Broadband-domain TIADC time mismatch background calibration method
The time error between TIADC channels is calculated by using a high-order Taylor series expansion method and iteratively converged. The output data is compensated by first-order and second-order derivatives, which solves the problem of excessive hardware resource consumption of TIADC in the wide frequency domain and realizes high-precision time mismatch calibration and low-power circuit design.
Patent Information
- Application Number
- CN202511546199.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-28
- Publication Date
- 2025-12-26
AI Technical Summary
Existing TIADC time mismatch calibration methods suffer from excessive hardware resource consumption and high power consumption in the wide frequency domain, and are particularly difficult to effectively calibrate higher-order error terms under high-frequency signal conditions.
By employing a high-order Taylor series expansion method, the time error between channels is calculated and iteratively converged. The output data is compensated by combining first-order and second-order derivatives, and a small number of first-order FIR differentiators are used to achieve accurate calibration of third-order and lower-order time mismatch errors.
High-precision TIADC time mismatch calibration was achieved in a wide frequency range, reducing hardware resource consumption and power consumption, improving the dynamic parameters of the analog-to-digital converter, and the circuit structure is simple and easy to implement.
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Figure CN121217138A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of TIADC calibration, and in particular relates to a wide-frequency domain TIADC time mismatch background calibration method. Background Technology
[0002] Time-interleaving technology is a technique that improves the sampling rate by cascading multiple sub-ADCs in parallel. Time-interleaved analog-to-digital converters (TIADCs) are characterized by low to medium accuracy and high speed, and are widely used in diverse industries such as medical imaging, industrial monitoring, and aerospace. However, due to various non-ideal factors, timing skew mismatch errors between the sub-ADC channels of a TIADC can cause spurious signals in the output spectrum, thus limiting the performance of the TIADC. As the input signal frequency increases, the proportion of higher-order error terms caused by timing skew gradually increases. In existing error compensation algorithms, to make the calibration method effective over a wider Nyquist frequency domain, the number of differentiators is generally increased or more complex filters are used to solve for higher-order derivatives, thereby eliminating higher-order derivative error terms and calibrating the TIADC timing skew error. For example, six first-order differentiators are cascaded to obtain the third-order derivative. However, to obtain higher-order derivatives using the above method, the number of differentiators must be increased exponentially, which will increase the circuit power consumption and area exponentially. Summary of the Invention
[0003] To address the shortcomings of the existing technology, the technical problem to be solved by the present invention is to provide a wideband TIADC time mismatch background calibration method.
[0004] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A wideband TIADC time mismatch background calibration method, wherein the TIADC has 2 m There are 1 channel, where m is a positive integer, and the following steps are included: S100, using the output data of the first channel of TIADC delayed by one clock cycle as the (2)th channel. m +1) channel output data; the (2)th channel's output data; m +1) channel represents the 2nd m The next channel after the first channel; the first channel of TIADC and the (2nd) channel. m +1) channels are used as initial reference channels; S200. Take the output data of every two adjacent reference channels as a set of reference data, and take the channel located in the middle of the two adjacent reference channels as the channel to be calibrated. Then, calibrate the channel to be calibrated using the reference data. S300: Add the calibrated channel as a new reference channel. Repeat step S200 until all channels of the TIADC are calibrated.
[0005] Furthermore, step S200 includes the following sub-steps: S210. Take the output data of each pair of adjacent reference channels as a set of reference data, and combine it with the output data of the corresponding channel to be calibrated to calculate the time error of the channel to be calibrated. S220. Perform error compensation on the output data of the channel to be calibrated based on the time error.
[0006] Furthermore, in step S210, the time error of the channel to be calibrated is calculated. t i The formula is:
[0007] in, t i Indicates the first i Time error of each channel; i Indicates the channel number; g It represents half the difference between the numbers of two adjacent reference channels; x i Indicates the first i Output data for each channel; E ( ) indicates the expected value.
