A method for non-linear analysis and calibration of a high-precision digital oscilloscope

Abstract

The application discloses a kind of high-precision digital oscilloscope nonlinear analysis and calibration method, comprising: subsection reorganization optimization process is used to extract the nonlinear error of digital oscilloscope at different working temperatures;Subsection type modeling fitting process is used to fit the nonlinear error, and obtain nonlinear error model;FPGA real-time calibration process, the error model is stored in high-precision digital oscilloscope FPGA, and is stored as calibration data table, and the output digital code of digital oscilloscope is determined by FPGA, and the corresponding error model in FPGA is found out in real time, and the nonlinear error value is obtained, and the nonlinear error value is compensated to real-time output digital code, and calibration compensation is completed;The method proposed in the application can enable high-precision digital oscilloscope to realize nonlinear digital calibration, so as to significantly improve its linearity and dynamic performance, including SFDR and ENOB.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of high-precision digital oscilloscope error compensation, and in particular to a non-linear analysis and calibration method for a high-precision digital oscilloscope. BACKGROUND

[0002] Digital oscilloscopes play a key role in scientific research, engineering applications, and industrial testing, and can capture signals completely and accurately and analyze waveforms precisely and reliably, providing effective support for the design, debugging, and troubleshooting of electronic devices and equipment. As the accuracy of measured signals and the integrity of the measurement of small signals are increasingly required, the resolution of digital oscilloscopes is gradually improved, and non-linearity, as a key parameter of digital oscilloscopes, becomes more important as the accuracy of oscilloscopes improves. The harmonic noise caused by non-linear errors significantly affects the dynamic performance of the device, such as the spurious-free dynamic range, signal-to-noise ratio, and total harmonic distortion, and directly affects the accuracy and reliability of the measurement. The linearity and dynamic performance indicators of domestic digital oscilloscopes have a considerable gap with foreign oscilloscopes, and the completeness of the functions of oscilloscopes is lacking. High-precision oscilloscope products on the market do not have non-linear calibration functions, and there are related method studies but no application to specific products.

[0003] The non-linear error of a digital oscilloscope is derived from the non-linearity of the front-end processing circuit (operational amplifier, filtering, and sample-and-hold) and the internal core ADC. For ADCs, the non-linear error is not large, but the introduction of the front-end circuit greatly deteriorates the linearity. The non-linearity introduced by the front-end processing circuit is the main component of the overall non-linearity of the oscilloscope, so the effective number of bits ENOB, spurious-free dynamic range SFDR, and other indicators of the digital oscilloscope are lower than those of the internal core ADC. Digital oscilloscopes are based on the principle of ADC analog-to-digital conversion, and have extended the working sampling rate and the amplitude range of the converted and collected signals, so there are similarities in the non-linear calibration method. The digital end calibration technology for the non-linearity of ADCs can be completely applied to digital oscilloscopes. Additional explanation: calibrating ADCs and digital oscilloscopes are similar but address different problems. Calibrating ADCs mainly corrects the non-linear error of the ADC device, while oscilloscopes mainly correct the error of the front-end circuit. There are many calibration techniques for digital oscilloscopes, but there are basically no digital calibration techniques for the non-linearity of oscilloscopes. There are many non-linear digital calibration techniques for ADCs, so the following background technology description and comparison is for ADC digital calibration techniques, which can be used as a common method for digital oscilloscope calibration.

[0004] Prior art and its defects:

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

[0006] An interpolation calibration method based on a neural network CN202410153774.1 uses a multi-layer neural network to learn and correct the nonlinearity error of a data acquisition system. The method inputs a plurality of first and second digital codes from an ADC output into a hybrid neural network to obtain first and second neural network output signals, adjusts the weights of the hybrid neural network based on a neural network loss function obtained from the neural network output signals to obtain a first digital signal, and finally processes the first digital signal based on an interpolation method to obtain an output signal. The method can analyze complex and difficult-to-model nonlinear relationships, but the neural network calibration requires a large amount of data, resulting in poor calibration real-time performance and occupying more hardware resources. The method can be applied to a digital oscilloscope, but for high-precision oscilloscopes, it may converge slowly or not at all, affecting the accuracy of the calibration.

[0007] A real-time calibration method based on LUT CN202410231506.7 first extracts the nonlinearity error of the system as pre-data and stores it in the ROM unit LUT table. The method uses a histogram algorithm based on the probability distribution of the sine code density (in accordance with the test method standard proposed by IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters) to extract the nonlinearity error. The method adds a one-bit perturbation to avoid discontinuous truncation and can be applied to a digital oscilloscope. The method has good calibration real-time performance and can be applied to high-precision calibration, but the amount of data required for pre-extraction of high-precision nonlinearity error is huge, and the extraction is difficult. The dynamic adaptability of the calibration is not good, and the LUT storage occupies a large storage space, making it difficult to implement the method under the condition of limited space resources of the oscilloscope. SUMMARY

[0008] The present application aims at the above-mentioned problems, and provides a nonlinear analysis and calibration method for a high-precision digital oscilloscope.

[0009] The nonlinear analysis and calibration method for the high-precision digital oscilloscope comprises:

[0010] a segmented reorganization optimization process for extracting nonlinear errors of the digital oscilloscope at different working temperatures;

[0011] a segmented modeling and fitting process for fitting the nonlinear errors to obtain a nonlinear error model;

[0012] an FPGA real-time calibration process for storing the error model in an FPGA of the high-precision digital oscilloscope as a calibration data table, and for real-time index lookup of the corresponding error model in the FPGA according to the output digital code of the digital oscilloscope to obtain a nonlinear error value, and for compensating the real-time output digital code with the nonlinear error value to complete the calibration and compensation.

