Interpolation method for error terms in vector network analyzer

Abstract

The invention belongs to the technical field of electronic signal processing, and discloses an interpolation method for an error term in a vector network analyzer, which comprises the following steps: acquiring a reference frequency point corresponding to an interpolation frequency point, finding N points closest to the reference frequency point in the original frequency points, calling a fitting algorithm, fitting a circular curve through calculation, obtaining a circle center and a radius, and calculating the error term in the vector network analyzer according to the circle center and the radius. Calculating a phase relative to the circle center, performing non-folding and linear interpolation on the phase to obtain a phase of an interpolation frequency point, calculating a polar coordinate of an interpolation point according to the circle center, the radius and the phase, and then obtaining a complex value of the interpolation point. Multi-point circular interpolation is performed on the basis of three-point circular interpolation, limitation of phase change is optimized, interpolation accuracy is improved, calculation times of circular curve fitting and phase non-folding are reduced through a reference frequency point mode, calculation efficiency is improved, and in engineering application, the error term interpolation algorithm can be used for solving the problem of error term interpolation in the prior art. The method has a better error term interpolation effect and a faster operation speed.

Description

Technical Field

[0001] This application relates to the technical field of electronic signal processing, and more specifically, to an interpolation method for error terms in a vector network analyzer. Background Art

[0002] A vector network analyzer is a test device for electromagnetic wave energy, used to measure the scattering parameters of RF and microwave devices, cable lines, connectors, etc. In practical applications, due to the influence of various factors such as the measurement environment, device accuracy, and signal interference, there are often certain errors in the measurement results. To improve the accuracy and reliability of the measurement, it is usually necessary to calculate the relevant error terms through calibration and then use the error terms to correct the measured values.

[0003] The interpolation method for error terms mainly performs mathematical processing on the calculated error terms, uses the known frequency points and interpolation algorithms to estimate the error values at unknown frequency points, and corrects the measurement results accordingly.

[0004] The old HP-8510A vector network analyzer would directly turn off the calibration when changing the frequency point, and the interpolation function for error terms did not appear until after the HP-8753A. Currently, there are various algorithms for error term interpolation, including interpolating the real and imaginary parts of complex numbers separately, using the Lagrange interpolation algorithm or cubic spline interpolation algorithm for amplitude and phase respectively, and using the three-point circular interpolation algorithm.

[0005] Among them, the algorithm for interpolating the real and imaginary parts of complex numbers separately has less computational complexity and a simple principle, but the result after error term interpolation using this algorithm has a large difference from the actual measurement data, and can only fit the change trend of the error terms.

[0006] Using the Lagrange interpolation algorithm or cubic spline interpolation algorithm for amplitude and phase respectively has a better interpolation effect for error terms such as transmission tracking and reflection tracking, but has a poor interpolation effect for error terms such as matching error terms whose response changes rapidly with frequency.

[0007] Currently, the three-point circular interpolation algorithm can interpolate error terms well when the phase change of the error terms is small, but when the phase change is large, the interpolation effect for amplitude and phase is not ideal, and this algorithm faces the problem of large computational complexity. Summary of the Invention

[0008] To solve the above problems, this application provides an interpolation method for error terms in a vector network analyzer.

[0009] The interpolation method for error terms in a vector network analyzer provided by this application adopts the following technical solutions:

[0010] An interpolation method for error terms in a vector network analyzer mainly includes the following steps:

[0011] Step 1: Obtain the reference frequency points corresponding to the interpolation frequency points, and find the N closest points (the value of N can be set) to the reference frequency points in the original frequency point array f_raw;

[0012] Step 2: Call the fitting algorithm. The N points are calculated and fitted to a circular curve to obtain the center and radius;

[0013] Step 3: Calculate the phases of the N points relative to the center of the circle and unfold the phases;

[0014] Step 4: Linearly interpolate the phases of the interpolation frequency points;

[0015] Step 5: Calculate the polar coordinates of the interpolation points based on the center of the circle, radius, and phases, and then obtain the complex values of the interpolation points;

