TIADC mismatch calibration method and circuit based on frequency domain cross-correlation coefficient

Abstract

The application discloses a TIADC mismatch calibration method and circuit based on a frequency domain cross-correlation coefficient. The method firstly converts the sub-channel ADC output to the frequency domain, solves the cross-correlation coefficient between adjacent channels, estimates the sampling time mismatch parameter, then controls the calibration module to calibrate the data through the sampling time mismatch parameter, and finally completes the compensation of the sampling time mismatch through repeated iteration. RLT design is carried out on the FPGA, and the mismatch calibration circuit is obtained. Compared with the prior art, the method is suitable for a multi-channel TIADC system, does not need an auxiliary channel, and only needs a small number of sampling points and a first-order differential compensation to complete the calibration. The simulation results show that under the input of any signal, the overall performance is better than that of the existing sampling time mismatch calibration algorithm.

Description

Technical Field

[0001] The present invention belongs to the technical field of electronic design and relates to TIADC mismatch calibration in an analog-to-digital conversion process, and in particular to a TIADC mismatch calibration method and circuit based on a frequency domain cross-correlation coefficient. Background Art

[0002] Digital-to-analog converters (ADCs) play a crucial role in modern digital systems. However, due to limitations in manufacturing processes and materials, single ADCs are no longer able to meet the high-speed sampling requirements of modern digital systems. To improve the sampling capabilities of ADC systems, time-interleaved digital-to-analog converters (TIADCs) have been proposed. However, TIADC systems suffer from bias mismatch, gain mismatch, and sampling time mismatch among their subchannels, which are the main factors limiting TIADC performance. Sampling time mismatch is the most severe. Therefore, sampling time mismatch calibration is of great research significance for improving TIADC system performance.

[0003] Calibration based on signal correlation coefficients is currently one of the most important TIADC calibration techniques, and many methods have been proposed. In 2011, El-Chammas M proposed a sampling mismatch calibration technique using a reference channel, but this requires additional ADC resources and the reference channel can interfere with the sampling ADC. In 2013, Razavi B proposed a sampling mismatch calibration technique suitable for dual channels, but it is only applicable to dual channels. In 2015, Xu B proposed a sampling mismatch calibration technique suitable for any channel, but it requires a large number of matrix operations and the additional solution of the first-order derivative of the cross-correlation coefficient, which will produce approximation errors and ultimately affect the estimation of the sampling mismatch parameters. Summary of the Invention

[0004] In view of the shortcomings of the existing technology, the present invention proposes a TIADC mismatch calibration method and circuit based on frequency domain cross-correlation coefficient.

[0005] The TIADC mismatch calibration method based on the frequency domain cross-correlation coefficient specifically includes the following steps:

[0006] Step 1: For the sampling signals of each sub-channel ADC of the TIADC system, solve the cross-correlation coefficient in the frequency domain, iteratively estimate the mismatch error at the sampling time, and obtain the mismatch error parameter:

[0007] s1.1. Perform Fourier transform on the sampled signal output by the ADC of each sub-channel to obtain the corresponding spectrum information.

[0008] s1.2. Calculate the product of the absolute values ​​of the spectra of two adjacent sub-channels as the mutual correlation coefficient between the adjacent sub-channels.

[0009] s1.3, Initialize the mismatch parameter μ of each sub-channel i , perform first-order differential calibration on the sampling signal output by each sub-channel ADC.

[0010] S1.4. Recalculate the cross-correlation coefficients between adjacent sub-channels based on the signal calibrated in S1.3.

[0011] s1.5. Select a sub-channel as the reference channel and assume that the sampling time offset of the sub-channel is △t i = 0, the adaptive step size iteration method is used to adjust the mismatch parameter μ of the sub-channel i Iterate, if after calibration A i Increase, then increase μ i If the value of A i If it decreases, μ i The value of the mutual correlation coefficient A between adjacent sub-channels before and after calibration i If the value is less than the set threshold, the mismatch parameter μ is output. i .

[0012] S1.6. According to the method of S1.5, starting from the first sub-channel, obtain the mismatch parameters of each sub-channel in turn as the final mismatch error parameters.

[0013] Step 2: Use the mismatch error parameters obtained through iteration to perform first-order differential calibration on the sampled signals output by the ADCs of each sub-channel of the TIADC system to complete the mismatch calibration of the TIADC system.

