CN108111169A - A kind of joint bearing calibration of the linear mismatches of four-way TIADC and non-linear mismatch - Google Patents

Abstract

The present invention provides one kind to be directed to the time-interleaved analog-digital converter of four-way（4‑TIADC）Linear mismatch and the method for non-linear mismatch joint correction, this method is by 4 TIADC to ideal input signal slightly over-sampling, and the frequency response multinomial of appropriate rank and Taylor series characterization system linearity mismatch properties and non-linear mismatch properties are respectively adopted, using the mismatch information on 4 TIADC systems output over-sampling band, design is based on normalization minimum mean-square error（NLMS）Algorithm linear mismatch error and non-linear mismatch error are concurrently carried out it is real-time while estimation while compensate, so as to obtain joint correction export.4 TIADC system linearities and nonlinearity erron are all accounted for scope and using the technology of combined in parallel correction by this method, and better calibration result is compensated so as to obtain comparing arbitrary single error.This method considers the mismatch errors of TIADC systems more comprehensively, and simple and practicable, and compensation effect is good.

Description

A Joint Correction Method for Linear Mismatch and Nonlinear Mismatch of Four-channel TIADC

technical field

The present invention relates to the technical field of signal sampling and processing, and more specifically, to a joint correction method for four-channel TIADC linear mismatch and nonlinear mismatch.

Background technique

With the continuous development of integrated circuit technology and the promotion of digital technology, the requirements for the sampling rate and sampling accuracy of the analog-to-digital conversion device ADC are getting higher and higher. Not only the data acquisition system is required to have a high sampling rate, but also a high sampling rate precision. In actual application, there is a high dependence on the real-time sampling rate and sampling accuracy. However, the maximum sampling rate of ADC is limited by its resolution. There is a contradiction between resolution and sampling rate. High sampling rate requires shorter conversion time, while high resolution requires longer conversion time. According to the current IC design process, to achieve a higher sampling rate, it is necessary to develop an ADC module based on a new structure and a new method. A system capable of realizing ultra-high-speed sampling provided by the prior art is a time-interleaved (Time-interleaved) ADC system (TIADC).

The ADC system of this structure uses M slices of single ADC modules with the same sampling rate f _s , adopts a parallel structure, and each ADC module samples at a time interval of 1/(M*f _s ) to achieve a sampling rate of The effect of M*f _s (total sampling rate f=M*f _s ). Theoretically, this M-channel parallel and alternate sampling ADC system can make the sampling rate of the entire system M times that of a single ADC module. However, due to the inherent shortcomings of the manufacturing process itself, it is impossible to make each ADC module exactly the same, so there will inevitably be mismatch errors between the ADC modules of each channel, and each ADC has its own differential and integral nonlinear characteristics, so Seriously reduces the signal-to-noise ratio of the entire ADC system.

At present, most methods mainly estimate and correct linear mismatch, such as gain error, time error, etc., and some methods estimate and correct the mismatch caused by the integral and differential nonlinearity of the analog-to-digital converter (ADC). However, in order to improve the overall performance of the TIADC, both linear and nonlinear mismatches should be considered and estimated and corrected. Previously, there was also a joint correction method for linear mismatch and nonlinear mismatch for dual-channel TIADC. In order to increase the sampling rate of the system to adapt to a wider range of application scenarios, it is necessary to expand the two-channel to four-channel or even more sampling channels. Research value and proven methods. Of course, the expansion of the number of sampling channels is bound to be accompanied by more complex aliasing errors that need to be analyzed and corresponding correction algorithms designed to compensate.

Contents of the invention

The present invention provides a four-channel TIADC linear mismatch and nonlinear A joint correction method for mismatches.

For realizing above-mentioned purpose of the invention, the technical scheme that adopts is:

A joint correction method for four-channel TIADC linear mismatch and nonlinear mismatch, comprising the following steps:

S1. Set the input signal x(t) to satisfy the Nyquist sampling theorem, and use slight oversampling to obtain the output y[n] of the 4-TIADCs system;

S2. Determine the order P of the channel frequency response function, and use the P-order polynomial to characterize the linear frequency response mismatch of the 4-TIADCs system: the time domain expression of the discrete frequency response function of each channel of the system is: 0≤m≤3, where α _m,p is the p-order polynomial coefficient of the m-th channel, and d _p [n] is the p-level discrete differentiator;

S3. order The expected linearity error can be expressed as Where x _p [n]=d _p [n]*x[n]; x[n] is the input of the 4-TIADCs system;

