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

Abstract

The invention discloses a TIADC mismatch calibration method and circuit based on a frequency domain cross correlation coefficient. According to the method, after ADC output of each sub-channel is converted to a frequency domain, a cross correlation coefficient between adjacent channels is solved, so that a sampling moment mismatch parameter is estimated and obtained, then a calibration module is controlled to carry out data calibration through the sampling moment mismatch parameter, and sampling moment mismatch compensation is finally completed through repeated iteration. And RLT design is carried out on the FPGA, so that a mismatch calibration circuit is obtained. Compared with the prior art, the method is suitable for a multi-channel TIADC system, an auxiliary channel is not needed, and calibration can be completed only through fewer sampling points and first-order differential compensation. A simulation result shows that under the input of any signal, the overall performance is superior to that of an existing sampling moment mismatch calibration algorithm.

Description

Technical Field

[0001] The 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] The digital-to-analog converter (ADC) plays an extremely important role in modern digital systems. However, due to the limitations of manufacturing processes and materials, a single ADC can no longer meet the high-speed sampling requirements of modern digital systems. In order to improve the sampling capability of the ADC system, the time-interleaved digital-to-analog converter (TIADC) was proposed. However, the sub-channels of the TIADC system have problems such as bias mismatch, gain mismatch and sampling time mismatch, which are the main reasons that restrict the performance of TIADC, among which the sampling time mismatch has the most serious impact. Therefore, sampling time mismatch calibration has important research significance for improving the performance of the TIADC system.

[0003] The calibration technology based on signal correlation coefficient is one of the most important TIADC calibration technologies at present, and many methods have been proposed. In 2011, El-Chammas M proposed a sampling time mismatch calibration technology using a reference channel, but it requires additional ADC resources and the reference channel will interfere with the sampling ADC. In 2013, Razavi B proposed a sampling time mismatch calibration technology suitable for dual channels, but it is only applicable to dual channels. In 2015, Xu B proposed a sampling time mismatch calibration technology suitable for any channel, but it requires a large number of matrix operations and an additional first-order derivative solution for the mutual correlation coefficient, which will produce approximate errors and ultimately affect the estimation of the sampling time mismatch parameters. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a TIADC mismatch calibration method and circuit based on frequency domain cross-correlation coefficient. The TIADC mismatch calibration method based on the frequency domain cross-correlation coefficient specifically includes the following steps: Step 1: For the sampling signals of each sub-channel ADC of the TIADC system, solve the mutual correlation coefficient in the frequency domain, estimate the mismatch error at the sampling time iteratively, and obtain the mismatch error parameter: s1.1. Perform Fourier transform on the sampled signal output by the ADC of each sub-channel to obtain the corresponding spectrum information.

[0005] 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.

[0006] s1.3, Initialize the mismatch parameter μ of each subchannel i, perform first-order differential calibration on the sampling signal output by each sub-channel ADC.

[0007] s1.4. Recalculate the cross-correlation coefficients between adjacent sub-channels for the signal calibrated in s1.3.

[0008] 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, and the mismatch parameter μ of the subchannel is adjusted using the adaptive step size iteration method. i Iterate, if after calibration A i Increases, then increases 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 is less than the set threshold, and the mismatch parameter μ is output at this time i .

[0009] s1.6. According to the method in s1.5, starting from the first sub-channel, the mismatch parameters of each sub-channel are obtained in turn as the final mismatch error parameters.

[0010] Step 2: Using the mismatch error parameters obtained by iteration, perform first-order differential calibration on the sampling signals output by each sub-channel ADC of the TIADC system to complete the mismatch calibration of the TIADC system.

[0011] The TIADC mismatch calibration circuit based on frequency domain mutual correlation coefficient comprises a clock frequency division module, an analog-to-digital conversion module, a data storage module, a parameter estimation module and an error calibration module.

[0012] The clock frequency division module is used to generate a clock sampling signal of the ADC in the analog-to-digital conversion module and clock signals of the data storage module, the parameter estimation module, and the error calibration module.

[0013] 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.

[0014] The data storage module is used to store the digital signal output by the analog-to-digital conversion module.

[0015] The parameter estimation module solves the mutual 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.

[0016] 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.

[0017] The present invention has the following beneficial effects: It can be applied to various types of signals and TIADC with any number of channels, without the need to set up additional reference channels. It can effectively suppress the noise caused by sampling time mismatch and improve the performance indicators of TIADC (SFDR, SNDR, etc.).