[0014] The invention discloses a TIADC mismatch calibration circuit based on frequency domain cross-correlation coefficient, comprising a clock frequency division module, an analog-to-digital conversion module, a data storage module, a parameter estimation module and an error calibration module.

[0015] The clock frequency division module is used to generate the clock sampling signal of the ADC in the analog-to-digital conversion module and the clock signals of the data storage module, the parameter estimation module, and the error calibration module.

[0016] The analog-to-digital conversion module is used to receive an external analog signal, sample it into a digital signal, and then output it to the data storage module.

[0017] The data storage module is used to store the digital signal output by the analog-to-digital conversion module.

[0018] The parameter estimation module solves the cross-correlation coefficient of the adjacent sub-channel ADC data in the data storage module, estimates the error parameter at the sampling moment, and outputs it to the error correction module.

[0019] The error calibration module compensates the ADC data of each sub-channel in the data storage module according to the error parameters at the sampling moment output by the parameter estimation module, returns the compensated signal to the parameter estimation module for iteration, solves the mismatch error parameters, and outputs the final calibrated signal.

[0020] The present invention has the following beneficial effects:

[0021] It can be applied to various types of signals and TIADCs with any number of channels without the need to set up additional reference channels. It can effectively suppress the clutter caused by sampling time mismatch and improve the performance indicators of TIADC (SFDR, SNDR, etc.).

[0022] TIADC calibration is based on self-extracted error parameters from frequency-domain cross-correlation, and a calibration circuit is designed on the FPGA. When the input signal is within the Nyquist frequency domain, this calibration technology improves the SNDR and SFDR of the 12-bit TIADC system by 30dB and 40dB, respectively. It is applicable to any channel TIADC and does not require the configuration of additional reference channels or extensive matrix calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Schematic diagram of the sampling module structure of the M-channel TIADC system

[0024] Figure 2 Schematic diagram of the sampling time mismatch of the TIADC system of the M channel

[0025] Figure 3 Output spectrum of the TIADC system with sampling time mismatch

[0026] Figure 4 The SNDR indicator changes of the TIADC system with sampling time mismatch under different frequency inputs.

[0027] Figure 5 Schematic diagram of the sampling time mismatch parameter iteration process.

[0028] Figure 6 This is a spectrum diagram of the TIADC system before calibration under single-tone sinusoidal signal input.

[0029] Figure 7 This is a diagram of the spectrum of the TIADC system after calibration under single-tone sinusoidal signal input.

[0030] Figure 8 This is the convergence curve of the mismatch parameter at the sampling moment under single-tone sinusoidal signal input.

[0031] Figure 9 This is a schematic diagram of the spectrum of the TIADC system before calibration under multi-tone sinusoidal signal input.

[0032] Figure 10 This is a schematic diagram of the spectrum of the TIADC system after calibration under multi-tone sinusoidal signal input.

[0033] Figure 11 This is a spectrum diagram of the TIADC system before calibration under random signal input.

[0034] Figure 12 This is a schematic diagram of the spectrum of the TIADC system after calibration under random signal input.

[0035] Figure 13 The following is a comparison of SDNR before and after TIADC calibration under single-tone sinusoidal signal input at different frequencies.

[0036] Figure 14 The following is a comparison of the SFNR before and after TIADC calibration under single-tone sinusoidal signal input at different frequencies.

[0037] Figure 15 The figure is a hardware structure diagram of a 4-channel TIADC based on FPGA. DETAILED DESCRIPTION

[0038] The following further explains the TIADC mismatch calibration method and circuit based on the frequency domain cross-correlation coefficient with reference to the accompanying drawings.

[0039] like Figure 1 The figure shows a TIADC system sampling module with M channels. The input signal is sampled in parallel by M low-speed sub-ADCs in an interleaved manner to increase the overall sampling rate. Sampling time mismatch is caused by inconsistent delays of each sub-channel due to clock deviation and clock circuit layout differences. Specifically, when each sub-channel ADC samples the input signal, there is a fixed time deviation between the actual sampling time and the ideal sampling time, causing each sub-channel of the TIADC system to sample the input signal in a non-ideal uniform interval. Figure 2 As shown, the dotted vertical line represents the sampling time under the ideal uniform interval, and the solid vertical line represents the actual sampling time of each channel. The ideal sampling interval is , the offset of the sampling time of the i-th sub-channel is , for analog input signals , the ADC output of the i-th sub-channel The time domain expression is:

[0040] (1)

[0041] =0,1,2… , n is the index of discrete time.