[0016] Further, Step 1 is detailed as follows:

[0017] In Step 1, obtaining the reference frequency points corresponding to the interpolation frequency points and finding the N closest points to the reference frequency points in the original frequency points includes:

[0018] For each interpolation frequency point, its range is within the range of the original frequency points;

[0019] Set the reference frequency point f_ref(i) of the i-th interpolation frequency point f_interp(i) as the first original frequency point f_raw(idx) that is greater than or equal to the interpolation frequency point f_interp(i), where idx represents the serial number of the original frequency point f_raw(idx) in the original frequency point array f_raw;

[0020] Then select the N closest points to the reference frequency point in the original frequency array f_raw.

[0021] Taking N as 3 as an example: The selected points are f_raw(idx - 1), f_raw(idx), and f_raw(idx + 1).

[0022] Further, Step 2 is detailed as follows:

[0023] When i is 1 or i > 1 and the reference frequency point f_ref(i) of the current interpolation frequency point is not equal to the previous reference frequency point f_ref(i - 1), fit the selected N points to a circular curve to obtain the coordinates (xc, yc) of the center of the circle in polar coordinates and the radius R. The calculation formulas for fitting the N points to a circular curve and obtaining the center and radius are as follows:

[0024]

[0025] Q = A / D;

[0026] xc = Q(1);

[0027] yc = Q(2);

[0028]

[0029] where A is a 3×3 matrix, D is a 3×1 matrix, Q is a 3×1 matrix, N is the number of points taken for the calculation, x i is the real part of the data point, y i is the imaginary part of the data point, and Q(1), Q(2), Q(3) are the 1st, 2nd, and 3rd elements of the matrix respectively.

[0030] Further, step 3 is detailed as follows:

[0031] After obtaining the coordinates (xc, yc) of the center of the circle in polar coordinates, calculate the phase thetaC of N points relative to the center of the circle. The calculation formula is as follows:

[0032] thetaC i = tan -1 ((y i - yc) / (x i - xc));

[0033] For the calculated phase thetaC, its phase value will be folded within (-π, π]. When the phase change is large, incorrect results will be produced for subsequent phase linear interpolation. Therefore, it is necessary to unfold the phase to obtain thetaC_unwrap.

[0034] Further, step 4 is detailed as follows:

[0035] Find the two reference frequency points f_ref1 and f_ref2 before and after the interpolation frequency point f_interp(i), and calculate the phase theta(i) of the interpolation frequency point by combining the unwrapped phases thetaC_unwrap1 and thetaC_unwrap2. The specific calculation formula is as follows:

[0036] temp = f_ref1 - f_ref2;

[0037] theta(i) = (f_interp(i) - f_ref2) / temp × thetaC_unwrap1 +

[0038] (f_interp(i) - f_ref1) / temp × thetaC_unwrap2;

[0039] Further, step 5 is specifically detailed as follows:

[0040] Calculate the polar coordinates (xe, ye) of the i-th interpolation point according to the coordinates (xc, yc) of the center of the circle in polar coordinates, the radius R, and the phase theta(i). The specific calculation formula is as follows:

[0041] xe(i) = R × cos(theta(i)) + xc;

[0042] ye(i) = R × sin(theta(i)) + yc;

[0043] Then obtain the complex value Interp_data(i) of the i-th interpolation point:

[0044] Interp_data(i) = xe + 1i * ye;

[0045] 1i represents an imaginary number, and xe + 1i * ye means that the real part of this data is xe and the imaginary part is ye.

