An adaptive background correction system applied to a pipeline ADC

Abstract

This invention claims protection for an adaptive background calibration system for pipelined ADCs, comprising: a sample-and-hold module, a first conversion unit, a second conversion unit, a low-speed, high-precision ADC, a pipelined ADC to be calibrated, an LMS adaptive filter, and a subtractor; capable of calibrating linear errors in the pipelined ADC caused by non-ideal factors such as capacitor mismatch, finite op-amp gain, and op-amp offset. By using a low-speed, high-precision ADC as a reference, connected in parallel with the pipelined ADC to be calibrated, and sending the difference between their digital outputs to a digital adaptive filter for processing, the output of the pipelined ADC continuously approximates the output of the low-speed, high-precision ADC, thereby achieving digital calibration. During this process, the normal conversion process remains unaffected and the conversion speed of the original ADC is not reduced, offering advantages such as high calibration accuracy, fast convergence speed, and strong tracking capability.

Description

Technical Field

[0001] This invention belongs to the field of analog integrated circuit design technology, and specifically relates to an adaptive calibration technique for pipelined ADCs. Background Technology

[0002] With the rapid development of integrated circuits and digital processing technology, higher demands are being placed on the speed and accuracy of ADCs in fields such as wireless communication, image acquisition and processing, and digital signal processing. Therefore, pipelined ADCs that balance high speed and high accuracy are widely used in many fields. However, the continuous shrinking of integrated circuit process dimensions, while driving the rapid development of digital integrated circuits, has also brought significant challenges to analog circuit design. When the accuracy of a pipelined ADC reaches 10 bits or more, many parameters in the pipelined ADC will change over time due to the influence of manufacturing processes and the chip operating environment. Furthermore, the existence of non-ideal factors such as noise, offset, and the limited bandwidth of operational amplifiers also limits the improvement of the overall accuracy of the pipelined ADC. Traditional analog circuit design has found it difficult to overcome this accuracy bottleneck. Therefore, calibration techniques are employed in the design of high-speed, high-precision pipelined ADCs.

[0003] Currently, calibration techniques for pipelined ADCs are mainly divided into two types: analog domain calibration and digital domain calibration. The former primarily uses methods such as capacitor fine-tuning and capacitor mismatch error averaging. This method requires high precision in the design of the capacitor system and increases the complexity of the clock phase and analog circuitry. Therefore, digital domain calibration techniques are widely used. Digital domain calibration techniques are also divided into front-end calibration and back-end calibration. Back-end calibration techniques can track and calibrate parameter changes caused by PVT changes in real time without interrupting the normal operation of the system. It is currently the most widely used calibration technique and, to some extent, represents the development direction of ADCs.

[0004] While digital calibration technology is widely used in pipelined ADC design, and numerous calibration algorithms have emerged, traditional back-end calibration techniques, such as the LMS algorithm with a fixed step size for updating tap weights, cannot simultaneously meet the requirements of fast convergence and small steady-state error. General variable-step LMS calibration algorithms establish a nonlinear relationship between step size and error based on a sigmoid function. However, due to the characteristics of the sigmoid function, this algorithm's curve becomes too steep near the origin, leading to rapid changes in the step size factor and increased error in steady state. Transforming the sigmoid function by shifting or flipping it makes the algorithm model overly complex, affecting its flexibility. Alternatively, establishing a nonlinear relationship between the step size factor and the number of iterations in the LMS algorithm based on the sigmoid function can improve convergence speed and anti-interference capability, but tracking performance is significantly insufficient. In summary, traditional back-end calibration techniques using the LMS algorithm and general variable-step LMS calibration algorithms cannot simultaneously and effectively address issues such as noise interference, poor system tracking performance, and high steady-state error.

