Adaptive Digital Correction of Analog Errors in MASH ADC’s—Part I: Off-Line and Blind On-Line Calibration

Cascaded delta–sigma (MASH) modulators for higher order oversampled analog-to-digital conversion rely on precise matching of contributions from different quantizers to cancel lower order quantization noise from intermediate delta–sigma stages. This first part of the paper studies the effect of analog imperfections in the implementation, such as finite gain of the amplifiers and capacitor ratio mismatch, and presents algorithms and architectures for digital correction of such analog imperfections, as well as gain and spectral distortion in the signal transfer function. Digital correction is implemented by linear finite-impulse response (FIR) filters, of which the coefficients are determined through adaptive off-line or on-line calibration. Of particular interest is an on-line “blind” calibration technique, that uses no reference and operates directly on the digital output during conversion, with the only requirement on the unknown input signal that its spectrum be bandlimited. Behavioral simulations on dual-quantization oversampled converters demonstrate near-perfect adaptive correction and significant improvements in signal-to-quantization-noise performance over the uncalibrated case, using as few as 5 FIR coefficients. An alternative on-line adaptation technique using test signal injection and experimental results from silicon are presented in the second part, in a companion paper [1].