[0013] Further, the nonlinear error comprises an integral nonlinear error and a differential nonlinear error, and the integral nonlinear error can be obtained by accumulating and summing the differential nonlinear error.

[0014] Further, the nonlinear error sequence of the digital oscilloscope is extracted based on a sinusoidal code density probability distribution histogram algorithm, and the specific algorithm is as follows:

[0015] (1)

[0016] (2)

[0017] In the formula, n is the resolution bit number of the digital oscilloscope, and DNL is the differential nonlinear 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, N is the resolution bit number of the digital oscilloscope.

[0018] Further, the sinusoidal code density probability distribution histogram algorithm comprises:

[0019] Combination of partitioning and conversion code value points: assuming that the resolution of the digital oscilloscope acquisition card is N bits, the ENOB is A bits, and the combination point scale is M bits, 1<M<(N-A-1), the entire digital code that can be output is reconstructed, and the mathematical structure of the combination point distribution constructed is:

[0020] (3)

[0021] The nonlinear error sequence of the combination point is expanded to obtain the nonlinear error sequence of the complete digital code, and the specific formula is as follows:

[0022] (4)

[0023] (5)

[0024] (6)

[0025] In the formula, k is the digital code value of the digital oscilloscope itself, K is the code value k corresponding to the recombined point corresponding to the number value, b is the slope parameter of the straight line, INL 1 is the nonlinear error sequence of the combination point, M is the combination point scale.

[0026] Further, the segmented modeling and fitting process specifically includes:

[0027] The segmented fitting modeling method based on the combined polynomial series model extracts the nonlinear error and respectively performs sequence segmentation, model parameter estimation, and error model establishment to obtain the model of the nonlinear deviation under balanced variable temperature and the key fitting parameters.

[0028] Further, the segmented fitting modeling method based on the combined polynomial series model includes:

[0029] Sequence segmentation includes extracting the high-precision N nonlinear error sequence of the 14-bit resolution digital oscilloscope under the working temperature characteristic y of the group A, B, C... Y , segmenting the nonlinear error sequence according to 14 bits as a unit, sorting the segmented nonlinear error sequence to obtain the segment subsequence sequence number i corresponding to the order N from 1 to 2(14);

[0030] Model parameter estimation, model parameter estimation is carried out on the sub-sequence, the quadratic function component is introduced into the combined polynomial series model, the sub-sequence is divided into two parts, and the parameter estimation input matrix of the quadratic function model component of the subdivided sub-sequence is obtained h x ) and the parameter estimation input diagonal matrix of the whole sub-sequence h , as follows:

[0031] (7)

[0032] In the formula, x is the number of subdivided fields, k is the code value, and h ( x ) is combined diagonally to obtain the diagonal matrix h , as follows:

[0033] (8)

[0034] Further calculation obtains the parameter estimation input matrix a of the polynomial series model component, as follows:

[0035] (9)

[0036] Further calculation obtains the model parameters of the quadratic function model component u , hu , as follows:

[0037] (10)

[0038] (11)

[0039] In the formula, I is a unit matrix with the same size, and L is the order of the polynomial series component;

[0040] Quadratic function model component parameters hu and the same serial number of nonlinear error sub-sequence under each working temperature characteristic A i ，B i …Y i The key parameters of the quadratic function component are calculated as follows: , as follows:

[0041] (12)

[0042] In summary, the key parameters of the final polynomial series component are calculated as follows: o i , as follows: ​

[0043] (13)

[0044] In the formula, the model key parameters are n i and o i , n i the key parameters corresponding to the quadratic function model component, o i the key parameters corresponding to the polynomial series component, and the corresponding subsequence mathematical model is fitted based on the two parameters INL i :

[0045] (14)

[0046] In the formula, INL i is a nonlinear error mathematical model corresponding to a subsegment with a serial number of i .

[0047] After fitting the nonlinear error model of each subsegment, the complete nonlinear error model is obtained by splicing, as follows:

[0048] (15).

[0049] Further, the FPGA real-time calibration specifically includes:

[0050] The error nonlinear error model 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, indexes the calibration data table in real time according to the position to obtain the nonlinear error value, compensates the found nonlinear error value to the real-time output digital code itself, then sequentially finds the calibration data table for the output data stream to complete the nonlinear error value correction.

[0051] Further, the determination of the combination point position is specifically as follows:

[0052] (16).

[0053] Further, the calibration is specifically as follows:

[0054] (17).

[0055] As described above, due to the adoption of the above technical solutions, the beneficial effects of the present application are:

[0056] The nonlinear analysis and calibration method of the high-precision digital oscilloscope of the application, the extraction method for the nonlinear error part is a segmented reorganization optimization algorithm based on the sine code density probability distribution histogram algorithm, relative to the traditional sine code density probability distribution histogram algorithm, the analysis data required by high resolution is too large, the high calculation data volume leads to the complexity of extracting the nonlinearity of the high-resolution digital oscilloscope is large, and the efficiency is low, the extraction method greatly reduces the analysis data required and the operation complexity by the division method of the combination point, solves the problem of high difficulty in extracting the nonlinearity of the high-precision digital oscilloscope, for example, for a 16-bit resolution digital oscilloscope, the test effective bit number is about 7 bits, when the traditional method is used to accurately analyze the nonlinear error, the analysis point number required is 35000000, when the segmented reorganization optimization algorithm is used, the combination point scale is 16, and the data required for actual measurement extraction is only 3000000000; Especially for a 30-bit resolution digital oscilloscope (the test effective bit number is about 14 bits), when the traditional method is used to accurately analyze the nonlinear error, the analysis point number required is 12800000000, when the segmented reorganization optimization algorithm is used, the combination point scale is 16384, and the data required for actual measurement extraction is only 40000000000.

