US 12,476,649 B2 · Digital correction method for dynamic range expansion of multiple ADCs

Abstract

A digital correction method for dynamic range expansion of multiple ADCs includes: obtaining gain and offset correction values of other channels relative to a standard channel CH1 based on iterative computations through positive and negative amplitude auxiliary values and positive and negative base values, then performing gain-offset error correction on the other channels, and then calculating phase differences of the other channels relative to the standard channel CH1 and constructing fractional delay filters with a Farrow structure corresponding to the channels, correcting sampling data X2, . . . , XM after performing the gain-offset error correction. Digital correction of sampling data collected from multiple channels in a multi-ADC system is realized while ensuring that respective dynamic ranges of the sampling data with different gains output by the multiple channels are not lost.

A digital correction method for dynamic range expansion of multiple analog-to-digital converters (ADCs), wherein a number of channels of the multiple ADCs is M;

and the digital correction method comprises the following steps:
step 1, obtaining a gain correction value Am, 1≤m≤M−1 and an offset correction value Bm, 1≤m≤M−1 of each channel in target channels of the M channels by iterative computations, and performing gain-offset error correction on each of the target channels based on the gain correction value Am and the offset correction value Bm;
wherein the M channels have different gains and different offset errors, and the M channels are denoted as CH1, CH2, CH3, . . . , CHM;
sampling data of the M channels CH1, CH2, CH3, . . . , CHM are respectively denoted as X1, X2, . . . , XM;
the channel CH1 of the M channels is determined as a reference channel, and the gain-offset error correction is performed on the channels CH2, CH3, . . . , CHM, as the target channels, of the M channels according to gain correction values A1, A2, . . . , AM−1 of the channels CH2, CH3, . . . , CHM relative to the channel CH1 and offset correction values B1, B2, . . . , BM−1 of the channels CH2, CH3, . . . , CHM relative to the channel CH1 by the following formula:
{
X
2
=
A
1
⁢
X
2
+
B
1
X
3
=
A
2
⁢
X
3
+
B
2
…
X
M
=
A
M
-
1
⁢
X
M
+
B
M
-
1
;
wherein the gain correction values A1, A2, . . . , AM−1 of the channels CH2, CH3, . . . , CHM relative to the channel CH1 and the offset correction values B1, B2, . . . , BM−1 of the channels CH2, CH3, . . . , CHM relative to the channel CH1 are obtained by performing the iterative computations on bipolar signals of the sampling data of two channels of the M channels;
and the obtaining the gain correction value Am and the offset correction value Bm comprises the following steps:
step 1.1, selecting a first sampling data segment with a length L from the sampling data of the channel CH1 and a second sampling data segment with the length L from the sampling data of the channel CHm+1, denoting the first sampling data segment corresponding to the channel CH1 as X1(0), X1(1), . . . , X1(L−1) and denoting the second sampling data segment corresponding to the channel CHm+1 as Xm+1(0), Xm+1(1), . . . , Xm+1(L−1);
initializing a number of the iterative computations i=1, initializing a positive amplitude auxiliary value P(0)=X1(0), initializing a negative amplitude auxiliary value N(0)=X1(0), initializing the gain correction value Am(0)=1, and initializing the offset correction value Bm(0)=0;
step 1.2, calculating a positive amplitude auxiliary value P(i) of an ith iterative computation and a negative amplitude auxiliary value N(i) of the ith iterative computation according to the following formula:
P
⁡
(
i
)
=
P
⁡
(
i
-
1
)
+
[
X
1
(
i
-
1
)
+
(
X
PMax
-
X
m
+
1
(
i
-
1
)
)
×
A
m
(
i
-
1
)
+
B
m
(
i
-
1
)
-
P
⁡
(
i
-
1
)
]
×
D
′
;
N
⁡
(
i
)
=
N
⁡
(
i
-
1
)
+
[
X
1
(
i
-
1
)
+
(
X
NMax
-
X
m
+
1
(
i
-
1
)
)
×
A
m
(
i
-
1
)
+
B
m
(
i
-
1
)
-
N
⁡
(
i
-
1
)
]
×
D
′
;
wherein XPMax represents a positive base value and is determined as a positive maximum value of a higher gain channel between the channel CH1 and the channel CHm+1;
XNMax represents a negative base value and is determined as a negative maximum value of the higher gain channel between the channel CH1 and the channel CHm+1;
Am(i−1) represents a gain correction value of an (i−1)th iterative computation;
Bm(i−1) represents an offset correction value of the (i−1)th iterative computation;
and D′ represents an iteration speed;
step 1.3, calculating a gain correction value Am(i) of the ith iterative computation and an offset correction value Bm(i) of the ith iterative computation according to the following formula:
A
m
(
i
)
=
P
⁡
(
i
)
-
N
⁡
(
i
)
X
PMax
-
X
NMax
;
⁢
B
m
(
i
)
=
X
PMax
×
N
⁡
(
i
)
-
X
NMax
×
P
⁡
(
i
)
2
×
(
X
PMax
-
X
NMax
)
;
step 1.4, calculating an error Δm(i) of the ith iterative computation according to the following formula:
Δ
m
(
i
)
=
X
1
(
i
)
-
[
A
m
(
i
)
×
X
m
+
1
(
i
)
+
B
m
(
i
)
]
;
and
step 1.5, determining whether the error Δm(i) is less than a set iteration precision;
