On-chip S parameter measurement uncertainty evaluation method based on covariance matrix

Abstract

The invention relates to an on-chip S parameter measurement uncertainty evaluation method based on a covariance matrix. The method comprises the following steps: constructing a calibration part uncertainty covariance matrix; obtaining a sensitivity coefficient of the SOLT calibration error model to the calibration piece based on a function relationship between the forward error model and the backward error model obtained through SOLT calibration and the true value of the calibration piece; constructing a Jacobian matrix based on the sensitivity coefficient, and transmitting the uncertainty from a calibration part uncertainty covariance matrix to an error model coefficient; constructing a Jacobian matrix according to the function relationship between the S parameter and the error model coefficient, and transmitting the uncertainty from the error model coefficient to the S parameter; transmitting the uncertainty of the S parameter to the amplitude and the phase to obtain a covariance matrix of the amplitude and phase information of the S parameter as B-class uncertainty; and calculating the synthesis uncertainty according to the A-class uncertainty and the B-class uncertainty. The method has the beneficial effect that the accuracy of the uncertainty evaluation result is improved.

Description

Technical Field

[0001] The invention relates to the technical field of electronic measurement, and in particular to an on-chip S parameter measurement uncertainty evaluation method based on a covariance matrix. Background Art

[0002] Scattering parameters (S parameters) are widely used in microwave signal transmission, and the most commonly used instrument for measuring S parameters is the Vector Network Analyzer (VNA). As the integration of chips increases, the size of the devices under test becomes smaller and smaller, and coaxial measurement connectors can no longer meet the chip measurement requirements.

[0003] Domestic and foreign experts have conducted a lot of research on VNA measurement uncertainty. Most methods directly analyze the measurement results of S parameters, that is, Class A uncertainty, without fully considering the impact of the instrument itself on the measurement uncertainty. The Class B uncertainty of the system itself is difficult to evaluate because of its complex influencing factors and the many measurement intermediate quantities in the equipment that cannot be measured, and is usually ignored. Moreover, most of the research is in the field of coaxial measurement, and there is little research on on-chip measurement uncertainty. Summary of the invention

[0004] Technical issues to be solved

[0005] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides an on-chip S parameter measurement uncertainty assessment method based on the covariance matrix, which solves the technical problem that Class B uncertainty is difficult to assess, resulting in inaccurate uncertainty assessment results.

[0006] Technical Solution

[0007] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0008] In a first aspect, the present invention provides an on-chip S-parameter measurement uncertainty assessment method based on a covariance matrix, comprising: obtaining a Class A uncertainty obtained by performing multiple measurements on a calibration piece;

[0009] Construct the uncertainty covariance matrix of the calibration parts;

[0010] The forward error model and the backward error model are obtained based on SOLT calibration;

[0011] The sensitivity coefficient of the SOLT calibration error model to the calibration piece is obtained according to the functional relationship between the forward error model coefficient and the true value of the calibration piece and the functional relationship between the backward error model coefficient and the true value of the calibration piece;

[0012] Constructing a Jacobian matrix based on the sensitivity coefficients to transfer the uncertainty from the calibration component uncertainty covariance matrix to the error model coefficients, and obtaining the covariance matrix of the error model coefficients;

[0013] According to the functional relationship between S parameters and error model coefficients, a Jacobian matrix is ​​constructed to transfer the uncertainty from the error model coefficients to the S parameters, and the covariance matrix of the real and imaginary parts of the S parameters is obtained;

[0014] The uncertainty of the S parameter is transferred to the amplitude and phase, and the covariance matrix of the S parameter amplitude and phase information is obtained as the type B uncertainty;

[0015] Calculate the combined uncertainty based on Type A uncertainty and Type B uncertainty.

[0016] Optionally, the calibration uncertainty covariance matrix is ​​as follows:

[0017]

[0018] Among them, S is a short-circuit component, O is an open-circuit component, L is a load component, and T is a through component.

[0019] Optionally, the functional relationship between the forward error model coefficient and the true value of the calibration piece is as follows:

[0020]

[0021] The functional relationship between the backward error model coefficient and the true value of the calibration piece is as follows:

[0022]

[0023] Among them, (e 00 , e′ 33 ) is the directional error, (e 10 e 01 , e′ 32 e′ 23 ) is the reflection scanning error, (e 11 , e′ 22 ) is the source matching error, (e 22 , e′ 11 ) is the load matching error, (e 10 e 32 , e′ 23 e′ 01 ) is the transmission scanning error, (e 30 , e′ 03 ) is the response isolation error, S11 is the reflection coefficient of port 1, S22 is the reflection coefficient of port 2, and S21 and S12 are the positive and negative transmission coefficients.

