CN116760412A - Time interleaving ADC calibrator based on ANN - Google Patents

Time interleaving ADC calibrator based on ANN Download PDF

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CN116760412A
CN116760412A CN202310826613.XA CN202310826613A CN116760412A CN 116760412 A CN116760412 A CN 116760412A CN 202310826613 A CN202310826613 A CN 202310826613A CN 116760412 A CN116760412 A CN 116760412A
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卢知非
唐鹤
彭析竹
张博文
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University of Electronic Science and Technology of China
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Abstract

The invention belongs to the technical field of integrated circuits, and particularly relates to an ANN-based time interleaving ADC calibrator. The calibrator provided by the invention comprises two functional networks, a nonlinear calibration network and a time sequence mismatch calibration network, wherein the nonlinear calibration network is used for inhibiting nonlinearity of each channel ADC in the TI ADC, so that nonlinear mismatch among channels is calibrated, and the time sequence mismatch calibration network is responsible for calibrating the time sequence mismatch among the channels. The TI ADC calibrator based on the ANN can calibrate the single-channel nonlinearity, the nonlinear mismatch between channels, the offset mismatch, the gain mismatch and the offset mismatch of the TI ADC at the same time, and improves the overall performance of the TI ADC. Due to the adoption of the ANN technology, the calibrator completes the calibration function after training based on a large amount of data, and has good robustness and universality.

