arXiv subjects

Ziad Hatab

Publications and source records attributed to Ziad Hatab.

9 recordsLinked to original sources

arXiv2025

The Choice of Line Lengths in Multiline Thru-Reflect-Line Calibration

This paper presents an analysis and rigorous procedure for determining the optimal lengths of line standards in multiline thru-reflect-line (TRL) calibration of vector network analyzers (VNAs). The solution is obtained through nonlinear constrained optimization of the eigenvalue problem in multiline TRL calibration. Additionally, we propose a simplified approach for near-optimal length selection based on predefined sparse rulers. Alongside the length calculation, we discuss the required number of lines to meet bandwidth requirements. The proposed methods are validated through measurements of multiple multiline TRL calibration kits on printed circuit boards of different materials and stackups, covering frequencies up to 150 GHz. A measurement-based Monte Carlo uncertainty analysis, using error boxes derived from impedance standard substrate measurements, demonstrates that the proposed line lengths distribute calibration uncertainty more evenly across lines compared to a commercial calibration kit. Practical examples are provided for various applications, including lossy and dispersive lines, as well as banded solutions for waveguides.

eess.SP↗

arXiv2025

Automatic Model Extraction of the Match Standard in Symmetric--Reciprocal--Match Calibration

This paper addresses the modeling of parasitics of the match standard in the symmetric-reciprocal-match (SRM) calibration method of vector network analyzers (VNAs). In the general SRM procedure, the match standard is assumed to be fully known. Here, we demonstrate that the match can be modeled with an arbitrary frequency-dependent model using a non-linear global optimization procedure. To highlight the validity of the suggested approach, numerical tests were conducted, demonstrating the ability to recover the match standard parasitic model down to software numerical precision. Additionally, we performed microstrip line measurements to compare the SRM calibration with match modeling to the multiline thru-reflect-line (TRL) calibration one, showing that automatic model extraction can achieve accuracy similar to using a match standard defined through multiline TRL calibration.

eess.SP↗

arXiv2023

Symmetric-Reciprocal-Match Method for Vector Network Analyzer Calibration

This paper proposes a new approach, the symmetric-reciprocal-match (SRM) method, for calibrating vector network analyzers (VNAs). The method involves using multiple symmetric one-port loads, a two-port reciprocal device, and a matched load. The load standards consist of two-port symmetric one-port devices, and at least three unique loads are used. However, the specific impedances of the loads are not specified. The reciprocal device can be any transmissive device, although a non-reciprocal device can also be used if only the one-port error boxes are of interest. The matched load is fully defined and can be asymmetric. We numerically demonstrated the proposed method's accuracy with synthetic data and with measurements of coaxial standards using a commercial short-open-load-reciprocal (SOLR) calibration kit with verification standards. An advantage of the proposed method is that only the match standard is defined, whereas the remaining standards are partially defined, either through symmetry or reciprocity.

eess.SP↗

arXiv2023

Validation of the Reference Impedance in Multiline Calibration with Stepped Impedance Standards

This paper presents a new technique for evaluating the consistency of the reference impedance in multiline thru-reflect-line (TRL) calibration. During the calibration process, it is assumed that all transmission line standards have the same characteristic impedance. However, these assumptions are prone to errors due to imperfections, which can affect the validity of the reference impedance after calibration. Our proposed method involves using multiple stepped impedance lines of different lengths to extract the broadband reflection coefficient of the impedance transition. This reflection coefficient can be used to validate the reference impedance experimentally without requiring fully defined standards. We demonstrate this method using multiline TRL based on microstrip structures on a printed circuit board (PCB) with an on-wafer probing setup.

physics.app-ph↗

arXiv2023

Indirect Measurement of Switch Terms of a Vector Network Analyzer with Reciprocal Devices

This paper presents an indirect method for measuring the switch terms of a vector network analyzer (VNA) using at least three reciprocal devices, which do not need to be characterized beforehand. This method is particularly suitable for VNAs that use a three-sampler architecture, which allows for applying first-tier calibration methods based on the error box model. The proposed method was experimentally verified by comparing directly and indirectly measured switch terms and performing a multiline thru-reflect-line (TRL) calibration.

physics.ins-det↗

arXiv2023

A Thru-free Multiline Calibration

This paper proposes a modification to the traditional multiline thru-reflect-line (TRL) or line-reflect-line (LRL) calibration method used for vector network analyzers (VNAs). Our proposed method eliminates the need for a thru (or line) standard by using an arbitrary transmissive two-port device in combination with an additional reflect standard. This combination of standards allows us to arbitrarily set the location of the calibration plane using physical artifacts. In contrast to the standard multiline TRL method, the suggested approach avoids a post-processing step to shift the calibration plane if a line standard is used. We demonstrate our proposed method with measurements on a printed circuit board (PCB) and compare it to the multiline TRL method with a perfectly defined thru.

physics.app-ph↗

arXiv2023

Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration

This study proposes a linear approach for propagating uncertainties in the multiline thru-reflect-line (TRL) calibration method for vector network analyzers. The multiline TRL formulation we are proposing applies the law of uncertainty propagation as outlined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) to both measurement and model uncertainties. In addition, we conducted a Monte Carlo analysis using a combination of measured and synthetic data to model various uncertainties, such as additive noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the Monte Carlo method and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.

eess.SP↗

arXiv2023

Propagation Constant Measurement Based on a Single Transmission Line Standard Using a Two-port VNA

This study presents a new method for measuring the propagation constant of transmission lines using a single line standard and without prior calibration of a two-port vector network analyzer (VNA). The method provides accurate results by emulating multiple line standards of the multiline calibration method. Each line standard is realized by sweeping an unknown network along a transmission line. The network need not be symmetric or reciprocal, but must exhibit both transmission and reflection. We performed measurements using a slab coaxial airline and repeated the measurements on three different VNAs. The measured propagation constant of the slab coaxial airline from all VNAs is nearly identical. By avoiding disconnecting or moving the cables, the proposed method eliminates errors related to repeatability of connectors, resulting in improved broadband traceability to SI units.

physics.ins-det↗

arXiv2022

Propagation of Measurement and Model Uncertainties through Multiline TRL Calibration

In this work, we present a linear uncertainty (LU) propagation treatment of measurement and model uncertainties in multiline thru-reflect-line (TRL) calibration. The proposed method is in accordance with the ISO Guide to the Expression of Uncertainty in Measurement (GUM). We demonstrate with numerical simulation based on the Monte Carlo (MC) method that our proposed LU method delivers identical uncertainty as the MC method but in a more efficient way.

eess.SP↗