Nonlinear analysis and calibration method for high-precision digital oscilloscope

Abstract

The invention discloses a non-linear analysis and calibration method for a high-precision digital oscilloscope, and the method comprises the steps: a segmented recombination optimization process which is used for extracting non-linear errors of the digital oscilloscope at different working temperatures; the sectional type building and combining process is used for fitting the non-linear error to obtain a non-linear error model; an FPGA real-time calibration process: storing the error model in a high-precision digital oscilloscope FPGA, storing the error model as a calibration data table, judging the digital oscilloscope to output a digital code through the FPGA, carrying out real-time indexing to search the corresponding error model in the FPGA, obtaining a nonlinear error value, and compensating the nonlinear error value to the real-time output digital code to complete calibration compensation; according to the method provided by the invention, nonlinear digital calibration of the high-precision digital oscilloscope can be realized, so that the linearity and the dynamic performance of the high-precision digital oscilloscope, including SFDR and ENOB, are remarkably improved.

Description

Technical Field

[0001] The invention relates to the field of error compensation of high-precision digital oscilloscopes, and in particular to a nonlinear analysis and calibration method for high-precision digital oscilloscopes. Background Art

[0002] Digital oscilloscopes play a key role in scientific research, engineering applications, industrial testing and other fields. They can capture signals completely and accurately and analyze waveforms accurately and reliably, providing effective support for the design, debugging and troubleshooting of electronic devices and equipment. With the increasing requirements for the accuracy of measured signals and the measurement integrity of tiny signals, the requirements for the resolution of digital oscilloscopes are also gradually increasing. As a key parameter of digital oscilloscopes, nonlinearity becomes more important as the accuracy of oscilloscopes increases. The harmonic noise caused by the nonlinear error significantly affects the dynamic performance of the equipment, such as spurious-free dynamic range, signal-to-noise ratio, total harmonic distortion, etc., which will directly affect the accuracy and reliability of the measurement. The linearity and dynamic performance indicators of domestic digital oscilloscopes are quite different from those of foreign oscilloscopes. The functional completeness of oscilloscopes is lacking. High-precision oscilloscope products on the market do not have nonlinear calibration functions. There are related methods for research, but they have not been applied to specific products.

[0003] The nonlinear error of a digital oscilloscope comes from the nonlinearity of the front-end processing circuit (op amp, filter, sample and hold) and the internal core ADC. For ADC, the nonlinear error is not large, but the introduction of the front-end circuit will greatly deteriorate the linearity. The nonlinearity introduced by the front-end processing circuit is the main component of the overall nonlinearity of the oscilloscope. Therefore, the effective number of bits ENOB, spurious-free dynamic range SFDR and other indicators of the digital oscilloscope are lower than its internal core ADC. Digital oscilloscopes are based on the ADC analog-to-digital conversion principle and expand the working sampling rate and the amplitude range of the converted acquisition signal. Therefore, there are similarities in the nonlinear calibration method. The partial digital end calibration technology of ADC nonlinearity can be fully applied to digital oscilloscopes. Additional explanation: ADC calibration and digital oscilloscope calibration are similar, but the problems they address are different. ADC calibration mainly corrects the nonlinear error of ADC devices, while oscilloscope calibration mainly corrects the error of the front-end circuit. At present, there are many calibration technologies specifically for digital oscilloscopes, but there is basically no digital calibration technology for oscilloscope nonlinearity. There are many digital calibration technologies for ADC nonlinearity. Therefore, the following background technology describes and compares the digital calibration technology of ADC, which can be used as a common method for digital oscilloscope calibration.

[0004] Existing technology and its defects:

[0005] High-precision digital oscilloscopes need to calibrate their own nonlinearity. The existing nonlinear calibration technology includes the adaptive filter calibration method CN201410837054.3. By introducing a shared capacitor array, with the support of an adaptive filter, the adaptive calibration of the analog-to-digital converter can be completed. It can be applied to digital oscilloscopes to calibrate nonlinear errors in real time, and can ensure high calibration accuracy without attenuating the input signal range. However, high-precision calibration occupies more resources and has limited response convergence speed for fast-changing signals, and has poor real-time performance.

[0006] The interpolation calibration method based on neural network CN202410153774.1 uses a multi-layer neural network to learn and correct the nonlinear error of the data acquisition system: the ADC outputs multiple groups of first and second digital codes, respectively, and inputs them into the hybrid neural network to obtain the first and second neural network output signals, obtains the neural network loss function based on the neural network output signal to adjust the weight of the hybrid neural network, obtains the first digital signal, and finally processes the first digital signal based on the interpolation method to obtain the output signal. This method can analyze complex nonlinear relationships that are difficult to model, but the neural network calibration requires a large amount of data, resulting in poor real-time calibration, and the implementation occupies more hardware resources. It can be applied to digital oscilloscopes, but for high-precision oscilloscopes, it may converge slowly or not converge at all, affecting the accuracy of the calibration.

[0007] The real-time calibration method based on LUT CN202410231506.7 first needs to extract the nonlinear error of the system as pre-data and store it in the ROM unit LUT table. The pre-extraction of the nonlinear error part of this method adopts a histogram algorithm based on the probability distribution of sinusoidal code density (in compliance with the test method standard proposed by IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters). The compensation value in the LUT is superimposed on the output code by looking up the table index, and then a one-bit disturbance is added to avoid discontinuous truncation. This method can be applied to digital oscilloscopes. This method has good real-time calibration and is suitable for high-precision calibration. However, the amount of data required for the pre-extraction of high-precision nonlinear errors is huge, the extraction difficulty is high, the dynamic adaptability of the calibration is not good, and the LUT storage virtual occupies a large storage space. It is difficult to implement this method under the condition of limited oscilloscope space resources. Summary of the invention

[0008] The object of the present invention is as follows: aiming at the above-mentioned problems, a non-linear analysis and calibration method for a high-precision digital oscilloscope of the present invention accurately and reliably extracts the non-linear error of the high-precision digital oscilloscope through a segmented recombination optimization algorithm. The segmented modeling and fitting method is applicable to the calibration of the digital oscilloscope at a wider operating temperature, alleviating the attenuation of the calibration effect caused by the fluctuation of the temperature characteristics. The FPGA real-time calibration does not require changing the circuit structure. The real-time calibration of the output data can be realized by loading the compensation data lookup table and the compensation unit obtained by segmented modeling through the program. The technical solution adopted by the present invention is as follows:

[0009] A non-linear analysis and calibration method for a high-precision digital oscilloscope, comprising:

[0010] A segmented recombination optimization process for extracting the non-linear error of the digital oscilloscope at different operating temperatures;

[0011] A segmented modeling and fitting process for fitting the non-linear error to obtain a non-linear error model;

[0012] An FPGA real-time calibration process, storing the error model in the FPGA of the high-precision digital oscilloscope as a calibration data table, determining the digital code output by the digital oscilloscope through the FPGA for real-time index lookup of the corresponding error model in the FPGA to obtain the non-linear error value, and compensating the non-linear error value to the real-time output digital code to complete the calibration compensation.