Description

Time interleaving ADC calibrator based on ANN
Technical Field
The invention belongs to the technical field of integrated circuits, and particularly relates to an ANN-based time interleaving ADC calibrator.
Background
The principle of a Time-Interleaved ADC (TI ADC) is shown in fig. 1, and N sub-ADCs are combined into one ADC system to be Interleaved and output, so as to increase the sampling rate of the ADC system by N times. However, time interleaved ADCs are susceptible to non-linearities and inter-channel mismatch, which introduces spikes and harmonics in the output spectrum, thereby degrading the overall performance of the ADC. Therefore, calibration for various errors in time-interleaved ADCs is essential.
Although the calibration technology of the time interleaved ADC is widely studied, the existing method based on the digital model still has the problems of limitation on input signals, additional circuit design or high-precision reference. Furthermore, calibration of different errors may interact and the complex interaction between the ADC and the various calibration modules complicates the design and control of the calibration process. In view of these limitations, a time-interleaved ADC calibrator based on an artificial neural network (Artificial Neural Network, ANN for short) is presented herein that can calibrate inter-channel nonlinearity and timing mismatch with high accuracy and is superior to previous work in terms of capability to reject spurs and harmonics. Furthermore, an ANN-based calibrator has also proven to be good at calibrating both random and broadband signals.
ANN is a computational model inspired by the human nervous system for solving complex machine learning and artificial intelligence tasks. ANNs consist of a large number of artificial neurons (also called nodes or units) that mimic interactions between neurons in the nervous system by connecting them. ANNs are widely used in many fields including image and speech recognition, natural language processing, predictive analysis, pattern recognition, and the like. The method has good nonlinear modeling capability and adaptability, and can learn and extract characteristics from a large amount of data. With advances in artificial intelligence technology, ANNs have become possible for error calibration of ADCs to improve performance and simplify the design complexity of analog front ends. Furthermore, ANNs are known to benefit from data enhancement of noise and other random errors during the training phase, which helps to enhance robustness in the context of ADC calibration.
Disclosure of Invention
The invention provides an analog-to-digital converter (ADC) calibration mechanism based on an analog-to-digital converter (ANN), and provides an analog-to-digital converter (TI ADC) calibrator based on the ANN.
The proposed ADC calibration mechanism is shown in FIG. 2, and the idea is to realize nonlinear vector mapping through ANN, thereby reconstructing the input signal of the ADC and inhibiting the harmonic wave and spurious generated in the ADC. Consider the analog input (also the desired ideal output) of an ADC as a vector in the time domain(sequence [ x ] 1 ,x 2 ,...,x L ]Wherein x is k Representing one input sample, L representing the vector length), the actual output is considered as vector +.>(sequence [ y ] 1 ,y 2 ,...,y L ]Wherein y is k Representing one output sample), VRM calibration is derived from the output of ADC +.>Recovery vector->
Note that the mapping of an ANN implementation needs to be bijective (bijective) to ensure that the inputs and outputs of the calibrator are in one-to-one correspondence. In order to ensure that ANN realizes the vector recovery mapping of bijection, the invention provides two methods: dimension expansion method and length expansion method, the idea of dimension expansion method is to expand by adding additional parametersIs expressed as:
wherein alpha is k And beta k Is an error-related parameter such as a signal derivative value used to calibrate a frequency-related error (e.g., a timing mismatch error in a TI ADC), a code used to calibrate each stage of a code-related error (e.g., an inter-stage gain error in a pipelined ADC), etc. By expanding input vectorsMore information is introduced, making the ANN more likely to implement bijections. In addition, the more dimensions provide more degrees of freedom for the ANN to better represent complex ADC input-output relationships, thereby achieving bijections.
The length increasing method refers to increasing the input vector of ANNLength L of (c). With increasing L, vector ∈>More signal information is carried, which tends to bijective the mapping through ANN. In addition, longer input vectors allow finer partitioning of the input space of the map, which helps reduce collisions (collisions) and ambiguities (ambigues) in the map, improving the accuracy and robustness of the ANN. Thus, an ANN with a larger L is more likely to complete the bias mapping and recover the expected signal.
Based on the theory above, the invention provides an ANN-based TI ADC calibrator, and a block diagram of the calibrator is shown in figure 3. The calibrator comprises two functional networks, a nonlinear calibration network (Nonlinearity Calibration Network, NCN) and a timing mismatch calibration network (Timing Mismatch Calibration Network, TMCN for short). The NCN is designed to suppress the nonlinearity of each channel ADC in the TI ADC, thereby calibrating the nonlinear mismatch between channels. On the other hand, TMCN is responsible for calibration of timing mismatch between channels. Each channel output of the TI ADC is fed into the NCN for nonlinear calibration, after which the mismatch and gain mismatch are eliminated by simple addition and multiplication. The calibrated outputs of each channel are then interleaved and fed, along with the corresponding derivative values, to the TMCN for timing mismatch calibration, the output of the TMCN being the expected calibration result and also the final output of the whole calibrator.
The specific structures of NCN and TMCN are as follows:
the structure of the NCN is shown in fig. 4, and is a convolutional neural network (convolutional neural network, CNN for short) which includes two layers, namely a calibration layer and an output layer. The calibration layer contains a calibration module and a matching module, and is used for convolution and residual addition processing to obtain features (features) for calibration. The output layer maps features to calibrated output vectors. The error calibration function of NCN is mainly implemented in the calibration layer, where the calibration module performs element convolution with ReLU (x) =max (0, x)) as an activation function to complete a short-cut of one residual. Network parameters to achieve the best performance NCN were determined by simulation: the number of characteristic channels is set to 32, a 1 x 1 convolution kernel is used in the output layer and matching module, and a 1 x 3 convolution kernel is used in the calibration module.