[0005] Traditional digital back-end calibration techniques for pipelined ADCs use variable step size LMS algorithms, such as the Sign Variable Step Size LMS (SVSS-LMS) algorithm and system. This involves determining the positive or negative deviation of the instantaneous input error and introducing a sign function (sign) to update the step size factor u(n), thus enabling faster weight updates based on the error. The size of the step size factor u(n) can be dynamically adjusted according to the speed of error convergence. However, this algorithm has several technical drawbacks. First, e(n), as the error factor, directly participates in the iteration of the step size factor, introducing random noise interference and slightly compromising the algorithm's tracking ability. Second, the variable step size method is used for updating some filter weight coefficients, resulting in a larger step size near convergence in low signal-to-noise ratio environments, leading to poor steady-state performance. Third, during weight updates, excessively large iteration increments can cause the tap weight coefficients to oscillate repeatedly around the optimal value, slowing down the convergence speed. This repeated occurrence of oscillations around the optimal value reduces calibration accuracy. The application example of this algorithm uses a 12-bit 100MS / s pipelined ADC. After calibration, the effective bit depth of the ADC can reach 11.52 bits, and the SFDR is 82.77dB.

[0006] This invention utilizes the correlation value e(n)e(n-1) of the error signal instead of e(n) to reduce the interference of random noise. To strengthen the relationship between the step size and the input signal, a step size feedback factor J(n) is added. This gives the algorithm good tracking ability. Furthermore, by substituting the L2 norm of J(n) as the independent variable into the step size relation, we obtain the updated step size relation expression: To prevent the algorithm from diverging due to a sudden increase in input signal power, a normalization algorithm is added to constrain u(n) during the weight coefficient vector update, i.e. Ψ is a constant set to avoid an excessively small denominator, with a value of 0.01. This algorithm application example uses a 14-bit 1GS / s pipelined ADC. After calibration, the effective bit depth of the ADC reaches 13.67 bits, and the SFDR is 85.91dB. If the ratio of the calibrated effective bit depth to the original ADC's effective bit depth is considered as the calibration accuracy, this algorithm achieves a calibration accuracy of 97.6%, while the variable step size LMS algorithm for the sign function achieves 96%, representing a 1.76% improvement in calibration accuracy. This algorithm effectively removes errors including capacitor mismatch, finite op-amp gain, and op-amp offset. Normal conversion processes are unaffected, and the original ADC's conversion speed is not reduced. It offers higher calibration accuracy, faster convergence speed, smaller steady-state error, and superior tracking capability. Summary of the Invention

[0007] This invention aims to solve the problems of the prior art mentioned above. It proposes an adaptive back-end calibration system for pipelined ADCs. The technical solution of this invention is as follows:

[0008] An adaptive back-end calibration system for pipelined ADCs includes:

[0009] The sample-and-hold module (1), first frequency conversion unit (2), second frequency conversion unit (6), low-speed high-precision ADC (3), pipelined ADC to be calibrated (4), LMS adaptive filter (5), and subtractor (7) are used to hold the level value of the input analog signal. Ideally, when in the sampling state, the output signal of the sample-and-hold module (1) changes with the input signal; when in the holding state, the output signal of the sample-and-hold module (1) is held at the level value of the input signal at the instant the holding command is received. The sample holding module (1) is connected to the pipeline ADC (4) to be calibrated and the first frequency conversion unit (2) respectively. The first frequency conversion unit (2) is used to reduce the frequency of the input signal, so that the analog input signal after frequency reduction is converted from analog to digital, and the output digital signal is used as the reference signal for ADC calibration. The first frequency conversion unit (2) is connected to the low-speed high-precision ADC (3). The pipeline ADC (4) to be calibrated is connected to the LMS adaptive filter (5). The LMS adaptive filter (5) is connected to the second frequency conversion unit (6) and the subtractor (7) respectively.

[0010] The pipeline ADC (4) to be calibrated performs analog-to-digital conversion on the input analog signal and uses the converted digital output as the input signal of the LMS adaptive filter (5); the low-speed high-precision ADC (3) performs analog-to-digital conversion on the analog input signal after frequency reduction by the first frequency conversion unit (2), and uses the digital signal output by the analog-to-digital conversion as the reference signal for ADC calibration;

[0011] The pipeline ADC (4) to be calibrated samples and quantizes the analog signal from the sample-and-hold module (1), and then inputs the output data into the LMS adaptive filter (5) to obtain the initial value. After being down-converted by the second frequency conversion unit (6), it is input into the subtractor (7). Meanwhile, the low-speed, high-precision ADC (3) also samples and quantizes the analog signal to obtain the output Dref(n). After being processed by the subtractor (7), the error signal e(n) is obtained, and the error is fed back to the LMS adaptive filter (5) for updating the tap weight coefficients. This iterative process makes the output of the pipeline ADC (4) to be calibrated gradually approach the output of the high-precision ADC (3), and finally completes the calibration of the pipeline ADC.

