RU2753828C1 - Method for calibration and determination of inherent systematic errors of vector network analyser - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to radio measuring equipment and can be used for calibration of measuring instruments for complex transmission and reflection coefficients of apparatuses - vector network analysers (VNAs). The technical result is achieved by using a measure of wave resistance, as well as idle load, and a coordinated load with unknown values of the complex reflection coefficients, calculated after measurements conducted by the proposed method according to the found correlations between the measured parameters.

EFFECT: simplification, expansion of operational capabilities of the method and increase in the accuracy of calibration.

1 cl, 8 dwg

Description

The invention relates to radio measuring equipment and can be used to calibrate meters of complex transmission and reflection coefficients of devices - vector network analyzers (VNA).

There is a known method of VAC calibration, based on the use of three reference loads: no-load (XX), short circuit (SC), matched load (CH), referred to in the literature as SOL (from the English. Short, Open, Load) (V.G. Guba , AA Ladur, AA Savin Classification and analysis of calibration methods for vector network analyzers // Reports of TUSUR - №2 (24) - part 1 - 2011). The method is as follows. With the help of the VNA, the ports of which need to be calibrated, measurements of the complex reflection coefficients of three reference loads - SC, XX and CH, are carried out, connecting them in turn to each of the calibrated ports. Comparing the measured complex reflection coefficients of the short-circuit, XX and MV loads with their reference values, which are known in advance, determine the intrinsic S-parameters of the VNA port. This operation is carried out with each VNA port.

However, this method has a significant drawback, which is that the values of the complex reflection coefficients of the reference loads SC, XX and CH must be measured in advance using a VNA of a higher accuracy class, which cannot be done if it is necessary to calibrate the reference VNA. It is also possible to calculate the parameters of the reference loads geometrically with the required accuracy, which is achievable only for a narrow class of loads, namely short-circuit loads. In this case, the errors in determining the complex reflection coefficients of the reference loads are fully included in the calibration error in which these loads are applied.

The known method of VNA calibration, based on the use of the first measure of wave impedance (MVR), the second MVR and mismatched load, called TRL (from the English.Thru, Reflect, Line) (Dunsmore, J. Handbook of Microwave Component Measurements // John Wiley & Sons , 2012, - p. 145,). The method is as follows. The two VNA ports to be calibrated are first connected to each other using the first MVC and the complex parameters of the scattering matrix of the resulting first circuit are measured. Then the first MVA is disconnected and the two ports of the vector network analyzer are connected using the second MVA and the complex parameters of the scattering matrix of the resulting second circuit are measured. After that, an unmatched load is connected in turn to each of the two ports, and its complex reflection coefficient is measured using each of the VNA ports. As a result of these measurements, a system of equations is obtained (Pozar, D. Microwave Engineering // John Wiley & Sons, 2005, - pp. 193-196,), the solution of which allows one to determine the intrinsic parameters of both VNA ports. Unlike the SOL method, the described TRL calibration method is not based on the use of known reference loads.

It should be noted that in the TRL method, the complex reflection coefficient of the mismatch load is calculated during the calibration process and therefore it is not necessary to know this coefficient in advance. The disadvantage of this method is that for its implementation, the electrical length of one of the MVS must be known, which must either be measured on some equipment of a higher accuracy class, or calculated based on the geometric dimensions of this MVS. The accuracy of this method depends entirely on both the quality of the MFM manufacturing and the accuracy of the connection of the measuring paths during the calibration process. Since in this method the manufacturing quality of the MCS cannot be controlled during the calibration process, the quality of the connections of the measuring paths made by the operator is normalized to the maximum error factor. This error coefficient is determined based on the imperfection of the method used to determine the electrical length of the MFM and the quality of its manufacture.