[0057] The fitting modeling analysis part adopts a segmented modeling fitting method based on a combination polynomial series, which can reliably fit the high-resolution nonlinear error under different working temperatures, can balance the nonlinear deviation caused by limited temperature change, is suitable for calibration of digital oscilloscopes under a wider working temperature, relieves the attenuation of calibration effect caused by temperature characteristic fluctuation, and improves the dynamic adaptability of high-precision digital oscilloscope calibration.

[0058] The calibration part adopts a FPGA real-time calibration method of reducing lookup table, adds a lookup table calibration algorithm in the rear-end FPGA of the digital oscilloscope, wherein the key is that the lookup table used for calibration adopts a reorganization structure based on the effective bit number, which can reduce the size of the calibration table by more than several times without affecting the accuracy and effect of calibration, effectively solves the problem of large storage space occupied by the LUT table in 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, and can be applied to various sampling rate bandwidths. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 is a network structure schematic diagram of the method of the application;

[0060] Figure 2 is a code value frequency accumulation statistical histogram in the sine code density probability distribution histogram algorithm in the method of the application;

[0061] Figure 3is the nonlinear diagram extracted by the segmented recombination optimization algorithm in the method of the application;

[0062] Fig. 4 (a) and Fig. 4 (b) are respectively the segmented fitting and complete fitting model diagrams of the error model in the method of the application;

[0063] Figure 5 is the digital code statistical distribution law diagram in the sinusoidal code density probability distribution histogram algorithm in the method of the application;

[0064] Fig. 6 (a) and Fig. 6 (b) are respectively the nonlinear error diagrams extracted by the segmented recombination optimization algorithm in the method of the application for an 18-bit and a 30-bit resolution high-precision digital oscilloscope;

[0065] Figure 7 is the deviation diagram of the nonlinear characteristics of an 18-bit resolution high-precision digital oscilloscope at different temperatures in the method of the application;

[0066] Figure 8 is the diagram showing the change of the nonlinear error of the extracted data of an 18-bit resolution precision digital oscilloscope before and after real-time calibration by the method of the application;

[0067] Figure 9 is the diagram showing the change of the nonlinear error of the extracted data of a 30-bit resolution precision digital oscilloscope before and after real-time calibration by the method of the application;

[0068] Fig. 10 (a) and Fig. 10 (b) are diagrams showing the change of the spectrum effect of an 18-bit and a 30-bit resolution precision digital oscilloscope before and after real-time calibration by the method of the application;

[0069] Figure 11 is the design digital circuit diagram of the FPGA real-time calibration of the reduced lookup table in the method of the application;

[0070] Figure 12 is the change amplitude diagram of the 69° model parameter group o compared with the 64° model parameter group o at a raised temperature in Embodiment 2 of the application;

[0071] Figure 13 is the change amplitude diagram of the 58° model parameter group o compared with the 64° model parameter group o at a lowered temperature in Embodiment 2 of the application;

[0072] Figure 14 is the effect diagram of the nonlinear error in the code value quantization process in the method of the application. DETAILED DESCRIPTION

[0073] The application will be described in detail below with reference to the accompanying drawings.

[0074] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application.

[0075] The present application provides a high-precision digital oscilloscope nonlinear analysis and calibration method, as shown in Figure 1 The segmented reorganization optimization algorithm based on the sine code density probability distribution histogram algorithm, the segmented modeling fitting method based on the combined polynomial series, and the FPGA real-time calibration method of the reduced lookup table are included; the segmented reorganization optimization algorithm accurately and reliably extracts the nonlinear error of the high-precision digital oscilloscope at different working temperatures, provides basic data support for a series of processes such as sequence segmentation, model parameter estimation and error model establishment for the segmented modeling fitting, and the integrated error model after parameter adjustment of the segmented modeling fitting is used as the compensation data lookup table for the FPGA real-time calibration.

[0076] Firstly, the segmented reorganization optimization algorithm greatly reduces the required code value amount and process calculation amount by regularly segmenting and reorganizing the code value points, can accurately and reliably extract the nonlinear error of the high-precision digital oscilloscope, especially when the resolution reaches 18 bits or more; the segmented modeling fitting method performs sequence segmentation, parameter estimation and error model establishment on the nonlinear errors extracted by the segmented reorganization under multiple working temperatures, obtains the key fitting parameters and the integrated error model under multiple temperature characteristics, and can balance the nonlinear deviation caused by limited temperature changes by changing the fitting parameter value to control the integrated model, which is more suitable for calibration of the digital oscilloscope under a wider working temperature, and relieves the attenuation of the calibration effect caused by the temperature characteristic fluctuation; the FPGA real-time calibration method does not need to change the circuit structure, and can realize real-time calibration of the output data by loading the compensation data lookup table and the compensation unit obtained by the segmented modeling. The higher the resolution of the digital oscilloscope, the higher the difficulty of calibration, as shown in Figure 8 and Figure 9 The calibration method proposed in the present application can reduce the nonlinear error of the high-precision digital oscilloscope by up to 99% or more, and can improve the highest resolution of the high-precision digital oscilloscope to 30 bits, and the spurious dynamic range, as shown in FIG. 10(a) and FIG. 10(b), the method of the present application can also greatly reduce the harmonic noise, improve the linearity of the oscilloscope, and the amplitude of the signal-to-noise ratio and the total harmonic distortion can be up to 110% or more.

