Measurement and Uncertainty Assessment using Vector Network Analyzer (VNA) up to Terahertz Frequency Band

In RF and microwave engineering, the vector network analyzers (VNAs) are commonly used for network analysis with great accuracy and precision. VNAs are complex and versatile instruments employed to characterize active and passive networks. The network characterization is defined in terms of scattering parameters (S-parameters). The S-parameters are ratios of wave quantities which provide information about reflection and transmission characteristics of the device under test (DUT). The VNA measurements are associated with different sources of errors; mainly classified as systematic, random and drift errors. During a VNA calibration procedure, the systematic errors are characterized and most of them are mathematically removed afterwards. The other sources of errors can possibly be minimized, however, they affect the S-parameter measurements and become different sources of uncertainty associated with the measurements. Therefore, the uncertainty analysis is also an integral part while doing measurements with VNAs. The aim of this thesis is to perform VNA measurements and uncertainty assessments in both coaxial and waveguide test-set environments. The frequency of interest ranges from few MHz up to Terahertz frequency band. The uncertainty analysis is performed both numerically and analytically. The uncertainty sources considered are the definitions of the calibration standards, VNA noise, repeatability and drift. The different uncertainty sources are linearly propagated to compute the final uncertainties associated with the measurements. The dimensional characterization of standards is also carried out. The thesis is based on several S-parameter measurement and uncertainty assessment comparisons. The research work presented in first four chapters has been carried out at Politecnico di Torino and Istituto Nazionale di Ricerca Metrologica (INRiM), Italy. The fifth and sixth chapter described the research activities conducted at National Physical Laboratory (NPL), UK. While the seventh chapter presented the research work carried out at Physikalisch-Technische Bundesanstalt (PTB), Germany. In the first chapter, a general introduction to the VNA measurements and uncertainty assessment is presented. The different measurement errors, calibration standards and the calibration techniques are also described. A brief description is also provided for the classification of the uncertainty components and the S-parameter uncertainty representation. An informal bilateral comparison concerning the S-parameter measurements and uncertainty evaluation at millimeter frequencies (50-110 GHz) is presented in the second chapter. This comparison has been conducted successfully between National Metrology Centre (NMC) A*STAR, Singapore and INRIM, Italy. The aim of this comparison was to assess the compatibility between high frequency measurement systems at both institutes. The electromagnetic computations based on mechanical characterization of the waveguide shim standards are also presented. In the third chapter, a comparison of different S-parameter calibration techniques at millimeter frequencies (75-110 GHz) is described. All the calibration standards were mechanically measured and different calibration techniques were used for tracing S-parameter measurements to the International System of Units (SI). The aim of this comparison was to analyze the efficiency of two different VNA calibration techniques in terms of S-parameter measurements and related uncertainty. The metrological comparison of two different software packages, VNA Tools II and MMS4, is described in fourth chapter. VNA Tools II is developed by Bundesamt für Metrologie (METAS), Switzerland. While, the Multiport Measurement Software version 4 (MMS4) is commercial software package developed by High Frequency Engineering (HFE), Switzerland. Both software packages are based on different mathematical models and have different implementation. However, a comparison is important to validate the reliability of both software packages for the uncertainty contributions considered. This comparison will also allow the metrologists to have more confidence in using these packages for S-parameter measurements and uncertainty analysis. In fifth and sixth chapter, the connection repeatability investigation and calibration comparison of VNA in WR05 waveguide (140-220 GHz) are presented respectively. The connection repeatability investigation is important to analyze the variability of the repeated measurements and flanges' alignment mechanisms especially at these frequencies because of the very small dimensions of the waveguide apertures. In calibration comparison, the behaviour of different calibration techniques is demonstrated. Finally, in the seventh chapter, the suitable verification artefacts to check the performance of VNAs including their applicability to coaxial and waveguide systems are described. The waveguide verification standards considered for analysis are: WR-05 (140-220 GHz) and WR-03 (220-325 GHz) cross-guides and a custom-made WR-03 (220-325 GHz) circular iris section. Moreover, a novel type N coaxial verification standard architecture (DC-18 GHz) based on an air-line has been designed, fabricated and analyzed.