TI-ADC mismatch error calibration method based on fully connected neural network

Abstract

The application discloses a TI-ADC mismatch error calibration method based on a full connection neural network. First, a TI-ADC mismatch error model is established, error signal data is generated, and a neural network training data set is constructed by using the data; then, a full connection neural network is built, and the training data set is used for training the full connection neural network to obtain a trained neural network; subsequently, the trained neural network is tested by using the error model to generate a TI-ADC signal with mismatch error, the output of the trained neural network is subjected to fast Fourier transform to obtain a frequency spectrum and a performance index; according to the test result, the network training parameters are adjusted, including the training iteration number, the data batch processing size, the loss function type, the training optimizer, the learning rate and the like, and the neural network is trained again; the training is repeatedly performed until the test result reaches an expected target; the algorithm is novel, the process is simple, and the overall performance of the TI-ADC can be effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of analog integrated circuit technology and relates to a mismatch error calibration method in TI-ADC (time-interleaved analog-to-digital converter), including the calibration of gain mismatch error, offset mismatch error and time mismatch error. Background Technology

[0002] In the field of integrated circuits, analog-to-digital converters (ADCs) are essential functional components. They convert continuous analog signals from nature into discrete digital signals in digital systems, acting as a bridge between the analog and digital worlds. There are many types of ADCs, including pipelined ADCs, successive approximation ADCs (SAR-ADCs), and time-interleaved ADCs (TI-ADCs). TI-ADCs have multiple sub-ADCs, each sampling the signal independently, forming a channel. During the synthesis stage, the outputs of each channel are sequentially arranged to form the final sampled result. If a TI-ADC contains N channels, and each sub-ADC has a sampling frequency of fs, then the TI-ADC sampling frequency can be increased to Nfs. Therefore, TI-ADCs are widely used in high-speed, high-precision applications.

[0003] However, in practice, due to design limitations, manufacturing defects, and environmental interference, the performance of TI-ADC can be affected, resulting in errors in the converted signal. The most significant errors in TI-ADC are gain mismatch error, offset mismatch error, and timing mismatch error. Gain mismatch error is caused by gain mismatch between sub-channel ADCs, offset mismatch error by offset mismatch between sub-channel ADCs, and timing mismatch error by clock skew in the sampling clocks of each sub-channel ADC. To improve TI-ADC performance and the quality of the converted signal, ADC calibration is necessary.

[0004] Traditional calibration methods generally fall into two categories: analog calibration and digital calibration. Analog calibration modifies or fine-tunes the design in the analog circuitry, while digital calibration uses digital circuitry to compensate for the ADC output signal. Traditional calibration methods often suffer from drawbacks such as complex algorithms and high resource consumption. In recent years, artificial intelligence (AI) technology has developed rapidly, with neural networks being a prime example. Neural network technology has been widely applied and proven effective in image recognition, human-computer interaction, and speech recognition. Therefore, neural networks offer a new approach to error calibration for TI-ADCs. Summary of the Invention

[0005] To address the gain mismatch error, offset mismatch error, and time mismatch error present in TI-ADCs, as well as the shortcomings of traditional calibration methods such as complex algorithms and high resource consumption, this invention proposes a novel method that combines neural networks to calibrate various mismatch errors of TI-ADCs. This method can partially eliminate the impact of TI-ADC mismatch errors on the signal and effectively improve the quality of the converted signal.

[0006] The overall implementation steps of the calibration method in this invention are as follows:

[0007] S1. The TI-ADC mismatch error model is established as follows:

[0008] S e =amp×sin(2πft)+E g ×sin(2π(fs / N×k±f)t)+E o ×sin(2π(fs / N×k)t)+E t ×sin(2π(fs / N×k±f)t)

[0009] Where amp is the signal amplitude, f is the signal frequency, t is the sampling time, and E g E represents the magnitude of the clutter caused by gain mismatch error. o E represents the magnitude of the clutter caused by mismatch error. t This indicates the magnitude of the noise caused by the time mismatch error, where fs is the sampling frequency of the TI-ADC and N is the number of channels;

[0010] S2. Construct the training dataset:

[0011] Based on the established TI-ADC mismatch error model, the parameters amp, f, N, k, and E are set. g E o E t The value of is selected, multiple sampling time points t are selected to obtain multiple signal data points that are continuous in time, which are used as a data sample of the input dataset. Multiple data samples are obtained by randomizing multiple parameters to form a training dataset.