The closest analogue to the claimed method of calibration and determination of intrinsic systematic errors of a vector network analyzer is a method of attestation of the intrinsic S-parameters of devices for measuring complex transmission and reflection coefficients of microwave two-port networks (patent No. 2482504 RF, IPC G01R 27/28), which consists in the fact that twice measure the reflection coefficients of three reference loads: SC, XX and CH, connecting them once directly to the certified measuring port, and the second time connecting each of them to the certified measuring port through a calibrated length transmission line - MVS with the calculated module and the phase of its transfer coefficient. Using the measured values of the reflection coefficients of three reference loads connected directly to the certified measuring port and through a line of calibrated length, as well as using the reference values of these loads and the calculated value of the MVS transfer coefficient, the dependences of the residual S-parameters characterizing the equivalent quadrupole of errors are obtained, which is constantly present between reference test port and load. By reducing the values of these residual S-parameters to the values of the parameters of an ideally matched input and output quadripole without loss, the calculated dependences of the values of the reflection coefficients of the reference loads XX and CH are found in the frequency range of the meter of the complex transmission and reflection coefficients of the microwave quadrupoles. The values of the reflection coefficients of the reference loads are selected in the vicinity of the frequencies, where the electric length of the MVS is a multiple of a quarter of the wavelength, excluding the vicinity of the singular points of its multiplicity to half the wavelength, and the amplitude-frequency and phase-frequency dependences of the reflection coefficients of each of the reference loads XX and CH are approximated by the selected values. As a result of the approximation, the true values of the reflection coefficients of the reference XX and CH are obtained, which are then used to calculate the true intrinsic S-parameters of the certified measuring port of the meter of the complex transmission and reflection coefficients of microwave two-port networks, which are used in measurements of the tested microwave two-port networks.

However, to implement such a method, it is necessary to first calculate the modulus and phase of the complex transmission coefficient of the MVS. But the error in reproducing the unit of wave impedance of the MVS in the form, for example, of a coaxial line with air filling is determined by the imperfection of the calculation formulas and the error of the measuring instruments with which the geometric dimensions of the measure are measured ... The most significant non-excluded systematic errors in reproducing the unit of wave impedance of the MVS based on a coaxial overhead line include errors arising from inaccurate measurement and unevenness of the diameters of the external and internal conductors of the MVS, the uncertainty of the values of the connecting gap formed by the difference in the lengths of the internal and external conductors of the MVS, and also misalignment of the inner and outer conductors along the length of the MVS. In addition, in the specified method, it is necessary that the reference or at least approximate values of the modulus and phase of the complex reflection coefficient of the loads XX and CH are known. These values can be calculated from the geometrical dimensions of the loads; however, for MV, the error in calculating the phase of the complex reflection coefficient is high.

Another disadvantage of this method is its narrow band, because with increasing frequency, the intrinsic attenuation in the MFM increases, its geometric length must be reduced, but at the same time the number of frequency neighborhoods decreases, where the MFM electrical length is a multiple of a quarter of the wavelength at low frequencies. This leads to an increase in the errors in the approximation of the modulus and phase of the complex reflection coefficients in the frequency range of each of the reference loads XX and CH, and in some cases - to the impossibility of making an approximation.

In the method taken as a prototype, the meter of parameters of microwave two-port networks will be called a vector network analyzer. Thus, it is emphasized that this method can be applied to any investigated frequency range, including optical (S. Iezekiel, B. Elamaran and RD Pollard, "Recent developments in lightwave network analysis," in Engineering Science and Education Journal, 2000. Dec. - vol. 9, - no. 6, - pp. 247-257,).

The technical result of the proposed method of calibration and determination of intrinsic systematic errors of the vector network analyzer is to simplify, expand the functionality of the method and increase the accuracy of calibration.

и нагрузок XX и СН с неизвестными параметрами

и

, присоединенных непосредственно к аттестуемому измерительному порту и через МВС, определяют значения комплексного коэффициента передачи МВС M_vs и полных комплексных коэффициентов отражения эталонных нагрузок XX М_хх и СН M_sn в окрестностях частот, где электрическая длина МВС кратна четверти длины волны, решая следующую систему уравненийTo achieve the technical result, a method is proposed for calibrating and determining the intrinsic systematic errors of a vector network analyzer (VNA), which consists in measuring the load of short circuit (SC), open circuit (XX) and matched load (CH), once by connecting them directly to the attested measuring port of the VNA, having obtained the values of the complex reflection coefficients of the three reference loads S _kx , S _xx , and S _sn, respectively, and the second time through the measure of wave impedance (MVR), obtaining the values S1 _kz , S1 _xx and S1 _sn, respectively, using the measured values of complex reflection coefficients of reference loads - short circuit loads with known parameters

and loads XX and CH with unknown parameters

and

connected directly to the certified measuring port and through the MVS, determine the values of the complex transfer coefficient MVS M _vs and the total complex reflection coefficients of the reference loads XX M _xx and CH M _sn in the vicinity of frequencies where the electrical length of the MVS is a multiple of a quarter of the wavelength, solving the following system of equations

where M1 _kz , M1 _xx , M1 _{sn are} defined by the relations:

и

значения которых затем используют для вычисления собственных S-параметров аттестуемого измерительного порта согласно системе уравнений:according to the calculated values of the complex reflection coefficients for the loads XX and CH M _xx and M _sn in the indicated frequency vicinity, in which the length of the MVS is a multiple of a quarter of the wavelength, approximate the modulus and phase of the complex reflection coefficients of each of the reference loads XX and CH

and

whose values are then used to calculate the intrinsic S-parameters of the certified measuring port according to the system of equations:

and then used to calculate the random and non-excluded systematic errors in determining the intrinsic S-parameters of the certified measuring port in the calibration frequency range, which are used in calculating the measurement errors of the subjects using VNA devices.

A significant difference between the proposed method and the prototype is that to calibrate and determine the intrinsic systematic errors of a vector network analyzer, you can use MVS, as well as XX and CH loads with unknown values of the complex reflection coefficients, which are calculated after measurements carried out by the proposed method according to the found relationships between measured parameters.

- а), б) и

- в), г) соответственно. На фиг. 7 показан пример вычисленных собственных S-параметров аттестуемого измерительного порта. На фиг. 8 показан пример вычисленных параметров Sk - остаточных S-параметров аттестуемого измерительного порта.FIG. 1 shows VAC, MVS, reference loads SC, XX and SN, with the help of which the proposed calibration method can be implemented. FIG. 2 and FIG. 3 shows the oriented graphs of the connection of the certified measuring port to the reference loads directly and through the MVC, respectively. FIG. 4 shows an example of the calculated frequency dependences of the AM _xx module - a) and the phase ϕM _xx - b) the complex reflection coefficient of the load XX; module AM _sn - c) and phase ϕM _sn - d) of the complex reflection coefficient of the MV load. FIG. 5 shows an example of the calculated modulus AM _vs - a) and the phase ϕM _vs - b) of the complex gain of the MBC. An example of the results of the approximation of M _xx and M _{sn is} shown in FIG. 6 as dependencies

- a), b) and

- c), d), respectively. FIG. 7 shows an example of the computed eigen S-parameters of a certified test port. FIG. 8 shows an example of the calculated parameters Sk - the residual S-parameters of the certified test port.

Let us consider how the proposed method of calibration and determination of intrinsic systematic errors of a vector network analyzer of a vector network analyzer is carried out.

The general principle of operation and the block diagram of the VNA are known and described (Khibel M. Fundamentals of vector circuit analysis. - M .: Publishing house MPEI, - 2009. - p. 26).

Calibration is performed as follows.

The complex reflection coefficients of the three reference loads - SC, XX and CH are measured twice, connecting them once directly to the certified measuring port, as in Fig. 1 a), connecting each of them for the second time to the certified measurement port through the MCM, as in FIG. 1 b).

Thus, for each of the six measurements, according to the formula for the input impedance of a two-port network (Pozar, D. Microwave Engineering // John Wiley & Sons, p. 192, 2005), systems of equations (1) and (2) are obtained:

,

и

- значения комплексных коэффициентов отражения эталонных нагрузок КЗ, XX и СН соответственно; S1_kz, S1_xx и S1_sn - измеренные комплексные коэффициенты отражения эталонных нагрузок КЗ, XX и СН соответственно, подключенных к аттестуемому измерительному порту через МВС;

,

и

- значения комплексных коэффициентов отражения МВС с последовательно присоединенными нагрузками КЗ, XX и СН соответственно.where: S ₁₁ , S ₂₁ S ₁₂ , S ₂₂ - own S-parameters of the certified measuring port; S _kz , S _xx , S _sn - measured complex reflection coefficients from reference loads SC, XX and CH, respectively, connected directly to the certified measuring port;

,

and

- the values of the complex reflection coefficients of the reference loads KZ, XX and SN, respectively; S1 _kz , S1 _xx and S1 _sn are the measured complex reflection coefficients of the reference loads SC, XX and CH, respectively, connected to the certified measuring port through the MVS;

,

and

- the values of the complex reflection coefficients of the MVS with the series connected loads KZ, XX and CH, respectively.