[0013] Further, the non-linear error includes integral non-linear error and differential non-linear error, and the integral non-linear error can be obtained by cumulatively summing the differential non-linear errors.

[0014] Further, the non-linear error sequence of the digital oscilloscope is extracted based on the sine code density probability distribution histogram algorithm, specifically as follows:

[0015]

[0016] In the formula, DNL is the differential non-linear error, V k is the conversion step width corresponding to the digital code, V LSB is the standard conversion width value, INL is the non-linear error, and N is the resolution bit number of the digital oscilloscope.

[0017] Further, the sine code density probability distribution histogram algorithm includes:

[0018] Partitioning and converting combined code value points: assuming that the resolution of the acquisition card of the digital oscilloscope is N bits, ENOB is A bits, and the combined point scale used is M bits, where 1 < M < (N - A - 1), reconstructing all the digital codes that can be output, and the mathematical structure of the combined point distribution constructed is:

[0019] 2^ N =1+2^ M *((2^ N -2) / 2^ M )+(2 M -1)+1 (3)

[0020] The nonlinear error sequence of the combined points is expanded to obtain the nonlinear error sequence of the complete digital code, which is as follows:

[0021] INL(k)=(INL1(K)+INL1(K+1)) / 2 (4)

[0022] b=(INL1(K)-INL1(K-1)) / 2 M (5)

[0023] INL(k)=INL1(k-1)+b*(k-2 M *(K-1)) (6)

[0024] Where k is the digital code value of the digital oscilloscope itself, K is the number value corresponding to the recombined point corresponding to the code value k, b is the straight line slope parameter, INL1 is the nonlinear error sequence of the combined point, and M is the scale of the combined point.

[0025] Furthermore, the piecewise modeling and fitting process specifically includes:

[0026] Based on the piecewise fitting modeling method of combined polynomial series model, the extracted nonlinear error is subjected to sequence segmentation, model parameter estimation and error model establishment, and the model of nonlinear deviation under balanced variable temperature and its key fitting parameters are obtained.

[0027] Furthermore, the piecewise fitting modeling method based on the combined polynomial series model includes:

[0028] Sequence segmentation includes extracting nonlinear errors A, B, C...Y of y groups of working temperature characteristics of a high-precision N-bit resolution digital oscilloscope, segmenting the nonlinear error sequence according to 14 bits as a unit, and sorting the segmented nonlinear error sequence to obtain corresponding sequence segment subsequence numbers i from 1 to 2 (N-14);

[0029] Model parameter estimation: perform model parameter estimation on the subsequence, introduce quadratic function components into the combined polynomial series model, perform quadratic division on the subsequence, and obtain the parameter estimation input matrix h(x) of the quadratic function model components of the subdivided subsegments and the parameter estimation input diagonal matrix h of the entire subsequence, which are specifically as follows:

[0030]

[0031] In the formula, x is the number of subdivision fields, k is the code value, and the diagonal matrix h is obtained by diagonally combining h(x), as shown in the following formula:

[0032] h=blkdiag(h(1),…,h(256)) (8)

[0033] The parameter estimation input matrix a of the polynomial technology model seam is further calculated as follows:

[0034]

[0035] The model parameters u and hu of the quadratic function model components are further calculated as follows:

[0036] u=Ia*inv((a')*a)*a' (10)

[0037] hu=inv(h'*u*h)*h'*u (11)

[0038] Where I is the unit matrix of the same size, and L is the order of the polynomial series components;

[0039] The component parameters hu of the quadratic function model and the nonlinear error sub-segment sequence A with the same serial number under each operating temperature characteristic i , B i …Y i , calculate the key parameter n of the most quadratic function component as follows:

[0040] n i =hu*(A i '+B i '+…+Y i ') / y (12)

[0041] In summary, the key parameters o of the final polynomial series components are calculated i , as follows:

[0042] o i =(inv(a'*a)*a'*(A i '-h*n i )+inv(a'*a)*a'*(B i '-h*n i )+…+inv(a'*a)*a'*(Y i '-h*n i )) / y (13)

[0043] In the formula, the key parameter of the model is n i and i , n i Corresponding to the key parameters of the quadratic function model component, o iThe key parameters of the corresponding polynomial series components are used to fit the corresponding subsequence mathematical model INL based on these two parameters. i :

[0044] INL i =h i *n i +a i *o i (14)

[0045] Where, INL i is the mathematical model of the nonlinear error corresponding to the sub-segment with sequence number i, h i , n i , a i , o i Refers to the parameter value of the sub-segment corresponding to sequence number i;

[0046] After fitting the nonlinear error models of each sub-segment, they are spliced ​​together to obtain a complete nonlinear error model, as shown in the following formula:

[0047]

[0048] Furthermore, the FPGA real-time calibration specifically includes:

[0049] The error nonlinear error model INL is stored in the ROM storage unit of the digital oscilloscope FPGA as a calibration data table. The FPGA first determines the combination point position of the output digital code, searches the calibration data table according to the real-time index of the position to obtain the nonlinear error value, compensates the found nonlinear error value to the real-time output digital code itself, and then searches the calibration data table for calibration of the output data stream in turn to complete the nonlinear error value correction.

[0050] Furthermore, the determination of the position of the combination point is specifically as follows:

[0051] K=(k-1) / 2 M +1 (16).

[0052] Furthermore, the calibration is as follows:

[0053] k 校准后 =k 原始码值 +INL1(K) (17).