[0024] Optionally, the Jacobian matrix constructed based on the sensitivity coefficients is as follows:

[0025]

[0026] Optionally, the functional relationship between the S parameters and the error model coefficients is as follows:

[0027]

[0028] Where A=(S11 M -e 00 ) / e 10 e 01 , B=S21 M / e 10 e 32 , C=S12 M / e′ 23 e′ 01 , D=(S22 M -e′ 33 ) / e′ 32 e′ 23 , E=(1+A·e 11 )·(1+D·e′ 22 )-B·C·e 22 ·e′ 11 , S11 M -S22 M These are the measured values ​​of the four S parameters of the DUT before VNA calibration.

[0029] Optionally, the Jacobian matrix constructed based on the functional relationship between the S parameters and the error model coefficients is as follows:

[0030]

[0031] Optionally, the covariance matrix of the real and imaginary parts of the S parameters is as follows:

[0032]

[0033] In a second aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the program is executed, the on-chip S parameter measurement uncertainty assessment method based on the covariance matrix as described in any one of the above-mentioned first aspects is implemented.

[0034] In a third aspect, the present invention provides a storage device comprising a storage medium and a processor, wherein the storage medium stores a computer program, and when the program is executed by the processor, the on-chip S parameter measurement uncertainty assessment method based on the covariance matrix as described in any one of the first aspects above is implemented.

[0035] Beneficial Effects

[0036] The beneficial effects of the present invention are as follows: the uncertainty assessment method of on-chip S parameter measurement based on the covariance matrix of the present invention is finally transferred to the uncertainty of on-chip S parameter measurement by the uncertainty of the on-chip calibration part through the calibration error model. The measurement object of the present application is the S parameter uncertainty of a section of transmission line calibration part on the standard substrate of the calibration part. After the VNA is calibrated by the SOLT calibration method, the Class B uncertainty assessment is performed on the transmission line measurement result each time. In order to eliminate the influence of human operation factors, multiple measurements are performed on the same measured part to assess its Class A uncertainty, and finally the combined uncertainty is calculated to improve the accuracy of the uncertainty assessment result. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 An equivalent signal flow diagram of a 12-term error model for SOLT calibration provided by an embodiment of the present invention;

[0038] Figure 2 A schematic diagram of a VNA used in a measurement system provided in an embodiment of the present invention;

[0039] Figure 3 A schematic diagram of a calibration component used in a measurement system provided in an embodiment of the present invention;

[0040] Figure 4 A schematic diagram of a probe used in a measurement system provided in an embodiment of the present invention;

[0041] Figure 5 A diagram showing the S parameter measurement results of a transmission line standard component under test provided by an embodiment of the present invention;

[0042] Figure 6 The relative uncertainty diagram of the S11 parameter amplitude and phase of the transmission line standard component under test provided by the embodiment of the present invention;

[0043] Figure 7 This is a relative uncertainty diagram of the amplitude and phase of the parameters of the S21 transmission line standard component under test provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation modes in conjunction with the accompanying drawings.

[0045] Domestic and foreign experts have conducted a lot of research on the measurement uncertainty of VNA. Most methods directly analyze the measurement results of S parameters, that is, Class A uncertainty, and do not fully consider the impact of the instrument itself on the measurement uncertainty. The Class B uncertainty of the system itself is difficult to evaluate because of its complex influencing factors and the inability to measure many intermediate quantities in the equipment, which is usually ignored. Moreover, most of the research is in the field of coaxial measurement, and there is little research on on-chip measurement uncertainty. In order to fully consider the correlation between the various measurement frequencies and variables of VNA and facilitate the transfer of the uncertainty of S parameters to other physical parameters, we will use the covariance matrix to evaluate the measurement uncertainty of VNA.

