Superconducting digital circuits are capable of producing high dynamic rang
e analog-to-digital converters (ADCs). We present sigma-delta architectures
using large (>100) oversampling ratios to give signal-to-noise ratios of g
reater than 100 dB in simulation. Three distinct designs, using two distinc
t mechanisms for feedback, are presented. All of the designs use only shunt
ed junctions, and are therefore compatible with HTS SNS junctions. Simulati
ons are presented for a modulator which creates feedback pulses by SQUID lo
be-crossings, a modulator which uses the transresistance of a SQUID for fee
dback, and a modulator which uses threshold crossings in both the first and
second loops for feedback.