Band Pass NS-DEM for SAR Pipeline ADCs

This paper describes a noise shaping dynamic element matching (NS-DEM) algorithm for successive approximation register analog to digital converters (SAR ADCs) to select which capacitors are used in a given conversion, modulating the mismatch errors in the unit capacitors of the capacitive digital to analog converter (C-DAC) into noise spectrally shaped with a function H(z) = 1 ± Z<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−a</sup>. This results in a strong attenuation of the noise around the zeroes of H(z) thus improving the signal to noise and distortion ratio (SNDR) of the ADC. Two implementations of the algorithm are proposed, one using H(z) = 1 − Z<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−a</sup> (odd filter) and another using H(z) = 1 + Z<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−a</sup> (even filter), in both, the SNDR of the ADC is kept high in 0.03 interval around the zeros of the mismatch filter transfer function corresponding to the relatively low oversampling ratio (OSR) of 16.7. Extensive monte carlo simulations using a MatLab high level model of the SAR pipeline ADC using the proposed DEM algorithm show that, in the worst case, an improvement of the spurious free dynamic range (SFDR) from 52dB to 79dB is achieved with C-DAC capacitor mismatch errors as large as 1%.