[0046] In summary, the present application includes at least the following beneficial technical effects:

[0047] This method has good interpolation effects on the transmission tracking error term, the reflection tracking error term, and the matching error term. It evolves from three-point circular interpolation to multi-point circular interpolation, optimizes the limitation of phase change, and improves the interpolation accuracy. By means of reference frequency points, the number of calculations for fitting the circular curve and phase non-folding is reduced, greatly improving the calculation efficiency. In engineering applications, it has better error term interpolation effects and faster running speeds compared to the previous error term interpolation algorithms. Description of the Drawings

[0048] Figure 1 It is a schematic diagram of the error term interpolation algorithm process;

[0049] Figure 2 It is a schematic diagram of the phase non-folding algorithm process;

[0050] Figure 3 It is the Smith chart of the original data and sparse data of Simulation 1 of the embodiment of the present application;

[0051] Figure 4 It is the amplitude and phase diagram of the original data and sparse data of Simulation 1 of the embodiment of the present application;

[0052] Figure 5 It is the Smith chart of the original data and interpolated data of Simulation 1 of the embodiment of the present application;

[0053] Figure 6 It is the amplitude and phase diagram of the original data and interpolated data of Simulation 1 of the embodiment of the present application;

[0054] Figure 7 For the Smith chart of the original data and sparse data in Simulation 2 of the embodiments of the present application;

[0055] Figure 8 For the amplitude and phase diagram of the original data and sparse data in Simulation 2 of the embodiments of the present application;

[0056] Figure 9 For the Smith chart of the original data and interpolated data in Simulation 2 of the embodiments of the present application;

[0057] Figure 10 For the amplitude and phase diagram of the original data and interpolated data in Simulation 2 of the embodiments of the present application. Detailed implementation manners

[0058] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application; obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0059] In the description of the present application, it should be noted that the orientation or positional relationship indicated by the terms "upper", "lower", "inner", "outer", "top / bottom end", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation to the present application. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0060] In the description of the present application, it should be noted that unless otherwise clearly specified and limited, the terms "installed", "provided with", "sheathed / connected", "connected", etc. should be understood in a broad sense. For example, "connected" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal communication of two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to specific situations.

[0061] The present application will be further described in detail below with reference to the accompanying drawings.

[0062] The embodiments of the present application disclose an interpolation method for error terms in a vector network analyzer, including the following steps:

[0063] Step 1: Obtain the reference frequency points corresponding to the interpolation frequency points, and find the N closest points (the value of N can be set) to the reference frequency points in the original frequency point array f_raw;

[0064] Step 2: Call the fitting algorithm. The N points are calculated and fitted to a circular curve to obtain the center and radius of the circle;

[0065] Step 3: Calculate the phases of the N points relative to the center of the circle and unfold the phases;

[0066] Step 4: Linearly interpolate the phases of the interpolation frequency points;

[0067] Step 5: Calculate the polar coordinates of the interpolation points based on the center of the circle, the radius, and the phases, and then obtain the complex values of the interpolation points;

[0068] Further, Step 1 is detailed as follows:

[0069] For each interpolation frequency point, its range is within the range of the original frequency points. Set the reference frequency point f_ref(i) of the i-th interpolation frequency point f_interp(i) as the first original frequency point f_raw(idx) that is greater than or equal to the interpolation frequency point f_interp(i), where idx represents the serial number of the original frequency point f_raw(idx) in the original frequency point array f_raw, and then select the N closest points to the reference frequency point in the original frequency array f_raw.

[0070] Taking N as 3 as an example: The selected points are f_raw(idx - 1), f_raw(idx), and f_raw(idx + 1).

[0071] Further, Step 2 is detailed as follows:

[0072] When i is 1 or i > 1 and the reference frequency point f_ref(i) of the current interpolation frequency point is not equal to the previous reference frequency point f_ref(i - 1), fit the selected N points to a circular curve to obtain the coordinates (xc, yc) of the center of the circle in polar coordinates and the radius R. The calculation formulas for fitting the N points to a circular curve and obtaining the center and radius of the circle are as follows:

[0073]

[0074] Q = A\D;

[0075] xc = Q(1);

[0076] yc = Q(2);

[0077]

[0078] Where A is a 3×3 matrix, D is a 3×1 matrix, Q is a 3×1 matrix, N is the number of points taken for the calculation, and x i is the real part of the data point, and y i is the imaginary part of the data point. Q(1), Q(2), and Q(3) are the first, second, and third elements of the matrix respectively.