[0008] Furthermore, in step S210, after calculating the time error... t i Then, time error was also considered. t i Perform iterative convergence until the change between two consecutive iterations is less than a pre-set reference threshold for that channel. th i The output value obtained after the iteration is taken as the first value. i Time error of each channel t i .
[0009] Furthermore, regarding time error t i The formula for iterative convergence is:
[0010] in, τ i [ k The ] represents the current iteration output value; τ i [ k-1] represents the output value of the last iteration, at the first iteration, τ i [ k- 1]=0; μ is a preset iteration parameter; the value of τ i [ k ] after the iteration is ended is taken as the time error of the first i channel t i .
[0011] Further, the S220 step includes the following sub-steps: S221, calculating the first-order compensation output data of the output data of each channel after first-order calibration, and obtaining first-order compensation multiplex data by multiplexing cal 1; S222, calculating the second-order compensation output data of the output data of each channel after second-order calibration, and obtaining second-order compensation multiplex data by multiplexing cal 2; S223, adding the first-order compensation output data and the second-order compensation output data of each channel in a predetermined proportion to obtain the output data of each channel after error compensation .
[0012] Further, in the S221 step, the first-order compensation output data cal i _1 is calculated according to the formula
[0013] wherein, cal i _1 represents the first-order compensation output data of the output data of the first i channel after first-order calibration; x i (n) (1) represents the first-order derivative of the output data of the first i channel with time deviation. x i .
[0014] Further, in the S222 step, the second-order compensation output data cal i _2 is calculated according to the formula
[0015] wherein, cal i _2 represents the second-order compensation output data of the output data of the first ithe second-order compensated output data of the output data of the i-th channel after the second-order calibration; x i (n) (2) the first-order derivative of x i (n) (1) x i (n) (3) the second-order derivative of x i (n) (1)
[0016] Further, in the S223 step, the formula for calculating the output data of the i-th channel after error compensation is
[0017] wherein, the output data of the i-th channel after error compensation. i
[0018] Further, in the S223 step, the formula for calculating the output data of the i-th channel after error compensation i
[0019] wherein, x i (4) the fourth-order derivative of x i
[0020] In the present application, the Taylor term of high-order Taylor series expansion is used to compensate the time mismatch error, and only the first-order and second-order derivative terms of the Taylor expansion term are needed to complete the accurate calibration of the third-order and below time mismatch error, which can greatly reduce the consumed hardware resources. Moreover, the present application is suitable for most time-interleaved analog-to-digital converters, improves the dynamic parameters of the analog-to-digital converter, and obtains good calibration accuracy. In addition, the calibration method is of a full-digital type, has strong portability, can achieve good calibration effect with a small number of first-order FIR differentiators, has small area and power consumption, and has a simple circuit structure and is easy to implement. BRIEF DESCRIPTION OF DRAWINGS
[0021] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and serve to explain the principles of the application. In the drawings: Figure 1 a schematic diagram of clock deviation of a TIADC.
[0022] a schematic diagram of clock deviation of a TIADC.Figure 2 Flow chart of an embodiment of the method for calibrating time mismatch of a wideband TIADC.
[0023] Figure 3 Block diagram of time error extraction for the first calibration of a four-channel TIADC.
[0024] Figure 4 Block diagram of time error extraction for the second calibration of a four-channel TIADC.
[0025] Figure 5 Flow chart of the process of generating first-order compensated output data for a four-channel TIADC.
[0026] Figure 6 Flow chart of the process of generating second-order compensated output data for a four-channel TIADC.
[0027] Figure 7 Data spectrum of a TIADC before calibration of band error when the input signal frequency is 88MHz and the sampling frequency is 500MHz.
[0028] Figure 8 Data spectrum of a TIADC after calibration using the conventional first-order Taylor compensation method when the input signal frequency is 88MHz and the sampling frequency is 500MHz.
