CN106374921B - Time-interleaved analog-digital converter linear distortion correction method based on poly phase - Google Patents

Abstract

The invention provides a linear distortion correction method for a time-interleaving analog-to-digital converter with low computational complexity. The method expresses the spectral characteristics of a channel through a transfer function, maps it to the frequency response of a high-order differentiator, and then differentiates the constructed differential The multi-phase decomposition process is carried out by the device, and an equivalent TIADC analytical model based on polyphase structure is given. According to the model, the crosstalk and error are extracted from the output signal, so as to complete the multi-channel correction. Experiments show that this method has low requirements on the working speed of the correction filter, is simple and easy to implement, has good compensation effect, and is extensive in the correction of general frequency mismatch errors.

Description

Linear Distortion Correction Method of Time Interleaved Analog-to-Digital Converter Based on Polyphase Decomposition

technical field

The invention relates to the technical field of signal sampling and processing, and more particularly, to a linear distortion correction method of a time-interleaving analog-to-digital converter based on polyphase decomposition.

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 practical applications, there is a high dependence on the real-time sampling rate and sampling accuracy. However, the maximum sampling rate of the ADC is limited by its resolution. The resolution and the sampling rate are contradictory. 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. The system that can realize ultra-high-speed sampling provided by the prior art is an ADC system using a time-interleaved structure.

The ADC system of this structure utilizes M pieces of single ADC module with the same sampling rate _{f s} , and adopts a parallel structure. The effect of M* _fs (total sampling rate f=M* _fs ). Theoretically, this ADC system with M channels alternately sampling in parallel can make the sampling rate of the whole system reach M times that of a single ADC module. However, due to the inherent shortcomings of the manufacturing process, 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, thereby seriously reducing the signal-to-noise ratio of the entire ADC system.

In the early days at home and abroad, when the mismatch of the ADC system is corrected, the front-end circuit is generally trimmed and the influence of the mismatch error is reduced by carefully laid out lines. The disadvantage of this method is that over time, temperature changes, and aging of electrical components will make the correction effect of the circuit ineffective. In order to overcome the shortcomings of this method, back-end processing methods can be used. At present, the correction algorithm for sampling results in the digital back-end is the key to future development.

However, the method of correction in the digital backend also has some problems, such as high complexity. In addition, most digital back-end correction methods must target specific error types, such as gain error, time error, etc., which limits the improvement of the performance of the correction system. Since the correction method based on the channel transfer function can transfer the effect of any linear filter error to frequency-response mismatch errors, it is different from the general gain-timing model based method. Compared with the calibration method, it has better generality and broadness.

The polyphase decomposition technique can effectively reduce the computational complexity. For the ADC structure of M-channel parallel alternate sampling, the application of polyphase decomposition technology can reduce the working rate of each sub-channel to 1/M of the original. Applying the method of polyphase decomposition to the TIADC model based on the channel transfer function can make the filter of each channel work at a lower working rate, thereby reducing the requirements for equipment and the cost of data processing.

SUMMARY OF THE INVENTION

In order to solve the above problems in the prior art, the present invention provides a linear distortion correction method for a time-interleaved analog-to-digital converter with low computational complexity. frequency response, and then perform polyphase decomposition processing on the constructed differentiator respectively, and give an equivalent TIADC analytical model based on polyphase structure. According to this model, the crosstalk and error are extracted from the output signal, so as to complete the multi-channel correction. .

In order to achieve the above purpose of the invention, the technical scheme adopted is:

A method for correcting linear distortion of a time-interleaved analog-to-digital converter based on polyphase decomposition, comprising the following steps:

S1. Confirm the channel number M of the time-interleaved analog-to-digital converter and the transfer function H _n (jω) of the nth channel, let H _n (jω) be expressed as:

in is the error parameter factor, p represents the order of the transfer function H _n (jω), (jω) ^p represents the frequency response of the p-order differentiator, p=1...P;

make Representing the frequency response of the p-order differentiator, equation (1) can be further expressed as:

S2. Write the transfer function of M channels as a column vector form:

in

S3. Design 1-P order digital differentiators, and determine the FIR coefficients of the 1-P order digital differentiator filters respectively;