[0018] The TIADC calibration is based on frequency domain cross-correlation self-extraction of error parameters, and a calibration circuit is designed on the FPGA; when the input signal is in the Nyquist frequency domain, after this calibration technology, the SNDR and SFDR of the 12-bit TIADC system are improved by 30dB and 40dB respectively; it can be applied to any channel TIADC, and there is no need to set up additional reference channels and a large number of matrix calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the M-channel TIADC system sampling module structure Figure 2 Schematic diagram of sampling time mismatch of TIADC system for M channels Figure 3 Output spectrum of the TIADC system with sampling time mismatch Figure 4 The SNDR indicator changes of the TIADC system with sampling time mismatch under different input frequencies.

[0020] Figure 5 Schematic diagram of the iterative process of mismatch parameters at sampling time.

[0021] Figure 6 This is a schematic diagram of the spectrum of the TIADC system before calibration under single-tone sinusoidal signal input.

[0022] Figure 7 This is a schematic diagram of the spectrum after TIADC system calibration under single-tone sinusoidal signal input.

[0023] Figure 8 This is the convergence curve of the mismatch parameter at the sampling time under single-tone sinusoidal signal input.

[0024] Fig. 9 This is a schematic diagram of the spectrum of the TIADC system before calibration under multi-tone sinusoidal signal input.

[0025] Fig.10This is a schematic diagram of the spectrum after TIADC system calibration under multi-tone sinusoidal signal input.

[0026] Fig.11 This is a schematic diagram of the spectrum of the TIADC system before calibration under random signal input.

[0027] Fig.12 This is a schematic diagram of the spectrum of the TIADC system after calibration under random signal input.

[0028] Fig.13 The SDNR comparison chart of TIADC before and after calibration under single-tone sinusoidal signal input of different frequencies.

[0029] Fig.14 The following is a comparison chart of SFNR before and after TIADC calibration under single-tone sinusoidal signal input of different frequencies.

[0030] Fig.15 This is a hardware structure diagram of a 4-channel TIADC based on FPGA. DETAILED DESCRIPTION

[0031] The following further explains the TIADC mismatch calibration method and circuit based on the frequency domain cross-correlation coefficient in conjunction with the accompanying drawings.

[0032] 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. The sampling time mismatch is caused by the inconsistent delay of each sub-channel due to clock deviation, clock circuit layout differences, etc. 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, so that each sub-channel of the TIADC system finally samples the input signal in a non-ideal uniform interval, such as 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 of is:

[0033] (1) =0,1,2… , n is the index of discrete time.

[0034] Time domain output of TIADC system It can be understood as the superposition of the ADC outputs of each channel: (2) right Perform Fourier transform to obtain the spectrum output of the TIADC system under sampling time mismatch : (3) in and They are and periodic impulse sequence The spectrum function of is the index of frequency aliasing, is the signal angular frequency, is the sampling angular frequency.

[0035] Output according to spectrum From the expression, we can see that the position of the error spur caused by the mismatch at the sampling time 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 This is the overall output spectrum of the TIADC system under a single-tone sinusoidal signal input when there is a mismatch in the sampling moment. The position of the mismatch error spurious spectrum line at the sampling moment can be intuitively seen. Figure 4 This is 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 larger the input signal frequency, the greater the impact of the sampling time mismatch.

[0036] The present invention proposes Figure 5 The TIADC mismatch calibration method based on the frequency domain cross-correlation coefficient shown in the figure specifically includes the following steps: Step 1: For the sampling signals of each sub-channel ADC of the TIADC system, solve the mutual correlation coefficient in the frequency domain, estimate the mismatch error at the sampling time iteratively, and obtain the mismatch error parameter: s1.1、Sampling signal of ADC output of each sub-channel Perform Fourier transform to obtain the corresponding spectrum information : (4) in is the phase factor.

[0037] s1.2. Calculate the product of the absolute values ​​of the spectra of two adjacent sub-channels as the correlation coefficient between adjacent sub-channels : (5) in, .

[0038] s1.3, Initialize the mismatch parameter μ of each subchannel i , the sampling signal of each sub-channel ADC output Perform a first-order difference calibration.

[0039] s1.4. Recalculate the cross-correlation coefficients between adjacent sub-channels for the signal calibrated in s1.3.

[0040] 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: Take the 0th subchannel as the reference channel, that is, assume , at this time the correlation coefficient between the 0th subchannel and the 1st subchannel is The real part of is only offset from the sampling time of the first sub-channel Related, and when hour, Reached maximum value.

