A DAC Output Error Correction Method Based on Digital Compensation

Abstract

This invention discloses a DAC output error correction method based on digital compensation, comprising: collecting amplitude deviation, phase shift, and timing jitter data of the DAC output signal through a quantum sensing DAC calibration and analysis platform to construct a multi-dimensional original error dataset; calling an operational amplifier offset dynamic coupling prediction model to analyze the coupling relationship and extract dynamic correlation features; separating harmonic components and screening error contribution factors based on a broadband DAC harmonic distortion correction model; calculating the gradient change law and extreme point position using a differential nonlinear gradient correction model; integrating the above features and parameters to construct a digital compensation parameter matrix, and dynamically adjusting the output code value through real-time digital modulation to achieve error correction. This method, through multi-model collaborative operation and full-process closed-loop processing, accurately captures the dynamic correlation and distribution characteristics of multi-source errors, achieves synchronous correction of multi-dimensional errors, and improves DAC output accuracy and operating condition adaptability.

Description

Technical Field

[0001] This invention relates to the field of digital-to-analog error correction technology, and in particular to a DAC output error correction method based on digital compensation. Background Technology

[0002] In electronic information and communication engineering, the digital-to-analog converter (DAC) is a core component for converting digital signals to analog signals, and its output accuracy directly affects the performance of the entire electronic system. With the rapid development of technologies such as broadband communication and quantum sensing, higher demands are placed on the output bandwidth, conversion rate, and linearity of DACs. However, during DAC operation, the dynamic changes in operational amplifier offset voltage, the cumulative effect of harmonic distortion, and errors caused by differential nonlinearity can lead to problems such as amplitude deviation, phase shift, and timing jitter in the output signal, severely affecting signal transmission quality and system stability. Traditional DAC calibration methods often rely on a single error correction mechanism, making it difficult to address the coupled effects of multiple error sources. Therefore, a technical solution that can integrate multi-dimensional error factors and achieve precise dynamic compensation is urgently needed to meet the stringent requirements of high-precision electronic systems for DAC output accuracy.

[0003] Existing technologies have two significant drawbacks: First, existing error correction methods do not fully consider the dynamic coupling characteristics of operational amplifier offset, and only use static calibration mode to compensate for a single error source. This fails to capture the dynamic correlation between operational amplifier offset and harmonic distortion and differential nonlinear error, resulting in a significant decrease in correction effect when multiple source errors are superimposed, making it difficult to adapt to error variation patterns under complex operating conditions. Second, existing technologies lack an integrated calibration analysis platform and a multi-model collaborative correction mechanism. They do not combine quantum sensing technology with harmonic distortion correction and differential nonlinear gradient correction, making it impossible to achieve high-precision acquisition of error data and synchronous correction of multi-dimensional errors. Furthermore, the construction of digital compensation parameters does not fully integrate the error gradient variation pattern and extreme point distribution characteristics, resulting in insufficient adaptability of compensation parameters and difficulty in achieving real-time dynamic correction of DAC output errors. Summary of the Invention

[0004] In order to overcome the shortcomings and deficiencies of the existing technology, the present invention provides a DAC output error correction method based on digital compensation.

[0005] The technical solution adopted in this invention is a DAC output error correction method based on digital compensation, comprising the following steps: S1, collecting amplitude deviation, phase offset, and timing jitter data of the DAC output signal through a quantum sensing DAC calibration and analysis platform to establish a multi-dimensional original error dataset; S2, calling the operational amplifier offset dynamic coupling prediction model to analyze the coupling relationship of the original error dataset and extracting the dynamic correlation features between the operational amplifier offset voltage and the output error; S3, separating harmonic components of the coupling correlation features based on a broadband DAC harmonic distortion correction model and selecting the error contribution factors corresponding to each harmonic; S4, using a differential nonlinear gradient correction model to perform gradient calculation on the harmonic error contribution factors to determine the gradient change law and extreme point position of the error distribution; S5, constructing a digital compensation parameter matrix by combining the dynamic correlation features, error contribution factors, and gradient change law, wherein the digital compensation parameter matrix includes amplitude compensation coefficients, phase calibration coefficients, and timing adjustment parameters; S6, performing real-time digital modulation on the DAC output signal based on the digital compensation parameter matrix, and correcting the error by dynamically adjusting the output code value, with the digital modulation process synchronously responding to changes in the position of the extreme point of the error distribution.

[0006] Furthermore, the expression for the operational amplifier offset dynamic coupling prediction model is as follows: This refers to the dynamic coupling quantity of the operational amplifier offset. The coupling coefficient is... This is the initial op-amp offset voltage. Clock frequency influence factor, For system clock frequency, The output voltage deviation sensitivity coefficient. For DAC output voltage deviation, To add weighting coefficients, The offset voltage of the i-th operational amplifier. Let i be the phase deviation influence coefficient of the i-th path. For the first Road signal phase deviation.

[0007] Furthermore, the expression for the broadband DAC harmonic distortion correction model is as follows: middle, This is the harmonic distortion correction factor. The fundamental amplitude, The fundamental angular frequency, For time variables, The initial phase of the fundamental wave. The harmonic order is... The amplitude correction factor for the m-th harmonic is... Let m be the amplitude of the m-th harmonic. The initial phase of the m-th harmonic. The integral correction factor for the m-th harmonic is given. It is the integral variable.

[0008] Furthermore, the expression for the differential nonlinear gradient correction model is: ,in, The differential nonlinear gradient value, For gradient operators, These are the original differential nonlinear coefficients. This represents the original differential nonlinear error value. The first derivative weighting coefficients are... For DAC input code value variables, The weighting coefficient is the squared second derivative.

[0009] Furthermore, the error acquisition model expression of the quantum sensing DAC calibration analysis platform is as follows: ,in, To comprehensively collect error values, This is the data acquisition accuracy coefficient. For amplitude deviation, For phase shift, For timing jitter, The covariance weighting coefficients are... The three-dimensional covariance is the sum of amplitude deviation, phase shift, and timing jitter.

[0010] Furthermore, the model expression for constructing the digital compensation parameter matrix is ​​as follows: in, For digital compensation parameter matrix, For amplitude compensation weight, For phase compensation weights, For time-series compensation weights, The amplitude-phase crossover compensation coefficient, For phase-timing crossover compensation coefficients, This is the timing-amplitude cross-compensation coefficient.

[0011] Further, step S3 includes the following sub-steps: S31, inputting the operational amplifier offset dynamic coupling correlation characteristics into the harmonic separation module of the broadband DAC harmonic distortion correction model, and decomposing the composite signal into the fundamental component and each harmonic component through frequency domain transformation; S32, extracting the amplitude and phase of each harmonic component after decomposition, and recording the characteristic parameters of the harmonic components at different frequencies; S33, calculating the contribution ratio of each harmonic to the DAC output error based on the characteristic parameters, and removing harmonic components with a contribution ratio lower than a set threshold; S34, mapping and associating the characteristic parameters corresponding to the retained high-contribution harmonic components with the error data to form a set of harmonic error contribution factors.