TMCN is specifically designed for timing mismatch calibration in TI ADC, a dimension expansion method is applied to the network to achieve bijective vector reply mapping:
wherein y is k Is one output sample of TI ADC, and y k ' represents y k And the corresponding first derivative value, N is the channel number. As shown in fig. 5, the TMCN adopts a fully connected neural network structure (fully connected neural network, abbreviated as FCNN) because of its superior performance and simple structure compared with other networks. The designed network comprises three layers, namely an input layer, a hidden layer and an output layer, all of which are fully connected and employ a ReLU as an activation function. The output result of each activated FCNN layer is expressed as:
wherein x is j Is the j-th input of the layer, and y i Is the output of the ith neuron, w ij And b i The weight and bias values, respectively. The input layer of the TMCN comprises 2N nodes, the hidden layer comprises 2048 nodes, and the output layer comprises N nodes. The input of the network is the TI ADC output sequence of length N and the corresponding derivative value, while the output is the calibrated output vector of length N with the timing mismatch removed, which is also the final output of the whole calibrator.
The technical scheme of the invention is as follows:
an ANN-based time interleaving ADC calibrator comprises a nonlinear calibration module, a mismatch module, an interleaving module, a band-pass differential filter and a time sequence mismatch calibration module;
the nonlinear calibration module is composed of N nonlinear calibration network units, corresponding to N output channels of the time interleaving ADC, and defining output code words [ B0, B1, B2, …, B (B-1) of the kth output channel of the time interleaving ADC]Conversion of k to quantized value y k Then y k K epsilon N, which is the input to the kth nonlinear calibration network element; each nonlinear calibration network unit consists of a first matching module, a second matching module, a first calibration module, a second calibration module, a third calibration module, a fourth calibration module and an output layer, wherein input data enter the nonlinear calibration network unit and are respectively input into the first matching module and the first calibration module, output data of the first calibration module are input into the second calibration module, output data of the second calibration module and output data of the first matching module are respectively input into the second matching module and the third calibration module after being combined, output data of the third calibration module is input into the fourth calibration module, output data of the fourth calibration module and output data of the second matching module are input into the output layer after being combined, and the output layer outputs data after nonlinear calibration of a corresponding channel; the first matching module and the second matching module are convolution layers, and the first calibration module, the second calibration module, the third calibration module and the fourth calibration module are ReLUPerforming element convolution for activating functions to complete a residual shortcut, using a 1×1 convolution kernel in the first matching module, the second matching module and the output layer, and using a 1×3 convolution kernel in the first calibration module, the second calibration module, the third calibration module and the fourth calibration module;
the mismatch module is used for respectively compensating offset mismatch and gain mismatch of the nonlinear calibrated data output by each nonlinear calibration network unit, and compensating the kth output nonlinear calibrated dataThe vector is obtained after mismatch compensation>
Wherein Δo k Is offset mismatch compensation, Δg k Is gain mismatch compensation;
the interleaving module is used for obtaining all vectorsInterleaving is carried out to obtain an interleaved vector +.>
Wherein m represents the round of single channel conversion;
the band-pass differential filter is used for matchingProcessing to obtain corresponding first derivative sequence +.>
The time sequence mismatch calibration module is based onAnd->Performing a timing mismatch Δt k The time sequence mismatch calibration module is a fully connected neural network, and comprises an input layer, a hidden layer and an output layer, and adopts a ReLU as an activation function, wherein the input layer comprises 2N nodes corresponding to +.>And->The output layer includes N nodes. The calculations of the activated FCNN layers are expressed as:
wherein x is j Is the j-th input of the layer, y i Is the output of the ith neuron of the layer, w ij Is the weight of the neuron, b i The bias of the ith neuron of this layer. By combiningAnd->Each element in the sequence is directly input to an input layer of the FCNN, and the FCNN can complete the time sequence mismatch delta t through forward propagation among neurons k Corresponding to the vector after completing the time sequence mismatch compensation And is also the output of the calibrator.
The whole calibrator work flow is shown in fig. 6, and the specific steps are as follows:
s1, a time interleaving ADC with the bit number of B is used for quantizing an input signal into a digital signal;
s2, outputting code word [ b ] of the kth channel 0 ,b 1 ,b 2 ,…,b (B-1) ] k Conversion to the corresponding quantized value y k ；
S3、NCN k Calibrating the output of the kth channel, NCN k Is the k-channel ADC output vector of the L-th lengthIn-channel non-linearly aligned sequences with output L length +.>
S4, to NCN k Output vector of (a)Performing a conventional mismatch Δo k Mismatch with gain Δg k Is compensated for: by subtracting the mismatch Δo k Then divided by (1+Δg) k ) Completing compensation to obtain vector->The concrete expression is as follows:
s5, willInterleaving is carried out to obtain an interleaved vector +.>Expressed as
Wherein N is the number of channels of the TI ADC, k is denoted as a kth channel, and m is denoted as the round of single-channel conversion;