[0029] Figure 9 Data spectrum of a TIADC after calibration using the method of the present embodiment when the input signal frequency is 88MHz and the sampling frequency is 500MHz.
[0030] Figure 10 Data spectrum of a TIADC after calibration using the conventional first-order Taylor compensation method when the input signal frequency is 170MHz and the sampling frequency is 500MHz.
[0031] Figure 11 Data spectrum of a TIADC after calibration using the method of the present embodiment when the input signal frequency is 170MHz and the sampling frequency is 500MHz. DETAILED DESCRIPTION
[0032] The embodiments of the present application will be described below through specific concrete examples, and the figures provided in the following examples only schematically illustrate the basic concepts of the present application, and the following examples and features in the examples can be combined with each other without conflict.
[0033] Please refer to Figure 1 , the clock deviation of a TIADC is schematically shown in the figure, in which, The input signal waveform is represented by clk_ADC01, which represents the ideal sampling time waveform of the first channel, clk_ADC02, which represents the actual sampling time waveform of the first channel, clk_ADC11, which represents the ideal sampling time waveform of the second channel, and clk_ADC12, which represents the actual sampling time waveform of the second channel. ∆T1 and ∆T2 represent the differences between the actual sampling time and the ideal sampling time of the first and second channels, respectively. ∆T1 represents the actual received sampling data time being later than the ideal sampling data time, and ∆T2 represents the actual received sampling data time being earlier than the ideal sampling data time. As long as the differences ∆T1 and ∆T2 between the actual received sampling data time and the ideal sampling data time are not zero, clock deviation will occur, resulting in sampling time mismatch error.
[0034] Please see Figure 2 , Figure 2 This is a flowchart of an embodiment of the wideband TIADC time mismatch background calibration method of the present invention. The wideband TIADC time mismatch background calibration method of this embodiment includes the following steps: S100, the TIADC has 2 m There are 1 (m) channels, where m is a positive integer. The output data of the 1st channel of the TIADC after a one-clock-cycle delay is taken as the (2)th channel. m +1) channel output data; the (2)th channel's output data; m +1) channel represents the 2nd m The next channel after the first channel; the first channel of TIADC and the (2nd) channel. m +1) channels are used as the initial reference channels.
[0035] S200. Take the output data of every two adjacent reference channels as a set of reference data, and take the channel located exactly in the middle of the two adjacent reference channels as the channel to be calibrated. Calibrate the channel to be calibrated using the reference data. Assume that the two adjacent reference channels are the j-th channel and the k-th channel, respectively; 0≤j<k≤2. m The channel in the very middle is the (i+j) / 2th channel. During the first calibration, the two reference channels are the 1st channel and the (i+j) / 2nd channel, respectively. m +1) channels, at this time, the channel to be calibrated is the (2)th channel. m / 2 +1) channels. This step may include the following sub-steps: S210. Take the output data of every two adjacent reference channels as a set of reference data, and combine it with the output data of the corresponding channel to be calibrated to calculate the time error of the channel to be calibrated. In this step, the time error of the channel to be calibrated is calculated. t i The formula is:
[0036] in, t i Indicates the first i Time error of each channel; i Indicates the channel number (here, the channel to be calibrated); g It represents half the difference between the numbers of two adjacent reference channels; x i Indicates the first i Output data for each channel; E ( ) indicates the expected value.
[0037] Of course, in order to improve time error t i The accuracy of this step is determined by calculating the time error. t i Then, time error was also considered. t i Perform iterative convergence until the change between two consecutive iterations is less than a pre-set reference threshold for that channel. th i The output value obtained after the iteration is used as the time error of that channel. t i This can reduce time error t i It has higher accuracy. It is more sensitive to time errors. t i The formula for iterative convergence is:
[0038] in, τ i [ k The ] represents the current iteration output value; τ i [ k- 1] represents the output value of the previous iteration. In the first iteration, τ i [ k- 1]=0; μ The iterative parameters are pre-set; the result obtained after the iteration is complete. τ i [ k The value of ] is used as the first i Time error of each channel t i .
