Increasing the Flux Measurement Range of an RF-SQUID Resonant Detection Circuit Using the Robust Symmetrical Number System

The design and simulation of a new low temperature Niobium radio frequency superconducting quantum interference devices (RF-SQUID) flux measurement architecture concept that uses N = 3 RF-SQUID rings (or channels) to significantly extend the range of the flux measurement capability beyond ±Φ₀/4 is presented. A resonant detection method based on a robust symmetrical number system (RSNS) preprocessing technique is shown to provide a large increase in the flux measurement range while producing a high-resolution representation of the input magnetic field. The RSNS preprocessing is a modular scheme in which a modulus number of comparators is used at the output of each RF SQUID. The number of comparators with logic 1 in each channel represents the integer values within each RSNS modulus sequence. When considered together, the integers within each sequence change one at a time at the next code position, resulting in an integer Gray code property. We show that the RSNS preprocessing has the feature that the maximum nonlinearity is less than a least significant bit.