[0054] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0055] The present invention discloses a nonlinear analysis and calibration method for a high-precision digital oscilloscope. The method used in the nonlinear error extraction part is a segmented reorganization optimization algorithm based on a sine code density probability distribution histogram algorithm. Compared with the traditional sine code density probability distribution histogram algorithm, which has the problem that the amount of analysis data required for high resolution is too large, and the high amount of calculation data leads to greater complexity and low efficiency in extracting the nonlinearity of a high-resolution digital oscilloscope, the present extraction method greatly reduces the amount of data required for analysis and the complexity of calculation through a combination point division method, thereby solving the problem of high difficulty in pre-extracting the nonlinearity of a high-precision digital oscilloscope. For example, for a 16-bit resolution digital oscilloscope, the amount of analysis data required for high resolution is too large, and the high amount of calculation data leads to greater complexity and low efficiency. Oscilloscope, the effective number of bits tested is about 7 bits. When using the traditional method to accurately analyze the nonlinear error, the number of analysis points required is 35,000,000. When using the segmented recombination optimization algorithm, the scale of the combination points is 16, and the amount of data required for actual measurement and extraction is only 300,000,000; especially for a 30-bit resolution digital oscilloscope (the effective number of bits tested is about 14 bits), the number of analysis points required for accurate analysis of nonlinear errors using the traditional method has reached 1280,000,000,000. When using the segmented recombination optimization algorithm, the scale of the combination points is 16,384, and the amount of data required for actual measurement and extraction is only 400,000,000,000;

[0056] The fitting modeling analysis part adopts a piecewise modeling fitting method based on combined polynomial series, which can reliably fit the high-resolution nonlinear error at different operating temperatures, balance the nonlinear deviation caused by limited temperature changes, and is suitable for calibration of digital oscilloscopes at wider operating temperatures, alleviating the attenuation of calibration effects caused by temperature characteristic fluctuations, and improving the dynamic adaptability of high-precision digital oscilloscope calibration;

[0057] The calibration part adopts the FPGA real-time calibration method of shrinking the lookup table, and adds the lookup table calibration algorithm to the back-end FPGA of the digital oscilloscope. The key is that the lookup table used for calibration adopts a reorganization structure based on the effective number of bits, which can reduce the size of the calibration table by more than several times without affecting the accuracy and effect of the calibration. It effectively solves the problem of large storage space occupied by the LUT table during high-precision calibration, is not limited by the space resources of the oscilloscope, and can quickly and accurately compensate and calibrate each output digital code, which can be suitable for usage scenarios with different sampling rate bandwidths. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of the network structure of the method of the present invention;

[0059] Figure 2 It is a cumulative statistical histogram of the number of code values ​​in the sinusoidal code density probability distribution histogram algorithm in the method of the present invention;

[0060] Figure 3The segmented reorganization optimization algorithm in the method of the present invention extracts 16 as a nonlinear schematic diagram;

[0061] FIG4(a) and FIG4(b) are schematic diagrams of the segmented fitting and complete fitting models of the error model in the method of the present invention, respectively;

[0062] Figure 5 A graph showing the statistical distribution law of digital codes in the sinusoidal code density probability distribution histogram algorithm in the method of the present invention;

[0063] FIG6(a) and FIG6(b) are schematic diagrams of nonlinear errors extracted by the segmented recombination optimization algorithm in the method of the present invention for a certain 18-bit and 30-bit resolution high-precision digital oscilloscope, respectively;

[0064] Figure 7 It is a deviation diagram of the nonlinear characteristics of a certain 18-bit resolution high-precision digital oscilloscope at different temperatures in the method of the present invention;

[0065] Figure 8 The graph of the nonlinear error before and after the data is extracted from the digital oscilloscope with 18-bit resolution accuracy after real-time calibration using the method of the present invention;

[0066] Fig. 9 The nonlinear error diagram of the extracted data of the digital oscilloscope with 30-bit resolution accuracy after real-time calibration using the method of the present invention is shown before and after;

[0067] FIG. 10( a ) and FIG. 10( b ) are diagrams showing the spectrum effect changes of a digital oscilloscope with 18-bit and 30-bit resolution accuracy before and after real-time calibration using the method of the present invention;

[0068] Fig.11 A schematic diagram of a digital circuit for designing real-time calibration of an FPGA for reducing the lookup table in the method of the present invention;

[0069] Fig.12 This is a graph showing the variation of the model parameter group o at 69° to 64° at elevated temperatures in Example 2 of the present invention;

[0070] Fig.13 This is a graph showing the variation of the model parameter group o at 58° to 64° when the temperature is reduced in Example 2 of the present invention;

[0071] Fig.14 This is a diagram showing the effect of nonlinear error on the code value quantization process in the method of the present invention. DETAILED DESCRIPTION

[0072] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0073] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0074] The present invention provides a nonlinear analysis and calibration method for a high-precision digital oscilloscope. Figure 1 As shown, it includes a segmented recombination optimization algorithm based on a sinusoidal code density probability distribution histogram algorithm, a segmented modeling fitting method based on a combined polynomial series, and an FPGA real-time calibration method for reducing the lookup table; the segmented recombination optimization algorithm accurately and reliably extracts the nonlinear error of the high-precision digital oscilloscope at different operating temperatures, and provides basic data support for the segmented modeling fitting as a series of processing such as sequence segmentation, model parameter estimation, and error model establishment. The comprehensive error model after parameter adjustment obtained by the segmented modeling fitting is used as a compensation data lookup table in FPGA real-time calibration.

[0075] First, the segmented reorganization optimization algorithm significantly reduces the number of required code values ​​and the amount of process calculations by regularly segmenting and reorganizing the code value points. It can accurately and reliably extract the nonlinear errors of high-precision digital oscilloscopes, especially when the resolution reaches 18 bits or more; the segmented modeling and fitting method performs sequence segmentation, parameter estimation and error model establishment on the nonlinear errors extracted by segmented reorganization under multiple groups of working temperatures, and obtains key fitting parameters and comprehensive error models under multiple groups of temperature characteristics. By changing the fitting parameter values ​​to adjust the comprehensive model, the nonlinear deviation caused by limited temperature changes can be balanced. It is more suitable for calibration of digital oscilloscopes under wider working temperatures, and alleviates the attenuation of calibration effects caused by temperature characteristic fluctuations; the FPGA real-time calibration method does not need to change the circuit structure. The compensation data lookup table and compensation unit obtained by segmented modeling can be loaded by the program to realize real-time calibration of the output data. The higher the resolution of the digital oscilloscope, the higher the difficulty of calibration. Figure 8 and Fig. 9 As shown, the calibration method proposed in the present invention can reduce the nonlinear error of the high-precision digital oscilloscope by more than 99%, and improve the resolution of the high-precision digital oscilloscope to 30 bits at most, and the spurious-free dynamic range, as shown in Figures 10(a) and 10(b), the method of the present invention also greatly reduces harmonic noise, improves the linearity of the oscilloscope, and the amplitudes of the signal-to-noise ratio and total harmonic distortion can reach more than 110%.

