CN107147392A - TIADC Mismatch Error Calibration Method Based on Adaptive Filtering and Taylor Series - Google Patents

Abstract

The invention discloses a TIADC mismatch error calibration method based on adaptive filtering and Taylor series, including channel signal acquisition, estimating the offset error of the sampling signal of channel 1, correcting the offset error of channel 1, fractional delay filtering, Estimate the gain error and time phase error of channel 1 with an adaptive filter, and correct the gain error and time phase error of channel 1. The invention has the characteristics of less sampling points and less calculation, and is suitable for portable acquisition devices such as hand-held oscilloscopes.

Description

TIADC Mismatch Error Calibration Method Based on Adaptive Filtering and Taylor Series

technical field

The invention relates to a TIADC mismatch error calibration method, in particular to a TIADC mismatch error calibration method based on adaptive filtering and Taylor series, and belongs to the field of instruments and meters.

Background technique

Parallel sampling system (TIADC) will produce offset error, gain error, and time phase error due to the non-ideal characteristics of the device. The dual-channel TIADC model is shown in Figure 1 below, with a sampling rate of f _s and a sampling period of T _s . The parameters g ₀ , o ₀ , Δt ₀ are the gain error, offset error and time phase error of channel 0 respectively, and the parameters g ₁ , o ₁ , Δt ₁ are the gain error, offset error and time phase error of channel 1 respectively . In actual work, channel 0 is used as the reference channel, and the gain error, offset error and time phase error g ₁ , o ₁ , Δt ₁ of channel 1 need to be estimated and corrected, so that g ₁ = g ₀ , o ₁ = o ₀ , and Δt ₁ =Δt ₀ , thereby completing the mismatch error correction of the entire system.

As shown in Figure 1, the standard signal source inputs channel 0 and channel 1 at the same time, with channel 0 as a reference, the data of the two channels after being discretized by the ADC is expressed as follows:

Among them, X ₀ (k) represents the sampling data of channel 0, and X ₁ (k) represents the sampling data of channel 1. The relationship between the data of channel 1 and the data of channel 0 can be expressed as

X ₁ (k)=(1+g ₁ )X ₀ (k+0.5-Δt ₁ /2)+o ₁ (2)

The correction techniques for the three main errors in TIADC focus on two major directions, that is, non-blind estimation and correction algorithms and blind estimation and correction algorithms for mismatch errors. The non-blind estimation and correction algorithm of mismatch error needs to periodically inject excitation signals into the acquisition system to obtain the error parameters of the system. The non-blind estimation and correction algorithm will affect the real-time performance of the acquisition system. The blind estimation and correction algorithm does not need to regularly inject excitation signals into the acquisition system, and completes the estimation and correction of system error parameters while the acquisition system measures the measured signal. Most of the existing blind estimation and correction algorithms adopt a closed-loop method for parameter estimation in the estimation process of the three main errors. Although blind estimation and correction algorithms do not need to regularly inject excitation signals into the acquisition system, the existing blind estimation and correction algorithms require a very large number of sampling points. The number of sampling points required for an estimation and correction process is mostly more than 10,000 and the calculation is complex, which imposes high requirements on the calculation and storage of the acquisition system, and is not suitable for use in portable instruments such as handheld oscilloscopes. In fact, for a TIADC system with well-designed hardware, the three mismatch errors of the system will not change drastically in a short period of time, and the system parameters calculated by the non-blind estimation correction algorithm after one correction can still be obtained within a certain period of time. The entire TIADC system brings about an improvement in the signal-to-noise ratio.

Contents of the invention

The technical problem to be solved by the present invention is to provide a TIADC mismatch error calibration method based on adaptive filtering and Taylor series.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A TIADC mismatch error calibration method based on adaptive filtering and Taylor series, comprising the following steps:

Step 1: channel signal acquisition: input the standard signal source X(t)=sin(w _in t) into channel 0 and channel 1 at the same time; the angular frequency frequency w _in of the standard signal source satisfies:

T _s is the sampling interval time, channel 0 is the reference channel, channel 0 and channel 1 are interleaved with the sampling interval time T _s , and channel 1 sampling signal X ₁ (k) is:

X ₁ (k)=(1+g ₁ )X ₀ (k+0.5-Δt ₁ /2)+o ₁ (2)

Where X ₀ (k) is the sampling signal of channel 0, g ₁ , o ₁ , Δt ₁ are the gain error, offset error and time phase error of channel 1 respectively;