[0042] Time domain output of the TIADC system It can be understood as the superposition of the ADC outputs of each channel:

[0043] (2)

[0044] right Perform Fourier transform to obtain the spectrum output of the TIADC system under sampling time mismatch :

[0045] (3)

[0046] in and They are and periodic impulse sequences The spectrum function of is the index of frequency aliasing, is the signal angular frequency, is the sampling angular frequency.

[0047] Output according to spectrum From the expression of , we can see that the position of the error spur caused by the mismatch at the sampling moment is related to the frequency of the input signal and is always located at and its amplitude increases as the input signal frequency increases. Figure 3 The overall output spectrum of the TIADC system under a single-tone sinusoidal signal input when there is a sampling time mismatch, which can intuitively show the position of the mismatch error spurious spectrum line at the sampling time. Figure 4 This figure shows the relationship between the input frequency of a single-tone sinusoidal signal and the SNDR of the TIADC system within the frequency band that meets the requirements of the Shannon sampling theorem. It can be seen that when there is a sampling time mismatch, the SNDR of the TIADC system continues to decrease with the increase of the input signal frequency, which means that the higher the input signal frequency, the greater the impact of the sampling time mismatch.

[0048] The present invention proposes Figure 5 The TIADC mismatch calibration method based on the frequency domain cross-correlation coefficient shown in FIG. 1 includes the following steps:

[0049] Step 1: For the sampling signals of each sub-channel ADC of the TIADC system, solve the cross-correlation coefficient in the frequency domain, iteratively estimate the mismatch error at the sampling time, and obtain the mismatch error parameter:

[0050] s1.1、Sampling signal of each sub-channel ADC output Perform Fourier transform to obtain the corresponding spectrum information :

[0051] (4)

[0052] in is the phase factor.

[0053] s1.2. Calculate the product of the absolute values ​​of the spectra of two adjacent sub-channels as the mutual correlation coefficient between adjacent sub-channels :

[0054] (5)

[0055] in, .

[0056] s1.3, Initialize the mismatch parameter μ of each sub-channel i , the sampling signal output by each sub-channel ADC Perform a first-order difference calibration.

[0057] S1.4. Recalculate the cross-correlation coefficients between adjacent sub-channels based on the signal calibrated in S1.3.

[0058] s1.5. According to the recalculated mutual correlation value, the mismatch parameter μ is adjusted by the gradient descent method with adaptive step size. i , the specific method is:

[0059] Take the 0th sub-channel as the reference channel, that is, assume , at this time the mutual correlation coefficient between the 0th sub-channel and the 1st sub-channel is The real part of the sample time is only offset from the first sub-channel Related, and when hour, Reached maximum value.

[0060] By comparing before and after calibration The size of the mismatch parameter is adjusted by Figure 5 As shown, when As it increases, continue to increase the mismatch parameter When the value of When it decreases, the mismatch parameter is reduced synchronously The value of the mismatch parameter After calibrating the first channel, repeat the above steps to obtain the mismatch parameters of the second channel. In this way, the mismatch parameters of each channel can be obtained in turn. .

[0061] s1.6. When the mutual correlation coefficients between the sub-channels are iterated to a stable state, the mismatch parameters of the channels at this time are output as the final mismatch error parameters.

[0062] Step 2: Obtain the first-order derivative of the sampling point through the derivative filter. Use the mismatch error parameter obtained by iteration to perform first-order differential calibration on the sampled signals output by each sub-channel ADC of the TIADC system to complete the mismatch calibration of the TIADC system. The specific method is as follows:

[0063] When the ideal sampling interval is When, Ideal sampling point of the channel and actual sampling points The sampling time mismatch error between can be expressed by Taylor expansion as:

[0064] (6)

[0065] in, is the first-order derivative under the ideal sampling state. In practical applications, the first-order derivative at the actual sampling point is selected. Instead, the calibrated signal It can be expressed as:

[0066] (7)

[0067] To further demonstrate the performance of this method, a 12-bit, 4-channel TIADC system was built in MATLAB. The specific simulation parameter settings are shown in Table 1:

[0068] Table 1

[0069] Parameter Type Numerical Sampling rate( ) / Ghz 3 Input frequency / Ghz 0.379 Quantization bit number / bit 12 Number of channels ( ) / indivual 4 Sampling time offset [0, 0.01, -0.02, 0.02] Input signal type Single tone signal, multi-tone signal, random signal Initial iteration step size ( ) 0.001

[0070] The input frequency is expressed as a ratio to the analog sampling rate, and the sampling time offset is expressed as a ratio to the ideal uniform sampling interval. The positive and negative values ​​represent delay and advance respectively. The first sub-channel is selected as the reference channel, so the sampling time offset of the first sub-channel is 0.

