CN115801009B - Method for compensating time offset error of TIADC parallel acquisition system - Google Patents

Method for compensating time offset error of TIADC parallel acquisition system Download PDF

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CN115801009B
CN115801009B CN202310044449.7A CN202310044449A CN115801009B CN 115801009 B CN115801009 B CN 115801009B CN 202310044449 A CN202310044449 A CN 202310044449A CN 115801009 B CN115801009 B CN 115801009B
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吴旭凡
程剑平
董业民
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Shanghai Xinchi Technology Group Co ltd
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Abstract

The invention discloses a method for compensating time offset errors of a TIADC parallel acquisition system, and belongs to the field of high-speed high-precision analog-digital conversion. The method comprises the following steps: calculating to obtain the output of the sub-channel band time mismatch error; calibrating and compensating the output of the sub-channel with time mismatch error; the differentiator is used for deriving and the output of the differentiator is corrected. The invention mainly aims at realizing the differentiator by using a five-point value differential formula by the compensation circuit, and greatly reducing the area required by the differentiator compared with the direct FIR filter for deriving; after the differentiator is adjusted by the differentiator correction module, the performance of the compensated signal is obviously better than that of the compensated signal.

Description

Method for compensating time offset error of TIADC parallel acquisition system
Technical Field
The invention relates to the technical field of high-speed high-precision analog-digital conversion, in particular to a method for compensating time offset errors of a TIADC parallel acquisition system.
Background
A time interleaved ADC is an architecture that loops through a set of M sub-ADCs, so the overall throughput is M times the sampling rate of each sub-ADC. Theoretically, any type or configuration of ADC may be used as a sub-ADC for TIADC. The principle structure of TIADC is shown in figure 1, and compared with a single-channel ADC, the architecture can keep the same precision as that of a sub-ADC and further improve the sampling rate. However, the timing of the channels of TIADC is shown in fig. 2, and various mismatch errors exist between the interleaved channels, which severely degrade the performance of the TI-ADC, wherein the time mismatch errors are most difficult to eliminate.
Assume that the sampling period of the whole system is
Figure SMS_1
Each sub-ADC sampling period is +.>
Figure SMS_2
Digital output of analog input signal after TIADC sampling quantization>
Figure SMS_3
The method comprises the following steps:
Figure SMS_4
wherein the method comprises the steps of
Figure SMS_5
For the output of sub-ADCs, +.>
Figure SMS_6
For TIADC output, +.>
Figure SMS_7
Is the sampling period of TIADC. For a pair of
Figure SMS_8
Performing discrete fourier transform can obtain the expression in the frequency domain as:
Figure SMS_9
Figure SMS_10
for the output frequency response of TIADC, +.>
Figure SMS_11
For the output frequency response of the ith sub-channel ADC, M is TIADC channel number, +.>
Figure SMS_12
Is the sampling angular frequency. If sampling time mismatch exists, sampling of TIADC is uneven, and the time mismatch error of the ith channel is assumed to be +.>
Figure SMS_13
Then the digital output of TIADC is:
Figure SMS_14
Figure SMS_15
for the error coefficient of the ith channel, usually +.>
Figure SMS_16
. For->
Figure SMS_17
Performing discrete fourier transform can obtain the expression in the frequency domain as:
Figure SMS_18
when the input signal is a sinusoidal signal:
Figure SMS_19
Figure SMS_20
to output the angular frequency +.>
Figure SMS_21
Is an impulse function. As can be seen from the formula, the time mismatch error presents redundant harmonics on the frequency spectrum, resulting in a substantial reduction in performance of TIADC, and the frequency point where the time mismatch error occurs on the frequency spectrum is located:
Figure SMS_22
frequency point and input frequency of time mismatch
Figure SMS_23
And sampling frequency->
Figure SMS_24
All that is involved, the introduced harmonics directly affect the SFDR (Spurious-Free-Dynamic-Range) of TIADC, thereby degrading the overall system performance.
Disclosure of Invention
The invention aims to provide a method for compensating time offset errors of a TIADC parallel acquisition system, which aims to solve the problems in the background technology.
In order to solve the technical problems, the invention provides a method for compensating time offset errors of a TIADC parallel acquisition system, which comprises the following steps:
calculating to obtain the output of the sub-channel band time mismatch error;
calibrating and compensating the output of the sub-channel with time mismatch error;
the differentiator is used for deriving and the output of the differentiator is corrected.
In one embodiment, calculating the output of the sub-channel band time mismatch error includes:
switching the 0 channel output to the reference channel output, and estimating
Figure SMS_25
Time mismatch error of sub-channels
Figure SMS_26
；
Switching the 0 channel output from the reference channel back to the 0 channel output after convergence, estimates
Figure SMS_27
Time mismatch error of sub-channel->
Figure SMS_28
；
Due to
Figure SMS_29
，/>
Figure SMS_30