[0076] Example 1

[0077] Segment Recombination Optimization Algorithm Based on Sine Code Density Probability Distribution Histogram Algorithm

[0078] The nonlinear error of a high-precision digital oscilloscope is caused by the combined effects of the front-end conditioning circuit, sampling and holding circuit, and ADC quantization circuit of its internal analog-to-digital converter ADC. As the most critical static error of a digital oscilloscope, it reflects the overall linear performance and directly affects the output harmonic noise of the digital oscilloscope, thus seriously restricting the upper limit of dynamic performance. The nonlinear error is divided into integral nonlinear error INL and differential nonlinear error DNL. The accumulation of differential nonlinear error is integral nonlinear error, which is also the error indicator that is focused on during linearization calibration. Fig.14 The figure shows the influence of nonlinear error in the code value quantization process.

[0079] The commonly used method for extracting the nonlinear error of a digital oscilloscope is the sinusoidal code density probability distribution histogram algorithm. This algorithm mainly collects a large number of digital code values ​​by inputting a single-cycle sinusoidal signal to the digital oscilloscope, and then statistically analyzes the probability distribution of the code values. The conversion width error of each digital code value is derived using the characteristics of the sinusoidal function, and the corresponding nonlinear error sequence can be further accumulated and calculated. The traditional sinusoidal code density probability distribution histogram algorithm applied to digital oscilloscopes is briefly described as follows: the over-range sinusoidal signal input to the digital oscilloscope is converted, and only one cycle of the converted digital code is collected. The distribution histogram of the number of code value occurrences is obtained through statistical analysis. When the input analog signal is a sine wave, such as Figure 5 As shown, at this time, the statistical distribution of the digital code conforms to the law of the bathtub curve. Based on the code value occurrence frequency distribution histogram, the code value occurrence frequency cumulative histogram is further processed, as shown in Figure 2 The figure shows a statistical histogram of the accumulated code value frequency. According to the accumulated frequency histogram, the proportion of all code values ​​less than or equal to the digital code K in the sample is determined, and the actual conversion critical voltage of the corresponding digital code is calculated. The critical voltage conversion formula is as follows:

[0080]

[0081] In the formula, S K is the number of times all code values ​​less than or equal to the digital code K appear in the sample, S is the total number of samples collected, V K is the edge voltage of the Kth digital code;

[0082] Subtract two adjacent critical voltage data to obtain the conversion step width P corresponding to the digital code. k ; The average of all digital code conversion steps is used as the proposed standard conversion width value V LSB ; Calculate the differential nonlinearity error DNL according to the following formula, and sum it to calculate the integral nonlinearity error:

[0083]

[0084] The above-mentioned sine code density probability distribution histogram algorithm has the problem of excessive amount of analysis data required for high resolution. When accurately analyzing the non-linear error of a 16-bit resolution digital oscilloscope, 35,000,000 analysis points are required; when accurately analyzing the non-linear error of an 18-bit resolution digital oscilloscope, 120,000,000 analysis points are required; however, when accurately analyzing the non-linear error of a 24-bit resolution digital oscilloscope, the number of analysis points required has reached 12,800,000,000; the high volume of calculation data results in a relatively high complexity and low efficiency in extracting the non-linearity of high-resolution digital oscilloscopes.

[0085] Based on the research of the histogram algorithm, this embodiment proposes a segmented recombination optimization algorithm based on the sine code density probability distribution histogram algorithm, which is applicable to the non-linearity extraction of high-precision digital oscilloscopes, improves the high and demanding requirements for the amount of acquisition and analysis data, reduces the analysis complexity, and thus greatly improves the extraction efficiency.

[0086] The segmented recombination optimization algorithm based on the sine code density probability distribution histogram algorithm includes (1) partitioning the segments and converting the combined code value points and (2) expanding the non-linear error sequence of the combined points;

[0087] (1) Partitioning the segments and converting the combined code value points

[0088] First, perform an effective number of bits index test on the high-resolution digital oscilloscope. Generally, the value of this index is much lower than the resolution of the system, which will result in redundant invalid resolution bits. The redundant points can be combined into one point through segment division and defined as an image point, which is convenient for the next step of using the sine code density probability distribution histogram algorithm to calculate and analyze the non-linearity of the combined points;

[0089] Suppose the resolution of the high-precision digital acquisition card is N bits and the ENOB is A bits. We use a combined point scale of M bits, where 1 < M < (N - A - 1), and reconstruct all the digital codes that can be output. Then the mathematical structure of the combined point distribution is:

[0090] 2^ N = 1 + 2^ M * ((2^ N - 2) / 2^ M ) + (2 M - 1) + 1 (3)

[0091] For example, under the premise of 16 bits of resolution, 10 bits of effective number of bits and 6 bits of redundancy, code values ​​1-16 correspond to a new combination code value point 1, 17-32 correspond to a new combination code value point 2, and so on. All original code values ​​can correspond to a combination code value point. Based on this, the collected code value points can be converted into the corresponding combination code value points at this time to obtain new code value data. Based on this principle, the total amount of code values ​​used to analyze nonlinear errors can be reduced by 16 times. By analogy, the larger the scale of combination point selection, the greater the reduction in the amount of analysis data. However, it should be noted that the selection of combination points cannot exceed the bit constraint range; and because redundant bits are omitted, the error of the nonlinear error sequence obtained based on the analysis of the combination point code value data is approximately within 1-5% of that obtained based on the analysis of the original code value data.