Step 2: Estimate the offset error of the sampled signal of channel 1

Step 3: Correct the offset error of channel 1:

In the formula is the sampling data of channel 1 after offset error correction;

Step 4: Fractional delay filtering: the sampled data of channel 1 after offset error correction Input fractional delay filter filtering, the system transfer function of fractional delay filter is:

where D = 0.5, (5)

The first-order Taylor series expansion of the sampling data of channel 1 after fractional delay filtering is

The derivative of X' ₀ (k) is calculated as:

X' ₀ (k)＝[-X ₀ (k+2)+8X ₀ (k+1)-8X ₀ (k-1)+X ₀ (k-2)]/[(48×π×f ₀ )/f _s ] (7)

Step 5: Estimate the gain error g ₁ and time phase error Δt ₁ of channel 1 with an adaptive filter.

The adaptive filter includes a weighting coefficient w ₀ adjustment unit, a weighting coefficient w ₁ adjustment unit, first to second accumulators, the sampling data X ₀ (k) of channel 0 input weighting coefficient w ₀ adjustment unit, the sampling data of channel 0 Derivative X' ₀ (k) input weighting coefficient w ₁ adjustment part, the output of weighting coefficient w ₀ adjustment part, weighting coefficient w ₁ adjustment part is sent to the first accumulator, the output of the first accumulator and the filtering data of channel 1 The second accumulator is subtracted, and the output of the second accumulator is used to control the weighting coefficient w ₀ adjustment unit and the weighting coefficient w ₁ adjustment unit, and adjust the weighting coefficient w ₀ and the weighting coefficient w ₁ according to the preset adjustment step size until The mean square error of the output of the second accumulator no longer decreases to the end;

_An estimate of the bias error g1 is:

The estimated time phase error Δt ₁ is:

Step 6: Correct the gain error and time phase error of channel 1:

In the formula, is the corrected channel 1 sample data, is the system transfer function of the time phase error correction filter.

The TIADC mismatch error calibration method based on adaptive filtering and Taylor series includes one reference channel and more than one calibration channel, and each calibration channel adopts the same calibration method as channel 1.

The technical effect obtained by adopting the above-mentioned technical scheme is:

1. The present invention has the characteristics of requiring less sampling points and less calculation, and is suitable for portable acquisition devices such as handheld oscilloscopes.

2. The present invention is also applicable to multi-channel TIADC systems.

Description of drawings

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Figure 1 is a TIADC system model;

Fig. 2 is a flow chart of the present invention;

Fig. 3 is a functional block diagram of the adaptive filter of the present invention.

detailed description

Example 1:

As shown in Figure 2, a TIADC mismatch error calibration method based on adaptive filtering and Taylor series includes the following steps:

Step 1: channel signal acquisition: input the standard signal source X(t)=sin(w _in t) into channel 0 and channel 1 at the same time; the angular frequency frequency w _in of the standard signal source satisfies:

T _s is the sampling interval time, channel 0 is the reference channel, channel 0 and channel 1 are interleaved with the sampling interval time T _s , and channel 1 sampling signal X ₁ (k) is:

X ₁ (k)=(1+g ₁ )X ₀ (k+0.5-Δt ₁ /2)+o ₁ (2)

Where X ₀ (k) is the sampling signal of channel 0, g ₁ , o ₁ , Δt ₁ are the gain error, offset error and time phase error of channel 1 respectively;

Step 2: Estimate the offset error of the sampled signal of channel 1

Step 3: Correct the offset error of channel 1:

In the formula is the sampling data of channel 1 after offset error correction;

Step 4: Fractional delay filtering: the sampled data of channel 1 after offset error correction Input fractional delay filter filtering, the system transfer function of fractional delay filter is:

where D = 0.5, (5)

Neglecting the ripple in the passband of the fractional delay filter, the sampling data of channel 1 after fractional delay filtering is:

Since Δt ₁ /2 itself is an item much smaller than 1, usually Δt ₁ /2≤0.05 for a TIADC system with well-designed hardware. Therefore, the Taylor series expansion of formula (6) and ignoring the terms above the second order give

The first-order Taylor series expansion of the sampling data of channel 1 after fractional delay filtering is

X' ₀ (k) is the derivative of , using the sampling data of channel 0 to complete the calculation, the calculation method is:

X' ₀ (k)＝[-X ₀ (k+2)+8X ₀ (k+1)-8X ₀ (k-1)+X ₀ (k-2)]/[(48×π×f ₀ )/f _s ] (8)

Step 5: Estimate the bias error g ₁ and the time phase error Δt ₁ of channel 1 with an adaptive filter.