[0077] Example 1

[0078] Segmented reorganization optimization algorithm based on sine code density probability distribution histogram algorithm

[0079] The nonlinear error of a high-precision digital oscilloscope is generated by the combined effects of its internal analog-to-digital converter (ADC) front-end conditioning circuit, sample-and-hold circuit, and ADC quantization circuit. As the most critical static error of a digital oscilloscope, it reflects the overall linearity and directly affects the output harmonic noise level, thus severely limiting the upper limit of dynamic performance. Nonlinear error is divided into integral nonlinear error (INL) and differential nonlinear error (DNL). The accumulation of differential nonlinear error is the integral nonlinear error, which is also a key error indicator to focus on during linearization calibration. Figure 14 The figure shows the effect of nonlinear error on code value quantization.

[0080] A common method for extracting nonlinear errors in digital oscilloscopes is the sinusoidal code density probability distribution histogram algorithm. This algorithm mainly involves acquiring a large number of digital code values ​​from a single-cycle sinusoidal input signal to the digital oscilloscope, statistically analyzing the probability distribution of the code values, and using the characteristics of the sine function to derive the conversion width error for each digital code value. Furthermore, the corresponding nonlinear error sequence can be accumulated and calculated. A brief description of the traditional sinusoidal code density probability distribution histogram algorithm applied to digital oscilloscopes: The algorithm converts an over-range sinusoidal input signal to the digital oscilloscope, acquires only one cycle of converted digital code, and statistically analyzes the histogram of the frequency distribution of code values. When the input analog signal is a sine wave, such as... Figure 5 As shown, the statistical distribution of the digital codes at this point conforms to the bathtub curve pattern. Further processing based on the histogram of code value occurrence frequency distribution yields a cumulative histogram of code value occurrence frequencies, as shown below. Figure 2 The figure shows a statistical histogram of the cumulative number of code values. Based on the cumulative 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 threshold voltage of the corresponding digital code is calculated. The threshold voltage conversion formula is as follows:

[0081] (18)

[0082] In the formula, S K This represents the number of times each code value less than or equal to the numeric code K appears in the sample. S To collect the total number of samples, V K The edge voltage of the Kth digital code;

[0083] Subtract each pair of adjacent critical voltage data to obtain the corresponding conversion step width of the digital code. P k The average of all digital code conversion steps is used as the proposed standard conversion width value. V LSB The differential nonlinear error DNL is calculated using the following formula, and the integral nonlinear error is calculated by summing these formulas:

[0084] (1)

[0085] (2)

[0086] The above-mentioned sine code density probability distribution histogram algorithm has a problem of too large amount of analysis data required for high resolution, 35,000,000 analysis points are required for accurate analysis of non-linear error of a 16-bit resolution digital oscilloscope, 120,000,000 analysis points are required for accurate analysis of non-linear error of an 18-bit resolution digital oscilloscope, and 12,800,000,000 analysis points are required for accurate analysis of non-linear error of a 24-bit resolution digital oscilloscope. The high amount of calculation data leads to high complexity and low efficiency of extraction of non-linearity of a high resolution digital oscilloscope.

[0087] The embodiment is based on research on the histogram algorithm, and proposes a segmented recombination optimization algorithm based on the sine code density probability distribution histogram algorithm, which can be applied to extraction of non-linearity of a high-precision digital oscilloscope, improves the high and harsh requirement for the amount of collected and analyzed data, reduces the analysis complexity, and greatly improves the extraction efficiency.

[0088] The segmented recombination optimization algorithm based on the sine code density probability distribution histogram algorithm includes (1) division of segments and conversion of combined code value points and (2) expansion of non-linear error sequences of the combined points.

[0089] (1) Division of segments and conversion of combined code value points

[0090] First, the effective bit number index of the high resolution digital oscilloscope is tested. Generally, the value of the index is much lower than the resolution of the system, which leads to redundant invalid resolution bits. The redundant points can be combined into one point, defined as an image point, to facilitate the next step of using the sine code density probability distribution histogram algorithm to calculate and analyze the non-linearity of the combined points.

[0091] Suppose that the resolution of the high-precision digital acquisition card is N bits, ENOB is A bits, the combined point scale is M bits, 1

[0092] (3)

[0093] For example, under the premise of resolution 16 bits, 10 bits of effective bits, 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. The new code value data is obtained by conversion. Based on this principle, the total amount of code values for analyzing non-linear errors can be reduced by 16 times. Similarly, the larger the scale of the combination point selection, the greater the reduction rate of the analysis data amount. However, it should be noted that the selection of combination points cannot exceed the bit constraint range. Moreover, because the redundant bits are saved, the non-linear error sequence obtained based on the combination point code value data analysis is approximately within 1-5% of the original code value data analysis error.

[0094] (2) Non-linear error sequence expansion of combination points

[0095] After determining the scale of the combination points and converting the original code values into combination point code value data, the conversion step width error DNL of the combination code value point K can be calculated based on the sinusoidal code density probability distribution histogram algorithm. The corresponding non-linear error INL is obtained by the accumulation formula:

[0096] (2)

[0097] The non-linear error sequence corresponding to the combination points is obtained. Because this is the analysis result of the redundant bits, the non-linear error of the redundant bits can be obtained by expansion through equivalence or a linear function. The expansion formula is as follows:

[0098] (4)

[0099] (5)

[0100] (6)

[0101] 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 slope parameter of the straight line, INL 1 is the non-linear error sequence of the combination points, M is the combination point scale, and the non-linear error sequence of the complete code value corresponding to the acquisition system is obtained by expansion; the effect diagram of the 16-digit oscilloscope non-linear error extraction by the piecewise recombination optimization algorithm is shown in Figure 3 .