,

и

комплексных коэффициентов отражения МВС с последовательно присоединенными нагрузками КЗ, XX и СН согласно ориентированному графу на фиг. 3 записывают:For values

,

and

complex reflection coefficients of the MVS with series connected loads SC, XX and CH according to the oriented graph in FIG. 3 write:

и

- S^м -параметры МВС, рассматриваемой в виде четырехполюсника.where

and

- S ^m -parameters of the MVS, considered in the form of a four-port network.

The values of S _kx , S _xx , S _sn and S1 _kz , S1 _xx , S1 _{sn are} determined directly as a result of the first (without MBC) and second (with MBC) series of measurements.

,

,

,

,

являются неизвестными. Таким образом, совместная система уравнений (1) и (2) с учетом (3) состоит из шести уравнений при восьми неизвестных.The values of S ₁₁ , S ₂₁ S ₁₂ , S ₂₂ ,

,

,

,

,

are unknown. Thus, the joint system of equations (1) and (2), taking into account (3), consists of six equations with eight unknowns.

вводят обозначение M_kz, показав тем самым, что значение M_kz является расчетной величиной, полученной с определенной погрешностью.Instead of notation

the designation M _kz is introduced, thereby showing that the value of M _kz is a calculated value obtained with a certain error.

и

на измеренные величины в левой части системы уравнений (3) наблюдают, когда длина МВС обеспечивает разность фаз между отраженными навстречу друг другу от ее соединителей волн в 180° и они, противофазно складываясь, компенсируют друг друга, что выполняется только для определенных частот. Эти частоты являются опорными для дальнейших расчетов. Поэтому точки различных зависимостей, соответствующих этим частотам, также будем называть опорными.Minimal influence of reflection coefficients

and

the measured values on the left side of the system of equations (3) are observed when the length of the MVS provides a phase difference between the waves reflected towards each other from its connectors of 180 ° and they, adding in antiphase, cancel each other out, which is performed only for certain frequencies. These frequencies are reference frequencies for further calculations. Therefore, the points of various dependences corresponding to these frequencies will also be called reference points.

и

математически эквивалентна равенству этих параметров нулю. Для опорных точек принимают

, и заменяют

и

на M1_kz, M1_xx M1_sn соответственно, а

,

и

на M_kz, М_хх и M_sn соответственно. При этом вместо (3) получают (4), а вместо (1) и (2) записывают (5):Parameter compensation

and

is mathematically equivalent to the equality of these parameters to zero. For reference points, take

, and replace

and

on M1 _kz , M1 _xx M1 _sn, respectively, and

,

and

on M _kz , M _xx and M _sn, respectively. In this case, instead of (3), one gets (4), and instead of (1) and (2), write (5):

The use of the new notation "M" is necessary to indicate that the formulas in which they are included are valid only for the vicinity of the control points. Taking into account the introduced designations, system (5) is obtained from six equations with six unknowns M _xx , M _sn , M _vs , S ₁₁ , S ₂₁ S ₁₂ , S ₂₂ .

Of the first three equations of system (5), they express the intrinsic S-parameters of the certified measuring port:

From the last three equations of system (5), M1 are expressed by the values of the complex reflection coefficients of the loads connected together with the MVS:

Substituting into the system of equations (7) the expressions for the eigen S-parameters of the certified measuring port from the system of equations (6), the system of equations (8) is obtained.

,

, правые и левые части уравнений (4) во всем диапазоне частот отличаются на величину остаточных S-параметров аттестуемого измерительного порта - Sk-параметров:In the general case, with the coefficients M _vs and

,

, the right and left sides of equations (4) in the entire frequency range differ by the value of the residual S-parameters of the certified measuring port - Sk-parameters:

Sk-parameters are parameters that differ from the S-parameters of an ideally matched input and output four-port network without loss, in which, in general, S ₁₁ and S ₂₂ are equal to zero and the product of S ₂₁ S ₁₂ is equal to one, by a value including:

1) non-excluded systematic errors of mismatches arising in detachable connectors of loads, MVS and calibrated measuring port.