[0039] S220. Perform error compensation on the output data of the channel to be calibrated based on the time error. This step may include the following sub-steps: S221, calculating first-order compensation output data of the output data of each channel after first-order calibration, and obtaining first-order compensation multiplex data by multiplexing cal 1. calculating first-order compensation output data cal i The formula of the first-order compensation output data is as follows
[0040] wherein, cal i The first-order compensation output data of the output data of the nth channel after first-order calibration is represented by i x i (n) (1) The output data of the nth channel with time deviation i x i The first-order derivative of the output data of the nth channel with time deviation
[0041] The first-order compensation output data of the output data of each channel after first-order calibration is integrated by a multiplexer cal i The first-order compensation output data of the output data of each channel after first-order calibration is integrated by a multiplexer cal 1.
[0042] S222, calculating second-order compensation output data of the output data of each channel after second-order calibration, and obtaining second-order compensation multiplex data by multiplexing cal 2. calculating second-order compensation output data cal i The formula of the second-order compensation output data is as follows
[0043] wherein, cal i The second-order compensation output data of the output data of the nth channel after second-order calibration is represented by i x i (n) (2) The first-order derivative of the output data of the nth channel with time deviation x i The first-order derivative of the output data of the nth channel with time deviation (1) x i The second-order derivative of the output data of the nth channel with time deviation (3) x i The second-order derivative of the output data of the nth channel with time deviation (1)
[0044] S223, add the first-order compensation output data and the second-order compensation output data of each channel in a predetermined ratio (in this embodiment, 2 / 3 of the first-order compensation output data and 1 / 3 of the second-order compensation output data are added), to obtain output data of each channel after error compensation The formula for calculating the output data of each channel after error compensation is
[0045] wherein, represents the output data of the i-th channel after error compensation. i
[0046] Substitute cal i _1and cal i _2and perform Taylor expansion to obtain
[0047] wherein, x i (4) represents the fourth-order derivative of x i . According to the above formula, the third-order and lower error terms in the error output data can be eliminated after compensation, that is, the three first-order differentiators in series are used to realize the elimination of the third-order and lower error terms in the output data, which can replace the first-order differentiator cascade mode to save resources. Of course, if the fourth-order and above error terms are to be eliminated, only one more first-order differentiator is needed, and similarly, if the fourth-order and above error terms are to be eliminated, one more first-order differentiator is needed for each order of error term. Compared with the cascade method of high-order derivation, the method of this embodiment can greatly reduce resource consumption.
[0048] S300, add the calibrated channel as a new reference channel, and repeat the S200 step until the calibration of all 2 m channels of the TIADC is completed.
[0049] The following will take a 4 four-channel TIADC (i.e., m=2) as an example to illustrate this embodiment. In the S100 step, the output data of the first channel after a clock period delay is taken as the output data of the fifth channel; and the first channel and the fifth channel of the TIADC are taken as the initial reference channels.
[0050] In the S200 step, when calibrated for the first time, the third channel is calibrated according to the first channel and the fifth channel. Please refer to Figure 3 , which is a time error extraction diagram of the third channel. In the diagram, Z -1 delay one clock cycle; abs represents taking absolute value; mean represents taking expectation value. The first path data is obtained by subtracting the output data of the first channel from the output data of the third channel and taking absolute value, the second path data is obtained by subtracting the output data of the first channel from the output data of the third channel after delaying one clock cycle (i.e. the output data of the fifth channel) and taking absolute value, and the time error of the third channel is obtained by taking expectation value of the second path data minus the first path data t 3; and through the preset reference threshold value th 3time error t 3iterative convergence, to obtain the final time error t 3. The final time error t 3is used to calibrate the output data of the third channel.