[0102] Figures 6(a) and 6(b) are schematic diagrams of the nonlinear error extracted from an 18-bit and a 30-bit high-precision digital oscilloscope, respectively, after the segmented recombination optimization algorithm, showing the effect of the method of extracting the nonlinear error, because the conventional algorithm cannot extract the nonlinear error at high resolution.

[0103] Segmented modeling and fitting method based on combined polynomial series

[0104] In the actual performance test of high-resolution digital oscilloscope, it is found that the working temperature of the internal device of the digital oscilloscope will significantly affect the nonlinear characteristics, such as Figure 7 As shown in the figure, the nonlinear deviation phenomenon occurs, and the nonlinear characteristics extracted at a single working temperature state cannot be universally applied to the analysis and calibration under the change of working temperature within a limited width. The method of the embodiment can comprehensively model and analyze the nonlinear error sequence of the digital oscilloscope under the change of working temperature, obtain a comprehensive mathematical model, and balance the nonlinear deviation caused by the change of temperature by changing the fitting parameter value to control the comprehensive model, so as to be applicable to the calibration under different working temperatures.

[0105] The embodiment adopts the method of modeling based on traditional polynomial series, proposes a segmented fitting modeling method based on combined polynomial series model, optimizes the traditional polynomial series, adds an additional quadratic function component to optimize and improve the model details, and further improves the reliability and fidelity of the model. By extracting the nonlinear error under multiple temperatures, the nonlinear error sequence is segmented, the model parameters are estimated, and the error model is established, to obtain the model of balancing the nonlinear deviation under the change of temperature and the key fitting parameters.

[0106] Extracting the nonlinear error sequence of a high-precision N-bit resolution digital oscilloscope under the change of working temperature y A、 B, C... Y The nonlinear error sequence is segmented by 14 bits, the segmented sequence is sorted, and the corresponding sequential segment number is from 1 to 2 (N-14) .

[0107] The model key parameters of the segmented subsequence are estimated, an additional quadratic function component is introduced into the model, the subsegment is further divided, and 256 subsegments are obtained. The parameter estimation input matrix h ( x ) of the quadratic function model component of the subsegment and the parameter estimation input diagonal matrix h of the entire subsequence are calculated, and the specific formula is as follows:

[0108] (7)

[0109] In the formula,​x from 1 to 256, total 256 h x ) Subdivision segment parameter estimation input matrix, x is the number of subdivision fields, k is the code value, a total of 64 columns, from left to right k l ) Corresponding to (from (-1) * 64 to (64-1) * 64-1), will x x h x ) Diagonal combination to get diagonal matrix h , as follows:

[0110] (8)

[0111] Further calculation of the polynomial technique model component parameter estimation input matrix a, as follows:

[0112] (9)

[0113] Further calculation of the model parameters of the quadratic function model component u , hu , as follows:

[0114] (10)

[0115] (11)

[0116] In the formula, h , u , a , h Large process operation parameters, no physical electrical signal meaning, I represent the same size unit matrix;

[0117] Quadratic function model component parameters hu and the same serial number of nonlinear error sub-sequence under each working temperature characteristic A i ，B i …Y i , the key parameters of the quadratic function component are calculated , as follows:

[0118] (12)

[0119] According to the polynomial series model input matrix a, the fitting parameters analyzed n and the same serial number of nonlinear error sub-sequence under each working temperature characteristic​​​​​A i ，B i …Y i The final polynomial series component key parameters can be calculated o i , as follows:

[0120] (13)

[0121] In the formula, the model key parameters are n i and o i , n i The key parameters corresponding to the quadratic function model component, o i The key parameters corresponding to the polynomial series component, based on the two parameters, the corresponding sub-sequence mathematical model is fitted INL i Each sub-sequence will correspond to a set of n i and o i parameters, a total of 2 (N-14) groups:

[0122] (14)

[0123] In the formula, INL i is the nonlinear error mathematical model corresponding to the sub-section with the serial number i h i ，n i ，a i ，o i , which refers to the parameter value corresponding to the sub-section with the serial number i INL i , which refers to the nonlinear error mathematical model corresponding to the sub-section with the serial number i h i ，n i ，a i ，o i , which refers to the parameter value corresponding to the sub-section with the serial number i

[0124] ​​​​The nonlinear error model of each sub-section is fitted and spliced to obtain a complete nonlinear error model, and the segmented modeling and fitting of nonlinear error are realized, as follows:

[0125] (15).

[0126] The method of this embodiment can integrate the nonlinear error characteristics under different working temperature characteristics by fitting, and can adjust the nonlinear deviation caused by temperature change by changing the parameters, and is suitable for nonlinear calibration under temperature fluctuation in a wide temperature range. For example, when the working temperature of the high-precision digital oscilloscope rises, the specified sub-section of the corresponding polynomial series model component can be adjusted by increasing the o i parameter, and the h i parameter of the specified sub-section of the quadratic function model component can be adjusted to make the integrated model more suitable for calibration at this time and at this temperature.

[0127] FIGS. 4(a) and 4(b) are schematic diagrams of segmented fitting of a nonlinear error model and complete model fitting, respectively.

