A Linear Model of Quantization Noise in Superconductor ADCs

Superconductor Delta-Sigma modulators feature quantum accurate feedback that allows them to operate in the ideal, quantization-noise limit. We have developed a linear model that predicts the quantization noise of the modulator analytically, by mapping the white quantization noise at the comparator to frequency-dependent noise at the output. The key advance was determination of the transimpedance of the Josephson comparator. Both first order modulators, such as the phase modulation/demodulation design, and our own second order modulator have been analysed. We conclude that first order modulators all have the same noise shaping performance irrespective of circuit parameter values and feedback gain. The primary constraint on circuit design is instead set by thermal noise considerations.