Josephson Waveforms Characterization of a Sigma-Delta Analog-to-Digital Converter for Data Acquisition in Metrology

Abstract

A sampling system based on a 24-bits sigma-delta analog-to-digital converter (ADC) was built and characterized in order to study the feasibility of using this type of ADCs in electrical metrology. The non-linearities of the sampling system have been studied and a model for postcorrecting the measured data points established. The Hammerstein model, consisting of a static non-linear part and a linear system, was employed. A 4-th order polynomial accounts for the non-linearities of the analog electronics and the input stages of the sigma delta ADC. The linear part corresponds to the transfer function of the decimation filters internal to the ADC. The parameters for the model of the system were determined using noiseless and drift-free waveforms from a Josephson waveform synthesizer. The performance of the sampling system was verified experimentally by comparing the measured root-mean-square (rms) value of sinusoidal signals with the results from an established method. The results obtained using the post-corrected samples from the sampling system at 125 Hz agreed to within 2 μV/V with the de facto standard in metrology laboratories, which uses a high accuracy digital voltmeter. Precision measurements are limited by the decimation filters inside the ADC and can only be carried out for frequencies below 1/24-th of the equivalent sampling rate. The characterization results have shown that the non-linearities have been compensated to 5 μV/V or better and the effective resolution exceeds 20 bits, over an input range of 1 V at the equivalent sampling rate of 32 kHz. The experimental validation has proved that it is possible to measure rms values of sinusoidal signals with 1 V peak amplitudes for frequencies up to 1.3 kHz with uncertainty of 8 μV/V, significantly improving the uncertainty achievable with de facto standard which reaches 8 μV/V at 500 Hz.