[0092] (2) Nonlinear error sequence expansion of combined points

[0093] After determining the scale of the combination point and converting the original code value into the combination point code value data, the conversion step width error DNL of the combination code value point K can be calculated based on the sine code density probability distribution histogram algorithm, and the corresponding nonlinear error INL can be obtained by the accumulation formula:

[0094]

[0095] The nonlinear error sequence corresponding to the combination point is obtained. Since the analysis result of the redundant bits is discarded at this time, the nonlinear error of the redundant bits can be obtained by equal value or linear function expansion. The expansion formula is as follows:

[0096] INL(k)=(INL1(K)+INL1(K+1)) / 2 (4)

[0097] b=(INL1(K)-INL1(K-1)) / 2 M (5)

[0098] INL(k)=INL1(k-1)+b*(k-2 M *(K-1)) (6)

[0099] In the formula, k is the digital code value of the digital oscilloscope itself, K is the number value corresponding to the recombined point corresponding to the code value k, b is the linear slope parameter, INL1 is the nonlinear error sequence of the combined point, M is the scale of the combined point, and the nonlinear error sequence of the complete code value corresponding to the acquisition system is obtained by expansion; the schematic diagram of the nonlinear error effect of the segmented reorganization optimization algorithm to extract 16 digital oscilloscopes is shown in Figure 3 shown.

[0100] As shown in Figure 6(a) and Figure 6(b), they are schematic diagrams of the nonlinear errors extracted from a high-precision digital oscilloscope with 18 and 30 bit resolutions respectively after the segmented reorganization optimization algorithm, demonstrating the extraction effect of this method, because conventional algorithms cannot extract nonlinear errors at high resolution.

[0101] A piecewise modeling fitting method based on combined polynomial series

[0102] In the actual performance test of high-resolution digital oscilloscopes, it was found that the operating temperature of the internal components of the digital oscilloscope will significantly affect the nonlinear characteristics, such as Figure 7 As shown, nonlinear deviation occurs, and the nonlinear characteristics extracted in a single working temperature state cannot be generally applied to analysis and calibration under working temperatures with a limited width. The method of this embodiment can be used to perform comprehensive modeling and analysis on the extracted nonlinear error sequence of the digital oscilloscope under the variable working temperature to obtain a comprehensive mathematical model. By changing the fitting parameter value to adjust the comprehensive model, the nonlinear deviation caused by the limited temperature change can be balanced to be applicable to calibration under different working temperatures.

[0103] This embodiment adopts a method based on traditional polynomial series modeling, and proposes a piecewise fitting modeling method based on a combined polynomial series model. The traditional polynomial series is optimized, and additional quadratic function components are added to optimize and improve the model details, further improving the reliability and realism of the model. The nonlinear errors extracted under multiple groups of temperatures are subjected to sequence segmentation, model parameter estimation, and error model establishment, thereby obtaining a model of nonlinear deviation under balanced variable temperature and its key fitting parameters.

[0104] Extract the nonlinear errors A, B, C...Y of the y groups of high-precision N-bit resolution digital oscilloscopes under the working temperature characteristics, segment the nonlinear error sequence into 14-bit units, sort the segments of the sequence, and number the corresponding segments from 1 to 2. (N-14) .

[0105] The key parameters of the model are estimated for the segmented subsequences. An additional quadratic function component is introduced into the model. First, the subsegments need to be further divided into 256 subdivided subsegments to analyze the quadratic function component of the model. The parameter estimation input matrix h(x) of the quadratic function model component of the subdivided subsegments and the parameter estimation input diagonal matrix h of the entire subsequence are calculated, as shown in the following formula:

[0106]

[0107] In the formula, x ranges from 1 to 256, with a total of 256 h(x) subdivision sub-segment parameter estimation input matrices, x is the number of subdivision fields, k is the code value, and there are 64 columns in total. From left to right, k(l) corresponds to (x-1)*64 to (x*64-1). The diagonal combination of h(x) gives the diagonal matrix h, as shown below:

[0108] h=blkdiag(h(1),…,h(256)) (8)

[0109] The parameter estimation input matrix a of the polynomial technology model seam is further calculated as follows:

[0110]

[0111] The model parameters u and hu of the quadratic function model components are further calculated as follows:

[0112] u=Ia*inv((a')*a)*a' (10)

[0113] hu=inv(h'*u*h)*h'*u (11)

[0114] Where h, u, a, h are process operation parameters and have no physical electrical signal meaning, and I represents the unit matrix of the same scale;

[0115] The component parameters hu of the quadratic function model and the nonlinear error sub-segment sequence A with the same serial number under each operating temperature characteristic i , B i …Y i , calculate the key parameter n of the most quadratic function component as follows:

[0116] n i =hu*(A i '+B i '+…+Y i ') / y (12)

[0117] According to the polynomial series model input matrix a, the analyzed fitting parameter n and the nonlinear error sub-segment sequence A with the same serial number under each operating temperature characteristic are i , B i …Y i , the key parameters of the final polynomial series components can be calculated i , as follows:

[0118] o i =(inv(a'*a)*a'*(A i '-h*n i )+inv(a”*a)*a'*(B i '-h*ni )+…+inv(a'*a)*a'*(Y i '-h*n i )) / y (13)

[0119] In the formula, the key parameter of the model is n i and i , n i Corresponding to the key parameters of the quadratic function model component, o i The key parameters of the corresponding polynomial series components are used to fit the corresponding subsequence mathematical model INL based on these two parameters. i , each subsequence will correspond to a set of n i and i Parameters, total 2 (N-14) Group:

[0120] INL i =h i *n i +a i *o i (14)

[0121] Where, INL i is the mathematical model of the nonlinear error corresponding to the sub-segment with sequence number i, h i , n i , a i , o i Refers to the parameter value of the sub-segment corresponding to sequence number i, INL i Refers to the nonlinear error mathematical model of the sub-segment corresponding to sequence number i, h i , n i , a i , o i Refers to the parameter value of the sub-segment corresponding to sequence number i;

[0122] After fitting the nonlinear error models of each sub-segment, they are spliced ​​together to obtain a complete nonlinear error model, realizing the piecewise modeling and fitting of the nonlinear error, as shown in the following formula:

[0123]

[0124] This embodiment adopts a method that can integrate the nonlinear error characteristics under different operating temperature characteristics through fitting, and adjust the model to balance the nonlinear deviation caused by temperature change by changing parameters in a targeted manner. It is suitable for nonlinear calibration under temperature fluctuations in a wide temperature band. For example, when the operating temperature of the device of a high-precision digital oscilloscope rises, the o of the specified sub-segment of the corresponding polynomial series model component can be increased. i Parameter, lower the h of the specified subsegment of the quadratic function model component model i The parameters make the comprehensive model more suitable for calibration at this time and temperature.