[0012] Further, S4 includes the following sub-steps: S41, importing the harmonic error contribution factor into the gradient calculation unit of the differential nonlinear gradient correction model, setting the step size of the input code value change, and traversing the entire range of input code values; S42, calculating the differential nonlinear error value corresponding to each input code value, and solving the error gradient value through the error difference between adjacent code values; S43, performing sliding window filtering on the gradient value to eliminate the interference of random noise on the gradient change law; S44, judging the rising and falling intervals of the error distribution through the positive and negative changes of the gradient value, and locating the error extreme point where the gradient value is zero.

[0013] Further, S5 includes the following sub-steps: S51, collecting coupling coefficients from dynamic correlation features, harmonic amplitude and phase parameters from error contribution factors, and gradient extreme value data from gradient change patterns to establish an original set of compensation parameters; S52, filtering and standardizing the parameters in the original set according to the parameter constraints of the digital compensation model, and removing invalid parameters; S53, classifying and assigning the standardized parameters to the corresponding compensation dimensions according to the functional requirements of amplitude compensation, phase calibration, and timing adjustment; S54, integrating the compensation parameters of each dimension through matrix operations to generate a dimension-matched digital compensation parameter matrix.

[0014] A digital compensation-based DAC output error correction method is implemented through different units, including: a quantum sensing multi-dimensional error acquisition unit, used to acquire amplitude deviation, phase shift, and timing jitter data of the DAC output signal and generate a raw error dataset, whose output is connected to an op-amp offset dynamic coupling feature analysis unit; an op-amp offset dynamic coupling feature analysis unit, used to call an op-amp offset dynamic coupling prediction model to analyze the coupling relationship in the raw error dataset and extract dynamic correlation features, whose output is connected to a broadband DAC harmonic error separation unit; and a broadband DAC harmonic error separation unit, used to separate harmonic components in the coupling features based on a broadband DAC harmonic distortion correction model and screen error contribution factors, whose output is connected to a differential nonlinear gradient operation unit. The system comprises the following components: a differential nonlinear gradient calculation unit, used to calculate the gradient change law of the error contribution factor through the differential nonlinear gradient correction model and locate the extreme point position; its output is connected to the digital compensation parameter matrix construction unit; a digital compensation parameter matrix construction unit, used to construct a compensation parameter matrix including amplitude compensation coefficient, phase calibration coefficient, and timing adjustment parameter by combining dynamic correlation characteristics, error contribution factor, and gradient change law; its output is connected to the DAC output real-time modulation unit; and a DAC output real-time modulation unit, used to dynamically adjust the code value of the DAC output signal according to the digital compensation parameter matrix and to correct errors in response to changes in the extreme point position. Its input is connected to the output of the digital compensation parameter matrix construction unit, and its output is directly connected to the DAC output link.

[0015] Beneficial Effects: This invention proposes a DAC output error correction method based on digital compensation. Utilizing a calibration analysis platform constructed with quantum sensing technology, it efficiently collects multi-dimensional raw error data. Combined with an operational amplifier offset dynamic coupling prediction model, it deeply analyzes the dynamic correlation characteristics between multi-source errors, completely overcoming the limitation of existing static calibration techniques in handling error coupling effects. This enables error correction to accurately match the error variation patterns under complex operating conditions. Through the synergistic operation of a broadband DAC harmonic distortion correction model and a differential nonlinear gradient correction model, it achieves harmonic component separation, error contribution factor screening, and gradient variation pattern analysis. Furthermore, it integrates multi-dimensional error parameters to construct a digital compensation parameter matrix, forming a multi-model collaborative correction mechanism. This compensates for the lack of an integrated calibration platform and synchronous correction capabilities in existing technologies. Simultaneously, based on the location of the error gradient extreme points, it dynamically adjusts the digital modulation strategy to ensure real-time adaptation between compensation parameters and error distribution, achieving synchronous and accurate correction of multi-source errors. This significantly improves the amplitude, phase, and timing accuracy of the DAC output signal, effectively meeting the stringent requirements of high-precision electronic systems for DAC output accuracy. It fundamentally solves the core problems of limited correction effects and insufficient adaptability in existing technologies. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method steps of the present invention;

[0017] Figure 2 This is a diagram showing the unit composition for implementing the method of the present invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] like Figure 1 As shown, a DAC output error correction method based on digital compensation includes the following steps:

[0020] S1. Collect amplitude deviation, phase shift and timing jitter data of DAC output signal through quantum sensing DAC calibration and analysis platform to establish a multi-dimensional error raw dataset;

[0021] Specifically, step S1 is implemented as follows: The quantum sensing DAC calibration and analysis platform is started, with the sampling frequency precisely set to 5 million data points per second and the acquisition duration set to 30 minutes. This comprehensively covers the entire operating voltage range of the DAC input voltage from 0 to full scale and the frequency range from 1kHz to 100MHz. The platform focuses on acquiring three core error data types: amplitude deviation, phase shift, and timing jitter. The amplitude deviation acquisition accuracy is strictly controlled within ±5 microvolts, the phase shift acquisition resolution is set to 0.1 milliradians, and the minimum time interval for timing jitter acquisition is 10 nanoseconds. Through the platform's built-in 8-channel synchronous acquisition module, the output signal is systematically acquired under different conditions, including the full range of DAC input code values ​​from 0000H to FFFFH and load resistances from 10Ω to 1kΩ. A fixed 2000 sets of sample data are acquired in each operating state to ensure coverage of various typical operating conditions such as light load, heavy load, low frequency, and high frequency. During the data acquisition process, relying on the built-in electromagnetic shielding structure and adaptive noise suppression algorithm of the quantum sensing unit, external electromagnetic interference and environmental noise with amplitude below 2 microvolts in the frequency range of 20MHz to 1GHz are effectively filtered. Finally, all the acquired multi-dimensional data are classified and integrated according to timestamp, input code value, and load conditions to form a multi-dimensional error raw dataset containing 1.2 million valid records. This dataset fully includes the dynamic change information of error in three dimensions: amplitude, phase, and time series. It provides high-fidelity, full-scenario basic data support for subsequent error coupling relationship analysis and compensation parameter construction. The completeness and accuracy of its data acquisition directly determine the targeting and final effect of the subsequent error correction process.

