# Error Correction Method of TIADC System Based on Parameter Estimation of Identification Model
## 1 Introduction
This method has high complexity and high hardware  
Figure 1: Working principle diagram of the TIADC system in an ideal state. costs, which are not suitable for practical applications. References [19; 20; 21] studied the correction structure of reference channel randomization. Since the requirement for noise is lower than that for harmonic or spurious, the reference channel randomization structure is an expedient scheme based on this principle. The randomization structure of the reference channel breaks the regularity of each channel and converts the harmonic or stray energy caused by all non-ideal factors into noise, including bias, gain, bandwidth mismatch and sampling time deviation. However, the reference channel randomization structure only converts harmonics or spurious into noise and does not eliminate these energies. Therefore, failure to really improve performance is the most fundamental flaw in this scheme. In the literature [22; 23], the investigators studied the structure of a single preceding Sample-and-Hold Amplifier (pre-SHA), which directly used a single pre-SHA to sample and hold the input signal, and then assigned the retained signal to each sub-ADC in sequence, which no longer needed their own SHA. The single pre-SHA structure not only completely solves the sampling time deviation, but also solves the imbalance, gain and bandwidth mismatch caused by numerous channels; and most importantly, a single pre-SHA determines the entire bandwidth, and this structure almost completely solves the bandwidth mismatch. Although a single pre-SHA structure seems to reduce hardware complexity, it violates the most essential idea of time alternation--parallel processing. For the two-channel TIADC system, the single pre-SHA structure can nearly achieve the requirement of speed doubling, but with the increase in the number of channels, the difficulty of realizing this method will increase to an unimaginable degree. Therefore, in the current research, this structure can only be implemented in a two-channel TIADC system that does not have universal applicability. In References [24; 25; 26], the split ADC correction structure was used by the researchers; this method is used to correct bias and gain mismatches. The hardware cost is also acceptable, and the method is novel and distinct. However, it still does not solve the correction problem of the sampling time deviation. This structure restricts the correction of sampling time deviation and is appropriate only for low-frequency input conditions with limited bandwidth. For various reasons, such as technology and conditions, many calibration algorithms in the current research are limited by the input signal and do not consider the broadband signal that is more widely used in practice, so they are not universally applicable. While some calibration algorithms improve system performance, they have flaws, such as complex calculations, difficult hardware implementation, resource waste, and so on, and they are also unable to balance performance and cost. In this paper, system identification theory is applied to the TIADC system, which can consider some unknown errors that cannot be quantified and can further improve the correction accuracy of the TIADC system. The remainder of this paper is introduced briefly as follows: Section 2 proposes a calibration method for TIADC system error based on system identification theory. Section 3 introduces the hardware platform of a 16-bit and four-channel TIADC high-speed data acquisition system used to validate the calibration method's feasibility. Section 4 provides an overview of the simulation and experimental results. Section 5 is a work summary.