Rapid full-analysis evaluation method for uncertainty of scattering parameters

Abstract

The invention discloses a rapid full-analysis evaluation method for uncertainty of scattering parameters, which comprises the steps of introducing noise and a non-ideal calibration standard twice in calibration and measurement processes and propagating the uncertainty in a mixed cross mode, and calculating the uncertainty of the scattering parameters according to mathematical analysis of a model in combination with a vector network calibration method. The method comprises the following steps: performing dimension increase, decomposition and calculation on a Jacobian matrix, and deducing a full analytic solution of the uncertainty of scattering parameters while fully considering the correlation, namely, a rapid full analytic evaluation method. According to the method, large-scale random sampling and iterative computation required by a Monte Carlo method are avoided, the operation efficiency is remarkably improved, covariance and correlation coefficients between real and imaginary parts of different scattering parameters can be provided, an effective tool is provided for accurately analyzing uncertainty sources, and the method has wide application prospects in the field of microwave measurement.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of uncertainty evaluation of scattering parameter measurement of microwave electronic devices and systems, and particularly relates to a fast and full-analytic evaluation method of scattering parameter uncertainty. BACKGROUND

[0002] The scattering parameter is a key performance indicator of most microwave electronic components and systems, and its accurate measurement is crucial to ensuring the quality of devices and systems. Currently, the measurement of S parameters mainly relies on vector network analyzers and their calibration algorithms (such as SOLT, TRL, etc.). These algorithms can correct the inherent errors of the system, but cannot completely eliminate measurement errors. The residual errors are often quantified in the form of uncertainty. Therefore, it is of great practical significance to accurately and efficiently evaluate the scattering parameter uncertainty of VNA measurement.

[0003] In existing uncertainty evaluation methods: the Monte Carlo method realizes uncertainty propagation through a large number of random samplings, but the calculation is time-consuming and cannot provide an analytic solution; the sensitivity analysis method can avoid random sampling, but it ignores the influence of the correlation between uncertainty sources; the method based on the covariance matrix balances the calculation efficiency and accuracy, but has not yet solved the joint propagation problem of uncertainty caused by noise and non-ideal calibration standards, mainly due to the lack of corresponding propagation models and decoupling methods. Therefore, the present application proposes a fast and full-analytic evaluation method of scattering parameter uncertainty, which can accurately represent the mixed cross-propagation mechanism of the joint propagation of noise and calibration standard uncertainty, improve the evaluation efficiency and accuracy of scattering parameter uncertainty, and realize a new method of fast and full-analytic evaluation to meet the higher requirements of modern microwave measurement for accuracy and efficiency. SUMMARY

[0004] The purpose of the present application is to provide a fast and full-analytic evaluation method of scattering parameter uncertainty.

[0005] To achieve the above purpose, the present application is implemented according to the following technical solutions: The present application comprises the following steps: Obtain noise data of the measurement receiver and the reference receiver at each port, and obtain calibration standard parameters by quantifying the influencing factors of non-ideal calibration standards; Construct a first-order measurement Jacobian matrix, input the noise data to calculate the uncertainty of the calibration standard measurement value and the uncertainty of the measurement value of the device to be measured at each port, construct a first-order theoretical Jacobian matrix, and input the calibration standard parameters to calculate the uncertainty of the single-port calibration standard theoretical value; The error terms of each port are calculated according to the scattering parameter measurement values and the scattering parameter theoretical values of each port calibration standard, and a first-order error Jacobian matrix is constructed by taking partial derivatives of the scattering parameter measurement values and the scattering parameter theoretical values of all calibration standards with respect to the error terms of each port, and the error term uncertainty matrix is obtained by inputting the calibration standard measurement value uncertainty and the calibration standard theoretical value uncertainty; A first-order scattering parameter Jacobian matrix is constructed by taking partial derivatives of the calibrated scattering parameter of the DUT with respect to the scattering parameter measurement values and the error terms, the measurement value uncertainty of the DUT and the error term uncertainty are propagated to the calibrated scattering parameter of the DUT through the first-order scattering parameter Jacobian matrix, and the perturbation method is combined with the Cauchy-Riemann equation to solve, and the scattering parameter uncertainty matrix of the DUT is obtained; The covariance matrix and the Pearson correlation coefficient between the real part and the imaginary part of different scattering parameters of the DUT are calculated according to the scattering parameter uncertainty matrix of the DUT; The port includes a single port and a double port; the single port includes port 1 and port 2; the port 1 includes a measurement receiver 1 and a reference receiver 1; the port 2 includes a measurement receiver 2 and a reference receiver 2; The calibration standard includes a single port calibration standard and a double port calibration standard; the single port calibration standard is required on both port 1 and port 2, including Short, Open and Load; the double port calibration standard is connected between port 1 and port 2, specifically Thru; The calibration standard parameter includes a theoretical scattering parameter, an amplitude uncertainty and a phase uncertainty; The diagonal elements of the error uncertainty matrix are the variances of the error terms, and the non-diagonal elements are the covariances between different error terms; The diagonal elements of the DUT scattering parameter uncertainty matrix are the variances of the real and imaginary parts of each scattering parameter of the DUT, and the non-diagonal elements are the covariances of the real and imaginary parts of different scattering parameters of the DUT.