As shown in Figure 3, the adaptive filter includes a weighting coefficient w ₀ adjustment unit, a weighting coefficient w ₁ adjustment unit, first to second accumulators, the sampling data X ₀ (k) of channel 0 input weighting coefficient w ₀ adjustment unit , the derivative X' ₀ (k) of the sampling data of channel 0 is input into the weighting coefficient w ₁ adjustment unit, and the output of the weighting coefficient w ₀ adjustment unit and the weighting coefficient w ₁ adjustment unit is sent to the first accumulator, and the output of the first accumulator Filtered data with channel 1 The second accumulator is subtracted, and the output of the second accumulator is used to control the weighting coefficient w ₀ adjustment unit and the weighting coefficient w ₁ adjustment unit, and adjust the weighting coefficient w ₀ and the weighting coefficient w ₁ according to the preset adjustment step size until The mean square error of the output of the second accumulator no longer decreases to the end;

_An estimate of the bias error g1 is:

The estimated time phase error Δt ₁ is:

Step 6: Correct the setting error and time phase error of channel 1:

In the formula, is the corrected channel 1 sample data, is the system transfer function of the time phase error correction filter.

Embodiment 2: The difference from Embodiment 1 is that it also includes channel 2, which adopts the same calibration method as that of channel 1 in embodiment 1.

Claims (3)

1. a kind of TIADC mismatch error calibration methods based on adaptive-filtering and Taylor series, it is characterised in that：Including following Step：

Step 1：Channel signal is gathered：By standard signal source X (t)=sin (w_inT) while input channel 0 and passage 1；Standard is believed The angular frequency frequency w in number source_inMeet：

T_sFor sampling interval duration, passage 0 is reference channel, passage 0 and the interval sampling interval time T of passage 1_sInterlaced sampling, leads to The sampled signal X of road 1₁(k) it is：

X₁(k)=(1+g₁)X₀(k+0.5-Δt₁/2)+o₁ (2)

Wherein X₀(k) it is the sampled signal of passage 0, g₁,o₁,Δt₁The respectively gain error of passage 1, biased error and time phase Position error；

Step 2：Estimate the biased error of the sampled signal of passage 1

Step 3：The biased error of correction channel 1：

In formulaFor the sampled data of the passage 1 after OFFSET ERROR CORRECTION；

Step 4：Fractional delay filter：By the sampled data of the passage 1 after OFFSET ERROR CORRECTIONInput fractional delay Filter filtering, the ssystem transfer function of fractional delay filter is:

Wherein D=0.5, (5)

The first order Taylor series expansion of the sampled data of passage 1 after fractional delay filter is handled is

X'₀(k) derivative for being, its computational methods is：

X'₀(k)=[- X₀(k+2)+8X₀(k+1)-8X₀(k-1)+X₀(k-2)]/[(48×π×f₀)/f_s] (7) step 5：With Sef-adapting filter estimates the gain error g of passage 1₁With time-skew error Δ t₁；

Step 6：The gain error and time-skew error of correction channel 1：

In formula,For the sampled data of the passage 1 of correction,Transmitted for the system of time-skew error correcting filter Function.

2. the TIADC mismatch error calibration methods according to claim 1 based on adaptive-filtering and Taylor series, it is special Levy and be：

Sef-adapting filter in the step 5 includes weight coefficient w₀Adjust part, weight coefficient w₁Adjust part, first to Second accumulator, the sampled data X of passage 0₀(k) weighted input coefficient w₀Adjust part, the derivative X' of the sampled data of passage 0₀ (k) weighted input coefficient w₁Adjust part, weight coefficient w₀Adjust part, weight coefficient w₁Adjust the output feeding first of part Accumulator, the output of the first accumulator and the filtering data of passage 1Subtract each other in the second accumulator, the second accumulator it is defeated Going out is used to control weight coefficient w₀Adjust part, weight coefficient w₁Part is adjusted, according to default regulation step-length adjustment weight coefficient w₀With weight coefficient w₁, terminate until the mean square error of the output of the second accumulator no longer reduces；

Biased error g₁Estimate be：

Time-skew error Δ t₁Estimate be：

。

3. the TIADC mismatch error calibration methods according to claim 1 based on adaptive-filtering and Taylor series, it is special Levy and be：Including 1 reference channel and more than 1 calibrated channel, each calibrated channel is used and the identical calibration side of passage 1 Method.