Analytical Uncertainty Evaluation of Material Parameter Measurements at THz Frequencies

Abstract

Material parameter extraction algorithms are studied and simplified both for transmission-reflection and transmission-only methods. The simplified relations, which are closed-form in some cases, are analyzed to establish the uncertainty sensitivity coefficients and therefore, to clarify the main uncertainty contributions and reduce the systematic and random errors. Simple closed-form expressions presented in this paper show the sensitivity of the extracted permittivity to each input parameter such as S21 (phase and amplitude), frequency, and the material thickness. Results are presented for several material slabs for three waveguide frequency ranges 75–110 GHz, 140–220 GHz, and 500–750 GHz using VNA-based free-space technique in the THz domain. Comparison of results (and the associated uncertainties) between different algorithms can help to choose the optimal one suitable for lossy or low-loss materials, and thin or thicker slabs. This can explain why the same set of S-parameters data usually gives different final results (permittivity and permeability) with different algorithms and verify the reliability of the calibration and extraction process.

Broadband Measurement of Substrate Complex Permittivity Using Optimized ABCD Matrix

“…The uncertainty budgets showing the main uncertainty contributions for and at 5/10/15/20 GHz are presented in Table 2 and 3. It can be observed from the results that the combined total standard uncertainty in our proposed technique is smaller than that of the recently published work, where the estimated uncertainty of and in the transmission-only method is 3%-4% and 10%-15%, respectively [23]. For the proposed two-line algorithm, it assumes that the transition and connection between MW connectors and transmission lines are mechanically and electrically identical, while in practical cases they are not likely to be completely the same.…”

“…Table 1 summarizes the comparison between the proposed extraction method and some reported ones in literature for Substrate Complex Permittivity Measurement. There are several sources of error and uncertainty in the measurement of dielectric characterization, mainly including the fabrication tolerance and the VNA measurement error [23]- [26]. Firstly, one of the main sources of error and uncertainty comes from the fabrication tolerance.…”

“…Generally, the VNA measurement uncertainty is related to the following terms, including VNA noise, linearity, drift, cable stability, and connector repeatability, all of which could contribute to the overall measurement uncertainty of S-parameters. Given nominal magnitude error of S-parameters approximately 0.015 due to VNA measurement uncertainty [23], the associated and at different frequencies can be obtained, which is shown in Fig. 7 (labelled as E_VNA).…”

Terahertz Channel Propagation Phenomena, Measurement Techniques and Modeling for 6G Wireless Communication Applications: a Survey, Open Challenges and Future Research Directions

“…One interesting method that can be used to obtain these parameters is by using calibrated RT simulators fed by experimental data where extensive simulations could be used along with different algorithms [289], [290] to extract material parameters such as the dielectric constant. The experimental data can be collected through simple free space reflection and transmission as well as only transmission measurements using a VNA, though each method has its own related uncertainty to be accounted for when it comes to parameter extraction [291].…”

Assessing the Impact of Data Filtering Techniques on Material Characterization at Millimeter-Wave Frequencies

“…In contrast to the conventional quasi-optical free-space system, the MCK system is compact and self-contained, eliminating the need for bulky mirrors or lenses. MCKs have been successfully utilised for material characterization at millimeter-wave and terahertz frequencies [11]- [13].…”