[0006] Further, the method for calculating the measurement value uncertainty of each port calibration standard comprises: A single port first-order measurement Jacobian matrix is constructed according to the single port calibration standard scattering parameter measurement value, the measurement receiver received level and the reference receiver received level, and the expression is: ; Wherein is the first-order measurement Jacobian matrix of the single port calibration standard , the port includes a measurement receiver and a reference receiver , , measuring receiver index, simultaneously representing port index and reference receiver index for calibration standard lower measuring receiver from port received level, for calibration standard lower port inner reference receiver received level, for calibration standard lower port scattering parameter measurement value of, by measuring receiver received level with reference receiver received level determines ratio of, representing real part partial derivative of real part with respect to, representing imaginary part partial derivative of real part with respect to, representing real part partial derivative of imaginary part with respect to, representing imaginary part partial derivative of imaginary part with respect to; According to single-port first-order measurement Jacobian matrix, input noise data is used to calculate single-port calibration standard measurement value uncertainty, and the expression is: ; wherein measurement value uncertainty of calibration standard lower port , noise data variance, , noise data real part and imaginary part of reference receiver connected port when measuring receiver , , noise data real part and imaginary part of reference receiver connected port when measuring receiver , transposed matrix of single-port first-order measurement Jacobian matrix; According to double-port calibration standard scattering parameter measurement value, measuring receiver received level and reference receiver received level, a double-port first-order measurement Jacobian matrix is constructed, and the expression is: ; wherein measurement receiver under Thru calibration standard measurement Jacobian matrix of the connected port measurement receiver under Thru calibration standard from port received level port under Thru calibration standard inner reference receiver measurement receiver under Thru calibration standard connected port scatter parameter measurement value of the connected port, by the measurement receiver received level reference receiver received level ratio determination According to the two-port first-order measurement Jacobian matrix, input noise data to calculate the two-port calibration standard measurement value uncertainty, the expression is: ; ; wherein measurement value uncertainty under two-port Thru calibration standard, measurement receiver under two-port Thru calibration standard connected port measurement value uncertainty, , noise data real part and imaginary part of the measurement receiver connected port under Thru calibration standard , , noise data real part and imaginary part of the reference receiver connected port under calibration standard Thru , transpose matrix of the two-port first-order measurement Jacobian matrix .

[0007] Further, the method for calculating the single-port calibration standard theoretical value uncertainty, comprising: According to the calibration standard parameter to construct the first-order theoretical Jacobian matrix, input calibration standard parameter to calculate the single-port calibration standard theoretical value uncertainty, the expression is: ; ; wherein single-port calibration standard theoretical value uncertainty of the single-port calibration standard, , theoretical value uncertainty of the single-port calibration standard, the next-order theoretical Jacobian matrix, the first-order theoretical Jacobian matrix the transpose matrix of the first-order theoretical Jacobian matrix, , , , , theoretical scattering parameter, amplitude, phase, amplitude uncertainty and phase uncertainty of the single-port calibration standard , the real part of the theoretical scattering parameter the partial derivative of the amplitude or phase.

[0008] Further, the method for calculating the theoretical value uncertainty of the single-port calibration standard comprises: calculating each-port error terms according to the measured values and the theoretical values of the scattering parameters of each-port calibration standard; the error terms include single-port error terms two-port error terms , , the category index; constructing a first-order error Jacobian matrix by taking the partial derivatives of each-port error terms with respect to the measured values and the theoretical values of the scattering parameters of all calibration standards, and the expression is: ; wherein the first-order error Jacobian matrix has a size of 20x26, denotes the partial derivative matrix of the real part and the imaginary part of the port 1 error term with respect to the real part and the imaginary part of the port 1 scattering parameter measured value , denotes the partial derivative matrix of the real part and the imaginary part of the two-port error term with respect to the real part and the imaginary part of the port 1 scattering parameter measured value , denotes the partial derivative matrix of the real part and the imaginary part of the two-port error term with respect to the real part and the imaginary part of the two-port scattering parameter measured value , denotes the partial derivative matrix of the real part and the imaginary part of the two-port error term with respect to the real part and the imaginary part of the port 2 scattering parameter measured value , denotes the partial derivative matrix of the real part and the imaginary part of the port 2 error term with respect to the real part and the imaginary part of the port 2 scattering parameter measured value , denotes the partial derivative matrix of the real part and the imaginary part of the port 1 error term partial derivative matrix of the real part and the imaginary part of the scattering parameter theoretical value respectively, denotes the two-port error term partial derivative matrix of the real part and the imaginary part of the scattering parameter theoretical value respectively, denotes the port 2 error term partial derivative matrix of the real part and the imaginary part of the scattering parameter theoretical value respectively; The input calibration standard measurement uncertainty and the calibration standard theoretical value uncertainty are used to obtain the error term uncertainty matrix, and the expression is as follows: ; wherein is the error term uncertainty matrix, is the transpose matrix of the first-order error Jacobian matrix .