The method comprises the steps of carrying out a first treatment on the surface of the The output of the sub-channel band time mismatch error expressed by the Taylor series expansion formula is as follows:
Figure SMS_31
Figure SMS_32
for the ideal output of the ith sub-channel, k is constant,/->
Figure SMS_33
To the k-th power of the time mismatch coefficient of the i-th channel,
Figure SMS_34
is the k-th derivative of the output of the ith channel.
In one embodiment, the output of the sub-channel with time mismatch error after calibration compensation is:
Figure SMS_35
Figure SMS_36
to 3 th-order of the time mismatch coefficient of the ith channel,/->
Figure SMS_37
Is the 3 rd order derivative of the output of the i-th channel.
In one embodiment, the differentiator calculates the first derivative value using a first order numerical differentiation formula based on a lagrangian interpolation polynomial of a five-point formula:
Figure SMS_38
Figure SMS_39
for the first order of TIADC output signal, < >>
Figure SMS_40
、/>
Figure SMS_41
、/>
Figure SMS_42
、/>
Figure SMS_43
Four sampling points adjacent to each other.
In one embodiment, modifying the output of the differentiator comprises:
let the original first derivative value be set to:
Figure SMS_44
correction coefficient
Figure SMS_45
Representing the deviation from the actual derivative value;
in obtaining the time mismatch error between the reference channel and the 0 channel
Figure SMS_46
And->
Figure SMS_47
Later, the relative error between the two channels is obtained>
Figure SMS_48
；
The same inputs are infused for the 0 channel and the reference channel, and then the outputs of the two channels are respectively:
Figure SMS_49
Figure SMS_50
for the output of the reference channel->
Figure SMS_51
Output of the 0 th channel; expansion to the first order with taylor series yields:
Figure SMS_52
Figure SMS_53
a derivative value for an ideal sampling point; since the differential value of the ideal point cannot be known, the actual output differential value is used>
Figure SMS_54
Approximate replacement->
Figure SMS_55
Finally expressed as:
Figure SMS_56
because it is assumed that there is a coefficient to be corrected between the output of the differentiator and the actual derivative value
Figure SMS_57
By extracting correction factors->
Figure SMS_58
Expressed by the formula:
Figure SMS_59
Figure SMS_60
is the reciprocal of the correction coefficient; because:
Figure SMS_61
bonding of
Figure SMS_62
The following steps are obtained:
Figure SMS_63
output of
Figure SMS_64
Finally expressed as:
Figure SMS_65
after obtaining the coefficient to be corrected, the final compensation is performed on the output of the differentiator
Figure SMS_66
The correction of the differentiator can be achieved.
The method for compensating the time offset error of the TIADC parallel acquisition system has the following beneficial effects:
(1) The invention mainly aims at realizing the differentiator by using a five-point value differential formula by the compensation circuit, and greatly reducing the area required by the differentiator compared with the direct FIR filter for deriving: only four registers, two multipliers and one adder are needed for one differentiator;
(2) The key path is shorter, and the synthesis is easier to realize higher frequency;
(3) The simulation shows that the structure designed by the traditional five-point value differential formula has the same error as the corrected differentiator structure, and the same frequency point can be improved by more than 30 dB.
Drawings
Fig. 1 is a schematic illustration of TIADC.
Fig. 2 is a timing diagram of the channels of TIADC.
Fig. 3 is a schematic diagram of a TIADC time mismatch error calibration circuit.
Fig. 4 is a schematic diagram of a calibration module configuration.
Fig. 5 is a schematic diagram of the differentiator modification block.
Fig. 6 is a schematic diagram of a differential structure after correction of coefficients.
FIG. 7 is a schematic diagram of a preferred embodiment of the present invention
Figure SMS_67
SFDR before frequency bin calibration.
FIG. 8 is a schematic diagram of a preferred embodiment of the present invention
Figure SMS_68
SFDR after frequency point calibration.
Detailed Description
The method for compensating the time offset error of the TIADC parallel acquisition system provided by the invention is further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are in a very simplified form and are all to a non-precise scale, merely for convenience and clarity in aiding in the description of embodiments of the invention.
The invention provides a method for compensating time offset errors of a TIADC parallel acquisition system, which improves the quality of sampling output signals of the system by compensating time mismatch errors and output errors of a differentiator under the condition that the offset and gain errors of the whole TIADC parallel acquisition system are assumed to be zero.
As shown in fig. 3, the compensation structure of the present invention needs to combine with the TIADC feedforward type time mismatch error estimation structure, in this embodiment, taking four channels as an example, firstly, 0 channel output is switched to reference channel output, and time mismatch errors of four sub-channels are estimated
Figure SMS_69
. Switching the 0 channel output from the reference channel back to the 0 channel output after convergence, estimating the time mismatch error of the four sub-channels>
Figure SMS_70
。
Typically the time mismatch error of the sub-channels is much smaller than 1, i.e
Figure SMS_71
，/>
Figure SMS_72
