Calculating S-Parameters and Uncertainties of Coaxial Air-Dielectric Transmission Lines

Abstract

Closed-form solutions are presented for calculating the reflection coefficient with corresponding uncertainty of metrology-grade 3.5 mm air-dielectric coaxial transmission lines for use as reference standards in S-parameter measurements up to 33 GHz. The closed-form solutions allow the calculation of the sensitivity coefficients required for calculating the propagation of uncertainties from the material and mechanical parameters of the transmission line toward its reflection coefficient uncertainties. The presented uncertainty framework evaluates every uncertainty source’s contribution, with uncertainties in reflection coefficient ranging from 1 · 10⁻³ up to 6 · 10⁻³. The approach is validated up to 33 GHz via a comprehensive measurement comparison of the reflection coefficient parameter for three 3.5 mm transmission lines with 16, 60, and 150 mm lengths. The values obtained by the proposed model agree well within the measurement uncertainties with known traceable calibration results of the transmission lines.