Incremental Learning for a Calibration of a High-precision SAR-ADC by Using the Bayesian Linear Regression

Abstract

In this paper, we discuss a high-precision and low-power analog-to-digital converter (ADC) which is required for wearable biomedical measurement sensors driven by a battery. In particular, we focus on the successive approximation register ADC (SAR-ADC), and propose its calibration algorithm using the machine learning. We derive a calibration function for the outputs of the SAR-ADC by taking into account its characteristics, and show the least squares method of determining the parameter values of the function to minimize the residual errors. Furthermore, from the practical viewpoint, we propose an incremental learning for the calibration, where additional data sets are selected on the basis of the Bayesian predictive distributions which are obtained at each additional learning step. Through numerical experiments, we observed that the mean residual errors obtained by the proposed method are less than 1 LSB, and the method needs a small amount of training data.

Behavior-Level Analysis of a Successive Stochastic Approximation Analog-to-Digital Conversion System for Multi-Channel Biomedical Data Acquisition

“…The mismatches of unit capacitances are considered to be δ C u /C u = 0.003, where δ C u is the standard deviation of capacitances C u . This value is smaller than that used in a previous study on a 15-bit SAR-ADC [15] because of the larger unit capacitance in the present study (C u = 1.2 pF). Although the dynamic digital threshold technique is used in this simulation, the non-linearity of capacitance was not considered because it depends on the details of the fabrication process [20].…”

“…The kT/C thermal noise generated at sampling was neglected because it is estimated to be 7.3 µV rms and to be much smaller than the buffer IR noise (50 µV rms ). The influence of this thermal noise in the learning mode on the tuning parameters w was relaxed by Bayesian linear regression [15], [23], as described in Appendix B. Moreover, the OS R oversampling and low-pass filtering described later herein can reduce the influence of thermal noise.…”

“…It corrects errors originated from capacitor mismatch in the internal capacitor DAC and non-ideality of the SF-ADC used for the additional quantization. This technique, which was developed based on previous studies on the SAR-ADC [15], [16], can combine the SF-ADC output for the residual signal with the SAR-ADC output to obtain high-precision output data.…”

“…Once these parameters are obtained, the encoding itself can be easily performed. In order to determine these parameters, machine learning, which is a kind of supervised learning based on error correction in a SAR-ADC [15], is introduced in the present study. Good parameter sets can predict calibrated data with small generalization errors (errors for unlearned data) by learning a small number of obtained data.…”

“…In the present study, the above minimization problem was solved by Bayesian linear regression [15], [23], as described in Appendix B. In this approach, only a set of parameters e and f , which is related to D U from the SAR-ADC mode, has a continuous degree of freedom.…”