[0012] S3. Construct a fully connected neural network, including an input layer, a hidden layer, and an output layer, with neurons in adjacent network layers interconnected.

[0013] S4. Use the constructed training dataset to train the neural network to obtain a trained neural network;

[0014] S5. Test the performance of the trained neural network. Specifically, use the method in S1 to generate a TI-ADC test signal containing errors. After inputting the test signal into the trained upgraded network, perform FFT processing on the output of the neural network to obtain the signal spectrum. Calculate the evaluation index based on the signal spectrum. Judge the performance of the neural network according to the set standards. If the performance of the neural network reaches the expected target, proceed to S7; otherwise, proceed to S6.

[0015] S6. Optimize the neural network, that is, adjust the training parameters, and return to S4;

[0016] S7. Use the trained neural network to calibrate the mismatch error of the TI-ADC.

[0017] The fully connected neural network in step S3 has the following specific structure: three layers in total, including an input layer, a hidden layer, and an output layer. The input layer consists of 1000 neurons, the hidden layer consists of 36 neurons, and the output layer consists of 1 neuron. This structure can be simplified as [1000, 36, 1].

[0018] The calibration algorithm proposed in this invention is applicable to sinusoidal signals of different frequencies and with different magnitudes of TI-ADC mismatch errors. It can effectively suppress the influence of TI-ADC gain mismatch error, offset mismatch error and time mismatch error on the converted signal, thereby improving the overall quality of the converted signal, improving the performance indicators (ENOB, SFDR, etc.) of the converted signal, and realizing error calibration of TI-ADC. Attached Figure Description

[0019] Figure 1 The following is a flowchart illustrating the main implementation steps of the calibration method of the present invention.

[0020] Figure 2 This is a diagram of the basic neuron structure of a neural network.

[0021] Figure 3 This is a schematic diagram of the fully connected neural network structure of the present invention.

[0022] Figure 4 This is a flowchart of the neural network training and testing process of the present invention.

[0023] Figure 5 This is the FFT spectrum analysis diagram of the signal before calibration.

[0024] Figure 6 This is the FFT spectrum analysis diagram of the calibrated signal of this invention. Detailed Implementation

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0026] This invention employs a neural network to calibrate the gain mismatch error, offset mismatch error, and timing mismatch error of a TI-ADC. The main implementation steps and process are as follows: Figure 1 As shown, the specific implementation steps include six steps: establishing the TI-ADC mismatch error model, constructing the neural network training dataset, building the neural network, training the neural network, testing the neural network performance, and optimizing the neural network.

[0027] Step 1: Establishing the TI-ADC mismatch error model.

[0028] Traditional methods for establishing the three error models for TI-ADC generally involve the following steps: first, generating signal data from multiple sub-channel ADCs; then, fine-tuning the gain, offset, and sampling clock of each channel ADC to ensure inconsistent gain and offset between channels and to offset the sampling clock of one or more channels; finally, arranging and synthesizing the signal data from all sub-channel ADCs to obtain the TI-ADC converted signal containing gain mismatch error, offset mismatch error, and time mismatch error. While this method can obtain a signal containing TI-ADC errors, the process is relatively cumbersome and not conducive to rapidly generating large amounts of signal data. For these considerations, this invention chooses to directly establish the TI-ADC error model from the frequency domain.

[0029] For a sinusoidal signal with frequency f, if the sampling frequency of the TI-ADC is fs and the number of channels is N, according to prior knowledge, the effects of the three types of mismatch errors all manifest as clutter components at specific frequency points of the signal. Specifically, the clutter component caused by gain mismatch error is located at the frequency point fs / N×k±f (k=0,1,…,N-1), the clutter component caused by offset mismatch error is located at the frequency point fs / N×k (k=0,1,…,N-1), and the clutter component caused by time mismatch error is located at the frequency point fs / N×k±f (k=0,1,…,N-1).