s6, willInput to bandpass differential filter to get +.>Corresponding derivative sequence->Impulse response h of bandpass differential filter bd [n]Expressed as:
wherein is y [ n ]]The corresponding hilbert transform value is used,to round down the function, k NB Representing the input signal at the kth of TI ADC NB Nyquist zone. And h is d [n]And h H [n]Impulse responses of the first-order differentiator and the hilbert transformer, respectively, wherein the first-order differentiator h of the L tap d [n]Expressed as:
while L-tapped hilbert transformer h H [n]Expressed as:
s7, willAnd->Input to TMCN for timing mismatch delta t k The input of TMCN is TI ADC output with N length and the corresponding derivative value sequence, and the output is vector with N length after finishing time sequence mismatch compensation>Also the output of the entire ANN-based TI ADC calibrator.
S8, completing calibration by the TI ADC calibrator based on the ANN.
The beneficial effects of the invention are as follows:
the ADC calibration mechanism based on the ANN is a general scientific theory and provides systematic theoretical support for ADC calibration based on the ANN. The TI ADC calibrator based on the ANN can calibrate the single-channel nonlinearity, the nonlinear mismatch between channels, the offset mismatch, the gain mismatch and the offset mismatch of the TI ADC at the same time, and improves the overall performance of the TI ADC. Due to the adoption of the ANN technology, the calibrator completes the calibration function after training based on a large amount of data, and has good robustness and universality.
Drawings
Fig. 1 is a functional block diagram of a time interleaved ADC.
Fig. 2 is a block diagram of an ANN-based ADC calibration mechanism according to the present invention.
Fig. 3 is a block diagram of an ANN-based TI ADC calibrator according to the present invention.
Fig. 4 is a schematic diagram of the structure of the NCN in the ANN-based TI ADC calibrator according to the present invention.
Fig. 5 is a schematic structural diagram of TMCN in an ANN-based TI ADC calibrator according to the present invention.
Fig. 6 is a calibration flow chart of the ANN-based TI ADC calibrator according to the present invention.
Fig. 7 is an effect diagram of simulation verification using the calibrator of the present invention.
FIG. 8 is a graph of test verification results for integrated calibration on a chip using the calibrator of the present invention.
FIG. 9 is a graph showing the effect of test verification on off-chip calibration using the calibrator of the present invention.
Detailed Description
The technical scheme of the invention has been described in detail in the summary section, and the practical applicability of the invention is illustrated by taking a 12-bit four-channel ADC as an example in combination with the accompanying drawings and simulation and test examples.
Examples
The example is a calibration performance simulation for a 12-bit four-channel 4GSps ADC with n=4, input signal frequency 230.68MHz and amplitude-1 dBFS. The specific workflow of the calibrator is as follows:
s1, a time interleaving ADC quantizes an input signal into a digital signal;
s2, output code word [ b ] of kth (k=0, 1,2,3, 4) channel 0 ,b 1 ,b 2 ,…,b 11 ] k Conversion to the corresponding normalized quantized value y k :
y k ＝2 11 b 0 +2 10 b 1 +2 9 b 2 +...+2 1 b 10 +2 0 b 11 (7)
S3, ncn for k=1, 2,3,4 k Calibrating the output of the kth channel, NCN k Is a k-channel ADC output vector of length l=9In-channel nonlinear-aligned sequences with output l=9 +.>
S4 for k=1, 2,3,4 for NCN k Output vector of (a)Performing a conventional mismatch Δo k Mismatch with gain Δg k Is compensated for: by subtracting the mismatch Δo k Then divided by (1+Δg) k ) Completing compensation to obtain vector->The concrete expression is as follows:
s5, for k=1, 2,3,4, willInterleaving is carried out to obtain an interleaved vector +.>Expressed as
Wherein N is the number of channels of the TI ADC, k is denoted as a kth channel, and m is denoted as the round of single-channel conversion;
s6, willThe first-order bandpass differential filter input to 33 taps gets +.>Corresponding derivative sequence->Since the input is in the first Nyquist zone, k in the first order bandpass differential filter NB =1, the impulse response at this time is,
s7, willAnd->Input to TMCN for timing mismatch delta t k The input of TMCN is TI ADC output with length of 4 and the corresponding derivative value sequence, and the output is vector with length of 4 after completing time sequence mismatch compensationAlso the output of the entire ANN-based TI ADC calibrator.
S8, completing calibration by the TI ADC calibrator based on the ANN.
The invention designs an ANN-based TI ADC calibrator which is used for simulation verification in a 12-bit 4GSps four-channel TI ADC model, wherein the model has single-channel interstage gain errors, DAC errors, noise, higher harmonics and offset/gain/timing mismatch among channels. Fig. 7 shows the ADC output spectra before and after the ANN-based TI ADC calibrator designed by the present invention, and it can be seen that the present invention greatly suppresses harmonics and spurious emissions, and the SNDR and SFDR of the ADC after calibration are respectively increased from 32.20dB and 32.76dB to 65.35dB and 87.05dB.
In addition, the TI ADC calibrator based on ANN designed by the present invention was verified on two actual ADC chips: one is a 12-bit 600MSps four-channel ADC prototype chip with an ANN-based TI ADC calibrator integrated on-chip. The other is a 12-bit 5.4GSps four-channel commercial ADC chip, and the TI ADC calibrator based on the ANN is realized through the outside of the chip.
Fig. 8 shows the test results before and after calibration of the 12-bit 600MSps four-channel ADC prototype chip of the ANN-based TI ADC calibrator designed by the present invention on-chip, and it can be seen that the ANN-based TI ADC calibration of the present invention effectively suppresses harmonics and spurs, and improves the SNDR and SFDR of the ADC from 32.79dB and 35.30dB to 62.45dB and 74.21dB, respectively.
Fig. 9 shows test results before and after calibration of a 12-bit 5.4GSps four-channel commercial ADC chip in a single tone test, which is designed by applying the ANN-based TI ADC calibrator according to the present invention, and it can be seen that the present invention effectively suppresses harmonics and spurs of the ADC itself. After an ANN based TI ADC calibration, the SNDR and SFDR of the ADC increased from 42.38dB and 43.17dB to 53.98dB and 78.25dB, respectively.