[0128] FPGA real-time calibration method of reduced lookup table

[0129] The FPGA real-time calibration method of reduced lookup table is proposed in this embodiment, without making changes to the hardware of the high-precision digital oscilloscope, and the compensation data lookup table obtained by the segmented modeling and the compensation unit can realize real-time calibration of the output data, as shown in Figure 11 .

[0130] First, the segmented reorganization optimization algorithm is used to accurately and reliably extract the nonlinear error of the high-precision digital oscilloscope under the set working temperature condition, and according to the demand for temperature adaptability bandwidth, it is determined whether fitting is needed and how many groups of data are selected for fitting. In the case of needing fitting, the segmented modeling and fitting method is used to establish an integrated error model, and the error model is stored in the ROM storage unit of the FPGA of the digital oscilloscope as a calibration data table. The FPGA first determines which combination point the output digital code belongs to; the determination method is as follows:

[0131] (16)

[0132] In the formula, k represents the digital original code value, K represents the digital code value.

[0133] According to the determination value, the compensation value is obtained by indexing the calibration data table in real time, and the found compensation value is compensated to the real-time output digital code itself, and the output data stream is sequentially table-looked up and calibrated, realizing fast and accurate correction of the nonlinear error value. The calibration formula is as follows:

[0134] (17)

[0135] The key is that the look-up table used for calibration adopts the combination point structure of segmented recombination based on the segmented recombination optimization algorithm, the size of the nonlinear error model is reduced, the size of the calibration table is reduced by more times without affecting the calibration accuracy and effect, the problem of large storage space occupied by the LUT table in high-precision calibration is effectively solved, the method can be applied to real-time calibration of high-precision high-resolution digital oscilloscopes, and after calibration, the nonlinear error of the digital oscilloscope can be reduced by more than 99%, the linearity of the device is greatly improved, the harmonic noise is reduced, and the dynamic performance can be improved by more than 110%.

[0136] The advantages of the present embodiment for the existing scheme are as follows:

[0137] 1. Compared with the adaptive filter calibration method, the method proposed in the embodiment has better real-time performance, the parallel processing capability of the FPGA is strong, and the compensation result can be quickly responded, which is not affected by the convergence speed of the adaptive filter, and can be applied to nonlinear calibration of digital oscilloscopes with 24-bit resolution and above different sampling rates and bandwidths (up to Gsa / s above).

[0138] 2. Compared with the interpolation calibration method based on the neural network, the neural network calibration method needs tens of thousands of multiplication and addition operations for each calibration data, which makes the algorithm produce large power consumption and area in the calibration unit, the method proposed in the embodiment has better real-time performance, and the calibration is mainly dependent on the LUT calibration data table stored in the FPGA, which occupies less hardware resources, and the accuracy of the calibration is not affected by the accuracy of the oscilloscope, and can be applied to nonlinear calibration of high-precision digital oscilloscopes.

[0139] 3. Compared with the existing real-time calibration method based on LUT, when the nonlinear error is pre-extracted for high-precision oscilloscopes, the calculation amount is too large to even exceed the operation capability load of a general computer, and when the LUT look-up table is implemented, in order to ensure the accuracy of the calibration, the memory space will be multiplied with the increase of the calibration accuracy, and the method proposed in the embodiment greatly reduces the amount of data required for pre-extraction and the operation difficulty, the space used for storing the calibration table in the FPGA is smaller, and the problem of limited space resources of the oscilloscope is avoided.

[0140] Embodiment 2

[0141] The reagent process application is carried out according to the following steps, and the analysis data process can be completed in MATLAB:

[0142] Step 1, according to the N-bit resolution digital oscilloscope operating temperature change lock to be balanced temperature range ta-tb, with controllable temperature t as a step to determine the temperature range ta, (ta+t), (ta+2t), …, tb is the operating temperature characteristic point to be analyzed;

[0143] Step 2, the SINAD of the high-precision digital oscilloscope to be calibrated, the SFDR index is tested, the effective number of bits ENOB is calculated according to SINAD, the combination point scale is determined according to the piecewise recombination optimization algorithm, and the mathematical structure of the reconstructed output digital code is determined;

[0144] The test calculation of SINAD and SFDR needs to input a sine signal with a frequency f 1 and an amplitude reaching more than 90% of the range to the digital oscilloscope, wherein the sampling rate of the digital oscilloscope is set to FS , 2 Y data points are collected for FFT transformation to analyze the index, and the power of 2 can avoid the truncation effect and prevent the negative influence of spectrum leakage on the index test, the input signal frequency f 1 is:

[0145] (19)

[0146] After FFT transformation of the collected data, the SINAD and SFDR are analyzed in the frequency domain as follows:

[0147] (20)

[0148] In the formula, SINAD is the signal-to-noise ratio / dB; V signal is the amplitude value of the fundamental signal in the frequency domain after FFT; V harmonic 2 _avg is the average of the square of the amplitude of the first 6 harmonics in the frequency domain after FFT; V noise 2 _avg is the average of the square of the amplitude of the noise except the first 6 harmonics and the fundamental signal in the frequency domain after FFT;

[0149] (21)

[0150] In the formula, SFDR is the spurious-free dynamic range (dBc); V other_max is the amplitude value of the maximum component except the fundamental signal in the frequency domain after FFT;

[0151] The calculation formula of ENOB is:

[0152] (22)

[0153] Step 3, monitor the high-precision digital oscilloscope temperature change, in the determined ta, (ta+t), (ta+2t), …, tb operating temperature points, according to the division combination point scale M and reconstruction structure, respectively for high-precision digital oscilloscope input frequency is fc And the amplitude exceeds the range of 10% of the sine signal, the collection of L data points, based on the piecewise recombination optimization algorithm for analysis of the nonlinear error INL A , INL B , …, INL K .

