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

Hatab, Ziad; Gadringer, Michael Ernst; Bösch, Wolfgang

doi:10.1109/tim.2023.3296123

Cited by 9 publications

(11 citation statements)

References 29 publications

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“…The data were processed offline in Python using the package scikit-rf [37]. The multiline TRL algorithm used is based on [38], and the uncertainty propagation through the calibration is based on the approach of [39], [40].…”

Section: B Results and Discussionmentioning

confidence: 99%

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

Hatab,

Gadringer,

Alterkawi

et al. 2023

IEEE Open J. Instrum. Meas.

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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.

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Section: B Results and Discussionmentioning

confidence: 99%

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

Hatab,

Gadringer,

Alterkawi

et al. 2023

IEEE Open J. Instrum. Meas.

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“…By composing (10) with (9), we obtain a new Möbius transformation that describes the input reflection coefficient from the left port using measurements of the right port. This relationship can be written as follows:…”

Section: Calibration Planementioning

confidence: 99%

“…To emulate an on-wafer setup accurately, we utilize error boxes from an actual on-wafer setup that was extracted using multiline TRL calibration on an ISS kit. Details on the measurement setup can be found in [10], where the accuracy of the CPW model was tested, and the measurement datasets are available via [32]. In this numerical setting, the objective is to generate SRM standards based on the CPW model and embed them in the error boxes of the actual VNA setup, introducing different randomness at each iteration to perform the MC analysis.…”

Section: B Statistical Numerical Analysismentioning

confidence: 99%

“…12. Regarding the geometric parameters of the CPW structure used for simulation, we employed the following values, which are based on the measured ISS [10]: signal width of 49.1 µm, ground width of 273.3 µm, conductor spacing of 25.5 µm, and conductor thickness of 4.9 µm. The substrate is made of lossless Alumina with a dielectric constant of 9.9.…”

Section: B Statistical Numerical Analysismentioning

confidence: 99%

“…Other self-calibration methods include thru-reflect-line (TRL) and multiline TRL [7]- [10], which use line standards of different lengths, thru connection, and symmetric unknown reflect standard. The thru standard in TRL is fully defined.…”

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confidence: 99%

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Symmetric-Reciprocal-Match Method for Vector Network Analyzer Calibration

Hatab,

Gadringer,

Bösch

2024

IEEE Trans. Instrum. Meas.

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This paper proposes a new approach, the symmetricreciprocal-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 demonstrated the accuracy of the proposed method with measurements of coaxial standards using a commercial METAS traceable short-open-load-reciprocal (SOLR) calibration kit with verification standards. In addition, we presented a numerical Monte Carlo analysis considering various uncertainty factors. 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.

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