2) the difference between the true value of the complex reflection coefficients of the reference loads XX and CH from the value found as a result of calibration

3) the difference between the true complex transfer coefficient of the MVS from the value found as a result of calibration

When deriving system (9), it is assumed without loss of generality (Dunsmore, J. Handbook of Microwave Component Measurements // John Wiley & Sons, p. 179, 2012) that the residual parameters Sk is in the measurements between the certified measuring port and the device under test. Residual S-parameters are expressed from system (9):

At the reference frequency points, the values of Sk ₁₁ and Sk ₂₂ tend to zero, and the product Sk ₂₁ Sk ₁₂ tends to unity:

Applying relations (11) to the system of equations (10) and taking into account the requirement for the denominator to differ from zero, one obtains:

Replacing M1 in (12) by expressions from the system of equations (8), we obtain system (12) with only two unknowns M _xx and M _sn . The system of equations (12) is analytically solved with respect to M _xx and M _sn and 12 roots are obtained. Each root corresponds to the value M _vs according to (13), as well as the values of the residual S-parameters of the port Sk according to the system of equations (10). Of this set of roots, only one root is correct, which is uniquely determined based on the correspondence of the found values to the physical meaning.

As a result of the analytical solution of the system (12) with respect to M _xx and S _sn , the frequency dependences of the modulus of the reflection coefficient AM _xx are obtained, as in Fig. 4 a), and the phase ϕ-M _xx , as in Fig. 4 b); module AM _sn , as in FIG. 4c), and the phase ϕM _sn , as in Fig. 4 d).

Substituting the found M _xx and M _sn into formula (13), the modulus AM _{vs is found} , as in Fig. 5 a), and the phase ϕM _vs , as in Fig. 5 b), the complex transmission coefficient of the MVS.

The frequencies corresponding to the reference points are found from the phase values ϕM _vs = ± 180 ° of the complex transfer coefficient of the MHM.

и

во всем диапазоне частот калибровки, пример которых приведен на фиг. 6.The values of the functions M _xx and M _sn in the vicinity of the reference points are used to calculate the approximating functions -

and

over the entire range of calibration frequencies, an example of which is shown in FIG. 6.

и

подставляют в систему уравнений (1), в результате чего определяют искомые собственные S-параметры аттестуемого измерительного порта, как, например, на фиг. 7, где на фиг. 7 а), в) и д) показаны модули, а на фиг. 7 б), г) и е) - фазы собственных параметров аттестуемого измерительного порта,Then the computed values

and

are substituted into the system of equations (1), as a result of which the sought-for eigen S-parameters of the certified measuring port are determined, as, for example, in FIG. 7, where in FIG. 7 a), c) and e) modules are shown, and in Fig. 7 b), d) and f) are the phases of the intrinsic parameters of the certified measuring port,

According to the own S-parameters of the certified measuring port found during the certification process, the actual values - Г _and - of the reflection coefficient of the device under test by the vector network analyzer are determined (Pozar, D. Microwave Engineering // John Wiley & Sons, p. 192, 2005):

where Г ^and - the measured value of the complex reflection coefficient, equal to the ratio of a ₀ - the measured incident signal to b ₀ - the measured reflected signal (see Fig. 2).

Г _and - the true value of the complex reflection coefficient of the tested four-port network; S ₁₁ - directivity, S ₂₂ - signal source mismatch, S ₂₁ S ₁₂ - uneven paths of the supplied and reflected signals (V.G. Guba, A.A. / Reports of TUSUR - №2 (24) - part 1-2011).

In accordance with GOST 8-381, it is assumed that the systematic error, which includes the port's own S-parameters, is preliminarily excluded during measurements.

The proposed method makes it possible to assess the influence of both random and non-excluded systematic measurement errors on the calibration results.

In this case, the presented algorithm for calculating the intrinsic S-parameters of the port is considered as a function of the known value of the complex reflection coefficient of the short-circuit load and the values S _kz , S _xx , S _sn and S1 _kz , S1 _xx , S1 _sn measured during calibration:

The random error according to GOST 8.207-76 is determined statistically for the method under consideration, carrying out a series of measurements and finding the standard deviations from the mean values of the measured values S _kz , S _xx , S _sn and S1 _kz , S1 _xx , S1 _sn .

