A Tensor-Based Extension for the Multi-Line TRL Calibration

Rolain, Yves; Ishteva, Mariya; Nechel, Evi Van; Ferranti, Francesco

doi:10.1109/tmtt.2016.2565474

Cited by 11 publications

(11 citation statements)

References 13 publications

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“…Furthermore, the criteria for deriving the equations are not provided, assuming that the reader will make an intensive reading of the previous publications. As a consequence, it seems that a certain misunderstanding of this calibration method is widespread [7,12,13] (some misconceptions will be commented on later). Therefore, the main objective of this section is to show the implementation options of the method, along with their implications in the final result, hoping to clarify any doubts that may arise about this calibration technique.…”

Section: Classical Multi-line Calibration Methodsmentioning

confidence: 99%

“…Therefore, the algorithm obtains a single γ ij for each line pair, since both exponentials are combined to obtain a more precise result. Contrary to the belief of [13], the results extracted independently from the two exponentials cannot be exactly the same because the calculation of eigenvalues is carried out through the measurement, M ij , instead of the ideal wave-chain matrix T ij . It is true that in [9] it has been demonstrated that, under the measurement errors hypothesis, both propagation constants are identical up to the consideration of the first order error.…”

Section: Determination Of the Propagation Constantmentioning

confidence: 96%

“…In [13] the propagation constant of a line is obtained from the decomposition of a tensor which includes the data of N simulations of N lines that only differ in length. However, many of the details of the procedure are omitted or insufficient when it comes to real measurements instead of simulations.…”

Section: Cpd Implementationmentioning

confidence: 99%

“…Therefore, some information about the line lengths should be used to fully determine the D matrix. In [13] an optimization is carried out, whose results are both the scale factors and the estimation of γ. In the implementation described here the obtainment of the propagation constant has been separated from the deduction of the scale factors in order to use the Gauss-Markov results.…”

Section: Cpd Solutionmentioning

confidence: 99%

“…In case a higher degree of accuracy in the measurement results is needed, it is possible to increase the number of calibration standards in what is known as multi-line thru-reflect-line (MTRL) calibration. Recently, the basic ideas for the implementation of a MTRL calibration using a tensor decomposition have been published in [12,13]. However, in these papers the calibration procedure is not fully completed, and some results are obtained through generic non-linear optimization, instead of using the well-known optimal Gauss-Markov formulation presented in [2,8,9].…”

Section: Introductionmentioning

confidence: 99%

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Multi-line TRL Calibration of Vector Network Analyzers: Classical versus Tensor Implementation

Buesa-Zubiria¹,

Esteban²

2022

Preprint

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<div>A comprehensive comparison between two multi-line thru-reflect-line calibration techniques is provided.</div><div>One of the methods is based on the classical combination of N measurements following the Gauss-Markov theorem.</div><div>The other one has been developed along this paper in a complete and detailed way using the recently published idea of considering each of the N measurements as part of a tensor.</div><div>The measurement of a calibration kit that covers from 500 MHz to 20.5 GHz has been carried out for both methods and the results discussed.</div><div>From the analysis of the results, it seems that the tensor approach could show some advantages in the (not uncommon) cases where a strictly white and Gaussian noise is not the only perturbation of the measurements. On the other hand, the decomposition of the tensor requires a higher computational effort, which would better be reduced.</div>

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Section: Classical Multi-line Calibration Methodsmentioning

confidence: 99%

Section: Determination Of the Propagation Constantmentioning

confidence: 96%

Section: Cpd Implementationmentioning

confidence: 99%

Section: Cpd Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multi-line TRL Calibration of Vector Network Analyzers: Classical versus Tensor Implementation

Buesa-Zubiria¹,

Esteban²

2022

Preprint

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A Measurement of Non-Coaxial RF Devices with Improved TRL Calibration Algorithm

Chen

Wang

et al. 2018

MATEC Web Conf.

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In order to test the S-parameters of non-coaxial RF (Radio Frequency) devices accurately, using ADS (Advanced Design System) to simulate and design a set of fixture and calibration pieces for noncoaxial RF device performance test, and the calibration pieces is used to calibrate the test fixture, remove the error introduced by the fixture, and obtain the real S parameters of non-coaxial RF microwave devices. Based on the study of various parameters of RF microwave devices, the Engen's TRL (Thru-Reflect-Line) calibration algorithm is studied in depth. An improved TRL calibration algorithm is proposed. And the use of MATLAB program to achieve two calibration algorithms to correct the system error introduced by the measuring fixture, so as to get the real performance parameters of the device under test. Through the test of the verification device, the agreement between the improved TRL algorithm and Engen's TRL algorithm is verified. The final design of the test fixture can be successfully applied to the network analyzer for noncoaxial RF devices S-parameter measurement.

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