[0022] S2, call the op-amp offset dynamic coupling prediction model to analyze the coupling relationship of the original error dataset and extract the dynamic correlation features between op-amp offset voltage and output error;

[0023] Specifically, step S2 is implemented as follows: The operational amplifier offset dynamic coupling prediction model, pre-trained based on a large amount of measured data, is invoked. The multi-dimensional error raw dataset obtained in step S1 is segmented according to time series and input into the model. The model uses a 3-layer convolutional feature extraction network and a 2-layer fully connected analytical network to analyze the dynamic correlation between the operational amplifier offset voltage and the output error layer by layer. During implementation, a coupling relationship analysis threshold is first set for the model. Abnormal data with amplitude deviations exceeding 5 microvolts and phase shifts exceeding 0.1 milliradians are marked as key analysis objects. Simultaneously, a fixed time window length of 10 milliseconds is set to segment and analyze the continuously collected data to accurately capture the dynamic characteristics of error changes over time. The model calculates the Pearson correlation coefficients between the op-amp offset voltage and amplitude deviation, phase shift, and timing jitter within each time window, selecting strongly correlated combinations with absolute correlation coefficients higher than 0.8. Then, through linear fitting and nonlinear regression algorithms, it extracts the quadratic function variation law of the op-amp offset voltage with time, input code value, and load conditions, as well as the mapping relationship between this law and various output errors, ultimately forming a dynamic correlation feature set including 20 core feature parameters. During this process, the model adaptively adjusts the convolution kernel size and fully connected layer weights by monitoring data distribution characteristics in real time, ensuring accurate extraction of core correlation features even under complex operating conditions such as high frequency and heavy load. This provides highly targeted and identifiable analysis objects for subsequent harmonic component separation and gradient calculation. The accuracy of its feature extraction directly affects the accuracy and efficiency of the entire error correction process.

[0024] S3, based on the broadband DAC harmonic distortion correction model, the harmonic components of the coupling correlation characteristics are separated, and the error contribution factors corresponding to each harmonic are screened out.

[0025] Specifically, step S3 is implemented as follows: Based on the broadband DAC harmonic distortion correction model, the dynamic correlation features extracted in step S2 are processed for harmonic component separation. During implementation, the model's frequency analysis range is first set to 1kHz to 100MHz, perfectly matching the DAC's operating bandwidth. Simultaneously, the upper limit of the harmonic order analysis is set to 15th order to ensure that the main harmonic components affecting output accuracy are included. The model uses a fast Fourier transform algorithm to decompose the composite electrical signal corresponding to the dynamic correlation features into a fundamental component and harmonic components from the 1st to the 15th orders. Then, the amplitude detection module and phase detection module calculate the peak amplitude, initial phase, and center frequency parameters of each harmonic component. By calculating the amplitude ratio and phase difference with the fundamental component, the degree of influence of each harmonic on the output error is quantitatively determined. Based on this, an error contribution factor screening threshold of 0.05 was set. The amplitude proportion and phase shift influence of each harmonic component were weighted and calculated with weights of 0.6 and 0.4, respectively. Harmonic components with weighted scores exceeding the threshold were selected as key error sources, forming a set of error contribution factors including 3 to 8 core harmonic parameters. During implementation, the model dynamically adjusted the frequency domain resolution to 10Hz to ensure the accuracy of harmonic component separation and avoid the omission of high-contribution harmonic components due to insufficient resolution. At the same time, a wavelet threshold denoising algorithm was used to remove spurious harmonic signals caused by high-frequency noise above 100MHz, ensuring the reliability and purity of the error contribution factors. This provides accurate and focused error analysis basis for subsequent differential nonlinear gradient calculations, directly affecting the efficiency of gradient calculation and the accuracy of extreme point location.

[0026] S4. A differential nonlinear gradient correction model is used to perform gradient calculation on the harmonic error contribution factor to determine the gradient variation law and extreme point location of the error distribution.

[0027] Specifically, step S4 is implemented as follows: A differential nonlinear gradient correction model is used to perform gradient calculations on the harmonic error contribution factors selected in step S3. During implementation, the step size of the input code value change is first set to one-tenth of 1 LSB, i.e., 0.1 LSB, to ensure the precision and accuracy of the calculation. The model uses the DAC input code value as the independent variable and the comprehensive error value corresponding to the error contribution factor as the dependent variable. Through an algorithm for calculating the error difference between adjacent code values, the difference in error values ​​between adjacent code values ​​is calculated point by point within the entire range of the input code value from 0000H to FFFFH, obtaining the gradient value of the error distribution. Then, a continuous gradient change curve is constructed through a data fitting algorithm. Subsequently, a gradient change rate threshold of 0.02 is set. By traversing the entire range of input code values, the slope trend of the gradient change curve is analyzed to identify the intervals where the gradient value is positive, negative, or close to zero. The rising segment, falling segment, and stationary segment of the error distribution are precisely divided, and the region where the error extrema may exist is determined. During implementation, a sliding window with a length of 50 code value units is used to perform moving average filtering on the gradient values, effectively eliminating the interference of random noise with an amplitude below 0.01 on the gradient calculation. At the same time, an extreme point determination condition is set. When the absolute value of the gradient values ​​corresponding to 5 consecutive adjacent code values ​​is less than 0.005 and the gradient signs of adjacent intervals change in opposite directions, it is determined to be an error extreme point. Finally, the input code value positions and corresponding error amplitudes of all extreme points are output, providing key feature information of error distribution for the subsequent construction of the digital compensation parameter matrix, ensuring that the compensation strategy can specifically address the error extreme region and improve the overall error correction effect.

[0028] S5. A digital compensation parameter matrix is ​​constructed by combining dynamic correlation characteristics, error contribution factors and gradient change laws. The digital compensation parameter matrix includes amplitude compensation coefficient, phase calibration coefficient and timing adjustment parameters.

[0029] Specifically, step S5 involves systematically constructing a digital compensation parameter matrix by integrating the dynamic correlation features extracted in step S2, the error contribution factors selected in step S3, and the gradient change patterns determined in step S4. During implementation, the three types of features and parameters are first preprocessed using a max-min normalization algorithm, mapping data of different dimensions and magnitudes to a numerical range of 0 to 1. Then, the weight coefficients of each parameter are set using the analytic hierarchy process (AHP). The weight coefficient for dynamic correlation features is set to 0.35, the weight coefficient for error contribution factors is set to 0.4, and the weight coefficient for gradient change patterns is set to 0.25. The weight coefficients for sub-parameters corresponding to high-contribution errors are proportionally increased. Based on the set weight coefficients, the coupling coefficients in the dynamic correlation features, the harmonic amplitude and phase parameters in the error contribution factors, and the gradient extrema and extreme point location information in the gradient change patterns are respectively categorized and integrated into three functional dimensions: amplitude compensation, phase calibration, and timing adjustment. In each dimension, the distribution pattern of each parameter is analyzed by statistical histogram to determine the value range of the compensation coefficient. The amplitude compensation coefficient covers the error deviation range of -10 microvolts to +10 microvolts, the phase calibration coefficient corresponds to the phase offset range of -0.5 milliradians to +0.5 milliradians, and the timing adjustment parameter matches the timing jitter amplitude of -50 nanoseconds to +50 nanoseconds. Finally, the parameters of the three dimensions are integrated by matrix transpose and weighted summation to form a digital compensation parameter matrix with 65,536 rows (corresponding to the input code value range) and 3 columns (corresponding to the three compensation dimensions). The completeness and accuracy of this matrix directly determine the error correction effect of the subsequent digital modulation process. Its parameter update frequency is synchronized with the error data acquisition frequency to ensure dynamic adaptation to error changes.