[0012] During the adaptive update of the tap coefficients of the LMS adaptive filter (5), the correlation value e(n)e(n-1) of the error signal is used to replace e(n); and the bottom characteristics of the step size factor are improved by introducing parameters, and the step size feedback factor J(n) is added. The expression of J(n) is:

[0013]

[0014] Where K represents an influence value of the step size feedback factor, x(n) represents the input signal of the adaptive filter, e(n) represents the error signal, and e(n-1) represents the error signal at the previous time step.

[0015] Furthermore, the LMS adaptive filter (5) introduces a hyperbolic tangent function based on the traditional adaptive background calibration method. It uses the L2 norm of the step size feedback factor and the correlation value of the error signal to adjust the step size, so that the output of the pipeline ADC to be calibrated gradually approaches the output of the low-speed, high-precision pipeline ADC. Specifically, it includes:

[0016] Let x(n) and w(n) represent the input signal and weight vector of the adaptive filter, respectively, and L be the order of the adaptive filter. Then the basic form of the LMS algorithm is as follows:

[0017]

[0018]

[0019]

[0020] Where x(nk) represents the input vector at time k, W k W represents the weight vector at time k. L-1 (n) represents the weight vector at time L-1;

[0021] The error calculation formula is:

[0022]

[0023] y(n) is the output signal of the adaptive filter, d(n) is the desired signal, and e(n) represents the error signal;

[0024] Step-by-step update:

[0025]

[0026] α, m, and β are the influence values ​​of the step size factor, which together control the shape of the step size curve. Among them, α plays a crucial role in the value of the step size, and as α increases, the value of the step size also increases. m and β have a significant impact on the shape of the step size function. In actual calibration algorithms, a trade-off needs to be made in the values ​​of α, m, and β.

[0027] Weight update:

[0028]

[0029] This represents a constant with a value of 0.01.

[0030] Furthermore, using the hyperbolic tangent function Based on this, parameters α, β, and m are introduced to jointly control the shape of the step size curve. Among them, parameter α plays a crucial role in the value of the step size; as α increases, the step size also increases, and the convergence speed of the algorithm improves. The step size factor has a non-linear relationship with the error signal and is used to control the convergence speed and convergence accuracy. The relationship between the step size factor and the error function is obtained as follows:

[0031]

[0032] Since the step size factor is positive, equation (8) becomes an even function:

[0033]

[0034] Then, replace e(n) with the correlation value e(n)e(n-1) of the error signal, add the step size feedback factor J(n), and substitute the second norm of the error signal into equation (9) to obtain equation (6).

[0035] Furthermore, when e(n) approaches 0, the limit of the step size u(n) is 0; when e(n) approaches infinity, the limit of the step size u(n) is α, that is, the maximum value of u(n) is α. The parameter α is a positive number. The larger α is, the larger the step size and the faster the convergence speed of the algorithm. The parameters β, m, and k determine the shape of the step size function. If K is chosen too large, the step size factor will be 0 or almost 0 before the error signal is zero, which will seriously slow down the convergence speed of the algorithm. The initial value of the step size u(n) is the maximum step size in the traditional LMS algorithm to make it converge quickly. When the algorithm approaches convergence, the step size factor is made to a smaller value to reduce the steady-state error.

[0036] Furthermore, the ADC to be calibrated is a 14-bit 1GS / s pipelined ADC, and the low-speed, high-precision ADC is a 14-bit cyclic ADC.