[0030] Based on the above theory, the proposed method for establishing the TI-ADC mismatch error model is as follows: First, an ideal, error-free sinusoidal signal S = amp × sin(2πft) is generated, where amp is the signal amplitude, f is the signal frequency, and t is the sampling time. Then, clutter components caused by the gain mismatch error, offset mismatch error, and time mismatch error of the TI-ADC are added to the ideal signal to obtain a signal S containing the three mismatch errors. e =amp×sin(2πft)+E g ×sin(2π(fs / N×k±f)t)+E o ×sin(2π(fs / N×k)t)+E t×sin(2π(fs / N×k±f)t), where E g E represents the magnitude of the clutter caused by gain mismatch error. o E represents the magnitude of the clutter caused by mismatch error. t This indicates the magnitude of the clutter caused by the time mismatch error. S e This is a sinusoidal signal that includes TI-ADC gain mismatch error, offset mismatch error, and time mismatch error.

[0031] Step 2: Constructing the neural network training dataset.

[0032] A training dataset is essential for training a neural network, and its quality directly affects the training effect. The neural network training dataset in this invention comprises two main parts: an input dataset and a training target dataset.

[0033] The input dataset is generated from the TI-ADC error model in step one. Given amp, f, N, k, and E in the formula described in step one... g E o E t This yields a signal containing the three mismatch errors of the TI-ADC. Taking 1000 consecutive sampling time points t, 1000 temporally continuous signal data points are obtained, which serve as a data sample for the input dataset. Within a certain range, amp, f, N, k, and E are randomly selected. g E o E t The values ​​of the parameters will yield a large number of data samples. All data samples are then combined to form the input dataset.

[0034] The training target dataset is derived from ideal signals. Taking the error-free ideal signals corresponding to the signals containing the three types of mismatch errors of the TI-ADC, 1000 consecutive data points are collected. The 500th data point is selected as the training target, which is a data sample in the training target dataset. For each data sample in the input dataset, there is a corresponding data point as its training target. All training target data points are combined to form the training target dataset. The input dataset and the training target dataset together constitute the neural network training dataset.

[0035] Step 3: Building the neural network.

[0036] To reduce algorithm complexity and training time, this invention employs a relatively simple fully connected neural network to calibrate the TI-ADC error. The most basic unit of a neural network is the neuron, and its structure is as follows: Figure 2 As shown. Where x i For neuron input, wi For each x i The corresponding weights are given by b, which is the neuron's bias term, and f is the activation function. The neuron's output y is obtained by the following formula:

[0037]

[0038] The activation function f is a non-linear function that introduces non-linear characteristics into a neural network to enhance its fitting ability. Common activation functions include the Sigmoid function, Tanh function, and ReLU function. A neural network consists of several layers, each containing multiple neurons. By connecting neurons in different layers according to certain relationships, neural networks with different structures can be formed. The fully connected neural network used in this invention connects all neurons between any two adjacent layers, while neurons within the same layer are not connected.

[0039] A schematic diagram of the fully connected neural network structure constructed in this invention is shown below. Figure 3 As shown, the network consists of three layers: an input layer, a hidden layer, and an output layer. The input layer comprises 1000 neurons, the hidden layer comprises 36 neurons, and the output layer comprises 1 neuron. Neurons in adjacent layers are connected one-to-one.

[0040] The fully connected neural network constructed in this invention uses the ReLU function as its activation function, and its formula is as follows:

[0041] f(x) = max(0,x).

[0042] The ReLU function is a maximum value function. When the input is less than 0, the output is 0, and when the input is greater than or equal to 0, the output remains unchanged.

[0043] Step 4: Training the neural network.

[0044] A single training iteration of a neural network consists of three processes: forward propagation, error calculation, and backpropagation. During forward propagation, an input layer neuron receives input data and calculates its output according to the neuron output formula from step three. The outputs of all input layer neurons then become the input data for hidden layer neurons, and the same calculation is performed again. The outputs of all hidden layer neurons then become the input data for output layer neurons, and the same calculation process is repeated. The output of the output layer neurons is the final output of the neural network's forward propagation process.

[0045] In the error calculation process, the output value of the neural network in the forward propagation is compared with the corresponding value of the training target data, and the error value between the two is calculated according to a certain calculation formula.