S4. Perform polyphase decomposition on the coefficients of the 1-P order digital differentiator filter to obtain the corresponding polyphase decomposition matrix H'(z), and substitute the obtained polyphase decomposition matrix H'(z) into the pseudo-circular matrix formula , the pseudo-circular matrices P(z ^M ) corresponding to the 1-P order digital differentiators are obtained respectively;

S5. Since d(z)H'(z)=P(z ^M )d(z), so It can be expressed as follows:

S6. Applying Noble's identity, the step S5 Convert to M×M transfer function matrix H(z) of M input and M output;

S7. Write the input and output of the matrix H(z) as column vectors:

but

S8. For the i-th channel, the output of this channel is:

in, represents the i+1th row of the pseudo-circular matrix obtained by the polyphase decomposition of the p-order differentiator;

S9. For Δ ^(p) in to estimate, the estimated result is Correct Y _i (z) to get the corrected output

S10. Correct the outputs of the M channels according to the steps of steps S8 and S9, and output the corrected results after obtaining the corrected results.

In the above scheme, the derivation formula of d(z)H'(z)=P(z ^M )d(z) is as follows:

Since the polyphase decomposition matrix H'(z) is defined as:

in

Defined as a pseudo-circular matrix.

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

Preferably, in the step S3, a genetic algorithm is used to optimize the FIR coefficients of the differentiator to match the frequency response of the ideal differentiator.

Compared with the prior art, the beneficial effects of the present invention are:

The invention provides a low-complexity time-interleaving analog-to-digital converter linear distortion correction method. The method expresses the spectral characteristics of a channel through a transfer function, and then maps it to the frequency response of a high-order differentiator, and then separately adjusts the constructed differentiator. The polyphase decomposition process is carried out, and the equivalent TIADC analytical model based on polyphase structure is given. According to the model, the crosstalk and error are extracted from the output signal, so as to complete the multi-channel correction. Experiments show that this method has low requirements on the working speed of the correction filter, is simple and easy to implement, has good compensation effect, and is extensive in the correction of general frequency mismatch errors.

Description of drawings

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

FIG. 2 is a schematic diagram of a time-interleaved analog-to-digital converter transfer function model.

FIG. 3 is a structural diagram of an interleaved analog-to-digital converter model based on a polyphase decomposition filter bank.

Fig. 4 is the principle block diagram of error correction.

FIG. 5 is a schematic diagram of the amplitude-frequency response of the first-order differentiator.

FIG. 6 is a schematic diagram of the amplitude-frequency response of the second-order differentiator.

FIG. 7 is a spectrogram of the output signal before correction.

Figure 8 is a spectrogram of the corrected output signal.

FIG. 9 is a flowchart of a calibration method.

Detailed ways

The accompanying drawings are for illustrative purposes only, and should not be construed as limitations on this patent;

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

Example 1

As shown in Figure 9, the method provided by the present invention comprises the following steps:

The first step is to confirm the channel number M of the time-interleaved analog-to-digital converter and the transfer function H _n (jω) of the nth channel, and let H _n (jω) be expressed as:

in is the error parameter factor, p represents the order of the transfer function H _n (jω), (jω) ^p represents the frequency response of the p-order differentiator, p=1...P;

make Representing the frequency response of the p-order differentiator, equation (1) can be further expressed as:

The second step is to write the transfer function of the M channels as a column vector form:

in

The third step is to design a 1-P order digital differentiator, and determine the FIR coefficients of the 1-P order digital differentiator filter respectively;

The fourth step is to perform polyphase decomposition on the coefficients of the 1-P order digital differentiator filter to obtain the corresponding polyphase decomposition matrix H'(z), and substitute the obtained polyphase decomposition matrix H'(z) into the pseudo-loop In the matrix formula, the pseudo-circular matrices P(z ^M ) corresponding to the 1-P order digital differentiators are obtained respectively;

The fifth step, since d(z)H'(z)=P(z ^M )d(z) is established, so It can be expressed as follows:

The sixth step, applying the Noble identity, converts H'(z) in step S5 into an M×M transfer function matrix H(z) with M input and M output;

The seventh step, write the input and output of the matrix H(z) in the form of column vectors:

but

The eighth step, for the i-th channel, the output of this channel is:

in, represents the i+1th row of the pseudo-circular matrix obtained by the polyphase decomposition of the p-order differentiator;

The ninth step, to Δ ^(p) in to estimate, the estimated result is Correct Y _i (z) to get the corrected output

The tenth step is to correct the outputs of the M channels according to the steps of steps S8 and S9, and output the corrected results after obtaining the corrected results.

