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

• Published in: IEEE transactions on instrumentation and measurement 2024, Vol.73, p.1-11
• Main Authors: Mubarak, Faisal Ali, Mascolo, Vincenzo, Hussain, Faizan, Rietveld, Gert
• Format: Article
• Language: English
• Subjects: Behavioral sciences; Closed form solutions; Coaxial transmission line; Conductors; Connectors; Exact solutions; Mechanical properties; Parameter uncertainty; Power transmission lines; precision air line; Reflectance; S-parameters; Scattering parameters; Transmission line measurements; Transmission lines; Uncertainty; vector network analyzer (VNA); VNA traceability
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2023.3338667

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\cdot 10^{-3} up to 6\cdot 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.