[0009] Further, the method for obtaining the scattering parameter uncertainty matrix of the measured object comprises the following steps: obtaining the scattering parameter measurement value of the measured object measurement receiver connection port , , denotes the measurement receiver index, and simultaneously denotes the port index and the reference receiver index, and the correction coefficient is calculated in combination with the error term, and the expression is as follows: ; wherein is the correction coefficient, , , is the port 1 error term, , , is the port 2 error term, , , , is the two-port error term, wherein , is the forward and reverse crosstalk error, which can be directly measured, , is the forward and reverse source matching error, , is the forward and reverse directional error, , is the forward and reverse reflection tracking error, , is the forward and reverse load matching error, , forward and backward transmission tracking errors; calculate correction coefficients according to error terms and error terms to measured values of the scattering parameters of the object under test correct the measured values of the scattering parameters of the object under test to obtain calibrated values of the scattering parameters of the object under test , the partial derivatives of the real and imaginary parts of the calibrated values of the scattering parameters of the object under test to the real and imaginary parts of the measured values of the scattering parameters of the object under test are constructed to form a first-order scattering parameter Jacobian matrix, and the expression is: ; wherein the first-order scattering parameter Jacobian matrix is 8x20, the real and imaginary parts of the calibrated values of the scattering parameters of the object under test are respectively differentiated to the real and imaginary parts of the measured values of the scattering parameters of the object under test , the partial derivative matrices are obtained, the real and imaginary parts of the calibrated values of the scattering parameters of the object under test are respectively differentiated to the real and imaginary parts of the single-port error terms , the partial derivative matrices are obtained, the real and imaginary parts of the calibrated values of the scattering parameters of the object under test are respectively differentiated to the real and imaginary parts of the two-port error terms , the partial derivative matrices are obtained; the measurement uncertainty of the object under test and the error term uncertainty are propagated to the calibrated scattering parameters of the object under test through the first-order scattering parameter Jacobian matrix, and the perturbation method is combined with the Cauchy-Riemann equation to solve, and the scattering parameter uncertainty matrix of the object under test is obtained, and the expression is:

[0010] wherein the scattering parameter uncertainty matrix of the object under test is the transpose matrix of the first-order scattering parameter Jacobian matrix .

[0011] Further, the covariance matrix and the Pearson correlation coefficient are used for quantitative analysis of the strength and direction of the linear correlation between different real and imaginary parts of the scattering parameters.

[0012] The beneficial effects of the present application are: The present application is a fast and full-analytical evaluation method for scattering parameter uncertainty, which has the following technical effects compared with the prior art: The application significantly improves the evaluation efficiency and accuracy of the scattering parameter uncertainty, realizes the fast and full analytical solution of the cross propagation behavior of the uncertainty in the calibration and measurement two stages based on the extended and decomposed Jacobian matrix, avoids the calculation burden of large-scale random sampling of the Monte Carlo method, and verifies the effectiveness of the proposed method through experimental comparison and verification, thereby enhancing the reliability and analytical of the scattering parameter measurement uncertainty evaluation result. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 A flowchart of the steps of the fast and full analytical evaluation method of the scattering parameter uncertainty of the application; Figure 2 A schematic diagram of the evaluation result of the scattering parameter uncertainty of the application in the embodiment of the fast and full analytical evaluation method, which quantifies the uncertainty introduced by the noise and non-ideal calibration standard as the calibration DUT scattering parameter uncertainty evaluation result; Figure 3 A comparison diagram of the quantitative results of the scattering parameter uncertainty evaluation of the proposed method and the Monte Carlo method in the embodiment of the application; Figure 4 A covariance graph between the real part and the imaginary part of different scattering parameters in the embodiment of the application; Figure 5 A Pearson correlation coefficient graph between the real part and the imaginary part of different scattering parameters in the embodiment of the application; Figure 6 An uncertainty transfer flowchart in the embodiment of the application. DETAILED DESCRIPTION

[0014] The application will be further described below through specific embodiments, and the illustrative embodiments of the application and the description are used to explain the application, but not as a limitation of the application.

[0015] The fast and full analytical evaluation method of the scattering parameter uncertainty of the application includes the following steps: As shown in the figure, in the embodiment, the following steps are included: Figure 1 Obtaining the noise data of the measurement receiver and the reference receiver at each port, quantifying the influencing factors of the non-ideal calibration standard to obtain the calibration standard parameters; Building a first-order measurement Jacobian matrix, inputting the noise data to calculate the calibration standard measurement value uncertainty and the measured piece measurement value uncertainty of each port, building a first-order theoretical Jacobian matrix, inputting the calibration standard parameters to calculate the single-port calibration standard theoretical value uncertainty; ​The error term of each port is calculated according to the scattering parameter measurement value and the scattering parameter theoretical value of each port calibration standard, and a first-order error Jacobian matrix is constructed by taking partial derivatives of the scattering parameter measurement value and the scattering parameter theoretical value of all calibration standards with respect to the error term of each port, and the error term uncertainty matrix is obtained by inputting the calibration standard measurement uncertainty and the calibration standard theoretical value uncertainty; The first-order scattering parameter Jacobian matrix is constructed by taking partial derivatives of the calibrated scattering parameter of the to-be-tested object with respect to the scattering parameter measurement value and the error term of the to-be-tested object, the measurement value uncertainty and the error term uncertainty of the to-be-tested object are propagated to the calibrated scattering parameter of the to-be-tested object through the first-order scattering parameter Jacobian matrix, the perturbation method is used in combination with the Cauchy-Riemann equation to solve, and the scattering parameter uncertainty matrix of the to-be-tested object is obtained; The covariance matrix and the Pearson correlation coefficient between the real part and the imaginary part of different scattering parameters of the to-be-tested object are calculated according to the scattering parameter uncertainty matrix of the to-be-tested object; The port includes a single port and a double port; the single port includes a port 1 and a port 2; the port 1 includes a measurement receiver 1 and a reference receiver 1; and the port 2 includes a measurement receiver 2 and a reference receiver 2; The calibration standard includes a single port calibration standard and a double port calibration standard; the single port calibration standard is required on the port 1 and the port 2, and includes a Short, an Open and a Load; and the double port calibration standard is connected between the port 1 and the port 2, and is specifically a Thru; The calibration standard parameter includes a theoretical scattering parameter, an amplitude uncertainty and a phase uncertainty; The diagonal elements of the error uncertainty matrix are the variances of the error terms, and the non-diagonal elements are the covariances between different error terms; The diagonal elements of the to-be-tested object scattering parameter uncertainty matrix are the variances of the real and imaginary parts of the scattering parameters of the to-be-tested object, and the non-diagonal elements are the covariances between the real and imaginary parts of different scattering parameters of the to-be-tested object.