Example 2

In this example, on the basis of Example 1, a specific experiment is carried out, and the experimental environment is as follows:

The test signal used is the multi-sine signal generated by the Ulead UTG9005D digital signal generator, the frequency is f ₁ =0.35f _s , f ₂ =0.275f _s , f ₃ =0.2f _s , and the sampling frequency f _s =320MHz . The time-interleaving analog-to-digital converter is made up of 4 pieces of AD9481 of ADI Company, and the sampling rate of each piece is 250Msps when working. The entire time-interleaved analog-to-digital converter operates at 1Gsps.

As shown in Figure 1, 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 uses the same sampling rate but different sampling times (adjacent channels differ by T _s time) to high-speed The input signal is sampled, and finally the output signal is combined to realize the analog-to-digital conversion of high-speed sampling. FIG. 2 is a schematic diagram of the model of the transfer function of each channel. This model can transfer any linear error to the parameters of the channel transfer function, which can be compensated by a unified method. FIG. 3 is a structural diagram of a time-interleaved analog-to-digital converter model based on a polyphase decomposition filter bank, which reveals the reasons for the error and aliasing of the output signal of the time-interleaved analog-to-digital converter. Fig. 4 is the principle block diagram of error correction.

The present invention takes the number of channels M=4 as an example, and in the polynomial model of the channel transfer function, it is assumed that the value of the parameter P is 2.

Then the transfer function of each channel is Assume

where diag(■) represents a diagonal matrix.

As described in Embodiment 1, the correction method provided by the present invention needs to use a differentiator. In this embodiment, the used differentiator is a linear-phase digital differentiator, and its generation method is to use a genetic algorithm to optimize the FIR coefficients of the differentiator to match the frequency response of an ideal differentiator.

It can be seen from the expression of the transfer function of each channel above that since P=2, first-order and second-order differentiators need to be designed, and the filter length is set to N=32, and the corresponding filter coefficients h1 and h2 are

h1＝[-0.0388 0.0526 -0.0234 0.0161 -0.0088 -0.0006 0.0125 -0.02670.0425 -0.0591 0.0754 -0.0899 0.1008 -0.1036 0.0792 0.3259 -0.3259 -0.07920.1036 -0.1008 0.0899 -0.0754 0.0591 -0.0425 0.0267 -0.0125 0.0006 0.0088 -0.0161 0.0234 -0.0526 0.0388];

h2＝[0.0006 -0.0009 0.0015 -0.0020 0.0026 -0.0035 0.0044 -0.00540.0072 -0.0093 0.0115 -0.0152 0.0205 -0.0293 0.0475 -0.0300 -0.0300 0.0475 -0.0293 0.0205 -0.0152 0.0115 -0.0093 0.0072 -0.0054 0.0044 -0.0035 0.0026 -0.0020 0.0015 - 0.0009 0.0006];

The amplitude-frequency responses corresponding to the designed first-order differentiator and second-order differentiator are shown in Figure 5 and Figure 6, respectively.

Polyphase decomposition of the above differentiator, the coefficients of the corresponding polyphase elements P _i (z)| _h1 and P _i (z)| _h2 are

P ₁ (z)| _h1 = [-0.0388 -0.0088 0.0425 0.1008 -0.3259 0.0899 0.0267 -0.0161]

P ₂ (z) | _h1 = [0.0526 -0.0006 -0.0591 -0.1036 -0.0792 -0.0754 -0.01250.0234]

P ₃ (z) | _h1 = [-0.0234 0.0125 0.0754 0.0792 0.1036 0.0591 0.0006 -0.0526]

P ₄ (z) | _h1 = [0.0161 -0.0267 -0.0899 0.3259 -0.1008 -0.0425 0.00880.0388]

P ₁ (z)| _h2 = [0.0006 0.0026 0.0072 0.0205 -0.0300 -0.0152 -0.0054 -0.0020]