[0051] Then, the second calibration is performed again in the step S200. Before calibration, the third channel is added as a reference channel, i.e. the reference channels are the first channel, the third channel and the fifth channel. The second channel is calibrated according to the first channel and the third channel, and the fourth channel is calibrated according to the third channel and the fifth channel. Please refer to Figure 4 , the time error of the second channel is calculated according to the output data of the first channel and the output data of the third channel t 2; and through the preset reference threshold value th 2time error t 2iterative convergence, to obtain the final time error t 2. The time error of the fourth channel is calculated according to the output data of the third channel and the output data of the fifth channel t 4; and through the preset reference threshold value th 4time error t 4iterative convergence, to obtain the final time error t 4. The final time error t 2and time error t 4are used to calibrate the output data of the second channel and the fourth channel respectively.
[0052] After calibrating the output data of the channels according to the time errors, the first-order compensation output data and the second-order compensation output data need to be calculated respectively. Please refer to Figure 5 , the method for calculating the first-order compensation multiplex data cal 1is as follows: first, the output data of the channels with time deviation x 1- x 4are passed through a multiplexer to obtain multiplex data x (n), and then the multiplex data x(n) first-order differential multiplexed data after passing through a first-order differentiator x (n) (1) . The first-order differential multiplexed data x (n) (1) is passed through a demultiplexer to obtain first-order differential data of each channel x 1(n) (1) x 4(n) (1) The first-order differential data of channels 2-4 x 2(n) (1) x 4(n) (1) is multiplied by the corresponding time error t 2- t 4 to generate first-order compensation terms of channels 2-4, and then the output data of channels 2-4 x 2- x 4 is subtracted by the corresponding first-order compensation terms to obtain first-order compensation output data of the output data of channels 2-4 after first-order calibration cal 2_1- cal 4_1. Since the first channel is a reference channel, the first-order differential data of the first channel x 1(n) (1) is directly taken as the first-order compensation output data of the first channel cal 1_1. The first-order compensation output data of each channel cal 1_1- cal 4_1 is integrated into one after passing through a multiplexer to obtain complete first-order compensation multiplexed data of the TIADC cal 1.
[0053] Please refer to Figure 6 , the method for calculating second-order compensation multiplexed data cal 2 is as follows: first-order compensation multiplexed data cal 1 is passed through a second-order differentiator to generate a first-order derivative of cal 1 x (n) (2) , and the first-order derivative of cal 1 x (n) (2) is passed through a third-order differentiator to generate a second-order derivative of digital signal cal 1 x (n) (3) . Then, the first-order derivative of cal 1 x (n) (2) is passed through a demultiplexer to obtain a first-order derivative corresponding to the first-order compensation output data of each channel x 1(n) (2) x 4(n)(2) and the second derivative of the first order compensation output data of the second to fourth channels cal 1(n) (3) x (n) (3) x 4(n) (3) x 2(n) (2) x 4(n) (2) x 2~4 t t 2~4 x 2(n) (3) x 4(n) (3) t i x i cal 2_2~4_2 cal x 1(n) (3) cal 1_2 cal 1_2~4_2 cal cal 2
[0054]
[0055] This represents the ADC output data with time mismatch error. This represents the ideal output data of the ADC without time mismatch error. This indicates the first ADC without time mismatch error. i Calculate the first to fourth derivatives of the ideal output data for each channel. Yes, the first i The estimated sampling time mismatch values for each channel. The Taylor expansion-based compensation calibration method primarily targets the correction of time mismatch errors. However, traditional methods based on first-order Taylor series expansions are only suitable for lower frequency input signals, and traditional higher-order compensation methods consume significant resources. As the frequency of the input signal increases, the proportion of higher-order error terms caused by sampling time mismatch gradually increases, thus requiring higher-order compensation to ensure calibration accuracy. However, hardware resource limitations must also be considered.