[0154] Input frequency fc And the number of sample collection points S The calculation method is:

[0155] (23)

[0156] (24)

[0157] In the formula, Fs The oscilloscope sampling rate;

[0158] Step 4, the nonlinear error INL A , INL B , …, INL K At ta, (ta+t), (ta+2t), …, tb multiple temperature points are compared, and the error curve has a certain deviation, and the similar multiple nonlinear errors are only retained one;

[0159] Step 5, the nonlinear error based on the piecewise modeling fitting algorithm for error model modeling and parameter fitting of the reserved specific operating temperature characteristic points, get fitting error model INL, model is divided into 2 (N-14) Therefore, there are two function components key parameter group n And the polynomial series component key parameter group o The corresponding representative meaning is:

[0160] (25)

[0161] (26)

[0162] Step 6, convert the fitted calibration model INL into two parts, a symbol component table INL_FH and an integer numerical component table INL_ZS, without retaining the decimal component; when converting the symbol table, when the INL corresponding numerical value is positive, the symbol table value is 0, when the INL corresponding numerical value is negative, the symbol table value is 1; when converting the integer table, the decimal numerical value needs to be converted into a bin binary numerical value recorded in the table; convert INL_FH and INL_ZS two tables into TXT text and save; in MATLAB, the dec2hex() instruction can be used to complete the conversion from decimal to binary, and the fprintf() series of instructions can be used to write the specified data into the target txt file; the specific steps are as follows:

[0163] Usage of instructions:

[0164] A = dec2hex(a);

[0165] Convert the decimal number a to binary number A

[0166] fid = fopen('b.txt','wt');

[0167] fprintf(fid,'%d\n',fh);

[0168] fclose(fid);

[0169] fopen creates and opens the corresponding specified txt file, and wt allows reading and writing; the fprintf function represents the table and specifies the format function, and writes the corresponding data into the txt according to the specified format; fclose closes the txt file read and written;

[0170] Step 7, convert the symbol component table INL_FH and the integer numerical component table INL_ZS into COE file format, import the txt data into the word document, replace all ^p (line feed) with English comma through the ctrl+H instruction, replace the last line with English semicolon, and add instruction words in the top two lines:

[0171] MEMORY_INITIALIZATION_RADIX=2;

[0172] MEMORY_INITIALIZATION_VECTOR=

[0173] Replace the modified results with the original txt file content and save it as a coe file format, generate a coe type file that can be stored in the FPGA ROM;

[0174] Step 8, design the 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. The FPGA signal preprocessing unit segments and reorganizes the received digital signal digital_singal, converts the original code value to the corresponding combination point code value, and obtains the reorganized lookup signal find_singal used for looking up the calibration table. The conversion method from the original digital signal digital_singal to the reorganized lookup signal find_singal is:

[0175] (27)

[0176] In the formula, M is the scale of the combination point.

[0177] Step 9, place the generated coe calibration table file into the ROM IP core of the FPGA as the calibration data table (inl_data) for lookup; according to the index lookup of the obtained lookup signal find_singal, find the calibration data inl_data(find_singal) corresponding to the bit sequence in the digital_singal table, and compensate the found calibration data to digital_singal to complete data calibration; the calibration method is represented as:

[0178] (28)

[0179] 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 signal collected in real time. The digital oscilloscope is input with a frequency f1 and an amplitude reaching more than 90% of the range fc and a frequency and an amplitude reaching more than 110% of the range of the sine signal, which can test and calculate the dynamic performance indicators and nonlinear characteristics of the digital oscilloscope after using the method of the present application. When the calibration effect decreases or the effect is poor for the edge temperature in the applicable temperature range, the internal parameter value of the segmented model sub-section parameter o can be changed to adjust the model and balance the nonlinear deviation caused by the variable temperature. The adjustment method example one is applied in the 16-bit resolution digital oscilloscope 6912D made by the 41st Research Institute of China Electronics Technology Group: the applicable balanced temperature interval of 6912D is 58-69°.

[0180] When the device operating temperature of the high-precision digital oscilloscope is at the upper edge of 69°, the effect is poor, and the o i parameters 20-50% of the 2-8 segments of the polynomial series model component can make the comprehensive model more suitable for calibration at this temperature.

[0181] Take 64° as the standard working temperature of the tested 6912D digital oscilloscope, and take single-section regulation as an example to show the balancing method. Figure 12 Fig. 2 is a diagram showing the change range of the key parameter o1 of the non-linear calibration model of the digital oscilloscope 6912D at 69° relative to that at 64°, Figure 12 As shown in Fig. 2, when the temperature rises to 69°, it can be seen that o1 as a whole presents a falling trend but some point values increase. It is particularly noted that the internal parameter in the third position is increased by 1.5 times and the internal parameter in the fifth position is increased by 3.5 times on the basis of the model parameter o1 at 64°, so that the calibration model is closer to the model at 69°; Figure 13 Fig. 3 is a diagram showing the change range of the key parameter o1 of the non-linear calibration model of the digital oscilloscope 6912D at 58° relative to that at 64°, Figure 13 As shown in Fig. 3, when the temperature drops to 58°, it can be seen that o1 as a whole presents a sharp increasing trend. It can be achieved that the calibration model is closer to the model at 58° and the balancing effect is realized by increasing the internal parameter in the third position by about 10 times, increasing the internal parameter in the seventh position by about 4 times and particularly increasing the internal parameter in the fifth position by 40 times on the basis of the model o1 at 64°.