[0037] The advantages and beneficial effects of this invention are as follows:

[0038] This invention proposes an adaptive background calibration technique for pipelined ADCs, which can calibrate linear errors caused by non-ideal factors such as capacitor mismatch, finite op-amp gain, and op-amp offset. By using a low-speed but high-precision ADC as a reference, connected in parallel with the pipelined ADC to be calibrated, and sending the difference between their digital outputs to a digital adaptive filter for processing, the output of the pipelined ADC continuously approximates the output of the low-speed but high-precision ADC, thereby achieving digital calibration. During this process, the normal conversion process remains unaffected and the conversion speed of the original ADC is not reduced. It offers advantages such as high calibration accuracy, fast convergence speed, and strong tracking capability.

[0039] 1. The innovation of this invention lies in the fact that, unlike traditional background calibration techniques that use the LMS algorithm, the algorithm of this invention establishes a nonlinear relationship between step size and error to satisfy the hyperbolic tangent function of the step size selection function. Based on this, when x is greater than 0, the function value lies between 0 and 1; when x is less than 0, the function value lies between -1 and 0. This allows for instantaneous changes in the step size, ensuring the step size factor reaches a large value in the early stages of the algorithm, enabling rapid convergence. As the algorithm approaches convergence, the step size factor decreases, reducing steady-state error. Simultaneously, parameters α, β, and m are introduced to jointly control the shape of the step size curve, and the hyperbolic tangent function's range is between -1 and 1. This avoids situations where the error is not zero while the step size factor is already zero or close to zero during step size iterations, ensuring the step size of adjacent iterations remains within a controllable range and accelerating convergence. The relationship between the step size factor and the error function is obtained as follows: Since the step size factor is positive, we can transform it into an even function to obtain... .

[0040] 2. Compared to the fixed-step LMS algorithm, the variable-step LMS algorithm has a faster convergence speed and lower steady-state error. However, existing variable-step algorithms, such as the S-function-based variable-step LMS algorithm, have an excessively steep curve near the origin, causing the step size factor to change rapidly and increasing the steady-state error. The variable-step LMS algorithm that introduces an exponential function uses too many exponential functions during operation, leading to excessive algorithm complexity. Existing variable-step algorithms cannot simultaneously and effectively address issues such as noise interference, poor system tracking performance, and high steady-state error. The pipeline ADC background calibration algorithm of this invention uses the correlation value e(n)e(n-1) of the error signal instead of e(n) to reduce random noise interference. To strengthen the relationship between the step size and the input signal, a step size feedback factor J(n) is added. This gives the algorithm good tracking ability. Furthermore, by substituting the L2 norm of J(n) as the independent variable into the step size relation, we obtain the updated step size relation expression: To prevent the algorithm from diverging due to a sudden increase in input signal power, a normalization algorithm is added to constrain u(n) during the weight coefficient vector update, i.e. Ψ is a constant set to avoid the denominator being too small, and its value is 0.01.

[0041] 3. This invention can improve the effective number of bits in a pipelined ADC. The pipelined ADC adaptive background calibration technology described in claim 1 introduces a hyperbolic tangent function and replaces the error factor e(n) with the correlation value e(n)e(n-1) of the error signal. Simultaneously, a step-size feedback factor J(n) is added for weight updates, causing the output of the pipelined ADC to continuously approximate the output of a low-speed, high-precision ADC, thereby achieving the calibration purpose. Simulation results show that this method can effectively remove errors including capacitor mismatch, finite op-amp gain, and op-amp offset. The normal conversion process is unaffected, the original ADC's conversion speed is not reduced, and the calibration accuracy is high, the convergence speed is fast, the steady-state error is smaller, and the tracking capability is superior. Attached Figure Description

[0042] Figure 1 This is a block diagram of a pipelined ADC calibration structure using the LMS algorithm, provided in a preferred embodiment of the present invention.

[0043] Figure 2 This is a flowchart of the LMS adaptive filtering algorithm used in this invention;

[0044] Figure 3 This is the curve showing the relationship between the error function and the step size factor in the calibration algorithm used in this invention;

[0045] Figure 4This is a comparison chart of the spectrum of the pipeline ADC before and after calibration in this invention. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0047] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0048] This application example uses a 14-bit 1GS / s pipelined ADC, which includes six 2.5-bit sub-stages and one 2-bit Flash ADC.

