A TIADC system sampling time error calibration method based on improved etgen step-by-step interpolation method

Abstract

The application discloses a TIADC system sampling time error calibration method based on an improved Etgen step-by-step interpolation method, which is improved from the Etgen step-by-step interpolation method, improves the Etgen step-by-step linear interpolation formula, and applies the Etgen step-by-step linear interpolation formula to the time error calibration field of a time-interleaved analog to digital converter (TIADC). When the order of the Etgen step-by-step interpolation method is gradually increased, the selection method of the added nodes is improved, the precision of the interpolation algorithm is improved, and the effect of the time error calibration method is improved. The application can adaptively adjust the order of the Etgen step-by-step interpolation method according to the frequency and precision requirements of a TIADC system sampling signal, and finally can realize real-time calibration of the TIADC time error in a pure digital domain, can calibrate signals within the entire Nyquist sampling frequency, and can be applied to TIADC systems with any number of channels.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of time-interleaved ADC time error calibration, and particularly relates to a TIADC system sampling time error calibration method based on an improved Etgen step-by-step interpolation method. BACKGROUND

[0002] The signal frequency in modern electronic systems is constantly increasing, and the signal is becoming more and more complex, for example, electronic systems such as radar, which require an analog-to-digital converter (ADC) to have high resolution while meeting certain sampling rates. However, the performance of a single ADC is difficult to meet both high speed and high sampling rate due to the limitations of manufacturing technology. Therefore, a time-interleaved analog-to-digital converter (TIADC) emerges as the times require.

[0003] TIADC is a parallel interleaved ADC that uses multiple ADC chips with lower sampling rates to achieve the required sampling rate by using parallel interleaved sampling. It is a relatively easy and inexpensive solution to improve the sampling rate. Although the sampling rate of the sampling system implemented by multiple ADC sub-chips using a time-interleaved structure can meet the requirements, the sub-channel chips cannot be completely consistent due to manufacturing process constraints during the production process, and the sampling clock accuracy of each channel is also difficult to meet the requirements of TIADC. Therefore, offset mismatch errors, gain mismatch errors and time mismatch errors will be generated, which seriously affect the performance of TIADC. Among the three mismatch errors, the calibration method of time mismatch error is more complex than the other two mismatch errors. Therefore, the research focus at home and abroad is on the time mismatch error calibration method of TIADC, and among these methods, the background calibration scheme in the all-digital domain is the current research hotspot. In this calibration scheme, the document (Yang Kui. TIADC system calibration algorithm research and implementation[D]. University of Electronic Science and Technology, 2015) proposes a method of using Lagrange interpolation filter to compensate for time mismatch error. This method has high precision and is suitable for TIADC systems with any number of sub-channels. However, the order of the Lagrange interpolation method is positively related to the frequency of the input signal, that is, as the frequency of the input signal increases, the order of the Lagrange interpolation filter also needs to be increased to achieve better calibration results. Therefore, the disadvantage of the Lagrange interpolation filter is that its order is fixed. If the order is too large, the calculation amount will be too large for input signals with low frequency, and if the order is too small, the calibration effect of input signals with high frequency will be poor. SUMMARY

[0004] To address the above problems, this invention proposes a sampling time error calibration method for TIADC systems based on an improved Etkin stepwise interpolation method. Its key features include: improving the Etkin stepwise linear interpolation formula and applying it to the TIADC time error calibration field; and improving the selection method of the added interpolation points when increasing the order of the Etkin stepwise interpolation method, thereby improving the accuracy of the interpolation algorithm. The advantage of this method is that the order of the Etkin stepwise interpolation method can be adaptively determined according to the frequency of the TIADC system sampling signal and the set accuracy requirements. This invention includes:

[0005] Obtain the sampled digital signal, number of channels, sampling rate, and relative time error of the TIADC system;

[0006] Select each sampled digital signal in sequence and calibrate it according to the following method:

[0007] Determine whether the sampled digital signal is a sampling point of the reference channel. If it is, the signal does not need to be calibrated, and the next signal is selected directly to continue the determination. If it is not, the sampled digital signal is calibrated using the Etkin stepwise interpolation method.