[0046] During backpropagation, the error value obtained during error calculation is used as the input data for the neural network, and the calculation is performed backward from the output layer. Based on the gradient descent principle, the partial derivatives of the error with respect to the weights *w* and biases *b* of each neuron are calculated sequentially from back to front. The weights *w* and biases *b* are adjusted based on the results to minimize the error between the neural network output and the training objective. The modified *w* and *b* are then used as the weights and biases for the next forward propagation calculation.

[0047] Combining the above process, the training process of a neural network is as follows: Figure 4 As shown.

[0048] The first step is to set the initial parameters.

[0049] Initial parameters include the initial weights w and initial biases b of each neuron. Before training begins, the initial weights and biases of each neuron need to be pre-set for the first forward propagation. In addition, initial parameters also include hyperparameters for the training process, such as batch size, number of training iterations (epochs), loss function, training optimizer, and training learning rate.

[0050] The second step is forward propagation.

[0051] The input data from the training dataset is fed into the neural network for computation. After the aforementioned forward propagation process, the network output is obtained.

[0052] The third step is to calculate the error.

[0053] The output of the neural network is compared with the target data, and the error value is calculated according to the formula. The error calculation is related to the batch size of the data. If the batch size is m, the error will be calculated only after m data points have been processed, and this error value will be used as the input value for backpropagation.

[0054] The fourth step is backpropagation.

[0055] Based on the error between the neural network output and the target data, backward calculation is performed from the end to the beginning. According to the gradient descent principle, the partial derivatives of the error with respect to the weight w and bias term b of each neuron are obtained, which are used as the basis for parameter updates.

[0056] Step 5: Parameter update.

[0057] Based on the results obtained during backpropagation, the weights w and biases b of each neuron are modified and updated. These new w and b are then used for the next forward propagation. The modifications to w and b are all aimed at reducing the error between the forward propagation output and the target data.

[0058] Step 6: Repeat steps 2 through 5. Repeat the forward propagation, error calculation, backpropagation, and parameter update processes. During this process, the error between the neural network's output and the target data continuously decreases, and the network neuron weights w and bias terms b also converge. Training ends when the preset number of training iterations is reached.

[0059] Step 5: Testing the performance of the neural network.

[0060] After the neural network training is complete, its performance needs to be tested. The testing method is as follows: A sinusoidal signal with gain mismatch error, offset mismatch error, and time mismatch error is generated using the TI-ADC error model described in step one or a traditional error model. 16384 consecutive data points are sampled as the original signal data. The original signal data is then input into the trained neural network in groups of 1000 data points for calculation, and the neural network output is used as the calibrated signal data.

[0061] The calibrated signal data is processed using a Fast Fourier Transform (FFT) to obtain a signal spectrum. Based on the spectrum, it is observed whether the clutter components generated by the TI-ADC mismatch error in the original signal have been effectively reduced. According to the FFT results, the effective resolution bits (ENOB) and spurious-free dynamic range (SFDR) of the signal are calculated, and the ENOB and SFDR of the calibrated signal are compared with those of the original signal to determine whether the calibration effect of the neural network has achieved the expected goal.

[0062] Step Six: Optimization of the Neural Network.

[0063] The trained neural network is then subjected to performance testing. If the test results meet the expected targets, it indicates that the neural network performance is up to standard and can be used for calibration of TI-ADC gain mismatch error, offset mismatch error, and timing mismatch error. If the test results do not meet the expected targets, it indicates that the neural network performance is insufficient and retraining is required to optimize the calibration performance of the neural network.

[0064] In the retraining phase, the parameters set before training are adjusted, including the number of training iterations (Epoch), batch size, loss function type, optimizer, and learning rate, and then the neural network is trained and tested again.

[0065] During training, the parameters can be adjusted by observing the trend of the error value (loss) after each forward propagation. The specific method is as follows:

[0066] If the loss gradually decreases from the start of neural network training and still shows a significant downward trend at the end of training, it indicates that the training is insufficient and the neural network weights and biases have not yet converged to their optimal values. In this case, increasing the number of training iterations can be considered.

[0067] If the loss shows a decreasing trend from the start of neural network training, but the decrease is slow, it indicates that the parameter update step size during training is too small, and the update magnitude is too small. In this case, increasing the learning rate can be considered.