[0049] Example

[0050] like Figure 1 As shown, the pipelined ADC calibration structure using the LMS algorithm consists of the following parts: a sample-and-hold module 1, a frequency conversion unit 2; a low-speed, high-precision ADC 3, an ADC to be calibrated 4, an LMS adaptive filter 5, and a subtractor 7. One part of the pipelined ADC 4 to be calibrated is connected to the analog input signal, and the other part is connected to the low-speed, high-precision ADC 3. One end of the LMS adaptive filter 5 is connected to the output of the pipelined ADC 4 to be calibrated, and the filtered output is then connected to the subtractor 7. Conversely, the other input of the subtractor 7 is connected to the low-speed, high-precision ADC 3.

[0051] The ADC4 in the calibration pipeline samples and quantizes the analog signal, outputting data Dn, which is then fed into the LMS adaptive filter 5 to obtain the initial value. After being down-converted by the frequency conversion unit 6, it is input into the subtractor 7. Meanwhile, the low-speed, high-precision ADC3 also samples and quantizes the analog signal to obtain the output Drefn. This output Drefn is then processed by the subtractor 7 to obtain the error signal en, which is fed back to the LMS adaptive filter 5 for updating the tap weight coefficients. Furthermore, the correlation value e(n)e(n-1) of the error signal is used instead of e(n) to reduce random noise interference. To strengthen the relationship between the step size and the input signal, a step size feedback factor J(n) is added. This gives the algorithm good tracking ability. To prevent the algorithm from diverging due to a sudden increase in the input signal power, a normalization algorithm is added to limit u(n) when updating the weight coefficient vector. This iterative process makes the output of the pipeline ADC(4) to be calibrated gradually approach the output of the low-speed high-precision ADC(3), and finally completes the calibration of the pipeline ADC.

[0052] like Figure 2The diagram shows the flowchart of the LMS adaptive filtering algorithm used in this invention. The relationship between the step size u(n) and the error e(n)e(n-1) is established, and a step size feedback factor J(n) is added. Unlike traditional background calibration techniques that use a fixed step size in the LMS algorithm, this invention uses the correlation value e(n)e(n-1) of the error signal to replace e(n), reducing the interference of random noise. Furthermore, by introducing parameters, the bottom characteristics of the step size factor are improved, thus addressing to some extent the shortcomings of the fixed-step LMS algorithm. The step size feedback factor J(n) is added, and the expression for J(n) is:

[0053]

[0054] With hyperbolic tangent function Based on this, parameters α, β, and m are introduced to jointly control the shape of the step size curve. Parameter α plays a crucial role in determining the step size; as α increases, the step size also increases, improving the algorithm's convergence speed. The step size factor has a non-linear relationship with the error signal and is used to control the convergence speed and accuracy. Furthermore, a "normalization" algorithm is incorporated to constrain u(n) during the weighted coefficient vector update. When e(n) approaches 0, the limit of the step size u(n) is 0; when e(n) approaches infinity, the limit of the step size u(n) is α, meaning the maximum value of u(n) is α. The parameter α is a positive number; the larger α is, the larger the step size and the faster the algorithm converges. Parameters β, m, and k determine the shape of the step size function. If K is chosen too large, the step size factor may already be 0 or almost 0 before the error signal is zero, severely slowing down the algorithm's convergence speed. The initial value of the step size u(n) is the maximum step size in the traditional LMS algorithm to enable it to converge quickly. When the algorithm approaches convergence, the step size factor is set to a smaller value to reduce the steady-state error.

[0055] The algorithm steps of this invention are described in the following steps:

[0056] Filtered output: y(n) = x(n)w T (n);

[0057] Let x(n) and w(n) represent the input signal and weight vector of the adaptive filter, respectively, and L be the order of the adaptive filter.

[0058] x(n)=[x(n)x(n-1)....x(n-M+1)];

[0059] w(n) = [w0(n)w1(n)...w M-1 (n)];

[0060] Estimation error: e(n) = d(n) - y(n);

[0061] y(n) is the output signal of the adaptive filter, d(n) is the desired signal, and e(n) represents the error signal.