[0030] S6 performs real-time digital modulation on the DAC output signal based on the digital compensation parameter matrix, and corrects errors by dynamically adjusting the output code value. The digital modulation process synchronously responds to changes in the position of the extreme points of the error distribution.

[0031] Specifically, step S6 is implemented as follows: Based strictly on the digital compensation parameter matrix constructed in step S5, the DAC output signal is digitally modulated in real time. During implementation, a lookup table mapping algorithm is first used to establish a one-to-one correspondence between the compensation parameter matrix and the DAC output code value. The amplitude compensation coefficient, phase calibration coefficient, and timing adjustment parameter in the matrix are converted into corresponding DAC output code value adjustment amounts. Amplitude compensation corresponds to the adjustment of the lowest 4 bits of the code value, phase calibration corresponds to the adjustment of the middle 4 bits, and timing adjustment corresponds to the adjustment of the highest 4 bits. The modulation update frequency is set to 1MHz, which is higher than the DAC's maximum output rate of 500kHz, ensuring real-time response to error changes. Simultaneously, the step precision of the code value adjustment is set to 0.1LSB, consistent with the input code value step size in step S4, to avoid overcompensation or undercompensation due to mismatched adjustment precision. During modulation, the built-in extreme point monitoring module tracks the location of the error distribution extreme points determined in step S4 in real time. When an extreme point shift of more than 10 code value units is detected, the updated parameters of the corresponding region in the compensation parameter matrix are retrieved synchronously, and the amplitude compensation, phase calibration, and timing offset of the output code value are dynamically adjusted. During implementation, the modulated DAC output signal is fed back to the quantum sensing DAC calibration and analysis platform in real time through a closed-loop feedback link to indirectly verify the adjustment effect. If the feedback data shows that the output error still exceeds the set threshold, the corresponding parameters in the compensation parameter matrix are fine-tuned through an incremental adjustment algorithm to optimize the modulation strategy. This ensures that under various operating conditions such as different input code values, different load conditions, and different operating frequencies, the error can be accurately corrected by dynamically adjusting the output code value, significantly improving the amplitude stability, phase accuracy, and timing consistency of the DAC output signal.

[0032] Preferably, the expression for the operational amplifier offset dynamic coupling prediction model is: This refers to the dynamic coupling quantity of the operational amplifier offset. The coupling coefficient is... This is the initial op-amp offset voltage. Clock frequency influence factor, For system clock frequency, The output voltage deviation sensitivity coefficient. For DAC output voltage deviation, To add weighting coefficients, The offset voltage of the i-th operational amplifier. Let i be the phase deviation influence coefficient of the i-th path. For the first Road signal phase deviation.

[0033] Specifically, the op-amp offset dynamic coupling prediction model is used to analyze the dynamic correlation between op-amp offset voltage and DAC output error. In implementation, the coupling coefficient is first set to a range of 0.1 to 0.9, the initial op-amp offset voltage measurement accuracy is controlled at the microvolt level, the clock frequency influence factor is set to 0.01 to 0.1 based on the actual range of the system clock frequency, the output voltage deviation sensitivity coefficient is calibrated to 1% to 5% of the output voltage range, and the superposition weighting coefficient is set to 0.3 to 0.7 after multiple experimental verifications. In practical applications, the model first acquires the initial op-amp offset voltage data, combines it with the system clock frequency and DAC output voltage deviation, quantifies the combined impact of clock frequency and voltage deviation on op-amp offset through sine function calculation, and then integrates the correlation between the offset voltage of each op-amp and the corresponding phase deviation through logarithmic calculation, finally obtaining the op-amp offset dynamic coupling quantity. During implementation, phase deviation influence coefficients of 0.2 to 0.8 were set for 1 to 8 operational amplifier channels respectively to ensure that the offset effect of each operational amplifier can be accurately quantified. This model achieves accurate prediction of operational amplifier offset coupling effect by dynamically integrating multi-dimensional parameters such as voltage, frequency and phase, providing core parameter support for subsequent error correction. Its prediction accuracy directly determines the accuracy of error analysis.

[0034] Preferably, the expression for the broadband DAC harmonic distortion correction model is: middle, This is the harmonic distortion correction factor. The fundamental amplitude, The fundamental angular frequency, For time variables, The initial phase of the fundamental wave. The harmonic order is... The amplitude correction factor for the m-th harmonic is... Let m be the amplitude of the m-th harmonic. The initial phase of the m-th harmonic. The integral correction factor for the m-th harmonic is given. It is the integral variable.

[0035] Specifically, the broadband DAC harmonic distortion correction model focuses on harmonic distortion correction. In implementation, the fundamental amplitude acquisition accuracy is set to millivolts, the initial phase measurement resolution to 0.1 milliradians, and the upper limit of the harmonic order is set to 15, covering the main distorting harmonic components. The amplitude correction factor for each harmonic ranges from 0.8 to 1.2, and the integral correction factor is set from 0.05 to 0.2. In application, the model first extracts the amplitude and phase parameters of the fundamental and harmonics through frequency domain analysis. Then, it constructs the time-domain signal expressions of the fundamental and harmonics using cosine functions. Integral operations are performed on each harmonic signal to compensate for the distortion caused by phase lag. Finally, the harmonic distortion correction coefficients are obtained by calculating the ratio of the fundamental signal to the composite harmonic signal. During implementation, the time variable is sampled at nanosecond intervals, and the integral variable covers the entire signal cycle to ensure comprehensive compensation for harmonic distortion. By integrating amplitude correction and integral correction mechanisms, the model achieves accurate correction of harmonic distortion in the broadband range, effectively improving the spectral purity of the DAC output signal and providing high-quality error data for subsequent gradient calculations.

[0036] Preferably, the expression for the differential nonlinear gradient correction model is: ,in, The differential nonlinear gradient value, For gradient operators, These are the original differential nonlinear coefficients. This represents the original differential nonlinear error value. The first derivative weighting coefficients are... For DAC input code value variables, The weighting coefficient is the squared second derivative.

[0037] Specifically, the differential nonlinear gradient correction model analyzes the gradient of the differential nonlinear error. In implementation, the measurement accuracy of the original differential nonlinear coefficients is set to 0.01 LSB, the first derivative weight coefficient ranges from 0.3 to 0.6, and the second derivative square weight coefficient ranges from 0.1 to 0.3. The input code value variable is adjusted in steps of one-tenth of the smallest code value unit. In application, the model first obtains the original differential nonlinear error value, quantifies the rate of change of the error with the input code value through first derivative calculation, then strengthens the nonlinear characteristics of the error change rate through second derivative square calculation, and finally integrates the above parameters through the gradient operator to obtain the differential nonlinear gradient value. During implementation, the entire range of input code values ​​is traversed to ensure the comprehensiveness of the gradient value calculation. A sliding window filter is used to process the gradient data, with a window length set to 50 code value units to eliminate random noise interference. This model accurately captures the gradient change pattern of the differential nonlinear error, providing a core basis for locating error extrema and significantly improving the targeting and accuracy of error correction.