[0008] The method for calibrating the sampled digital signal using the Etkin successive interpolation method is as follows:

[0009] Step 1: Initialize j = 1 and initialize the sampled digital signal x. i The first-order Etkin interpolation polynomial P 0,1 (x i ) and P 1,1 (x i );

[0010] Step 2: Let j = j + 1, and add one other sampled digital signal as an interpolation point, and initialize P. j,1 (x i Then calculate P. j,2 (x i ),P j,3 (x i ...P j,j-1 (x i );

[0011] Step 3: Calculate the sampled digital signal x i The j-th order Etkin interpolation polynomial P j-1,j (x i ), P j,j (x i );

[0012] Step 4: Calculate the remainder |P j-1,l (x i )-P j,l (x i )|;

[0013] Step 5, judging whether the remainder meets the accuracy requirement or reaches the set maximum order, if the accuracy requirement is met or the maximum order is reached, the sampling digital signal x i The calibration is completed, P j-1,j (x i ) is the calibration value of x i , otherwise, the higher order Aitken interpolation polynomial is calculated according to the method of step 2 to step 5 until the above two conditions are met.

[0014] In step 1 of the Aitken progressive interpolation calibration method, P 0,1 (x i ) and P 1,1 (x i ) are initialized according to formula (1) and formula (2) respectively:

[0015] P 0,1 (x i ) = x i (1)

[0016] P 1,1 (x i ) = x i+1 (2)

[0017] In step 2 of the Aitken progressive interpolation calibration method, the calculation method of P j,2 (x i ), P j,3 (x i )……P j,j-1 (x i ) is shown in formula (3):

[0018] P j,l (x i ) = P l-2,l-1 (x i ) + h l-2,j (P l-2,l-1 (x i ) - P j,l-1 (x i )) (3)

[0019] In formula (3), P j,l (x i ) represents the l-order Aitken progressive interpolation polynomial of the sampling digital signal x i , and the subscript j is only used to distinguish the calibration values obtained by using different sampling digital signals for interpolation operation, and has no other special meaning. Therefore, formula (3) shows that an l-order interpolation polynomial can be obtained by linear combination of two (l-1) -order interpolation polynomials. According to the definition of Aitken progressive interpolation method, the calculation formula of the coefficient h is shown in formula (4):

[0020]

[0021] representing the sampling time of the i th sampling digital signal with time error, n i is the theoretical sampling time of the i d,e th sampling digital signal, which cannot be accurately obtained, so h i cannot be calculated according to the definition of the Aitken successive interpolation formula; and n and n i are expanded according to formula (5) and formula (6):

[0022]

[0023] m s = iT i (6)

[0024] Finally, formula (4) can be simplified as formula (7):

[0025]

[0026] In formula (7), a represents the relative time error.

[0027] In step 2 of the Aitken successive interpolation calibration method, one other sampling digital signal is added as an interpolation point, and the selection method of the interpolation point is as follows:

[0028] Suppose that the j j,1 th Aitken successive interpolation polynomial of the sampling digital signal x i is to be calculated, then the i th sampling digital signal is added for interpolation operation, and the sampling digital signal is used to initialize P i (x i-2 ):

[0029]

[0030] According to this method of adding interpolation points, the sampling digital signal x i-1 to be calibrated is located at the midpoint of the interpolation points {…x i , x i+1 , x i+2 , …} (the midpoint for the sampling time), and the accuracy of the Aitken successive interpolation method is improved.