[0062] Step-by-step update: ;

[0063] Tap weight coefficient update: ；

[0064] like Figure 3 The figure shows the relationship curve between the error function and the step size factor in the calibration algorithm. Figure 3 (a) shows the step size curves when β=20, m=600, k=0.6, and α=0.1, 0.2, and 0.3 respectively; Figure 3 (b) shows the step size curves when α=0.3, m=600, k=0.6, and β=15, 25, and 50 respectively; Figure 3 (c) shows the step size curves when α=0.3, β=20, k=0.6, and m takes values ​​of 60, 600, and 6000 respectively; Figure 3 (d) is the step size curve when α=0.3, β=20, m=600, and k takes values ​​of 0.3, 0.6, and 0.9.

[0065] from Figure 3 It can be seen that the parameter α plays a crucial role in determining the step size. As α increases, the step size also increases accordingly, while satisfying... In this case, the convergence speed of the algorithm is improved. The parameters β, m, and k have a significant impact on the shape of the step size function. It can be seen that the smaller β is, the larger m is, and the smaller k is, the smaller the step size will be for the same error value. Furthermore, from... Figure 3 (d) It can be seen that if k is chosen too large, the step size factor will be 0 or almost 0 before the error signal is 0, which will seriously slow down the convergence of the algorithm. In this invention, the values ​​of α, β, m and k are considered in a compromise.

[0066] like Figure 4 The figure shown is a comparison of the spectrum before and after calibration of the 14-bit 1GS / s non-ideal pipelined ADC according to the present invention. Figure 4 (a) shows the FFT test results of an uncalibrated non-ideal pipeline ADC. It can be seen that under the influence of errors such as capacitor mismatch, interstage gain error and comparator offset, the effective number of bits decreased from 14 bits to 8.37 bits, and the SNDR was 52.08dB. Figure 4(b) is the spectrum diagram after calibration using the adaptive calibration technique proposed in this invention for pipeline ADC. It can be seen that by replacing the error factor e(n) with the correlation value e(n)e(n-1) of the error signal and adding a step size feedback factor J(n) for weight update, the effective number of bits increases from 8.37 bits to 13.67 bits, and the SNDR increases from 52.08dB to 84.10dB, which can effectively improve the accuracy of pipeline ADC.

[0067] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, a computer can be, for example, a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email device, game console, tablet computer, wearable device, or any combination of these devices.