[0046] As the most scientific method for evaluating uncertainty, the covariance matrix can fully consider the correlation between random variables, which can facilitate the coordinated transfer of uncertainty between multiple variables such as S parameters. The covariance matrix is ​​a semi-positive definite matrix, the elements on the diagonal are the variance of each random variable, and the elements on the off-diagonal are the covariance between random variables. When performing matrix operations for uncertainty transfer, the covariance will affect the variance, thus affecting the uncertainty assessment results, that is, reflecting the correlation between variables.

[0047] When using the covariance matrix to evaluate multivariate Type A uncertainty, the covariance of non-diagonal elements can effectively retain the correlation between variables; when evaluating Type B uncertainty, due to the complexity of the sources of measurement system uncertainty, multiple transfers are often required to trace back to the final source, and covariance matrix operations can also provide convenience. In the transfer process, the correlation between variables in the previous covariance matrix will affect the uncertainty of the next covariance matrix. This evaluation method can obtain more scientific results.

[0048] The covariance matrix is ​​a semi-positive definite matrix. The covariance matrix constructed for d random variables is shown in formula (1): the elements on the diagonal are the variance of each random variable, and the elements on the off-diagonal are the covariance of the corresponding random variables. In this way, the influence of correlation can be reflected when performing uncertainty transfer operations.

[0049]

[0050] Assume that there is a functional relationship Y=F(X) between the random variable X (mean is X0) and the random variable Y. Assume that F is continuously differentiable near X0. If F(X) is expanded by the first order Taylor at X0, we can get:

[0051] Y=F(X)≈F(X0)+J·(X-X0)+L(2)

[0052] In formula (2), J is the Jacobian matrix, where each element J ijIt represents the sensitivity coefficient of the i-th variable in Y to the j-th variable in X. L is the high-order remainder of Taylor expansion. It only needs to be considered when the first-order Taylor expansion cannot meet the requirements. In most cases, it can be ignored. J ij The calculation method of is shown in formula (3):

[0053]

[0054] Through the Jacobian matrix, the covariance matrix of the random variable X can be transferred to the random variable Y, as shown in formula (4):

[0055] ∑Y=E[(Y-Y0)(Y-Y0) * ]≈E[J(X-X0)(J(X-X0)) * ]=J·∑X·J * (4)

[0056] When evaluating measurement uncertainty, both Type A and Type B uncertainties should be considered. Type A uncertainty is to find the covariance matrix of K measurement results to obtain ∑r; Type B uncertainty is to construct a covariance matrix ∑S for the measurement system of each measurement. k , to describe the uncertainty of the measurement, which involves a complex uncertainty transfer relationship. After evaluating the uncertainty of type A and type B respectively, the combined uncertainty can be calculated according to formula (5). It can be seen that as the number of measurements K increases, the uncertainty of type A will gradually decrease, while the uncertainty of type B will not change significantly, that is, in the combined uncertainty, the uncertainty of type B will account for the main component.

[0057]

[0058] On-chip measurement configures a traditional VNA with an on-chip probe station, that is, the VNA coaxial measurement port is connected to the probe, and the chip is tested under microscope magnification. SOLT is a commonly used on-chip measurement calibration algorithm, based on four completely known calibration parts, and after calibration parts de-embedding calibration, that is, removing the error network between the VNA test port and the probe tip measurement plane, 12 error model coefficients are obtained. Its equivalent signal flow diagram is as follows Figure 1 As shown, usually, the two responses isolate the error term (e 30 , e′ 03 ) can be ignored, and the 12-item error model is simplified to 10 items.

[0059] In order to better understand the above technical solution, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a clearer and more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0060] In a first aspect, this embodiment provides an on-chip S parameter measurement uncertainty assessment method based on a covariance matrix, comprising:

[0061] Obtain the Type A uncertainty obtained by making multiple measurements of the calibration component;

[0062] Construct the uncertainty covariance matrix of the calibration parts;

[0063] Based on SOLT calibration, the antecedent error model and the posterior error model are obtained;

[0064] The sensitivity coefficient of the SOLT calibration error model to the calibration piece is obtained according to the functional relationship between the forward error model coefficient and the true value of the calibration piece and the functional relationship between the backward error model coefficient and the true value of the calibration piece;

[0065] Constructing a Jacobian matrix based on the sensitivity coefficients to transfer the uncertainty from the calibration component uncertainty covariance matrix to the error model coefficients, and obtaining the covariance matrix of the error model coefficients;

[0066] According to the functional relationship between the S parameters and the error model coefficients, the Jacobian matrix is ​​constructed to transfer the uncertainty from the error model coefficients to the S parameters, and the covariance matrix of the real and imaginary parts of the S parameters is obtained;

[0067] The uncertainty of the S parameter is transferred to the amplitude and phase, and the covariance matrix of the S parameter amplitude and phase information is obtained as the type B uncertainty;

[0068] Calculate the combined uncertainty based on Type A uncertainty and Type B uncertainty.

