A　digital　background　calibration　technique　for　capacitors　mismatch　in　multi-bit　delta-sigma　modulator　is　proposed　in　this　paper.　The　approach　is　correlation-based,　in　which　a　single-bit　pseudo-random　noise　(PN)　is　used　to　identify　the　error　module,　minimizing　the　analog　circuit　overhead.　This　algorithm　works　by　estimating　every　DAC　capacitor　in　turn　with　the　PN　signal　injection　and　compensates　for　capacitor　mismatch　in　digital　domain.　It　is　simple　and　requires　minor　circuit　modification　in　analog　domain.　The　tradeoff　involved　is　the　dynamic　range　degradation　due　to　PN　injection.　Behavior　level　simulations　demonstrate　effective　compensation　for　capacitors　mismatch　in　a　second-order　modulator.　©　2011　IEEE.