. Therefore, the Taylor series expansion formula is used for representing the output +.>
Figure SMS_73
：
Figure SMS_74
。
Figure SMS_75
K is a constant (k=1, 2, …) for the ideal output of the ith sub-channel,>
Figure SMS_76
k-th power of the time mismatch coefficient of the ith channel,/-th power of>
Figure SMS_77
Is the k-th derivative of the output of the ith channel. The compensation structure compensates according to the calibration module structure of fig. 4 after obtaining the output of the sub-channel band time mismatch error according to the conventional high-order cascade structure, and the final output result is:
Figure SMS_78
Figure SMS_79
to 3 th-order of the time mismatch coefficient of the ith channel,/->
Figure SMS_80
For the output of the ith channel, +.>
Figure SMS_81
Is the 3 rd order derivative of the output of the i-th channel. The calibrated output removes the first and second order error terms because the performance of the final output is related to the estimation of the time mismatch error on the one hand and the accuracy of the derivative with the differentiator on the other hand.
The differentiator usually adopts a direct type FIR filter structure, and the order is designed to be more than 30 orders to meet the performance requirement, and the differentiator adopts a first order numerical differential formula of a Lagrange interpolation polynomial based on a five-point formula to calculate the first derivative value of a TIADC output signal:
Figure SMS_82
Figure SMS_83
for the first order of TIADC output signal, < >>
Figure SMS_84
、/>
Figure SMS_85
、/>
Figure SMS_86
、/>
Figure SMS_87
Four sampling points adjacent to each other. Since there is a large deviation between the error derived by the five-point value differential formula and the actual derivative value, the output of the differentiator is corrected again, and the structure is as shown in fig. 6, and the original first derivative value is set as:
Figure SMS_88
Figure SMS_89
is a correction coefficient. A coefficient exists between the derivative value obtained by the five-point value differentiation method and the actual derivative value ∈>
Figure SMS_90
Representing the deviation from the actual derivative value, an additional differentiator modification block is introduced as shown in fig. 5.
In obtaining the time mismatch error between the reference channel and the 0 channel
Figure SMS_91
And->
Figure SMS_92
Later, the relative error between the two channels can be obtained +.>
Figure SMS_93
：
Figure SMS_94
The same inputs are infused for the reference channel and the 0 channel, and then the outputs of the two channels are respectively:
Figure SMS_95
Figure SMS_96
for the output of the reference channel->
Figure SMS_97
Is the output of channel 0. Expansion to the first order with the taylor series can result in:
Figure SMS_98
Figure SMS_99
is the derivative value of the ideal sampling point. Since the differential value of the ideal point cannot be known, the actual output differential value is used>
Figure SMS_100
Approximate replacement->
Figure SMS_101
Finally expressed as:
Figure SMS_102
because it is assumed that there is a coefficient to be corrected between the output of the differentiator and the actual derivative value
Figure SMS_103
Correction coefficient is extracted by the structure of fig. 5 +.>
Figure SMS_104
Expressed by the formula: />
Figure SMS_105
Figure SMS_106
Is the reciprocal of the correction coefficient. Because:
Figure SMS_107
bonding of
Figure SMS_108
It can be derived that:
Figure SMS_109
output of
Figure SMS_110
Finally expressed as:
Figure SMS_111
after the coefficients to be corrected are obtained, as shown in FIG. 6, the output of the differentiator is finally compensated
Figure SMS_112
The correction of the differentiator can be realized, and the signal performance after final compensation can be better improved.
The invention compensates the time mismatch errors existing among multiple channels in TIADC by using a Taylor series expansion formula, and the performance is mainly dependent on the time mismatch errorsDifference of difference
Figure SMS_113
And the accuracy of the differentiator output, the invention mainly improves the performance of the signal after compensation by improving the accuracy of the differentiator output.
After the differentiator is adjusted by the differentiator correction module with the structure of fig. 5, the performance of the compensated signal is obviously better than that of the compensated signal. Compared with the direct FIR type filter for deriving, the current structure can have better performance under the same time mismatch error and the same compensation structure by comparing the performance of the 33-order direct FIR type filter. The invention is illustrated with a 4-channel structure that is suitable for TIADC in a multi-channel structure. Based on the above calibration scheme, the four-channel TIADC is set with time mismatch errors of [ -1 mill, -2 mill, -3 mill, -4 millrespectively]The reference channel is set without time mismatch error, in
Figure SMS_114
And (5) calibrating the frequency points. From fig. 7 and 8, it can be seen that the SFDR of the output signal after calibration is increased from 46.62dB to 102.11dB, and the calibration effect is very obvious.
The above description is only illustrative of the preferred embodiments of the present invention and is not intended to limit the scope of the present invention, and any alterations and modifications made by those skilled in the art based on the above disclosure shall fall within the scope of the appended claims.