[0069] Optionally, the calibration uncertainty covariance matrix is ​​as follows:

[0070]

[0071] Among them, S is a short-circuit component, O is an open-circuit component, L is a load component, and T is a through component.

[0072] Optionally, the functional relationship between the forward error model coefficient and the true value of the calibration piece is as follows:

[0073]

[0074] The functional relationship between the backward error model coefficient and the true value of the calibration piece is as follows:

[0075]

[0076] Among them, (e 00 , e′ 33 ) is the directional error, (e 10 e 01 , e′ 32 e′ 23 ) is the reflection scanning error, (e 11 , e′ 22 ) is the source matching error, (e 22 , e′ 11 ) is the load matching error, (e 10 e 32 , e′ 23 e′ 01 ) is the transmission scanning error, (e 30 , e′ 03 ) is the response isolation error, S11 is the reflection coefficient of port 1, S22 is the reflection coefficient of port 2, and S21 and S12 are the positive and negative transmission coefficients.

[0077] Optionally, the Jacobian matrix constructed based on the sensitivity coefficients is as follows:

[0078]

[0079] Optionally, the functional relationship between the S parameters and the error model coefficients is as follows:

[0080]

[0081] Where A=(S11 M -e 00 ) / e 10 e 01 , B=S21 M / e 10 e 32 , C=S12 M / e′ 23 e′ 01 , D=(S22 M -e′ 33 ) / e′ 33 e′ 23 , E=(1+A·e 11 )·(1+D·e′ 23 )-B·C·e 22 ·e′ 11 , S11 M -S22 M These are the measured values ​​of the four S parameters of the DUT before VNA calibration.

[0082] Optionally, the Jacobian matrix constructed based on the functional relationship between the S parameters and the error model coefficients is as follows:

[0083]

[0084] Optionally, the covariance matrix of the real and imaginary parts of the S parameters is as follows:

[0085]

[0086] In the S parameter measurement, the dual-port measurement measures four S parameters simultaneously, including the reflection coefficient S11 of port 1, the reflection coefficient S22 of port 2, and the positive and negative transmission coefficients S21 and S12 (for transmission lines, it is believed that the larger the transmission coefficient, the better the transmission effect, and the smaller the reflection coefficient, that is, the smaller the loss, the better the transmission performance). The final result is the S parameter uncertainty covariance matrix:

[0087]

[0088] In this covariance matrix, the main diagonal stores the variance of the real and imaginary parts of the parameters S11, S12, S21, and S22 from top to bottom, and the non-diagonal is the covariance. The four calibration components are Short (S), Open (O), Thru (T), and Load (L). re is the real part and im is the imaginary part.

[0089] When using VNA to measure S parameters, there is an error network between the actual measurement plane and the test port. For on-chip measurements, it is caused by probes, VNA connection lines, etc. Calibration is required before use, that is, to obtain the error model coefficients of the corrected error network. During the SOLT calibration process, a total of 12 error model coefficients are obtained for the two error networks before and after, which are directional error (e 00 , e′ 33 ), reflection scanning error (e 10 e 01 , e′ 32 e′ 23 ), source matching error (e 11 , e′ 22 ), load matching error (e 22 , e′ 11 ), transmission tracking error (e 10 e 32 , e′ 23 e′ 01 ) and response isolation error (e 30 , e′ 03), usually the two response isolation errors can be ignored. According to the functional relationship between the remaining 10 error model coefficients and the calibration parts, the VNA will calculate the corresponding error model coefficients according to the calibration parts values ​​measured during the calibration process, that is, meet the VNA calibration requirements (when measuring, the VNA will calculate the actual value based on the measured value of the device under test and the error model coefficients). Therefore, when evaluating the uncertainty, the uncertainty will also be transferred from the calibration parts to the error model coefficients, and then to the S parameter measurement value of the device under test.

