Simulation results on A/D converter dithering

Abstract

Dithering improves the linearity of A/D converters (ADCs). Wagdy and Goff (1994) have developed a criterion for assessing the deviation of ADC transfer characteristics from the unity-gain line. This criterion is based on a closed-form formula for the deviation factor D derived from the characteristic function of the ADC quantization error function. This approach was extended further by Wagdy (1996) to include nonideal ADCs. The results in that work pertain to additive dither, but a closed-form formula for subtractive dither may be very difficult to derive. In this paper, the ADC is modeled and dither is simulated using a software random number generator. First, additive dithering with continuous (analog) uniform (rectangular) probability density function (RPDF) is considered. The cases of an ADC with no errors, single-bit error, or multi-bit errors are investigated. Results are in excellent agreement with the previous ones, which validates the formulae therein. Second, the author presents new results using discrete (digital) rectangular dither (DRPDF). This dither type is generated via a D/A converter (DAC) whose number of bits, k, is greater by del than the ADC number of bits, m. For various values of del, subtractively-dithered ADCs outperform additively-dithered ones as far as D is concerned. Also, the effect of increasing del on D for an ADC is investigated for the subtractive dither case, thus providing some quantitative results which are useful for the designer.