calibration method used on a vector network analyzer on the permittivity uncertainty, and quantitatively clarified that it is essential to develop a highly accurate S-parameter measurement system to perform permittivity measurements using the T/R method accurately.