Convergence analysis of a background interstage gain calibration technique for pipelined ADCs

A mathematical framework for the convergence analysis of a pipelined ADC with background gain calibration is presented. The constraints on adaptation step size for mean convergence, for mean-squared convergence, and for signal-to-adaptation-noise ratio are derived. Furthermore, expressions for steady-state tap noise and for signal-to-adaptation-noise ratio are derived. The analysis results are verified with simulations.