[0056] Please see Figure 7 This is a data spectrum of the TIADC with pre-band error calibration at an input signal frequency of 88MHz and a sampling frequency of 500MHz. Please refer to [link / reference]. Figure 8 The image shows the data spectrum of the TIADC after calibration using the traditional first-order Taylor compensation method with an input signal frequency of 88MHz and a sampling frequency of 500MHz. (Comparison) Figure 7 and Figure 8 It can be seen that using the traditional calibration method improved the dynamic performance SNDR parameter by 31 dB and the SFDR parameter by 34.98 dB. Please refer to [link / reference]. Figure 9 The image shows the data spectrum after calibration using the third-order Taylor compensation method of this embodiment under the same conditions. Compared with the traditional compensation method, it improves the SNDR parameter by 0.1dB and the SFDR parameter by 0.2dB. This indicates that when the input signal frequency is low, the difference between the compensation method of this embodiment and the traditional first-order Taylor compensation method is not significant.
[0057] Please see Figure 10 The image shows the data spectrum of the TI ADC after calibration using the traditional first-order Taylor compensation method at an input signal frequency of 170MHz and a sampling frequency of 500MHz. Calibration using the traditional first-order Taylor compensation method improved the dynamic performance SNDR parameter by 30.46dB and SFDR parameter by 30.02dB, but the calibration effect was significantly worse than that at lower input frequencies. Please refer to [link to relevant documentation]. Figure 11Compared with the data spectrum graph calibrated by the third-order Taylor compensation method of the embodiment in the same case, the traditional compensation method is improved by 1.5dB in the SNDR parameter and 4.1dB in the SFDR parameter. At this time, the third-order calibration method of the embodiment is obviously more accurate than the traditional first-order calibration method. Therefore, when the input signal frequency increases, only a small number of differentiators are needed to achieve higher calibration accuracy in the Nyquist frequency domain. The small number of differentiators results in small overall calibration circuit area, low power consumption, low delay, and easy digital circuit implementation.
[0058] In the embodiment, the Taylor term of the high-order Taylor series expansion is used to compensate for the time mismatch error. Only the first and second derivative terms of the Taylor expansion term are needed to complete the accurate calibration of the third-order and below time mismatch error, which can greatly reduce the hardware resources consumed. When the input signal frequency is close to the Nyquist frequency, the errors caused by non-ideal factors such as nonlinearity of the sample-and-hold circuit, aperture jitter, clock phase noise, integral nonlinearity (INL) and differential nonlinearity (DNL) of the amplifier and analog-to-digital converter, and bandwidth limitation increase in proportion at high frequencies. The phase response of the system usually changes dramatically and is more nonlinear when it is close to the Nyquist frequency, and a low-order linear model such as Taylor first-order compensation is not enough to accurately describe the complex nonlinearity, memory effect and dynamic characteristics of the system in the high frequency band and the edge area. The Taylor series expands a function near a point into a polynomial form, and uses the first N terms of the polynomial to approximate the error compensation function of the system. Therefore, the higher the order, the higher the accuracy of the polynomial approximation, and the finer the nonlinear characteristics and higher-order dynamic effects that can be captured. Therefore, when the input signal frequency increases, the proportion of high-order error terms of the sampling time increases, and the error cannot be calibrated by low-order compensation, the method of the embodiment can eliminate high-order error terms, ensure accuracy, and only sacrifice part of the power consumption. It can be implemented for most time-interleaved analog-to-digital converters, improves the dynamic parameters of the analog-to-digital converter, and achieves good calibration accuracy. The calibration method proposed in the embodiment is a full-digital type and has strong portability. A small number of first-order FIR differentiators can achieve good calibration effect, and the area and power consumption are small. The circuit structure is simple and easy to implement.
[0059] The above embodiments only express the preferred embodiments of the present application, which are described in detail and specifically, but cannot be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled persons in the art, without departing from the concept of the present application, several modifications and improvements can be made, which are within the scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.