[0071] When the input signal frequency is 0.379 When a single-tone sinusoidal signal is used, the output spectrum of the TIADC system before and after calibration is compared. Figure 6 、 Figure 7 As shown in the figure, it can be seen that after calibration, the spurious spectrum generated by the sampling time mismatch is well suppressed to a level below -80dB, and the SNDR and SFDR are improved from 34.8dB and 37.7dB before calibration to 67.7dB and 87.9dB after calibration, respectively, with good improvement effect. The corresponding sampling time error parameter iterative convergence curves of each channel are shown in Figure 8As shown in the figure, after a certain number of iterations, the errors of the three channels finally converge to the preset values, indicating that this method can accurately extract the sampling mismatch error. The error parameters can be converged after about 30 iterations. Each iteration requires 16 sampling points, that is, only 500 sampling points are needed to complete the calculation of the mismatch parameters.

[0072] On this basis, we continue to simulate the input of multi-tone signals and random signals to test the effectiveness of this method. The simulation results of the multi-tone signal input are as follows: Figure 9 and Figure 10 The input is a random signal and the simulation results are shown as follows. Figure 11 and Figure 12 By comparing the TIADC system output spectrum before and after calibration, it can be found that the spurious spectral lines caused by sampling time mismatch are well suppressed at the -80dB level, indicating that this method is fully adaptable to various signal input conditions and can effectively complete the sampling time mismatch calibration of the TIADC system.

[0073] In order to better verify the performance of this method, single-tone sinusoidal signals of different frequencies were simulated and input, and the SNDR and SFDR before and after TIADC system calibration were calculated and compared. The results are shown in the figure below. Figure 13 、 Figure 14 As shown in the figure, within the frequency band that meets the requirements of Shannon sampling theorem, this method can significantly improve the SNDR and SFDR of the TIADC system with sampling time mismatch, especially the improvement in the high-frequency part is more obvious, which is improved by at least 30dB and 50dB respectively. This shows that this method can adapt to input signals of different frequencies and has good applicability.

[0074] TIADC mismatch calibration circuit based on frequency domain cross-correlation coefficient, such as Figure 15 As shown, it includes a clock division module, an analog-to-digital conversion module, a data storage module, a parameter estimation module and an error calibration module.

[0075] The analog-to-digital conversion module samples and quantizes the input signal through each sub-channel, and then inputs the data into the data storage and processing module. The parameter estimation module is mainly used to implement complex Fourier transform. In this embodiment, the base-2 butterfly operation is used to achieve this, which can reduce the time complexity of N-point DFT from the original Reduce to In this embodiment, each subchannel performs a 16-point radix-2 butterfly operation in each iteration, which is divided into four levels of operations. The next level of operation is performed after the previous level of operation is completed. Therefore, during hardware design, by time-division multiplexing the adder, multiplier, and butterfly operation module, the overall circuit resource consumption is reduced, the design efficiency and performance are improved, and it is also more conducive to subsequent maintenance and modification.

Claims

1. A TIADC mismatch calibration method based on frequency domain cross-correlation coefficient, characterized by: The specific steps are as follows: Step 1: For the sampling signals of each sub-channel ADC of the TIADC system, solve the cross-correlation coefficient in the frequency domain, perform gradient descent iteration with adaptive step size on the mismatch error at the sampling time, and obtain the mismatch error parameter; s1.1、Sampling signal y output by ADC of each sub-channel i [n] Perform Fourier transform to obtain the corresponding spectrum information Y i (jω): in is the phase factor; i=0,1,2…M-1, M represents the number of channels in the TIADC system; T is the desired sampling interval; △t i is the offset of the sampling time of the ith sub-channel; k is the index of frequency aliasing, ω is the signal angular frequency; X(e jω ) is the spectrum function; s1.