[0031] The calculation process of the Aitken successive interpolation method for calibrating the sampling digital signal can refer to Figure 2 . BRIEF DESCRIPTION OF DRAWINGS

[0032] In order to make the technical solutions in the embodiments of the present application or the prior art clearer, the accompanying drawings needed in the embodiments or prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description only show some embodiments of the present application, and for those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0033] Figure 1 is a total flowchart of a TIADC system sampling time error calibration method based on an improved Etgen step-by-step interpolation method of the present application;

[0034] Figure 2 is a calculation flowchart of the Etgen step-by-step interpolation method when calibrating each sampling digital signal of the present application;

[0035] Figure 3 is a frequency spectrum diagram of a calibration signal before (upper diagram) and after (lower diagram) simulation by the method of the present application, wherein the normalized frequency of an input digital signal is 0.05;

[0036] Figure 4 is Figure 3 a curve diagram of the order used when calibrating 100 sampling digital signals;

[0037] Figure 5 is a frequency spectrum diagram of a calibration signal before (upper diagram) and after (lower diagram) simulation by the method of the present application, wherein the normalized frequency of an input digital signal is 0.35;

[0038] Figure 6 is Figure 5 a curve diagram of the order used when calibrating 100 sampling digital signals; DETAILED DESCRIPTION

[0039] The technical solutions in the specific embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present application (each Etgen interpolation polynomial P b,c (x i ), abbreviated as P b,c ) in the following description:

[0040] S101 Assume that the sampling rate f s of a TIADC system, sampling digital signals x0, x1, …, x k and the number of channels M have been obtained, it is assumed that the time errors of each sub-channel have been estimated and are 0, Δt1, …, Δt m-1 , the 0th channel is assumed to be a reference channel, so Δt0=0, and the relative time errors are 0, a1, …, a M-1 , wherein a=Δt / Ts T s Let T be the sampling interval of the TIADC system, and T s =1 / f s ;

[0041] S102 initializes i = 0;

[0042] S103 selects the i-th sampled digital signal x i Assuming this method selects channel 0 as the reference channel, then the determination of x... i Is it the sampled digital signal of channel 0? If x i If it is the sampled digital signal of channel 0, then jump to S106; if x i If it is not a sampling point of channel 0, proceed to S103;

[0043] S104 Initialize P 0,1 =x i P 1,1 =x i+1 Initialize j = 1; P b,c Represents the sampled digital signal x i The value after calibration using the Etkin stepwise interpolation method, where the subscript c indicates the order and the subscript b is only used to distinguish the calibration value obtained by interpolation operation using different sampled digital signals, and has no other special meaning;

[0044] S105 Let j = j + 1, and increase the number of... Interpolation is performed on the sampled digital signal, i.e., P is initialized. j,1 :

[0045]

[0046] Initialize l = 2;

[0047] If l>j-1, then proceed to S106; and if l≤j-1, then calculate P using the improved Etkin stepwise interpolation formula (2). j,l :

[0048] P j,l =P l-2,l-1 +h l-2,j (P l-2,l-1 -P j,l-1 (2)

[0049] Among them, according to Etkin's successive interpolation formula, h d,e The definition is shown in equation (3):

[0050]

[0051] Continue to accumulate l and calculate P. j,l Until P is calculatedj,2 P j,3 ,……,P j,j-1 .

[0052] S106 higher order Aitken's successive interpolation method to calibrate the value P j-1,j and P j,j :

[0053] P j-1,j = P j-2,j-1 +h j-2,j-1 (P j-2,j-1 -P j-1,j-1 ) (4)

[0054] P j,j = P j-2,j-1 +h j-2,j (P j-2,j-1 -P j,j-1 ) (5)

[0055] S107 calculate the error (or called the remainder) of the interpolation polynomial P err :

[0056] P err = |P j-1,l -P j,l | (6)

[0057] S108 if P err <ε or j = j max , then the sampling digital signal x i calibration is completed, the final x i calibration value y i equal to:

[0058] y i = P j-1,j (7)

[0059] Let i = i + 1, and according to the method of S103 to S108 calibration of the next sampling digital signal x i .

[0060] If not meet the condition of P err <ε or j = j max , then according to the method of S105 to S108 increase interpolation point to calculate higher order Aitken interpolation polynomial, until the condition is met;

[0061] According to the above steps to calibrate all the sampling digital signal after the output of the calibrated digital signal y0, y1, …, y k .

