Explicit formula for channel mismatch effects in time-interleaved ADC systems

A time-interleaved ADC system is an effective way to implement a high-sampling-rate ADC with relatively slow circuits. In the system, several channel ADCs operate at interleaved sampling times as if they were effectively a single ADC operating at a much higher sampling rate. However, mismatches such as offset, gain mismatches among channel ADCs as well as timing skew of the clocks distributed to them degrade S/N of the ADC system as a whole. This paper analyzes the channel mismatch effects in the time-interleaved ADC system. Previous analysis showed the effect for each mismatch individually, however in this paper we derive explicit formula for the mismatch effects when all of offset, gain and timing mismatches exist together. We have clarified that the gain and timing mismatch effects interact each other but the offset mismatch effect is independent from them, and this can be seen clearly in frequency domain. We also discuss the bandwidth mismatch effect. The derived formula can be used for calibration algorithms to compensate for the channel mismatch effects