[0125] FIG4( a ) and FIG4( b ) are schematic diagrams of the nonlinear error model segmented fitting and the complete model fitting, respectively.

[0126] FPGA real-time calibration method to reduce the size of the lookup table

[0127] This embodiment proposes an FPGA real-time calibration method for reducing the lookup table. No modification is made to the hardware of the high-precision digital oscilloscope. The compensation data lookup table and compensation unit obtained by segmented modeling can be loaded into the program to achieve real-time calibration of the output data. Fig.11 shown.

[0128] Firstly, the nonlinear error of the high-precision digital oscilloscope under the set working temperature condition is accurately and reliably extracted by using the segmented reorganization optimization algorithm. Whether fitting is required and the number of data groups to be selected for fitting are determined according to the demand for temperature adaptability bandwidth. If fitting is required, the segmented modeling fitting method is used to establish the comprehensive error model INL. The error model is stored in the ROM storage unit of the digital oscilloscope FPGA as a calibration data table. The FPGA first determines which combination point the output digital code belongs to; the judgment method is as follows:

[0129] K=(k-1) / 2 M +1 (16)

[0130] Wherein, k represents the digital original code value, and K represents the digital code value.

[0131] The compensation value is obtained by looking up the calibration data table according to the real-time index of the judgment value, and the compensation value is compensated to the real-time output digital code itself. The output data stream is calibrated in turn by looking up the table to realize the fast and accurate correction of the nonlinear error value. The calibration formula is as follows:

[0132] k 校准后 =k 校准前 +INL1(K) (17)

[0133] The key is that the lookup table used for calibration adopts a segmented reorganization combination point structure based on the segmented reorganization optimization algorithm, which reduces the size of the nonlinear error model. Without affecting the accuracy and effect of the calibration, the size of the calibration table is reduced by more than several times, effectively solving the problem of large storage space occupied by the LUT table during high-precision calibration. It can be applied to the real-time calibration of high-precision and high-resolution digital oscilloscopes. After calibration, the nonlinear error of the digital oscilloscope can be reduced by more than 99%, which greatly improves the linearity of the device, reduces harmonic noise, and can improve the dynamic performance by more than 110%.

[0134] The advantages of this embodiment over the existing solution are as follows:

[0135] 1. Compared with the adaptive filtering calibration method, the method proposed in this embodiment has better real-time performance. The FPGA has strong parallel processing capabilities and can quickly respond to the output compensation results. It will not be affected by the convergence speed of the adaptive filter and can be applied to the nonlinear calibration of digital oscilloscopes with different sampling rate bandwidths of 24 bits or above (up to Gsa / s or above).

[0136] 2. Compared with the interpolation calibration method based on neural network, the neural network calibration method requires tens of thousands of multiplication and addition operations for each calibration of a data, which makes the algorithm generate large power consumption and area in the calibration unit. The method proposed in this embodiment has better real-time performance, and the calibration implementation mainly relies on the LUT calibration data table stored in the FPGA, which occupies relatively less hardware resources, and the accuracy of the calibration is not affected by the accuracy of the oscilloscope, and can be applied to the nonlinear calibration of high-precision digital oscilloscopes.

[0137] 3. Compared with the proposed LUT-based real-time calibration method, the amount of calculation is too large when extracting nonlinear errors for high-precision oscilloscopes, and even exceeds the computing power load of general computers. In addition, in order to ensure the accuracy of the calibration when implementing the LUT lookup table calibration, the memory space will increase exponentially with the improvement of the calibration accuracy. The method proposed in this embodiment greatly reduces the amount of data and the difficulty of calculation required for the pre-extraction, and the space used by the FPGA to store the calibration table is smaller, avoiding the problem of limited space resources of the oscilloscope.

[0138] Example 2

[0139] The method provided by the present invention is used to carry out the reagent process application, which is specifically implemented according to the following steps, wherein the data analysis process can be completed in MATLAB:

[0140] Step 1, according to the working temperature change of the N-bit resolution digital oscilloscope, the temperature range ta-tb to be balanced is locked, and ta, (ta+t), (ta+2t), ..., tb in this temperature range are determined with the controllable temperature t as the step, as the working temperature characteristic points to be analyzed;

[0141] Step 2, test the signal-to-noise ratio (SINAD) and spurious-free dynamic range (SFDR) of the high-precision digital oscilloscope to be calibrated, calculate the effective number of bits (ENOB) based on SINAD, determine the combination point scale based on the segmented reconstruction optimization algorithm, and reconstruct the mathematical structure of the output digital code;

[0142] The test calculation of SINAD and SFDR requires the digital oscilloscope to input a sinusoidal signal with a frequency of f1 and an amplitude of more than 90% of the range, where the sampling rate of the digital oscilloscope is set to FS, and the pre-collection is 2 YData points are used for FFT transformation to analyze indicators. Collecting the power of 2 can avoid the truncation effect and prevent the negative impact of spectrum leakage on indicator testing. The input signal frequency f1 is:

[0143]

[0144] After FFT transformation of the collected data, SINAD and SFDR are analyzed in the frequency domain as follows:

[0145]

[0146] Where SINAD is the signal-to-noise ratio / dB; V signal is the amplitude value of the baseband signal in the frequency domain after FFT; It is the mean of the square of the amplitude of the first 6 harmonics in the frequency domain after FFT; It is the mean value of the square of the noise amplitude in the frequency domain after FFT, except for the first 6 harmonics and the fundamental frequency signal;

[0147]

[0148] Where SFDR is the spurious-free dynamic range (dBc); V other_max It is the amplitude value of the maximum component outside the fundamental frequency in the frequency domain after FFT;

[0149] The calculation formula for ENOB is:

[0150]

[0151] Step 3, monitor the temperature change of the high-precision digital oscilloscope. Under the determined working temperature points of ta, (ta+t), (ta+2t), ..., tb, according to the division combination point scale M and the reconstruction structure, respectively input a sinusoidal signal with a frequency of fc and an amplitude exceeding 10% of the range to the high-precision digital oscilloscope, collect L data points, and analyze based on the segmented reconstruction optimization algorithm to obtain the nonlinear error INL corresponding to multiple temperature points of ta, (ta+t), (ta+2t), ..., tb. A , INL B ,…,INL K .