[0079] Furthermore, step 3 is detailed as follows:

[0080] After obtaining the coordinates (xc, yc) of the center of the circle in polar coordinates, calculate the phase thetaC of the N points relative to the center of the circle. The calculation formula is as follows:

[0081] thetaC i = tan -1 ((y i - yc) / (x i - xc));

[0082] For the calculated phase thetaC, its phase value will be folded within (-π, π]. When the phase changes greatly, incorrect results will be produced for subsequent phase linear interpolation. Therefore, it is necessary to unfold the phase to obtain thetaC_unwrap.

[0083] Furthermore, step 4 is detailed as follows:

[0084] Find the two reference frequency points f_ref1 and f_ref2 before and after the interpolation frequency point f_interp(i), and calculate the phase theta(i) of the interpolation frequency point by combining the unwrapped phases thetaC_unwrap1 and thetaC_unwrap2. The specific calculation formula is as follows:

[0085] temp = f_ref1 - f_ref2;

[0086] theta(i) = (f_interp(i) - f_ref2) / temp × thetaC_unwrap1 +

[0087] (f_interp(i) - f_ref1) / temp × thetaC_unwrap2;

[0088] Furthermore, step 5 is detailed as follows:

[0089] Calculate the polar coordinates (xe, ye) of the i-th interpolation point according to the coordinates (xc, yc) of the center of the circle in polar coordinates, the radius R, and the phase theta(i). The specific calculation formula is as follows:

[0090] xe(i) = R × cos(theta(i)) + xc;

[0091] ye(i) = R × sin(theta(i)) + yc;

[0092] Subsequently, the complex value Interp_data(i) of the i-th interpolation point is obtained:

[0093] Interp_data(i) = xe + 1i * ye;

[0094] 1i represents the imaginary number, and xe + 1i * ye represents that the real part of the data is xe and the imaginary part is ye.

[0095] The following simulation verification is carried out according to the interpolation method of the error term proposed by the present invention:

[0096] Simulation 1

[0097] A set of error term data with 201 points is thinned by 8 times (remaining 26 points). The original data Smith chart and the thinned data Smith chart are as Figure 3 shown, and the original data amplitude-phase chart and the thinned data amplitude-phase chart are as Figure 4 shown;

[0098] The interpolation method of the error term proposed by the present invention is used for the thinned error term to obtain the interpolated error term data;

[0099] The interpolated error term data is compared with the original 201-point error term data to verify the result. The Smith comparison chart is as Figure 5 shown, and the amplitude-phase comparison chart is as Figure 6 shown.

[0100] It can be seen from the simulation results that in the case of thinning the data by 8 times in Simulation 1, the interpolation method of the error term proposed by the present invention has good interpolation effects in both amplitude and phase, and the interpolated error term data almost coincides with the original data curve.

[0101] Simulation 2

[0102] Another set of error term data with 201 points is thinned by 10 times (remaining 21 points). The original data Smith chart and the thinned data Smith chart are as Figure 7 shown, and the original data amplitude-phase chart and the thinned data amplitude-phase chart are as Figure 8 shown;

[0103] The interpolation method of the error term proposed by the present invention is used for the thinned error term to obtain the interpolated error term data;

[0104] The interpolated error term data is compared with the original 201-point error term data to verify the result. The Smith comparison chart is as Figure 9As shown, its amplitude-phase contrast diagram is as Figure 10 shown.

[0105] It can be seen from the simulation results that in the case where the simulation 2 has 10 times sparser data, the interpolation method of the error term proposed by the present invention still has a good interpolation effect both in terms of amplitude and phase, and the error term data after interpolation almost coincides with the original data curve.

[0106] The above are all preferred embodiments of the present application, and the protection scope of the present application is not limited thereby. Therefore, all equivalent changes made according to the structure, shape, and principle of the present application should be covered within the protection scope of the present application.