Claims (1)

1. A method for compensating for time offset errors in a TIADC parallel acquisition system, comprising:
calculating to obtain the output of the sub-channel band time mismatch error;
calibrating and compensating the output of the sub-channel with time mismatch error;
the differentiator is adopted for deriving, and the output of the differentiator is corrected;
the output of the sub-channel band time mismatch error obtained by calculation comprises the following steps:
switching the 0 channel output to the reference channel output to estimate x sub-channelsTime mismatch error r of tracks ref ，r 1 ，...，r x ；
Switching the 0-channel output from the reference channel back to the 0-channel output after convergence, estimating the time mismatch error r of the x sub-channels 0 ，r 1 ，...，r x ；
Due to r i <<1, i=0, 1,2,; the output of the sub-channel band time mismatch error expressed by the Taylor series expansion formula is as follows:
Figure FDA0004165777160000011
x i (n) is the ideal output of the ith sub-channel, k is a constant,
Figure FDA0004165777160000012
k-th power of the time mismatch coefficient of the ith channel,/-th power of>
Figure FDA0004165777160000013
A k-order derivative of the output of the ith channel;
the output after calibration compensation for the output of the sub-channel band time mismatch error is:
Figure FDA0004165777160000014
Figure FDA0004165777160000015
to the 3 rd power of the time mismatch coefficient of the ith channel, x '' i (n) is a 3-order derivative of the output of the ith channel;
the differentiator calculates a first derivative value using a first order numerical differential equation of a lagrangian interpolation polynomial based on a five-point equation:
Figure FDA0004165777160000016
y' (n) is a first-order derivative of the TIADC output signal, and y (n+2), y (n+1), y (n-1) and y (n-2) are four sampling points which are adjacent to each other front and back;
correcting the output of the differentiator includes:
the original first derivative value is set as:
Figure FDA0004165777160000021
correction coefficient r derivator Representing the deviation from the actual derivative value;
in obtaining the time mismatch error r of the reference channel and the 0 channel ref And r 0 Later, a relative error r between the two channels is obtained 0-ref ＝r 0 -r ref ；
The same inputs are infused for the 0 channel and the reference channel, and then the outputs of the two channels are respectively:
y ref (n)＝x(n)
y 0 (n)＝x(n+r 0-ref )
y ref (n) is the output of the reference channel, y 0 (n) is the output of the 0 th channel; expansion to the first order with taylor series yields:
y 0 (n)＝x(n+r 0-ref )≈x(n)+r 0-ref x(n)
x' (n) is the derivative value of the ideal sampling point; since the differential value of the ideal point cannot be known, the actual differential value y 'is used' 0 (n) approximately replaces x' (n), and is finally expressed as:
y 0 (n)≈x(n)+r 0-ref y 0 ′(n)
because there is a coefficient r to be corrected between the output of the differentiator and the actual derivative value derivator By extracting correction coefficient g derivator Expressed by the formula:
Figure FDA0004165777160000022
g derivator is the reciprocal of the correction coefficient; because:
y 0 (n)-r 0-ref r derivator y 0 (n)＝y 0 (n)-r 0-ref y 0 (n)+r 0-ref (r derivator -1)y 0 (n)
＝x(n)+r 0-ref (r derivator -1)y 0 (n)
binding y ref (n) =x (n) gives:
y ref (n)-[y 0 (n)-r 0-ref r derivator y 0 (n)]＝r 0-ref (r derivator -1)y 0 (n)
output g derivator Finally expressed as:
Figure FDA0004165777160000023
after obtaining the coefficient to be corrected, g is compensated at the final output of the differentiator derivator The correction of the differentiator can be achieved.
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