Claims (1)

1. The time interleaving ADC calibrator based on the ANN is characterized by comprising a nonlinear calibration module, a mismatch module, an interleaving module, a band-pass differential filter and a time sequence mismatch calibration module;
the nonlinear calibration module is composed of N nonlinear calibration network units, corresponding to N output channels of the time interleaving ADC, and defining output code words [ B0, B1, B2, …, B (B-1) of the kth output channel of the time interleaving ADC]Conversion of k to quantized value y k Then y k K epsilon N, which is the input to the kth nonlinear calibration network element; each nonlinear calibration network unit consists of a first matching module, a second matching module, a first calibration module, a second calibration module, a third calibration module, a fourth calibration module and an output layer, wherein input data enter the nonlinear calibration network unit and are respectively input into the first matching module and the first calibration module, output data of the first calibration module are input into the second calibration module, output data of the second calibration module and output data of the first matching module are respectively input into the second matching module and the third calibration module after being combined, output data of the third calibration module is input into the fourth calibration module, output data of the fourth calibration module and output data of the second matching module are input into the output layer after being combined, and the output layer outputs data after nonlinear calibration of a corresponding channel; the first matching module and the second matching module are convolution layers, the first calibration module, the second calibration module, the third calibration module and the fourth calibration module perform element convolution by taking a ReLU as an activation function to complete a shortcut of residual error, a convolution kernel of 1 multiplied by 1 is used in the first matching module, the second matching module and the output layer, and a convolution kernel of 1 multiplied by 1 is used in the first calibration module, the second calibration module, the third calibration module and the fourth calibration moduleA convolution kernel of 1 x 3 is used;
the mismatch module is used for respectively compensating offset mismatch and gain mismatch of the nonlinear calibrated data output by each nonlinear calibration network unit, and compensating the kth output nonlinear calibrated dataThe vector is obtained after mismatch compensation>
Wherein Δo k Is offset mismatch compensation, Δg k Is gain mismatch compensation;
the interleaving module is used for obtaining all vectorsInterleaving is carried out to obtain an interleaved vector +.>
Wherein m represents the round of single channel conversion;
the band-pass differential filter is used for matchingProcessing to obtain corresponding first derivative sequence +.>
The time sequence mismatch calibration module is based onAnd->Performing a timing mismatch Δt k The time sequence mismatch calibration module is a fully connected neural network, and comprises an input layer, a hidden layer and an output layer, and adopts a ReLU as an activation function, wherein the input layer comprises 2N nodes corresponding to +.>And->The output layer comprises N nodes, and the calculation of each layer of the fully-connected neural network after activation is expressed as follows:
wherein x is j Is the j-th input of the layer, y i Is the output of the ith neuron of the layer, w ij Is the weight of the neuron, b i The bias of the ith neuron of the layer is achieved byAnd->Each element in the sequence is directly input to an input layer of a fully-connected neural network, and the fully-connected neural network can finish the sequence mismatch delta t through forward propagation among neurons k Corresponding to vector +.> And is also the output of the calibrator.
CN202310826613.XA 2023-07-06 2023-07-06 Time interleaving ADC calibrator based on ANN Pending CN116760412A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117408315A (en) * 2023-10-25 2024-01-16 合肥工业大学 Forward reasoning module for background calibration of pipeline analog-to-digital converter

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117408315A (en) * 2023-10-25 2024-01-16 合肥工业大学 Forward reasoning module for background calibration of pipeline analog-to-digital converter

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