[0038] Preferably, the error acquisition model expression of the quantum sensing DAC calibration analysis platform is: ,in, To comprehensively collect error values, This is the data acquisition accuracy coefficient. For amplitude deviation, For phase shift, For timing jitter, The covariance weighting coefficients are... The three-dimensional covariance is the sum of amplitude deviation, phase shift, and timing jitter.

[0039] Specifically, the error acquisition model of the quantum sensing DAC calibration and analysis platform is used to integrate multi-dimensional acquisition errors. During implementation, the acquisition accuracy coefficient is set to a range of 0.9 to 0.99 to ensure the reliability of the acquired data, and the covariance weighting coefficient is set to 0.2 to 0.4 to balance the coupling effects of amplitude, phase, and timing errors. In application, the model first acquires amplitude deviation, phase shift, and timing jitter data separately, with amplitude deviation acquisition accuracy at the microvolt level, phase shift at the milliradian level, and timing jitter at the nanosecond level. Then, the absolute deviations of the three types of errors are integrated through square root calculation, and the coupling degree of the three types of errors is quantified through three-dimensional covariance calculation to finally obtain the comprehensive acquisition error value. During implementation, the data acquisition frequency is set to 5 million data points per second, and the acquisition duration covers 30 minutes to ensure data representativeness. This model, through the integration and coupling analysis of multi-dimensional errors, provides a comprehensive error assessment basis for the subsequent construction of compensation parameters, effectively improving the completeness of error correction.

[0040] Preferably, the model expression for constructing the digital compensation parameter matrix is: in, For digital compensation parameter matrix, For amplitude compensation weight, For phase compensation weights, For time-series compensation weights, The amplitude-phase crossover compensation coefficient, For phase-timing crossover compensation coefficients, This is the timing-amplitude cross-compensation coefficient.

[0041] Specifically, the model for constructing the digital compensation parameter matrix aims to integrate multi-dimensional compensation parameters. During implementation, the amplitude compensation weight is set to range from 0.3 to 0.5, the phase compensation weight from 0.2 to 0.4, the timing compensation weight from 0.1 to 0.3, and the cross-compensation coefficient from 0.05 to 0.15 to balance the influence of main compensation and cross-compensation. In application, the model first obtains three core parameters: operational amplifier offset dynamic coupling, harmonic distortion correction coefficients, and differential nonlinear gradient values. Then, it calculates the amplitude, phase, and timing single-dimensional compensation parameters according to the set weights. The coupling effects of different dimensional parameters are integrated through the cross-compensation coefficient, ultimately constructing a three-dimensional compensation parameter matrix. During implementation, the number of rows in the matrix corresponds to the full range of input code values ​​(65536 rows), and the number of columns corresponds to the three compensation dimensions (3 columns), ensuring accurate matching between the parameter matrix and the DAC's operating state. This model provides comprehensive and accurate parameter support for real-time digital modulation by systematically integrating multi-source error compensation parameters, achieving synchronous correction of multi-dimensional errors.

[0042] Preferably, step S3 includes the following sub-steps: S31, inputting the operational amplifier offset dynamic coupling correlation characteristics into the harmonic separation module of the broadband DAC harmonic distortion correction model, and decomposing the composite signal into fundamental component and harmonic components through frequency domain transformation; S32, extracting the amplitude and phase of each harmonic component after decomposition, and recording the characteristic parameters of the harmonic components at different frequencies; S33, calculating the contribution ratio of each harmonic to the DAC output error based on the characteristic parameters, and removing harmonic components with a contribution ratio lower than a set threshold; S34, mapping and associating the characteristic parameters corresponding to the retained high-contribution harmonic components with the error data to form a set of harmonic error contribution factors.

[0043] Specifically, step S3 includes sub-steps S31 to S34: S31 first inputs the operational amplifier offset dynamic coupling correlation characteristics into the harmonic separation module of the broadband DAC harmonic distortion correction model, starts the frequency domain transformation algorithm, sets the number of transformation sampling points to 1024 points to ensure the resolution of signal decomposition, and uses this algorithm to accurately decompose the composite signal into the fundamental component and each harmonic component, maintaining the integrity of the signal's amplitude and phase information during the decomposition process; S32 starts the amplitude and phase extraction process for each harmonic component after decomposition, setting the amplitude extraction accuracy to the microvolt level and the phase extraction resolution to the milliradian level, and records the core characteristic parameters such as amplitude, phase, and frequency of the harmonic components at different frequencies one by one through a dedicated detection module, with the parameter recording interval consistent with the signal sampling period; S33 based on the extracted characteristic parameters... A weighted calculation method is used to determine the contribution ratio of each harmonic to the DAC output error. Contribution ratio calculation weights are set, with amplitude accounting for 0.6 and phase influence for 0.4. A contribution ratio threshold of 5% is set to eliminate harmonic components below this threshold, preventing invalid parameters from consuming computational resources. In step S34, the characteristic parameters corresponding to the retained high-contribution harmonic components are mapped and associated with the original error data, establishing a one-to-one correspondence between parameters and errors. This forms a structured set of harmonic error contribution factors, including key information such as harmonic frequency, error contribution value, and phase offset. This provides focused and accurate input data for the gradient calculation in subsequent step S4. The entire step-by-step implementation process ensures the efficiency and accuracy of harmonic separation and contribution factor selection through inter-module collaboration.

[0044] Preferably, step S4 includes the following sub-steps: S41, importing the harmonic error contribution factor into the gradient calculation unit of the differential nonlinear gradient correction model, setting the step size of the input code value change, and traversing the entire range of input code values; S42, calculating the differential nonlinear error value corresponding to each input code value, and solving the error gradient value through the error difference between adjacent code values; S43, performing sliding window filtering on the gradient value to eliminate the interference of random noise on the gradient change law; S44, judging the rising and falling intervals of the error distribution through the positive and negative changes of the gradient value, and locating the error extreme point where the gradient value is zero.