[0152] The calculation method of input frequency fc and sample acquisition points S is:

[0153] L=2 N-M ×500 / 0.728 (23)

[0154]

[0155] Where Fs is the oscilloscope sampling rate;

[0156] Step 4: calculate the nonlinear error INL at multiple temperature points: ta, (ta+t), (ta+2t), …, tb A , INL B ,…,INL K For comparison, the error curves with certain deviations are retained, and only one nonlinear error is retained among multiple nonlinear errors with similar curves;

[0157] Step 5: Based on the segmented modeling and fitting algorithm, the nonlinear error of the specific operating temperature characteristic point is modeled and fitted to obtain the fitting error model INL. The model is divided into two parts: (N-14) segment, so there are quadratic function component key parameter group n and polynomial series component key parameter group o, the corresponding representative meanings are:

[0158]

[0159] Step 6, convert the fitted calibration model INL into two parts: a symbol component table INL_FH and an integer value component table INL_ZS, without retaining the decimal component; when converting the symbol table, when the corresponding value of INL is a positive number, the symbol table value is 0, and when the corresponding value of INL is a negative number, the symbol table value is 1; when converting the integer table, it is necessary to convert the decimal value into a bin binary value and record it in the table; convert the two tables INL_FH and INL_ZS into TXT text and save; in MATLAB, the decimal to binary conversion can be completed using the dec2hex() instruction, and the fprintf() series of instructions can be used to write the specified data into the target txt file; the details are as follows:

[0160] Instruction usage instructions:

[0161] A = dec2hex(a);

[0162] Convert the decimal number a to binary number A

[0163] fid = fopen('b.txt','wt');

[0164] fprintf(fid,'%d\n',fh);

[0165] fclose(fid);

[0166] fopen creates and opens the corresponding specified txt file, wt allows reading and writing; fprintf function represents the tabulation and formatting function, writing the corresponding data into txt in the specified format; fclose closes the read and written txt file;

[0167] Step 7: Convert the symbolic component table INL_FH and the integer value component table INL_ZS into the COE file format. You need to import the txt data into a word document, use the ctrl+H command to replace all ^p (line breaks) with English commas, replace the last line with an English semicolon, and add command words to the top two lines:

[0168] MEMORY_INITIALIZATION_RADIX=2;

[0169] MEMORY_INITIALIZATION_VECTOR=

[0170] Replace the original txt file content with the modified result and save it as coe file format to generate a coe type file that can be stored in FPGAROM;

[0171] Step 8, design a calibration unit program based on the FPGA real-time calibration algorithm of the reduced lookup table, which is composed of a signal preprocessing unit and an index lookup table calibration unit, wherein the FPGA signal preprocessing unit reorganizes the received digital signal digital_singal in segments, converts the original code value into the corresponding combination point code value, and obtains the reorganized lookup table signal find_singal for looking up the calibration table. The conversion method from the original digital signal digital_singal to the reorganized lookup table signal find_singal is:

[0172] find_singal=(digital_singal-1) / 2 M +1 (27)

[0173] In the formula, M is the scale of the combination point;

[0174] Step 9, put the generated coe calibration table file into the ROM IP core of the FPGA as the calibration data table (inl_data) for search; find the calibration data inl_data (find_singal) of the bit sequence in the digital_singal table according to the obtained table lookup signal find_singal index, and compensate the found calibration data to digital_singal to complete the data calibration; the calibration method is expressed as:

[0175] digital_singal=digital_singal+inl_data(find_singal) (28)

[0176] Step 10, solidify the FPGA calibration program in the high-precision digital oscilloscope FPGA. When the oscilloscope collects and displays data in real time, the FPGA accurately compensates and calibrates each collected signal in real time. The digital oscilloscope is respectively input with a frequency f1 and an amplitude of more than 90% of the range and a frequency fc and an amplitude of 110% of the range. The dynamic performance index and nonlinear characteristics of the digital oscilloscope after using the patent method can be tested and calculated; when the calibration effect decreases or the edge temperature effect in the applicable temperature range is poor, the model can be adjusted by changing the internal parameter value of the segmented model sub-segment parameter o to balance the nonlinear deviation caused by the variable temperature; Example 1 of the control method is applied in the domestic 16-bit resolution digital oscilloscope 6912D of China Electronics Technology Group Corporation 41 Institute: the applicable balanced temperature range of 6912D is 58-69°;

[0177] When the device operating temperature of the high-precision digital oscilloscope is at the upper edge of 69°, the effect is poor. By lowering the 2-8 segments of the polynomial series model component, i The parameter 20-50% makes the comprehensive model more suitable for calibration at this time and temperature;

[0178] Taking 64° as the standard operating temperature of the tested 6912D digital oscilloscope and single-stage regulation as an example, this equalization method is demonstrated. Fig.12 Key parameters of the first subsection of the nonlinear calibration model for the digital oscilloscope 6912D at 69° relative to that at 64° 1 Schematic diagram of the change range, Fig.12 When the temperature rises to 69°, it can be seen that o 1 The overall trend is falling, but some points are increasing, especially at the 64° model parameter o 1 On this basis, the third internal parameter is increased by 1.5 times, and the fifth internal parameter is increased by 3.5 times, so that the calibration model is closer to 69°.

[0179] The following model; Fig.13 Key parameters of the nonlinear calibration model for the digital oscilloscope 6912D at 58° relative to that at 64° 1 Schematic diagram of the change range, Fig.13 The temperature dropped to 58°

[0180] When 1 The overall trend is drastic, which can be seen in the 64° model o 1 On the basis of the above, the third internal parameter is increased by about 10 times, the seventh internal parameter is increased by about 4 times, and the fifth internal parameter is especially increased by 40 times, which can make the calibration model closer to 58°.

[0181] The model below achieves equilibrium.