и

соответственно.The methodological component of the non-excluded systematic error is determined by the values of Sk - the residual S-parameters of the certified measuring port, an example, the results of which are shown in Fig. 8. These parameters are determined according to system (10), in which M1 is replaced by expressions from system (8), and M _xx and M _sn is replaced by

and

respectively.

Thus, the component of the non-excluded systematic error in measuring the load Г _and introduced by the residual S-parameters of the port is calculated by the formula (16), excluding the higher-order terms (Douglas K. Rytting, "Improved RF Hardware and Calibration Methods," p 35, eq . (3). Url: http://na.support.keysight.com/faq/symp.pdf):

Another component Residual stress T _and the measurement error associated with the non-excluded systematic error determining complex reflection coefficient of a load fault. This component is determined using expression (15) in accordance with GOST 8.381-2009.

In contrast to the method taken as a prototype, in which it is required to know in advance the calculated complex transmission coefficient of the MVS and the complex reflection coefficients of the short-circuit, XX and CH loads, in the claimed method it is necessary to know only the values of the modulus and phase of the complex reflection coefficient of the short-circuit load, thereby increasing the accuracy calibration.

Calibration by the claimed method can be carried out using several MVS of different lengths, which makes it possible to obtain more points for approximating the modulus and phase of the complex reflection coefficients of the reference loads XX and CH, thereby expanding the range of calibration frequencies.

In addition, the proposed method allows one to determine the random and non-excluded systematic errors in determining the intrinsic S-parameters of the certified measuring port in the range of calibration frequencies that the VNA calibrated by the proposed method possesses.

In addition, the application of approximation methods to the values of the modulus and phase of the complex reflection coefficients of XX and CH loads at the reference points, determined using the proposed method, makes it possible to determine the initially unknown values of the modulus and phase of the complex reflection coefficient of the XX and CH loads and the values of the modulus and phase of the complex transmission coefficient of the MVS ...

Along with the stated advantages, the inventive method makes it possible to control the degree of influence of the manufacturing quality of the MVS and standard load connectors on the calibration error, by determining the frequency dependences of the residual S-parameters of the port. Parameter Sk ₂₁ Sk ₁₂ - residual unevenness of the paths of the supplied and reflected signals, most of all depends on the quality of the MVS, namely, its matching and attenuation in accordance with GOST 18238-72. The Sk ₁₁ parameter can be used to estimate the residual directivity of the network analyzer port, and Sk ₂₂ can be used to judge the residual mismatch of the signal source. It also allows for the detection of operator errors while calibrating the VNA.

All of the above allows us to talk about a significant expansion of the functionality of the proposed method in comparison with the prototype, its simplification.

Claims (8)

A method of calibrating and determining the intrinsic systematic errors of a vector network analyzer (VNA), which consists in measuring the loads of short circuit (SC), no-load (XX) and matched load (CH), once, connecting them directly to the certified measuring port of the VNA , having obtained the values of the complex reflection coefficients of the three reference loads S _kx , S _xx , and S _sn, respectively, and the second time through the measure of wave impedance (MVR), obtaining the values of S1 _kz , S1 _xx and S1 _sn, respectively, using these measured values of the complex reflection coefficients reference loads - short circuit loads with known parameters

and loads XX and CH with unknown parameters

and

connected directly to the certified measuring port and through the MVS, as well as using the reference value of the complex reflection coefficient of the short circuit load M _kz , determine the values of the complex transmission coefficient of the MVS M _vs and the total complex reflection coefficients of the reference loads XX M _xx and CH M _sn in the vicinity of the frequencies, where the electrical length of the MVS is a multiple of a quarter of the wavelength, solving the following system of equations

where M1 _kz , M1 _xx M1 _{sn are} defined by the relations:

according to the calculated values of the complex reflection coefficients for the loads XX and CH M _xx and M _sn in the specified frequency vicinity, in which the length of the MVS is a multiple of a quarter of the wavelength, approximate the modulus and phase of the complex reflection coefficients of each of the reference loads XX and CH

and

over the entire range of calibration frequencies, the values of which are used to calculate the intrinsic S-parameters of the certified measuring port according to the system of equations:

and then used to calculate the random and non-excluded systematic errors in determining the intrinsic S-parameters of the certified measuring port in the calibration frequency range, which are used in calculating the measurement errors of the subjects using VNA devices.

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