Claims

1. An interpolation method for error terms in a vector network analyzer, characterized in that, It includes the following steps: Step 1: Obtain the reference frequency points corresponding to the interpolation frequency points, and find the N points closest to the reference frequency points in the original frequency point array f_raw; Step 2: Call the fitting algorithm, and the N points are calculated and fitted into a circular curve to obtain the center and radius; Step 3: Calculate the phases of the N points relative to the center of the circle, and unfold the phases; Step 4: Linearly interpolate the phases of the interpolation frequency points; Step 5: Calculate the polar coordinates of the interpolation points according to the center of the circle, radius and phase, and then obtain the complex values of the interpolation points.

2. The interpolation method for error terms in a vector network analyzer according to claim 1, wherein In Step 1, obtaining the reference frequency points corresponding to the interpolation frequency points and finding the N points closest to the reference frequency points in the original frequency points includes: For each interpolation frequency point, its range is within the range of the original frequency points; Set the reference frequency point f_ref(i) of the i-th interpolation frequency point f_interp(i) as the first original frequency point f_raw(idx) that is greater than or equal to the interpolation frequency point f_interp(i), where idx represents the serial number of the original frequency point f_raw(idx) in the original frequency point array f_raw; Then select the N points closest to the reference frequency point in the original frequency array f_raw.

3. The interpolation method for error terms in a vector network analyzer according to claim 2, wherein In Step 2, calling the fitting algorithm, and the N points are calculated and fitted into a circular curve to obtain the center and radius includes: When i is 1 or i>1 and the reference frequency point f_ref(i) of the current interpolation frequency point is not equal to the previous reference frequency point f_ref(i-1), fit the selected N points into a circular curve to obtain the coordinates (xc, yc) of the center of the circle in polar coordinates and the radius R; The calculation formulas for fitting the N points into a circular curve and obtaining the center and radius are as follows: Q = A\D; xc = Q(1); yc = Q(2); Where A is a 3×3 matrix, D is a 3×1 matrix, Q is a 3×1 matrix, N is the number of points taken for the calculation, x i is the real part of the data point, y i is the imaginary part of the data point, and Q(1), Q(2), and Q(3) are the first, second, and third elements of the matrix, respectively.

4. The interpolation method for error terms in a vector network analyzer according to claim 3, characterized in that In Step 3, calculating the phases of the N points relative to the center of the circle and unfolding the phases includes: After obtaining the coordinates (xc, yc) of the center of the circle in polar coordinates, calculate the phase thetaC of the N points relative to the center of the circle. The calculation formula is as follows: thetaC i = tan -1 ((y i - yc) / (x i - xc)); For the calculated phase thetaC, unfold the phase to obtain thetaC_unwrap.

5. The interpolation method for error terms in a vector network analyzer according to claim 4, characterized in that, In Step 4, linearly interpolating the phases of the interpolation frequency points includes: Find the two adjacent reference frequency points f_ref1 and f_ref2 of the interpolation frequency point f_interp(i), and calculate the phase theta(i) of the interpolation frequency point by combining the unfolded phases thetaC_unwrap1 and thetaC_unwrap2. The specific calculation formula is as follows: temp = f_ref1 - f_ref2; theta(i) = (f_interp(i) - f_ref2) / temp × thetaC_unwrap1 + (f_interp(i) - f_ref1) / temp × thetaC_unwrap2.

6. The interpolation method for error terms in a vector network analyzer according to claim 5, characterized in that In Step 5, calculating the polar coordinates of the interpolation points according to the center of the circle, radius and phase, and then obtaining the complex values of the interpolation points includes: Calculate the polar coordinates (xe, ye) of the i-th interpolation point according to the coordinates (xc, yc) of the center of the circle in polar coordinates, the radius R, and the phase theta(i). The specific calculation formula is as follows: xe(i) = R × cos(theta(i)) + xc; ye(i) = R × sin(theta(i)) + yc; Subsequently, obtain the complex value Interp_data(i) of the i-th interpolation point: Interp_data(i) = xe + 1i * ye; 1i represents the imaginary number, and xe + 1i * ye means that the real part of this data is xe and the imaginary part is ye.

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