Modeling and Measuring Error Contributions in Stepwise Synthesized Josephson Sine Waves

Synthesizing Josephson stepwise approximated sine waves to produce an AC quantum standard is limited by errors in the waveform transitions between quantized voltages. Many parameters have an impact on the shape of the transients. A simple model with a single equivalent time constant can be used to evaluate the influence of these parameters. Measurements of the transients allow establishment of the value of the equivalent time constant and prediction of the response to variations of the parameters. We have experimentally confirmed the influence of changes in the bias current used for the quantized voltages and in the microwave power applied. Under usual operating conditions, the model predicts that increasing the number of samples per period nonlinearly reduces the difference between measured and ideal root-mean-square (rms) values. This behavior was confirmed through measurements with thermal converters.