[0068] If the loss does not show a smooth decreasing trend after the neural network starts training, but instead oscillates up and down or does not converge at all, it indicates that the parameter update step size is too large during training, and the update amplitude is too large. In this case, reducing the learning rate can be considered.

[0069] If the loss stops decreasing after reaching a certain value during neural network training, but the network test results are unsatisfactory, it indicates that the network training may be trapped in a local optimum. In this case, consider changing the type of optimizer or adjusting the initial weights and bias parameters before training begins, and then retrain.

[0070] Step 7: Use the obtained neural network to calibrate the mismatch error of the TI-ADC.

[0071] This embodiment uses Python code to build a 4-channel TI-ADC model, including gain mismatch error, offset mismatch error, and time mismatch error models. The TI-ADC sampling frequency is set to 100MHz, and a large amount of data containing the three mismatch errors is generated to construct a neural network training dataset. The neural network is then trained, tested, and optimized. Performance testing is performed on the optimized neural network. A 10.17MHz sine wave signal is generated using the error model, and -60dBc gain mismatch error, offset mismatch error, and time mismatch error are added. The neural network is then used to calibrate the signal containing these errors, obtaining the calibrated result. Figure 5 The image shown is the FFT spectrum of the signal before calibration. Figure 6 The image shows the FFT spectrum of the signal after neural network calibration. A comparison of the two images shows that neural network calibration effectively suppressed clutter components caused by TI-ADC mismatch errors. The ENOB of the calibrated signal increased from 8.48 bits to 13.43 bits compared to before calibration, and the SFDR increased from 59.81 dBc to 96.87 dBc, demonstrating a significant calibration effect.

[0072] In summary, the TI-ADC mismatch error calibration method based on a fully connected neural network of this invention is simple in principle, novel in approach, and easy to operate. Simulation verification shows that the calibration effect is significant, effectively eliminating the errors caused by gain mismatch, offset mismatch, and time mismatch in TI-ADC, thereby improving the overall performance of TI-ADC and enhancing the quality of the converted signal.

Claims

1. A TI-ADC mismatch error calibration method based on a fully connected neural network, characterized in that, Includes the following steps: S1. The TI-ADC mismatch error model is established as follows: S e =amp×sin(2πft)+E g ×sin(2π(fs / N×k±f)t)+E o ×sin(2π(fs / N×k)t)+E t ×sin(2π(fs / N×k±f)t) Where amp is the signal amplitude, f is the signal frequency, t is the sampling time, and E g E represents the magnitude of the clutter caused by gain mismatch error. o E represents the magnitude of the clutter caused by mismatch error. t This indicates the magnitude of the noise caused by the time mismatch error, where fs is the sampling frequency of the TI-ADC and N is the number of channels; S2. Construct the training dataset: Based on the established TI-ADC mismatch error model, the parameters amp, f, N, k, and E are set. g E o E t The value of is selected, multiple sampling time points t are selected to obtain multiple signal data points that are continuous in time, which are used as a data sample of the input dataset. Multiple data samples are obtained by randomizing multiple parameters to form a training dataset. S3. Construct a fully connected neural network, including an input layer, a hidden layer, and an output layer, with neurons in adjacent network layers interconnected. S4. Use the constructed training dataset to train the neural network to obtain a trained neural network; S5. Test the performance of the trained neural network. Specifically, use the method in S1 to generate a TI-ADC test signal containing errors. After inputting the test signal into the trained neural network, perform FFT processing on the output of the neural network to obtain the signal spectrum. Calculate the evaluation index based on the signal spectrum. Judge the performance of the neural network according to the set standard. If the performance of the neural network reaches the expected target, proceed to S7; otherwise, proceed to S6. S6. Optimize the neural network, that is, adjust the training parameters, and return to S4; S7. Use the trained neural network to calibrate the mismatch error of the TI-ADC.

2. The TI-ADC mismatch error calibration method based on a fully connected neural network according to claim 1, characterized in that, In the fully connected neural network, the input layer contains 1000 neurons, the hidden layer contains 36 neurons, and the output layer contains 1 neuron; the structure is simplified as [1000, 36, 1].

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