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Calibration of a Digital Cross-correlator for Johnson Noise Thermometry

Theoretical analyses of the effects of quantization, differential and integral non-linearities on digital correlators measuring noise power are reviewed. The theoretical results are then applied to the measurement and modelling of errors in two 15-bit analogue-to-digital converters (ADCs) used in a high-accuracy Johnson noise thermometer. The experimental results support the theory and show that a significant fraction of the correlator error can be modelled by an error in the sign bit of the ADCs. This error cannot be modelled by a truncated Taylor series. For the ADCs tested, the model fits the observed non-linearities with an accuracy of 10 ppm relative to the noise variance.