[0182] The principles and implementation methods of the present invention are described in this article using specific embodiments. The description of the above embodiments is only used to help understand the method and core ideas of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A nonlinear analysis and calibration method for a high-precision digital oscilloscope, characterized in that: Including: A segmented recombination optimization process for extracting the non - linear error of a digital oscilloscope at different operating temperatures; A segmented analog fitting process for fitting the non - linear error to obtain a non - linear error model; An FPGA real - time calibration process, which stores the error model in the FPGA of a high - precision digital oscilloscope as a calibration data table. The FPGA determines the digital code output by the digital oscilloscope and performs real - time index search in the FPGA to find the corresponding error model, obtains the non - linear error value, and compensates the non - linear error value to the real - time output digital code to complete the calibration compensation.

2. The nonlinear analysis and calibration method of a high-precision digital oscilloscope according to claim 1, characterized in that: The non - linear error includes integral non - linear error and differential non - linear error. The integral non - linear error can be obtained by cumulatively summing the differential non - linear errors.

3. The nonlinear analysis and calibration method of a high-precision digital oscilloscope according to claim 2, characterized in that: Extract the non - linear error sequence of the digital oscilloscope based on the sine - code density probability distribution histogram algorithm, specifically as follows: Where DNL is the differential nonlinearity error, V k is the conversion step width corresponding to the digital code, V LSB is the standard conversion width value, INL is the nonlinear error, and N is the number of bits of resolution of the digital oscilloscope.

4. The nonlinear analysis and calibration method of a high-precision digital oscilloscope according to claim 3, characterized in that: The sine - code density probability distribution histogram algorithm includes: Partitioning and converting combined code value points: Assume that the resolution of the digital oscilloscope acquisition card is N bits, the ENOB is A bits, and the combined point scale is M bits, where 1 < M < (N - A - 1). Reconstruct all the digital codes that can be output, and the mathematical structure of the combined point distribution is: 2 ^N =1+2 ^M *((2 ^N -2) / 2 ^M )+(2 M The nonlinear error sequence of the combination point of -1)+1(3) is expanded to obtain the nonlinear error sequence of the complete digital code, which is as follows: INL(k)=(INL1(K)+INL1(K + 1)) / 2(4) b=(INL1(K)-INL1(K-1)) / 2 M (5) INL(k)=INL1(K-1)+b*(k-2 M *(K-1))(6) In the formula, k is the digital code value of the digital oscilloscope itself, K is the corresponding number value of the recombined point corresponding to the code value k, b is the linear slope parameter, INL1 is the non - linear error sequence of the combined point, and M is the combined point scale.

5. The nonlinear analysis and calibration method of a high-precision digital oscilloscope according to claim 1, characterized in that: The segmented analog fitting process specifically includes: A segmented fitting modeling method based on a combined polynomial series model, which respectively performs sequence segmentation, model parameter estimation, and error model establishment on the extracted non - linear error to obtain a model of non - linear deviation under balanced variable temperature and its key fitting parameters.

6. The nonlinear analysis and calibration method of a high-precision digital oscilloscope according to claim 5, characterized in that: The segmented fitting modeling method based on a combined polynomial series model includes: Sequence segmentation, including extracting the non - linear errors A, B, C…Y of the high - precision N - bit resolution digital oscilloscope under y groups of operating temperature characteristics, segmenting the non - linear error sequence in units of 14 bits, sorting the segmented non - linear error sequence, and obtaining the corresponding sequential segmented subsequence serial numbers i from 1 to 2(N - 14); Model parameter estimation, performing model parameter estimation on the subsequence, introducing a quadratic function component into the combined polynomial series model, and performing secondary partitioning on the subsequence to obtain the parameter estimation input matrix h(x) of the quadratic function model component of the refined sub - segments and the parameter estimation input diagonal matrix h of the entire subsequence, specifically as follows: In the formula, x is the number of refined fields, k is the code value, and the diagonal matrix h is obtained by diagonally combining h(x), as follows: h = blkdiag(h(1),…,h(256)) (8) Further calculate the parameter estimation input matrix a of the polynomial technology model segment, specifically as follows: Further calculate the model parameters u and hu of the quadratic function model component, specifically as follows: u = I - a*inv((a')*a)*a' (10) hu=inv(h'*u*h)*h'*u (11) Where I is the unit matrix of the same size, and L is the order of the polynomial series components; The component parameters hu of the quadratic function model and the nonlinear error sub-segment sequence A with the same serial number under each operating temperature characteristic i , B i …Y i , calculate the key parameter n of the most quadratic function component as follows: n i =hu*(A i '+B i '+…+And i ') / and(12) In summary, the key parameters o of the final polynomial series components are calculated i , as follows: o i =(inv(a'*a)*a'*(A i '-h*n i )+inv(a'*a)*a'*(B i '-h*n i )+…+inv(a'*a)*a'*(Y i '-h*n i )) / y (13) In the formula, the key parameter of the model is n i and i , n i Corresponding to the key parameters of the quadratic function model component, o i The key parameters of the corresponding polynomial series components are used to fit the corresponding subsequence mathematical model INL based on these two parameters. i : INL i =h i *n i +a i *o i (14) Where, INL i is the mathematical model of the nonlinear error corresponding to the sub-segment with sequence number i, h i , n i , a i , o i Refers to the parameter value of the sub-segment corresponding to sequence number i; After fitting the nonlinear error models of each sub-segment, they are spliced ​​together to obtain a complete nonlinear error model, as shown in the following formula:

7. The nonlinear analysis and calibration method of a high-precision digital oscilloscope according to claim 1 or 6, characterized in that: The FPGA real-time calibration specifically includes: The error nonlinear error model INL is stored in the ROM storage unit of the digital oscilloscope FPGA as a calibration data table. The FPGA first determines the combination point position of the output digital code, searches the calibration data table according to the real-time index of the position to obtain the nonlinear error value, compensates the found nonlinear error value to the real-time output digital code itself, and then searches the calibration data table for calibration of the output data stream in turn to complete the nonlinear error value correction.

8. The nonlinear analysis and calibration method of a high-precision digital oscilloscope according to claim 7, characterized in that: The specific formula for determining the position of the combination point is as follows: K=(k-1) / 2 M +1(16)。 9. The nonlinear analysis and calibration method of a high-precision digital oscilloscope according to claim 7, characterized in that: The calibration is specifically as follows: k 校准后 =k 原始码值 +INL1(K)(17).

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