[0016] In the embodiment, the method for calculating the calibration standard measurement uncertainty of each port includes: The single port first-order measurement Jacobian matrix is constructed according to the single port calibration standard scattering parameter measurement value, the measurement receiver received level and the reference receiver received level, and the expression is: ; Wherein is the first-order measurement Jacobian matrix of the single port calibration standard , the port includes the measurement receiver and the reference receiver , , Measure receiver index, This also indicates the port index and the reference receiver index. For calibration standards Lower measurement receiver From port Received voltage level For calibration standards Down port Internal reference receiver Received voltage level For calibration standards Down port The scattering parameter measurements are obtained from the measurement receiver. Received level With reference receiver Received level The ratio is determined. Indicates the real part For the real part The partial derivative, Indicates the imaginary part For the real part The partial derivative, Indicates the real part imaginary part The partial derivative, Indicates the imaginary part imaginary part The partial derivative; Based on the first-order measurement Jacobian matrix of the single-port port, the uncertainty of the single-port calibration standard measurement value is calculated using the input noise data, expressed as follows: ; in For calibration standards Down port The measurement uncertainty, For the variance of the noise data, , For calibration standards Downlink port Time measurement receiver The real and imaginary parts of the noise data. , For calibration standards Downlink port Time reference receiver The real and imaginary parts of the noise data. This is the transpose of the first-order measurement Jacobian matrix for a single port. Based on the measured values ​​of the scattering parameters of the two-port calibration standard, the received level of the measurement receiver, and the received level of the reference receiver, a first-order measurement Jacobian matrix for the two-port system is constructed, expressed as follows: ; wherein measurement receiver under Thru calibration standard first order measurement Jacobian matrix of the connected port measurement receiver under Thru calibration standard from port received level port under Thru calibration standard internal reference receiver received level, measurement receiver under Thru calibration standard connected port scatter parameter measurement value of the connected port, measurement receiver received level reference receiver received level ratio is determined; According to the two-port first order measurement Jacobian matrix, the input noise data is used to calculate the measurement value uncertainty of the two-port calibration standard, and the expression is: ; ; wherein measurement value uncertainty of the two-port Thru calibration standard, measurement receiver under two-port Thru calibration standard connected port measurement value uncertainty when , noise data real part and imaginary part of the measurement receiver when connected port under Thru calibration standard , noise data real part and imaginary part of the reference receiver when connected port under calibration standard Thru transpose matrix of the two-port first order measurement Jacobian matrix ; In practical application, taking port 1 of the single-port device under calibration standard Short as an example, the first order measurement Jacobian matrix is constructed according to the calibration standard scatter parameter measurement value, the measurement receiver received level and the reference receiver received level: ; The measurement value uncertainty caused by the noise of port 1 of the single-port device under calibration standard Short is calculated: ; ​​For the two-port device under the calibration standard Thru, the two-port first-order measurement Jacobian matrix is constructed according to the two-port scattering parameter measurement value, the measurement receiver received level and the reference receiver received level: ; ; ; ; The measurement value uncertainty caused by the two-port device noise under the calibration standard Thru is calculated: ; ;

[0017]

[0018]

[0019] Thus, the each-port calibration standard measurement value uncertainty is obtained 、 、 、 、 、 、 .

[0020] In the embodiment, the method for calculating the single-port calibration standard theoretical value uncertainty comprises: The first-order theoretical Jacobian matrix is constructed according to the calibration standard parameters, and the single-port calibration standard theoretical value uncertainty is calculated by inputting the calibration standard parameters, and the expression is: ; ; Wherein is the theoretical value uncertainty of the single-port calibration standard , , is the first-order theoretical Jacobian matrix of the single-port calibration standard , is the transpose matrix of the first-order theoretical Jacobian matrix , 、 、 、 、 is the theoretical scattering parameter, amplitude, phase, amplitude uncertainty and phase uncertainty of the single-port calibration standard under the calibration standard Thru, is the real part of the theoretical scattering parameter partial derivatives of the amplitude or phase; In practical application, taking port 1 of the single-port device under the calibration standard Short as an example, a first-order theoretical Jacobian matrix is constructed according to the calibration standard parameters, and the single-port calibration standard theoretical value uncertainty is calculated by inputting the calibration standard parameters: ; ; Thus, the single-port calibration standard theoretical value uncertainty is obtained 、 、 .

