# Error Correction Method of TIADC System Based on Parameter Estimation of Identification Model
## 1 Introduction  
Data acquisition systems have been widely used in instrument measurement, communication, aerospace and medical fields [1; 2; 3; 4; 5; 6; 7; 8]. As the core component of a data acquisition system, an analog-to-digital converter (ADC) is the only way to achieve analog/digital conversion, the performance of the ADC has a direct impact on the performance of the data acquisition system [9]. With the development of electronic information technology and the increase in the complexity of the testing environment, the frequency and bandwidth of the simulated signal to be tested are getting higher and higher, and at the same time, ourrequirements for the observation of signal details are also increasing. Forasmuch as these practical factors, we put forward higher requirements for the performance of ADC. The ADC's performance is primarily determined by two factors: sampling speed and sampling accuracy [10]; the higher the sampling speed of ADC, the higher the frequency of the analog signal that can be collected and the more accurate the real-time change of the analog signal that can be observed; and the higher the sampling accuracy of the ADC, the more accurate the digital quantization of the analog signal. To meet the requirements of real-time sampling and processing of analog signals, the sampling rate of ADC should be improved as much as possible under the condition of a certain sampling accuracy. Most data acquisition systems designed in practical engineering applications use the multi-channels of a single ADC to complete synchronous acquisition. However, the single-channel performance of ADC has reached a bottleneck, which greatly limits the improvement in the performance of the data acquisition system. For ADC to consider both the high sampling rate and high resolution, high circuit design and manufacturing processes are needed, which greatly increases the cost of data acquisition systems. Therefore, based on the consideration of cost, if we want to maximize the acquisition ability of the data acquisition system, the sampling theory of Time-Interleaved ADC (TIADC) proposed by [PERSON] and [PERSON], in 1980, can be used [11]. The basic principle of TIADC is to use several ADCs with low sampling rates to sample a simulated signal under the same clock frequency and different clock phases to improve the sampling rate of the data acquisition system. In the ideal state, the sampling rate of the n-channel TIADC system is n times that of a single sub-ADC. As shown in Figure 1, the working principle diagram of the TIADC system in the ideal state is shown. Using TIADC sampling technology can greatly improve data acquisition system performance, but it also introduces a new issue--channel mismatch. Bias mismatch, gain mismatch, time mismatch, and bandwidth mismatch are the most common types of channel mismatch [12; 1, 13; 1]. Channel mismatch will seriously reduce the spurious-free dynamic range (SFDR), signal-to-noise ratio (SNR) and distortion rate (SNDR) of the TIADC system. These mismatch errors are derived from the manufacturing process deviation and the physical factors of specific circuits, which are usually difficult to predict and avoid. Therefore, in practical engineering applications, the data acquisition system using TIADC is affected by mismatches, resulting in the deterioration of the dynamic performance of the acquisition system [15]. To solve the problem of a TIADC system caused by channel mismatch, many scholars worldwide have conducted much research on the channel mismatch error of TIADC. In reference [16; 17; 18], the researchers used a calibration structure with a reference ADC. A premise for using this method is that the accuracy of the reference ADC must be higher than the requirements of TIADC, and its sampling rate must be lower than or even far below TIADC. Although this method can correct the bias and gain mismatch based on statistics, it is powerless for the unstatisticsable sampling time deviation and bandwidth mismatch caused by high-frequency sampling.