[0068] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0069] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. An adaptive background correction system applied to a pipeline ADC, characterized in that, The application relates to a calibration method for a pipeline ADC, which comprises a sample-and-hold module (1), a first frequency conversion unit (2), a second frequency conversion unit (6), a low-speed high-precision ADC (3), a pipeline ADC (4) to be calibrated, an LMS adaptive filter (5) and a subtractor (7); the sample-and-hold module (1) is used for holding the level value of an input analog signal; in an ideal condition, when in a sampling state, the output signal of the sample-and-hold module (1) changes along with the change of the input signal; when in a holding state, the output signal of the sample-and-hold module (1) keeps the level value of the input signal at the moment when the holding command is connected; the sample-and-hold module (1) is connected with the pipeline ADC (4) to be calibrated and the first frequency conversion unit (2) respectively; the first frequency conversion unit (2) is used for reducing the frequency of the input signal, so that the analog input signal after frequency reduction is subjected to analog-digital conversion, and the output digital signal is used as a reference signal for ADC calibration; the first frequency conversion unit (2) is connected with the low-speed high-precision ADC (3); the pipeline ADC (4) to be calibrated is connected with the LMS adaptive filter (5); the LMS adaptive filter (5) is connected with the second frequency conversion unit (6) and the subtractor (7) respectively. The pipeline ADC (4) to be calibrated is used for carrying out analog-digital conversion on the input analog signal, and the converted digital output is used as the input signal of the LMS adaptive filter (5); the low-speed high-precision ADC (3) is used for carrying out analog-digital conversion on the analog input signal after frequency reduction by the first frequency conversion unit (2), and the digital signal output by the analog-digital conversion is used as the reference signal for ADC calibration. The output data of the analog signal sampling and quantization of the sample-and-hold module (1) are input into the LMS adaptive filter (5) by the pipeline ADC (4) to be calibrated; after the initial value is obtained, the output data are input into the subtractor (7) after frequency reduction by the second frequency conversion unit (6); the low-speed high-precision ADC (3) is also used for sampling and quantizing the analog signal to obtain the output Dref(n); then the error signal e(n) is obtained by the subtractor (7), and the error is fed back to the LMS adaptive filter (5) for updating the tap weight coefficient; the output of the pipeline ADC (4) to be calibrated gradually approaches the output of the high-precision ADC (3) through the repeated process, and the calibration of the pipeline ADC is finally completed. In the tap coefficient adaptive updating process of the LMS adaptive filter (5), the correlation value e(n)e(n-1) of the error signal is used instead of e(n); the bottom characteristics of the step factor are improved by introducing a parameter, and the step feedback factor J(n) is added, and the expression of J(n) is as follows: J(n)=Kx(n)e(n-1) / [x(n)e(n-1)+x(n-1)e(n-1)] J(n)=Kx(n)e(n-1) / [x(n)e(n-1)+x(n-1)e(n-1)] wherein K represents an influence value of the step feedback factor, x(n) represents the input signal of the adaptive filter, e(n) represents the error signal, and e(n-1) represents the error signal at the last moment. The LMS adaptive filter (5) introduces the hyperbolic tangent function on the basis of the traditional adaptive background calibration method, uses the two-norm of the step feedback factor and the correlation value of the error signal to adjust the step, and makes the output of the pipeline ADC to be calibrated gradually approach the output of the low-speed high-precision pipeline ADC, and the calibration method comprises the following steps. ​ 2. The adaptive background calibration system for a pipeline ADC of claim 1, wherein, ​ Let x(n) and w(n) represent the input signal and weight vector of adaptive filter respectively, and L is the order of adaptive filter, then the basic form of LMS algorithm is as follows: where x(n-k) represents the input vector at time k, W k represents the weight vector at time k, W L-1 (n) represents the weight vector at time L-1; The error calculation formula is: y(n) is the output signal of adaptive filter, d(n) is the expected signal, and e(n) represents the error signal; Step length update: α, m, and β are the influence values of step length factors, which jointly control the shape of step length curve; among them, α plays a crucial role in the value of step length, and with the increase of α, the value of step length is also larger; m and β have a greater influence on the shape of step length function; in the actual calibration algorithm, the values of α, m, and β need to be considered in a balanced manner; Weight update: represents a constant and has a value of 0.

01.

3. The adaptive background calibration system for a pipeline ADC of claim 2, wherein, Based on the hyperbolic tangent function The parameters α, β, m are introduced to control the shape of step curve, in which the parameter α plays a crucial role in the value of step, and the value of step increases with the increase of α, and the convergence speed of algorithm is improved. The step factor and error signal are nonlinear relationship, which is used to control the convergence speed and convergence accuracy, and the relationship between step factor and error function is obtained: Since the step length factor is positive, formula (8) becomes an even function: Then, the correlation value e(n)e(n-1) of error signal is used to replace e(n), a step length feedback factor J(n) is added, and the two-norm of e(n)e(n-1) is taken as the independent variable to be substituted into formula (9), to obtain formula (6).

4. The adaptive background calibration system for a pipeline ADC of claim 3, wherein, When e(n) approaches 0, the limit of step length u(n) is 0, and when e(n) approaches infinity, the limit of step length u(n) is α, that is, the maximum value of u(n) is α; the value of parameter α is a positive number, and the larger α is, the larger the step length is, and the higher the convergence speed of the algorithm is; parameters β, m, and k determine the shape of step length function, if K is too large, the step length factor will be 0 or almost 0 when the error signal is not 0, which will seriously slow down the convergence speed of the algorithm; The initial value of step length u(n) is the maximum step length in the traditional LMS algorithm, so that it can converge quickly, and when the algorithm approaches convergence, the step length factor is made to have a smaller value, so as to reduce the steady-state error.

5. An adaptive background correction system for a pipeline ADC according to any one of claims 1-4, characterized in that, The to-be-calibrated ADC adopts a 14bit 1GS / s pipeline ADC, and the low-speed high-precision ADC adopts a 14bit Cyclic ADC.

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