S4. Order the linear error coefficient 0≤p≤P-1, assuming that its estimated value at a certain moment is Using y[n] to approximately replace x[n] in step S3 to reconstruct the linear error, the estimated value of the linear error at a certain moment is in _yp [n]= _dp [n]*y[n];

S5. Determine the order L of the nonlinear transfer function, and use the Taylor series to characterize the nonlinear mismatch characteristics of the 4-TIADCs system channel: the nonlinear transfer characteristic function of each channel of the system 0≤m≤3, where Represents the coefficient of the lth order of the Taylor polynomial of the mth channel of the 4-TIADCs system, and x ^l [n] represents the lth power of x[n];

S6. Order The expected nonlinear error can be expressed as:

S7. Order nonlinear error coefficient 2≤l≤L, assuming that its estimated value at a certain moment is Using y[n] to approximately replace x[n] in step S6 to reconstruct the nonlinear error, the estimated value of the nonlinear error at a certain moment is in y ^l [n] represents the l power of y[n];

S8. Use the output y[n] of the 4-TIADCs system to subtract the linear mismatch error reconstructed in step S4 and the nonlinear mismatch error reconstructed in step S7 to obtain the compensated result Output, that is, the corrected output at a certain moment

Preferably, the estimated value of the linear error coefficient in the step S4 and an estimate of the non-linear error coefficient in S7 The specific estimation process is as follows:

Design the corresponding high-pass filter f[n], so that the cut-off frequency of the high-pass filter f[n] is higher than the cut-off frequency of the ideal sampling signal, and define the cost function in when and When ε[n]→0, the NLMS algorithm is designed to iteratively estimate the linear error coefficient R ^p and the nonlinear error coefficient S ^l . The iterative formula is as follows:

Among them, μ _t and μ _h are convergence factors, and cont is a small positive number to avoid division by zero.

Preferably, the differentiator used in the step S3 is a linear phase digital differentiator.

Compared with prior art, the beneficial effect of the present invention is:

The invention solves the technical defect that the existing TIADC technology only estimates and compensates the linear mismatch error or the nonlinear mismatch error, and the correction effect is not good, and compared with the dual-channel sampling, the sampling channel is extended to four channels The sampling rate can be increased to adapt to a wider range of application scenarios. The present invention provides a method for joint correction of linear mismatch and nonlinear mismatch of a four-channel time-interleaved analog-to-digital converter (4-TIADC). The method uses 4-TIADC to slightly oversample the ideal input signal and respectively Using frequency response polynomials of appropriate order and Taylor series to characterize the linear and nonlinear mismatch characteristics of the system, using the 4-TIADC system to output the mismatch information on the oversampling band, the design is based on the normalized minimum mean square error ( NLMS) algorithm performs real-time estimation and compensation for linear mismatch error and nonlinear mismatch error in parallel, so as to obtain joint correction output. This method takes both the linear and nonlinear errors of the 4-TIADC system into consideration and adopts a parallel joint correction technique, so that a better correction effect can be obtained than any single error compensation. This method considers the mismatch error of the TIADC system more comprehensively, is simple and easy to implement, and has a good compensation effect.

Description of drawings

FIG. 1 is a schematic structural diagram of a time-interleaved analog-to-digital converter.

Figure 2 is a schematic diagram of a four-channel TIADC model with linear and nonlinear mismatch.

Fig. 3 is a basic block diagram of the joint correction method provided by the present invention.

Fig. 4 is a schematic diagram of implementation of the adaptive joint correction method provided by the present invention.

Fig. 5 is a flowchart of the calibration method.

Detailed ways

The accompanying drawings are for illustrative purposes only and cannot be construed as limiting the patent;

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

Example 1

As shown in Figure 5, the method provided by the present invention specifically includes the following steps:

S1. Set the input signal x(t) to satisfy the Nyquist sampling theorem, and use slight oversampling to obtain the output y[n] of the 4-TIADCs system;

S2. Determine the order P of the channel frequency response function, and use the P-order polynomial to characterize the linear frequency response mismatch of the 4-TIADCs system: the time domain expression of the discrete frequency response function of each channel of the system is: 0≤m≤3, where α _m,p is the p-order polynomial coefficient of the m-th channel, and d _p [n] is the p-level discrete differentiator;

S3. order The expected linearity error can be expressed as where _xp [n]= _dp [n]*x[n];

S4. Order Assume that its estimated value at a certain moment is Using y[n] to approximately replace x[n] in step S3 to reconstruct the linear error, the estimated value of the linear error at a certain moment is in _yp [n]= _dp [n]*y[n];