when the error Δm(i) is less than the set iteration precision, determining the gain correction value Am(i) of the ith iterative computation and the offset correction value Bm(i) of the ith iterative computation as the gain correction value Am and the offset correction value Bm;
or when the error Δm(i) is equal to or greater than the set iteration precision, determining i=i+1 and returning and performing the step 1.2;
step 2, obtaining delays of the M channels, constructing a fractional delay filter with a Farrow structure, and performing delay correction on the M channels;
wherein the step 2 comprises the following steps:
step 2.1, obtaining the delays of the target channels, comprising:
inputting standard signals with same frequency and same phase into the M channels CH1, CH2, CH3, . . . , CHM;
performing fast Fourier transform (FFT) on the sampling data of the M channels CH1, CH2, CH3, . . . , CHM to obtain results corresponding to the M channels CH1, CH2, CH3, . . . , CHM;
and obtaining phases φm, m=1, 2, . . . , M of the M channels CH1, CH2, CH3, . . . , CHM according to real parts REm and imaginary parts IMm, m=1, 2, . . . , M of the results by using the following formula:
φ
m
=
arc
⁢
tan
⁡
(
IM
m
RE
m
)
,
m
=
1
,
2
,
…
,
M
;
obtaining phase differences Δφ1, Δφ2, . . . , ΔφM−1 of the channels CH2, CH3, . . . , CHM relative to the channel CH1 by the following formula:
Δφ
m
=
φ
m
+
1
-
φ
1
,
m
=
1
,
2
,
…
,
M
-
1
;
obtaining the delays τm, m=1, 2, . . . , M−1 of the channels CH2, CH3, . . . , CHM relative to the channel CH1 by the following formula:
τ
m
=
k
′
360
⁢
°
⁢
f
0
⁢
Δφ
m
;
where f0 represents a frequency of each of the standard signals, and k′ represents a sampling rate of each of the multiple ADCs;
step 2.2, designing the fractional delay filter with the Farrow structure, comprising:
determining a coefficient of a fractional delay filter base on Lagrange interpolation by obtaining a maximum flatness in a passband of the fractional delay filter based on Lagrange interpolation;
and the coefficient of the fractional delay filter based on Lagrange interpolation being expressed as follows:
h
⁡
(
n
)
=
∏
k
=
0
k
≠
n
P
⁢
D
-
k
n
-
k
,
n
=
0
,
1
,
2
,
…
,
P
;
wherein P represents an order of the fractional delay filter based on Lagrange interpolation, D=P−2+d, and d represents a fractional delay within a range of 0≤d≤1;
using a wave filter with a Farrow structure to approximate the determined coefficient h(n) of the fractional delay filter based on Lagrange interpolation, thereby obtaining the fractional delay filter with the Farrow structure within the fractional delay of 0≤d≤1 by using the wave filter with the Farrow structure, and obtaining a polynomial h′(n) for the coefficient h(n) of the fractional delay filter based on Lagrange interpolation according to D=P−2+d, and the polynomial h′(n) for the coefficient h(n) of the fractional delay filter based on Lagrange interpolation being expressed by the following formula:
h
′
(
n
)
=
∑
P
=
0
P
⁢
c
P
(
n
)
⁢
d
P
,
n
=
0
,
1
,
2
,
…
,
P
;
wherein cP(n) represents a coefficient of the fractional delay filter with the Farrow structure;
wherein for the channels CH2, CH3, . . . , CHM, the delays τm, m=1, 2, . . . , M−1 are determined as d respectively, and a polynomial for the coefficient of the fractional delay filter with the Farrow structure corresponding to the channels CH2, CH3, . . . , CHM respectively is obtained as follows:
h
m
(
n
)
=
∑
P
=
0
P
⁢
c
P
(
n
)
⁢
τ
m
P
,
n
=
0
,
1
,
2
,
…
,
P
,
m
=
1
,
2
,
…
,
M
-
1
;
wherein for the channel CH1, a decimal delay τ0 is a constant and is determined as d, and a polynomial for the coefficient of the fractional delay filter with the Farrow structure corresponding to the channel CH1 is obtained as follows:
h
0
(
n
)
=
∑
P
=
0
P
⁢
c
P
(
n
)
⁢
τ
0
P
,
n
=
0
,
1
,
2
,
…
,
P
;
step 2.3, performing the delay correction on the M channels, comprising:
performing half-band interpolation on the sampling data X1 corresponding to the channel CH1 and the sampling data X2, . . . , XM corresponding to the channels CH2, CH3, . . . , CHM after the gain-offset error correction performed in the step 1 to obtain processed sampling data, and inputting the processed sampling data into the fractional delay filters h0(n), h1(n), . . . , hM−1(n) with the Farrow structure corresponding to the M channels CH1, CH2, CH3, . . . , CHM respectively to perform delay filtering, and then performing half-band extraction after the delay filtering to obtain delay-corrected sampling data X1, X2, . . . , XM, thereby completing the delay correction on the M channels;
and
step 3, data integration, comprising:
integrating the delay-corrected sampling data X1, X2, . . . , XM to obtain a multi-ADC acquisition signal.

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Digital correction method for dynamic range expansion of multiple ADCs

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Digital correction method for dynamic range expansion of multiple ADCs

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Abstract

Claims2