2. Calculate the product of the absolute values ​​of the spectra of two adjacent sub-channels as the mutual correlation coefficient A between adjacent sub-channels i : A i =|Y i-1 (jω)·Y i (jω)|=e -jωΩ ·(X(e jω )) 2 in, s1.3, Initialize the mismatch parameter μ of each sub-channel i , the sampling signal y output by each sub-channel ADC i [n] Perform first-order differential calibration; S1.

4. Recalculate the cross-correlation coefficients between adjacent sub-channels based on the signal calibrated in S1.

3. s1.

5. According to the recalculated mutual correlation value, the mismatch parameter μ is adjusted by the gradient descent method with adaptive step size. i , the specific method is: Taking the 0th sub-channel as the reference channel, that is, assuming △t0 = 0, the real part of the cross-correlation coefficient A0 between the 0th sub-channel and the 1st sub-channel is only related to the sampling time offset △t1 of the 1st sub-channel, and when △t1 = 0, A0 reaches its maximum value; By comparing the size of A0 before and after calibration, the mismatch parameter size is adjusted. When A0 increases, the value of the mismatch parameter μ1 is increased. When A0 decreases, the value of the mismatch parameter μ1 is reduced synchronously. After calibrating the first channel with the mismatch parameter μ1, repeat the above steps to obtain the mismatch parameter μ2 of the second channel. In this way, the mismatch parameter μ of each channel can be obtained in turn. i ; s1.

6. When the cross-correlation coefficients between the sub-channels are iterated to a stable state, the mismatch parameters of the channels at this time are output as the final mismatch error parameters; Step 2: Use the mismatch error parameters obtained through iteration to perform first-order differential calibration on the sampled signals output by the ADCs of each sub-channel of the TIADC system to complete the mismatch calibration of the TIADC system.

2. The TIADC mismatch calibration method based on frequency domain cross-correlation coefficient according to claim 1, wherein: The cross-correlation coefficient is calculated by performing Fourier transform on the sampling signal output by the ADC of each sub-channel to obtain the corresponding spectrum information, and calculating the product of the absolute values ​​of the spectra of two adjacent sub-channels as the cross-correlation coefficient between adjacent sub-channels.

3. The TIADC mismatch calibration method based on frequency domain cross-correlation coefficient according to claim 1, wherein: The specific method for calculating the mismatch error parameters is: Initialize the mismatch parameter μ of each subchannel i , perform first-order differential calibration on the sampling signals output by the ADC of each sub-channel; recalculate the cross-correlation coefficients between adjacent sub-channels based on the calibrated signals; Take the 0th sub-channel as the reference channel, assume that its sampling time offset is 0, and iterate its mismatch parameter μ0; Use the iterated mismatch parameter μ0 to perform first-order differential calibration on the sampled signal output by the ADC of the 0th sub-channel. Modify the mismatch error parameter according to the value of the cross-correlation coefficient after calibration until the cross-correlation coefficient between adjacent sub-channels before and after two iterations is less than the set threshold. Output the mismatch parameter at this time. The calibrated i-th channel is used as the reference channel, and the i+1-th sub-channel is calibrated until the mismatch error parameters of all sub-channels are obtained.

4. The TIADC mismatch calibration method based on frequency domain cross-correlation coefficient according to claim 3, wherein: If the cross-correlation coefficient A between adjacent sub-channels after calibration i As it increases, the mismatch parameter μ increases. i If the value of A i If it decreases, μ i value.

5. A TIADC mismatch calibration circuit based on frequency domain cross-correlation coefficient, characterized by: Used to implement the mismatch calibration method according to any one of claims 1 to 4, comprising a clock frequency division module, an analog-to-digital conversion module, a data storage module, a parameter estimation module and an error calibration module; The clock frequency division module is used to generate the clock sampling signal of the ADC in the analog-to-digital conversion module and the clock signal of the data storage module, the parameter estimation module, and the error calibration module; The analog-to-digital conversion module is used to receive external analog signals, sample them into digital signals, and then output them to the data storage module; The data storage module is used to store the digital signal output by the analog-to-digital conversion module; The parameter estimation module solves the cross-correlation coefficient of the adjacent sub-channel ADC data in the data storage module, estimates the error parameter at the sampling moment, and outputs it to the error correction module; The error calibration module compensates the ADC data of each sub-channel in the data storage module according to the error parameters at the sampling moment output by the parameter estimation module, returns the compensated signal to the parameter estimation module for iteration, solves the mismatch error parameters, and outputs the final calibrated signal.

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