[0041] By comparing before and after calibration The size of the mismatch parameter is adjusted by Figure 5 As shown, when As the mismatch parameter increases, When When the mismatch parameter is reduced, 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. .

[0042] s1.6. When the mutual correlation coefficients between the sub-channels are iterated to a stable state, the mismatch parameters of each channel at this time are output as the final mismatch error parameters.

[0043] Step 2: Get the first-order derivative of the sampling point through the derivative filter, and use the mismatch error parameter obtained by iteration to perform first-order differential calibration on the sampling signal 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: When the ideal sampling interval is At that time, Channel ideal sampling point and the actual sampling point The sampling time mismatch error between can be expressed by Taylor expansion as: (6) 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: (7) In order 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: Table 1 Parameter Type Numeric Sampling rate (#timg#) / Ghz 3 Input frequency / Ghz 0.379#timg# Number of quantization bits / bit 12 Number of channels (#timg#) / 4 Sampling time offset [0, 0.01, -0.02, 0.02]#timg# Input signal type Single tone signal, multi-tone signal, random signal Initial iteration step size (#timg#) 0.001#timg# 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.

[0044] 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 respectively improved from 34.8dB and 37.7dB before calibration to 67.7dB and 87.9dB after calibration, with good improvement effect. The corresponding sampling time error parameter iterative convergence curves of each channel are shown in Figure 8 As shown in the figure, after a certain number of iterations, the errors of the three channels finally converge near the preset values, indicating that this method can accurately extract the sampling mismatch error. The error parameters can converge after about 30 iterations, and each iteration requires 16 sampling points, that is, only 500 sampling points are needed to complete the calculation of the mismatch parameters.

[0045] 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 input multi-tone signal are as follows: Fig. 9 and Fig.10 The input is a random signal and the simulation results are shown in Fig.11 and Fig.12 By comparing the output spectrum of the TIADC system before and after calibration, it can be found that the spurious spectrum lines caused by the sampling time mismatch are well suppressed at the level of -80dB, which shows that this method can fully adapt to the input of various signals and can effectively complete the sampling time mismatch calibration of the TIADC system.

[0046] 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 of the TIADC system before and after calibration were calculated and compared. The results are shown in Figure 2. Fig.13 , Fig.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, indicating that this method can adapt to input signals of different frequencies and has good applicability.

[0047] TIADC mismatch calibration circuit based on frequency domain cross-correlation coefficient, such as Fig.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.

[0048] 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 implement it, which can reduce the time complexity of N-point DFT from the original Reduce to In this embodiment, each sub-channel performs a 16-point radix-2 butterfly operation in each iteration, which is divided into 4 levels of operations, and the next level of operations is performed after the previous level of operations is completed. Therefore, in hardware design, by time-division multiplexing the adder, multiplier and butterfly operation module, the overall circuit resource effect is reduced, and the efficiency and performance of the design are improved, which is also more conducive to subsequent maintenance and modification.

Claims

1. A TIADC mismatch calibration method based on frequency domain cross-correlation coefficient, characterized in that: The specific steps are as follows: Step 1: For the sampling signals of each sub-channel ADC of the TIADC system, solve the mutual correlation coefficient in the frequency domain, perform gradient descent iteration with an adaptive step size on the mismatch error at the sampling moment, and obtain the mismatch error parameter; Step 2: Using the mismatch error parameters obtained by iteration, perform first-order differential calibration on the sampling signals output by each sub-channel ADC 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 as claimed in claim 1, characterized in that: The method for calculating the cross-correlation coefficient is: 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 spectrum 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 as claimed in claim 1, characterized in that: 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 sampled signals output by the ADC of each sub-channel; recalculate the cross-correlation coefficients between adjacent sub-channels for 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, and 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, and output the mismatch parameter at this time; The calibrated i-th channel is used as a reference channel to calibrate the i+1-th sub-channel until the mismatch error parameters of all sub-channels are obtained.

4. The TIADC mismatch calibration method based on frequency domain cross-correlation coefficient as claimed in claim 3, characterized in that: If the correlation coefficient A between adjacent sub-channels after calibration i Increases, then the mismatch parameter μ increases i If the value of A i If it decreases, μ i The value of .

5. A TIADC mismatch calibration circuit based on frequency domain cross-correlation coefficient, characterized in that: Used to implement the mismatch calibration method as described in 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 an external analog signal, sample it into a digital signal, and then output it 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 mutual correlation coefficient of the adjacent sub-channel ADC data in the data storage module, estimates the error parameter at the sampling time, 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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