Abstract: To eliminatethe three main mismatch errors of themulti-channel time-interleavedanalog-to-digitalconverter (TIADC), which are offset mismatch errorbetweenchannel, channel gain mismatch error and sampling time mismatch errorof channel, a background calibration algorithmfor in chip digital circuits isproposed.By adding a way of reference ADC and statistical accumulation, the algorithms perform correlation operation on the output of the calibrated channel and reference channel in order to extract the error information in the background, and then iterates compensation for the mismatch errors through the analog circuit, so as to achieve the purpose of calibration.The algorithm is applied to the 12 bits 3 GS/s four channels TIADC model circuit.When the normalized frequency of input signal is f_in/f_s=0.16569, after calibration, the ENOB and SNR increase from 4.176 5 bits and 26.812 8 dB to 11.699 3 bits and 72.102 3 dB, respectively, and the calibration effect is obvious.In addition, the algorithm is not strictly limited to input signal type, input frequency and inter channel calibration order, and can be extended to any number of channels.