[0090] The following is a specific example to further illustrate an on-chip S parameter measurement uncertainty assessment method based on a covariance matrix of the present application:

[0091] Build a VNA-based on-chip measurement system. The VNA used is E8361A. Figure 2 As shown, the FORMFACTOR on-chip calibration component 101-190C is as follows Figure 3 As shown in the figure and the InfinityProbe probe (GSG-150) of FORMFACTOR Figure 4 shown.

[0092] The nominal circuit parameters of the short-circuit and open-circuit components of the calibration components used in the InfinityGSG-150 probe measurement are shown in Table 1:

[0093] Table 1

[0094] C-Open(InAir) L-Short <![CDATA[-6.7·10 -15 F]]> <![CDATA[8.2·10 -12 H]]>

[0095] To evaluate the Type B uncertainty of S-parameter measurement, it is necessary to trace the source of its measurement uncertainty, that is, the process from the uncertainty of the calibration component to the uncertainty of the error model coefficient and then to the uncertainty of the S-parameter measurement value.

[0096] Compared with coaxial calibration parts, on-chip calibration parts are more difficult to process, and the loss of calibration parts for each calibration is much greater than that of coaxial calibration parts. There is no nominal uncertainty when leaving the factory, so calibration part manufacturers integrate multiple calibration parts into a standard substrate. On a standard substrate, there are multiple identical open circuit, short circuit, load, through and transmission line calibration parts. In this embodiment, a calibrated VNA is used to measure the four calibration parts separately. If the true value cannot be calculated, the average of multiple measurement results is used as the true value of the calibration part; the calibration part is measured multiple times, and its Class A uncertainty is calculated as the input uncertainty for uncertainty transfer in subsequent measurement processes; if the nominal uncertainty of the calibration part can be accurately known, the uncertainty assessment result will be more scientific, and the nominal uncertainty of the calibration part will eventually be traced back to its length parameter.

[0097] The short-circuit equivalent circuit model is characterized by inductance characteristics, as shown in equation (6), and its equivalent inductance parameter L is given by the standard substrate manufacturer.

[0098]

[0099] In formula (6), f is the frequency; Z0 is the equivalent impedance, usually 50Ω.

[0100] Taking the short-circuit component as an example, when constructing the uncertainty covariance matrix of the short-circuit component, in order to facilitate the subsequent transmission of uncertainty, the complex variable should be converted into two real variables, the real part and the imaginary part, for storage and calculation. Because the two probe measurement ports need to be calibrated separately during calibration, there is ∑S11 at each frequency point. S ,∑S22 S The uncertainty matrix ∑Γ of the short circuit component can be obtained by concatenating the two covariance matrices into block diagonal matrices. S :

[0101]

[0102] There are two methods for on-chip open circuit calibration. You can use the open circuit components on the standard substrate for calibration, or you can lift the probe and suspend it in the air for open circuit calibration. The method used in this embodiment is to lift the probe and suspend it in the air. In this calibration method, the true value of the open circuit component can be calculated from the equivalent capacitance C of the probe suspended in the air given by the standard substrate manufacturer. Its equivalent circuit model is shown in formula (8), and the uncertainty of the open circuit calibration can be ignored.

[0103]

[0104] For load components and through components, this embodiment uses a calibrated VNA to perform multiple measurements on the calibration components to obtain an average value as the calibration component true value. Similarly, for open circuit components and short circuit components, although there are nominal parameters and true value calculation formulas, the wear of the on-chip calibration components will affect the actual calibration results. If there is a large error between the measurement results of the calibration components by the calibrated VNA and the calibration component true value calculation results, the measurement results of the calibration components should be used as the standard, or calibration components with less wear should be replaced for calibration.

[0105] The uncertainty matrices of the four calibration components are concatenated as block diagonal matrices (it is assumed that the uncertainties of each calibration component are independent of each other and have no correlation), and the input uncertainty matrix ∑Γ of the overall calibration component can be obtained. SS , among the four calibration parts, the through part is a two-port calibration part, namely ∑Γ T is an 8x8 covariance matrix, and the other three calibration pieces are all 4x4 covariance matrices. Finally, we get:

[0106]

[0107] The 10 error models obtained during SOLT calibration can be divided into a forward error model and a backward error model. The forward error model coefficients have the following functional relationship with the true value of the calibration piece:

[0108]

[0109] Similarly, the functional relationship between the backward error model and the true value of the calibration piece is:

[0110]

[0111] Combine the above 10 formulas to solve the sensitivity coefficient of the SOLT calibration error model to the calibration part (use the real part and imaginary part of each error term to calculate the partial derivative of the real part and imaginary part of each calibration part respectively), construct the Jacobian matrix, and transfer the uncertainty from the calibration part to the error model coefficient. The Jacobian matrix is ​​shown in formula (12):

[0112]

[0113] ∑EM 20×20 =J EM *∑Γ SS *J′ EM (13)

[0114] According to the functional relationship between S parameters and error model coefficients, the Jacobian matrix is ​​constructed to transfer the uncertainty from the error model to the S parameters. The functional relationship is shown in formula (14):

[0115]

[0116] In formula (14), A=(S11 M -e 00 ) / e 10 e 01 ,B=S21 M / e 10 e 32 ,C=S12 M / e′ 23 e′ 01 ,D=(S22 M -e′ 33 ) / e′ 32 e′ 23 ,E=(1+A·e 11 )·(1+D·e′ 22 )-B·C·e 22 ·e′ 11 , S11 M -S22 M These are the measured values ​​of the four S parameters of the DUT before VNA calibration.

[0117] By analogy with equations (12) and (13), the Jacobian matrix of the four S parameters to the error model coefficients can be constructed, as shown in equation (15). Then, the uncertainty can be transferred from the error model coefficients to the S parameters by equation (16).

[0118]

[0119] ∑S 8×8 =J S *∑EM*J′ S (16)

[0120] ∑S is an 8x8 covariance matrix. The main diagonal stores the uncertainty of the real and imaginary parts of S11, S12, S21, and S22 in turn, and the off-diagonal elements are the covariances between the S parameter variables. In the process of uncertainty transfer calculation, the expression of real and imaginary parts is convenient for calculation, but in the actual evaluation of uncertainty, S parameters are usually expressed in amplitude and phase. Therefore, the uncertainty of S parameters needs to be transferred to its amplitude and phase, as shown in formula (17):

[0121]

[0122] According to the functional relationship between the amplitude, phase, real part and imaginary part in equation (16), by analogy with equations (16) and (17), the covariance matrix of the amplitude and phase information of the four S parameters can be obtained. The specific process is omitted here.

[0123] When evaluating the uncertainty of S parameters, the uncertainty of the calibration component will have a direct impact on the uncertainty of the measurement results. When evaluating the uncertainty, the present application will ignore the coupling effect between the probe tip and other adjacent metal areas introduced by the integration of the standard substrate, the electromagnetic effect of the standard substrate substrate, and other effects. During the probe measurement, factors such as contact position, angle, depth, and contact area are considered to be included in the Class A uncertainty assessment of multiple repeatable measurements.

[0124] The measurement object of this application is a transmission line calibration piece on the same standard substrate, and the measurement frequency band is equally spaced sampling within the range of 10MHz-67GHz. The S parameter measurement results are as follows: Figure 5 As shown, it can be seen that its transmission coefficient (S12, S21) is near 0dB, and the reflection coefficient (S11, S22) is below -20dB, and the overall performance is good.

[0125] The results of the synthetic uncertainty evaluation of transmission line standard components are as follows: Figure 6 and Figure 7As shown, only the uncertainty diagrams of S11 and S21 are given here, and the parameters of S12 and S22 are similar. It can be seen that the relative uncertainties of the overall amplitude and phase of the transmission coefficient S21 are within 5%; compared with S21, the uncertainty of the reflection coefficient S11 parameter is significantly larger, but it also basically meets the requirement of less than 5%. The amplitude uncertainty has some point uncertainties between 5% and 10% after 48GHz. This is probably because the amplitude measurement result of the S11 parameter of the transmission line standard is very small, and it is more sensitive to the uncertainty transfer algorithm, that is, the input uncertainty of the calibration component is slightly larger in the high frequency band. Compared with the transmission coefficient with a much larger measured value, the reflection coefficient amplitude uncertainty evaluation result is more affected. The overall uncertainty of this standard meets the requirement of less than 5%, and the performance is good.

[0126] In a second aspect, an embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the program is executed, the on-chip S parameter measurement uncertainty assessment method based on the covariance matrix as described in any one of the above-mentioned first aspects is implemented.