[0045] Specifically, step S4 includes sub-steps S41 to S44: S41 first imports the harmonic error contribution factor into the gradient calculation unit of the differential nonlinear gradient correction model, sets the input code value change step size to one-tenth of the minimum code value unit, and clarifies that the input code value traversal range is the full range, progressing sequentially from the minimum input code value to the maximum input code value to ensure coverage of all working states; S42, for each input code value, calculates the corresponding differential nonlinear error value through the error detection unit, uses the adjacent code value error difference algorithm to perform difference calculation between the current code value error and the previous code value error to obtain the error gradient value corresponding to each code value, maintaining a calculation accuracy of 0.01 units during the calculation process; S43, processes the calculated gradient... The gradient value initiates a sliding window filtering process, setting the window length to 50 code value units. A moving average algorithm is used to smooth the gradient values ​​within the window, effectively eliminating the interference of random noise on the gradient change pattern. The fluctuation amplitude of the filtered gradient value is controlled within the set range. S44 uses the gradient value analysis module to determine the error distribution trend. When the gradient value changes from positive to negative or from negative to positive, it is marked as the boundary point between the rising and falling intervals of the error distribution. When the gradient value approaches zero, it is determined to be the location of the error extremum point. At the same time, the input code value and error amplitude corresponding to the extremum point are recorded, providing key error distribution feature information for the subsequent construction of compensation parameters. Each sub-step is closely connected to ensure the accuracy of gradient calculation and extremum point location.

[0046] Preferably, step S5 includes the following sub-steps: S51, collecting coupling coefficients from dynamic correlation features, harmonic amplitude and phase parameters from error contribution factors, and gradient extreme value data from gradient change patterns to establish an original set of compensation parameters; S52, filtering and standardizing the parameters in the original set according to the parameter constraints of the digital compensation model, and removing invalid parameters; S53, classifying and assigning the standardized parameters to the corresponding compensation dimensions according to the functional requirements of amplitude compensation, phase calibration, and timing adjustment; S54, integrating the compensation parameters of each dimension through matrix operations to generate a dimension-matched digital compensation parameter matrix.

[0047] Specifically, step S5 includes sub-steps S51 to S54: S51 first initiates the parameter collection process, comprehensively collecting coupling coefficients from dynamic correlation features, harmonic amplitude and phase parameters from error contribution factors, and gradient extreme value data from gradient change patterns. The data collection accuracy is set to be consistent with the previous acquisition accuracy to ensure data integrity. All collected data is integrated to form an original set of compensation parameters, which is then stored according to data type. S52, based on the parameter constraints of the digital compensation model, the parameters in the original set are screened, removing abnormal parameters that exceed the reasonable value range. Subsequently, a standardization process is initiated, uniformly mapping parameters of different dimensions and magnitudes to a numerical range of 0 to 1. During standardization, the relative values ​​between parameters are maintained. The relationships remain unchanged; S53, according to the functional requirements of amplitude compensation, phase calibration, and timing adjustment, classifies and assigns the standardized parameters to the corresponding compensation dimensions, and sets up a dedicated parameter storage area for each dimension to ensure the convenience of parameter retrieval, while recording the weight ratio of each parameter in the corresponding dimension; S54 integrates the compensation parameters of each dimension through matrix operations, setting the number of matrix rows to the full range of input code values ​​and the number of columns to the three compensation dimensions. During the operation, a weighted summation algorithm is used to generate a dimension-matched digital compensation parameter matrix by combining the weight ratio of each parameter. This matrix includes the specific compensation parameters corresponding to each input code value, providing a direct basis for digital modulation in step S6. The implementation of each sub-step ensures the comprehensiveness, accuracy, and adaptability of the compensation parameter matrix.

[0048] The op-amp offset dynamic coupling prediction model is a technical model specifically designed to analyze the dynamic correlation between op-amp offset voltage and DAC output error. It focuses on the coupling relationship between op-amp offset and amplitude deviation, phase shift, and timing jitter under different operating conditions. By integrating multi-dimensional parameters, it achieves correlation feature extraction, solving the problem that traditional static models cannot capture the dynamic correlation of errors. The implementation process of this model is as follows: Using the multi-dimensional error dataset collected by the quantum sensing DAC calibration and analysis platform as input, the coupling relationship resolution threshold is set to an amplitude deviation of 5 microvolts and a phase shift of 0.1 milliradians. A fixed time window of 10 milliseconds is used to segment and analyze the data. A 3-layer convolutional feature extraction network and a 2-layer fully connected analytical network are used to calculate the Pearson correlation coefficient between the operational amplifier offset voltage and various output errors. Strongly correlated combinations with an absolute correlation coefficient higher than 0.8 are selected. Then, through linear fitting and nonlinear regression algorithms, the quadratic function variation law of the operational amplifier offset with time, input code value, and load conditions, and its mapping relationship with the error are extracted, forming a dynamic correlation feature set including 20 core feature parameters. Simultaneously, the size of the convolutional kernel and the weights of the fully connected layers are adaptively adjusted to adapt to complex operating conditions. This accurately captures the dynamic coupling effect of the operational amplifier offset, breaking the limitations of static calibration, providing a targeted analysis object for subsequent harmonic separation, avoiding analytical bias caused by the superposition of multiple source errors, and ensuring the specificity and accuracy of error analysis. This model fills the gap in existing technology that ignores the impact of operational amplifier offset dynamic coupling, elevates error analysis from a single dimension to a multi-dimensional dynamic correlation level, makes error source location more accurate, provides high-quality preliminary data support for the entire error correction process, helps improve the overall effect and operating condition adaptability of DAC output error correction, and meets the stringent requirements of high-precision electronic systems for error analysis.

[0049] The broadband DAC harmonic distortion correction model is a technical model used to separate the fundamental and harmonic components in the DAC output signal and screen key error sources. It is specifically designed to address the output error problem caused by the accumulation of harmonic distortion in broadband scenarios and achieves accurate quantification of harmonic errors through frequency domain analysis. The implementation process of this model is as follows: taking the operational amplifier offset dynamic coupling correlation characteristics as input, the frequency analysis range is set to 1kHz to 100MHz, which is fully matched with the DAC operating bandwidth. The upper limit of harmonic order resolution is set to 15th order to cover the main harmonic components. The composite signal is decomposed into the fundamental wave and each harmonic component through the fast Fourier transform algorithm. The amplitude extraction accuracy is set to microvolt level and the phase extraction resolution is set to 0.1 milliradian. The peak amplitude, initial phase and center frequency parameters of each harmonic are collected one by one. The amplitude ratio and phase difference of each harmonic to the fundamental wave are calculated. The weighted calculation rule is set according to the amplitude ratio of 0.6 and the phase influence of 0.4. The error contribution factor screening threshold of 0.05 is set. Harmonic components with weighted scores below the threshold are eliminated, and 3 to 8 high contribution harmonic parameters are retained to form a structured error contribution factor set. At the same time, false harmonic signals are eliminated through 10Hz frequency domain resolution adjustment and wavelet threshold noise reduction algorithm. This model accurately separates harmonic components within a wide bandwidth, quantifies the contribution of each harmonic to the output error, and identifies key error sources. This provides focused and clean error data for subsequent gradient calculations, preventing invalid harmonic components from interfering with subsequent processing. This model overcomes the limitations of traditional harmonic correction models in broadband scenarios, such as insufficient resolution and low filtering accuracy. It achieves precise separation of harmonic components and efficient screening of high-contribution error sources, ensuring that error correction can specifically address major harmonic distortion issues. This improves the spectral purity of the DAC output signal in broadband applications, providing crucial technical support for signal conversion in high-precision communication, quantum sensing, and other fields.