[0021] In the embodiment, the method for calculating the single-port calibration standard theoretical value uncertainty comprises: calculating each-port error terms according to the scattering parameter measurement values and the scattering parameter theoretical values of each-port calibration standards; the error terms include single-port error terms , double-port error terms , 、 is a category index; a first-order error Jacobian matrix is constructed by taking partial derivatives of each-port error terms with respect to the scattering parameter measurement values and the scattering parameter theoretical values of all calibration standards, and the expression is: ; wherein is the first-order error Jacobian matrix, and the size is 20*26, represents the partial derivative matrix of the real part and the imaginary part of the port 1 error term with respect to the real part and the imaginary part of the port 1 scattering parameter measurement value , represents the partial derivative matrix of the real part and the imaginary part of the double-port error term with respect to the real part and the imaginary part of the port 1 scattering parameter measurement value , represents the partial derivative matrix of the real part and the imaginary part of the double-port error term with respect to the real part and the imaginary part of the double-port scattering parameter measurement value , represents the partial derivative matrix of the real part and the imaginary part of the double-port error term with respect to the real part and the imaginary part of the port 2 scattering parameter measurement value , represents the partial derivative matrix of the real part and the imaginary part of the port 2 error term with respect to the real part and the imaginary part of the port 2 scattering parameter measurement value , represents the partial derivative matrix of the real part and the imaginary part of the port 1 error term with respect to the real part and the imaginary part of the scattering parameter theoretical value , denotes the two-port error term partial derivative matrices of the real and imaginary parts of the scattering parameter theoretical value , denotes the port 2 error term partial derivative matrices of the real and imaginary parts of the scattering parameter theoretical value ; the error term uncertainty matrix is obtained by inputting the calibration standard measurement uncertainty and the calibration standard theoretical value uncertainty, and the expression is: ; wherein is the error term uncertainty matrix, is the transpose matrix of the first-order error Jacobian matrix ; In practical applications, the error terms of each port are calculated according to the scattering parameter measurement value and the scattering parameter theoretical value of the calibration standard of each port. First, the single-port error term , is calculated, and the expression is: ; ; ; ; ; ; wherein , , is the port 1 error term, , , is the port 2 error term, , , , is the two-port error term, wherein , is the forward and reverse crosstalk error, which can be directly measured, , is the forward and reverse source matching error, , is the forward and reverse directional error, , is the forward and reverse reflection tracking error, , is the forward and reverse load matching error, , is the forward and reverse transmission tracking error, , 、 , theoretical value of the scattering parameter of receiver 1 at port 1 under the single-port calibration standard, 、 、 theoretical value of the scattering parameter of receiver 2 at port 2 under the single-port calibration standard; According to the single-port error terms 、 and the measured value of the two-port scattering parameter under the calibration standard Thru, the two-port error terms are calculated, and the expression is: ; ; ; ; wherein 、 are the forward and reverse crosstalk errors, which can be directly measured; The partial derivatives of each port error term with respect to the measured value and the theoretical value of the scattering parameter of all calibration standards are taken to construct a first-order error Jacobian matrix, and the expression is: ; wherein the same row elements in each partial derivative matrix are the real parts and imaginary parts of the same error term with respect to the real parts and imaginary parts of all measured values / theoretical values, and the number of rows is the sum of the number of real parts and imaginary parts of all error terms of the same port, which is specifically: ; ; ; ; ; ; ; ; wherein 、 、 、 、 、 、 、 have sizes of 6x6, 8x6, 8x8, 8x6, 6x6, 6x6, 8x6, 6x6; According to the first-order error Jacobian matrix , the measured value uncertainty of each port calibration standard , , , , , , ) and single-port calibration standard theoretical value uncertainty ( , , ) to construct the uncertainty matrix of error terms.

[0022] In the embodiment, the method for obtaining the uncertainty matrix of the scattering parameter of the to-be-tested member comprises the following steps: obtaining the scattering parameter measurement value of the to-be-tested member connection port , , , wherein the index of the measurement receiver is represented by i, , wherein the index of the port and the index of the reference receiver are represented by j and k respectively, the correction coefficient is calculated in combination with the error terms, and the expression is as follows: ; wherein is the correction coefficient, , , is the error term of port 1, , , is the error term of port 2, , , , is the double-port error term, wherein , is the forward and reverse crosstalk error, which can be directly measured, , is the forward and reverse source matching error, , is the forward and reverse directivity error, , is the forward and reverse reflection tracking error, , is the forward and reverse load matching error, , is the forward and reverse transmission tracking error; the correction coefficient is calculated according to the error terms and the error terms are corrected to obtain the scattering parameter value of the to-be-tested member after calibration , and the scattering parameter value of the to-be-tested member after calibration is obtained. The first-order scattering parameter Jacobian matrix is constructed by taking the partial derivative of the scattering parameter value of the to-be-tested member after calibration with respect to the scattering parameter measurement value of the to-be-tested member and the error terms, and the expression is as follows: ; wherein is the first order scattering parameter Jacobian matrix with size 8x20, is the calibrated scattering parameter value of the DUT is the real part and the imaginary part of the scattering parameter measurement value of the DUT is the partial derivative matrix of the real part and the imaginary part of the scattering parameter measurement value of the DUT is the calibrated scattering parameter value of the DUT is the real part and the imaginary part of the single-port error term is the partial derivative matrix of the real part and the imaginary part of the single-port error term is the calibrated scattering parameter value of the DUT is the real part and the imaginary part of the two-port error term is the partial derivative matrix of the real part and the imaginary part of the two-port error term the measurement uncertainty of the DUT and the error term uncertainty are propagated to the calibrated scattering parameter of the DUT through the first order scattering parameter Jacobian matrix, and the scattering parameter uncertainty matrix of the DUT is obtained by solving the perturbation method combined with the Cauchy-Riemann equation, and the expression is:

[0023] wherein is the scattering parameter uncertainty matrix of the DUT, is the transpose matrix of the first order scattering parameter Jacobian matrix . In practical applications, the calibrated scattering parameter value of the DUT is expressed as: ; ; ; ; The calibrated scattering parameter value of the DUT is used to derive the partial derivative of the scattering parameter measurement value of the DUT and the error term , to construct the first order scattering parameter Jacobian matrix, and the expression is: ; ; ; ; wherein , , the size is 8x8, 8x12, 8x8. The measurement value uncertainty of the DUT and the error term uncertainty The scattering parameters of the DUT after calibration are propagated through the first-order scattering parameter Jacobian matrix, the perturbation method is combined with the Cauchy-Riemann equation to solve, and the scattering parameter uncertainty matrix of the DUT is obtained.

[0024] In the embodiment, the covariance matrix and the Pearson correlation coefficient are used to quantitatively analyze the strength and direction of the linear correlation between different scattering parameter real and imaginary parts.

[0025] As Figure 2 shown, the evaluation results of the uncertainty introduced by the noise and the non-ideal calibration standard in the method FFEM in the embodiment of the application are given, which are quantified as the uncertainty of the scattering parameters of the DUT after calibration, wherein, Figure 2 (a) represents the influence of the uncertainty of different non-ideal calibration standards on S 11 and S 22 ; Figure 2 (b) represents the influence of the uncertainty of different non-ideal calibration standards on S 12 and S 21 ; Figure 2 (c) represents the influence of the non-ideal calibration standard and the noise ensemble on S 11 and S 22 ; Figure 2 (d) represents the influence of the non-ideal calibration standard and the noise ensemble on S 12 and S 21 ; The results show that in the SOLT calibration method: 1) the non-ideal load standard is the main source of the reflection coefficient uncertainty, but has less influence on the transmission coefficient; 2) the uncertainty of the reflection coefficient is generally much higher than that of the transmission coefficient; 3) the influence of the noise is more significant in the transmission coefficient; In order to verify the correctness of the proposed scattering parameter uncertainty evaluation method, a 40 dB attenuator is selected as the DUT and the SOLT method is selected as the calibration method for performance verification. The verification steps are as follows: the uncertainty of the noise and the non-ideal calibration standard is transferred to the 12 error terms of the SOLT method and then to the scattering parameters of the DUT after calibration, and the quantified results of the scattering parameter uncertainty evaluation of the proposed method are compared with the Monte Carlo method. As Figure 3 shown, the comparison of the evaluation results of the scattering parameter uncertainty of the proposed method and the Monte Carlo method in the embodiment of the application is given, including the reflection and transmission coefficients, wherein, Figure 3 (a) represents the uncertainty evaluation results of port 1 reflection coefficient S 11 of the two methods; Figure 3(b) represents the uncertainty evaluation results of two-port transmission coefficient S 12 by two methods; Figure 3 (c) represents the uncertainty evaluation results of two-port transmission coefficient S 21 by two methods; Figure 3 (d) represents the uncertainty evaluation results of port 2 reflection coefficient S 22 by two methods; Experiments show that the proposed FFEM method replaces random sampling by analytical solution, and the quantization results of the scattering parameter uncertainty evaluation are highly consistent with the Monte Carlo method results, verifying the effectiveness thereof; The scattering parameter uncertainty matrix obtained through step S4 is extracted from the non-diagonal elements to obtain the covariance values between different S parameter real and imaginary parts, the characteristics of which can be observed with respect to frequency variation, and meanwhile, each covariance value can be divided by the standard deviation product of the corresponding scattering parameter real and imaginary parts to calculate the Pearson correlation coefficient, and then the correlation between different S parameter real and imaginary parts can be quantitatively analyzed; As shown in Figures 4-5 , the covariance and Pearson correlation coefficient between different scattering parameter real and imaginary parts in the embodiment of the present application are given, and the results show that: 1) except that the real part covariance of S 11 and S 22 is always positive, the rest of the covariance fluctuates around zero, which indicates that there are only two groups of continuous positive correlation in the entire frequency band, namely the real parts of S 11 and S 22 and the imaginary parts thereof; 2) only the Pearson coefficient of S 11 and S 22 real parts is close to 1, showing strong linear positive correlation; 3) the coefficient between the real part of S 12 and the real and imaginary parts of S 21 fluctuates between 1 and -1, showing alternating positive and negative correlation with respect to frequency; 4) the coefficient signs between the rest of the parameters are indefinite, but are close to 0, indicating weak linear correlation.

