Modeling of superconducting first- and second-order low-pass sigma-delta modulators

Here we present our studies of first- and second-order superconducting low-pass sigma-delta modulators with the filtering function realized using an RL-circuit. These modulators have been simulated for different circuit parameters using device level simulations. A linear discrete time model of the first-order modulator has been done. Simulations of the first-order sigma-delta modulator operating at an oversampling ratio of 128 and a bandwidth of 60 MHz give a maximum SNR of 70 dB using a resistance of only 1 mΩ. The SNR dependence on the parameters of the RL-filter is well predicted by the linear model. Some circuit parameters give however rise to harmonic distortions which can not be predicted by the simple linear model. Under the same conditions, the performance of second-order sigma-delta modulators was found to have a maximum SNR of only 82 dB. We conclude that the estimated upper bound on SNR for superconducting RL-filtered low-pass sigma-delta modulators, is for physical realizable circuits not high enough to give an advantage over other techniques.