Claims
1. A wideband TIADC time mismatch background calibration method, the TIADC having 2 m channels, m being a positive integer, characterized in that, The method comprises the following steps: S100, using the output data of the first channel of TIADC delayed by one clock cycle as the (2)th channel. m +1) channel output data; the (2)th channel's output data; m +1) channel represents the 2nd m The next channel after the first channel; The first channel and the (2 m +1) channel of the TIADC are taken as the initial reference channels; S200, taking the output data of each two adjacent reference channels as a set of reference data, taking a channel located at the middle of the two adjacent reference channels as a to-be-calibrated channel, and calibrating the to-be-calibrated channel by using the reference data; S300, adding the calibrated channel as a new reference channel, and repeating the step S200 until the calibration of all channels of the TIADC is completed.
2. The wideband TIADC time mismatch background calibration method of claim 1, wherein: The step S200 comprises the following sub-steps: S210, taking the output data of each two adjacent reference channels as a set of reference data, and combining the output data of the corresponding to-be-calibrated channel to calculate the time error of the to-be-calibrated channel; S220, performing error compensation on the output data of the to-be-calibrated channel according to the time error.
3. The wideband TIADC time mismatch background calibration method of claim 2, wherein: In the step S210, the time error of the channel to be calibrated is calculated t i The formula is: wherein t i denotes the time error of the i channel; i denotes the number of the channel; g denotes half of the difference between the numbers of two adjacent reference channels; x i denotes the output data of the i channel; E denotes the expectation value.
4. The wideband TIADC time mismatch background calibration method of claim 3, wherein: In the step S210, the time error t i is calculated t i The iteration converges until the change value between two successive iterations is less than the preset reference threshold value of the channel th i , and the output value obtained after the iteration is taken as the time error of the first channel i t i . 5. The wideband TIADC time mismatch background calibration method of claim 4, wherein: Time error t i The formula for iterative convergence is: wherein, τ i [ k ] represents the output value of the current iteration; τ i [ k- 1] represents the output value of the previous iteration, and at the first iteration, τ i [ k- 1]=0; μ is a preset iteration parameter; the value of τ i [ k ] obtained after the iteration is taken as the time error of the i channel t i .
6. The wideband TIADC time mismatch background calibration method according to any one of claims 2-5, wherein: The step S220 comprises the following sub-steps: S221. Calculate the first-order compensated output data of each channel after first-order calibration, and obtain the first-order compensated multiplexed data by multiplexing. cal 1; S222, calculate the second-order compensation output data of the output data of each channel after the second-order calibration, and obtain the second-order compensation multiplexing data through multiplexing cal 2; S223, add the first-order compensation output data and the second-order compensation output data of each channel in a predetermined ratio to obtain output data of each channel after error compensation .
7. The wideband TIADC time mismatch background calibration method of claim 6, wherein: In the S221 step, the first-order compensation output data is calculated cal i The formula of the first-order compensation output data is wherein, cal i _1 represents the first order compensated output data of the output data of the first i channel after a first order calibration; x i (n) (1) represents the first order derivative of the output data of the first i channel with time offset x i .
8. The wideband TIADC time mismatch background calibration method of claim 7, wherein: In the S222 step, the second order compensation output data is calculated cal i The formula of the second order compensation output data is in, cal i _2 indicates the first i Second-order compensated output data after second-order calibration of the output data of each channel; x i (n) (2) express x i (n) (1) The first derivative; x i (n) (3) express x i (n) (1) The second derivative of .
9. The wideband TIADC time mismatch background calibration method of claim 8, wherein: In the step S223, the formula for calculating the output data of the channel after error compensation is wherein, represents the output data of the first i channel after error compensation.
10. The wideband TIADC time mismatch background calibration method of claim 9, wherein: In the step S223, the output data of the first channel after error compensation is calculated by the formula i wherein x i (4) represents x i the fourth derivative of