Uncertainty propagation for microwave scattering parameter measurements subject to time-domain and time-gating transformations

• Published in: Measurement : journal of the International Measurement Confederation Vol. 235; p. 114891
• Main Authors: Skinner, James, Gruber, Maximilian, Eichstädt, Sascha, Appleby, Roger, Ridler, Nick M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2024
• Subjects: discrete Fourier transform; Scattering parameters; Time-domain; Time-gating; Uncertainty propagation; Vector network analyser; Uncertainty propagation; Vector network analyser; Scattering parameters; Time-domain; Time-gating; discrete Fourier transform
• ISSN: 0263-2241; 1873-412X
• DOI: 10.1016/j.measurement.2024.114891

•Uncertainty propagation for S-parameter measurements subject to time-domain and time-gating transformations has been demonstrated.•This is the first demonstration of explicit propagation of uncertainties of S-parameters through time-domain and time-gating transformations in the published literature.•A mismatched coaxial 'Beatty' air line is used as a demonstration device; results agreed with models & theory.•Sources of uncertainty in the S-parameter measurements are located in time and subsequently attributed to specific aspects of the device under test.•Numerous applications of the demonstrated technique in the wider field of microwave measurements are possible. Analysis of the scattering (S-)parameters of devices and materials often involves the inspection of a particular interface or feature. Time-gating functions offered by vector network analysers have routinely been used to gate S-parameters in the time-domain to separate the device or material interface from other physical features of the network. To date, explicit uncertainty propagation through this process has not been demonstrated. PyDynamic, a Python software package, has been developed to explicitly propagate uncertainty between domains (i.e., frequency and time) and through the gating process. This paper presents the application of PyDynamic to S-parameter measurements of a coaxial device, namely a Beatty line, where the analysis presents results in the transformed time-domain and time-gated frequency-domain with uncertainties. In this demonstration, following time-gating of a Beatty line impedance discontinuity, the time-gated and transformed reflection S-parameters show a reduction in uncertainty from up to approximately 0.0025 U linear magnitude and up to 5 degrees in phase to less than 0.0005 U linear magnitude and 0.2 degrees in phase.