[0127] In a third aspect, an embodiment of the present invention provides a storage device, comprising a storage medium and a processor, wherein the storage medium stores a computer program, and when the program is executed by the processor, the on-chip S parameter measurement uncertainty assessment method based on the covariance matrix as described in any one of the first aspects above is implemented.

[0128] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0129] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include these modifications and variations.

[0130] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may alter, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A method for evaluating the uncertainty of on-chip S-parameter measurement based on a covariance matrix, characterized in that: include: Obtain the Type A uncertainty obtained by making multiple measurements of the calibration component; Construct the uncertainty covariance matrix of the calibration parts; Based on SOLT calibration, the antecedent error model and the posterior error model are obtained; The sensitivity coefficient of the SOLT calibration error model to the calibration piece is obtained according to the functional relationship between the forward error model coefficient and the true value of the calibration piece and the functional relationship between the backward error model coefficient and the true value of the calibration piece; Constructing a Jacobian matrix based on the sensitivity coefficients to transfer the uncertainty from the calibration component uncertainty covariance matrix to the error model coefficients, and obtaining the covariance matrix of the error model coefficients; According to the functional relationship between S parameters and error model coefficients, a Jacobian matrix is ​​constructed to transfer the uncertainty from the error model coefficients to the S parameters, and the covariance matrix of the real and imaginary parts of the S parameters is obtained; The uncertainty of the S parameter is transferred to the amplitude and phase, and the covariance matrix of the S parameter amplitude and phase information is obtained as the type B uncertainty; Calculate the combined uncertainty based on Type A uncertainty and Type B uncertainty.

2. A method for evaluating the uncertainty of S-parameter measurement on a chip based on a covariance matrix according to claim 1, characterized in that: The uncertainty covariance matrix of the calibration parts is as follows: Among them, S is a short-circuit component, O is an open-circuit component, L is a load component, and T is a through component.

3. A method for evaluating the uncertainty of S-parameter measurement on a chip based on a covariance matrix according to claim 2, characterized in that: The forward error model coefficients have a functional relationship with the true value of the calibration piece as follows: The functional relationship between the backward error model coefficient and the true value of the calibration piece is as follows: Among them, (e 00 , e ′ 33 ) is the directional error, (e 10 e 01 , e ′ 32 e ′ 23 ) is the reflection scanning error, (e 11 , e ′ 22 ) is the source matching error, (e 22 , e ′ 11 ) is the load matching error, (e 10 e 32 , e ′ 23 e ′ 01 ) is the transmission scanning error, (e 30 , e ′ 03 ) is the response isolation error, S11 is the reflection coefficient of port 1, S22 is the reflection coefficient of port 2, and S21 and S12 are the positive and negative transmission coefficients.

4. A method for evaluating the uncertainty of S-parameter measurement on a chip based on a covariance matrix according to claim 3, characterized in that: The Jacobian matrix constructed based on the sensitivity coefficients is as follows:

5. A method for evaluating the uncertainty of S-parameter measurement on a chip based on a covariance matrix according to claim 4, characterized in that: The functional relationship between S parameters and error model coefficients is as follows: Where A=(S11 M -e 00 ) / e 10 e 01 , B=S21 M / e 10 e 32 , C=S12 M / e ′ 23 e ′ 01 , D=(S22 M -e ′ 33 ) / e ′ 32 e ′ 23 , E=(1+A·e 11 )·(1+D·e ′ 22 )-B·C·e 22 ·e ′ 11 , S11 M -S22 M These are the measured values ​​of the four S parameters of the DUT before VNA calibration.

6. A method for evaluating the uncertainty of S-parameter measurement on a chip based on a covariance matrix according to claim 5, characterized in that: The Jacobian matrix constructed based on the functional relationship between the S parameters and the error model coefficients is as follows:

7. A method for evaluating the uncertainty of S-parameter measurement on a chip based on a covariance matrix according to claim 6, characterized in that: The covariance matrix of the real and imaginary parts of the S parameters is as follows:

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the on-chip S parameter measurement uncertainty assessment method based on the covariance matrix as described in any one of claims 1 to 7 is implemented.

9. A storage device comprising a storage medium and a processor, wherein the storage medium stores a computer program, wherein: When the processor executes the computer program, the on-chip S parameter measurement uncertainty assessment method based on the covariance matrix as described in any one of claims 1 to 7 is implemented.

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