[0026] The above only describes the preferred embodiments of the present application, and is not intended to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A fast fully-analytical method for scatter parameter uncertainty evaluation, characterized in that, The method comprises the following steps: S1, obtaining noise data of the measurement receiver and the reference receiver at each port, quantifying the influence factors of the non-ideal calibration standard to obtain calibration standard parameters; S2, constructing a first-order measurement Jacobian matrix, inputting the noise data to calculate the uncertainty of the calibration standard measurement value of each port and the uncertainty of the measurement value of the measured object, constructing a first-order theoretical Jacobian matrix, and inputting the calibration standard parameters to calculate the uncertainty of the single-port calibration standard theoretical value; S3, calculating the error term of each port according to the scattering parameter measurement value and the scattering parameter theoretical value of each port calibration standard, constructing a first-order error Jacobian matrix by taking the partial derivative of the scattering parameter measurement value and the scattering parameter theoretical value of all calibration standards with respect to the error term of each port, and inputting the calibration standard measurement value uncertainty and the calibration standard theoretical value uncertainty to obtain the error term uncertainty matrix; S4, constructing a first-order scattering parameter Jacobian matrix by taking the partial derivative of the calibrated scattering parameter of the measured object with respect to the scattering parameter measurement value of the measured object and the error term, propagating the measured object measurement value uncertainty and the error term uncertainty to the calibrated scattering parameter of the measured object through the first-order scattering parameter Jacobian matrix, and solving by using the perturbation method combined with the Cauchy-Riemann equation to obtain the scattering parameter uncertainty matrix of the measured object; S5, calculating the covariance matrix and Pearson correlation coefficient between the real part and the imaginary part of different scattering parameters of the measured object according to the scattering parameter uncertainty matrix of the measured object; The ports include single ports and double ports; the single ports include port 1 and port 2; the port 1 contains a measurement receiver 1 and a reference receiver 1; the port 2 contains a measurement receiver 2 and a reference receiver 2; The calibration standards include single-port calibration standards and double-port calibration standards; the single-port calibration standards are required on the port 1 and the port 2, and include Short, Open and Load; The double-port calibration standard is connected between the port 1 and the port 2, and specifically is Thru; The calibration standard parameters include theoretical scattering parameters, amplitude uncertainty and phase uncertainty; The diagonal elements of the error uncertainty matrix are the variances of the error terms, and the non-diagonal elements are the covariances between different error terms; The diagonal elements of the scattering parameter uncertainty matrix of the measured object are the variances of the real and imaginary parts of the scattering parameters of the measured object, and the non-diagonal elements are the covariances between the real and imaginary parts of different scattering parameters of the measured object.

2. The method of fast full analytical evaluation of scattering parameter uncertainty according to claim 1, characterized in that, The method for calculating the uncertainty of the measurement value of each port calibration standard comprises: According to the single-port calibration standard scattering parameter measurement value, the measurement receiver received level and the reference receiver received level, a single-port first-order measurement Jacobian matrix is constructed, and the expression is: ； in For single-port calibration standards Down port The first-order measurement Jacobian matrix of the port Internally includes a measurement receiver and reference receiver , , Indicates the index of the measurement receiver. It also represents the port index and the reference receiver index. For calibration standards Lower measurement receiver From port Received voltage level For calibration standards Down port Internal reference receiver Received voltage level For calibration standards Down port The scattering parameter measurements are obtained from the measurement receiver. Received level With reference receiver Received level The ratio is determined. Indicates the real part For the real part The partial derivative, Indicates the imaginary part For the real part The partial derivative, Indicates the real part imaginary part The partial derivative, Indicates the imaginary part imaginary part The partial derivative; According to the single-port first-order measurement Jacobian matrix, the noise data is inputted to calculate the single-port calibration standard measurement value uncertainty, and the expression is: ； wherein is the calibration standard lower port measurement value uncertainty, is the noise data variance, , is the calibration standard lower connection port noise data real and imaginary parts of the measurement receiver at time , is the calibration standard lower connection port noise data real and imaginary parts of the reference receiver at time is the transpose of the single-port first-order measurement Jacobian matrix; According to the double-port calibration standard scattering parameter measurement value, the measurement receiver received level and the reference receiver received level, a double-port first-order measurement Jacobian matrix is constructed, and the expression is: ； wherein measuring receivers under a two-port Thru calibration standard connection port the first order measurement Jacobian matrix, measuring receivers under a Thru calibration standard from port received level, port internal reference receiver received level, measuring receivers under a Thru calibration standard connection port scatter parameter measurements of the connection port, by the measuring receiver received level with the reference receiver received level determined as a ratio; According to the double-port first-order measurement Jacobian matrix, the noise data is inputted to calculate the double-port calibration standard measurement value uncertainty, and the expression is: ； ； wherein is the measurement uncertainty of the receiver under the two-port Thru calibration standard, is the measurement uncertainty of the receiver under the two-port Thru calibration standard, is the measurement uncertainty of the receiver under the two-port Thru calibration standard, is the measurement uncertainty of the receiver under the two-port Thru calibration standard, , is the measurement uncertainty of the receiver under the two-port Thru calibration standard, is the measurement uncertainty of the receiver under the two-port Thru calibration standard, is the measurement uncertainty of the receiver under the two-port Thru calibration standard, , is the measurement uncertainty of the receiver under the two-port Thru calibration standard, is the measurement uncertainty of the receiver under the two-port Thru calibration standard, is the measurement uncertainty of the receiver under the two-port Thru calibration standard, is the transpose of the two-port first-order measurement Jacobian matrix .