[0050] The differential nonlinear gradient correction model is a technical model used to analyze the gradient variation law of harmonic error contribution factors and locate error extrema. It achieves in-depth mining of error distribution characteristics through precise calculation of the error gradient, providing a core basis for constructing compensation parameters. The model's implementation process is as follows: Using the harmonic error contribution factor as input, the input code value variation step size is set to 0.1 LSB, covering the entire range of input code values ​​from minimum to maximum. The input code value is used as the independent variable, and the comprehensive error value as the dependent variable. The error gradient value is calculated point-by-point using an adjacent code value error difference algorithm, constructing a continuous gradient variation curve. A gradient change rate threshold of 0.02 is set. The gradient curve slope change is analyzed by traversing the entire input code value range. A moving average filter with a sliding window of 50 code value units in length is used to eliminate random noise interference with amplitudes below 0.01. The extrema determination condition is that the absolute value of the gradient values ​​of five consecutive adjacent code values ​​is less than 0.005 and the gradient signs are reversed. Finally, the input code value position and error amplitude corresponding to the extrema point are output. This model accurately captures the gradient variation of differential nonlinear errors, clearly identifying the rising and falling segments and extreme points of the error distribution. This provides key characteristic information about the error distribution for constructing the digital compensation parameter matrix, ensuring that the compensation strategy can specifically address the extreme error regions and avoid blind compensation. The model solves the problem of accurately locating error extreme points in existing technologies. Through gradient calculation, it achieves quantitative analysis of the error distribution characteristics, enabling the construction of compensation parameters to be accurately adapted based on the dynamic error distribution. This significantly improves the targeting and efficiency of error correction, laying a core technological foundation for real-time dynamic correction of DAC output errors and helping high-precision electronic systems achieve more stable signal output performance.

[0051] The quantum sensing DAC calibration and analysis platform is an integrated device used to collect multi-dimensional error data from DAC output and provide high-fidelity raw data support. It combines quantum sensing technology with multi-channel synchronous acquisition capabilities to achieve high-precision, full-scenario acquisition of error data. The platform's implementation process is as follows: After startup, the sampling frequency is set to 5 million data points per second, with a collection time of 30 minutes, covering the entire operating range of DAC input voltage from 0 to full scale and frequency from 1kHz to 100MHz. Through an 8-channel synchronous acquisition module, 2000 sets of sample data are collected for each state under different operating conditions with input code values ​​from 0000H to FFFFH and load resistances from 10Ω to 1kΩ. The platform focuses on collecting three core error parameters: amplitude deviation, phase offset, and timing jitter. The amplitude deviation acquisition accuracy is controlled within ±5 microvolts, the phase offset resolution is 0.1 milliradians, and the timing jitter acquisition minimum interval is 10 nanoseconds. Relying on the built-in electromagnetic shielding structure and adaptive noise suppression algorithm, external electromagnetic interference from 20MHz to 1GHz and environmental noise with amplitudes below 2 microvolts are filtered out. The collected data are classified and integrated according to timestamp, input code value, and load conditions to form a multi-dimensional original error dataset containing 1.2 million valid records. This model provides comprehensive, accurate, and high-fidelity foundational data for all subsequent error analysis and correction processes, ensuring that models such as op-amp offset dynamic coupling prediction and harmonic distortion correction can be analyzed based on the true error distribution, avoiding correction deviations caused by data distortion. This model overcomes the limitations of traditional calibration equipment, such as single-dimensional data acquisition, insufficient precision, and weak anti-interference capabilities. Through the high sensitivity of quantum sensing technology and a multi-channel synchronous acquisition design, it achieves full-scene coverage and high-precision capture of error data, providing reliable data support for multi-model collaborative correction. This gives the entire error correction process solid raw data support, making it a core foundational device for improving DAC output error correction performance.

[0052] like Figure 2As shown, a DAC output error correction method based on digital compensation is implemented through different units, including: a quantum sensing multi-dimensional error acquisition unit, used to acquire amplitude deviation, phase shift, and timing jitter data of the DAC output signal and generate a raw error dataset, whose output is connected to an op-amp offset dynamic coupling feature analysis unit; an op-amp offset dynamic coupling feature analysis unit, used to call the op-amp offset dynamic coupling prediction model to analyze the coupling relationship in the raw error dataset and extract dynamic correlation features, whose output is connected to a broadband DAC harmonic error separation unit; and a broadband DAC harmonic error separation unit, used to separate harmonic components in the coupling features based on a broadband DAC harmonic distortion correction model and screen error contribution factors, whose output is connected to a differential nonlinear gradient operation unit. The system consists of several interconnected components: a differential nonlinear gradient calculation unit (DCLT unit) for calculating the gradient change of the error contribution factor using a differential nonlinear gradient correction model and locating extreme points; a digital compensation parameter matrix construction unit for constructing a compensation parameter matrix that combines dynamic correlation characteristics, error contribution factors, and gradient change patterns; a DAC output real-time modulation unit for dynamically adjusting the code value of the DAC output signal based on the digital compensation parameter matrix and correcting errors in response to changes in extreme point locations; an input connected to the output of the digital compensation parameter matrix construction unit; and an output directly connected to the DAC output link.

[0053] A digital compensation-based DAC output error correction method integrates three models: operational amplifier offset dynamic coupling prediction, broadband harmonic distortion correction, and differential nonlinear gradient correction. This forms a complete processing chain covering error correlation analysis, harmonic separation, and gradient calculation, overcoming the limitations of existing single-source error calibration techniques. It comprehensively captures the dynamic correlation between operational amplifier offset, harmonic distortion, and differential nonlinearity, achieving synchronous response and coordinated correction of multi-source errors. This completely solves the problem of poor correction performance due to the superposition of multiple errors under complex operating conditions. Simultaneously, a dedicated calibration analysis platform is built using quantum sensing technology, significantly improving the dimensionality and accuracy of error data acquisition. This provides highly reliable data support for subsequent compensation parameter construction, overcoming the shortcomings of traditional methods such as one-sided data acquisition and difficulty in reflecting the true error distribution.

[0054] This invention analyzes the variation law of error gradient and locates the extreme point to construct a dynamically updated compensation parameter matrix. This enables the digital modulation process to respond in real time to the dynamic changes in error distribution, breaking the limitation of poor adaptability of traditional static compensation parameters. This real-time adjustment mechanism based on the dynamic characteristics of error ensures that the compensation strategy always accurately matches the error change trend, significantly improving the stability and adaptability of correction under different operating conditions. Simultaneously, the combination of multi-model collaboration and real-time modulation achieves a closed-loop processing of the entire process from error acquisition and analysis to correction. This solves the problem of existing technologies lacking an integrated mechanism and being unable to achieve multi-dimensional error synchronous correction, significantly improving the amplitude, phase, and timing accuracy of the DAC output signal, fully meeting the stringent requirements of high-precision electronic systems.

