Systematic errors in digital cross correlators due to quantization and differential nonlinearity

The errors in digital cross correlators caused by quantization and differential nonlinearity are discussed. It is shown that if there is sufficient uncorrelated noise, the effects of quantization are negligible. Analytic expressions for errors caused by differential nonlinearity in a cross correlator measuring Gaussian noise are derived. A procedure for calibrating digital cross correlators is outlined. The results of the analysis are verified to high accuracy by computer simulation of digital cross correlators based on nonideal analog-to-digital converters. The results find direct application in high-accuracy Johnson noise thermometry.