text: One well-known class of analog-to-digital converters (ADCs) is based on oversampling, in which a single-bit quantizer with feedback is used to generate a fast bit sequence that can accurately represent an analog input signal in the band of interest. This requires high sampling rates, for which superconducting electronics is particularly well suited.
  The established approach to an oversampling low-pass ADC is based on sigma—delta (ΣΔ) modulation (also called delta-sigma [ΔΣ] modulation), in which the input signal minus a feedback signal is integrated before quantization. This is well known to result in “noise shaping”, where the quantization noise associated with the data conversion is shifted outside the frequency band of interest. The shifted noise may then be eliminated by a subsequent digital filter. This approach has been generalized to higher order, with multiple integrators and multiple feedback loops, by which the noise-shifting is further enhanced. For the higher order approach to work properly, each integrator must be well isolated from its neighbor. In conventional semiconductor technology, this isolation is achieved with transistor amplifiers.
  A further known generalization of ΣΔ modulators is achieved by replacing the integrators by high-Q resonators. This suppresses the quantization noise at a resonant frequency rather than at low-frequencies, and forms the basis for a bandpass ADC. Again, improved higher-order performance requires good isolation between the resonators.
  Superconducting circuits based on Josephson junctions, in configurations known as rapid single-flux-quantum (RSFQ) logic, can switch on the picosecond timescale, leading to high sampling rates. Przybysz et al. in U.S. Pat. No. 5,140,324 described a first order, single stage, low-pass sigma—delta ADC based on Josephson junctions. Later this was extended to a first order, single stage, bandpass sigma—delta ADC in U.S. Pat. No. 5,341,136. Both of these patents are incorporated herein by reference.
  Lee et al. in U.S. Pat. No. 6,157,329, incorporated herein by reference, demonstrated that one can avoid a feedback loop in a superconducting bandpass ΣΔ modulator by making use of a special feature of Josephson circuits, known as implicit feedback. This technique provides electrical feedback without an explicit loop. However, this approach is applicable only to first-order, one stage, feedback. So far a higher order bandpass ADC in fully superconducting technology has not been achieved.