3. The method of fast full analytical evaluation of scattering parameter uncertainty according to claim 1, characterized in that, The method for calculating the uncertainty of the single-port calibration standard theoretical value comprises: A first-order theoretical Jacobian matrix is constructed according to the calibration standard parameters, and single-port calibration standard theoretical value uncertainty is calculated by inputting the calibration standard parameters, and the expression is as follows: ； ； in For single-port calibration standard The theoretical uncertainty, , For single-port calibration standard Next-order theoretical Jacobian matrix, A first-order theoretical Jacobian matrix The transpose of the matrix, , , , , For single-port calibration standards The theoretical scattering parameters, amplitude, phase, amplitude uncertainty, and phase uncertainty are given below. The real part of the theoretical scattering parameter Partial derivative with respect to amplitude or phase.

4. The method of fast full analytical evaluation of scattering parameter uncertainty according to claim 1, wherein, The method for calculating single-port calibration standard theoretical value uncertainty comprises: calculating error terms for each port according to the scattering parameter measurement values and the scattering parameter theoretical values of the calibration standard of each port; the error terms include single-port error terms , two-port error terms , , is a category index; A first-order error Jacobian matrix is constructed by taking partial derivatives of each port error term on all calibration standard scattering parameter measurement values and scattering parameter theoretical values, and the expression is as follows: ； where is the first order error Jacobian matrix of size 20 x 26, denotes the real and imaginary parts of the port 1 error term denotes the real and imaginary parts of the port 1 scattering parameter measurement denotes the real and imaginary parts of the port 1 scattering parameter measurement denotes the real and imaginary parts of the two-port error term denotes the real and imaginary parts of the two-port scattering parameter measurement denotes the real and imaginary parts of the two-port scattering parameter measurement denotes the real and imaginary parts of the two-port error term denotes the real and imaginary parts of the two-port scattering parameter measurement denotes the real and imaginary parts of the two-port scattering parameter measurement denotes the real and imaginary parts of the two-port error term denotes the real and imaginary parts of the two-port scattering parameter measurement denotes the real and imaginary parts of the two-port scattering parameter measurement denotes the real and imaginary parts of the port 2 error term denotes the real and imaginary parts of the port 2 scattering parameter measurement denotes the real and imaginary parts of the port 2 scattering parameter measurement denotes the real and imaginary parts of the port 1 error term denotes the real and imaginary parts of the scattering parameter theoretical value denotes the real and imaginary parts of the scattering parameter theoretical value denotes the real and imaginary parts of the two-port error term denotes the real and imaginary parts of the scattering parameter theoretical value denotes the real and imaginary parts of the scattering parameter theoretical value denotes the real and imaginary parts of the port 2 error term denotes the real and imaginary parts of the scattering parameter theoretical value denotes the real and imaginary parts of the scattering parameter theoretical value Error term uncertainty matrix is obtained by inputting calibration standard measurement value uncertainty and calibration standard theoretical value uncertainty, and the expression is as follows: ； wherein is the error term uncertainty matrix, is the first order error Jacobian matrix is the transpose matrix.

5. The method of fast full analytical evaluation of scattering parameter uncertainty according to claim 1, wherein, The method for obtaining the scattering parameter uncertainty matrix of the measured object comprises: Acquisition of a measurement receiver of a piece under test Connection port Scattering parameter measurement value , Indicates the measurement receiver index, Indicates the port index and the reference receiver index at the same time, and the correction coefficient is calculated in combination with the error term, and the expression is: ； wherein is a correction factor, , , is a port 1 error term, , , is a port 2 error term, , , , is a two-port error term, wherein , are forward and reverse crosstalk errors, which can be measured directly, , are forward and reverse source matching errors, , are forward and reverse directional errors, , are forward and reverse reflection tracking errors, , are forward and reverse load matching errors, , are forward and reverse transmission tracking errors; calculating correction coefficients from the error term and the error term to the measured value of the scatter parameter of the object under test correcting the measured value of the scatter parameter of the object under test using the calibration value a first-order Jacobian matrix of the scatter parameter is constructed by taking the partial derivative of the calibrated value of the scatter parameter of the object under test with respect to the measured value of the scatter parameter of the object under test and the error term, expressed as: ； wherein is the first order scattering parameter Jacobian matrix, of size 8 x 20, is the calibrated DUT scattering parameter value is the real and imaginary parts of the DUT scattering parameter measurement value is the partial derivative matrix of the real and imaginary parts of the DUT scattering parameter measurement value is the calibrated DUT scattering parameter value is the partial derivative matrix of the real and imaginary parts of the single port error term is the partial derivative matrix of the real and imaginary parts of the single port error term is the calibrated DUT scattering parameter value is the partial derivative matrix of the real and imaginary parts of the two port error term is the partial derivative matrix of the real and imaginary parts of the two port error term The measured value uncertainty of the object under test and the error term uncertainty The scattering parameter uncertainty matrix of the object under test is obtained by propagating the calibrated scattering parameters of the object under test through the first-order scattering parameter Jacobian matrix, using the perturbation method and combining the Cauchy-Riemann equation, and the expression is: ； wherein is the uncertainty matrix of the scatter parameters of the object under test, is the Jacobian matrix of the first order scatter parameters is the transpose matrix of the Jacobian matrix.

6. The method of fast full analytical evaluation of scattering parameter uncertainty according to claim 1, characterized in that: The covariance matrix and the Pearson correlation coefficient are used for quantitatively analyzing the strength and direction of linear correlation between different scattering parameter real and imaginary parts.

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