[0182] The principles and implementation manners of the present application are described by using specific embodiments in the present application. The above embodiment is only used to help understand the method of the present application and its core idea. It should be noted that the ordinary skilled in the art can make some improvements and modifications to the present application without departing from the principles of the present application. These improvements and modifications also fall within the protection scope of the present application.

Claims

1. A method of non-linear analysis and calibration of a high-precision digital oscilloscope, characterized in that, Comprise: Segmented reorganization optimization process for extracting nonlinear error of digital oscilloscope at different operating temperatures; Segmented modeling fitting process for fitting the nonlinear error to obtain a nonlinear error model, specifically comprising: A segmented fitting modeling method based on a combined polynomial series model, which is used to sequentially segment, estimate model parameters, and establish error models for the extracted nonlinear error to obtain a model of nonlinear deviation under balanced temperature and key fitting parameters thereof; The segmented fitting modeling method based on the combined polynomial series model comprises: Sequence segmentation, including extracting high-precision N of a high-precision digital oscilloscope y Nonlinear error sequence under group operating temperature characteristics A, B, C…Y , segmenting the nonlinear error sequence by 14 bits as a unit, sorting the segmented nonlinear error sequence to obtain a segmented subsequence sequence number corresponding to the order i from 1 to 2 ( N -14); Model parameter estimation, performing model parameter estimation on the sub-sequence, introducing a quadratic function component to the combined polynomial series model, performing quadratic division on the sub-sequence to obtain a parameter estimation input matrix of the quadratic function model component of the subdivided sub-sequence h x and a parameter estimation input diagonal matrix of the entire sub-sequence h as follows:​ （7） In the formula, x is the number of subfields, k is the code value, and h ( x ) is a diagonal matrix obtained by diagonal combination h as follows: （8） Further calculation to obtain a parameter estimation input matrix a of the polynomial series model component, specifically as follows: （9） Further calculate the model parameters of the quadratic function model component u , hu , as follows: （10） （11） wherein I is an identity matrix of the same size, and L is the order of the polynomial series component; Quadratic function model component parameters hu and the same serial number of nonlinear error sub-sequence under each operating temperature characteristic A i ， B i …Y i , calculate the key parameters of the quadratic function component as follows: （12） In summary, the final polynomial series component key parameters are calculated o i as follows: （13） In the formula, the model key parameters are n i and o i , n i the key parameters corresponding to the quadratic function model component, o i the key parameters corresponding to the polynomial series component, and the corresponding sub-sequence mathematical model is fitted based on the two parameters INL i : （14） wherein INL i is a nonlinear error mathematical model corresponding to the sub-segment with the serial number of i . Splicing the nonlinear error model of each sub-section after fitting to obtain a complete nonlinear error model, as follows: （15）； FPGA real-time calibration process, the nonlinear error model is stored in the high-precision digital oscilloscope FPGA as a calibration data table, and the corresponding error model in the FPGA is found by indexing the digital oscilloscope output digital code in real time to obtain the nonlinear error value, which is compensated to the real-time output digital code to complete the calibration compensation.

2. The method of non-linear analysis and calibration of a high precision digital oscilloscope as claimed in claim 1, wherein, The nonlinear error includes integral nonlinear error and differential nonlinear error, and the integral nonlinear error can be obtained by cumulatively summing the differential nonlinear error.

3. The method of non-linear analysis and calibration of a high precision digital oscilloscope according to claim 2, characterized in that, The nonlinear error sequence of the digital oscilloscope is extracted based on a sine code density probability distribution histogram algorithm, specifically as follows: （1） （2） wherein, k is the digital code value of the digital oscilloscope itself, DNL is the differential non-linearity error, V k is the digital code corresponding conversion step width, V LSB is the standard conversion width value, INL is the non-linearity error, N is the resolution bit number of the digital oscilloscope.

4. The method of non-linear analysis and calibration of a high precision digital oscilloscope according to claim 3, characterized in that, The sine code density probability distribution histogram algorithm comprises: The partitioning and conversion of the combined code value points: assuming 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, 1<M<(N-A-1), the entire digital code that can be output is reconstructed, and the mathematical structure of the combined point distribution is constructed as follows: （3） The nonlinear error sequence of the combined points is expanded to obtain the nonlinear error sequence of the complete digital code, specifically as follows: （4） （5） （6） wherein, k is a digital code value of the digital oscilloscope itself, K is a code value k corresponds to the recombined point corresponding number value, b is a straight line slope parameter, INL 1 is a nonlinear error sequence of the combined point, M is a combined point scale.

5. The method of non-linear analysis and calibration of a high precision digital oscilloscope as claimed in claim 1, wherein, The FPGA real-time calibration specifically comprises: The nonlinear error model is stored in the ROM storage unit of the digital oscilloscope FPGA as a calibration data table, the FPGA first determines the combined point position of the output digital code, and finds the nonlinear error value by indexing the calibration data table in real time according to the combined point position, and compensates the found nonlinear error value to the real-time output digital code itself, then finds the calibration data table in sequence to calibrate the output data stream, and completes the nonlinear error value correction.

6. The method of non-linear analysis and calibration of a high precision digital oscilloscope as claimed in claim 4, wherein, The determination of the combined point position is specifically as follows: （16）。 7. The method of non-linear analysis and calibration of a high precision digital oscilloscope as claimed in claim 4, wherein, The calibration is specifically as follows: （17）。

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