S5. Determine the order L of the nonlinear transfer function, and use the Taylor series to characterize the nonlinear mismatch characteristics of the 4-TIADCs system channel: the nonlinear transfer characteristic function of each channel of the system 0≤m≤3, where Represents the coefficient of the lth order of the Taylor polynomial of the mth channel of the 4-TIADCs system, and x ^l [n] represents the lth power of x[n];

S6. Order The expected nonlinear error can be expressed as Where v[n]=x[n]+e _t [n] represents the sampled discrete signal generated by the input signal through the channel frequency response function, since the error e _t [n] is very small relative to the input signal x[n], so they are relatively Added to the power operation, e _t [n] can be ignored, that is, v ^l [n]=(x[n]+e _t [n]) ^l ≈ x ^l [n], then the expected nonlinear error can be approximately expressed for

S7. Order Suppose its estimated value at a certain moment is Using y[n] to approximately replace x[n] in step S6 to reconstruct the nonlinear error, the estimated value of the nonlinear error at a certain moment is in y ^l [n] represents the l power of y[n];

S8. Use the output y[n] of the 4-TIADCs system to subtract the linear mismatch error reconstructed in step S4 and the nonlinear mismatch error reconstructed in step S7 to obtain the compensated result Output, that is, the corrected output at a certain moment

In the specific implementation process, the estimated value of the linear error coefficient in the step S4

and an estimate of the non-linear error coefficient in S7

The specific estimation process is as follows:

Design the corresponding high-pass filter f[n], so that the cut-off frequency of the high-pass filter f[n] is higher than the cut-off frequency of the ideal sampling signal, and define the cost function in when and When ε[n]→0, the NLMS algorithm is designed to iteratively estimate the linear error coefficient R ^p and the nonlinear error coefficient S ^l . The iterative formula is as follows:

Among them, μ _t and μ _h are convergence factors, and cont is a small positive number to avoid division by zero.

Example 2

On the basis of embodiment 1, this embodiment has carried out concrete experiment:

Figure 1 is a schematic diagram of the structure of a time-interleaved analog-to-digital converter. The input signal is input by M channels, and each channel samples the high-speed input signal at the same sampling rate but at different sampling times (difference between adjacent channels). Finally, The output signals are combined to realize the analog-to-digital conversion of high-speed sampling. In the experiment of this embodiment, the narrow-band input signal is tested, and multi-tone sinusoidal signals with 22 frequencies are used as input, and the TIADC output y[n] before correction is obtained through the four-channel TIADC system shown in Figure 2.

A third-order frequency response polynomial is used to model the linear mismatch of the TIADC system, that is, P=3, and a third-order (that is, P=3) linear polynomial is used to approximate the channel frequency response function, and the linear error parameter is obtained as: R ⁰ =[ 0.005,0.003,0.01] ^T , R ¹ ＝[-0.01,0.02,-0.003] ^T , R ² ＝[0.001,-0.001,0.004] ^T , use the fdatool filter design toolkit of matlab to design a 40-order filter Differentiators, and get more advanced differentiators with convolution operations.

Also use the third-order (ie L=3) nonlinear polynomial to describe the nonlinear characteristics, and the parameters of each channel are set as follows: The nonlinear error parameters obtained are S ² =10 ^-4 [2,-1.5,-3,-0.5] ^T , and S ³ =10 ^-4 [1.75,-0.75,1.75,2.25] ^T .

As shown in Figure 3, it is the basic block diagram of this embodiment, adopting a parallel mode to jointly estimate and correct the linear mismatch and nonlinear mismatch, and Figure 4 shows the specific schematic diagram of the adaptive joint correction method, setting the convergence factor μ _t =0.005, μ _h =0.0005, using the fdatool toolkit to design a 40-order high-pass filter.

Observing the iterative process of linear mismatch parameters and nonlinear mismatch parameters during the experiment, the convergence curve changes a lot at the beginning, but basically reaches the convergence state after the sampling data point reaches 10 ⁴ , and the main influencing parameters can be in the Converge to the exact value within the allowable range of error.

Before the signal is corrected, there are many signal spikes due to aliasing mismatch, that is, there are a large number of noise spikes, and the error plane rises (at -75dBc) due to the existence of nonlinear mismatch. At this time, the SFDR (Spurious-free dynamic range) is 34.08dBc, signal-to-noise ratio SNR=31.8631dB. After the correction, the signal peak due to the mismatch basically disappears, the noise spectrum is suppressed, and the error plane drops from the previous -75dBc to -100dBc, the corrected SFDR=54.451dBc, SNR=52.0186dB, basically reaching Calibration for desired effect.