[0062] Figure 3are the frequency spectrum diagrams before (upper picture) and after (lower picture) calibration when simulating the method of the present application, wherein the normalized frequency of the input digital signal is 0.05, the number of sampling digital signal points is 51200, ε=0.0002, j max =100, and the number of channels is 4, it can be seen that the spurious spectrum caused by time error has been basically eliminated in the calibrated frequency spectrum diagram;

[0063] Figure 4 are Figure 3 the curve diagrams of the order used when calibrating 100 sampling digital signals, wherein the picture title is the average order when calibrating the 51200 sampling digital signals;

[0064] Figure 5 are the frequency spectrum diagrams before (upper picture) and after (lower picture) calibration when simulating the method of the present application, wherein the normalized frequency of the input digital signal is 0.35, the number of sampling digital signal points is 51200, ε=0.0002, j max =100, and the number of channels is 4, it can be seen that the spurious spectrum caused by time error has been basically eliminated in the calibrated frequency spectrum diagram;

[0065] Figure 6 are Figure 5 the curve diagrams of the order used when calibrating 100 sampling digital signals, wherein the picture title is the average order when calibrating the 51200 sampling digital signals, it can be seen that the average order when the normalized frequency of the input digital signal is 0.35 is about 20 higher than the average order when the normalized frequency of the input digital signal is 0.05, which indicates that the order required by the Ertkin interpolation calibration method will also increase accordingly when the frequency of the input signal increases;

[0066] The above only discloses one preferred embodiment of the present application, and of course cannot limit the scope of the rights of the present application, and those skilled in the art can understand that all or part of the above-mentioned embodiments can be implemented, and equivalent changes made according to the claims of the present application still belong to the scope covered by the present application.

Claims

1. A TIADC system sampling time error calibration method based on improved Ettlinger step-by-step interpolation method, characterized in that, The application relates to a method for calibrating a TIADC system. The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: Step 1, initialize j = 1 and initialize the sampled digital signal x i The 1st order Eta-Kin interpolation polynomials P 0,1 (x i ) and P 1,1 (x i ), P 0,1 (x i ) and P 1,1 (x i ) are initialized according to equations (1) and (2) respectively: P 0,1 (x i )=x i (1)P 1,1 (x i )=x i+1 (2); Step 2, let j=j+1, and add one other sampling digital signal as an interpolation point, and the interpolation point is selected by the following method: Suppose we want to calculate the sampled digital signal x i For the j-th order Etkin successive interpolation polynomial, it is necessary to add the th... Interpolate the sampled digital signal and initialize P with the sampled digital signal. j,1 (x i ): Then calculate P j,2 (x i ), P j,3 (x i ), …, P j,j-1 (x i ) as shown in equation (4): P j,l (x i )=P l-2,l-1 (x i )+h l-2,j (P l-2,l-1 (x i )-P j,l-1 (x i )) (4) Wherein, the definition of the coefficient h is shown in formula (5): In formula (4), P j,l (x i ) represents the l-order Aitken stepwise interpolation polynomial of the sampled digital signal x i , and subscript j is only used to distinguish the calibration values obtained by using different sampled digital signals for interpolation operation, and has no other special meaning. The formula indicates that two l-1 order Aitken interpolation polynomials can be combined linearly to obtain an l-order Aitken interpolation polynomial; in formula (5), α represents a relative time error; Step 3, computing the sampled digital signal x i the j-th order interpolating polynomial P j-1,j (x i ) of the j-th order interpolating polynomial P j,j (x i ) is shown in equations (6) and (7), respectively: P j-1,j (x i )=P j-2,j-1 (x i )+h j-2,j-1 (P j-2,j-1 (x i )-P j-1,j-1 (x i )) (6) Step 4, compute the remainder |P j-1,l (x i )-P j,l (x i )|; Step 5, judge whether the remainder meets the accuracy requirement or reaches the set maximum order, if the accuracy requirement is met or the maximum order is reached, the sampling digital signal x i Calibration is completed, P j-1,j (x i ) is the calibration value of x i , otherwise, calculate the higher order Aitken interpolation polynomial according to the method of step 2 to step 5 until the above two conditions are met.

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