P ₂ (z)| _h2 = [-0.0009 -0.0035 -0.0093 -0.0293 0.0475 0.0115 0.00440.0015]

P ₃ (z) | _h2 = [0.0015 0.0044 0.0115 0.0475 -0.0293 -0.0093 -0.0035 -0.0009]

P ₄ (z) | _h2 = [-0.0020 -0.0054 -0.0152 -0.0300 0.0205 0.0072 0.00260.0006]

Substitute the above data into the pseudo-circular matrix formula to get two 4×4 matrices and corresponding to the two differentiators.

calculate Since the ideal sampling data X(z) cannot be obtained in the actual system, the output data Y(z) is used as the approximate data of X(z) to calculate, i=0,1,2,3, p=1,2.

get After the crosstalk error signal According to the above description, it can be calculated that:

Therefore, the corrected signal can be obtained by the following subtraction operation:

The effect of the correction can be obtained by comparing Fig. 7 and Fig. 8. Fig. 7 is the output spectrum of the multi-sine signal after passing through the time-interleaving analog-to-digital converter, and Fig. 8 is the output spectrum of the time-interleaving analog-to-digital converter after passing the correction. It can be seen from the figure that before the signal is corrected, there are a large number of noise spurs, and the amplitude can reach -40dB at the highest. After correction, the noise spectrum is suppressed, and the amplitude of the highest burr can be reduced to about -85dB.

From the above experimental results, it can be concluded that the method provided by the present invention has low requirements on the working speed of the correction filter, is simple and easy to implement, has good compensation effect, and is extensive in the correction of general frequency mismatch errors.

Obviously, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the embodiments of the present invention. For those of ordinary skill in the art, changes or modifications in other different forms can also be made on the basis of the above description. There is no need and cannot be exhaustive of all implementations here. Any modifications, equivalent replacements and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the claims of the present invention.

Claims (3)

1. A time-interleaved analog-to-digital converter linear distortion correction method based on polyphase decomposition is characterized in that: the method comprises the following steps:

s1, confirming the channel number M of a time-interleaving analog-to-digital converter and the transfer function H of an nth channel_n(j ω), let H_n(j ω) is represented by:

whereinFor the error parameter factor, p denotes the transfer function H_n(j ω) order, (j ω)^pRepresents the frequency response of a P-order differentiator, P is 1 … P;

order toRepresenting the frequency response of a p-order differentiator, equation (1) may be further expressed as:

s2, writing the transfer functions of the M channels into column vectorsIn the form of:

wherein

S3, designing 1-P order digital differentiators, and respectively determining FIR coefficients of filters of the 1-P order digital differentiators;

s4, carrying out multiphase decomposition on the coefficients of the filter of the digital differentiators with the orders of 1-P to obtain corresponding multiphase decomposition matrixes H '(z), and substituting the obtained multiphase decomposition matrixes H' (z) into a pseudo-cyclic matrix formula to obtain pseudo-cyclic matrixes P (z) corresponding to the digital differentiators with the orders of 1-P^M)；

S5. since d (z) H' (z) ═ P (z)^M) d (z) are thereforeCan be expressed as follows:

s6, applying a Noble identity to carry out the step S5An M multiplied by M transfer function matrix H (z) converted into M input and M output;

s7, writing the input and output of the matrix H (z) into the form of column vectors:

then

S8, for the ith channel, the output of the channel is as follows:

wherein, row i +1 representing the resulting pseudo-cyclic matrix decomposed polyphase by a p-order differentiator;

s9. for delta^(p)In (1)Performing estimation, the estimation result isFor Y_i(z) correcting to obtain a corrected output

And S10, correcting the output of the M channels according to the steps of S8 and S9, and outputting the corrected result.

2. The polyphase decomposition based time-interleaved analog-to-digital converter linear distortion correction method of claim 1, characterized in that: the differentiator used in the step S3 is a linear phase digital differentiator.

3. The polyphase decomposition based time-interleaved analog-to-digital converter linear distortion correction method of claim 2, characterized in that: in step S3, the FIR coefficients of the differentiator are optimized by using a genetic algorithm to match the frequency response of the ideal differentiator.