This paper proposes a digital background calibration method that mitigates the effects of errors of 2/sup nd/ order analog loop filter in multi-bit cascaded sigma-delta modulators. In contrast to methods in which the general approach of adaptive FIR filtering is taken, coefficient values determining both /spl omega/ and Q of the noise transfer function are measured by a complex estimation technique in which the sampling clock signal divided by four is injected. Measured coefficient values are periodically applied to digital IIR noise cancellation filters. Digital hardware is greatly simplified compared with the FIR filter approach. Not only DC gain error but also frequency dependent gain errors are compensated by the proposed method. The out-of-band test tone can be easily removed by a decimation filter, therefore background calibration is possible. The effectiveness of this method is verified through computer simulation.