[0055] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," "link," and "fix" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0056] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various equivalent changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for correcting DAC output error based on digital compensation, characterized in that, Includes the following steps: S1. Collect amplitude deviation, phase shift, and timing jitter data of the DAC output signal using a quantum sensing DAC calibration and analysis platform to establish a multi-dimensional original error dataset. S2. Use an operational amplifier offset dynamic coupling prediction model to analyze the coupling relationship of the original error dataset and extract the dynamic correlation characteristics between the operational amplifier offset voltage and the output error. S3. Based on a broadband DAC harmonic distortion correction model, separate the harmonic components of the coupling correlation characteristics and select the error contribution factors corresponding to each harmonic. S4. Use a differential nonlinear gradient correction model to perform gradient calculations on the harmonic error contribution factors to determine the gradient change law and extreme point location of the error distribution. S5. Combine the dynamic correlation characteristics, error contribution factors, and gradient change law to construct a digital compensation parameter matrix, which includes amplitude compensation coefficients, phase calibration coefficients, and timing adjustment parameters. S6. Perform real-time digital modulation of the DAC output signal based on the digital compensation parameter matrix, and correct the error by dynamically adjusting the output code value. The digital modulation process synchronously responds to changes in the extreme point location of the error distribution. The expression for the operational amplifier offset dynamic coupling prediction model is as follows: This refers to the dynamic coupling quantity of the operational amplifier offset. The coupling coefficient is... This is the initial op-amp offset voltage. Clock frequency influence factor, For system clock frequency, The output voltage deviation sensitivity coefficient. For DAC output voltage deviation, To add weighting coefficients, The offset voltage of the i-th operational amplifier. Let i be the phase deviation influence coefficient of the i-th path. For the first Road signal phase deviation; The expression for the broadband DAC harmonic distortion correction model is as follows: middle, This is the harmonic distortion correction factor. The fundamental amplitude, The fundamental angular frequency, For time variables, The initial phase of the fundamental wave. The harmonic order is... The amplitude correction factor for the m-th harmonic is... Let m be the amplitude of the m-th harmonic. The initial phase of the m-th harmonic. The integral correction factor for the m-th harmonic is given. For integration variables; The expression for the differential nonlinear gradient correction model is: ,in, The differential nonlinear gradient value, For gradient operators, These are the original differential nonlinear coefficients. This represents the original differential nonlinear error value. The first derivative weighting coefficients are... For DAC input code value variables, The weighting coefficient is the squared second derivative.

2. The DAC output error correction method based on digital compensation according to claim 1, characterized in that, The error acquisition model expression of the quantum sensing DAC calibration and analysis platform is as follows: ,in, To comprehensively collect error values, This is the data acquisition accuracy coefficient. For amplitude deviation, For phase shift, For timing jitter, The covariance weighting coefficients are... The three-dimensional covariance is the sum of amplitude deviation, phase shift, and timing jitter.

3. The DAC output error correction method based on digital compensation according to claim 1, characterized in that, The model expression for constructing the digital compensation parameter matrix is ​​as follows: in, For digital compensation parameter matrix, For amplitude compensation weight, For phase compensation weights, For time-series compensation weights, The amplitude-phase crossover compensation coefficient, For phase-timing crossover compensation coefficients, This is the timing-amplitude cross-compensation coefficient.

4. The DAC output error correction method based on digital compensation according to claim 1, characterized in that, S3 includes the following sub-steps: S31, inputting the operational amplifier offset dynamic coupling correlation characteristics into the harmonic separation module of the broadband DAC harmonic distortion correction model, and decomposing the composite signal into the fundamental component and each harmonic component through frequency domain transformation; S32, extracting the amplitude and phase of each harmonic component after decomposition, and recording the characteristic parameters of the harmonic components at different frequencies; S33, calculating the contribution ratio of each harmonic to the DAC output error based on the characteristic parameters, and removing harmonic components with a contribution ratio lower than a set threshold; S34, mapping and associating the characteristic parameters corresponding to the retained high-contribution harmonic components with the error data to form a set of harmonic error contribution factors.

5. The DAC output error correction method based on digital compensation according to claim 1, characterized in that, The S4 includes the following sub-steps: S41, importing the harmonic error contribution factor into the gradient calculation unit of the differential nonlinear gradient correction model, setting the input code value change step size, and traversing the entire range of input code values. S42, calculate the differential nonlinear error value corresponding to each input code value, and solve the error gradient value by the error difference between adjacent code values; S43, perform sliding window filtering on the gradient value to eliminate the interference of random noise on the gradient change law; S44, determine the rising and falling intervals of the error distribution by the positive and negative changes of the gradient value, and locate the error extreme point where the gradient value is zero.

6. The DAC output error correction method based on digital compensation according to claim 1, characterized in that, S5 includes the following sub-steps: S51, collecting coupling coefficients from dynamic correlation features, harmonic amplitude and phase parameters from error contribution factors, and gradient extreme value data from gradient change patterns to establish an original set of compensation parameters; S52, filtering and standardizing the parameters in the original set according to the parameter constraints of the digital compensation model, and removing invalid parameters; S53, classifying and assigning the standardized parameters to the corresponding compensation dimensions according to the functional requirements of amplitude compensation, phase calibration, and timing adjustment; S54, integrating the compensation parameters of each dimension through matrix operations to generate a dimension-matched digital compensation parameter matrix.

7. A DAC output error correction method based on digital compensation according to any one of claims 1-6, characterized in that, This method is implemented through different units, including: a quantum sensing multi-dimensional error acquisition unit, used to acquire amplitude deviation, phase shift, and timing jitter data of the DAC output signal and generate a raw error dataset, whose output is connected to an op-amp offset dynamic coupling feature analysis unit; an op-amp offset dynamic coupling feature analysis unit, used to call the op-amp offset dynamic coupling prediction model to analyze the coupling relationship in the raw error dataset and extract dynamic correlation features, whose output is connected to a broadband DAC harmonic error separation unit; a broadband DAC harmonic error separation unit, used to separate harmonic components in the coupling features based on a broadband DAC harmonic distortion correction model and screen error contribution factors, whose output is connected to a differential nonlinear gradient operation unit; and a differential nonlinear gradient operation unit. The calculation unit is used to calculate the gradient change law of the error contribution factor through the differential nonlinear gradient correction model and locate the extreme point. Its output is connected to the digital compensation parameter matrix construction unit. The digital compensation parameter matrix construction unit is used to construct a compensation parameter matrix including amplitude compensation coefficient, phase calibration coefficient and timing adjustment parameter by combining dynamic correlation characteristics, error contribution factor and gradient change law. Its output is connected to the DAC output real-time modulation unit. The DAC output real-time modulation unit is used to dynamically adjust the code value of the DAC output signal according to the digital compensation parameter matrix and to correct the error in response to the change of extreme point position. Its input is connected to the output of the digital compensation parameter matrix construction unit and its output is directly connected to the DAC output link.

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