Example 3

On the basis of embodiment 1, this embodiment adopts the same system parameters and differentiator and high-pass filter as in embodiment 2, and has carried out specific experiments:

The experiment test broadband input signal of this embodiment _adopts a Gaussian white noise _with a mean value of zero and a variance of 1 to pass through a low-pass filter ( Satisfy the system oversampling condition), the obtained signal is used as the input of TIADC, through the four-channel TIADC system shown in Figure 2, the TIADC output y[n] before correction is obtained.

Set the convergence factor μ _t = 0.1, μ _h = 0.01, pass the signal y[n] through the specific implementation schematic diagram of the adaptive joint correction method shown in Figure 4, and observe the iteration of the linear mismatch parameter and the nonlinear mismatch parameter during the experiment In the process, the convergence curve changes greatly at the beginning, but basically reaches the convergence state after the sampling data point reaches 10 ⁴ , and the main influencing parameters can converge to accurate values within the allowable range of error.

Before the signal is corrected, due to the existence of linear and nonlinear errors, error signal energy is generated in the oversampling band without signal energy. The error plane is about -88.99dBc, and the signal-to-noise ratio SNR at this time is 34.7593dB; After the correction, the error plane on the oversampling band drops to about -120dBc, and the corrected signal-to-noise ratio SNR=61.2817dB, and the correction effect is good.

Apparently, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, other changes or changes in different forms can be made on the basis of the above description. It is not necessary and impossible to exhaustively list all the implementation manners here. All modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (3)

1. a kind of joint bearing calibration of linear mismatches of four-way TIADC and non-linear mismatch, it is characterised in that：Including following step Suddenly：

S1. input signal x (t) is set to meet nyquist sampling theorem, and 4-TIADCs systems are obtained using slight over-sampling Output y [n]；

S2. determine the exponent number P of channel frequence receptance function, lost using the characterization 4-TIADCs system linearities frequency response of P rank multinomials Match somebody with somebody：The discrete frequency receptance function time-domain expression of each passage of system isWherein α_m,p For the p rank multinomial coefficients of m passages, d_p[n] is p grades of discrete differential devices；

S3. make It is expected that linearity error can be expressed asWherein x_p [n]=d_p[n]*x[n]；X [n] is the input of 4-TIADCs systems；

S4. linearity error coefficient is madeAssuming that its estimate at certain moment isLinearity error is reconstructed using the x [n] in y [n] approximate substitution step S3, is obtained The estimate of certain time line error isWherein y_p[n]=d_p[n]*y[n]；

S5. nonlinear transfer function exponent number L is determined, the non-linear mismatch using Taylor series characterization 4-TIADCs system channels is special Property:The nonlinear transmission characteristic function of each passage of systemWhereinRepresent 4-TIADCs The coefficient of the l ranks of system m passage Taylor polynomials, x^l[n] represents the l powers of x [n]；

S6. make It is expected that nonlinearity erron can be expressed as：

S7. nonlinearity erron coefficient is madeAssuming that its estimate at some moment isNonlinearity erron is reconstructed using the x [n] in y [n] approximate substitution step S6, obtains some time Carve nonlinearity erron estimate beWhereiny^l [n] represents the l power of y [n]；

S8. using 4-TIADCs systems output y [n] subtract step S4 reconstruct linear mismatch error and step S7 reconstruct it is non- Linear mismatch error, the result after being compensatedIt is exported, i.e. the correction output at certain moment

2. the joint bearing calibration of the linear mismatches of four-way TIADC according to claim 1 and non-linear mismatch, feature It is：The estimate of linear error coefficient in the step S4It is and non-linear in S7 The estimate of error coefficientSpecific estimation procedure it is as follows：

Corresponding high-pass filter f [n] is designed, the cutoff frequency of high-pass filter f [n] is made to be higher than the cut-off of ideal signal Frequency defines cost function WhereinWhenAndWhen, ε [n] → 0, with This design NLMS algorithm is to linearity error coefficients R^pWith nonlinearity erron coefficient S^lEstimation is iterated, iterative formula is as follows：

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Wherein μ_tAnd μ_hIt is convergence factor, cont is the positive number of a very little, avoids zero except problem.

3. the joint bearing calibration of the linear mismatches of four-way TIADC according to claim 1 and non-linear mismatch, feature It is：The differentiator used in the step S3 is linear phase digital differentiator.